Q JEE Advanced 2025

If $ \alpha=\int_{\frac{1}{2}}^2 \frac{\tan ^{-1} x}{2 x^2-3 x+2} d x $ then the value of $\sqrt{7} \tan \left(\frac{2 \alpha \sqrt{7}}{\pi}\right)$...

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Q JEE Advanced 2025

Let $ \alpha=\frac{1}{\sin 60^{\circ} \sin 61^{\circ}}+\frac{1}{\sin 62^{\circ} \sin 63^{\circ}}+\cdots+\frac{1}{\sin 118^{\circ} \sin 119^{\circ}} $ Then the value of $\left(\frac{\operatorname{cosec} 1^{\circ}}{\alpha}\right)^2$ is...

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Q JEE Advanced 2025

Let $\mathbb{R}$ denote the set of all real numbers. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow(0,4)$ be functions...

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Q JEE Advanced 2025

For a non-zero complex number $z$, let $\arg (z)$ denote the principal argument of $z$, with $-\pi

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Q JEE Advanced 2025

Consider the vectors $...

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Q JEE Advanced 2025

A factory has a total of three manufacturing units, $M_1, M_2$, and $M_3$, which produce bulbs independent of each other....

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Q JEE Advanced 2025

Let $a_0, a_1, \ldots, a_{23}$ be real numbers such that $ \left(1+\frac{2}{5} x\right)^{23}=\sum_{i=0}^{23} a_i x^i $ for every real number...

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Q JEE Advanced 2025

Let $y(x)$ be the solution of the differential equation $ x^2 \frac{d y}{d x}+x y=x^2+y^2, \quad x>\frac{1}{e} $ satisfying $y(1)=0$....

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Q JEE Advanced 2025

Let $\mathbb{R}$ denote the set of all real numbers. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $...

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Q JEE-Advanced 2025

A linear octasaccharide (molar mass $=1024 \mathrm{~g} \mathrm{~mol}^{-1}$ ) on complete hydrolysis produces three monosaccharides: ribose, 2-deoxyribose and glucose. The...

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Q JEE Advanced 2025

Let $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right)$ be two distinct points on the ellipse $ \frac{x^2}{9}+\frac{y^2}{4}=1 $ such that $y_1>0$, and...

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Q JEE-Advanced 2025

The sum of the spin only magnetic moment values (in B.M.) of $\left[\mathrm{Mn}(\mathrm{Br})_6\right]^{3-}$ and $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$ is $\_\_\_\_$ .

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Q JEE Advanced 2025

Let $S$ denote the locus of the mid-points of those chords of the parabola $y^2=x$, such that the area of...

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Q JEE-Advanced 2025

An electrochemical cell is fueled by the combustion of butane at 1 bar and 298 K . Its cell potential...

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Q JEE-Advanced 2025

At 300 K , an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of...

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Q JEE Advanced 2025

Let $I=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$ and $P=\left(\begin{array}{ll}2 & 0 \\ 0 & 3\end{array}\right)$. Let $...

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Q JEE-Advanced 2025

Consider a reaction $A+R \rightarrow$ Product. The rate of this reaction is measured to be $\mathrm{k}[\mathrm{A}][\mathrm{R}]$. At the start of...

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Q JEE-Advanced 2025

Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from $...

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Q JEE Advanced 2025

Let S denote the locus of the point of intersection of the pair of lines $...

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Q JEE-Advanced 2025

The solubility of barium iodate in an aqueous solution prepared by mixing 200 mL of 0.010 M barium nitrate with...

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Q JEE Advanced 2025

The total number of real solutions of the equation $...

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Q JEE-Advanced 2025

The density (in $\mathrm{gcm}^{-3}$ ) of the metal which forms a cubic close packed (ccp) lattice with an axial distance...

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Q JEE Advanced 2025

Let $\mathbb{R}$ denote the set of all real numbers. Then the area of the region $...

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Q JEE-Advanced 2025

For the reaction sequence given below, the correct statement(s) is(are)

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Q JEE-Advanced 2025

For the reaction sequence given below, the correct statement(s) is(are)

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Q JEE-Advanced 2025

The compound(s) with $\mathrm{P}-\mathrm{H}$ bond(s) is(are)

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Q JEE Advanced 2025

Let $x_0$ be the real number such that $e^{x_0}+x_0=0$. For a given real number $\alpha$, define $...

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Q JEE-Advanced 2025

The correct statement(s) about intermolecular forces is(are)

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Q JEE-Advanced 2025

The correct reaction/reaction sequence that would produce a dicarboxylic acid as the major product is

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Q JEE-Advanced 2025

Monocyclic compounds P,Q and S are the major products formed in the reaction sequences given below.

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Q JEE Advanced 2025

Match the compounds in List-I with the appropriate observations in List-II and choose the correct option.

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Q JEE-Advanced 2025

The complete hydrolysis of $\mathrm{ICl}, \mathrm{ClF}_3$ and $\mathrm{BrF}_5$, respectively, gives

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Q JEE Advanced 2025

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-Advanced 2025

During sodium nitroprusside test of sulphide ion in an aqueous solution, one of the ligands coordinated to the metal ion...

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Q JEE Advanced 2025

The correct match of the group reagents in List-I for precipitating the metal ion given in List-II from solutions, is

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Q JEE Advanced 2025

The pair(s) of diamagnetic ions is(are)

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Q JEE Advanced 2025

Regarding the molecular orbital (MO) energy levels for homonuclear diatomic molecules, the INCORRECT statement(s) is(are)

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Q JEE-Advanced 2025

Let $\mathbb{R}$ denote the set of all real numbers. For a real number $x$, let $[x]$ denote the greatest integer...

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Q JEE ADVANCED_2025

List-I shows various functional dependencies of energy (E) on the atomic number (Z). Energies associated with certain phenomena are given...

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Q JEE ADVANCED_2025

A circuit with an electrical load having impedance $Z$ is connected with an $A C$ source as shown in the...

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Q JEE-Advanced 2025

Consider the following frequency distribution

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Q JEE ADVANCED_2025

List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of...

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Q JEE ADVANCED_2025

Consider an electron in the $\mathrm{n}=3$ orbit of a hydrogen-like atom with atomic number Z . At absolute temperature T...

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Q JEE ADVANCED_2025

A single slit diffraction experiment is performed to determine the slit width using the equation, $\frac{b d}{D}=\mathrm{m} \lambda$, where b...

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Q JEE ADVANCED_2025

A solid glass sphere of refractive index $n=\sqrt{3}$ and radius $R$ contains a spherical air cavity of radius $\frac{R}{2}$, as...

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Q JEE-Advanced 2025

For all $x>0$, let $y_1(x), y_2(x)$, and $y_3(x)$ be the functions satisfying $$ \begin{array}{ll} \frac{d y_1}{d x}-(\sin x)^2 y_1=0, &...

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Q JEE ADVANCED_2025_

Two identical plates P and Q, radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures $T_P$...

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Q JEE-Advanced 2025

Let $\mathbb{R}$ denote the set of all real numbers. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function such that $f(x)>0$...

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Q JEE ADVANCED_2025_

A cube of unit volume contains $35 \times 10^7$ photons of frequency $10^{15} \mathrm{~Hz}$. If the energy of all the...

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Q JEE-Advanced 2025

Let $\alpha$ and $\beta$ be the real numbers such that $...

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Q JEE MAIN_2025_S1

A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg . Suppose that...

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Q JEE-Advanced 2025

Let $S$ be the set of all seven-digit numbers that can be formed using the digits 0,1 and 2 ....

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Q JEE-Advanced 2025

For any two points $M$ and $N$ in the X Y -plane, let $\overrightarrow{M N}$ denote the vector from $M$...

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Q JEE-Advanced 2025

Let the set of all relations $R$ on the set $\{a, b, c, d, e, f\}$, such that $R$ is...

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Q JEE ADVANCE_2025

Length, breadth and thickness of a strip having a uniform cross section are measured to be $...

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Q JEE-Advanced 2025

Let $L_1$ be the line of intersection of the planes given by the equations $$ 2 x+3 y+z=4 \text {...

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Q JEE Advanced 2025

The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in...

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Q JEE Advanced 2025

The monomer $(X)$ involved in the synthesis of Nylon 6,6 gives positive carbylamine test. If 10 moles of $X$ are...

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Q JEE Advanced 2025

Considering ideal gas behavior, the expansion work done (in kJ ) when 144 g of water is electrolyzed completely under...

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Q JEE Advanced 2025

Molar volume ( $V_m$ ) of a van der Waals gas can be calculated by expressing the van der Waals...

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Q JEE-Advanced 2025

Consider the matrix $$ P=\left(\begin{array}{lll} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0...

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Q JEE ADVANCED_2025_

Figure 1 shows the configuration of main scale and Vernier scale before measurement. Fig. 2 shows the configuration corresponding to...

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Q JEE Advanced 2025

At $25^{\circ} \mathrm{C}$, the concentration of $\mathrm{H}^{+}$ions in $1.00 \times 10^{-3} \mathrm{M}$ aqueous solution of a weak monobasic acid having...

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Q JEE-Advanced 2025

Let $\mathbb{R}$ denote the set of all real numbers. Define the function $f: \mathbb{R} \rightarrow \mathbb{R}$ by $$ f(x)=\left\{\begin{array}{cc} 2-2...

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Q JEE Advanced 2025

In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to $\mathrm{Cr}^{3+}$. The current (in amperes) that flows...

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Q JEE ADVANCED_2025

A conducting square loop initially lies in the XZ plane with its lower edge hinged along the X -axis. Only...

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Q JEE Advanced 2025

For the reaction sequence given below, the correct statement(s) is(are) (In the options, X is any atom other than carbon...

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Q JEE ADVANCED 2025

Three students $S_1, S_2$, and $S_3$ are given a problem to solve. Consider the following events: $U:$ At least one...

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Q JEE-Advanced 2025

Let $\mathbb{R}$ denote the set of all real numbers. Let $a_i, b_i \in \mathbb{R}$ for $i \in\{1,2,3\}$. Define the functions...

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Q JEE Advanced 2025

Consider the depicted hydrogen (H) in the hydrocarbons given below. The most acidic hydrogen (H) is

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Q JEE ADVANCED_2025

In a scattering experiment, a particle of mass 2 m collides with another particle of mass m , which is...

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Q JEE Advanced 2025

One of the products formed from the reaction of permanganate ion with iodide ion in neutral aqueous medium is

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Q JEE Advanced 2025

The correct order of the wavelength maxima of the absorption band in the ultraviolet-visible region for the given complexes is

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Q JEE ADVANCED 2025

The center of a disk of radius $r$ and mass $m$ is attached to a spring of spring constant $k$,...

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Q JEE Advanced 2025

The heating of $\mathrm{NH}_4 \mathrm{NO}_2$ at $60-70^{\circ} \mathrm{C}$ and $\mathrm{NH}_4 \mathrm{NO}_3$ at $200-250^{\circ} \mathrm{C}$ is associated with the formation of...

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Q JEE ADVANCED 2025

In a scattering experiment, a particle of mass 2m collides with another particle of mass m, which is initially at...

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Q JEE ADVANCED 2025

The center of a disk of radius r and mass m is attached to a spring of spring constant k,...

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