JEE Main 2025 — 2 April, Evening Shift

Arrange the following in order of magnitude of work done by the system/on the system at constant temperature. (a) $\mid$ Wreversible| for expansion in infinite stages (b) |Wirreversible for expansion in single state (c) $\left|W_{\text {reversible }}\right|$ for compression in infinite stages (d) |Wirreversible| for compression in single stage Choose the correct answer from the options given below.

Which among the following molecules is (a) involved in $s p^{3} d$ hybridization, (b) has different bond lengths and (c) has lone pair of electrons on the central atom?

Match List-I with List-II.

Choose the correct answer from the options given below.

Formation of $\mathrm{Na}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right]$, a purple coloured complex formed by addition of sodium nitroprusside in sodium carbonate extract of salt indicates the presence of

Electronic configuration of four elements $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $D$ are given below :

(A) $1 s^{2} 2 s^{2} 2 p^{3}$

(B) $1 s^{2} 2 s^{2} 2 p^{4}$

(C) $1 s^{2} 2 s^{2} 2 p^{5}$

(D) $1 s^{2} 2 s^{2} 2 p^{2}$

Which of the following is the correct order of increasing electronegativity (Pauling's scale)?

A tetrapeptide, " $x$ " on complete hydrolysis produced glycine (Gly), alanine (Ala), valine (Val), leucine (Leu) in equimolar proportion each. The number of tetrapeptides (sequences) possible involving each of these amino acids is:

The nature of oxide $\left(\mathrm{TeO}_{2}\right)$ and hydride $\left(\mathrm{TeH}_{2}\right)$ formed by Te, respectively are:

The type of hybridization and the magnetic property of $\left[\mathrm{MnCl}_{6}\right]^{3-}$ are,

The $d$-orbital electronic configuration of the complex among $\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+},\left[\mathrm{CoF}_{6}\right]^{3-},\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$

and $\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ that has the highest CFSE is

In Dumas' method for estimation of nitrogen, $0.5\ \text{g}$ of an organic compound gave $60\;\ \text{mL}$ of nitrogen collected at $300\ \text{K}$ temperature and $715\;\ \text{mm \;Hg}$ pressure. The percentage composition of nitrogen in the compound (Aqueous tension at $300\ \text{K} = 15\;\ \text{mm \;Hg}$) is $\_\_\_\_\_$ %.

In 3,3-dimethylhex-1-en-4-yne, there are $\_\_\_\_\_$ $s p^{3}$, $\_\_\_\_\_$ $s p^{2}$ and $\_\_\_\_\_$ $s p$ hybridised carbon atoms respectively.

When a concentrated solution of sulphanilic acid and 1-naphthylamine is treated with nitrous acid at $273\,\mathrm{K}$ and acidified with acetic acid, the mass (in g) of $0.1\,\mathrm{mol}$ of the product formed is required to be found. (Given molar masses in $\mathrm{g\,mol^{-1}}$: $H=1$, $C=12$, $N=14$, $O=16$, $S=32$)

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process?

Match List -I with List-II.

LIST-I (Reaction)	LIST-II (Name of Reaction)
P.	1. Lucas reaction
Q.	2. Finkelstein reaction
R.	3. Fitting reaction
S.	4. Gatterman reaction

Choose the correct answer from the options given below:

Consider the following reactions. Form these reactions which reaction will give carboxylic acid as a major product?

Choose the correct answer from the options given below:

$x$ ' $g$ of NaCl is added to water in a beaker with a lid. The temperature of the system is raised form $1^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$. Which out of the following plots, is best suited for the change in the molarity ( M ) of the solution with respect to temperature? [Consider the solubility of NaCl remains unchanged over the temperature range]

Consider the following chemical equilibrium of the gas phase reaction at a constant temperature : $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ If $p$ being the total pressure, $K_{p}$ is the pressure equilibrium constant and $\alpha$ is the degree of dissociation, then which of the following is true at equilibrium?

When 1 g each of compounds $A B$ and $A B_{2}$ are dissolved in 15 g of water separately, they increased the boiling point of water by 2.7 K and 1.5 K respectively. The atomic mass of A (in amu) is $\_\_\_\_\_$ $\times 10^{-1}$ (Nearest integer) (Given: Molal boiling point elevation constant is 0.5 $\mathrm{K} \mathrm{kg} \mathrm{mol}^{-1}$ )

$0.2 \%(\mathrm{w} / \mathrm{v})$ solution of NaOH is measured to have resistivity $870.0 \mathrm{~m} \Omega \mathrm{~m}$. The molar conductivity of the solution will be $\_\_\_\_\_$ $\times 10^{2} \mathrm{mS} \mathrm{dm}^{2} \mathrm{~mol}^{-1}$. (Nearest integer)

For the reaction $A \rightarrow B$ the following graph was obtained. The time required (in seconds) for the concentration of $A$ to reduce to $2.5 \mathrm{~g} \mathrm{~L}^{-1}$ (if the initial concentration of $A$ was $50 \mathrm{~g} \mathrm{~L}^{-1}$ ) is $\_\_\_\_\_$ . (Nearest integer) Given: $\log 2=0.3010$

The spin-only magnetic moment value of $\mathrm{M}^{\mathrm{n+}}$ ion formed among $\mathrm{Ni}, \mathrm{Zn}, \mathrm{Mn}$ and Cu that has the least

enthalpy of atomisation is $\_\_\_\_\_$ . (in nearest integer) Here $n$ is equal to the number of diamagnetic complexes

among $\mathrm{K}_{2}\left[\mathrm{NiCl}_{4}\right]$, $\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Cl}_{2}, \mathrm{~K}_{3}\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]$ and $\left[\mathrm{Cu}\left(\mathrm{PPh}_{3}\right)_{3} \mathrm{I}\right]$

Consider the above sequence of reactions. 151 g of 2-bromopentane is made to react. Yield of major product P is

$80 \%$ whereas Q is $100 \%$. Mass of product Q obtained is $\_\_\_\_\_$ g. (Given molar mass in

$\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{O}: 16, \mathrm{Br}$ : 80)

If $\lim _{x \rightarrow 0} \frac{\cos (2 x)+a \cos (4 x)-b}{x^{4}}$ is finite, then $(a+b)$ is equal to :

If $\sum_{r=0}^{10}\left(\frac{10^{r+1}-1}{10^{r}}\right) \cdot{ }^{11} C_{r+1}=\frac{\alpha^{11}-11^{11}}{10^{10}}$, then $\alpha$ is equal to:

Let $(a, b)$ be the point of intersection of the curve $x^{2}$ $=2 y$ and the straight line $y-2 x-6=0$ in the second quadrant. Then the integral $I=\int_{a}^{b} \frac{9 x^{2}}{1+5^{x}} d x$ is equal to:

If $\theta \in\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]$, then the number of solutions of $\sqrt{3} \operatorname{cosec}^{2} \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0$, is

equal to

If the mean and the variance of $6,4, a, 8, b, 12,10$, 13 are 9 and 9.25 respectively, then $a+b+a b$ is equal

to :

If the domain of the function $f(x)=\frac{1}{\sqrt{10+3 x-x^{2}}}+\frac{1}{\sqrt{x+|x|}}$ is $(a, b)$, then $(1+a)^{2}+b^{2}$ is

equal to :

Given three indentical bags each containing 10 balls, whose colours are as follows :

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is $p$ and if the ball is Green, the probability that it is from bag III is $q$, then the value of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is :

The line $L_{1}$ is parallel to the vector $\vec{a}=-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and passes through the point $(7,6,2)$ and the line $L_{2}$ is parallel to the vector $\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}$ and passes through the point $(5,3,4)$. The shortest distance between the lines $L_{1}$ and $L_{2}$ is:

The number of ways, in which the letters $A, B, C, D$, $E$ can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is:

Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function. If $10 \int_{1}^{x} f(t) d t=5 x f(x)-x^{5}-9$ for all

$x \geq 1$, then the value of $f(3)$ is :

If the image of the point $P(1,0,3)$ in the line joining the points $A(4,7,1)$ and $B(3,5,3)$ is $Q(\alpha, \beta, \gamma)$, then

$\alpha+\beta+\gamma$ is equal to :

Let the point $P$ of the focal chord $P Q$ of the parabola $y^{2}=16 x$ be $(1,-4)$. If the focus of the parabola divides the chord $P Q$ in the ratio $m: n, g c d(m, n)=$ 1 , then $m^{2}+n^{2}$ is equal to:

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is:

Let $\vec{a}=2 \hat{i}-3 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and a vector $\vec{c}$ be such that $(\vec{a}-\vec{c}) \times \vec{b}=-18 \hat{i}-3 \hat{j}+12 \hat{k}$

and $\vec{a} \cdot \vec{c}=3$. If $\vec{b} \times \vec{c}=\vec{d}$, then $|\vec{a} \cdot \vec{d}|$ is equal to :

$4 \int_{0}^{1}\left(\frac{1}{\sqrt{3+x^{2}}+\sqrt{1+x^{2}}}\right) d x-3 \log _{e}(\sqrt{3})$ is equal to:

The number of terms of an A.P. is even, the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the A.P. is :

If the system of equations

$2 x+\lambda y+3 z=5$

$3 x+2 y-z=7$

$4 x+5 y+\mu z=9$

has infinitely many solutions, then $\left(\lambda^{2}+\mu^{2}\right)$ is equal to

Let $A$ be a $3 \times 3$ real matrix such that $A^{2}(A-2 I)-$ $4(A-I)=0$, where $I$ and $O$ are the identity and

null matrices, respectively. If $A^{5}=\alpha A^{2}+\beta A+\gamma$ l, where $\alpha, \beta$ and $\gamma$ are real constants, then $\alpha+\beta+\gamma$ is equal to:

Let the area of the triangle formed by a straight line $L: x+b y+c=0$ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line $L$ makes an angle of $45^{\circ}$ with the positive $x$ axis, then the value of $b^{2}+c^{2}$ is:

If the sum of the first 10 terms of the series $\frac{4.1}{1+4.1^{4}}+\frac{4.2}{1+4.2^{4}}+\frac{4.3}{1+4.3^{4}}+\ldots$. is $\frac{m}{n}, \quad$ where

$\operatorname{gcd}(m, n)$, then $m+n$ is equal to $\qquad$ .

If the set of all $a \in R-\{1\}$, for which the roots of the equation $(1-a) x^{2}+2(a-3) x+9=0$ are

positive is $(-\infty,-\alpha] \cup[\beta, \gamma)$, then $2 \alpha+\beta+\gamma$ is equal to $\_\_\_\_$ .

If $y=\cos \left(\frac{\pi}{3}+\cos ^{-1} \frac{x}{2}\right)$, then $(x-y)^{2}+3 y^{2}$ is equal to

Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}+2 y \sec ^{2} x=2 \sec ^{2} x+3 \tan x \cdot \sec ^{2} x$

such that $y(0)=\frac{5}{4}$. Then $12\left(y\left(\frac{\pi}{4}\right)-e^{-2}\right)$ is equal to $\qquad$

Let $A(4,-2), B(1,1)$ and $C(9,-3)$ be the vertices of a triangle $A B C$. Then the maximum area of the parallelogram $A F D E$, formed with vertices $D, E$ and $F$ on the sides $B C, C A$ and $A B$ of the triangle $A B C$ respectively, is $\qquad$ -

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

Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.

Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.

In the light of the above statements, choose the most appropriate answer from the options given below.

Energy released when two deuterons $\left({ }_{1} \mathrm{H}^{2}\right)$ fuse to form a helium nucleus

$\left({ }_{2} \mathrm{He}^{4}\right)$ is (Given: Binding energy per nucleon

of ${ }_{1} \mathrm{H}^{2}=1.1 \mathrm{MeV}$ and binding energy per nucleon

of ${ }_{2} \mathrm{He}^{4}=7.0 \mathrm{MeV}$ )

The moment of inertia of a circular ring of mass $M$ and diameter $r$ about a tangential axis lying in the

plane of the ring is

Consider a circular loop that is uniformly charged and has a radius $a \sqrt{2}$. Find the position along

the positive $z$-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in $x y$ plane at the origin

Two water drops each of radius ' $r$ ' coalesce to form a bigger drop. If ' $T$ is the surface tension, the surface energy released in this process is

If $\mu_{0}$ and $\varepsilon_{0}$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_{0} \varepsilon_{0}}\right)$ is

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

A bi-convex lens has radius of curvature of both the surfaces same as $1 / 6 \mathrm{~cm}$. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides ( $R_{1} \neq R_{2}$ ), without any change in lens power then possible combination of $R_{1}$ and $R_{2}$ is

Given a charge $q$, current $I$ and permeability of vacuum $\mu_0$. Which of the following quantity has the dimension of momentum?

A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$. The distance travelled and displacement, respectively, are

An electron with mass ' $m$ ' with an initial velocity $(t=0) \vec{v}=v_{0} \hat{i}\left(v_{0}>0\right)$ enters a magnetic field $\vec{B}=B_{0} \hat{j}$. If the initial de-Broglie wavelength at $t=0$ is $\lambda_{0}$ then its value after time ' $t$ ' would be:

A solenoid having area $A$ and length $I$ is filled with a material having relative permeability 2 . The magnetic energy stored in the solenoid is:

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is:

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$-direction in 0.3 sec . The crest $P$ is at $x=0$ at $t=0 \mathrm{sec}$ and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?

In a moving coil galvanometer, two moving coils $M_{1}$ and $M_{2}$ have the following particulars :

$R_{1}=5 \Omega, N_{1}=15, A_{1}=3.6 \times 10^{-3} \mathrm{~m}^{2}, B_{1}=0.25 \mathrm{~T}$

$R_{2}=7 \Omega, N_{2}=21, A_{2}=1.8 \times 10^{-3} \mathrm{~m}^{2}, B_{2}=0.50 \mathrm{~T}$

Assuming that torsional constant of the springs are same for both coils, what will be the ratio

of voltage sensitivity of $M_{1}$ and $M_{2}$ ?

Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $T_{1}$ to $T_{2}$ is proportional to $\left(T_{2}-T_{1}\right)$. Choose the correct answer from the options given below:

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of

$\mathrm{Li}^{++}$ion in its ground state is given by $\frac{1}{X} a_{0}$,

where $X=$ $\qquad$ -. (Where $a_{0}$, is the first Bohr's radius.)

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of $2 \mathrm{rad} / \mathrm{s}^{2}$. Moment of inertia of the wheel is $\qquad$ $\mathrm{kgm}^{2}$. (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^{2}$ )

The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is $\qquad$ m.

The internal energy of air in $4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}$ sized room at 1 atmospheric pressure will be $\qquad$ $\times 10^{6} \mathrm{~J}$. (Consider air as diatomic molecule)

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to

$60^{\circ}$. The refractive index of the prism material is $\sqrt{2}$.

The angle of incidence (in degrees) is $\qquad$ -

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km

from the earth's surface. Kinetic energy of the satellite in this orbit is $\qquad$

$\times 10^{10} \mathrm{~J}$. (Mass of earth $=6 \times 10^{24} \mathrm{~kg}$,

Radius of earth $=6.4 \times 10^{6} \mathrm{~m}$, Gravitational constant

$=6.67 \times 10^{-11}$ $\mathrm{Nm}^{2} \mathrm{~kg}^{-2}$ )