Q JEE Advance 2023

PARAGRAPH "I" Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is...

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Q JEE Advance 2023

Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is...

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Q JEE ADVANCED 2023

Let $z$ be a complex number satisfying $|z|^3+2 z^2+4 \bar{z}-8=0$, where $\bar{z}$ denotes the complex conjugate of $z$. Let the...

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Q JEE ADVANCED 2023

Let $\ell_1$ and $\ell_2$ be the lines $\vec{r}_1=\lambda(\hat{i}+\hat{j}+\hat{k})$ and $\vec{r}_2=(\hat{j}-\hat{k})+\mu(\hat{i}+\hat{k})$, respectively. Let $X$ be the set of all the planes...

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Q JEE Advanced 2023

Consider the given data with frequency distribution $$ \begin{array}{lllllll} \mathrm{x} 1 & 3 & 8 & 11 & 10 &...

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Q JEE Advanced 2023

Let $\alpha, \beta$ and $\gamma$ be real numbers. Consider the following system of linear equations $$ \begin{aligned} & x+2 y+z=11...

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Q JEE Advanced 2023

Let $a$ and $b$ be two nonzero real numbers. If the coefficient of $x^5$ in the expansion of $...

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Q JEE Advanced 2023

Let $P$ be the plane $\sqrt{3} \mathrm{x}+2 \mathrm{y}+3 \mathrm{z}=16$ and let $\mathrm{S}=\left\{\alpha \hat{\mathrm{i}}+\beta \hat{\mathrm{j}}+\gamma \hat{\mathrm{k}}: \alpha^2+\beta^2+\gamma^2=1\right.$ and the distance of...

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Q JEE Advanced 2023

Let $A=\left\{\frac{1967+1686 i \sin \theta}{7-3 i \cos \theta}: \theta \in \mathbb{R}\right\}$. If $A$ contains exactly one positive integer $n$, then...

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Q JEE Advanced 2023

Let $\overbrace{75 \ldots . .57}^r$ denote the $(r+2)$ digit number where the first and the last digits are 7 and...

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Q JEE Advanced 2023

Let $n \geq 2$ be a natural number and $f:[0,1] \rightarrow \mathbb{R}$ be the function defined by $$ f(x)= \begin{cases}n(1-2...

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Q JEE Advanced 2023

Let $\tan ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ for $x \in \mathbb{R}$. Then the number of real solutions of the equation $...

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Q JEE Advanced 2023

Let $P$ be a point on the parabola $y^2=4 a x$, where $a>0$. The normal to the parabola at $P$...

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Q JEE Advanced 2023

Let $\mathrm{X}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}: \frac{\mathrm{x}^2}{8}+\frac{\mathrm{y}^2}{20}

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Q JEE ADVANCED 2023

Let $Q$ be the cube with the set of vertices $\left\{\left(x_1, x_2, x_3\right) \in \mathbb{R}^3: x_1, x_2, x_3 \in\{0,1\}\right\}$. Let...

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Q JEE Advance 2023

A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of $\mathrm{Sn} / \mathrm{HCl}$ gives a major product, which on...

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Q JEE Advance 2023

A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of $\mathrm{Sn} / \mathrm{HCl}$ gives a major product, which on...

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Q JEE Advanced 2023

Let $f:(0,1) \rightarrow \mathbb{R}$ be the function defined as $f(x)=\sqrt{n}$ if $x \in\left[\frac{1}{n+1}, \frac{1}{n}\right)$ where $n \in \mathbb{N}$. Let $...

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Q JEE Advance 2023

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at 1 bar pressure is given. $\mathrm{S}_{\mathrm{t}}$ and $\mathrm{S}_0$ are...

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Q JEE Advanced 2023

Let $f:[0,1] \rightarrow[0,1]$ be the function defined by $f(x)=\frac{x^3}{3}-x^2+\frac{5}{9} x+\frac{17}{36}$. Consider the square region $S=[0,1] \times[0,1]$. Let $...

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Q JEE Advance 2023

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at 1 bar pressure is given. $\mathrm{S}_{\mathrm{t}}$ and $\mathrm{S}_0$ are...

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Q JEE Advance 2023

The reaction of 4-methyloct-1-ene $(\mathbf{P}, 2.52 \mathrm{~g})$ with HBr in the presence of $\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}\right)_2 \mathrm{O}_2$ gives two isomeric...

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Q JEE Advance 2023

50 mL of 0.2 molal urea solution (density $=1.012 \mathrm{~g} \mathrm{~mL}^{-1}$ at 300 K ) is mixed with 250 mL...

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Q JEE Advance 2023

For $\mathrm{He}^{+}$, a transition takes place from the orbit of radius 105.8 pm to the orbit of radius 26.45 pm...

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Q JEE Advance 2023

Consider the following molecules: $\mathrm{Br}_3 \mathrm{O}_8, \mathrm{~F}_2 \mathrm{O}, \mathrm{H}_2 \mathrm{~S}_4 \mathrm{O}_6, \mathrm{H}_2 \mathrm{~S}_5 \mathrm{O}_6$, and $\mathrm{C}_3 \mathrm{O}_2$. Count the number...

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Q JEE Advance2023

Let $T_1$ and $T_2$ be two distinct common tangents to the ellipse $E: \frac{x^2}{6}+\frac{y^2}{3}=1$ and the parabola $P: y^2=12 x$....

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Q JEE Advance 2023

Among $\left[\mathrm{I}_3\right]^{+},\left[\mathrm{SiO}_4\right]^{4-}, \mathrm{SO}_2 \mathrm{Cl}_2, \mathrm{XeF}_2, \mathrm{SF}_4, \mathrm{ClF}_3, \mathrm{Ni}(\mathrm{CO})_4, \mathrm{XeO}_2 \mathrm{~F}_2,\left[\mathrm{PtCl}_4\right]^{2-}, \mathrm{XeF}_4$, and $\mathrm{SOCl}_2$, the total number of species having $\mathrm{sp}^3$...

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Q JEE Advanced 2023

A cylindrical furnace has height $(H)$ and diameter $(D)$ both 1 m . It is maintained at temperature 360 K...

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Q JEE Advanced 2023

A cylindrical furnace has height $(H)$ and diameter $(D)$ both 1 m . It is maintained at temperature 360 K...

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Q JEE_Advanced_2023

Let $S=(0,1) \cup(1,2) \cup(3,4)$ and $T=\{0,1,2,3\}$. Then which of the following statements is (are) true?

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Q JEE Advance2023

$\mathrm{H}_2 \mathrm{~S}$ (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this reaction, the number of moles of...

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Q JEE Advanced 2023

$S_1$ and $S_2$ are two identical sound sources of frequency 656 Hz . The source $S_1$ is located at $O$...

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Q JEE Advanced 2023

$S_1$ and $S_2$ are two identical sound sources of frequency 656 Hz . The source $S_1$ is located at $O$...

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Q JEE Advance2023

In the following reactions, $\mathbf{P}, \mathbf{Q}, \mathbf{R}$, and $\mathbf{S}$ are the major products

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Q JEE Advanced 2023

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the $P-V$ diagrams...

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Q JEE Advance2023

The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match...

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Q JEE Advance 2023

Consider an obtuse angled triangle ABC in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and...

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Q JEE Advance2023

Match the reactions in List-I with the features of their products in List-II and choose the correct option.

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Q JEE Advance 2023

Let $C_1$ be the circle of radius 1 with center at the origin. Let $C_2$ be the circle of radius...

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Q JEE Advanced 2023

In a radioactive decay process, the activity is defined as $\mathrm{A}=-\frac{\mathrm{dN}}{\mathrm{dt}}$, where $N(t)$ is the number of radioactive nuclei at...

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Q JEE Advance2023

Match the electronic configurations in List-I with appropriate metal complex ions in List-II and choose the correct option. [Atomic Number:...

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Q JEE Advance2023

Match the reactions (in the given stoichiometry of the reactants) in List-I with one of their products given in List-II...

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Q JEE Advanced 2023

An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner...

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Q JEE Advanced 2023

A string of length 1 m and mass $2 \times 10^{-5} \mathrm{~kg}$ is under tension $T$. When the string vibrates,...

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Q JEE Advance 2023

Let $\mathrm{A}_1, \mathrm{~A}_2, \mathrm{~A}_{3, \ldots} \ldots \mathrm{~A}_8$, be the vertices of a regular octagon that lie on a circle of...

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Q JEE Advance 2023

Let $X$ be the set of all five digit numbers formed using $1,2,2,2,4,4,0$. For example, 22240 is in $X$ while...

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Q JEE Advance 2023

For $x \in \mathbb{R}$, let $y(x)$ be a solution of the differential equation $\left(x^2-5\right) \frac{\mathrm{dy}}{\mathrm{dx}}-2 x y=-2 x\left(x^2-5\right)^2$ such that...

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Q JEE Advance 2023

Let $S$ be the set of all twice differentiable functions $f$ from $\mathbb{R}$ to $\mathbb{R}$ such that $\frac{d^2 f}{d x^2}(x)>0$...

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Q JEE Advanced 2023

A rectangular conducting loop of length 4 cm and width 2 cm is in the $x y$-plane, as shown in...

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Q JEE Advance 2023

Let $f:(0,1) \rightarrow \mathbb{R}$ be the function defined as $f(x)=[4 x]\left(x-\frac{1}{4}\right)^2\left(x-\frac{1}{2}\right)^2$, where $[x]$ denotes the greatest integer less than or...

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Q JEE Advanced 2023

A thin circular coin of mass 5 gm and radius $4 / 3 \mathrm{~cm}$ is initially in a horizontal $...

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Q JEE Advanced 2023

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $...

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Q JEE Advanced 2023

An annular disk of mass $M$, inner radius $a$ and outer radius $b$ is placed on a horizontal surface with...

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Q JEE Advanced 2023

A monochromatic light wave is incident normally on a glass slab of thickness $d$, as shown in the figure. The...

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Q JEE Advance 2023

Atoms of metals $x, y$, and $z$ form face-centred cubic (fcc) unit cell of edge length $L_x$, body-centred cubic (bcc)...

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Q JEE Advance2023

In a one-litre flask, 6 moles of A yndergoes the reaction $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{P}(\mathrm{g})$. The progress of product formation at...

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Q JEE Advance 2023

Let $\mathrm{M}=\left(\mathrm{a}_{\mathrm{iij}}\right), \mathrm{i}, \mathrm{j} \in\{1,2,3\}$, be the $3 \times 3$ matrix such that $\mathrm{a}_{\mathrm{ij}}=1$ if $\mathrm{j}+1$ is divisible by i...

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Q JEE Advance 2023

Let the position vectors of the points $P, Q, R$ and $S$ be $...

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Q JEE Advance 2023

\begin{aligned} &\text { The complex(es), which can exhibit the type of isomerism shown by }\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Br} 2\right] \text {, is(are)...

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Q JEE Advance2023

One mole of an ideal mpnoatomic gas undergoes two reversible processes $(A \rightarrow B$ and $B \rightarrow C)$ as shown...

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Q JEE Advance2023

The plot of $\log k_f$ versus $1 / \mathrm{T}$ for a reversible reaction $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{P}(\mathrm{g})$ is shown.Pre-exponential factors for...

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Q JEE Advance 2023

A disaccharide X cannot be oxidised by bromine water. The acid hydrolysis of X leads to a laevorotatory solution. The...

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Q JEE Advance 2023

In the following reactions, P, Q, R, and S are the major products. The correct statement about P, Q, R,...

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Q JEE Advance2023

A gas has a compressibility factor of 0.5 and a molar volume of $0.4 \mathrm{dm}^3 \mathrm{~mol}^{-1}$ at a temperature of...

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Q JEE Advance 2023

Consider the following statements related to colloids. (I) Lyophobic colloids are not formed by simple mixing of dispersed phase and...

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Q JEE Advance 202

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability...

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Q JEE Advanced 2023

A particle of mass $m$ is moving in the $x y$-plane such that its velocity at a point $(x, y)$...

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Q JEE Advanced 2023

Young's modulus of elasticity $Y$ is expressed in terms of three derived quantities, namely, the gravitational constant $G$, Planck's constant...

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Q JEE Advanced 2023

An electric dipole is formed by two charges +𝑞 and −𝑞 located in 𝑥𝑦-plane at (0, 2) mm and (0,...

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Q JEE Advanced 2023

A thin conducting rod MN of mass 20 gm , length 25 cm and resistance $10 \Omega$ is held on...

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Q JEE Advanced 2023

A series LCR circuit is connected to a $45 \sin (\omega t)$ Volt source. The resonant angular frequency of the...

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Q JEE Advance2023

The stoichiometric reaction of 516 g of dimethyldichlorosilane with water results in a tetrameric cyclic product X in $75 \%$...

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Q JEE Advanced 2023

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct...

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Q JEE Advance2023

In the given reaction scheme, P is a phenyl alkyl ether, Q is an aromatic compound; R and S are...

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Q JEE Advance 2023

Let $f:[1, \infty) \rightarrow \mathbb{R}$ be a differentiable function such that $f(1)=\frac{1}{3}$ and $...

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Q JEE Advanced 2023

List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate...

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Q JEE Advance 2023

$$ \text { The correct molecular orbital diagram for } F_2 \text { molecule in the ground state is }...

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Q JEE Advance2023

On decreasing the pH from 7 to 2 , the solubility of a sparingly soluble salt $(\mathrm{MX})$ of a weak...

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Q JEE Advanced 2023

Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless...

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Q JEE Advnced 2023

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight...

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Plotting $1 / \mathrm{L}_{\mathrm{a}}$ against $\mathrm{c} / \mathrm{mm}$ for aqueous solutions of a monobasic weak acid $(\mathrm{HX})$ resulted in a...

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Q JEE Advanced 2023

A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas ( $\gamma=5 / 3$ )...

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Q JEE Advanced 2023

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from...

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Q JEE Advance2023

In the scheme given below, $\mathbf{X}$ and $\mathbf{Y}$, respectively, are

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Q JEE Advanced 2023

An optical arrangement consists of two concave mirrors $M_1$ and $M_2$, and a convex lens $L$ with a common principal...

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Q JEE Advanced 2023

A Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to level $n=3$ in...

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Q JEE Advanced 2023

Two satellites P and Q are moving in different circular orbits around the Earth (radius $R$ ). The heights of...

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Q JEE Advance2023

Consider the following reaction scheme and choose the correct option(s) for the major products Q, R and S.

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Q JEE Advanced 2023

One mole of an ideal gas expands adiabatically from an initial state ( $T_{\mathrm{A}}, V_0$ ) to final state (...

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Q JEE Advance2023

In the following reactions, $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, and S are the major products.

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Q JEE Advanced 2023

A container has a base of $50 \mathrm{~cm} \times 5 \mathrm{~cm}$ and height 50 cm , as shown in the...

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Q JEE Advanced 2023

A bar of mass $M=1.00 \mathrm{~kg}$ and length $\mathrm{L}=0.20 \mathrm{~m}$ is lying on a horizontal frictionless surface. One end of...

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Q JEE Advanced 2023

In a circuit shown in the figure, the capacitor C is initially uncharged and the key K is open. In...

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Q JEE Advance 2023

The dorrect statement(s) related to processes involved in the extraction of metals is(are)

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Q JEE Advanced 2023

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface...

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Q JEE Advanced 2023

A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of...

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