JEE Main 2025 — 2 April, Morning Shift

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II:

Statement I: Vanillin

react with NaOH and also with Tollen's reagent.

Statement II: Vanillin

undergo self aldol condensation very easily.

In the light of the above statements, choose the correct answer from the options given below :

A solution is made by mixing one mole of volatile liquid $A$ with 3 moles of volatile liquid $B$. The vapour pressure of pure $A$ is 200 mm Hg and that of the solution is 500 mm Hg . The vapour pressure of pure $B$ and the least volatile component of the solution, respectively, are

The correct order of basic nature in aqueous solution for the bases

$\mathrm{NH}_{3}, \mathrm{H}_{2} \mathrm{~N}-\mathrm{NH}_{2}, \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2},\left(\mathrm{CH}_{3} \mathrm{CH}_{2}\right)_{2} \mathrm{NH}$ and $\left(\mathrm{CH}_{3} \mathrm{CH}_{2}\right)_{3} \mathrm{~N}$ is

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II:

Statement I: The metallic radius of AI is less than that of Ga .

Statement II: The ionic radius of $\mathrm{Al}^{1++}$ is less than that of $\mathrm{Ga}^{3+}$

In the light of the above statements, choose the correct answer from the options given below :

Consider the following compound ( X )

The most stable and least stable carbon radicals, respectively, produced by homolytic cleavage of corresponding $\mathrm{C}-\mathrm{H}$ bond are :

Among $\mathrm{SO}_{2}, \mathrm{NF}_{3}, \mathrm{NH}_{3}, \mathrm{XeF}_{2}, \mathrm{CIF}_{3}$ and $\mathrm{SF}_{4}$, the hybridization of the molecule with non-zero dipole

moment and highest number of lone-pairs of electrons on the centre atom is :

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II:

Statement I: In octahedral complexes, when $\Delta_{0}$ $<\mathrm{P}$ high spin complex are formed.

Statement II: In tetrahedral complexes because of $\Delta_{t} < P$ high spin complex are formed.

In the light of the above statements, choose the correct answer from the options given below :

A molecule with the formula $A X_{4} Y$ has all its elements from p-block. Element $A$ is rarest, monoatomic, non-radioactive from its group and has the lowest ionization enthalpy value among $A$, $X$ and $Y$. Elements $X$ and $Y$ have first and second highest electronegativity values respectively among all the known elements. The shape of the molecule is:

Designate whether each of the following compounds is aromatic or not aromatic.

Two vessels $A$ and $B$ are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true?

If equal volumes of $A B_{2}$ and XY (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $\mathrm{AY}_{2}$ at 300 K ? (Given $\mathrm{K}_{\text {sp }}\left(\right.$ at 300 K ) for $\mathrm{AY}_{2-}=5.2 \times 10^{-7}$ )

On complete combustion 1.0 g of an organic compound ( X ) gave 1.46 g of $\mathrm{CO}_{2}$ and 0.567 g of $\mathrm{H}_{2} \mathrm{O}$. The

empirical formula mass of compound ( X ) is $\_\_\_\_\_$ g. (Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{C}: 12, \mathrm{H}: 1, \mathrm{O}: 16$ )

The property/properties that show irregularity in first four elements of group-17 is/are

(A) Covalent radius

(B) Electron affinity

(C) Ionic radius

(D) First ionization energy

Choose the correct answer from the options given below:

Choose the correct tests with respective observations.

(A) $\mathrm{CuSO}_{4}$ (acidified with acetic acid) + $\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \rightarrow$ Chocolate brown precipitate.

(B) $\mathrm{FeCl}_{3}+\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \rightarrow$ Prussian blue precipitate.

(C) $\mathrm{ZnCl}_{2}+\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]$, neutralised with $\mathrm{NH}_{4} \mathrm{OH}$ $\rightarrow$ White or bluish white precipitate.

(D) $\mathrm{MgCl}_{2}+\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right] \rightarrow$ Blue precipitate.

(E) $\mathrm{BaCl}_{2}+\mathrm{K}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]$, neutralised with $\mathrm{NaOH} \rightarrow$ White precipitate.

Choose the correct answer from the options given below :

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

$\mathrm{CaCO}_{3}(\mathrm{~s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{CaCl}_{2}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{I})$ Consider the above reaction, what

mass of $\mathrm{CaCl}_{2}$ will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of $\mathrm{CaCO}_{3}$ ? (Given: Molar mass of

$\mathrm{Ca}, \mathrm{C}, \mathrm{O}, \mathrm{H}$ and Cl are 40, $12,16,1$ and $35.5 \mathrm{~g} \mathrm{~mol}^{-1}$, respectively)

Identify the correct statement among the following:

0.1 mol of the following given antiviral compound $(P)$ will weigh $\_\_\_\_\_$ $\times 10^{-1} \mathrm{~g}$ (Given : molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}$ : 14, O:16, F: 19, I: 127

For the reaction $A \rightarrow$ products. The concentration of $A$ at 10 minutes is $\_\_\_\_\_$ $\times 10^{-3}$ $\mathrm{mol\ L^{-1}}$ (nearest integer). The reaction was started with $2.5 \mathrm{~mol} \mathrm{~L}^{-1}$ of A.

From the plot: slope $= 76.92$ (appropriate units).

Consider the following equilibrium, $\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})$

0.1 mol of CO along with a catalyst is present in a $2 \mathrm{dm}^{3}$ flask maintained at 500 K . Hydrogen is introduced into

the flask until the pressure is 5 bar and 0.04 mol of $\mathrm{CH}_{3} \mathrm{OH}$ is formed. The $\mathrm{K}_{\mathrm{p}}^{\theta}$ is $\_\_\_\_\_$ $10^{-3}$ (nearest

integer). Given : $\mathrm{R}=0.08 \mathrm{dm}^{3}$ bar $\mathrm{K}^{-1} \mathrm{~mol}^{-1}$ Assume only methanol is formed as the product and the

system follows ideal gas behaviour.

Consider the following electrochemical cell at standard condition.

$\mathrm{Au}(\mathrm{s})\left|\mathrm{QH}_{2}, \mathrm{Q}\right| \mathrm{NH}_{4} \mathrm{X}(0.01 \mathrm{M})| | \mathrm{Ag}^{+}(1 \mathrm{M}) \mid \mathrm{Ag}(\mathrm{s})$

$\mathrm{E}_{\text {cell }}=+0.4 \mathrm{~V}$

The couple $\mathrm{QH}_{2} / \mathrm{Q}$ represents quinhydrone electrode, the half cell reaction is given below :

$\left[\right.$ Given : $\mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{0}=+0.8 \mathrm{~V}$ and $\left.\frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.06 \mathrm{~V}\right]$

The $\mathrm{pK}_{b}$ value of the ammonium halide salt $\left(\mathrm{NH}_{4} \mathrm{X}\right)$ used here is $\_\_\_\_\_$ . (nearest integer)

A transition metal（M）among Mn，Cr，Co and Fe has the highest standard electrode potential $\left(\mathrm{M}^{3+} / \mathrm{M}^{2+}\right)$ ．If forms a metal complex of the type $\left[\mathrm{M}(\mathrm{CN})_{6}{ }^{4-}\right.$ ．The number of electrons present in the $\mathrm{e}_{\mathrm{g}}$ orbital of the complex is $\_\_\_\_\_$

Let $a \in \mathbb{R}$ and $A$ be a matrix of order $3 \times 3$ such that $\operatorname{det}(A)=-4$ and $A+I=\left[\begin{array}{lll}1 & a & 1\\ 2 & 1 & 0\\ a & 1 & 2\end{array}\right]$, where $I$

is the identity matrix of order $3 \times 3$. If $det ((a+1) adj((a -1) A))$ is $2^{m} 3^{n}, m, n \in\{0,1,2, \ldots, 20\}$, then

$m+n$ is equal to

Let $P_{n}=\alpha^{n}+\beta^{n}, n \in N$. If $P_{10}=123, P_{9}=76, P_{8}=47$ and $P_{1}=1$, then the quadratic equation having roots $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ is:

Let $A B C D$ be a tetrahedron such that the edges $A B$, $A C$ and $A D$ are mutually perpendicular. Let the areas of the triangles $A B C, A C D$ and $A D B$ be $5,6$ and $7$ square units respectively. Then the area (in square units) of the $\triangle B C D$ is equal to

If $S$ and $S^{\prime}$ are the foci of the ellipse $\frac{x^{2}}{18}+\frac{y^{2}}{9}=1$ and $P$ be a point on the ellipse, then $\min \left(S P \cdot S^{\prime} P\right)+$ $\max \left(S P \cdot S^{\prime} P\right)$ is equal to

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a twice differentiable function such that $(\sin x \cos y)(f(2 x+2 y)-f(2 x-2 y))=(\cos x \sin y)(f(2 x$ $+2 y)+f(2 x-2 y)$ ), for all $x, y \in \mathbb{R}$. If $\quad f^{\prime}(0)=\frac{1}{2}$, then the value of $24 f^{\prime \prime}\left(\frac{5 \pi}{3}\right)$ is :

The term independent of $x$ in the expansion of $\left(\frac{(x+1)}{\left(x^{2 / 3}+1-x^{1 / 3}\right)}-\frac{(x-1)}{\left(x-x^{1 / 2}\right)}\right)^{10}, x>1$, is:

Let $A$ be the set of all function $f: \mathbb{Z} \rightarrow \mathbb{Z}$ and $R$ be a relation on $A$ such that

$R=\{(f, g\}: f(0)=g(1)$ and $f(1)=g(0)$. Then $R$ is:

Let $a_{1}, a_{2}, a_{3}$, be in an A.P. such that $\sum_{k=1}^{12} a_{2 k-1}=-\frac{72}{5} a_{1}, a_{1} \neq 0$. If $\sum_{k=1}^{n} a_{k}=0$, then $n$

is:

If the system of linear equations

$3 x+y+\beta z=3$

$2 x+\alpha y-z=-3$

$x+2 y+z=4$

has infinitely many solutions, then the value of $22 \beta-9 \alpha$ is:

The number of sequences of ten terms, whose terms are either $0$ or $1$ or $2 ,$ that contain exactly five $1$s and exactly three $2$ s , is equal to:

Let $A=\left[\begin{array}{cc}\alpha & -1\\ 6 & \beta\end{array}\right], \alpha>0$, such that $\operatorname{det}(A)=0$ and $\alpha+\beta=1$. If $I$ denotes $2 \times 2$ identity

matrix, then the matrix, $(I+A)^{8}$ is

The largest $n \in N$ such that $3^{n}$ divides $50 !$ Is

Let the focal chord $P Q$ of the parabola $y^{2}=4 x$ make an angle of $60^{\circ}$ with the positive $x$-axis, where $P$ lies in the first quadrant. If the circle, whose one diameter is $P S, S$ being the focus of the parabola, touches the $y$-axis at the point $(0, \alpha)$, then $5 \alpha^{2}$ is equal to:

Let the vertices $Q$ and $R$ of the triangle $P Q R$ lie on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}, Q R=5$ and the

coordinates of the point $P$ be $(0,2,3)$. If the area of the triangle $P Q R$ is $\frac{m}{n}$ then:

If the function $f(x)=2 x^{3}-9 a x^{2}+12 a^{2} x+1$, where a $>0$, attains its local maximum and local

minimum values at $p$ and $q$, respectively, such that $p^{2}=q$, then $f(3)$ is equal to

If $\theta \in[-2 \pi, 2 \pi]$, then the number of solutions of $2 \sqrt{2} \cos ^{2} \theta+(2-\sqrt{6}) \cos \theta-\sqrt{3}=0$, is equal to

For $\alpha, \beta, \gamma \in \mathbb{R}$, if $\lim _{x \rightarrow 0} \frac{x^{2} \sin \alpha x+(\gamma-1) e^{x^{2}}}{\sin 2 x-\beta x}=3$, then $\beta+\gamma-\alpha$ is equal to

Let one focus of the hyperbola $\mathrm{H}: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ be at $(\sqrt{10}, 0)$ and the corresponding directrix be

$x=\frac{9}{\sqrt{10}}$. If $e$ and $I$ respectively are the eccentricity and the length of the latus rectum of H , then $9\left(e^{2}+l\right)$ is equal to

Let $z$ be a complex number such that $|z|=1$. If $\frac{2+k^{2} z}{k+\bar{z}}=k z, k \in \mathbf{R}$, then the maximum distance of $k+i k^{2}$ from the circle $|z-(1+2 i)|=1$ is

Lef $f: \mathbb{R} \rightarrow \mathbb{R}$ be a thrice differentiable odd function satisfying

$f^{\prime}(x) \geq 0, f^{\prime \prime}(x)=f(x), f(0)=0, f^{\prime}(0)=3$. Then $9 f\left(\log _{e} 3\right)$ is equal to $\qquad$ .

If the area of the region $\{(x,y): |4 - x^2| \le y \le x^2, \, y \le 4, \, x \ge 0\}$ is $80\sqrt{2}\alpha - \beta$, where $\alpha, \beta \in \mathbb{N}$, then $\alpha + \beta$ is equal to

Let [•] denote the greatest integer function. If $\int_{0}^{e^{3}}\left[\frac{1}{e^{x-1}}\right] d x=\alpha-\log _{e} 2$, then $\alpha^{3}$ is equal to $\_\_\_\_$ -.

Three distinct numbers are selected randomly from the set $\{1,2,3, \ldots, 40\}$. If the probability, that the selected members are in an increasing G.P., is $\frac{m}{n}, \operatorname{gcd}(m, n)=1$, then $m+n$ is equal to $\_\_\_\_$

The absolute difference between the squares of the radii of the twocircles passing through the point $(-9,4)$ and touching the lines $x+y=3$ and $x-y=3$ , is equal to $\_\_\_\_$.

The battery of a mobile phone is rated as 4.2 V , 5800 mAh . How much energy is stored in it when fully charged?

A river is flowing from west to east direction with speed of $9 \mathrm{~km} \mathrm{~h}^{-1}$. If a boat capable of moving at a maximum speed of $27 \mathrm{~km} \mathrm{~h}^{-1}$ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of $150^{\circ}$ to direction of river flow, then the width of the river is

Moment of inertia of a rod of mass ' $M$ ' and length ' $L$ ' about an axis passing through its center and normal to its length is ' $\alpha$ '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is

Considering Bohr's atomic model for hydrogen atom: (A) The energy of H atom in ground state is same as energy of $\mathrm{He}^{+}$ion in its first excited state. (B) The energy of H atom in ground state is same as that for $\mathrm{Li}^{++}$ion in its second excited state. (C) The energy of H atom in its ground state is same as that of $\mathrm{He}^{+}$ion for its ground state. (D) The energy of $\mathrm{He}^{+}$ion in its first excited state is same as that for $\mathrm{Li}^{++}$ion in its ground state. Choose the correct answer from the options given below:

The equation for real gas is given by $\left(P+\frac{a}{V^{2}}\right)(V-b)=R T$, where $P, V, T$ and $R$

are the pressure, volume, temperature and gas constant, respectively. The dimension of $a b^{-2}$

is equivalent to that of

The relationship between the magnetic susceptibility $(\chi)$ and the magnetic permeability $(\mu)$ is

given by: ( $\mu_{0}$ is the permeability of free space and $\mu_{r}$ is relative permeability)

In an adiabatic process, which of the following statements is true?

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

A light wave is propagating with plane wave fronts of the type $x+y+z=$ constant. The angle made

by the direction of wave propagation with the $x$-axis is

Let $B_{1}$ be the magnitude of magnetic field at centre of a circular coil or radius $R$ carrying current $I$. Let $B_{2}$ be the magnitude of magnetic field at an axial distance ' $x$ ' from the center. For $x: R=4, \frac{B_{2}}{B_{1}}$ is :

A particle is subjected to two simple harmonic motions as: $x_{1}=\sqrt{7} \sin 5 t \mathrm{~cm}$ and

$x_{2}=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}$ where $x$ is displacement and $t$ is

time in seconds. The maximum acceleration of the particle is $x \times 10^{-2} \mathrm{~ms}^{-2}$.

The value of $x$ is :

A small bob of mass 100 mg and charge $+10 \mu \mathrm{C}$ is connected to an insulating string of

length 1 m . It is brought near to an infinitely long non-conducting sheet of charge density ' $\sigma$ ' as

shown in figure. If string subtends and angle of $45^{\circ}$ with the sheet at equilibrium the charge

density of sheet will be. (Given $\varepsilon_{0}=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}$

and acceleration due to gravity, $\left.g=10 \frac{\mathrm{~m}}{\mathrm{~s}^{2}}\right\}$

A monochromatic light is incident on a metallic plate having work function $\phi$. An electron, emitted

normally to the plate from a point $A$ with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the

plate at a point $B$. The distance between $A$ and $B$ is: (Given: The magnitude of charge of an

electron is $e$ and mass is $m, h$ is Planck's constant and $c$ is velocity of light. Take the magnetic

field exists throughout the path of electron)

A point charge $+q$ is placed at the origin. A second point charge $+9 q$ is placed at $(d, 0,0)$ in Cartesian coordinate system. The point in between them where the electric field vanishes is:

A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V . For a $400 \Omega$ resistor connected in series, the zener current is found to be 4 times load current. The load current $\left(I_{L}\right)$ and load resistance $\left(R_{L}\right)$ are :

Consider two infinitely large plane parallel conducting plates as shown below. Two plates are uniformly charged with a surface charge density $+\sigma$ and $-2 \sigma$. The force experienced by a point charge $+q$ placed at the mid point between two plates will be :

A cord of negligible mass is around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest.

If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m , would be :

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in figure. Distance of the image of an object ' $O$ ', is ( $C$ is the center of curvature of the spherical surface and $R$ is the radius of curvature)

A person travelling on a straight line moves with a uniform velocity $v_{1}$ for a distance $x$ and with a uniform velocity $v_{2}$ for the next $\frac{3}{2} x$ distance. The average velocity in this motion is $\frac{50}{7} \mathrm{~m} / \mathrm{s}$. If $v_{1}$ is $5 \mathrm{~m} / \mathrm{s}$ then $v_{2}=$ $\qquad$ $\mathrm{m} / \mathrm{s}$.