Q JEE MAIN 2023

Let $z$ be a complex number such that $\left|\frac{z-2 i}{z+i}\right|=2, z \neq-i$. Then $z$ lies on the circle of radius...

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If the curve $y=f(x)$ passes through the point ( $1, \mathrm{e}$ ) and satisfies the differential equation $...

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$\lim _{x \rightarrow 2} \frac{\sin \left(x^3-5 x^2+a x+b\right)}{(\sqrt{x-1}-1) \log _e(x-1)}=m$, then $a+b+m$ is equal to :

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Let a line $L$ passing through the point $(1,1,1)$ be perpendicular to both the vectors $2 \hat{i}+2 \hat{j}+\hat{k}$ and $...

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Q JEE-Main_2026

If $\stackrel{\square}{a}$ and $\ddot{b}$ are two vectors such that $|\stackrel{\square}{a}|=2$ and $|\stackrel{n}{b}|=3$, then the maximum value of $...

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Q JEE MAIN 2026

A uniform disc of radius $R$ and mass $M$ is free to oscillate about the axis $A$ as shown in...

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If the point of intersection of the lines $\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7}$ and $\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2 a}{7}$ lies on $x y$-plane, then the value of...

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Q JEE-Main_2026

Let $\mathrm{S}=\{x \in[-\pi, \pi]: \sin x(\sin x+\cos x)=\mathrm{a}, \mathrm{a} \in Z\}$. Then $\mathrm{n}(\mathrm{S})$ is equal to :

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Q JEE MAIN 2026

The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from $T_1$ to $T_2$ resulting in...

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Q JEE MAIN 2026

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion...

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Q JEE-Main 2024

Let an ellipse $\frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1, \mathrm{a}

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Q JEE MAIN_2026

A water spray gun is attached to a hose of cross sectional area $30 \mathrm{~cm}^2$. The gun comprises of 10...

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Q JEE MAIN_2026

Let the mid points of the sides of a triangle $A B C$ be $\left(\frac{5}{2}, 7\right),\left(\frac{5}{2}, 3\right)$ and $(4,5)$. If...

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Q JEE MAIN_2026

If the mean of the data

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A metal string A is suspended from a rigid support and its free end is attached to a block of...

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\begin{aligned} &\text { The number of elements in the set }\\ &S=\left\{(r, k): k \in \boldsymbol{Z} \text { and }{...

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Q JEE MAIN_2026

The height in terms of radius of the earth $(R)$, at which the acceleration due to gravity becomes $\frac{g}{9}$, where...

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Q JEE MAIN_2026

The number of seven-digit numbers, that can be formed by using the digits $1,2,3,5$ and 7 such that each digit...

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If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24 t$ and...

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Q JEE MAIN_2026

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common...

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Q JEE MAIN_2026

At $\mathrm{t}=0$, a body of mass 100 g starts moving under the influence of a force $...

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Q JEE MAIN_2026

Let $A=\left[\begin{array}{ll}1 & 2 \\ 1 & \alpha\end{array}\right]$ and $B=\left[\begin{array}{ll}3 & 3 \\ \beta & 2\end{array}\right]$. If $A^2-4 A+I=O$ and...

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Q JEE MAIN_2026

Two cars A and B are moving in the same direction along a straight line with speeds $...

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Q JEE MAIN_2026

Let $\alpha, \beta \in \mathbf{R}$ be such that the system of linear equations $$ \begin{aligned} & x+2 y+z=5 \\ &...

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Q JEE MAIN_2026

Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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Q JEE MAIN_2026

Let $x$ and $y$ be real numbers such that $50\left(\frac{2 x}{1+3 i}-\frac{y}{1-2 i}\right)=31+17 i, i=\sqrt{-1}$. Then the value of $...

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Q JEE MAIN_2026

Let $\alpha, \alpha+2, \alpha \in \mathbf{Z}$, be the roots of the quadratic equation $x(x+2)+(x+1)(x+3)+(x+2)(x+4)+\ldots .+(x+\mathrm{n}-1)(x+\mathrm{n}+1)=4 \mathrm{n}$ for some $...

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Q JEE MAIN_2026

A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\text {rd }}$ of its initial volume $\left(V_0=3\right.$ litre $)$ by applying required...

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Q JEE MAIN_2026

An ideal gas undergoes a process maintaining relation between pressure ( $P$ ) and volume ( $V$ ) as $P=P_{\mathrm{o}}\left(1+\left(\frac{V_{\mathrm{o}}}{V}\right)^2\right)^{-1}$,...

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Q JEE MAIN_2026

In a Young double slit experiment, the wavelength of incident light is 6000 A , the separation between slits $S_1$...

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Q JEE MAIN_2026

Arrange the following resultant mixtures in increasing order of their pH values A. $10 \mathrm{~mL} 0.2 \mathrm{MCa}(\mathrm{OH})_2+25 \mathrm{~mL} 0.1 \mathrm{MHCl}$...

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Q JEE MAIN_2026

Solid carbon, CaO and $\mathrm{CaCO}_3$ are mixed and allowed to attain equilibrium at TK . $$ \begin{aligned} & \mathrm{CaCO}_3(\mathrm{~s}) \mathrm{f}...

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Q JEE MAIN_2026

Consider the reaction $$ 2 \mathrm{H}_2 \mathrm{~S}(\mathrm{~g})+3 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(\mathrm{l})+2 \mathrm{SO}_2(\mathrm{~g}) $$ The magnitude of enthalpy change for...

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Q JEE MAIN_2026

Consider two radiations of wavelengths

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Q JEE MAIN_2026

' $x$ ' is the product which is obtained from benzene by reacting it with carbon monoxide and hydrogen chloride...

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Q JEE MAIN 2026

Decomposition of a hydrocarbon follows the equation $\mathrm{k}=\left(5.5 \times 10^{11} \mathrm{~s}^{-1}\right) \mathrm{e}^{\frac{-28000 \mathrm{~K}}{\mathrm{~T}}}$. The activation energy of reaction is $\_\_\_\_$...

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Q JEE MAIN 2026

In a closed flask at 600 K , one mole of $\mathrm{X}_2 \mathrm{Y}_4(\mathrm{~g})$ attains equilibrium as given below :$...

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Q JEE MAIN_2026

Number of paramagnetic complexes among the following is $\_\_\_\_$ .

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Q JEE MAIN 2026

500 mL of $0.2 \mathrm{M} \mathrm{MnO}_4^{-}$solution in basic medium when mixed with 500 mL of 1.5 M KI solution, oxidises...

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Q JEE MAIN 2026

An alkane $(Y)$ requires 8 moles of oxygen for complete combustion and on chlorination with $\mathrm{Cl}_2 / \mathrm{h} \nu,(\mathrm{Y})$ gives...

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Q JEE MAIN 2026

An excess of $\mathrm{AgNO}_3$ is added to 100 mL of a 0.05 M solution of tetraaquadichloridochromium (III) chloride. The number...

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Q JEE MAIN 2026

Treatment of a gas ' $X$ ' with a freshly prepared ferrous sulphate solution gives a compound ' $Y$ '...

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Q JEE MAIN_2026

Consider the reaction $\mathrm{Xf} \quad \mathrm{Y}$ at 300 K . If $\Delta \mathrm{H}^0$ and K are $28.40 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and...

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Q JEE MAIN_2026

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with $t_{1 / 2}=3$ hour. The...

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Q JEE MAIN 2026

Consider the following reactions. Total number of electrons in the $\pi$ bonds and lone pair of electrons in the product...

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Q JEE MAIN_2026

The incorrect statement from the following with respect to carbohydrates is :

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Q JEE MAIN 2026

The number of compounds from the following which can undergo reaction with $\mathrm{Br}_2 / \mathrm{KOH}$ (alcoholic) to give respective products...

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Q JEE MAIN_2026

Which statements are True A. In Hoffmann bromamide degradation, 4 moles of NaOH and 2 moles of $\mathrm{Br}_2$ are consumed...

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Q JEE MAIN 2026

Consider the following organic reaction sequence. Choose the final product $(X)$ from the following (consider the major product in all...

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Q JEE MAIN_2026

Consider the following reaction.

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Q JEE MAIN 2026

Consider the following reaction.Statement I: In the above reaction, product formed will be a mixture of benzyl alcohol and iodobenzene.Statement...

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Q JEE MAIN_2026

4.7 g of phenol is heated with Zn to give product X . If this reaction goes to $60 \%$...

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An optically active alkyl bromide $\mathrm{C}_4 \mathrm{H}_9 \mathrm{Br}$, reacts with ethanolic KOH to form major compound $[\mathrm{A}]$ which reacts with...

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Q JEE MAIN_2026

Given below are two statements:

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Q JEE MAIN_2026

Consider the following sequence of reactions

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Q JEE MAIN 2026

' $x$ ' is the product which is obtained by the hydrolysis of prop-1-yne in the presence of mercuric sulphate...

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First and second ionization enthalpies of lithium are $520 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $7297 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. Energy required to convert...

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Q JEE MAIN 2026

Shown below is the structure of methyl acetate with three different $\alpha, \beta$ and $\gamma$ carbon-oxygen bonds.The correct order of...

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Q JEE MAIN_2026

n -Butane on monochlorination under photochemical condition gives an optically active compound "P". "P" on further chlorination gives dichloro compounds....

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Q JEE MAIN_2026

Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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Q JEE MAIN 2026

Given below are two statements :Statement I: A mixture of $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}$ (sugar) and NaCl can be separated by...

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Q JEE MAIN_2026

The total number of aromatic compounds/species from the following is

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Q JEE MAIN_2026

Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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Q JEE MAIN_2026

Arrange the following compounds according to increasing order of boiling points. $$ \mathrm{n}-\mathrm{C}_4 \mathrm{H}_9 \mathrm{OH}(\mathrm{~A}), \mathrm{n}-\mathrm{C}_4 \mathrm{H}_9 \mathrm{NH}_2(\mathrm{~B}), \mathrm{n}-\mathrm{C}_4 \mathrm{H}_{10}(\mathrm{C})...

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Q JEE MAIN 2026

Which of the following sequences of hybridisation, geometry and magnetic nature are correct for the given coordination compounds?A. $\left[\mathrm{NiCl}_4\right]^{2-}-\mathrm{sp}^3$, tetrahedral,...

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Q JEE MAIN_2026

Given below are two statements for catalytic properties of transition metals. Statement I: First row transition metals which act as...

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Q JEE MAIN 2026

The correct order of first $\left(\Delta_i \mathrm{H}_1\right)$ and second $\left(\Delta_i \mathrm{H}_2\right)$ ionisation enthalpy values of Cr and Mn are :A....

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Q JEE MAIN_2026

Given below are two statements Statement I : The number of pairs among $\left[\mathrm{Ti}^{4+}, \mathrm{V}^{2+}\right],\left[\mathrm{V}^{2+}, \mathrm{Mn}^{2+}\right],\left[\mathrm{Mn}^{2+}, \mathrm{Fe}^{3+}\right]$ and $\left[\mathrm{V}^{2+}, \mathrm{Cr}^{2+}\right]$...

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Q JEE MAIN_2026

Consider the following sequence of reactions The major product P is:

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Q JEE MAIN_2026

Find the correct statements related to group 15 hydrides. A. Reducing nature increases from $\mathrm{NH}_3$ to $\mathrm{BiH}_3$ B. Tendency to...

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Q JEE MAIN 2026

Given below are two statements :Statement I: $\mathrm{F}_2 \mathrm{O}

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Given below are two statements: Statement I: 3-phenylpropene reacts with HBr and gives secondary alkyl bromide having a chiral carbon...

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Q JEE MAIN_2026

Match List - I with List - II.

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Q JEE MAIN 2026

In a period, the first ionisation enthalpy of the element at extreme left and the negative electron gain enthalpy of...

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Q JEE MAIN_2026

Given below are two statements: Statement I: Methane can be prepared by decarboxylation of sodium ethanoate, Kolbe's electrolysis of sodium...

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Q JEE MAIN 2026

For a general redox reactionAnode: $\quad \operatorname{Red}_1 \rightarrow \mathrm{O}_1^{\mathrm{n}_1^{+}}+\mathrm{n}_1 \mathrm{e}^{-}$,Cathode: $\mathrm{O} x_2+\mathrm{n}_2 \mathrm{e}^{-} \rightarrow \operatorname{Red}_2^{\mathrm{n}_2-}$,Which of the following statement is...

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Q JEE MAIN_2026

Given below are two statements :

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Given below are two statements: Statement I: 2,6-diethylcyclohexanone and 6-methyl-2-n-propylcyclohexanone are metamers. Statement II: 2,2,6,6 - tetramethylcyclohexanone exhibits keto-enol tautomerism....

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Q JEE MAIN 2026

Given is a concentrated solution of a weak electrolyte $A_x B_y$ of concentration ' $c$ ' and dissociation constant '...

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Given at 298 K : $$ \begin{aligned} & \mathrm{E}_{\mathrm{Fe}^{2+} / \mathrm{Fe}}^{!}=\mathrm{X} \text { Volt } \\ & \mathrm{E}_{\mathrm{Fe}^{3+} / \mathrm{Fe}}^{!}=\mathrm{Y}...

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Q JEE MAIN_2026

$R_f$ value for 2-methylpropene in a solvent system (Ethyl acetate + ether) is 0.42 . 2-methylpropene is treated with dilute...

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Q JEE MAIN 2026

Given below are two statements Statement I: $\mathrm{H}_2 \mathrm{O}$ molecules move from the chamber 1 to chamber 2 .Statement II:...

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Q JEE MAIN_2026

Consider the following reactions in which all the reactants and products are present in gaseous state

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Which of the following are true about the energy of the given d-orbitals of a tetrahedral complex? A. $...

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Q JEE MAIN 2026

Match List - I with List - II.Given $V_1$ and $V_2$ are initial and final volumes respectively.Choose the correct answer...

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Q JEE MAIN_2026

Which of the following statements are not correct? A. For water, magnitude of $K_b$ is more than the magnitude of...

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Q JEE MAIN_2026

Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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Q JEE MAIN 2026

Given below are two statements :Statement I : The number of compounds among $\mathrm{SO}_2, \mathrm{SO}_3, \mathrm{SF}_4, \mathrm{SF}_6$ and $\mathrm{H}_2 \mathrm{~S}$...

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Q JEE MAIN_2026

Bromine trifluoride autoionizes to form $\mathrm{BrF}_2^{\oplus}$ and $\mathrm{BrF}_4^{!}$. The shapes of the cation and anion are respectively $\_\_\_\_$ and $\_\_\_\_$...

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Q JEE MAIN_2026

Given below are two statements : Given : Molar mass of $\mathrm{C}, \mathrm{H}, \mathrm{O}, \mathrm{Cl}$ are $12,1,16$ and $...

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Q Jee Main 2026

The major product of which of the following reaction is not obtained by rearrangement reaction?

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The correct statements among the following are. A. Basic vanadium oxide is used in the manufacture of $\mathrm{H}_2 \mathrm{SO}_4$. B....

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Q JEE MAIN 2026

The Bohr radius of a hydrogen like species is 70.53 pm . The species and the stationary state ( n...

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Q JEE MAIN_2026

Match List - I with List - II.

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Given below are two statements: Statement I: Aluminium is more electropositive than thallium as the standard electrode potential value of...

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Q JEE MAIN 2026

Which of the following contain the same number of atoms? (Given : Molar mass in $\mathrm{gmol}^{-1}$ of $\mathrm{H}, \mathrm{He}, \mathrm{O}$...

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Q JEE MAIN 2026

Let $f(x)=\left\{\begin{array}{ll}x^3+8 ; & x

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Consider the following data. $\mathrm{BaSO}_4$ is sparingly soluble in water. If the conductivity of the saturated $\mathrm{BaSO}_4$ solution is $...

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Let the image of the point $\mathrm{P}(0,-5,0)$ in the line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2}$ be the point R and the image of the...

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Q JEE MAIN 2026

Let the line $x-y=4$ intersect the circle $\mathrm{C}:(x-4)^2+(y+3)^2=9$ at the points Q and R . If $\mathrm{P}(\alpha, \beta)$ is a...

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Q JEE MAIN 2026

Let $f$ be a polynomial function such that $\log _2(f(x))=\left(\log _2\left(2+\frac{2}{3}+\frac{2}{9}+\ldots \ldots \infty\right)\right) \cdot \log _3\left(1+\frac{f(x)}{f(1 / x)}\right), x>0 \quad$...

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Q JEE MAIN 2026

If $\left(1-x^3\right)^{10}=\sum_{\mathrm{r}=0}^{10} \mathrm{a}_{\mathrm{r}} x^{\mathrm{r}}(1-x)^{30-2 \mathrm{r}}$, then $\frac{9 \mathrm{a}_9}{\mathrm{a}_{10}}$ is equal to $\_\_\_\_$ .

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One mole each of He and A(g) are taken in a 10 L closed flask and heated to 400 K...

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Consider the circle C : $x^2+y^2-6 x-8 y-11=0$. Let a variable chord AB of the circle C subtend a right...

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Let $\mathrm{R}=\left\{(x, y) \in \mathbf{N} \times \mathbf{N}: \log _{\mathrm{e}}(x+y) \leq 2\right\}$. Then the minimum number of elements, required to be...

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Let a line $L_1$ pass through the origin and be perpendicular to the lines $$ \begin{aligned} & \mathrm{L}_2: \overrightarrow{\mathrm{r}}=(3+\mathrm{t}) \hat{i}+(2...

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When 0.25 moles of a non-volatile, non-ionizable solute was dissolved in 1 mole of a solvent the vapour pressure of...

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If $\int_{\pi / 6}^{\pi / 4}\left(\cot \left(x-\frac{\pi}{3}\right) \cot \left(x+\frac{\pi}{3}\right)+1\right) d x=\alpha \log _{\mathrm{e}}(\sqrt{3}-1)$, then $9 \alpha^2$ is equal to

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The sum of squares of all the real solutions of the equation $\log _{(x+1)}\left(2 x^2+5 x+3\right)=4-\log _{(2 x+3)}\left(x^2+2 x+1\right)$ is...

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Let $\frac{x^2}{f\left(a^2+7 a+3\right)}+\frac{y^2}{f(3 a+15)}=1$ represent an ellipse with major axis along $y$-axis, where $f$ is a strictly decreasing positive function...

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Let $f(x)=\left\{\begin{array}{cc}\frac{1}{3} & , x \leq \pi / 2 \\ \frac{\mathrm{~b}(1-\sin x)}{(\pi-2 x)^2} & , x>\pi / 2\end{array}\right.$. If $f$...

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Let $f:(1, \infty) \rightarrow \mathbf{R}$ be a function defined as $f(x)=\frac{x-1}{x+1}$. Let $f^{i+1}(x)=f\left(f^i(x)\right), i=1,2, \ldots, 25$, where $f^1(x)=f(x)$. If $...

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Arrange the following isothermal processes in order of the magnitude of the work ( $\mathrm{p}-\mathrm{V}$ ) involved between states 1...

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Let $y=y(x)$ be the solution of the differential equation $...

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The pairs among $$ \mathrm{A}=\left[\mathrm{SO}_3^{2-}, \mathrm{CO}_3^{2-}\right], \mathrm{B}=\left[\mathrm{O}_2^{2-}, \mathrm{F}_2\right], \mathrm{C}=\left[\mathrm{CN}^{-}, \mathrm{CO}\right], \mathrm{D}=\left[\mathrm{NH}_3, \mathrm{H}_3 \mathrm{O}^{+}\right] \text {and } \mathrm{E}=\left[\mathrm{MnO}_4^{2-}, \mathrm{CrO}_4^{2-}\right] $$ that...

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The value of the integral $\int_0^2 \frac{\sqrt{x\left(x^2+x+1\right)}}{(\sqrt{x+1})\left(\sqrt{x^4+x^2+1}\right)} \mathrm{d} x$ is equal to:

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\text { The value of the integral } \int_{-1}^1\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right) \mathrm{d} x \text { is equal to: }

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Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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Let the foot of perpendicular from the point $(\lambda, 2,3)$ on the line $\frac{x-4}{1}=\frac{y-9}{2}=\frac{z-5}{1}$ be the point $(1, \mu, 2)$....

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Q JEE MAIN 2026

The area of the region $\left\{(x, y): x^2-8 x \leq y \leq-x\right\}$ is:

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Let $\overrightarrow{\mathrm{a}}=4 \hat{i}-\hat{j}+3 \hat{k}, \overrightarrow{\mathrm{~b}}=10 \hat{i}+2 \hat{j}-\hat{k}$ and a vector $\overrightarrow{\mathrm{c}}$ be such that $2(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})+3(\overrightarrow{\mathrm{~b}} \times \overrightarrow{\mathrm{c}})=\overrightarrow{0}$. If...

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For the function $f(x)=\mathrm{e}^{\sin |x|}-|x|, x \in \mathbf{R}$, consider the following statements: Statement I : $f$ is differentiable for all...

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Q JEE MAIN_2026

If shortest wavelength of hydrogen atom in Lyman series is $x$, then longest wavelength in Balmer series of $\mathrm{He}^{+}$is:

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Let $\alpha=3 \sin ^{-1}\left(\frac{6}{11}\right)$ and $\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$, where inverse trigonometric functions take only the principal values. Given below are...

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An oxide of iron contains $69.9 \%$ iron, its empirical formula, is: (Given : Molar mass of Fe and O...

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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be such that $f(x y)=f(x) f(y)$, for all $x, y \in \mathbf{R}$ and $...

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Let $O$ be the vertex of the parabola $y^2=4 x$ and its chords $O P$ and $O Q$ are perpendicular...

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Let $\mathrm{A}=\left[\begin{array}{ccc}1 & 3 & -1 \\ 2 & 1 & \alpha \\ 0 & 1 & -1\end{array}\right]$ be a...

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For a reaction $\mathrm{A} \rightarrow \mathrm{P}$ at TK , the half life $\left(\mathrm{t}_{1 / 2}\right)$ is plotted as a function...

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If a straight line drawn through the point of intersection of the lines $4 x+3 y-1=0$ and $3 x+4 y-1=0$,...

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Let $\lim _{x \rightarrow 2} \frac{(\tan (x-2))\left(\mathrm{r} x^2+(\mathrm{p}-2) x-2 \mathrm{p}\right)}{(x-2)^2}=5$ for some $\mathrm{r}, \mathrm{p} \in \mathbf{R}$. If the set of...

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At 298 K , the molar conductivity of $x \%(\mathrm{w} / \mathrm{w}) \mathrm{MX}$ solution (aqueous) is $123.5 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$. The...

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A person has three different bags and four different books. The number of ways, in which he can put these...

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20 g hemoglobin in a 1 L aqueous solution (A) at 300 K is separated from pure water by semi...

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If $26\left(\frac{2^3}{3}\left({ }^{12} \mathrm{C}_2\right)+\frac{2^5}{5}\left({ }^{12} \mathrm{C}_4\right)+\frac{2^7}{7}\left({ }^{12} \mathrm{C}_6\right)+\cdots+\frac{2^{13}}{13}\left({ }^{12} \mathrm{C}_{12}\right)\right)=3^{13}-\alpha$, then $\alpha$ is equal to :

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A set of four observations has mean 1 and variance 13 . Another set of six observations has mean 2...

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Let $\overrightarrow{\mathrm{a}}=2 \hat{i}+3 \hat{j}+3 \hat{k}$ and $\overrightarrow{\mathrm{b}}=6 \hat{i}+3 \hat{j}+3 \hat{k}$. Then the square of the area of the triangle with...

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The shortest distance between the lines $\frac{x-4}{1}=\frac{y-3}{2}=\frac{z-2}{-3}$ and $\frac{x+2}{2}=\frac{y-6}{4}=\frac{z-5}{-5}$ is:

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RMgI when treated with ice cold water liberated a gas which occupied $1.4 \mathrm{dm}^3 / \mathrm{g}$ at STP. The gas...

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If $\sin \left(\tan ^{-1}(x \sqrt{2})\right)=\cot \left(\sin ^{-1} \sqrt{1-x^2}\right), x \in(0,1)$, then the value of $x$ is:

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A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means...

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Let $x=9$ be a directrix of an ellipse $E$, whose centre is at the origin and eccentricity is $\frac{1}{3}$. Let...

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Let $\alpha=3+4+8+9+13+14+\ldots$ upto 40 terms. If $(\tan \beta)^{\frac{\alpha}{1020}}$ is a root of the equation $x^2+x-2=0, \beta \in\left(0, \frac{\pi}{2}\right)$, then $...

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The total number of unpaired electrons present in the $\mathrm{d}^3, \mathrm{~d}^4$ (low spin) $\mathrm{d}^5$ (high spin), $\mathrm{d}^6$ (high spin) and...

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The eccentricity of an ellipse $E$ with centre at the origin $O$ is $\frac{\sqrt{3}}{2}$ and its directrices are $...

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Let $\quad A=\left[\begin{array}{ccc}\alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5\end{array}\right] \quad$...

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Let $C$ be a circle having centre in the first quadrant and touching the $x$-axis at a distance of 3...

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A paper dipped in a dil. $\mathrm{H}_2 \mathrm{SO}_4$ solution of ' $X$ ' upon treatment with $\mathrm{SO}_2$ gas turns into...

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If the system of linear equations: $$ \begin{aligned} & x+y+z=6 \\ & x+2 y+5 z=10 \\ & 2 x+3 y+\lambda...

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A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is...

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Given below are two statements : In the light of the above statements, choose the correct answer from the options...

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Let the mean and the variance of seven observations $2,4, \alpha, 8, \beta, 12,14, \alpha

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The number of values of $z \in £$, satisfying the equations $|z-(4+8 i)|=\sqrt{10}$ and $|z-(3+5 i)|+|z-(5+11 i)|=4 \sqrt{5}$, is :

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Identify the incorrect statement about tertiary structure of proteins.

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A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The...

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Consider the relation R on the set $\{-2,-1,0,1,2\}$ defined by $(\mathrm{a}, \mathrm{b}) \in \mathrm{R}$ if and only if $1+\mathrm{ab}>0$. Then,...

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The sum $1+\frac{1}{2}\left(1^2+2^2\right)+\frac{1}{3}\left(1^2+2^2+3^2\right)+\ldots$ upto 10 terms is equal to:

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Let $\mathrm{A}=\left[\begin{array}{lll}1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1\end{array}\right]$ and $...

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The sum of all possible values of $\theta \in[0,2 \pi]$, for which the system of equations : $$ \begin{aligned} &...

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Given below are two statements : Statement I: Heating benzamide with bromine in an ethanolic solution of sodium hydroxide will...

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Let $S=\left\{z \in £: z^2+\sqrt{6} i z-3=0\right\}$. Then $\sum_{z \in S} z^8$ is equal to:

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Given below are two statements : In the light of the above statements, choose the correct answer from the options...

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Consider the quadratic equation $\left(\mathrm{n}^2-2 \mathrm{n}+2\right) x^2-3 x+\left(\mathrm{n}^2-2 \mathrm{n}+2\right)^2=0, \mathrm{n} \in \mathbf{R}$. Let $\alpha$ be the minimum value of the...

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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $f(x)=\frac{2 x^2-3 x+2}{3 x^2+x+3}$. Then $f$ is :

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Complete the following reaction sequence and give the name of major product ‘P’

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Identify the correct IUPAC name of hydrocarbon $(x)$ containing three primary carbon atoms and with molar mass $72 \mathrm{~g} \mathrm{~mol}^{-1}$.

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IUPAC name of the some alkenes are given below. Find out the correct stability order. A. 2-Methylbut-2-ene B. cis-But-2-ene C....

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Match List - I with List - II Choose the correct answer from the options given below :

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Identify the correct statements from the following A. $\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$ is the most stable complex among $\left[\mathrm{Fe}(\mathrm{OH})_6\right]^{3-},\left[\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$ and $\left[\mathrm{Fe}(\mathrm{SCN})_6\right]^{3-}$...

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Given below are two statements : Statement I: Presence of large number of unpaired electrons in transition metal atoms results...

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Given below are two statements : Statement I: Aluminium upon reaction with NaOH forms $\left[\mathrm{Al}(\mathrm{OH})_6\right]^{3-}$ ion. Statement II : The...

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Given below are two statements : Statement 1 : The number of pairs among $...

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One half cell in a voltaic cell is constructed by dipping silver rod in $\mathrm{AgNO}_3$ solution of unknown concentration, other...

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The reaction $\mathrm{A}(\mathrm{g}) \mathrm{f} \quad \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ was initiated with the amount ' a ' of $\mathrm{A}(\mathrm{g})$. At equilibrium it is...

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The correct order of molar heat capacities measured at 298 K and 1 bar is :

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Consider the following data for the reaction $$ X_2(g)+Y_2(g) f \quad 2 X Y(g) $$ at 600 K . The...

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The covalent radii of atoms $A$ and $B$ are $r_A$ and $r_B$, respectively. The covalent bond length and total length...

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Which of the following statement(s) is/are true ? A. If two orbitals have the same value of $(\mathrm{n}+l)$, the orbital...

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What volume of hydrogen gas at STP would be liberated by action of 50 mL of $\mathrm{H}_2 \mathrm{SO}_4$ of $...

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If the half life of a first order reaction is 6.93 minutes then the time required for completion of $...

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The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below $...

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One mole of phenol is treated with dilute $\mathrm{HNO}_3$ at 298 K to give a mixture of products. The mixture...

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In an estimation of sulphur by Carius method 0.2 g of the substance gave 0.6 g of $\mathrm{BaSO}_4$. The percentage...

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Consider the following species: $$ \mathrm{BrF}_5, \mathrm{XeF}_5^{-}, \mathrm{BF}_4^{-}, \mathrm{ICl}_4^{-}, \mathrm{XeF}_4, \mathrm{SF}_4, \mathrm{NH}_4^{+}, \mathrm{ClF}_3, \mathrm{XeF}_2, \mathrm{ICl}_2^{-} $$ Number of species having...

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Given below are two statements: Statement I: Sodium dichromate and potassium dichromate are classified as primary standards in titrimetric analysis....

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Identify the correct statements. A. Glucose exists in two anomeric forms. B. Anomers of glucose differ in configuration at $\mathrm{C}-1$...

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Identify the incorrect statements. Choose the correct answer from the options given below:

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Consider compounds A, B and C with following structural formulae For the conversion of $B$ from $A$, reagent (D) required...

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Benzyl isocyanide can be obtained from Choose the correct answer from the options given below :

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For the following Friedel Craft’s alkylation reaction, which of the statements are correct? A. Major product is n -propyl benzene....

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" P " is a hydrocarbon of molecular formula:- $\mathrm{C}_8 \mathrm{H}_{14}$. On ozonolysis, " P " forms "Q". "Q" on...

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Given below are two statements: Statement I: On the basis of inductive effect, the order of stability of alkyl carbanions...

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Given below are two statements: Statement I: Each electron in $\mathrm{e}_{\mathrm{g}}$ orbitals destabilizes the orbitals by $+0.6 \Delta_{\mathrm{o}}$ and each...

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The correct statements about metal carbonyls are A. The metal-carbon bonds in metal carbonyls possess both $\sigma$ and $\pi$ character....

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Which of the following is NOT a physical or chemical characteristics of interstitial compounds?

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Correct statements from the following are: A. Nitrogen in oxidation states from +1 to +4 disproportionates in acid medium. B....

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Given below are two statements: Statement I: The correct order of electronegativity of fluorine, oxygen and nitrogen is $\mathrm{F}>\mathrm{O}>\mathrm{N}$. Statement...

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First order gas phase reaction $$ \mathrm{A} \rightarrow \mathrm{~B}+\mathrm{C} $$ $p_i=$ initial pressure of gas $\mathrm{A}, p_t=$ total pressure of...

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$\mathrm{M}_3 \mathrm{~A}_2$ is a sparingly soluble salt of molar mass $y \mathrm{~g} \mathrm{~mol}^{-1}$ and solubility $x \mathrm{~g} \mathrm{~L}^{-1}$. The ratio...

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What is the mole fraction of water in $10 \%$ by weight $(\mathrm{w} / \mathrm{w})$ of aqueous urea solution? [Given:...

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Identify the correct statements from the following : A. Heisenberg uncertainty principle is applicable to electrons. B. The size of...

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Arrange the following atomic orbitals of multi electron atoms in order of increasing energy. Choose the correct answer from the...

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How many grams of residue is obtained by heating 2.76 g of silver carbonate? (Given : Molar mass of $...

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In sulphur estimation, $2.0 \times 10^{-3} \mathrm{~mol}$ of an organic compound $(\mathrm{X})$ (molar mass $76 \mathrm{~g} \mathrm{~mol}^{-1}$ ) gave 0.4813...

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For a first order reaction $\mathrm{A} \rightarrow \mathrm{B}$ $x=$ $\_\_\_\_$ min. (Nearest integer)

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An electrochemical cell, consist of the following two redox couples, $\mathrm{M}^{x+}(\mathrm{aq}) / \mathrm{M}(\mathrm{s})\left[\mathrm{E}_{\text {red }}^{\ominus}=+0.15 \mathrm{~V}\right]$ and $...

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For the following reaction at $50^{\circ} \mathrm{C}$ and at 2 atm pressure, $$ 2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \mathrm{f} \quad 2 \mathrm{~N}_2...

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If 3.365 g of ethanol $(l)$ is burnt completely in a bomb calorimeter at 298.15 K , the heat produced...

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Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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Among $\mathrm{Fe}^{3+}, \mathrm{Pb}^{2+}, \mathrm{Cu}^{2+}$ and $\mathrm{Mn}^{2+}$, identify the one that gets precipitated out while passing $\mathrm{H}_2 \mathrm{~S}$ in presence of...

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A D-aldotetrose on oxidation with concentrated $\mathrm{HNO}_3$ resulted in optically inactive dicarboxylic acid. The structure of the D -aldotetrose is:

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The strongest conjugate acid will result from:

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The descending order of acidity among the following compounds is: Choose the correct answer from the options given below:

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The following structures are

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Compound $(\mathrm{X})$ is subjected to the sequence of reactions as shown above. Molar mass of the major product $(\mathrm{Y})$ formed...

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Consider the given graph showing variation of reactant concentration with time. Three different reactions were started with identical initial concentration...

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Consider $|\mathrm{x}|$ is the difference in oxidation states of Mn in highest manganese fluoride and highest manganese oxide. The ions...

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Consider the metal complexes $\left[\mathrm{Ni}(\mathrm{en})_3\right]^{2+}(\mathrm{A}),\left[\mathrm{NiCl}_4\right]^{2-}(\mathrm{B})$ and $\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_6\right]^{2+}(\mathrm{C})$. Choose the CORRECT option by considering the number of unpaired electrons present in...

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Pairs of elements with the same number of electrons in their respective 4 f orbital are [Atomic number. Eu-63, Gd-64,...

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The electronegativity of a group 13 element ' $E$ ' is same as that of Ge (on Pauling scale and...

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The $1^{\text {st }}$ ionization enthalpy for Mg is $+737 \mathrm{~kJ} / \mathrm{mol}$. The most probable estimated value of the...

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Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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20 mL of a solution of acetic acid required 28.4 mL of 0.1 M NaOH for its neutralization. A solution...

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At $27^{\circ} \mathrm{C}, 0.1 \mathrm{M}, 1 \mathrm{LK}_4\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ aqueous solution and $0.1 \mathrm{M}, 1 \mathrm{LFeCl}_3$ aqueous solution are placed in a...

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Which of the following pictorial diagram most correctly represents the $\pi^*$ ( $\pi$ antibonding) molecular orbital between two atoms if...

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The species having identical radii according to the Bohr's theory are: A. H (first orbit) B. $\mathrm{He}^{+}$(first orbit) C. $\mathrm{He}^{+}$(Second...

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The correct order of total number of atoms present in (A) 2 moles of cyclohexane (B) 684 g of sucrose...

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A non-volatile, non-electrolyte solid solute when dissolved in 40 g of a solvent, the vapour pressure of the solvent decreased...

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The pH of a solution obtained by mixing 5 mL of $0.1 \mathrm{MNH}_4 \mathrm{OH}$ solution with 250 mL of $...

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2.0 g of a bromo hydrocarbon $(\mathrm{X})$ was subjected to Carius analysis, gave 3.36 g of AgBr . The percentage...

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Consider the following sequence of reactions to give the major product (X) P g of the major product (X) formed...

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According to Lewis theory, the total number of $\sigma$ bond-pairs and lone pair of electrons around the central atom of...

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Identify the colour of compound ' X ' in the sequence of the reaction.

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Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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Given below are two statements: In the light of the above statements, choose the correct answer from the options given...

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Product C of the following reaction sequence will be

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Amongst the following, the total number of compounds soluble in aqueous NaOH at room temperature is:

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Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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An alkene (X) on ozonolysis followed by reduction gives following products The alkene ( X ) is :

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Increasing order of electron withdrawing power of following functional groups is: a. -CN b. -COOH c. $-\mathrm{NO}_2$ d. -1

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Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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Correct statements from the following are A. Potassium dichromate is an oxidising agent and it oxidises $\mathrm{FeSO}_4$ to $\mathrm{Fe}_2\left(\mathrm{SO}_4\right)_3$ in...

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Which of the following is correct set of 4 quantum numbers of $19^{\text {th }}$ electron in Chromium (Atomic number...

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The correct statements among the following are, A. $\mathrm{Mo}(\mathrm{VI})$ and $\mathrm{W}(\mathrm{VI})$ are less stable than $\mathrm{Cr}(\mathrm{VI})$. B. $\mathrm{Ce}^{4+}$ and $\mathrm{Tb}^{4+}$...

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Given below are two statements: Statement 1 : The covalency of oxygen is generally two but it can exceed upto...

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A monoatomic anion ( $\mathrm{A}^{-}$) has 45 neutrons and 36 electrons. Atomic mass, group in the periodic table and physical...

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Consider the first order reaction $\mathrm{R} \rightarrow \mathrm{P}$. The fraction of molecules decomposed in the given first order reaction can...

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In order to oxidise a mixture of 1 mole each of $\mathrm{FeC}_2 \mathrm{O}_4, \mathrm{Fe}_2\left(\mathrm{C}_2 \mathrm{O}_4\right)_3, \mathrm{FeSO}_4$ and $\mathrm{Fe}_2\left(\mathrm{SO}_4\right)_3$ in acidic...

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At $\mathrm{T}(\mathrm{K})$, the equilibrium constant of $\mathrm{A}_2(g)+\mathrm{B}_2(g) \mathrm{f} \mathrm{C}(g)$ is $2.7 \times 10^{-5}$. What is the equilibrium constant for $...

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Given below are two statements: , Statement 1 : For an ideal gas, heat capacity at constant volume is always...

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What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum...

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Number of moles and number of molecules in 1.4187 L of $\mathrm{SO}_2$ at STP respectively are

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Consider the following reactions sequence When the product $(\mathrm{P})$ is subjected to Carius analysis using $\mathrm{AgNO}_3, 1.0 \mathrm{~g}$ of the...

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Number of paramagnetic ions among the following $d$ - and $f$-block metal ions is $\_\_\_\_$ . $$ \mathrm{Mn}^{2+}, \mathrm{Cu}^{2+}, \mathrm{Zn}^{2+},...

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Consider the following two half-cell reactions along with the standard reduction potential given : $$ \begin{array}{ll} \mathrm{CO}_2+6 \mathrm{H}^{+}+6 \mathrm{e}^{-} \rightarrow...

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Consider the following gas phase reaction being carried out in a closed vessel at $25^{\circ} \mathrm{C}$. The pressure of $\mathrm{C}(\mathrm{g})$...

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The surface of sodium metal is irradiated with radiation of wavelength $x \mathrm{~nm}$. The kinetic energy of ejected electrons is...

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Thyroxine is derivative of Tyrosine and single letter symbol of Tyrosine amino acid is $Y$. Among $\mathrm{Fe}^{2+}, \mathrm{Fe}^{3+}, \mathrm{Cr}^{2+}$ and...

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Among $\mathrm{Fe}^{2+}, \mathrm{Fe}^{3+}, \mathrm{Cr}^{2+}$ and $\mathrm{Zn}^{2+}$, the ion that shows positive borax bead test and with highest ionisation enthalpy is...

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Identify compounds A and E in the following reaction sequence.

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A molecule $(X)$ with following structure under mild acidic condition is hydrolysed to produce $(\mathrm{Y})$ and (Z). Identify the correct...

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An organic compound " $x$ " where molar ratio of $\mathrm{C}, \mathrm{O}$ and H are equal, on treatment with $...

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Correct statements regarding alkyl halides $(\mathrm{R}-\mathrm{X})$ among the following are : A. Alcohol being less polar solvent as compared to...

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The compound $(\mathrm{X})$ on (i) on heating in the presence of anhydrous $\mathrm{AlCl}_3$ and HCl gas gives 2,4-dimethyl pentane (ii)...

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Q JEE MAIN_2026

Given below are two statements : In the light of the above statements, choose the correct answer from the options...

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Q JEE MAIN_2026

Complete combustion of Xg of an organic compound gave 0.25 g of $\mathrm{CO}_2$ and 0.12 g of $\mathrm{H}_2 \mathrm{O}$. If...

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Q JEE MAIN_2026

Which of the following complexes will show coordination isomerism? A. $\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]\left[\mathrm{Ag}(\mathrm{CN})_2\right]$ B. $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]\left[\mathrm{Cr}(\mathrm{CN})_6\right]$ c. $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]\left[\mathrm{Co}(\mathrm{CN})_6\right]$ D. $\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_6\right]\left[\mathrm{Co}(\mathrm{CN})_6\right]$ E. $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ Choose...

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Q JEE MAIN_2026

Given below are two statements: Statement I: Among $\mathrm{Zn}, \mathrm{Mn}, \mathrm{Sc}$ and Cu , the energy required to remove the...

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Q JEE MAIN_2026

Given below are two statements: Statement I: The second ionization enthalpy of $\mathrm{B}, \mathrm{Al}$ and Ga is in the order...

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Q JEE MAIN_2026

The correct set that contains all kinds (basic, acidic, amphoteric and neutral) of oxides is :

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Q JEE MAIN_2026

Consider the reaction $\mathrm{aX} \rightarrow \mathrm{bY}$, for which the rate constant at $30^{\circ} \mathrm{C}$ is $1 \times 10^{-3} \mathrm{~mol}^{-1} \mathrm{Ls}^{-1}$....

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Q JEE MAIN_2026

At $25^{\circ} \mathrm{C}, 20.0 \mathrm{~mL}$ of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH . The...

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Q JEE MAIN 2026

Let $y=y(x)$ be the solution of the differential equation $...

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Q JEE MAIN 2026

If $S=\left\{\theta \in[-\pi, \pi]: \cos \theta \cos \frac{5 \theta}{2}=\cos 7 \theta \cos \frac{7 \theta}{2}\right\}$, then $n(S)$ is equal to $\_\_\_\_$...

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Q JEE MAIN 2026

From the point $(-1,-1)$, two rays are sent making angles of $45^{\circ}$ with the line $x+y=0$. These rays get reflected...

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Q JEE MAIN 2026

Let $A=\{1,4,7\}$ and $B=\{2,3,8\}$. Then the number of elements, in the relation $...

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Q JEE MAIN_2026

For the functions $f(\theta)=\alpha \tan ^2 \theta+\beta \cot ^2 \theta$, and $g(\theta)=\alpha \sin ^2 \theta+\beta \cos ^2 \theta, \alpha>\beta>0$, let...

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Q JEE MAIN_2026

If $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{j}-\hat{k}$ and $\vec{c}$ be three vectors such that $\vec{a} \times \vec{c}=\vec{b}$ and $\vec{a} \cdot \vec{c}=3$, then $...

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Q JEE MAIN_2026

Let the centre of the circle $x^2+y^2+2 g x+2 f y+25=0$ be in the first quadrant and lie on the...

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Q JEE MAIN_2026

Let $A=\left[\begin{array}{ccc}-1 & 1 & -1 \\ 1 & 0 & 1 \\ 0 & 0 & 1\end{array}\right]$ satisfy $...

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Solution A is prepared by dissolving 1 g of a protein (molar mass $=50000 \mathrm{~g} \mathrm{~mol}^{-1}$ ) in 0.5 L...

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Q JEE MAIN_2026

Gas ' $A$ ' undergoes change from state ' $X$ ' to state ' $Y$ '. In this process, the...

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Q JEE MAIN_2026

Let $e$ be the base of natural logarithm and let $f:\{1,2,3,4\} \rightarrow\left\{1, e, e^2, e^3\right\}$ and $...

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Q JEE MAIN_2026

The area of the region $\left\{(x, y): 0 \leq y \leq 6-x, y^2 \geq 4 x-3, x \geq 0\right\}$ is:

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Q JEE MAIN_2026

The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32 \cos ^4 x}{1+e^{\sin x}}\right) d x$ is:

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Q JEE MAIN 2026

Let $f:[1, \infty) \rightarrow \mathbf{R}$ be a differentiable function defined as $f(x)=\int_1^x f(\mathrm{t}) \mathrm{dt}+(1-x)\left(\log _0 x-1\right)+\mathrm{e}$. Then the value of...

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Q JEE MAIN 2026

The value of $\lim _{x \rightarrow 0}\left(\frac{x^2 \sin ^2 x}{x^2-\sin ^2 x}\right)$ is:

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Q JEE MAIN_2026

Let a line L be perpendicular to both the lines $\mathrm{L}_1: \frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and $\mathrm{L}_2: \frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}$. If $\theta$ is the acute...

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Q JEE MAIN 2026

Let $\left(2^{1-a}+2^{1+a}\right), f(a),\left(3^a+3^{-a}\right)$ be in A.P. and $\alpha$ be the minimum value of $f(a)$. Then the value of the integral...

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Q JEE MAIN_2026

$\mathrm{SF}_4$ is isostructural with: A. $\mathrm{BrF}_4{ }^{!}$ B. $\mathrm{CH}_4$ C. $\mathrm{IF}_4^{\oplus}$ D. $\mathrm{XeF}_4$ E. $\mathrm{XeO}_2 \mathrm{~F}_2$ Choose the correct answer...

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Q JEE MAIN_2026

Let the image of the point $\mathrm{P}(1,6, a)$ in the line $\mathrm{L}: \frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}, b>0$, be $\left(\frac{a}{3}, 0, a+c\right)$. If $...

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Q JEE MAIN 2026

Let $f(x)=\lim _{y \rightarrow 0} \frac{(1-\cos (x y)) \tan (x y)}{y^3}$. Then the number of solutions of the equation $...

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Q JEE MAIN 2026

Let $S=\{\theta \in(-2 \pi, 2 \pi): \cos \theta+1=\sqrt{3} \sin \theta\}$. Then $\sum_{\theta \in S} \theta$ is equal to:

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Q JEE MAIN 2026

Let $O$ be the origin, $\overrightarrow{O P}=\vec{a}$ and $\overrightarrow{O Q}=\vec{b}$. If $R$ is the point on $\overrightarrow{O P}$ such that...

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Q JEE MAIN_2026

The first and second ionization constants of a weak dibasic acid $\mathrm{H}_2 \mathrm{~A}$ are $8.1 \times 10^{-8}$ and $...

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Q JEE MAIN 2026

\text { Let } 0

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If the distance of the point $(a, 2,5)$ from the image of the point $(1,2,7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is...

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Q JEE MAIN 2026

Let a triangle PQ R be such that $P$ and $Q$ lie on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ and are at a...

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Q JEE MAIN_2026

The ratio of mass percentage $(\mathrm{w} / \mathrm{w})$ of $\mathrm{C}: \mathrm{H}$ in a hydrocarbon is $12: 1$. It has two...

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Q JEE MAIN 2026

If the eccentricity $e$ of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, passing through $(6,4 \sqrt{3})$, satisfies $15\left(e^2+1\right)=34 e$, then the length of the...

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Q JEE MAIN 2026

Let the eccentricity e of a hyperbola satisfy the equation $6 \mathrm{e}^2-11 \mathrm{e}+3=0$. If the foci of the hyperbola are...

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Q JEE MAIN 2026

A bag contains ( $\mathrm{N}+1$ ) coins - N fair coins, and one coin with 'Head' on both sides. A...

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Q JEE MAIN 2026

Let the directrix of the parabola $\mathrm{P}: y^2=8 x$, cut $x$-axis at the point A . Let $\mathrm{B}(\alpha, \beta), \alpha>1$,...

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Q JEE MAIN 2026

A data consists of 20 observations $x_1, x_2, \ldots, x_{20}$. If $\sum_{i=1}^{20}\left(x_i+5\right)^2=2500$ and $\sum_{i=1}^{20}\left(x_i-5\right)^2=100$, then the ratio of mean to...

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Q JEE MAIN 2026

Let the point P be the vertex of the parabola $y=x^2-6 x+12$. If a line passing through the point P...

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Q JEE MAIN 2026

If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{26}$ and $(1-\alpha x)^{28}, \alpha \neq 0$,...

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Q JEE MAIN_2026

At the transition temperature $T, A f \quad B$ and $\Delta G^0=105-35 \log T$ where $A$ and $B$ are two...

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Q JEE MAIN_2026

For reaction $\mathrm{A} \rightarrow \mathrm{P}$, rate constant $\mathrm{k}=1.5 \times 10^3 \mathrm{~s}^{-1}$ at $27^{\circ} \mathrm{C}$ If activation energy for the above...

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Q JEE MAIN_2026

One mole of an alkane $(x)$ requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen...

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Q JEE MAIN_2026

Consider the isomers of hydrocarbon with molecular formula $\mathrm{C}_5 \mathrm{H}_{10}$. These isomers do not decolourise $\mathrm{KMnO}_4$ solution. These isomers are...

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Q JEE MAIN 2026

A variable $X$ takes values $0,0,2,6,12,20, \ldots, n(n-1)$ with frequencies $...

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Q JEE MAIN 2026

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be...

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Q JEE MAIN 2026

A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing...

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Q JEE MAIN 2026

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6...

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Q JEE MAIN 2026

The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms...

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Q JEE MAIN 2026

The coefficient of $x^2$ in the expansion of $\left(2 x^2+\frac{1}{x}\right)^{10}, x \neq 0$, is :

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Q JEE MAIN 2026

The value of $1^3-2^3+3^3-\ldots+15^3$ is:

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Q JEE MAIN 2026

Let $A_1, A_2, A_3, \ldots \ldots . ., A_{39}$ be 39 arithmetic means between the numbers 59 and 159 ....

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Q JEE MAIN 2026

Let the set of all values of $k \in \mathrm{i}$ such that the equation $z(\bar{z}+2+i)+k(2+3 i)=0, z \in \mathrm{C}$, has...

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Q JEE MAIN 2026

If the sum of the first 10 terms of the series $...

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Q JEE MAIN 2026

Let M be a $3 \times 3$ matrix such that $...

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Q JEE MAIN 2026

Let $e_1$ and $e_2$ be two distinct roots of the equation $x^2-a x+2=0$. Let the sets $\left\{a \in \mathrm{i}: e_1\right.$...

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Q JEE MAIN 2026

If $f: \mathbf{N} \rightarrow \mathbf{Z}$ is defined by $$ f(n)=\left|\begin{array}{ccc} n & -1 & -5 \\ -2 n^2 & 3(2...

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Q JEE MAIN 2026

Let one root of the quadratic equation in $x$ : $$ \left(k^2-15 k+27\right) x^2+9(k-1) x+18=0 $$ be twice the other....

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Q JEE MAIN 2026

Let $z_1, z_2 \in £$ be the distinct solutions of the equation $z^2+4 z-(1+12 i)=0$. Then $\left|z_1\right|^2+\left|z_2\right|^2$ is equal to...

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Q JEE MAIN 2026

Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x)=\sin ^{-1}\left(\frac{x+[x]}{3}\right)$ is $[\alpha, \beta)$, then $\alpha^2+\beta^2$...

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Q JEE MAIN 2026

Let $\alpha, \beta$ be the roots of the equation $x^2-x+\mathrm{p}=0$ and $\gamma, \delta$ be the roots the equation $...

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Q JEE MAIN_2026

The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring...

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Q JEE MAIN_2026

Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of $5 \mathrm{~m} / \mathrm{s}$ and...

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Q JEE MAIN_2026

The stored charge in the capacitor in steady state of the following circuit is $\_\_\_\_$ $\mu \mathrm{C}$.

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Q JEE MAIN_2026

A 5 mg particle carrying a charge of $5 \pi \times 10^{-6} \mathrm{C}$ is moving with velocity of $...

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Q JEE MAIN_2026

Some distant star is to be observed by some telescope of diameter of objective lens a, at an angular resolution...

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Q JEE MAIN_2026

A parallel plate capacitor is having separation between plates 0.885 mm . It has a capacitance of $1 \mu \mathrm{~F}$...

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Q JEE MAIN_2026

The output Y for the given inputs A and B to the circuit is :

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Q JEE MAIN_2026

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same Q value...

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$K_1$ and $K_2$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the...

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Light ray incident along a vector $\overrightarrow{A O}(\overrightarrow{A O}=2 \hat{i}-3 \hat{j})$ emerges out along vector $\overrightarrow{O B}(\overrightarrow{O B}=C \hat{i}-4 \hat{j})$...

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Q JEE MAIN_2026

Two point charges $\mathrm{q}_1=3 \mu \mathrm{C}$ and $\mathrm{q}_2=-4 \mu \mathrm{C}$ are placed at points $(2 \hat{i}+3 \hat{j}+3 \hat{k})$ and $(\hat{i}+\hat{j}+\hat{k})$...

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Q JEE MAIN_2026

A 30 cm long solenoid has 10 turns per cm and area of $5 \mathrm{~cm}^2$. The current through the solenoid...

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Q JEE MAIN_2026

A current carrying circular loop of radius 2 cm with unit normal $\hat{n}=\frac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $...

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Q JEE MAIN_2026

A monochromatic source of light operating at 15 kW emits $2.5 \times 10^{22}$ photons $/ \mathrm{s}$. The region of an...

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Q JEE MAIN_2026

A spherical liquid drop of radius $R$ acquires the terminal velocity $v_1$ when falls through a gas of viscosity $\eta$....

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A liquid of density $600 \mathrm{~kg} / \mathrm{m}^3$ flowing steadily in a tube of varying cross-section. The cross-section at a...

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Q JEE MAIN_2026

A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t=0$ the...

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Q JEE MAIN_2026

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $R$. If the...

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Q JEE MAIN_2026

A thin biconvex lens is prepared from the glass $(\mu=1.5)$ both curved surfaces of which have equal radii of 20...

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Q JEE MAIN_2026

A gas balloon is going up with a constant velocity of $10 \mathrm{~m} / \mathrm{s}$. When this balloon reached a...

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Q JEE MAIN_2026

A car moving with a speed of $54 \mathrm{~km} / \mathrm{h}$ takes a turn of radius 20 m . A...

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Q JEE MAIN_2026

Consider the equation $H=\frac{x^p \dot{o}^q E^r}{t^s}$ Where $\mathrm{H}=$ magnetic field $; \mathrm{E}=$ electric field, $\mathrm{E}=$ permittivity, $\mathrm{x}=$ distance, $\mathrm{t}=$ time...

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Q JEE MAIN_2026

A new unit ( $\alpha$ ) of length is chosen such that it is equal to the speed of light...

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Q JEE MAIN_2026

A concave mirror of focal length 10 cm forms an image which is double the size of object when the...

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Q JEE MAIN_2026

and 2 V and internal resistance $2 \Omega$ and $1 \Omega$, respectively connected in parallel, gave a current of 1...

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Q JEE MAIN_2026

A moving coil of galvanometer when shunted with $2 \Omega$ resistance gives a full scale deflection for a current of...

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Q JEE MAIN 2026

Let $f$ be a twice differentiable function such that $...

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The de Broglie wavelength for an electron accelerated through the potential difference of $V_1$ volt is $\lambda_1$. When the potential...

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Q JEE MAIN 2026

Let $\mathrm{A}, \mathrm{B}$ and C be the vertices of a variable right angled triangle inscribed in the parabola $y^2=16 x$....

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Q JEE MAIN_2026

A block takes $t$ time to slide down a plane inclined at $45^{\circ}$ to the horizontal. If the surface is...

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Let $y=y(x)$ be the solution of the differential equation $x \sin \left(\frac{y}{x}\right) d y=\left(y \sin \left(\frac{y}{x}\right)-x\right) d x, y(1)=\frac{\pi}{2}$ and...

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Q

If $\frac{\pi}{4}+\sum_{p=1}^{11} \tan ^{-1}\left(\frac{2^{p-1}}{1+2^{2 p-1}}\right)=\alpha$, then $\tan \alpha$ is equal to $\_\_\_\_$ .

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Q JEE MAIN 2026

If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3}-x^4\right)^n, x \neq 0$, is zero,...

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Q JEE MAIN 2026

Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins...

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Let $\mathrm{A}=\{1,2,3,4,5,6\}$. The number of one-one functions $f: \mathrm{A} \rightarrow \mathrm{A}$ such that $f(1) \geq 3, f(3) \leq 4$ and...

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Let $\mathrm{A}, \mathrm{B}$ be points on the two half-lines $x-\sqrt{3}|y|=\alpha, \alpha>0$ at a distance of $\alpha$ from their point of...

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Q JEE MAIN_2026

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height...

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Q JEE MAIN 2026

Let $f(x)=\left\{\begin{array}{cc}e^{x-1} & , x

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Q JEE MAIN 2026

The value of the integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\left(\frac{4-\operatorname{cosec}^2 x}{\cos ^4 x}\right) d x$ is:

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Q JEE MAIN 2026

From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are...

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Refer to the logic circuit given below. For two inputs ( $\mathrm{A}=1, \mathrm{~B}=1$ ) and ( $\mathrm{A}=0, \mathrm{~B}=1$ ), output...

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Q JEE MAIN 2026

The integral $\int_0^1 \cot ^{-1}\left(1+x+x^2\right) d x$ is equal to:

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Q JEE MAIN 2026

Let $f: \mathrm{i} \rightarrow \mathrm{i}$ be a differentiable function such that $f\left(\frac{x+y}{3}\right)=\frac{f(x)+f(y)}{3}$ for all $x, y \in \mathrm{i}$, and $f^{\prime}(0)=3$....

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Q JEE MAIN 2026

Let $y=y(x)$ be the solution of the differential equation: $$ \frac{d y}{d x}+\left(\frac{6 x^2+\left(3 x^2+2 x^3+4\right) e^{-2 x}}{\left(x^3+2\right)\left(2+e^{-2 x}\right)}\right) y=2+e^{-2...

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Q JEE MAIN_2026

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive...

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Q JEE MAIN 2026

The value of the integral $\int_0^{\infty} \frac{\log _e(x)}{x^2+4} d x$ is:

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Q JEE MAIN 2026

The area of the region bounded by the curves $x+3 y^2=0$ and $x+4 y^2=1$ is equal to:

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Q JEE MAIN 2026

The product of all possible values of $\alpha$, for which $...

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$\mathrm{A}=\{(a, b, c): a, b, c$ are non-negative integers and $a+b+2 c=22\}$. Then $n(\mathrm{~A})$ is equal to:

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Q JEE MAIN_2026

The energy released if hydrogen atoms are combined to form ${ }_2^4 \mathrm{He}$ is $\_\_\_\_$ MeV . (Take binding energies...

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Q JEE MAIN 2026

The area of the region $\mathrm{R}=\left\{(x, y): x y \leq 27,1 \leq y \leq x^2\right\}$ is equal to:

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Q JEE MAIN 2026

Let for some $\alpha \in \mathrm{i}, f: \mathrm{i} \rightarrow \mathrm{i}$ be a function satisfying $f(x+y)=f(x)+2 y^2+y+\alpha x y$ for all...

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Q JEE MAIN_2026

A sphere of capacitance 100 pF is charged to a potential of 100 V . Another identical uncharged metal sphere...

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Q JEE MAIN 2026

The shortest distance between the lines $\vec{r}=\left(\frac{1}{3} \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\frac{8}{3} \hat{\mathrm{k}}\right)+\lambda(2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+6 \hat{\mathrm{k}})$ and $...

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The square of the distance of the point of intersection of the lines $\vec{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda(a \hat{i}-\hat{j}), a \neq 0$ and $...

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Q JEE MAIN 2026

If $\left(2 \alpha+1, \alpha^2-3 \alpha, \frac{\alpha-1}{2}\right)$ is the image of $(\alpha, 2 \alpha, 1)$ in the line $\frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}$, then the...

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Q JEE MAIN 2026

Let $\vec{a}=\sqrt{7} \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{j}+2 \hat{k}$. If $\vec{r}$ is a vector such that $\vec{r} \times \vec{a}+\vec{a} \times \vec{b}=\overrightarrow{0}$ and $...

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Q JEE MAIN 2026

The shortest distance between the lines $\vec{r}=\left(\frac{1}{3} \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\frac{8}{3} \hat{\mathrm{k}}\right)+\lambda(2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+6 \hat{\mathrm{k}})$ and $...

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Q JEE MAIN 2026

The square of the distance of the point $\mathrm{P}(5,6,7)$ from the line $\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4}$ is equal to:

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$\max _{0 \leq x \leq \pi}\left(16 \sin \left(\frac{x}{2}\right) \cos ^3\left(\frac{x}{2}\right)\right)$ is equal to:

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The sum of all the integral values of $p$ such that the equation $...

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A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at...

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Let $\mathrm{H}: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be a hyperbola such that the distance between its foci is 6 and the distance between its...

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Q JEE MAIN 2026

In an equilateral triangle P Q R , let the vertex $P$ be at $(3,5)$ and the side Q R...

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The electric potential as a function of $x, y$ is given by $V=5\left(x^2-y^2\right) V$. The electric field at a point...

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Q JEE MAIN 2026

Let $\mathrm{P}(3 \cos \alpha, 2 \sin \alpha), \alpha \neq 0$, be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1, \mathrm{Q}$ be a...

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Let P be a moving point on the circle $x^2+y^2-6 x-8 y+21=0$. Then, the maximum distance of P from the...

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A spring stretches by 2 mm when it is loaded with a mass of 200 g . From equilibrium position...

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In the expansion of $\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x>0$, if the term independent of $x$ is $(221) \mathrm{k}$, then k is...

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Q JEE MAIN 2026

Let a focus of the ellipse $\mathrm{E}: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be $\mathrm{S}(4,0)$ and its eccentricity be $\frac{4}{5}$. If the point $\mathrm{P}(3, \alpha)$...

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Q JEE MAIN 2026

For 10 observations $x_1, x_2, \ldots, x_{10}$, if $\sum_{i=1}^{10}\left(x_i+2\right)^2=180$ and $\sum_{i=1}^{10}\left(x_i-1\right)^2=90$, then their standard deviation is:

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If 2 mole of an ideal monoatomic gas at temperature T , is mixed with 6 mole of another ideal...

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Let $\alpha=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \infty$ and $\beta=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\ldots \infty$. Then the value of $(0.2)^{\log _{\sqrt{5}}(\alpha)}+(0.04)^{\log _5(\beta)}$ is equal to:

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The mean deviation about the mean for the data

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Let $A=\left[\begin{array}{ccc}4 & -2 & 8 \\ 3 & 8 & -7\end{array}\right]$ and $\operatorname{det}(\mathrm{A}-\alpha \mathrm{I})=0$, where $\alpha$ is a real...

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A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is $528 \mathrm{dm}^3$ (dm :...

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A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two...

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If the quadratic equation $(\lambda+2) x^2-3 \lambda x+4 \lambda=0, \lambda \neq-2$, has two positive roots, then the number of possible...

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Q JEE MAIN 2026

If $\alpha=1$ and $\beta=1+i \sqrt{2}$, where $i=\sqrt{-1}$ are two roots of the equation $...

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Figure represents the extension $(\Delta \mathrm{l})$ of a wire of length 1 meter, suspended from the ceiling of the room...

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Let $\tan A, \tan B$, where $A, B \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, be the roots of the quadratic equation $x^2-2 x-5=0$. Then...

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Q JEE MAIN 2026

Above equation has one solution using graph. Let $\mathrm{S}=\left\{z \in £: z^2+4 z+16=0\right\}$. Then $\sum_{z \in \mathrm{~S}}|z+\sqrt{3} \mathrm{i}|^2$ is equal...

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$$ \sum_{n=1}^{10}\left(\frac{528}{n(n+1)(n+2)}\right) \text { is equal to: } $$

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Two identical bodies A and B of equal masses have initial velocities $\vec{v}_1=4 \hat{i} \mathrm{~m} / \mathrm{s}$ and $...

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Consider the system of linear equations in $x, y, z$ : $$ \begin{aligned} & x+2 y+t z=0 \\ & 6...

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If the system of equations:

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Let A be a $3 \times 3$ matrix such that $$ \mathrm{A}^{\mathrm{T}}\left[\begin{array}{l} 1 \\ 0 \\ 1 \end{array}\right]=\left[\begin{array}{l} 5 \\...

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Q JEE MAIN 2026

Let the sum of the first $n$ terms of an A.P. be $3 n^2+5 n$. Then the sum of squares...

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Let $a, b \in £$. Let $\alpha, \beta$ be the roots of the equation $x^2+a x+b=0$. If $\beta-\alpha=\sqrt{11}$ and $...

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For the function $f:[1, \infty) \rightarrow[1, \infty)$ defined by $f(x)=(x-1)^4+1$, among the two statements: (I) The set $...

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For an electromagnetic wave propagating through vacuum, $\vec{k}, \vec{E}$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively....

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A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic...

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A body of mass 1 kg moves along a straight line with a velocity $\mathrm{v}=2 \mathrm{x}^2$. The work done by...

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A solid sphere (A) of mass 5 m and a spherical shell (B) of mass m , both having same...

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Match List - I with List - II. Choose the correct answer from the options given below :

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The percentage error in the calculated volume of a sphere, if there is $2 \%$ error in its diameter measurement,...

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A three coulomb charge moves from the point $(0,-2,-5)$ to the point $(5,1,2)$ in an electric field expressed as $...

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The energy released when $\frac{7}{17.13} \mathrm{~kg}$ of ${ }_3^7 \mathrm{Li}$ is converted into ${ }_2^4 \mathrm{He}$ by proton bombardment is...

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Q JEE MAIN_2026

An unpolarized light of intensity $\mathrm{I}_0$ passes through polarizer and then through a certain optically active solution and finally it...

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Refer to the circuit diagram given below. The heat generated across the $6 \Omega$ resistance in 100 second is $...

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A LCR series circuit driven with $E_{\mathrm{rms}}=90 \mathrm{~V}$ at frequency $f_d=30 \mathrm{~Hz}$ has resistance $\mathrm{R}=80 \Omega$, an inductance with inductive...

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The ratio of momentum of the photons of the $1^{\text {st }}$ and $2^{\text {nd }}$ line of Balmer series...

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An inductor of inductance 10 mH having resistance of $100 \Omega$ is connected to battery of E.M.F. 1.0 V through...

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A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm...

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A spherical interface lens of radius R separates two media of refractive indices 1 and 1.4 respectively as shown in...

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A point light source emits E.M. waves in free space. A detector, placed at a distance of Lm, measures the...

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The maximum rated power of the LED is 2 mW and it is used in the circuit with input voltage...

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A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the...

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A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required...

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In interference experiment the path difference between two interfering waves at a point A on the screen is $...

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Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of...

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The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's...

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The position of center of mass of three masses $2 \mathrm{~kg}, 3 \mathrm{~kg}$ and 15 kg placed with respect to...

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A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released...

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A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre...

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A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can...

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Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These...

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The rain drop of mass 1 g , starts with zero velocity from a height of 1 km . It...

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The potential energy of a particle changes with distance x from a fixed origin as $V=\frac{A \sqrt{x}}{x+B}$, where A and...

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The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length I and diameter $d$. The...

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The number of points in the interval [2,4], at which the function $f(x)=\left[x^2-x-\frac{1}{2}\right]$, where [-] denotes the greatest integer function,...

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Q JEE Main 2026

If the area of the region bounded by $16 x^2-9 y^2=144$ and $8 x-3 y=24$ is A , then $...

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Let A be the point $(3,0)$ and circles with variable diameter AB touch the circle $x^2+y^2=36$ internally. Let the curve...

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Consider the matrices $\mathrm{A}=\left[\begin{array}{ll}2 & -2 \\ 4 & -2\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ll}3 & 9 \\ 1 & 3\end{array}\right]$. If matrices...

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A circular loop of radius 20 cm and resistance $2 \Omega$ is placed in a time varying magnetic field $...

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The number of points, at which the function $f(x)=\max \left\{6 x, 2+3 x^2\right\}+|x-1| \cos \left|x^2-\frac{1}{4}\right|, x \in(-\pi, \pi)$, is not...

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Let $\mathrm{A}=\{2,3,4,5,6\}$. Let R be a relation on the set $\mathrm{A} \times \mathrm{A}$ given by $(x, y) \mathrm{R}(z, w)$ if...

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When an external resistance of $5 \Omega$ is connected across terminals of a cell, a current of 0.25 A flows...

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Let $\overrightarrow{a_k}=\left(\tan \theta_k\right) \hat{i}+\hat{j}$ and $\overrightarrow{b_k}=\hat{i}-\left(\cot \theta_k\right) \hat{j}$, where $\theta_k=\frac{2^{k-1} \pi}{2^n+1}$, for some $n \in \mathbb{N}, n>5$. Then the value...

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A series LCR circuit with R $=20 \Omega, \mathrm{~L}=1.6 \mathrm{H}$ and $\mathrm{C}=40 \mu \mathrm{~F}$ is connected to a variable frequency...

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Let $x=x(y)$ be the solution of the differential equation $2 y^2 \frac{\mathrm{~d} x}{\mathrm{~d} y}-2 x y+x^2=0, y>1, x(\mathrm{e})=\mathrm{e}$. Then $x\left(\mathrm{e}^2\right)$...

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If $\mathrm{A}=\frac{\sin 3^{\circ}}{\cos 9^{\circ}}+\frac{\sin 9^{\circ}}{\cos 27^{\circ}}+\frac{\sin 27^{\circ}}{\cos 81^{\circ}}$ and $\mathrm{B}=\tan 81^{\circ}-\tan 3^{\circ}$, then $\frac{\mathrm{B}}{\mathrm{A}}$ is equal to $\_\_\_\_$ .

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The heat extracted out of x gram of water initially at $50^{\circ} \mathrm{C}$ to cool it down to $0^{\circ} \mathrm{C}$...

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Let $f(x)=\int\left(\frac{x^2+2 x-15}{x^2}\right) \mathrm{d} x$. If $f(4)=14 \log _e(3)$ and $f(7)=\log _e\left(2^\alpha-3^\beta\right), \alpha, \beta \in \mathbf{N}$, then $\alpha+\beta$ is equal...

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A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of...

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Let $f(x)$ be a polynomial of degree 5 , and have extrema at $x=1$ and $x=-1$. If $...

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Consider the parabola $\mathrm{P}: y^2=4 k x$ and the ellipse $\mathrm{E}: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. Let the line segment joining the points of...

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The value of $\int_0^{20 \pi}\left(\sin ^4 x+\cos ^4 x\right) \mathrm{d} x$ is equal to :

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A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and...

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Two adjacent sides of a parallelogram PQRS are given by $\overrightarrow{\mathrm{PQ}}=\hat{j}+\hat{k}$ and $\overrightarrow{\mathrm{PS}}=\hat{i}-\hat{j}$. If the side PS is rotated about...

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In a semiconductor p-n diode, the doping concentrations on p-side and $n$-side are $10^{15} \mathrm{atoms} / \mathrm{cm}^3$ and $10^{18}$ atoms...

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Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}=\left(1+x+x^2\right)\left(1-y+y^2\right), y(0)=\frac{1}{2}$. Then $(2 y(1)-1)$ is equal to Options...

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Let the point $A$ be the foot of perpendicular drawn from the point $P(a, b, 0)$ on the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-\alpha}{3}$....

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Let $\int_{-2}^2(|\sin x|+[x \sin x]) d x=2(3-\cos 2)+\beta$, where [ ] is the greatest integer function. Then $\beta \sin \left(\frac{\beta}{2}\right)$...

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Assuming the experimental mass of ${ }_6^{12} \mathrm{C}$ as 12 u , the mass defect of ${ }_6^{12} \mathrm{C}$ atom...

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The area of the region $\{(x, y): y \leq \pi-|x|, y \unlhd x \sin x \mid, y \geq 0\}$ is:

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An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is...

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Let $f$ be a real polynomial of degree $n$ such that $f(x)=f^{\prime}(x) f^{\prime \prime}(x)$, for all $x \in \mathbb{R}$. If...

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If $y=\tan ^{-1}\left(\frac{3 \cos x-4 \sin x}{4 \cos x+3 \sin x}\right)+2 \tan ^{-1}\left(\frac{x}{1+\sqrt{1-x^2}}\right)$, then $\frac{d y}{d x}$ at $x=\frac{\sqrt{3}}{2}$ is...

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The maximum intensity in a Young's double slit experiment is $\mathrm{I}_0$. Distance between the slits (d) is $5 \lambda$, where...

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The square of the distance of the point $(-2,-8,6)$ from the line $\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1}$ along the line $\frac{x+5}{1}=\frac{y+5}{-1}=\frac{z}{2}$ is equal to:

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A line with direction ratios $1,-1,2$ intersects the lines $\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3}$ and $\frac{x+1}{-1}=\frac{y-2}{1}=\frac{z}{4}$ at the points P and Q , respectively....

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An object $A B$ is placed 15 cm on the left of a convex lens $P$ of focal length 10...

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Let the vectors $\overrightarrow{\mathrm{a}}=-\hat{i}+\hat{j}+3 \hat{k}$ and $\overrightarrow{\mathrm{b}}=\hat{i}+3 \hat{j}+\hat{k}$. For some $\lambda, \mu \in \mathbf{R}$, let $\overrightarrow{\mathrm{c}}=\lambda \overrightarrow{\mathrm{a}}+\mu \overrightarrow{\mathrm{b}}$. If $...

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Suppose that two chords, drawn from the point $(1,2)$ on the circle $x^2+y^2+x-3 y=0$ are bisected by the $y$-axis. If...

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A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following...

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Let $P=\left\{\theta \in[0,4 \pi]: \tan ^2 \theta \neq 1\right\}$ and $...

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Let the vertex $A$ of a triangle ABC be $(1,2)$, and the mid-point of the side AB be $(5,-1)$. If...

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Let the line $\mathrm{L}_1: x+3=0$ intersect the lines $\mathrm{L}_2: x-y=0$ and $\mathrm{L}_3: 3 x+y=0$ at the points A and B...

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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Let the parabola $y=x^2+p x+q$ passing through the point $(1,-1)$ be such that the distance between its vertex and the...

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Suppose that the mean and median of the non-negative numbers $21,8,17, a, 51,103, b, 13,67,(a>b)$, are 40 and 21 ,...

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Let O be the origin, and P and Q be two points on the rectangular hyperbola $x y=12$ such that...

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A particle of charge q and mass m is projected from origin with an initial velocity $\vec{v}=\left(\frac{v_0}{\sqrt{2}} \hat{x}+\frac{v_0}{\sqrt{2}} \hat{y}\right)$. There...

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Let the smallest value of $k \in \mathbb{N}$, for which the coefficient of $x^3$ in $(1+x)^3+(1+x)^4+(1+x)^5+\ldots+(1+x)^{99}+(1+k x)^{100}, x \neq 0$,...

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Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines...

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Under steady state condition the potential difference across the capacitor in the circuit is_____V.

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The mean and variance of $n$ observations are 8 and 16 , respectively. If the sum of the first (...

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The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are...

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The first term of an A.P. of 30 non-negative terms is $\frac{10}{3}$. If the sum of this A.P. is the...

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A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for...

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A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic...

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Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-side regular polygon. If $p_{n+1}-p_n=66$,...

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\text { Let } A=\left[\begin{array}{ccc} 1 & 1 & 2 \\ -2 & 0 & 1 \\ 1 & 3...

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Let $\mathrm{S}=\left\{\mathrm{A}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]: a, b, c, d \in\{0,1,2,3,4\}\right.$ and $\left.\mathrm{A}^2-4 \mathrm{~A}+3 \mathrm{I}=0\right\}$ be a set...

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If for $3 \leq \mathrm{r} \leq 30,\left({ }^{30} \mathrm{C}_{30-\mathrm{r}}\right)+3\left({ }^{30} \mathrm{C}_{31-\mathrm{r}}\right)+3\left({ }^{30} \mathrm{C}_{32-\mathrm{r}}\right)+\left({ }^{30} \mathrm{C}_{33-\mathrm{r}}\right)={ }^{\mathrm{m}} \mathrm{C}_{\mathrm{r}}$, then m equals...

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Match List - I with List - II. Choose the correct answer from the options given below :

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The number of functions $f:\{1,2,3,4\} \rightarrow\{a, b, c\}$, which are not onto, is:

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The sum $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\cdots$ up to 8 terms, is :

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An ideal gas at pressure P and temperature T is expanding such that $\mathrm{PT}^3=$ constant. The coefficient of volume expansion...

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If the set of all solutions of $\left|x^2+x-9\right|=|x|+\left|x^2-9\right|$ is $[\alpha, \beta] \cup[\gamma, \infty)$, then $\left(\alpha^2+\beta^2+\gamma^2\right)$ is equal to:

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Eight mercury drops, each of radius r, coalesce to form a bigger drop. The surface energy released in this process...

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Let [ • ] denote the greatest integer function. If the domain of the function $f(x)=\cos ^{-1}\left(\frac{4 x+2[x]}{3}\right)$ is $...

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Let $a_1, a_2, a_3, \ldots$ be an A.P. and $g_1=a_1, g_2, g_3, \ldots$ be an increasing G.P. If $a_1=a_2+g_2=1$ and...

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A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius...

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3. If the system of equations $$ \begin{aligned} & x+5 y+6 z=4 \\ & 2 x+3 y+4 z=7 \\ &...

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Let the circles $\mathrm{C}_1:|z|=\mathrm{r}$ and $\mathrm{C}_2:|z-3-4 \mathbf{i}|=5, z \in \mathbb{C}$, be such that $\mathrm{C}_2$ lies within $\mathrm{C}_1$. If $z_1$ moves...

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An object of uniform density rolls up the curved path with the initial velocity $v_0$ as shown in the figure....

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A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first $2 s$...

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Let $\alpha, \beta$ be the roots of the equation $x^2-3 x+\mathrm{r}=0$, and $\frac{\alpha}{2}, 2 \beta$ be the roots of the...

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The velocity (v) versus time (t) plot of a particle is shown in the figure, for a time interval of...

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A mass of 1 kg is kept on a inclined plane with $30^{\circ}$ inclination with respect to horizontal plane and...

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In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are...

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Match List - I with List - II where h (Planck's constant), G (gravitational constant) and c (speed of light...

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In the given circuit below inductance values of $L_1, L_2$ and $L_3$ are same. The magnetic energy stored in the...

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The charged particle moving in a uniform magnetic field of $(3 \hat{i}+2 \hat{j}) \mathrm{T}$ has an acceleration $...

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A transverse wave on a string is described by $y=3 \sin (36 t+0.018 x+\pi / 4)$. where $x, y$ are...

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From 18 m height above the ground a ball is dropped from rest. The height above the ground at which...

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A cube has side length 5 cm and modulus of rigidity $10^5 \mathrm{~N} / \mathrm{m}^2$. The displacement produced by a...

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For the given logic circuit, which of the following inputs combination will make both LED-1 and LED-2 to glow?

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An a.c. source of angular frequency $\omega$ is connected across a resistor R and a capacitor C in series. The...

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Two wires as shown in the figure below, made of steel and have breaking stress of $...

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A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex...

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Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V . The work...

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A ray of light passing through an equilateral prism is having velocity $2.12 \times 10^8 \mathrm{~m} / \mathrm{s}$ in the...

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In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is $2.4 \mu \mathrm{~m}$....

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Refer to the figure given below, current between terminals A and B is $\_\_\_\_$ A.

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A displacement current of 4.0 A can be set up in the space between two parallel plates of $...

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In the hydrogen atom, the electron makes a transition from the higher orbit (i) to a lower orbit (f). The...

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5.33 g of $\mathrm{CrCl}_3 \cdot 6 \mathrm{H}_2 \mathrm{O}$, which is a $1: 3$ electrolyte, is dissolved in water and is...

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An electron of mass m is moving in an electric field $\vec{E}=-2 E_{\mathrm{o}} \hat{i}\left(\mathrm{E}_0=\right.$ constant $\left.>0\right)$, with an initial velocity...

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Refer to the figure given below. The values of $\mathrm{I}_1, \mathrm{I}_2$ and $\mathrm{I}_3$ are $\_\_\_\_$ .

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Consider the following statements: A. Zeroth law of thermodynamics gives concept of temperature B. First law of thermodynamics gives concept...

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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

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The Young's modulus of steel wire of radius r and length L is Y. If the radius r and length...

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A wedge $Y$ with mass of 10 kg and all frictionless surfaces and the inclined surface making $37^{\circ}$ with horizontal....

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Three masses $m_1=4 \mathrm{~kg}, m_2=4 \mathrm{~kg}$ and $m_3=6 \mathrm{~kg}$ are suspended from a fixed smooth frictionless pulley as shown in...

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When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's...

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$\mathrm{L}, \mathrm{C}$ and R represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $\mathrm{ML}^2 \mathrm{~T}^{-4} \mathrm{~A}^{-2}$ corresponds to...

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In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right...

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A body of mass 2 kg begins to move under the influence of time dependent force $...

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A salt with few drops of conc. HCl gives apple green colour in flame test. The group precipitate of the...

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Consider the three aromatic molecules (P, Q and R) whose structures have been given below :

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Match the following

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The velocity of a particle executing simple harmonic motion along $x$-axis is described as $v^2=50-x^2$, where x represents displacement. If...

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The surface tension of a soap solution is $3.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}$. The work required to increase the...

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A 1 kg block subjected to two simultaneous forces $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}) \mathrm{N}$ and $(3 \hat{i}-\hat{j}-2 \hat{k}) \mathrm{N}$ is...

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An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is...

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The voltage and the current between A and B points shown in the circuit are _____.

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For the given molecule, "x", the preferred site for the attack of the electrophile is :

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In IUPAC nomenclature, the correct order of decreasing priority of functional group is:

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Given below are two statements: Statement (I) : Benzyl chloride reacts faster in $\mathrm{S}_{\mathrm{N}} 1$ mechanism than ethyl chloride. Statement...

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Consider a circuit consisting of a capacitor $(20 \mu \mathrm{~F})$, resistor $(100 \Omega)$ and two identical diodes as shown in...

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Given below are two statements: Statement (I) : 1, 2, 3-Trihydroxypropane can be separated from water by simple distillation. Statement...

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An insulated wire is wound so that it forms a flat coil with $\mathrm{N}=200$ turns. The radius of the innermost...

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Match List - I with List - II. List - I List - II

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A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If...

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A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm...

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Two 4 bits binary numbers, $\mathrm{A}=1101$ and $\mathrm{B}=1010$ are given in the inputs of a logic circuit shown in figure...

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A voltmeter with internal resistance of $x \Omega$ can be used to measure upto 20 V . In order to...

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One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$...

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A string A of length 0.314 m and Young's modulus $2 \times 10^{10} \mathrm{~N} / \mathrm{m}^2$ is connected to another...

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A slit of width $a$ is illuminated by light of wavelength $\lambda$. The linear separation between $1^{\text {st }}$ and...

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The graph shows variation of stopping potential $V_0$ with the frequency $v$ of the incident radiation for three photosensitive metals...

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The two projectiles are projected with the same initial velocities at the $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal....

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Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass...

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The time taken by a block of mass $m$ to slide down from the highest point to the lowest point...

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The increase in the pressure required to decrease the volume $(\Delta \mathrm{V})$ of water is $...

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In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm. If...

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Moment of inertia about an axis A B for a rod of mass 40 kg and length 3 m is...

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If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the...

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5 moles of unknown gas is heated at constant volume from $10^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$. The molar specific heat...

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Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the...

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In a Young's double slit experiment, the intensity at some point on the screen is found to be $\frac{3}{4}$ times...

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The equation of motion of a particle is given by $x=a \sin (50 t+\pi / 3) \mathrm{cm}$. The particle will...

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The binding energy per nucleon of ${ }_{83}^{209} \mathrm{Bi}$ is $\_\_\_\_$ MeV . [Take $...

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A circular current loop of radius $R$ is placed inside square loop of side length $L(L ? R)$ such that...

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The figure given below shows an LCR series circuit with two switches $S_1$ and $S_2$. When switch $S_1$ is closed...

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One side of an equilateral prism is painted by a transparent material of refractive index $n_2$. The refractive index of...

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Two point charges $8 \mu \mathrm{C}$ and $-2 \mu \mathrm{C}$ are located at $x=2 \mathrm{~cm}$ and $x=4 \mathrm{~cm}$, respectively on...

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Two metal plates $(A, B)$ are kept horizontally with separation of $\left(\frac{12}{\pi}\right) \mathrm{cm}$, with plate $A$ on the top. An...

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Two resistors of $200 \Omega$ and $400 \Omega$ are connected in series with a battery of 100 V . A...

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An electromagnetic wave travels in free space along the $x$-direction. At a particular point in space and time, $...

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A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after...

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If an air bubble of diameter 2 mm rises steadily through a liquid of density $2000 \mathrm{~kg} / \mathrm{m}^3$ at...

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A mixture of carbon dioxide and oxygen has volume $8310 \mathrm{~cm}^3$, temperature 300 K , pressure 100 kPa and mass...

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The surface tension of a soap bubble is $0.03 \mathrm{~N} / \mathrm{m}$. The work done in increasing the diameter of...

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In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale...

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If a body of mass 1 kg falls on the earth from infinity, it attains velocity $(v)$ and kinetic energy...

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If X and Y are the inputs, the given circuit works as _____ .

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A particle having charge $10^{-9} \mathrm{C}$ moving in $x-y$ plane in fields of $0.4 \hat{j} \mathrm{~N} / \mathrm{C}$ and $...

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Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes...

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A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating...

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Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are...

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Refer the figure given below. m1 and m2 are refractive indices of air and lens material. The height of image...

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For a thin symmetric prism made of glass (refractive index 1.5 ), the ratio of incident angle and minimum deviation...

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A tub is filled with water and a wooden cube $10 \mathrm{~cm} \times 10 \mathrm{~cm} \times 10 \mathrm{~cm}$ is placed...

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A uniform wire of length $l$ of weight w is suspended from the roof with a weight of W at...

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$1 \mu \mathrm{C}$ charge moving with velocity $\vec{v}=(\hat{i}-2 \hat{j}+3 \hat{k}) \mathrm{m} / \mathrm{s}$ in the region of magnetic field $...

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A vessel contains $0.15 \mathrm{~m}^3$ of a gas at pressure 8 bar and temperature $140^{\circ} \mathrm{C}$ with $c_p=3 R$ and...

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In single slit diffraction pattern, the wavelength of light used is 628 nm and slit width is 0.2 mm ,...

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A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $...

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Angular momentum of an electron in a hydrogen atom is $\frac{3 h}{\pi}$, then the energy of the electron is $\_\_\_\_$...

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An electromagnetic wave travelling in $x$-direction is described by field equation $\mathrm{E}_y=300 \sin \omega\left(t-\frac{x}{\mathrm{c}}\right)$. If the electron is restricted to...

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For a certain metal, when monochromatic light of wavelength $\lambda$ is incident, the stopping potential for photoelectrons is $3 \mathrm{~V}_0$....

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Which of the following sets includes all the species that will change the orange colour of $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ in...

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Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of...

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Given below are two statements: Statement (I): Oxidising power of halogens decreases in the order $\mathrm{F}_2>\mathrm{Cl}_2>\mathrm{Br}_2>\mathrm{I}_2$, which is the basis...

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When a coil is placed in a time dependent magnetic field the power dissipated in it is $P$. The number...

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Given below are two statements: Statement (I): The first ionisation enthalpy of the elements $\mathrm{Na}, \mathrm{Mg}, \mathrm{Cl}$ and Ar follows...

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For the given circuit (shown in part (A)) the time dependent input voltage vin (t) and corresponding output v0(t) are...

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$t_{100 \%}$ is the time required for the $100 \%$ completion of the reaction while $t_{1 / 2}$ is the...

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An electrochemical cell is constructed using half cells in the direction of spontaneous change $$ \mathrm{Fe}(\mathrm{OH})_2(\mathrm{~s})+2 \mathrm{e}^{-} \rightarrow \mathrm{Fe}(\mathrm{~s})+2 \mathrm{OH}^{-}(\mathrm{aq})...

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Two short electric dipoles A and B having dipole moment p1 and p2 respectively are placed with their axis mutually...

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The solubility product constants of $\mathrm{Ag}_2 \mathrm{CrO}_4$ and AgBr are 32 x and 4 y respectively at 298 K ....

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The equation of a plane progressive wave is given by $y=5 \cos \pi\left(200 t-\frac{x}{150}\right)$ where x and y are in...

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19.5 g of fluoro acetic acid (molar mass $=78 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is dissolved in 500 g of water at...

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Two charged conducting spheres S1 and S2 of radii 8 cm and 18 cm are connected to each other by...

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Heat is supplied to a diatomic gas at constant pressure. Then the ratio of DQ : DU : DW is...

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A parallel plate air capacitor has a capacitance C. When it is half filled as show in figure with a...

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Consider the following data. (i) $2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{Al}_2 \mathrm{Cl}_6(\mathrm{aq})+3 \mathrm{H}_2(\mathrm{~g})+1200 \mathrm{~kJ} / \mathrm{mol}$ (ii) $...

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A particle is rotating in a circular path and at any instant its motion can be described as $\theta=\frac{5 t^4}{40}-\frac{t^3}{3}$....

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Given below are two statements :Statement (I): The correct sequence of bond lengths in the following species is : $$...

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A planet $\left(P_1\right)$ is moving around the star of mass $2 M$ in the orbit of radius $R$. Another planet...

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The position of an object having mass 0.1 kg as a function of time t is given as $...

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The velocity of a particle is given as $\vec{v}=-x \hat{i}+2 y \hat{j}-z \hat{k} \mathrm{~m} / \mathrm{s}$. The magnitude of acceleration...

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What is the energy (in $\mathrm{J}^{-1}$ atom-required for the following process? $$ \mathrm{Li}^{2+}(\mathrm{g}) \rightarrow \mathrm{Li}^{3+}(\mathrm{g})+\mathrm{e}^{-} $$ (Take the ionization energy...

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The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm . The...

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The mass of iron converted into $\mathrm{Fe}_3 \mathrm{O}_4$ by the action of 18 g of steam is : (Given :...

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The dimensional formula of $\frac{1}{2} \epsilon_0 \mathrm{E}^2$ ( $\epsilon_0=$ permittivity of vacuum and $\mathrm{E}=$ electric field) is $\mathrm{M}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}} \mathrm{T}^{\mathrm{c}}$....

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The number of elements in the set $\left\{x \in\left[0,180^{\circ}\right]: \tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan x \tan \left(x-50^{\circ}\right)\right\}$ is $\_\_\_\_$ .

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Let S be a set of 5 elements and $\mathrm{P}(\mathrm{S})$ denote the power set of S . Let E be...

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Let z=(1+i)(1+2i)(1+3i)...(1+n i), where $i=\sqrt{-1}$. If $|z|^2=44200$, then $n$ is equal to

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Let $(h, k)$ lie on the circle $\mathrm{C}: x^2+y^2=4$ and the point $(2 h+1,3 k+2)$ lie on an ellipse with...

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Let [t] denote the greatest integer less than or equal to t. If the function $...

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Let $\vec{a}=2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$ and $\vec{b}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. If $\vec{c}$ is a vector such that $2(\vec{a} \times \vec{c})+3(\vec{b} \times \vec{c})=\overrightarrow{0}$...

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The smallest positive integral value of $a$, for which all the roots of $x^4-a x^2+9=0$ are real and distinct, is...

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Let $f$ be a function such that $3 f(x)+2 f\left(\frac{m}{19 x}\right)=5 x, x \neq 0$, where $m=\sum_{i=1}^9(i)^2$. Then $f(5)-f(2)$ is...

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Let $y=y(x)$ be a differentiable function in the interval $(0, \infty)$ such that $y(1)=2$, and $...

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Consider the following three statements for the function $f:(0, \infty) \rightarrow \mathbb{R}$ defined by $f(x)=\left|\log _e x\right|-|x-1|$ : (I) $f$...

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A volume of $x \mathrm{~mL}$ of $5 \mathrm{M} \mathrm{NaHCO}_3$ solution was mixed with 10 mL of $2 \mathrm{MH}_2 \mathrm{CO}_3$ solution...

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Using a variable frequency acavoltage source the maximum current measured in the given LCR circuit is 50 mA for $...

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The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at $V_{\mathrm{z}}=5 \mathrm{~V}$ and...

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200 cc of $x \times 10^{-3} \mathrm{M}$ potassium dichromate is required to oxidise 750 cc of 0.6 M Mohr's salt...

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The space between the plates of a parallel plate capacitor of capacitance $C$ (without any dielectric) is now filled with...

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In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes...

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The equation of the electric field of an electromagnetic wave propagating through free space is given by: $...

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A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in...

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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)....

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Consider the dissociation equilibrium of the following weak acid $\mathrm{HA} \boxtimes \mathrm{H}^{+}(\mathrm{aq})+\mathrm{A}^{-}(\mathrm{aq})$ If the pKa of the acid is 4...

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0.53 g of an organic compound $(\mathrm{x})$ when heated with excess of nitric acid (concentrated) and then with silver nitrate...

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In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their...

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X is the number of geometrical isomers exhibited by $\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)\left(\mathrm{H}_2 \mathrm{O}\right) \mathrm{BrCl}\right]$. Y is the number of optically inactive isomer(s)...

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In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg ,...

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Consider the following redox reaction taking place in acidic medium $$ \mathrm{BH}_4^{-}(a q)+\mathrm{ClO}_3^{-}(a q) \longrightarrow \mathrm{H}_2 \mathrm{BO}_3^{-}(a q)+\mathrm{Cl}^{-}(a q) $$...

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Two small balls with masses m and 2 m are attached to both ends of a rigid rod of length...

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A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity ( $...

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500 mL of 1.2 M KI solution is mixed with 500 mL of $0.2 \mathrm{MKMnO}_4$ solution in basic medium. The...

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The correct statement among the following is:

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In period 4 of the periodic table, the elements with highest and lowest atomic radii are respectively.

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Given below are two statements: Statement 1: The number of pairs, from the following, in which both the ions are...

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Which of the following point in Figure 2 most accurately represents the nodal surface as shown in Figure 1

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The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to...

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$$ \mathrm{Ph}-\mathrm{CH}=\mathrm{CH}_2 \xrightarrow[\mathrm{HBr}]{(\mathrm{PhCOO})_2} \text { Product } $$ Consider the above reaction A. The reaction proceeds through a more stable...

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In the given pentapeptide, find out an essential amino acid $(\mathrm{Y})$ and the sequence present in the pentapeptide:

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Consider the following reactions giving major product. Identify the correct reaction.

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Given below are two statements: Statement I: Griss-llosvay test is used for the detection of nitrite ion, which involves the...

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Regarding the hydrides of group 15 elements $\mathrm{EH}_3(\mathrm{E}=\mathrm{N}, \mathrm{P}, \mathrm{As}, \mathrm{Sb})$, select the correct statement from the following: A. The...

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Which one of the following is not a measurable quantity?

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Given below are two statements: Statement I: The number of species among $\mathrm{BF}_4^{-}, \mathrm{SiF}_4, \mathrm{XeF}_4$ and $\mathrm{SF}_4$, that have unequal...

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The speed of a longitudinal wave in a metallic bar is $400 \mathrm{~m} / \mathrm{s}$. If the density and Young's...

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Given below are the four isomeric compounds (P,Q, S)

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A particle starts moving from time $t=0$ and its coordinate is given as $x(t)=4 t^3-3 t$ A. The particle returns...

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Given below are two statements for the following reaction sequence.

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An organic compound undergoes first order decomposition. The time taken for decomposition to $\left(\frac{1}{8}\right)^{\text {th }}$ and $\left(\frac{1}{10}\right)^{\text {th }}$...

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Identify the correct statements : A. Electrostatic field lines form closed loops . B. The electric field lines point radially...

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The time period of a simple harmonic oscillator is $T=2 \pi \sqrt{\frac{k}{m}}$. Measured value of mass $(m)$ of the object...

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Consider a weak base ' B ' of $\mathrm{pK}_{\mathrm{b}}=5.699$ ' $x$ ' mL of 0.02 M HCl and ' y...

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Method used for separation of mixture of products ( B and C ) obtained in the following reaction is

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Consider the following reaction sequence

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At $T(K), 2$ moles of liquid $A$ and 3 moles of liquid $B$ are mixed. The vapour pressure of ideal...

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CORRECT order of stability for the following is $\mathrm{CH}_2=\mathrm{CH}^{-}, \mathrm{CH}_3-\mathrm{CH}_2^{-}, \mathrm{CH} \equiv \mathrm{C}^{-}$

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$20.0 \mathrm{dm}^3$ of an ideal gas ' X ' at 600 K and 0.5 MPa undergoes isothermal reversible expansion until...

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The equivalent resistance between the points $A$ and $B$ in the following circuit is $\frac{x}{5} \Omega$. The value of $x$...

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A convex lens of refractive index 1.5 and focal length $f=18 \mathrm{~cm}$ is immersed in water. The difference in focal...

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A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from...

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The ratio of de Broglie wavelength of a deutron with kinetic energy $E$ to that of an alpha particle with...

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If $\sum_{r=1}^{2 s}\left(\frac{r}{r^4+r^2+1}\right)=\frac{p}{q}$, where $p$ and $q$ are positive integers such that $\operatorname{gcd}(p, q)=1$, then $p+q$ is equal to $\_\_\_\_$。

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The displacement of a particle, executing simple harmonic motion with time period $T$, is expressed as $x(t)=A \sin \omega t$,...

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If the distance of the point $\mathrm{P}(43, \alpha, \beta), \beta

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A particle of mass $m$ falls from rest through a resistive medium having resistive force, $F=-k v$, where $v$ is...

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Let $A=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$ and $B$ be two matrices such that $A^{100}=100 B+I$. Then the sum...

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Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side...

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Let $f$ be a differentiable function satisfying $f(x)=1-2 x+\int_0^x \mathrm{e}^{(x-t)} f(t) \mathrm{dt}, x \in \mathbf{R}$ and let $...

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Grignard reagent $\mathrm{RMgBr}(\mathrm{P})$ reacts with water and forms a gas $(\mathrm{Q})$. One gram of Q occupies $1.4 \mathrm{dm}^3$ at STP....

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The magnetic field at the centre of a current carrying circular loop of radius $R$ is $16 \mu \mathrm{~T}$. The...

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Three persons enter in a lift at the ground floor. The lift will go upto $...

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When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark...

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Molar conductivity of a weak acid HQ of concentration 0.18 M was found to be $1 / 30$ of the...

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Given below are two statements: Statement I : A plane wave after passing through prism remains as plane wave but...

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Given below are two statements : Statement I: $25^{13}+20^{13}+8^{13}+3^{13}$ is divisible by 7 . Statement II: The integral part of...

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A block of mass 5 kg is moving on an inclined plane which makes an angle of $30^{\circ}$ with the...

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Let $Q(a, b, c)$ be the image of the point $P(3,2,1)$ in the line $\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$. Then the distance of $Q$...

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Let $P Q R$ be a triangle such that $\overrightarrow{P Q}=-2 \hat{i}-\hat{j}+2 \hat{k}$ and $...

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Two wires $A$ and $B$ made of different materials of lengths 6.0 cm and 5.4 cm , respectively and area...

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A chromium complex with a formula $\mathrm{CrCl}_3 \cdot 6 \mathrm{H}_2 \mathrm{O}$ has a spin only magnetic moment value of 3.87...

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The value of $\sum_{\mathrm{r}=1}^{20}\left(\left|\sqrt{\pi\left(\int_0^{\mathrm{r}} \mathrm{x}|\sin \pi \mathrm{x}| \mathrm{dx}\right)}\right|\right)$ is $\_\_\_\_$ .

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The half-life of ${ }^{65} \mathrm{Zn}$ is 245 days. After $x$ days, $75 \%$ of original activity remained. The value...

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Let $$ \begin{aligned} & A=\{z \in \mathbb{C}:|z-2| \leqslant 4\} \text { and } \\ & B=\{z \in \mathbb{C}:|z-2|+|z+2|=5\} \end{aligned} $$...

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If $k=\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{2}{3}\right)\right)+\tan \left(\frac{1}{2} \sin ^{-1}\left(\frac{2}{3}\right)\right)$, then the number of solutions of the equation $...

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For the two cells having same EMF $E$ and internal resistance $r$, the current passing through the external resistor $...

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For some $\theta \in\left(0, \frac{\pi}{2}\right)$, let the eccentricity and the length of the latus rectum of the hyperbola $...

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In a G.P., if the product of the first three terms is 27 and the set of all possible values...

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In the following $p-V$ diagram the equation of state along the curved path is given by $(V-2)^2=4 a p$ where...

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0.25 g of an organic compound " A " containing carbon, hydrogen and oxygen was analysed using the combustion method....

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Let $y=y(x)$ be the solution of the differential equation $$ x \frac{d y}{d x}-\sin 2 y=x^3\left(2-x^3\right) \cos ^2 y, x...

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The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index $=1.7$...

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Given below are two statements:

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Assuming in forward bias condition there is a voltage drop of 0.7 V across a silicon diode, the current through...

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For three unit vectors $\vec{a}, \vec{b}, \vec{c}$ satisfying $|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|^2+|\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}}|^2+|\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{a}}|^2=9$ and $|2 \overrightarrow{\mathrm{a}}+\mathrm{k} \overrightarrow{\mathrm{b}}+\mathrm{k} \overrightarrow{\mathrm{c}}|=3$, the positive value of k is...

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$A \longrightarrow B$ (first reaction) $\mathrm{C} \longrightarrow \mathrm{D}$ (second reaction) Consider the above two first-order reactions. The rate constant for...

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If the distances of the point $(1,2, a)$ from the line $\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$ along the lines $\mathrm{L}_1: \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}$ and $\mathrm{L}_2: \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}$...

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For strong electrolyte $\Lambda_m$ increases slowly with dilution and can be represented by the equation $$ \Lambda_{\mathrm{m}}=\Lambda_{\mathrm{m}}^{\cdot}-A c^{1 / 2}...

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"X" is an oxoanion of the lightest element of group 7 (in the periodic table). The metal is in +6...

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Two positively charged particles and have been accelerated across the same potential difference of 200 keV as shown below.

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At 298 K , the mole percentage of $\mathrm{N}_2(\mathrm{~g})$ in air is $80 \%$. Water is in equilibrium with air...

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Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15...

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The common difference of the A.P: $a_1, a_2, \ldots, a_{\mathrm{m}}$ is 13 more than the common difference of the A.P....

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The heat of atomisation of methane and ethane are ' $\mathrm{x}{ }^{\prime} \mathrm{kJmol}^{-1}$ and ' $\mathrm{y}{ }^{\prime} \mathrm{kJmol}^{-1}$ respectively. The...

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Let $\mathrm{A}_2 \mathrm{~B}$ and $C$ be three $2 \times 2$ matrices with real entries such that $B=(I+A)^{-1}$ and $\mathrm{A}+\mathrm{C}=\mathrm{I}$. If...

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Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^{\circ} \mathrm{C}$...

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From the following, how many compounds contain at least one secondary alcohol?

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The electric field of an electromagnetic wave travelling through a medium is given by $...

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The mean and variance of 10 observations are 9 and 34.2 , respectively. If 8 of these observations are 2,3,5,10,11,13,15,21,...

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The value of $...

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The number of isoelectronic species among $\mathrm{Sc}^{3+}, \mathrm{Cr}^{2+}, \mathrm{Mn}^{3+}, \mathrm{Co}^{3+}$ and $\mathrm{Fe}^{3+}$ is ' $n^{\prime}$. If ' $n$ ' moles...

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Given below are two statements:

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The correct order of acidic strength of the major products formed in the given reactions, is : A. $...

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Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop...

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The area of the region $\mathrm{R}=\left\{(x, y): x y \leq 8,1 \leq y \leq x^2, x \geq 0\right\}$ is

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A student performed analysis of aliphatic organic compound ' $X$ ' which on analysis gave $\mathrm{C}=61.01 \%$, $...

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Given below are two statements: Statement I: Cross aldol condensation between two different aldehydes will always produce four different products....

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Let $f$ be a polynomial function such that $f\left(\mathrm{x}^2+1\right)=\mathrm{x}^4+5 \mathrm{x}^2+2$, for all $\mathrm{x} \in \mathbb{R}$. Then $\int_0^3 f(\mathrm{x}) \mathrm{dx}$ is...

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Structures of four disaccharides are given below. Among the given disaccharides, the non-reducing sugar is :

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Given below are two statementsi Statement I: The function $f: \mathbf{R} \rightarrow \mathbf{R}$ defined by $f(x)=\frac{x}{1+|x|}$ is one-one. Statement II:...

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Two circular dises of radius each 10 cm are joined at their centres by a rod of length 30 cm...

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If $\int\left(\frac{1-5 \cos ^2 x}{\sin ^5 x \cos ^2 x}\right) d x=f(x)+\mathrm{C}$, where C is the constant of integration, then...

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The wavelength of spectral line obtained in the spectrum of $\mathrm{Li}^{2+}$ ion, when the transition takes place between two levels...

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Consider the following reactions $$ \begin{aligned} & \mathrm{Na}_2 \mathrm{~B}_4 \mathrm{O}_7 \xrightarrow{\Delta} 2 \mathrm{X}+\mathrm{Y} \\ & \mathrm{CuSO}_4+\mathrm{Y} \xrightarrow{\text { Non-Luminous flame...

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In the potentiometer, when the cell in the secondary circuit is shunted with $4 \Omega$ resistance, the balance is obtained...

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The sum of the coefficients of $x^{499}$ and $x^{500}$ in $(1+x)^{1000}+x(1+x)^{999}+x^2(1+x)^{998}+\ldots+x^{1000}$ is :

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If $\alpha, \beta$, where $\alpha

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Match List - I with List - II according to shape. Choose the correct answer from the options given below...

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The electric current in the circuit is given as $i=i_0(t / T)$. The r.m.s current for the period $t=0$ to...

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In the Group analysis of cations, $\mathrm{Ba}^{2+} \& \mathrm{Ca}^{2+}$ are precipitated respectively as

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A bag contains 10 balls out of which $k$ are red and $(10-k)$ are black, where $...

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Let $f(x)=\int \frac{\mathrm{d} x}{x^{\left(\frac{2}{3}\right)}+2 x^{\left(\frac{1}{2}\right)}}$ be such that $f(0)=-26+24 \log _{\mathrm{e}}(2)$. If $f(1)=\mathrm{a}+\mathrm{b} \log _{\mathrm{e}}(3)$, where $\mathrm{a}, \mathrm{b} \in \mathbf{Z}$,...

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10 kg of ice at $-10^{\circ} \mathrm{C}$ is added to 100 kg of water to lower its temperature from $...

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Let $\mathrm{S}=\left\{x^3+a x^2+b x+c: a, b, c \in \mathrm{~N}\right.$ and $\left.a, b, c \leq 20\right\}$ be a set of polynomials....

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The correct order of $\mathrm{C}, \mathrm{N}, \mathrm{O}$ and F in terms of second ionisation potential is

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Let $y=y(x)$ be the solution of the differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y=x^2 \cot x, x \in(0, \pi)$. If $y\left(\frac{\pi}{2}\right)=\frac{\pi}{2}$,...

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Let . Let be the number of 9 -digit numbers formed using the digits of the set S such that...

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Consider the following aqueous solutions. I. 2.2 g Glucose in 125 mL of solution. II. 1.9 g Calcium chloride in...

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Let $\mathrm{P}_1: y=4 x^2$ and $\mathrm{P}_2: y=x^2+27$ be two parabolas. If the area of the bounded region enclosed between $P_1$...

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Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line $...

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Let $z$ be a complex number such that $|z-6|=5$ and $|z+2-6 i|=5$. Then the value of $z^3+3 z^2-15 z+141$ is...

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$X$ and $Y$ are the number of electrons involved, respectively during the oxidation of $I^{-}$to $I_2$ and $S^{2-}$ to $S$...

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Let $f(x)=\lim _{\boldsymbol{\theta} \rightarrow 0}\left(\frac{\cos \pi x-x^{\left(\frac{2}{\boldsymbol{\theta}}\right)} \sin (x-1)}{1+x^{\left(\frac{2}{\boldsymbol{\theta}}\right)}(x-1)}\right), x \in \mathbf{R}$. Consider the following two statements : (I) $f(x)$...

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The wavelength of photon ' $A$ ' is 400 nm . The frequency of photon ' $B$ ' is $...

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In Dumas method for estimation of nitrogen, 0.50 g of an organic compound gave 70 mL of nitrogen collected at...

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If $\frac{\tan (\mathrm{A}-\mathrm{B})}{\tan \mathrm{A}}+\frac{\sin ^2 \mathrm{C}}{\sin ^2 \mathrm{~A}}=1, \mathrm{~A}, \mathrm{~B}, \mathrm{C} \in\left(0, \frac{\pi}{2}\right)$, then

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Let $P$ be a point in the plane of the vectors $\overrightarrow{A B}=3 \hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{A C}=\hat{i}-\hat{j}+3 \hat{k}$ such that...

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The hydrogen spectrum consists of several spectral lines in Lyman series $\left(\mathrm{L}_1, \mathrm{~L}_2, \mathrm{~L}_3 \ldots ; \mathrm{L}_1\right.$ has lowest energy...

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Consider the following statements about manganate and permanganate ions. Identify the correct statements. A. The geometry of both manganate and...

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The plot of $\log _{10} \mathrm{~K} v s \frac{1}{\mathrm{~T}}$ gives a straight line. The intercept and slope respectively are (where...

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$\frac{6}{3^{26}}+\frac{10 \cdot 1}{3^{25}}+\frac{10 \cdot 2}{3^{24}}+\frac{10 \cdot 2^2}{3^{23}}+\ldots+\frac{10 \cdot 2^{24}}{3}$ is equal to :

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Consider two Group IV metal ions $\mathrm{X}^{2+}$ and $\mathrm{Y}^{2+}$. A solution containing $0.01 \mathrm{MX}^{2+}$ and $0.01 \mathrm{MY}^{2+}$ is saturated with...

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The sum of all the elements in the range of $$ \begin{aligned} & f(x)=\operatorname{Sgn}(\sin x)+\operatorname{Sgn}(\cos x)+\operatorname{Sgn}(\tan x)+\operatorname{Sgn}(\cot x), x \neq...

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The reactions which produce alcohol as the product are: A. $\mathrm{CH}_4+\mathrm{O}_2 \xrightarrow[\Delta]{\mathrm{Mo}_2 \mathrm{O}_3}$ B. $...

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Electricity is passed through an acidic solution of $\mathrm{Cu}^{2+}$ till all the $\mathrm{Cu}^{2+}$ was exhausted, leading to the deposition of...

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Identify the correct statements: The presence of $-\mathrm{NO}_2$ group in benzene ring A. activates the ring towards electrophilic substitutions. B....

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Given below are two statements: Statement I: $\mathrm{K}>\mathrm{Mg}>\mathrm{Al}>\mathrm{B}$ is the correct order in terms of metallic character. Statement II: Atomic...

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The cyclic cations having the same number of hyperconjugation are Choose the correct answer from the options given below :

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Let $y=x$ be the equation of a chord of the circle $\mathrm{C}_1$ (in the closed half-plane $x \geq 0$ )...

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The value of $\sum_{k=1}^{\infty}(-1)^{k+1}\left(\frac{k(k+1)}{k!}\right)$ is

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Consider the elements $\mathrm{N}, \mathrm{P}, \mathrm{O}, \mathrm{S}, \mathrm{Cl}$ and F . The number of valence electrons present in the elements...

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If $g(x)=3 x^2+2 x-3, f(0)=-3$ and $4 g(f(x))=3 x^2-32 x+72$, then $f(g(2))$ is equal to:

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Let the circle $x^2+y^2=4$ intersect $x$-axis at the points $\mathrm{A}(\mathrm{a}, 0), \mathrm{a}>0$ and $\mathrm{B}(\mathrm{b}, 0)$. Let $...

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Find out the statements which are not true. A. Resonating structures with more number of covalent bonds and lesser charge...

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Observe the following equilibrium in a 1 L flask. $$ A(g) \rightleftharpoons B(g) $$ At $\mathrm{T}(\mathrm{K})$, the equilibrium concentrations of...

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Given below are two statements : Statement I : The increasing order of boiling point of hydrogen halides is $\mathrm{HCl}

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Arrange the following carbanions in the decreasing order of stability. Choose the correct answer from the options given below:

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For the given reaction; $$ \mathrm{CaCO}_3+2 \mathrm{HCl} \longrightarrow \mathrm{CaCl}_2+\mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2 $$ If $90 \mathrm{gCaCO}_3$ is added to 300 mL of...

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The probability distribution of a random variable X is given below : If $E(X)=\frac{263}{15}$, then $P(X

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A soap bubble of surface tension $0.04 \mathrm{~N} / \mathrm{m}$ is blown to a diameter of 7 cm . If...

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A student has planned to prepare acetanilide from aniline using acetic anhydride. The student has started from 9.3 g of...

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Which of the following reaction is NOT correctly represented ?

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Let the ellipse $\mathrm{E}: \frac{x^2}{144}+\frac{y^2}{169}=1$ and the hyperbola $\mathrm{H}: \frac{x^2}{16}-\frac{y^2}{\lambda^2}=-1$ have the same foci. If e and L respectively denote...

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An ellipse has its center at $(1,-2)$, one focus at $(3,-2)$ and one vertex at $(5,-2)$. Then the length of...

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One mole of $\mathrm{Cl}_2(\mathrm{~g})$ was passed into 2 L of cold 2 M KOH solution. After the reaction, the concentrations...

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A point charge $q=1 \mu \mathrm{C}$ is located at a distance 2 cm from one end of a thin insulating...

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Total number of alkali insoluble solid sulphonamides obtained by reaction of given amines with Hinsberg's reagent is________. Aniline, N-Methylaniline, Methanamine,...

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If the solution curve $y=f(x)$ of the differential equation $$ \left(x^2-4\right) y^{\prime}-2 x y+2 x\left(4-x^2\right)^2=0, x>2, $$ passes through the...

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Considering the principal values of inverse trigonometric functions, the value of the expression $\tan \left(2 \sin ^{-1}\left(\frac{2}{\sqrt{13}}\right)-2 \cos ^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)$ is...

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The wavelength of light absorbed for the following complexes are in the order

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A student has been given 0.314 g of an organic compound and asked to estimate Sulphur. During the experiment, the...

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The correct increasing order of spin-only magnetic moment values of the complex ions $\left[\mathrm{MnBr}_4\right]^{2-}(\mathrm{A}),\left[\mathrm{Cu}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}(\mathrm{B}),\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}(\mathrm{C})$ and $\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}(\mathrm{D})$ is :

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Pair of species among the following having same bond order as well as paramagnetic character will be-

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Let the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}$ be $\frac{5}{16}, a>2$. If $\alpha$ is such that $a, 4, \alpha, b$...

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Consider the following gaseous equilibrium in a closed container of volume ' $V$ ' at $T(K)$. $$ \mathrm{P}_2(\mathrm{~g})+\mathrm{Q}_2(\mathrm{~g}) \boxtimes \quad...

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Let [.] denote the greatest integer function. Then $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{12(3+[x])}{3+[\sin x]+[\cos x]}\right) \mathrm{d} x$ is equal to :

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Consider the following two reactions A and B. Numerical value of [molar mass of $x+$ molar mass of $y$ ]...

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Two liquids $A$ and $B$ form an ideal solution at temperature $T K$. At $T K$, the vapour pressures of...

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Let S denote the set of 4-digit numbers abcd such that $a>b>c>d$ and P denote the set of 5-digit numbers...

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Given below are two statements: Statement I: ' $\mathrm{C}-\mathrm{Cl}^{\prime}$ bond is stronger in $\mathrm{CH}_2=\mathrm{CH}-\mathrm{Cl}$ than $\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{Cl}$ Statement II: The given...

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Let $A=\left[\begin{array}{ccc}0 & 2 & -3 \\ -2 & 0 & 1 \\ 3 & -1 & 0\end{array}\right]$ and $B$...

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The number of possible tripeptides formed involving alanine (ala), glycine (gly) and valine (val), where no amino acid has been...

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At $27^{\circ} \mathrm{C}$ in presence of a catalyst, activation energy of a reaction is lowered by $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The...

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The unsaturated ether on acidic hydrolysis produces carbonyl compounds as shown below:- $$ \begin{aligned} \mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}- & \mathrm{O}-\mathrm{CH}=\mathrm{CH}_2 \\ & \downarrow...

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A hydroxy compound $(\mathrm{X})$ with molar mass $122 \mathrm{~g} \mathrm{~mol}^{-1}$ is acetylated with acetic anhydride, using a large excess of...

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The number of elements in the set $\mathrm{S}=\left\{x: x \in[0,100]\right.$ and $\left.\int_0^x t^2 \sin (x-t) d t=x^2\right\}$ is $\_\_\_\_$ .

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A student is given one compound among the following compounds that gives positive test with Tollen's reagent. The compound is...

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If the image of the point $\mathrm{P}(a, 2, a)$ in the line $\frac{x}{2}=\frac{y+a}{1}=\frac{z}{1}$ is Q and the image of Q...

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Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used...

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Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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The velocity (v) - Distance (x) graph is shown in figure. Which graph represents acceleration(a) versus distance $(x)$ variation of...

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'W' g of a non-volatile electrolyte solid solute of molar mass ${ }^{\prime} \mathrm{M}^{\prime} \mathrm{gmol}^{-1}$ when dissolved in 100 mL...

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Choose the INCORRECT statement

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In the Young's double slit experiment the intensity produced by each one of the individual slits is $I_{\mathrm{o}}$. The distance...

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Match the List-I with List-II Choose the correct answer from the options given below:

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Let $\sum_{k=1}^n a_k=\alpha n^2+\beta n$. If $a_{10}=59$ and $a_6=7 a_1$, then $\alpha+\beta$ is equal to

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Consider three metal chlorides $\mathrm{x}, \mathrm{y}$ and z , where x is water soluble at room temperature, $y$ is sparingly...

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A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased...

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An equilateral triangle OAB is inscribed in the parabola $y^2=4 x$ with the vertex O at the vertex of the...

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Given below are two statements: Statement I: The number of paramagnetic species among $\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{TiF}_6\right]^{3-}, \mathrm{V}_2 \mathrm{O}_5$ and $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ is 3...

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A flexible chain of mass m hangs between two fixed points at the same level. The inclination of the chain...

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Consider a mixture ' X ' which is made by dissolving 0.4 mol of $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{SO}_4\right] \mathrm{Br}$ and 0.4 mol...

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Identify the correct truth table of the given logic circuit.

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The correct stability order of the following diazonium salts is

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Total number of unpaired electrons present in the central metal atoms/ions of $\left[\mathrm{Ni}(\mathrm{CO})_4\right],\left[\mathrm{NiCl}_4\right]^{2-},\left[\mathrm{PtCl}_2\left(\mathrm{NH}_3\right)_2\right],\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ and $\left[\mathrm{Pt}(\mathrm{CN})_4\right]^{2-}$ is $\_\_\_\_$ .

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If the mean and the variance of the data are $\mu$ and 19 respectively, then the value of $\lambda+\mu$ is

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Among the following, the CORRECT combinations are A. $\mathrm{IF}_3 \rightarrow \mathrm{~T}$-shaped $\left(\mathrm{sp}^3 \mathrm{~d}\right)$ B. $\mathrm{IF}_5 \rightarrow$ Square pyramidal $\left(\mathrm{sp}^3 \mathrm{~d}^2\right)$...

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A moving coil galvanometer of resistance $100 \Omega$ shows a full scale deflection for a current of 1 mA ....

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If $z=\frac{\sqrt{3}}{2}+\frac{i}{2}, i=\sqrt{-1}$, then $\left(z^{201}-i\right)^8$ is equal to

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A cubical block of density $\rho_b=600 \mathrm{~kg} / \mathrm{m}^3$ floats in a liquid of density $\rho_{\mathrm{e}}=900 \mathrm{~kg} / \mathrm{m}^3$. If...

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Let $\mathrm{A}=\{0,1,2, \ldots, 9\}$. Let R be a relation on A defined by $(x, y) \in \mathrm{R}$ if and only...

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Two liquids A and B form an ideal solution. At 320 K, the vapour pressure of the solution, containing 3...

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The number of ways, in which 16 oranges can be distributed to four children such that each child gets at...

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$$ X_2(g)+Y_2(g) \boxtimes \quad 2 Z(g) $$ $\mathrm{X}_2(\mathrm{~g})$ and $\mathrm{Y}_2(\mathrm{~g})$ are added to a 1 L flask and it is...

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Let $\mathrm{I}(x)=\int \frac{3 d x}{(4 x+6)\left(\sqrt{4 x^2+8 x+3}\right)}$ and $\mathrm{I}(0)=\frac{\sqrt{3}}{4}+20$. If $\mathrm{I}\left(\frac{1}{2}\right)=\frac{a \sqrt{2}}{b}+\mathrm{c}$, where $...

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Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectric ( $k_1$ and $\mathrm{k}_2$...

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A student has been given a compound " $x$ " of molecular formula- $\mathrm{C}_6 \mathrm{H}_7 \mathrm{~N} \cdot x$ ' is...

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The least value of $\left(\cos ^2 \theta-6 \sin \theta \cos \theta+3 \sin ^2 \theta+2\right)$ is

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The area of the region enclosed between the circles $x^2+y^2=4$ and $x^2+(y-2)^2=4$ is:

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Given below are two statements:

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The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an...

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Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One...

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A solution is prepared by dissolving 0.3 g of a non-volatile non-electrolyte solute ' A ' of molar mass $...

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When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V...

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Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $\vec{a} \times \vec{b}=2(\vec{a} \times \vec{c})$. If $|\vec{a}|=1,|\vec{b}|=4,|\vec{c}|=2$, and the angle between...

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Given below are statements about some molecules/ions. Identify the CORRECT statements. A. The dipole moment value of $\mathrm{NF}_3$ is higher...

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The work functions of two metals $\left(M_A\right.$ and $\left.M_B\right)$ are in the $1: 2$ ratio. When these metals are exposed...

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Let PQ be a chord of the hyperbola $\frac{x^2}{4}-\frac{y^2}{b^2}=1$, perpendicular to the $x$-axis such that OPQ is an equilateral triangle,...

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Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have...

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Arrange the following alkenes in decreasing order of stability. Choose the correct answer from the options given below:

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If the points of intersection of the ellipses $x^2+2 y^2-6 x-12 y+23=0$ and $4 x^2+2 y^2-20 x-12 y+35=0$ lie on...

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$\mathrm{A} \rightarrow \mathrm{D}$ is an endothermic reaction occurring in three steps (elementary). (i) $\mathrm{A} \rightarrow \mathrm{B} \Delta \mathrm{H}_i=+\mathrm{ve}$ (ii) $...

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A thin uniform rod $(\mathrm{X})$ of mass M and length L is pivoted at a height $\left(\frac{L}{3}\right)$ as shown in...

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The oxidation state of chromium in the final product formed in the reaction between KI and acidified $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$...

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The sum of all the real solutions of the equation $\log _{(x+3)}\left(6 x^2+28 x+30\right)=5-2 \log _{(6 x+10)}\left(x^2+6 x+9\right)$ is equal...

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Given below are two statements: Statement I: Hybridisation, shape and spin only magnetic moment of $\mathrm{K}_3\left[\mathrm{Co}\left(\mathrm{CO}_3\right)_3\right]$ is $\mathrm{sp}^3 \mathrm{~d}^2$, octahedral...

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A mixed ether ${ }^{(P)}$, when heated with excess of hot concentrated hydrogen iodide produces two different alkyl iodides which...

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The system of linear equations $$ \begin{aligned} & x+y+z=6 \\ & 2 x+5 y+a z=36 \\ & x+2 y+3 z=b...

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Consider two sets $\mathrm{A}=\{x \in \mathbb{Z}:(|x-3|-3) \mid \leq 1\}$ and $\mathrm{B}=\left\{x \in \mathbb{R}-\{1,2\}: \frac{(x-2)(x-4)}{x-1} \log _e(|x-2|)=0\right\}$. Then the number of...

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Let $A(1,2)$ and $C(-3,-6)$ be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to...

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In case of vertical circular motion of a particle by a thread of length $r$ if the tension in the...

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Let $\vec{a}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}, \vec{b}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}, \vec{c}=\lambda \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\vec{v}=\vec{a} \times \vec{b}$. If $\vec{v} \cdot \vec{c}=11$ and the length of...

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A regular hexagon is formed by six wires each of resistance $r \Omega$ and the corners are joined to the...

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Let $\frac{\pi}{2}

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Five persons $P_1, P_2, P_3, P_4$ and $P_5$ recorded object distance $(u)$ and image distance $(v)$ using same convex lens...

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If $f(x)=\left\{\begin{array}{cc}\frac{a|x|+x^2-2(\sin |x|)(\cos |x|)}{x} & , x \neq 0 \\ b & , x=0\end{array}\right.$ is continuous at $x=0$, then $a+b$...

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In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division...

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The reading of the ammeter (A) in steady state in the following circuit (assuming negligible internal resistance of the ammeter)...

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Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$...

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In the given figure the blocks $\mathrm{A}, \mathrm{B}$ and $C$ weigh $4 \mathrm{~kg}, 6 \mathrm{~kg}$ and 8 kg respectively. The...

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The number of $3 \times 2$ matrices A , which can be formed using the elements of the set $\{-2,-1,0,1,2\}$...

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Let ( $2 \alpha, \alpha$ ) be the largest interval in which the function $f(t)=\frac{|t+1|}{t^2}, t2$, is $\_\_\_\_$

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A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4...

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A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature $50^{\circ} \mathrm{C}$....

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A short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 Gauss, experiences a torque...

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Three masses and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are...

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The number of numbers greater than 5000 , less than 9000 and divisible by 3, that can be formed using...

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Let a line L passing through the point $\mathrm{P}(1,1,1)$ be perpendicular to the lines $\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-1}{1}$ and $\frac{x-17}{1}=\frac{y-71}{1}=\frac{z}{0}$. Let the line...

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There are three co-centric conducting spherical shells $\mathrm{A}, \mathrm{B}$ and $C$ of radii $\mathrm{a}, \mathrm{b}$ and $c$ respectively $(c>b>a)$ and...

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A boy throws a ball into air at $45^{\circ}$ from the horizontal to land it on a roof of a...

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An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and...

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Let a differentiable function f satisfy the equation $\int_0^{36} f\left(\frac{t x}{36}\right) d t=4 \alpha f(x)$. If $y=f(x)$ is a standard...

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The number of the real solutions of the equation: $x|x+3|+|x-1|-2=0$ is

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Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy...

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Let $\mathrm{A}_1$ be the bounded area enclosed by the curves $y=x^2+2, x+y=8$ and $y$-axis that lies in the first quadrant....

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The mean and variance of a data of 10 observations are 10 and 2 , respectively. If an observations $\alpha$...

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The electrostatic potential in a charged spherical region of radius $r$ varies as $V=a r^3+b$, where $a$ and $b$ are...

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In Carius method 0.2425 g of an organic compound gave 0.5253 g silver chloride. The percentage of chlorine in the...

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From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then...

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A brass wire of length 2 m and radius 1 mm at $27^{\circ} \mathrm{C}$ is held taut between two rigid...

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Let $\alpha, \beta \in \mathbb{R}$ be such that the function $f(x)=\left\{\begin{array}{ll}2 \alpha\left(x^2-2\right)+2 \beta x & , x

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Identify the INCORRECT statements from the following: A. Notation ${ }_{12}^{24} \mathrm{Mg}$ represents 24 protons and 12 neutrons. B. Wavelength...

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Given below are two statements: Statement I: For all elements, greater the mass of the nucleus, greater is the binding...

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Consider an A.P.: $a_1, a_2, \ldots, a_{\mathrm{n}} ; a_1>0$. If $a_2-a_1=\frac{-3}{4}, a_{\mathrm{n}}=\frac{1}{4} a_1$, and $\sum_{\mathrm{i}=1}^{\mathrm{n}} a_{\mathrm{i}}=\frac{525}{2}$, then $\sum_{\mathrm{i}=1}^{17} a_1$ is...

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Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as...

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Two resistors $2 \Omega$ and $3 \Omega$ are connected in the gaps of bridge as shown in figure. The null...

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Which statements are NOT TRUE about $\mathrm{XeO}_2 \mathrm{~F}_2$ ? A. It has a see-saw shape. B. Xe has 5 electron...

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Let $\mathrm{S}=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\ldots$ up to 13 terms. If $13 \mathrm{~S}=\frac{2^k}{n!}, k \in \mathrm{~N}$, then $n+k$ is equal to

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An object is projected with kinetic energy K from a point A at an angle 60° with the horizontal. The...

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Let $A(1,0), B(2,-1)$ and $C\left(\frac{7}{3}, \frac{4}{3}\right)$ be three points. If the equation of the bisector of the angle A B...

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Q JEE MAIN 2026

Which of the following statements are TRUE about Haloform reaction?:

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A spring of force constant $15 \mathrm{~N} / \mathrm{m}$ is cut into two pieces. If the ratio of their length...

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Let $R$ be a relation defined on the set $\{1,2,3,4\} \times\{1,2,3,4\}$ by $\mathrm{R}=\{((a, b),(c, d)): 2 a+3 b=3 c+4 d\}$....

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In hydrogen atom spectrum, (R → Rydberg's constant) A. the maximum wavelength of the radiation of Lyman series is $...

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Q JEE MAIN 2026

Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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Let $f(t)=\int\left(\frac{1-\sin \left(\log _e t\right)}{1-\cos \left(\log _e t\right)}\right) d t, t>1$. If $f\left(e^{\pi / 2}\right)=-e^{\pi / 2}$ and $...

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Observe the following reactions at $\mathrm{T}(\mathrm{K})$. I. A → products. II. $5 \mathrm{Br}^{-}(\mathrm{aq})+\mathrm{BrO}_3^{-}(\mathrm{aq})+6 \mathrm{H}^{+}(\mathrm{aq}) \rightarrow 3 \mathrm{Br}_2(\mathrm{aq})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l})$ Both...

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If $\cot x=\frac{5}{12}$ for some $x \in\left(\pi, \frac{3 \pi}{2}\right)$, then $...

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For the series LCR circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown in the figure, the power...

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Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total...

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In a microscope of tube length 10 cm two convex lenses are arranged with focal length of 2 cm and...

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Let $\mathrm{S}=\left\{z \in \mathbb{C}:\left|\frac{z-6 i}{z-2 i}\right|=1\right.$ and $\left.\left|\frac{z-8+2 i}{z+2 i}\right|=\frac{3}{5}\right\}$. Then $\sum_{z \in \mathrm{~S}}|z|^2$ is equal to

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The number of 4 -letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is ______.

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The value of $\frac{\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ} \cos 40^{\circ} \cos 60^{\circ} \cos 80^{\circ}}$ is equal to

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Two electrons are moving in orbits of two hydrogen like atoms with speeds $3 \times 10^5 \mathrm{~m} / \mathrm{s}$ and...

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From the first 100 natural numbers, two numbers first $a$ and then $b$ are selected randomly without replacement. If the...

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The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest...

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Let $f$ be a twice differentiable non-negative function such that $(f(x))^2=25+\int_0^x\left((f(\mathrm{t}))^2+\left(f^{\prime}(\mathrm{t})\right)^2\right) d t$. Then the mean of $...

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The exit surface of a prism with refractive index $n$ is coated with a material having refractive index $\frac{n}{2}$. When...

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Let the area of the region bounded by the curve $y=\max \{\sin x, \cos x\}$, lines $x=0, x=\frac{3 \pi}{2}$, and...

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Q JEE MAIN 2026

Given below are two statements: Statement I: The second ionisation enthalpy of Na is larger than the corresponding ionisation enthalpy...

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The crystal field splitting energy of $\left[\mathrm{Co}(\text { oxalate })_3\right]^{3-}$ complex is ' $n$ ' times that of the $...

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Two resistors of $100 \Omega$ each are connected in series with a 9 V battery. A voltmeter of $400 \Omega$...

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Let $|\mathrm{A}|=6$, where A is a $3 \times 3$ matrix. If $...

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Let each of the two ellipses $\mathrm{E}_1: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(a>b)$ and $\mathrm{E}_2: \frac{x^2}{\mathrm{~A}^2}+\frac{y^2}{\mathrm{~B}^2}=1,(\mathrm{~A}

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Consider all the structural isomers with molecular formula $\mathrm{C}_5 \mathrm{H}_{11} \mathrm{Br}$ are separately treated with $\mathrm{KOH}(\mathrm{aq})$ to give respective substitution...

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Let the direction cosines of two lines satisfy the equations: $4 l+m-n=0$ and $2 m n+10 n l+3 l m=0$....

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Density of water at $4^{\circ} \mathrm{C}$ and $20^{\circ} \mathrm{C}$ are $1000 \mathrm{~kg} / \mathrm{m}^3$ and $998 \mathrm{~kg} / \mathrm{m}^3$ respectively....

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If the domain of the function $$ f(x)=\log _{\left(10 x^2-17 x+7\right)}\left(18 x^2-11 x+1\right) $$ is $...

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lodoform test can differentiate between A. Methanol and Ethanol B. $\mathrm{CH}_3 \mathrm{COOH}$ and $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{COOH}$ C. Cyclohexene and cyclohexanone...

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x mg of pure HCl was used to make an aqueous solution. 25.0 mL of $0.1 \mathrm{MBa}(\mathrm{OH})_2$ solution is used...

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A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone...

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Let $\vec{a}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}, \vec{b}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and $\vec{c}=\vec{a} \times \vec{b}$. Let $\vec{d}$ be a vector such that $|\vec{d}-\vec{a}|=\sqrt{11},|\vec{c} \times \vec{d}|=3$ and...

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A cylindrical block of mass $M$ and area of cross section $A$ is floating in a liquid of density $\rho$...

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For the following gas phase equilibrium reaction at constant temperature, $$ \mathrm{NH}_3(\mathrm{~g}) \rightleftharpoons 1 / 2 \mathrm{~N}_2(\mathrm{~g})+3 / 2 \mathrm{H}_2(\mathrm{~g})...

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Let $729,81,9,1, \ldots$. be a sequence and $\mathrm{P}_n$ denote the product of the first $n$ terms of this sequence. If...

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Given below are two statements: Statement I: $\left(\mathrm{CH}_3\right)_3 \stackrel{\oplus}{\mathrm{C}}$ is more stable than $\stackrel{\oplus}{\mathrm{C}} \mathrm{H}_3$ as nine hyperconjugation interactions are...

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Let $\alpha$ and $\beta$ respectively be the maximum and the minimum values of the function $$ f(\theta)=4\left(\sin ^4\left(\frac{7 \pi}{2}-\theta\right)+\sin ^4(11...

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Three charges $+2 q,+3 q$ and $-4 q$ are situated at $(0,-3 a),(2 a, 0)$ and $(-2 a, 0)$ respectively...

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For the thermal decomposition of reaction AB(g), the following is constructed. The half life of the reaction is ' $x$...

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Let the lines $\mathrm{L}_1: \vec{r}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}+\lambda(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}), \lambda \in \mathbb{R} \quad$ and $...

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Let $\mathrm{S}=\{z: 3 \leq 2 z-3(1+\mathrm{i}) \mid \leq 7\}$ be a set of complex numbers. Then $...

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Match the LIST-I with LIST-II Choose the correct answer from

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A wire of uniform resistance $\lambda \Omega / \mathrm{m}$ is bent into a circle of radius $r$ and another piece...

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Let a circle of radius 4 pass through the origin O , the points $\mathrm{A}(-\sqrt{3} a, 0)$ and $\mathrm{B}(0,-\sqrt{2} b)$,...

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Consider the general reaction given below at 400 K $$ x \mathrm{~A}(\mathrm{~g}) \rightleftharpoons y \mathrm{~B}(\mathrm{~g}) . $$ The values of...

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The velocity of sound in air is doubled when the temperature is raised from $0^{\circ} \mathrm{C}$ to $\alpha^{\circ} \mathrm{C}$. The...

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Number of solutions of $\sqrt{3} \cos 2 \theta+8 \cos \theta+3 \sqrt{3}=0, \theta \in[-3 \pi, 2 \pi]$ is :

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Suppose there is a uniform circular disc of mass Mkg and radius rm shown in figure. The shaded regions are...

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Elements X and Y belong to Group 15. The difference between the electronegativity values of ' X ' and phosphorus...

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The vertices $B$ and $C$ of a triangle $A B C$ lie on the line $\frac{x}{1}=\frac{1-y}{-2}=\frac{z-2}{3}$. The coordinates of $A$...

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The correct statements from the following are : A. Ionic radii of trivalent cations of group 13 elements decreases down...

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A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains...

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The moment of inertia of a square loop made of four uniform solid cylinders, each having radius $R$ and length...

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The size of the images of an object, formed by a thin lens are equal when the object is placed...

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Identify the CORRECT set of details from the following : A. $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ : Inner orbital complex ; d $...

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Compound ‘P’ undergoes the following sequence of reactions : ‘P’ is :

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The average energy released per fission for the nucleus of ${ }_{92}^{235} \mathrm{U}$ is 190 MeV . When all the...

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Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as...

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Given below are two statements : Statement I: Sublimation is used for the separation and purification of compounds with low...

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A small metallic sphere of diameter 2 mm and density $10.5 \mathrm{~g} / \mathrm{cm}^3$ is dropped in glycerine having viscosity...

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Both human DNA and RNA are chiral molecules. The chirality in DNA and RNA arises due to the presence of

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When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that...

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A simple pendulum of string length 30 cm performs 20 oscillations in 10 s . The length of the string...

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Match List - I with List - II. Choose the correct answer from the options given below :

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The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k=3$ and permeability of $...

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Consider the above electrochemical cell where a metal electrode ( $M$ ) is undergoing redox reaction by forming $...

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The sum of all possible values of $\mathrm{n} \in \mathbf{N}$, so that the coefficients of $x_2 x^2$ and $x^3$ in...

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Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current...

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Identify the molecule $(\mathrm{X})$ with maximum number of lone pairs of electrons (obtained using Lewis dot structure) among $...

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If the function $f(x)=\frac{e^x\left(e^{\tan x-x}-1\right)+\log _e(\sec x+\tan x)-x}{\tan x-x}$ is continuous at $x=0$, then the value of $f(0)$ is equal...

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Let the mean and variance of 8 numbers $-10,-7,-1, x, y, 9,2,16$ be $\frac{7}{2}$ and $\frac{293}{4}$, respectively. Then the mean...

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A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane...

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From the given following (A to D) cyclic structures, those which will not react with Tollen's reagent are :

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A prism of angle $75^{\circ}$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index 1.5 only at...

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The value of $\frac{{ }^{100} C_{50}}{51}+\frac{{ }^{100} C_{51}}{52}+\ldots .+\frac{{ }^{100} C_{100}}{101}$ is:

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It is noticed that $\mathrm{Pb}^{2+}$ is more stable than $\mathrm{Pb}^{4+}$ but $\mathrm{Sn}^{2+}$ is less stable than $\mathrm{Sn}^{4+}$. Observe the following...

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One mole of an ideal diatomic gas expands from volume V to 2 V isothermally at a temperature $27^{\circ} \mathrm{C}$...

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The statements that are incorrect about the nickel(II) complex of dimethylglyoxime are : A. It is red in colour. B....

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Among the statements :

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The de Broglie wavelength of an oxygen molecule at $27^{\circ} \mathrm{C}$ is $x \times 10^{-12} \mathrm{~m}$. The value of $x$...

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For the given logic gate circuit, which of the following is the correct truth table?

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Four persons measure the length of a rod as $20.00 \mathrm{~cm}, 19.75 \mathrm{~cm}, 17.01 \mathrm{~cm}$ and 18.25 cm . The...

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Which of the following pair of nuclei are isobars of the element?

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Given above is the concentration vs time plot for a dissociation reaction : $\mathrm{A} \rightarrow \mathrm{nB}$ Based on the data...

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Consider the following compounds Arrange these compounds in the increasing order of reactivity with nitrating mixture.

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Match List - I with List - II. Choose the correct answer from the options given below :

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An air bubble of volume $2.9 \mathrm{~cm}^3$ rises from the bottom of a swimming pool of 5 m deep. At...

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Given, (A) $\mathrm{n}=5, \mathrm{~m}_{\ell}=-1$ (B) $\mathrm{n}=3,1=2, \mathrm{~m}_{\ell}=-1, \mathrm{~m}_{\mathrm{s}}=+\frac{1}{2}$ The maximum number of electron(s) in an atom that can have the...

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Let $\cos (\alpha+\beta)=-\frac{1}{10}$ and $\sin (\alpha-\beta)=\frac{3}{8}$, where $0

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But-2-yne and hydrogen (one mole each) are separately treated with (i) $\mathrm{Pd} / \mathrm{C}$ and (ii) $\mathrm{Na} /$ liq. $\mathrm{NH}_3$...

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MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K . $...

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Identify the metal ions among $\mathrm{Co}^{2+}, \mathrm{Ni}^{2+}, \mathrm{Fe}^{2+}, \mathrm{V}^{3+}$ and $\mathrm{Ti}^{2+}$ having a spin-only magnetic moment value more than 3.0...

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Let $S$ be the set of the first 11 natural numbers. Then the number of elements in $...

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Given below are two statements : Statement I: $\left[\mathrm{CoBr}_4\right]^{2-}$ ion will absorb light of lower energy than $\left[\mathrm{CoCl}_4\right]^{2-}$ ion. Statement...

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Let $[\cdot]$ be the greatest integer function. If $\alpha=\int_0^{64}\left(x^{1 / 3}-\left[x^{1 / 3}\right]\right) \mathrm{d} x$, then $...

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Let a vector $\overrightarrow{\mathrm{a}}=\sqrt{2} \hat{i}-\hat{j}+\lambda \hat{k}, \lambda>0$, make an obtuse angle with the vector $\overrightarrow{\mathrm{b}}=-\lambda^2 \hat{i}+4 \sqrt{2} \hat{j}+4 \sqrt{2} \hat{k}$...

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Suppose $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. and $a^2, 2 b^2, c^2$ are in G.P. If $a

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A cup of water at $5^{\circ} \mathrm{C}$ (system) is placed in a microwave oven and the oven is turned on...

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A substance ${ }^{\prime} \mathrm{X}$ ' ( 1.5 g ) dissolved in 150 g of a solvent ${ }^{\prime} \mathrm{Y}$...

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A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are...

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Let $n$ be the number obtained on rolling a fair die. If the probability that the system $$ \begin{aligned} &...

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The osmotic pressure of a living cell is 12 atm at 300 K . The strength of sodium chloride solution...

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Consider the following sequence of reactions. Assuming that the reaction proceeds to completion, then 137 mg of 4 -nitrotoluene will...

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Let $[\bullet]$ denote the greatest integer function, and let $f(x)=\min \left\{\sqrt{2} x, x^2\right\}$. Let $\mathrm{S}=\left\{x \in(-2,2)\right.$ : the function $\mathrm{g}(x)=|x|\left[x^2\right]$...

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A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of...

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Let L be the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z+3}{6}$ and let S be the set of all points $(\mathrm{a}, \mathrm{b}, \mathrm{c})$ on L...

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Inductance of a coil with $10^4$ turns is 10 mH and it is connected to a dc source of 10...

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' $x$ ' is the product which is obtained from propanenitrile and stannous chloride in the presence of hydrochloric acid...

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The first and second ionization constants of $\mathrm{H}_2 \mathrm{X}$ are $2.5 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively. The concentration...

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The value of the integral $\int_{\frac{\pi}{24}}^{\frac{5 \pi}{24}} \frac{\mathrm{~d} x}{1+\sqrt[3]{\tan 2 x}}$ is :

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In the given electrochemical cell, $\mathrm{Ag}(\mathrm{s})|\mathrm{AgCl}(\mathrm{s})| \mathrm{FeCl}_2(\mathrm{aq}), \mathrm{FeCl}_3(\mathrm{aq}) \mid \mathrm{Pt}(\mathrm{s})$ at 298 K , the cell potential $\left(\mathrm{E}_{\text {cell }}\right)$...

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A circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$...

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Let $f(x)=\left\{\begin{array}{ll}\frac{\mathrm{a} x^2+2 \mathrm{ax}+3}{4 x^2+4 x-3} & , x \neq-\frac{3}{2}, \frac{1}{2} \\ \mathrm{~b} & , x=-\frac{3}{2}, \frac{1}{2}\end{array}\right.$ be continuous at...

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A small bob $A$ of mass $m$ is attached to a massless rigid rod of length 1 m pivoted at...

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The correct sequence of reagents for the above conversion of X to Y is :

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A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to...

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On heating a mixture of common salt and $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ in equal amount along with concentrated $\mathrm{H}_2 \mathrm{SO}_4$ in...

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The correct trend in the first ionization enthalpies of the elements in the $3^{\text {rd }}$ period of periodic table...

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If $\alpha$ and $\beta(\alpha

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Two charges $7 \mu \mathrm{C}$ and $-2 \mu \mathrm{C}$ are placed at $(-9,0,0) \mathrm{cm}$ and $(9,0,0) \mathrm{cm}$ respectively in an...

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Given below are two statements: Statement I: The correct order in terms of bond dissociation enthalpy is $\mathrm{Cl}_2>\mathrm{Br}_2>\mathrm{F}_2>\mathrm{I}_2$. Statement II:...

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Which one of the following graphs accurately represents the plot of partial pressure of $\mathrm{CS}_2$ vs its mole fraction in...

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Let $y=y(x)$ be the solution of the differential equation $x^4 \mathrm{~d} y+\left(4 x^3 y+2 \sin x\right) \mathrm{d} x=0$, $x>0, y\left(\frac{\pi}{2}\right)=0$....

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Two shorts dipoles ( $\mathrm{A}, \mathrm{B}$ ), A having charges $\pm 2 \mu \mathrm{C}$ and length 1 cm and B...

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Let $\mathrm{A}=\{-2,-1,0,1,2,3,4\}$. Let R be a relation on A defined by $x \mathrm{Ry}$ if and only if $...

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A paratrooper jumps from an aeroplane and opens a parachute after $2 s$ of free fall and starts deaccelerating with...

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Let the line $y-x=1$ intersect the ellipse $\frac{x^2}{2}+\frac{y^2}{1}=1$ at the points A and B . Then the angle made by...

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Which of the following statements regarding the energy of the stationary state is true in the following one - electron...

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The current passing through a conducting loop in the form of equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$ is 2...

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parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius...

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A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t=0$ this block is...

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For a closed circuit Daniell cell, which of the following plots is the accurate one at a given temperature?

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Let the domain of the function $f(x)=\log _3 \log _5\left(7-\log _2\left(x^2-10 x+85\right)\right)+\sin ^{-1}\left(\left|\frac{3 x-7}{17-x}\right|\right)$ be ( $\alpha, \beta$ ]. Then...

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The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by, $$ E_y=20 \sin...

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Let $\vec{a}=2 \hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\lambda \hat{j}+2 \hat{k}, \lambda \in Z$ be two vectors. Let $\vec{c}=\vec{a} \times \vec{b}$ and $\vec{d}$ be...

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Given below are some of the statements about Mn and $\mathrm{Mn}_2 \mathrm{O}_7$. Identify the correct statements. A. Mn forms the...

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A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio...

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Let $f(x)=[x]^2-[x+3]-3, x \in \mathbf{R}$, where $[\cdot]$ is the greatest integer function. Then Options

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Two loudspeakers ( $L_1$ and $L_2$ ) are placed with a separation of 10 m , as shown in figure....

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A rectangle is formed by the lines $x=0, y=0, x=3$ and $y=4$. Let the line L be perpendicular to $...

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Given below are four compounds: (a) n-propyl choride (b) iso-propyl chloride (c) sec-butyl chloride (d) neo-pentyl chloride Percentage of carbon...

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The internal energy of a monoatomic gas is 3 nRT . One mole of helium is kept in a cylinder...

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Let the locus of the mid-point of the chord through the origin O of the parabola $y^2=4 x$ be the...

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Three identical coils $C_1, C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly...

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The mass of benzanilide obtained from the benzoylation reaction of 5.8 g of aniline, if yield of product is $...

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If the enthalpy of sublimation of Li is $155 \mathrm{~kJ} \mathrm{~mol}^{-1}$, enthalpy of dissociation of $\mathrm{F}_2$ is $150 \mathrm{~kJ} \mathrm{~mol}^{-1}$,...

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Among the statements (S1) : If $\mathrm{A}(5,-1)$ and $\mathrm{B}(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then...

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The correct increasing order of $\mathrm{C}-\mathrm{H}(\mathrm{A}), \mathrm{C}-\mathrm{O}(\mathrm{B}), \mathrm{C}=\mathrm{O}(\mathrm{C})$ and $C \equiv N(D)$ bonds in terms of covalent bond length is:

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Among the following oxides of 3 d elements, the number of mixed oxides are $\_\_\_\_$ $...

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The area of the region $\mathrm{A}=\left\{(x, y): 4 x^2+y^2 \leq 8\right.$ and $\left.y^2 \leq 4 x\right\}$ is:

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Let $\overrightarrow{\mathrm{a}}=-\hat{i}+\hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=\hat{i}-\hat{j}-3 \hat{k}, \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{d}}=\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}}$. Then $(\vec{a}-\vec{b}) \cdot \vec{d}$ is equal to:

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Given below are two statements: Statement I: Crystal Field Stabilization Energy $(\mathrm{CFSE})$ of $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ is greater than that of...

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Consider $A \xrightarrow{k_1} B$ and $C \xrightarrow{k_2} D$ are two reactions. If the rate constant $\left(k_1\right)$ of the $...

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If $\lim _{x \rightarrow 0} \frac{\mathrm{e}^{(\mathrm{a}-1) x}+2 \cos \mathrm{~b} x+(\mathrm{c}-2) \mathrm{e}^{-x}}{x \cos x-\log _{\mathrm{e}}(1+x)}=2$, then $\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2$ is equal to:

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Match the LIST-I with LIST-II

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An insulated cylinder of volume $60 \mathrm{~cm}^3$ is filled with a gas at $27^{\circ} \mathrm{C}$ and 2 atmospheric pressure, Then...

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Consider the following electrochemical cellin $$ \mathrm{Pt}\left|\mathrm{O}_2(\mathrm{~g})(\mathrm{lbar})\right| \mathrm{HCl}(\mathrm{aq}) \| \mathrm{M}^{2+}(\mathrm{aq}, 1.0 \mathrm{M}) \mid \mathrm{M}(\mathrm{~s}) $$ The pH above which, oxygen...

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If the mean deviation about the median of the numbers $\mathrm{k}, 2 \mathrm{k}, 3 \mathrm{k}, \ldots \ldots, 1000 \mathrm{k}$ is...

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Let $f(x)=\int \frac{\left(2-x^2\right) \cdot \mathrm{e}^x}{(\sqrt{1+x})(1-x)^{3 / 2}} \mathrm{~d} x$. If $f(0)=0$, then $f\left(\frac{1}{2}\right)$ is equal to :

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A conducting circular loop is rotated about its diameter at a constant angular speed of 100rad / s in a...

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The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is :$...

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Let $S$ and $S^{\prime}$ be the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ and $P(\alpha, \beta)$ be a point on the ellipse...

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The energy of first (lowest) Balmer line of H atom is $x \mathrm{~J}$. The energy (in J ) of second...

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A simple pendulum has a bob with mass $m$ and charge q . The pendulum string has negligible mass. When...

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Let the domain of the function $f(x)=\log _3 \log _5 \log _7\left(9 x-x^2-13\right)$ be the interval $(\mathrm{m}, \mathrm{n})$. Let the...

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A cylindrical conductor of length 2 m and area of cross-section $0.2 \mathrm{~mm}^2$ carries an electric current of 1.6 A...

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Let $f$ and $g$ be functions satisfying $f(x+y)=f(x) f(y), f(1)=7$ and $g(x+y)=g(x y), g(1)=1$, for all $x, y \in \mathbf{N}$....

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The correct statements are: A. Activation energy for enzyme catalysed hydrolysis of sucrose is lower than that of acid catalysed...

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If $X=\left[\begin{array}{c}x \\ y \\ z\end{array}\right]$ is a solution of the system of equations $A X=B$, where $...

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Electric field in a region is given by $\vec{E}=A x \hat{i}+B y \hat{j}$, where $A=10 \mathrm{~V} / \mathrm{m}^2$ and $...

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Two masses $m$ and 2 m are connected by a light string going over a pulley (disc) of mass 30...

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If $y=y(x)$ satisfies the differential equation $16(\sqrt{x+9 \sqrt{x}})(4+\sqrt{9+\sqrt{x}}) \cos y \mathrm{~d} y=(1+2 \sin y) \mathrm{d} x, x>0$ and $y(256)=\frac{\pi}{2}, y(49)=\alpha$,...

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Given below are two statements: Statement I: The correct order in terms of atomic/ionic radii is $\mathrm{Al}>\mathrm{Mg}>\mathrm{Mg}^{2+}>\mathrm{Al}^{3+}$. Statement II: The...

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Consider the following reaction : The product Y formed is :

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Dissociation of a gas $\mathrm{A}_2$ takes place according to the following chemical reaction. At equilibrium, the total pressure is 1...

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The volume of an ideal gas increases 8 times and temperature becomes $(1 / 4)^{\text {th }}$ of initial temperature...

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A capacitor $P$ with capacitance $10 \times 10^{-6} \mathrm{~F}$ is fully charged with a potential difference of 6.0 V and...

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The correct order of reactivity of the following benzyl halides towards reaction with KCN is :

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Sodium fusion extract of an organic compound $(\mathrm{Y})$ with $\mathrm{CHCl}_3$ and chlorine water gives violet color to the $\mathrm{CHCl}_3$ layer....

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An electric power line having total resistance of $2 \Omega$, delivers 1 kW of power at 250 ym the percentage...

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Consider an equilateral prism (refractive index $\sqrt{2}$ ). A ray of light is incident on its one surface at a...

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Decomposition of A is a first order reaction at $\mathrm{T}(\mathrm{K})$ and is given by $\mathrm{A}(\mathrm{g}) \longrightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$. In a closed...

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Which of the following are true for a single slit diffraction ? A. Width of central maxima increases with increase...

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The temperature at which the rate constants of the given below two gaseous reactions become equal is _____K. (Nearest integer)...

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Let ABC be a triangle. Consider four points $\mathrm{p}_1, \mathrm{p}_2, \mathrm{p}_3, \mathrm{p}_4$ on the side AB , five points $...

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$$ \mathrm{A}+2 \mathrm{~B} \longrightarrow \mathrm{AB}_2 $$ 36.0 g of 'A' (Molar mass: $60 \mathrm{~g} \mathrm{~mol}^{-1}$ ) and 56.0 g of...

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If $\frac{\cos ^2 48^{\circ}-\sin ^2 12^{\circ}}{\sin ^2 24^{\circ}-\sin ^2 6^{\circ}}=\frac{\alpha+\beta \sqrt{5}}{2}$, where $\alpha, \beta \in \mathbb{N}$, then $\alpha+\beta$ is equal...

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Consider the following electrochemical cell at 298 K $\mathrm{Pt}\left|\mathrm{HSnO}_2^{-}(\mathrm{aq})\right| \mathrm{Sn}(\mathrm{OH})_6{ }^{2-}(\mathrm{aq})\left|\mathrm{OH}^{-}(\mathrm{aq})\right| \mathrm{Bi}_2 \mathrm{O}_3(\mathrm{~s}) \mid \mathrm{Bi}(\mathrm{s})$. If the reaction quotient at...

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If $\int(\sin x)^{\frac{-11}{2}}(\cos x)^{\frac{-5}{2}} d x=-\frac{p_1}{q_1}(\cot x)^{\frac{9}{2}}-\frac{p_2}{q_2}(\cot x)^{\frac{5}{2}}-\frac{p_3}{q_3}(\cot x)^{\frac{1}{2}}+\frac{p_4}{q_4}(\cot x)^{\frac{-3}{2}}+\mathrm{C}$, where $p_i$ and $q_i$ are positive integers with $\operatorname{gcd}\left(p_i, q_i\right)=1$...

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Match List-I with List-II. Choose the correct answer from the options given below:

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The IUPAC name of the following compound is :

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The correct truth table for the given input data of the following logic gate is : Inputs

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Let $A$ be a $3 \times 3$ matrix such that $A+A^T=O$. If $...

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The cycloalkene ( $X$ ) on bromination consumes one mole of bromine per mole of ( $X$ ) and gives...

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When 1 g of compound $(\mathrm{X})$ is subjected to Kjeldahl's method for estimation of nitrogen, $...

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Let $\alpha=\frac{-1+i \sqrt{3}}{2}$ and $\beta=\frac{-1-i \sqrt{3}}{2}, i=\sqrt{-1}$. If$(7-7 \alpha+9 \beta)^{20}+(9+7 \alpha-7 \beta)^{20}+(-7+9 \alpha+7 \beta)^{20}+(14+7 \alpha+7 \beta)^{20}=m^{10}$

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Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end...

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Given below are two statements: Statement I: The Henry's law constant $\mathrm{K}_{\mathrm{H}}$ is constant with respect to variations in solution's...

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Identify the correct statements : A. Hydrated salts can be used as primary standard. B. Primary standard should not undergo...

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Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio...

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As compared with chlorocyclohexane, which of the following statements correctly apply to chlorobenzene? A. The magnitude of negative charge is...

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If the sum of the first four terms of an A.P. is 6 and the sum of its first six...

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Among $\mathrm{H}_2 \mathrm{~S}, \mathrm{H}_2 \mathrm{O}, \mathrm{NF}_3, \mathrm{NH}_3$ and $\mathrm{CHCl}_3$, identify the molecule $(\mathrm{X})$ with lowest dipole moment value. The number...

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Given below are two statements : Statement I : For a mechanical system of many particles total kinetic energy is...

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Let the solution curve of the differential equation $x d y-y d x=\sqrt{x^2+y^2} d x, x>0, y(1)=0$, be $y=y(x)$. Then...

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Two p -block elements X and Y form fluorides of the type $\mathrm{EF}_3$. The fluoride compound $\mathrm{XF}_3$ is a Lewis...

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Which of the following mixture gives a buffer solution with $\mathrm{pH}=9.25$ ? Given: $\mathrm{pK}_{\mathrm{b}}\left(\mathrm{NH}_4 \mathrm{OH}\right)=4.75$

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In parallax method for the determination of focal length of a concave mirror, the object should always be placed :

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The number of solutions of $\tan ^{-1} 4 x+\tan ^{-1} 6 x=\frac{\pi}{6}$, where $-\frac{1}{2 \sqrt{6}}

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A cylindrical tube $A B$ of length $l$, closed at both ends contains an ideal gas of 1 mol having...

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The correct order of the rate of reaction of the following reactants with nucleophile by $\mathrm{S}_{\mathrm{N}} 1$ mechanism is :...

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' A ' is a neutral organic compound $\left(\mathrm{M} . \mathrm{F}: \mathrm{C}_8 \mathrm{H}_9 \mathrm{ON}\right)$. On treatment with aqueous $...

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Correct statements regarding Arrhenius equation among the following are. A. Factor $e^{-E a / R T}$ corresponds to fraction of...

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A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses...

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If the chord joining the points $\mathrm{P}_1\left(x_1, y_1\right)$ and $\mathrm{P}_2\left(x_2, y_2\right)$ on the parabola $y^2=12 x$ subtends a right angle...

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Given below are two statements: Statement I: Sucrose is dextrorotatory. However, sucrose upon hydrolysis gives a solution having mixture of...

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The minimum frequency of photon required to break a particle of mass 15.348 amu into $4 \alpha$ particles is $\_\_\_\_$...

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Given below are two statements : Statement I: Elements ' $X$ ' and ' $Y$ ' are the most and...

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In an open organ pipe $v_3$ and $v_6$ are $3^{\text {rd }}$ and $6^{\text {th }}$ harmonic frequencies, respectively. If...

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The coefficient of $x^{48}$ in $(1+x)+2(1+x)^2+3(1+x)^3+\ldots+100(1+x)^{100}$ is equal to

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Given below are two statements: Statement I: The halogen that makes longest bond with hydrogen in HX, has the smallest...

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$\left[\mathrm{Ni}\left(\mathrm{PPh}_3\right)_2 \mathrm{Cl}_2\right]$ is a paramagnetic complex. Identify the INCORRECT statements about this complex. A. The complex exhibits geometrical isomerism. B....

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Given below are two statements : Statement I: A satellite is moving around earth in the orbit very close to...

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Match the LIST-I with LIST-II Choose the correct answer from the options given below:

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The value of $\int_{\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1}{[x]+4}\right) d x$, where $[\cdot]$ denotes the greatest integer function, is

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Net gravitational force at the center of a square is found to be $F_1$ when four particles having mass M...

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$\mathrm{A} \rightarrow$ product (First order reaction). Three sets of experiment were performed for a reaction under similar experimental conditions: Run...

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The compound $\mathrm{A}, \mathrm{C}_8 \mathrm{H}_8 \mathrm{O}_2$ reacts with acetophenone to form a single product via cross-Aldol condensation. The compound A...

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If $\epsilon, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $...

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If the domain of the function $f(x)=\sin ^{-1}\left(\frac{5-x}{3+2 x}\right)+\frac{1}{\log _{\varepsilon}(10-x)}$ is $(-\infty, \alpha] \cup[\beta, \gamma)-\{\delta\}$, then $6(\alpha+\beta+\gamma+\delta)$ is equal to

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Given below are two statements: Statement I: Benzene is nitrated to give nitrobenzene, which on further treatment with $...

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At $\mathrm{T}(\mathrm{K}), 100 \mathrm{~g}$ of $98 \% \mathrm{H}_2 \mathrm{SO}_4(\mathrm{w} / \mathrm{w})$ aqueous solution is mixed with 100 g of $...

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If $\mathrm{A}=\left[\begin{array}{ll}2 & 3 \\ 3 & 5\end{array}\right]$, then the determinant of the matrix $\left(\mathrm{A}^{2025}-3 \mathrm{~A}^{2024}+\mathrm{A}^{2023}\right)$ is

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Consider the following reduction processes : $$ \begin{aligned} & \mathrm{Al}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(\mathrm{~s}), \mathrm{E}^0=-1.66 \mathrm{~V} \\ & \mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+},...

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Let the set of all values of $r$, for which the circles $(x+1)^2+(y+4)^2=r^2$ and $x^2+y^2-4 x-2 y-4=0$ intersect at two...

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Given below are two statements : Statement I: An object moves from position $r_1$ to position $r_2$ under a conservative...

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Given below are two statements Statement I: $\mathrm{C}\mathrm{Po}>\mathrm{O}$ is the correct order in terms of the magnitude of electron gain...

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Choose the correct answer from the options given below:

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The dibromo compound $[P]$ (molecular formula: $\mathrm{C}_9 \mathrm{H}_{10} \mathrm{Br}_2$ ) when heated with excess sodamide followed by treatment with dilute...

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The correct order of reactivity of $\mathrm{CH}_3 \mathrm{Br}$ in methanol with the following nucleophiles is $\mathrm{F}^{-}, \mathrm{I}^{-}, \mathrm{C}_2 \mathrm{H}_5 \mathrm{O}^{-}$and...

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If the image of the point $\mathrm{P}(1,2, a)$ in the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{7-\mathrm{z}}{2}$ is $\mathrm{Q}(5, b, \mathrm{c})$, then $a^2+b^2+c^2$ is equal...

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If the line $\alpha x+2 y=1$, where $\alpha \in \mathbb{R}$, does not meet the hyperbola $x^2-9 y^2=9$, then a possible...

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Using a simple pendulum experiment $g$ is determined by measuring its time period $T$. Which of the following plots represent...

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The number of elements in the relation $\mathrm{R}=\left\{(x, y): 4 x^2+y^2

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Let $f:[1, \infty) \rightarrow \mathbb{R}$ be a differentiable function. If $6 \int_1^x f(t) d t=3 x f(x)+x^3-4$ for all $...

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Consider the following data: $\Delta_f \mathrm{H}^{!} \quad($ Methane, g$)=-\mathrm{XkJ} \mathrm{mol}^{-1}$ Enthalpy of sublimation of graphite $=\mathrm{Y} \mathrm{kJ} \mathrm{mol}^{-1}$ Dissociation enthalpy...

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Let $\mathrm{P}(10,2 \sqrt{15})$ be a point on the hyperbola $\frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{~b}^2}=1$, whose foci are S and $\mathrm{S}^{\prime}$. If the length of...

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The number of distinct real solutions of the equation $x|x+4|+3|x+2|+10=0$ is

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Figure shows the circuit that contains three resistances ( $9 \Omega$ each) and two inductors ( 4 mH each). The...

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Let $\mathrm{C}_{\mathrm{r}}$ denote the coefficient of $x^{\mathrm{r}}$ in the binomial expansion of $...

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By usual analysis, 1.00 g of compound $(\mathrm{X})$ gave 1.79 g of magnesium pyrophosphate. The percentage of phosphorus in compound...

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Let $\mathrm{S}=\left\{z \in \mathbb{C}: 4 z^2+\bar{z}=0\right\}$. Then $\sum_{z \in \mathrm{~S}}|z|^2$ is equal to:

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The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series...

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Aqueous HCl reacts with $\mathrm{MnO}_2(\mathrm{~s})$ to form $\mathrm{MnCl}_2(\mathrm{aq}), \mathrm{Cl}_2(\mathrm{~g})$ and $\mathrm{H}_2 \mathrm{O}(l)$. What is the weight (in g ) of...

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If a random variable X has the probability distribution then $\mathrm{P}(3

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Five positive charges each having charge $q$ are placed at the vertices of a pentagon as shown in the figure....

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Let $\alpha, \beta$ be the roots of the quadratic equation $12 x^2-20 x+3 \lambda=0, \lambda \in Z$. If $...

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Let $\mathrm{P}(\alpha, \beta, \gamma)$ be the point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4 \sqrt{14}$ from the point $(1,-1,0)$...

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Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures, pressures and number densities are same. The...

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Let $f(x)=x^{2025}-x^{2000}, x \in[0,1]$ and the minimum value of the function $f(x)$ in the interval $[0,1]$ be $(80)^{80}(n)^{-81}$. Then $n$...

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Consider the above sequence of reactions. The number of bromine atom(s) in the final product (P) will be:

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Match List - I with List - II.Choose the correct answer from the options given below:

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A first row transition metal ( $M$ ) does not liberate $H_2$ gas from dilute HCl .1 mol of aqueous...

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Match List - I with List - II. Choose the correct answer from the options given below :

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Find the correct combination of and D inputs which can cause the LED to glow.

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Consider a solution of $\mathrm{CO}_2(\mathrm{~g})$ dissolved in water in a closed container. Which one of the following plots correctly represents...

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Let the line $x=-1$ divide the area of the region $\left\{(x, y): 1+x^2 \leq y \leq 3-x\right\}$ in the ratio...

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consider the following spectral lines for atomic hydrogen : A. First line of Paschen series B. Second line of Balmer...

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When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height...

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Two distinct numbers $a$ and $b$ are selected at random from $1,2,3, \ldots, 50$. The probability, that their product ab...

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Given below are two statements : Statement I: The first ionization enthalpy of Cr is lower than that of Mn...

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Given below are two statements: Statement I: Pressure of a fluid is exerted only on a solid surface in contact...

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In the reaction, $2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \rightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq})+6 \mathrm{Cl}^{-}(\mathrm{aq})+3 \mathrm{H}_2(\mathrm{~g})$

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A 'p'-block element $(\mathrm{E})$ and hydrogen form a binary cation $\left(\mathrm{EH}_{\mathrm{x}}\right)^{+}$, while $\mathrm{EH}_3$ on treatment with $\mathrm{K}_2 \mathrm{HgI}_4$ in alkaline...

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3, 3-Dimethyl-2-butanol cannot be prepared by : Choose the correct answer from the options given below :

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Let the relation $R$ on the set $M=\{1,2,3, \ldots, 16\}$ be given by $$ \mathrm{R}=\{(x, y): 4 y=5 x-3, x,...

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The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr...

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A projectile is thrown upward at an angle $60^{\circ}$ with the horizontal. The speed of the projectile is $...

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Given below are two statements: Statement I: Phenol on treatment with $\mathrm{CHCl}_3$ / aq. KOH under refluxing condition, followed by...

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The wavelength of light, while it is passing through water is 540 nm . The refractive index of water is...

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Let $\overrightarrow{\mathrm{AB}}=2 \hat{i}+4 \hat{j}-5 \hat{k}$ and $\overrightarrow{\mathrm{AD}}=\hat{i}+2 \hat{j}+\lambda \hat{k}, \lambda \in \mathbb{R}$. Let the projection of the vector $\vec{v}=\hat{i}+\hat{j}+\hat{k}$ on...

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A meter bridge with two resistances $\mathrm{R}_1$ and $\mathrm{R}_2$ as shown in figure was balanced (null point) at 40 cm...

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The formal changes on the atoms marked as (1) to (4) in the Lewis representation of $\mathrm{HnO}_3$ molecule respectively are

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A laser beam has intensity of $4.0 \times 10^{14} \mathrm{~W} / \mathrm{m}^2$. The amplitude of magnetic field associated with beam...

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Light is incident on a metallic plate having work function $110 \times 10^{-20} \mathrm{~J}$. If the produced photoelectrons have zero...

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In a microscope the objective is having focal length $f_0=2 \mathrm{~cm}$ and eye-piece is having focal length $f_e=4 \mathrm{~cm}$. The...

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The escape velocity from a spherical planet $A$ is $10 \mathrm{~km} / \mathrm{s}$. The escape velocity from another planet $B$...

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10 mole of oxygen is heated at constant volume from $30^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. The change in the internal...

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Consider the transition metal ions $\mathrm{Mn}^{3+}, \mathrm{Cr}^{3+}, \mathrm{Fe}^{3+}$ and $\mathrm{Co}^{3+}$ and all form low spin octahedral complexes. The correct decreasing...

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The heat generated in 1 minute between points $A$ and $B$ in the given circuit, when a battery of $...

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Two identical thin rods of mass $M \mathrm{~kg}$ and length $L \mathrm{~m}$ are connected as shown in figure. Moment of...

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XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation...

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A collimated beam of light of diameter 2 mm is propagating along $x$-axis. The beam is required to be expanded...

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An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at...

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Six point charges are kept $60^{\circ}$ apart from each other on the circumference of a circle of radius $R$ as...

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A point charge of $10^{-8} \mathrm{C}$ is placed at origin. The work done in moving a point charge $...

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$7.9 \mathrm{MeV} \alpha$-particle scatters from a target material of atomic number 79 . From the given data the estimated diameter...

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Initially a satellite of 100 kg is in a circular orbit of radius $1.5 \mathrm{R}_{\mathrm{E}}$. This satellite can be moved...

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Two strings $(A, B)$ having linear densities $\mu_A=2 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and, $\mu_B=4 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$...

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The given circuit works as :

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A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of...

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An aluminium and steel rods having same lengths and cross-sections are joined to make total length of 120 cm at...

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A diatomic gas $(\gamma=1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the...

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In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed...

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A particle having electric charge $3 \times 10^{-19} \mathrm{C}$ and mass $6 \times 10^{-27} \mathrm{~kg}$ is accelerated by applying an...

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The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal...

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A uniform rod of mass $m$ and length $l$ suspended by means of two identical inextensible light strings as shown...

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An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma=10 \mathrm{mho} / \mathrm{m}$. The ratio of...

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If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus...

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As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes...

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A body of mass 2 kg is moving along $x$-direction such that its displacement as function of time is given...

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A light wave described by $E=60\left[\sin \left(3 \times 10^{15}\right) t+\sin \left(12 \times 10^{15}\right) t\right]$ (in SI units) falls on a...

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A large drum having radius $R$ is spinning around its axis with angular velocity $\omega$, as shown in figure. The...

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An infinitely long straight wire carrying current $I$ is bent in a planer shape as shown in the diagram. The...

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If P is a point on the circle $x^2+y^2=4, \mathrm{Q}$ is a point on the straight line $5 x+y+2=0$ and...

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The energy of an electron in an orbit of the Bohr's atom is $-0.04 E_0 \mathrm{eV}$ where $\mathrm{E}_0$ is the...

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If $...

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Let the maximum value of $\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2$ for $x \in\left[-\frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}}\right]$ be $\frac{m}{n} \pi^2$, where $\operatorname{gcd}(m, n)=1$....

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If $\int_0^1 4 \cot ^{-1}\left(1-2 x+4 x^2\right) \mathrm{d} x=\operatorname{atan}^{-1}(2)-\operatorname{blog}_{\mathrm{e}}(5)$, where $\mathrm{a}, \mathrm{b} \in \mathbf{N}$, then $(2 \mathrm{a}+\mathrm{b})$ is equal to

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Two known resistances of $R \Omega$ and $2 R \Omega$ and one unknown resistance $X \Omega$ are connected in a...

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Let $[\cdot]$ denote the greatest integer function and $f(x)=\lim _{\mathrm{n} \rightarrow \infty} \frac{1}{\mathrm{n}^3} \sum_{\mathrm{k}=1}^{\mathrm{n}}\left[\frac{\mathrm{k}^2}{3^x}\right]$. Then $12 \sum_{\mathrm{j}=1}^{\infty} f(\mathrm{j})$ is equal...

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A river of width 200 m is flowing from west to east with a speed of . A boat, moving...

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The largest $\mathrm{n} \in \mathbf{N}$, for which $7^{\mathrm{n}}$ divides $101!$, is :

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Let z be the complex number satisfying $|z-5| \leq 3$ and having maximum positive principal argument. Then $...

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Surface tension of two liquids (having same densities), $T_1$ and $T_2$, are measured using capillary rise method utilizing two tubes...

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If the system of equations $$ \begin{aligned} & 3 x+y+4 z=3 \\ & 2 x+\alpha y-z=-3 \\ & x+2 y+z=4...

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Let $\mathrm{A}=\{2,3,5,7,9\}$. Let R be the relation on A defined by $x \mathrm{R} y$ if and only if $...

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Let $y=y(x)$ be the solution of the differential equation $...

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A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity...

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For a triangle A B C, let $\vec{p}=\overrightarrow{B C}, \vec{q}=\overrightarrow{C A}$ and $\vec{r}=\overrightarrow{B A}$. If $|\vec{p}|=2 \sqrt{3},|\vec{q}|=2$ and $\cos \theta=\frac{1}{\sqrt{3}}$,...

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For the matrices $\mathrm{A}=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ll}-29 & 49 \\ -13 & 18\end{array}\right]$, if $...

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Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is...

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Let $\mathrm{A}=\left\{x:\left|x^2-10\right| \leq 6\right\}$ and $\mathrm{B}=\{x:|x-2|>1\}$. Then

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Let $a_1, \frac{a_2}{2}, \frac{a_3}{2^2}, \ldots, \frac{a_{10}}{2^9}$ be a G.P. of common ratio $\frac{1}{\sqrt{2}}$. If $a_1+a_2+\ldots+a_{10}=62$, then $a_1$ is equal to:

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If the area of the region $\left\{(x, y): 1-2 x \leq y \leq 4-x^2, x \geq 0, y \geq 0\right\}$...

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A random variable X takes values $0,1,2,3$ with probabilities $\frac{2 a+1}{30}, \frac{8 a-1}{30}, \frac{4 a+1}{30}, b$ respectively, where $...

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A battery with EMF $E$ and internal resistance $r$ is connected across a resistance $R$ The power consumption in $R$...

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Given below are two statements : Statement I: In a Young's double slit experiment, the angular separation of fringes will...

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Let $\alpha$ and $\beta$ be the roots of the equation $x^2+2 a x+(3 a+10)=0$ such that $\alpha

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The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of . The frequency of this simple...

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Let the line $\mathrm{L}_1$ be parallel to the vector $-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and pass through the point $(2,6,7)$, and...

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Let the line L pass through the point $(-3,5,2)$ and make equal angles with the positive coordinate axes. If the...

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Consider the following reactions : $$ \begin{aligned} & \mathrm{NaCl}+\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{~A}+\mathrm{KHSO}_4+\mathrm{NaHSO}_4+\mathrm{H}_2 \mathrm{O} \\ & \mathrm{~A}+\mathrm{NaOH} \rightarrow \mathrm{~B}+\mathrm{NaCl}+\mathrm{H}_2...

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The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of...

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Consider the following equation:

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Let one end of a focal chord of the parabola $y^2=16 x$ be $(16,16)$. If $\mathrm{P}(\alpha, \beta)$ divides this focal...

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Use the following data : One mole each of $\mathrm{A}_2(\mathrm{~g})$ and $\mathrm{B}_2(\mathrm{~g})$ are taken in a 1 L closed flask...

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Let $y^2=12 x$ be the parabola with its vertex at O . Let P be a point on the parabola...

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The pH and conductance of a weak acid $(\mathrm{HX})$ was found to be 5 and $4 \times 10^{-5} \mathrm{~S}$, respectively....

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If the line $\alpha x+4 y=\sqrt{7}$, where $\alpha \in \mathbf{R}$, touches the ellipse $3 x^2+4 y^2=1$ at the point P...

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Pre-exponential factors of two different reactions of same order are identical. Let activation energy of first reaction exceeds the activation...

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Two cars A and B each of mass $10^3$kg are moving on parallel tracks separated by a distance of 10...

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Given below are two statements : Statement I: When an electric discharge is passed through gaseous hydrogen, the hydrogen molecules...

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Let $f(x)=x^3+x^2 f^{\prime}(1)+2 x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in \mathbf{R}$. Then the value of $f^{\prime}(5)$ is:

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For the reaction, $\mathrm{N}_2 \mathrm{O}_4 \rightleftharpoons 2 \mathrm{NO}_2$, graph is plotted as shown below. Identify correct statements. A. Standard free...

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The r.m.s. speed of oxygen molecules at 47ºC is equal to that of the hydrogen molecules kept at ….. ºC....

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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that $f^{\prime \prime}(x)>0$ for all $x \in \mathbf{R}$ and...

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Which of the following graphs between pressure 'p' versus volume 'V' represents the maximum work done?

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The electric field in a plane electromagnetic wave is given by : $$ E_y=69 \sin \left[0.6 \times 10^3 x-1.8 \times...

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The positive integer $n$, for which the solutions of the equation $x(x+2)+(x+2)(x+4)+\cdots+(x+2 n-2)(x+2 n)=\frac{8 n}{3}$ are two consecutive even integers,...

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Identify the correct statements. A. Arginine and Tryptophan are essential amino acids. B. Histidine does not contain heterocyclic ring in...

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A parallel plate capacitor has capacitance $C$, when there is vacuum within the parallel plates. A sheet having thickness $...

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Identify correct statements from the following : A. Propanal and propanone are functional isomers. B. Ethoxyethane and methoxypropane are metamers....

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$6 \int_0^\pi|(\sin 3 x+\sin 2 x+\sin x)| d x$ is equal to $\_\_\_\_$ .

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Given below are two statements: Statement I: Among $\left.\left[\mathrm{Cu}\left(\mathrm{NH}_3\right)_4\right]^{2+},\left[\mathrm{Ni}(\mathrm{en})_3\right)\right]^{2+},\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_6\right]^{2+}$ and $\left[\mathrm{Mn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$, $\left[\mathrm{Mn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ has the maximum number of unpaired...

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A capacitor C is first charged fully with potential difference of V0 and disconnected from the battery. The charged capacitor...

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A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest....

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Given below are two statements : Statement I : The number of species among $\mathrm{SF}_4, \mathrm{NH}_4^{+},\left[\mathrm{NiCl}_4\right]^{2-}, \mathrm{XeF}_4,\left[\mathrm{PiCl}_4\right]^{2-}, \mathrm{SeF}_4$ and $\left.[\mathrm{NiCN})_4\right]^{2-}$,...

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Consider a modified Bernoulli equation. $$ \left(P+\frac{A}{B t^2}\right)+\rho g(h+B t)+\frac{1}{2} \rho V^2=\text { constant } $$ If $t$ has the...

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$\mathrm{MnO}_4{ }^{2-}$, in acidic medium, disproportionates to :

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From the following, the least stable structure is :

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A 4 kg mass moves under the influence of a force $\vec{F}=\left(4 t^3 \hat{i}-3 t \hat{j}\right) \mathrm{N}$ where $t$ is...

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For some $\quad \alpha, \beta \in \mathbf{R}, \quad$ let $\quad A=\left[\begin{array}{ll}\alpha & 2 \\ 1 & 2\end{array}\right] \quad$ and $...

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The total length of potentiometer wire AB is 50 cm in the arrangement as shown in figure. If P is...

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An organic compound " P " of molecular formula $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_3$ gives positive lodoform test but negative Tollen's test....

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In an experiment the values of two spring constants were measured as $k_1=(10 \pm 0.2) \mathrm{N} / \mathrm{m}$ and $...

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An organic compound $(\mathrm{P})$ on treatment with aqueous ammonia under hot condition forms compound $(\mathrm{Q})$ which on heating with $\mathrm{Br}_2$...

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Let $S=\{(m, n): m, n \in\{1,2,3, \ldots, 50\}\}$. If the number of elements ( $\mathrm{m}, \mathrm{n}$ ) in S such...

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Let $a_1=1$ and for $n \geq 1, a_{n+1}=\frac{1}{2} a_n+\frac{n^2-2 n-1}{n^2(n+1)^2}$. Then $\left|\sum_{n=1}^{\infty}\left(a_n-\frac{2}{n^2}\right)\right|$ is equal to

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Elements $P$ and $Q$ form two types of non-volatile, non-ionizable compounds $P Q$ and $P Q_2$. When 1 g of...

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Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in...

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The charge stored by the capacitor C in the given circuit in the steady state is ….$\mu \mathrm{C}$.

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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that the quadratic equation $f(x) \mathrm{m}^2-2 f^{\prime}(x) \mathrm{m}+f^{\prime \prime}(x)=0$...

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In Carius method, 0.75 g of an organic compound gave 1.2 g of barium sulphate, find percentage of sulphur (molar...

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Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an initial...

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14.0 g of calcium metal is allowed to react with excess HCl at 1.0 atm pressure and 273 K ....

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Let O be the vertex of the parabola $x^2=4 y$ and Q be any point on it. Let the locus...

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Q JEE MAIN 2026

A conducting circular loop of area $1.0 \mathrm{~m}^2$ mmmmm is placed perpendicular to a magnetic field which varies as $...

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Q JEE MAIN 2026

The sum of all the roots of the equation $(x-1)^2-5|x-1|+6=0$, is :

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Q JEE MAIN_2026_

80 mL of a hydrocarbon on mixing with 264 mL of oxygen in a closed U-tube undergoes complete combustion. The...

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Q JEE MAIN 2026

A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27ºC to 87ºC. The...

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Q JEE MAIN 2026

The value of $\operatorname{cosec} 10^{\circ}-\sqrt{3} \sec 10^{\circ}$ is equal to :

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Q JEE MAIN_2026

Given below are two statements : Statement I: The number of pairs among $\left[\mathrm{SiO}_2, \mathrm{CO}_2\right],\left[\mathrm{SnO}, \mathrm{SnO} \mathrm{O}_2\right],\left[\mathrm{PbO}, \mathrm{PbO}_2\right]$ and $...

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Q JEE MAIN 2026

If $x^2+x+1=0$, then the value of $\left(x+\frac{1}{x}\right)^4+\left(x^2+\frac{1}{x^2}\right)^4+\left(x^3+\frac{1}{x^3}\right)^4+\ldots .+\left(x^{25}+\frac{1}{x^{25}}\right)^4$ is:

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Q JEE MAIN 2026

Potential energy (V) versus distance (x) is given by the graph. Rank various regions as per the magnitudes of the...

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Q JEE MAIN 2026

If the coefficient of x in the expansion of $\left(a x^2+b x+c\right)(1-2 x)^{26}$ is -56 and the coefficients of $x^2$...

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Q JEE MAIN_2026_

A hydrocarbon ' P ' $\left(\mathrm{C}_4 \mathrm{H}_8\right)$ on reaction with HCl gives an optically active compound ' Q ' $...

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Q JEE MAIN 2026

Let PQ and MN be two straight lines touching the circle $x^2+y^2-4 x-6 y-3=0$ at the points A and B...

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Q JEE MAIN_2026_

Identify A in the following reaction.

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Q JEE MAIN 2026

Let $(\alpha, \beta, \gamma)$ be the co-ordinates of the foot of the perpendicular drawn from the point $(5,4,2)$ on the...

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Q JEE MAIN_2026_

Which of the following represents the correct trend for the mentioned property? A. $\mathrm{F}>\mathrm{P}>\mathrm{S}>\mathrm{B}$ - First lonization Energy B. $\mathrm{Cl}>\mathrm{F}>\mathrm{S}>\mathrm{P}$...

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Q JEE MAIN_2026

Consider the following reactions. $\mathrm{PbCl}_2+\mathrm{K}_2 \mathrm{CrO}_4 \rightarrow \mathrm{~A}+2 \mathrm{KCl}$ (Hot solution) $$ \begin{aligned} & \mathrm{A}+\mathrm{NaOH} \rightleftharpoons \mathrm{~B}+\mathrm{Na}_2 \mathrm{CrO}_4 \\ &...

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Q JEE MAIN 2026

Let the mean and variance of 7 observations $2,4,10, x, 12,14, y, x>y$, be 8 and 16 respectively. Two numbers...

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Q JEE MAIN 2026

The value of $\int_{-\pi / 6}^{\pi / 6}\left(\frac{\pi+4 x^{11}}{1-\sin (|x|+\pi / 6)}\right) d x$ is equal to:

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Q JEE MAIN 2026

Let the foci of a hyperbola coincide with the foci of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$. If the eccentricity of the hyperbola...

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Q JEE MAIN 2026

Let $f: \mathbf{R} \rightarrow(0, \infty)$ be a twice differentiable function such that $f(3)=18, f^{\prime}(3)=0$ and $f^{\prime \prime}(3)=4$. Then $...

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Q JEE MAIN 2026

The number of strictly increasing functions $f$ from the set $\{1,2,3,4,5,6\}$ to the set $\{1,2,3, \ldots, 9\}$ such that $...

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Q JEE MAIN 2026

Let $y=y(x)$ be the solution curve of the differential equation $\left(1+x^2\right) d y+\left(y-\tan ^{-1} x\right) d x=0, y(0)=1$. Then the...

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Q JEE MAIN 2026

Let $\vec{c}$ and $\vec{d}$ be vectors such that $|\vec{c}+\vec{d}|=\sqrt{29}$ and $\vec{c} \times(2 \hat{i}+3 \hat{j}+4 \hat{k})=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \times \vec{d}$....

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Q JEE MAIN 2026

Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive terms such that $a_2 \cdot a_3 \cdot a_4=64$ and...

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Q JEE MAIN 2026

Let $\overrightarrow{\mathrm{a}}=-\hat{i}+2 \hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=8 \hat{i}+7 \hat{j}-3 \hat{k}$ and $\overrightarrow{\mathrm{c}}$ be a vector such that $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}}$. If $...

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Q JEE MAIN 2026

Let a point A lie between the parallel lines $L_1$ and $L_2$ such that its distances from $L_1$ and $L_2$...

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Q JEE MAIN 2026

The number of relations, defined on the set $\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}\}$, which are both reflexive and symmetric, is equal...

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Q JEE MAIN 2026

The area of the region, inside the ellipse $x^2+4 y^2=4$ and outside the region bounded by the curves $y=|x|-1$ and...

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Q JEE MAIN 2026

If the domain of the function $f(x)=\cos ^{-1}\left(\frac{2 x-5}{11-3 x}\right)+\sin ^{-1}\left(2 x^2-3 x+1\right)$ is the interval $[\alpha, \beta]$, then $...

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