JEE Main 4 April 2025 Shift 1 Question Paper

Question 1

Let $f, g:(1,\infty)	o\mathbb{R}$ be defined as $f(x)=\dfrac{2x+3}{5x+2}$ and $g(x)=\dfrac{2-3x}{1-x}$. If the range of the function $f\circ g:[2,4]	o\mathbb{R}$ is $[\alpha,\beta]$, then $\dfrac{1}{\beta-\alpha}$ is equal to

Accepted Answer

(D) 56

Answer

(A) 68

Answer

(B) 29

Answer

(C) 2

Question 2

Consider the sets $A=\{(x,y)\in\mathbb{R}	imes\mathbb{R}:x^2+y^2=25\}$, $B=\{(x,y)\in\mathbb{R}	imes\mathbb{R}:x^2+9y^2=144\}$, $C=\{(x,y)\in\mathbb{Z}	imes\mathbb{Z}:x^2+y^2\le4\}$, and $D=A\cap B$. The total number of one-one functions from the set $D$ to the set $C$ is:

Accepted Answer

(C) 17160

Answer

(A) 15120

Answer

(B) 19320

Answer

(D) 18290

Question 3

Let $A=\{1,6,11,16,\ldots\}$ and $B=\{9,16,23,30,\ldots\}$ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then $n(A\cup B)$ is

Accepted Answer

(C) 3761

Answer

(A) 3814

Answer

(B) 4027

Answer

(D) 4003

Question 4

For an integer $n\ge2$, if the arithmetic mean of all coefficients in the binomial expansion of $(x+y)^{2n-3}$ is 16, then the distance of the point $P(2n-1, n^2-4n)$ from the line $x+y=8$ is:

Accepted Answer

(D) $3\sqrt{2}$

Answer

(A) $\sqrt{2}$

Answer

(B) $2\sqrt{2}$

Answer

(C) $5\sqrt{2}$

Question 5

The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is:

Accepted Answer

(A) $\dfrac{129}{182}$

Answer

(B) $\dfrac{103}{182}$

Answer

(C) $\dfrac{17}{26}$

Answer

(D) $\dfrac{19}{26}$

Question 6

Let the shortest distance between the lines $\dfrac{x-3}{3}=\dfrac{y-\alpha}{-1}=\dfrac{z-3}{1}$ and $\dfrac{x+3}{-3}=\dfrac{y+7}{2}=\dfrac{z-\beta}{4}$ be $3\sqrt{30}$. Then the positive value of $5\alpha+\beta$ is:

Accepted Answer

(B) 46

Answer

(A) 42

Answer

(C) 48

Answer

(D) 40

Question 7

If $\displaystyle\lim_{x	o1}\dfrac{(x-1)(6+\lambda\cos(x-1))+\mu\sin(1-x)}{(x-1)^3}=-1$, where $\lambda,\mu\in\mathbb{R}$, then $\lambda+\mu$ is equal to

Accepted Answer

(A) 18

Answer

(B) 20

Answer

(C) 19

Answer

(D) 17

Question 8

Let $f:[0,\infty)	o\mathbb{R}$ be differentiable function such that $f(x)=1-2x+\displaystyle\int_0^x e^{x-t}f(t)\,dt$ for all $x\in[0,\infty)$. Then the area of the region bounded by $y=f(x)$ and the coordinate axes is

Accepted Answer

(B) $\dfrac{1}{2}$

Answer

(A) $\sqrt{5}$

Answer

(C) $\sqrt{2}$

Answer

(D) 2

Question 9

Let $A$ and $B$ be two distinct points on the line $L:\dfrac{x-6}{3}=\dfrac{y-7}{2}=\dfrac{z-7}{-2}$. Both $A$ and $B$ are at a distance $2\sqrt{17}$ from the foot of perpendicular drawn from the point $(1,2,3)$ on the line $L$. If $O$ is the origin, then $\overrightarrow{OA}\cdot\overrightarrow{OB}$ is equal to:

Accepted Answer

(B) 47

Answer

(A) 49

Answer

(C) 21

Answer

(D) 62

Question 10

Let $f:\mathbb{R}	o\mathbb{R}$ be a continuous function satisfying $f(0)=1$ and $f(2x)-f(x)=x$ for all $x\in\mathbb{R}$. If $\displaystyle\lim_{n	o\infty}\left\{f(x)-f\left(\dfrac{x}{2^n}ight)ight\}=G(x)$, then $\displaystyle\sum_{r=1}^{10}G(r^2)$ is equal to:

Accepted Answer

(B) 385

Answer

(A) 540

Answer

(C) 420

Answer

(D) 215

Question 11

$1+3+5^2+7+9^2+\ldots$ upto 40 terms is equal to

Accepted Answer

(B) 41880

Answer

(A) 43890

Answer

(C) 33980

Answer

(D) 40870

Question 12

In the expansion of $\left(\sqrt[3]{2}+\dfrac{1}{\sqrt[3]{3}}ight)^n$, $n\in\mathbb{N}$, if the ratio of $15^{	ext{th}}$ term from the beginning to the $15^{	ext{th}}$ term from the end is $\dfrac{1}{6}$, then the value of ${}^nC_3$ is:

Accepted Answer

(C) 2300

Answer

(A) 4060

Answer

(B) 1040

Answer

(D) 4960

Question 13

Considering the principal values of the inverse trigonometric functions, $\sin^{-1}\left(\dfrac{\sqrt{3}}{2}x+\dfrac{1}{2}\sqrt{1-x^2}\right)$, $-\dfrac{1}{2}<x<\dfrac{1}{\sqrt{2}}$, is equal to:

Accepted Answer

(B) $\dfrac{\pi}{6}+\sin^{-1}x$

Answer

(A) $\dfrac{\pi}{4}+\sin^{-1}x$

Answer

(C) $-\dfrac{5\pi}{6}-\sin^{-1}x$

Answer

(D) $\dfrac{5\pi}{6}-\sin^{-1}x$

Question 14

Consider two vectors $\vec{u}=3\hat{i}-\hat{j}$ and $\vec{v}=2\hat{i}+\hat{j}-\lambda\hat{k}$, $\lambda>0$. The angle between them is given by $\cos^{-1}\left(\dfrac{\sqrt{5}}{2\sqrt{7}}\right)$. Let $\vec{v}=\vec{v_1}+\vec{v_2}$, where $\vec{v_1}$ is parallel to $\vec{u}$ and $\vec{v_2}$ is perpendicular to $\vec{u}$. Then the value of $|\vec{v_1}|^2+|\vec{v_2}|^2$ is equal to:

Accepted Answer

(B) 14

Answer

(A) $\dfrac{23}{2}$

Answer

(C) $\dfrac{25}{2}$

Answer

(D) 10

Question 15

Let the three sides of a triangle are on the lines $4x-7y+10=0$, $x+y=5$ and $7x+4y=15$. Then the distance of its orthocentre from the orthocentre of the triangle formed by the lines $x=0$, $y=0$ and $x+y=1$ is

Accepted Answer

(B) $\sqrt{5}$

Answer

(A) 5

Answer

(C) $\sqrt{20}$

Answer

(D) 20

Question 16

The value of $\displaystyle\int_{-1}^{1}\dfrac{\left(1+\sqrt{|x|-x}\right)e^x+\left(\sqrt{|x|-x}\right)e^{-x}}{e^x+e^{-x}}\,dx$ is equal to:

Accepted Answer

(D) $1+\dfrac{2\sqrt{2}}{3}$

Answer

(A) $3-\dfrac{2\sqrt{2}}{3}$

Answer

(B) $2+\dfrac{2\sqrt{2}}{3}$

Answer

(C) $1-\dfrac{2\sqrt{2}}{3}$

Question 17

The length of the latus-rectum of the ellipse, whose foci are $(2,5)$ and $(2,-3)$ and eccentricity is $\dfrac{4}{5}$, is

Accepted Answer

(D) $\dfrac{18}{5}$

Answer

(A) $\dfrac{6}{5}$

Answer

(B) $\dfrac{50}{3}$

Answer

(C) $\dfrac{10}{3}$

Question 18

Consider the equation $x^2+4x-n=0$, where $n\in[20,100]$ is a natural number. Then the number of all distinct values of $n$, for which the given equation has integral roots, is equal to

Accepted Answer

(C) 6

Answer

(A) 7

Answer

(B) 8

Answer

(D) 5

Question 19

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is

Accepted Answer

(B) $\dfrac{28}{75}$

Answer

(A) $\dfrac{11}{15}$

Answer

(C) $\dfrac{2}{15}$

Answer

(D) $\dfrac{3}{5}$

Question 20

If $10\sin^4	heta+15\cos^4	heta=6$, then the value of $\dfrac{27\,\mathrm{cosec}^6	heta+8\sec^6	heta}{16\sec^8	heta}$ is:

Accepted Answer

(A) $\dfrac{2}{5}$

Answer

(B) $\dfrac{3}{4}$

Answer

(C) $\dfrac{3}{5}$

Answer

(D) $\dfrac{1}{5}$

Question 21

If the area of the region $\{(x,y):|x-5|\le y\le4\sqrt{x}\}$ is $A$, then $3A$ is equal to ______.

Accepted Answer

368

Question 22

Let $A=\begin{bmatrix}\cos	heta & 0 & -\sin	heta\0 & 1 & 0\\sin	heta & 0 & \cos	heta\end{bmatrix}$. If for some $	heta\in(0,\pi)$, $A^2=A^T$, then the sum of the diagonal elements of the matrix $(A+I)^3+(A-I)^3-6A$ is equal to ______.

Accepted Answer

6

Question 23

Let $A=\{z\in\mathbb{C}:|z-2-i|=3\}$, $B=\{z\in\mathbb{C}:\mathrm{Re}(z-iz)=2\}$ and $S=A\cap B$. Then $\displaystyle\sum_{z\in S}|z|^2$ is equal to ______.

Accepted Answer

22

Question 24

Let $C$ be the circle $x^2+(y-1)^2=2$, $E_1$ and $E_2$ be two ellipses whose centres lie at the origin and major axes lie on $x$-axis and $y$-axis respectively. Let the straight line $x+y=3$ touch the curves $C$, $E_1$ and $E_2$ at $P(x_1,y_1)$, $Q(x_2,y_2)$ and $R(x_3,y_3)$ respectively. Given that $P$ is the mid-point of the line segment $QR$ and $PQ=\dfrac{2\sqrt{2}}{3}$, the value of $9(x_1y_1+x_2y_2+x_3y_3)$ is equal to ______.

Accepted Answer

46

Question 25

Let $m$ and $n$ be the number of points at which the function $f(x)=\max\{x,x^3,x^5,\ldots,x^{21}\}$, $x\in\mathbb{R}$, is not differentiable and not continuous, respectively. Then $m+n$ is equal to ______.

Accepted Answer

3

Question 26

The mean free path and the average speed of oxygen molecules at 300 K and 1 atm are $3	imes10^{-7}$ m and 600 m/s, respectively. Find the frequency of its collisions.

Accepted Answer

(C) $2	imes10^{9}$/s

Answer

(A) $2	imes10^{10}$/s

Answer

(B) $9	imes10^{9}$/s

Answer

(D) $5	imes10^{9}$/s

Question 27

A small mirror of mass $m$ is suspended by a massless thread of length $l$. Then the small angle through which the thread will be deflected when a short pulse of laser of energy $E$ falls normal on the mirror ($c$ = speed of light in vacuum and $g$ = acceleration due to gravity)

Accepted Answer

(D) $	heta=\dfrac{2E}{mc\sqrt{gl}}$

Answer

(A) $	heta=\dfrac{3E}{4mc\sqrt{gl}}$

Answer

(B) $	heta=\dfrac{E}{mc\sqrt{gl}}$

Answer

(C) $	heta=\dfrac{E}{2mc\sqrt{gl}}$

Question 28

Two liquids A and B have $	heta_A$ and $	heta_B$ as contact angles in a capillary tube. If $K=\dfrac{\cos	heta_A}{\cos	heta_B}$, then identify the correct statement:

Accepted Answer

(C) $K$ is negative, then liquid A has concave meniscus and liquid B has convex meniscus.

Answer

(A) $K$ is negative, then liquid A and liquid B have convex meniscus.

Answer

(B) $K$ is negative, then liquid A and liquid B have concave meniscus.

Answer

(D) $K$ is zero, then liquid A has convex meniscus and liquid B has concave meniscus.

Question 29

Which of the following are correct expression for torque acting on a body? A. $\vec{	au}=\vec{r}	imes\vec{L}$  B. $\vec{	au}=\dfrac{d}{dt}(\vec{r}	imes\vec{p})$  C. $\vec{	au}=\vec{r}	imes\dfrac{d\vec{p}}{dt}$  D. $\vec{	au}=I\vec{\alpha}$  E. $\vec{	au}=\vec{r}	imes\vec{F}$  ($\vec{r}$ = position vector; $\vec{p}$ = linear momentum; $\vec{L}$ = angular momentum; $\vec{\alpha}$ = angular acceleration; $I$ = moment of inertia; $\vec{F}$ = force; $t$ = time). Choose the correct answer from the options given below:

Accepted Answer

(C) B, C, D and E Only

Answer

(A) B, D and E Only

Answer

(B) C and D Only

Answer

(D) A, B, D and E Only

Question 30

In a Young's double slit experiment, the slits are separated by 0.2 mm. If the slits separation is increased to 0.4 mm, the percentage change of the fringe width is:

Accepted Answer

(C) 50%

Answer

(A) 0%

Answer

(B) 100%

Answer

(D) 25%

Question 31

An alternating current is represented by the equation, $i=100\sqrt{2}\sin(100\pi t)$ ampere. The RMS value of current and the frequency of the given alternating current are

Accepted Answer

(C) 100 A, 50 Hz

Answer

(A) $100\sqrt{2}$ A, 100 Hz

Answer

(B) $\dfrac{100}{\sqrt{2}}$ A, 100 Hz

Answer

(D) $50\sqrt{2}$ A, 50 Hz

Question 32

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^P L^Q T^R A^S$, where value of $Q$ and $R$ are

Accepted Answer

(D) $(1,-1)$

Answer

(A) $(3,-5)$

Answer

(B) $(-2,2)$

Answer

(C) $(-2,1)$

Question 33

When an object is placed 40 cm away from a spherical mirror an image of magnification $\dfrac{1}{2}$ is produced. To obtain an image with magnification of $\dfrac{1}{3}$, the object is to be moved:

Accepted Answer

(A) 40 cm away from the mirror.

Answer

(B) 80 cm away from the mirror.

Answer

(C) 20 cm towards the mirror.

Answer

(D) 20 cm away from the mirror.

Question 34

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: In photoelectric effect, on increasing the intensity of incident light the stopping potential increases.
Reason R: Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(B) A is false but R is true

Answer

(A) Both A and R are true but R is NOT the correct explanation of A

Answer

(C) A is true but R is false

Answer

(D) Both A and R are true and R is the correct explanation of A

Question 35

If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass $m$ having position vector $\vec{r}=a(\hat{i}\cos\omega t+\hat{j}\sin\omega t)$. The direction of force is

Accepted Answer

(A) Opposite to the direction of $\vec{r}$

Answer

(B) Opposite to the direction of $\vec{L}$

Answer

(C) Opposite to the direction of $\vec{P}$

Answer

(D) Opposite to the direction of $\vec{L}	imes\vec{P}$

Question 36

A body of mass $m$ is suspended by two strings making angles $	heta_1$ and $	heta_2$ with the horizontal ceiling with tensions $T_1$ and $T_2$ simultaneously. $T_1$ and $T_2$ are related by $T_1=\sqrt{3}\,T_2$. The angles $	heta_1$ and $	heta_2$ are

Accepted Answer

(B) $	heta_1=60^\circ$, $	heta_2=30^\circ$ with $T_2=\dfrac{mg}{2}$

Answer

(A) $	heta_1=30^\circ$, $	heta_2=60^\circ$ with $T_2=\dfrac{3mg}{4}$

Answer

(C) $	heta_1=45^\circ$, $	heta_2=45^\circ$ with $T_2=\dfrac{3mg}{4}$

Answer

(D) $	heta_1=30^\circ$, $	heta_2=60^\circ$ with $T_2=\dfrac{4mg}{5}$

Question 37

Current passing through a wire as function of time is given as $I(t)=0.02\,t+0.01$ A. The charge that will flow through the wire from $t=1$ s to $t=2$ s is:

Accepted Answer

(D) 0.04 C

Answer

(A) 0.06 C

Answer

(B) 0.02 C

Answer

(C) 0.07 C

Question 38

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\dfrac{1}{2}mgR$, where $R$ is the radius of earth.
Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
In the light of the above statements, choose the correct answer from the option given below:

Accepted Answer

(A) A False but R is true

Answer

(B) Both A and R are true and R is the correct explanation of A

Answer

(C) A is true but R is false

Answer

(D) Both A and R are true but R is NOT the correct explanation of A

Question 39

The Boolean expression $Y=A\bar{B}C+\bar{A}\bar{C}$ can be realised with which of the following gate configurations. A. One 3-input AND gate, 3 NOT gates and one 2-input OR gate, One 2-input AND gate, B. One 3-input AND gate, 1 NOT gate and one 2-input NOR gate and one 2-input OR gate C. 3-input OR gate, 3 NOT gates and one 2-input AND gate. Choose the correct answer from the options given below

Accepted Answer

(B) A, B Only

Answer

(A) B, C Only

Answer

(C) A, B, C Only

Answer

(D) A, C Only

Question 40

In an experiment with a closed organ pipe, it is filled with water by $\dfrac{1}{5}$th of its volume. The frequency of the fundamental note will change by

Accepted Answer

(A) 25%

Answer

(B) 20%

Answer

(C) $-20$%

Answer

(D) $-25$%

Question 41

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $	heta_1$ and $	heta_2$ from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

Accepted Answer

(D) $	heta_1 l_2=	heta_2 l_1$

Answer

(A) $	heta_1 l_1^2=	heta_2 l_2^2$

Answer

(B) $	heta_1 l_1=	heta_2 l_2$

Answer

(C) $	heta_1 l_1=	heta_2 l_2^2$

Question 42

Two infinite identical charged sheets and a charged spherical body of charge density $\rho$ are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is:

Accepted Answer

(C) $\vec{E}_C
e\vec{E}_D$; $\vec{E}_A>\vec{E}_B$

Answer

(A) $\vec{E}_A=\vec{E}_B$; $\vec{E}_C=\vec{E}_D$

Answer

(B) $\vec{E}_A>\vec{E}_B$; $\vec{E}_C=\vec{E}_D$

Answer

(D) $|\vec{E}_A|=|\vec{E}_B|$; $\vec{E}_C>\vec{E}_D$

Question 43

Two small spherical balls of mass 10 g each with charges $-2\,\mu C$ and $2\,\mu C$, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of $100\,\mu C/m^2$ such that length of rod makes an angle of $30^\circ$ with electric field generated by charge sheet. Net torque acting on the rod is: (Take $\varepsilon_0:8.85	imes10^{-12}$ C$^2$/Nm$^2$)

Accepted Answer

(B) 1.12 Nm

Answer

(A) 112 Nm

Answer

(C) 2.24 Nm

Answer

(D) 11.2 Nm

Question 44

Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius $5^{	ext{th}}$ orbit of the electron in $Li^{2+}$ and $He^{+}$ is

Accepted Answer

(D) $\dfrac{2}{3}$

Answer

(A) $\dfrac{3}{2}$

Answer

(B) $\dfrac{4}{9}$

Answer

(C) $\dfrac{9}{4}$

Question 45

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is $\sqrt{\dfrac{x}{5}}$ where $x=$ ______.

Accepted Answer

4

Question 46

Two slabs with square cross section of different materials (1, 2) with equal sides ($l$) and thickness $d_1$ and $d_2$ such that $d_2=2d_1$ and $l>d_2$. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is $	heta_2=2	heta_1$. If the shear moduli of material 1 is $4	imes10^9$ N/m$^2$, then shear moduli of material 2 is $x	imes10^9$ N/m$^2$, where value of $x$ is ______.

Accepted Answer

1

Question 47

Distance between object and its image (magnified by $-\dfrac{1}{3}$) is 30 cm. The focal length of the mirror used is $\left(\dfrac{x}{4}\right)$ cm, where magnitude of value of $x$ is ______.

Accepted Answer

45

Question 48

Four capacitor each of capacitance 16 $\mu$F are connected as shown in the figure. The capacitance between points A and B is ______ (in $\mu$F).

Accepted Answer

64

Question 49

Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $\dfrac{1}{\sqrt{2}}$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is ______ mV.

Accepted Answer

10

Question 50

XY is the membrane / partition between two chambers 1 and 2 containing sugar solutions of concentration $c_1$ and $c_2$ ($c_1>c_2$) mol L$^{-1}$ (shown in the figure). For the reverse osmosis to take place identify the correct condition. (Here $p_1$ and $p_2$ are pressures applied on chamber 1 and 2) (A) Membrane/Partition; Cellophane, $p_1>\pi$ (B) Membrane/Partition; Porous, $p_2>\pi$ (C) Membrane/Partition; Parchment paper, $p_1>\pi$ (D) Membrane/Partition; Cellophane, $p_2>\pi$. Choose the correct answer from the option given below:

Accepted Answer

(C) A and C only

Answer

(A) B and D only

Answer

(B) A and D only

Answer

(D) C only

Question 51

Let us consider a reversible reaction at temperature, T. In this reaction, both $\Delta H$ and $\Delta S$ were observed to have positive values. If the equilibrium temperature is $T_e$, then the reaction becomes spontaneous at:

Accepted Answer

(C) $T>T_e$

Answer

(A) $T=T_e$

Answer

(B) $T_e>T$

Answer

(D) $T_e=5T$

Question 52

Which of the following molecules(s) show/s paramagnetic behavior? (A) $O_2$ (B) $N_2$ (C) $F_2$ (D) $S_2$ (E) $Cl_2$. Choose the correct answer from the options given below:

Accepted Answer

(D) A & D only

Answer

(A) B only

Answer

(B) A & C only

Answer

(C) A & E only

Question 53

Aldol condensation is a popular and classical method to prepare $\alpha,\beta$-unsaturated carbonyl compounds. This reaction can be both intermolecular and intramolecular. Predict which one of the following is not a product of intramolecular aldol condensation?

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 54

One mole of an ideal gas expands isothermally and reversibly from 10 dm$^3$ to 20 dm$^3$ at 300 K. $\Delta U$, $q$ and work done in the process respectively are: (Given: $R=8.3$ JK$^{-1}$ mol$^{-1}$, $\ln 10=2.3$, $\log 2=0.30$, $\log 3=0.48$)

Accepted Answer

(D) 0, 1.718 kJ, $-1.718$ kJ

Answer

(A) 0, 21.84 kJ, $-1.26$ kJ

Answer

(B) 0, $-17.18$ kJ, 1.718 J

Answer

(C) 0, 21.84 kJ, 21.84 kJ

Question 55

Which one of the following complexes will have $\Delta_0=0$ and $\mu=5.96$ B.M.?

Accepted Answer

(D) $[Mn(SCN)_6]^{4-}$

Answer

(A) $[Fe(CN)_6]^{4-}$

Answer

(B) $[Co(NH_3)_6]^{3+}$

Answer

(C) $[FeF_6]^{4-}$

Question 56

For $A_2+B_2\rightleftharpoons 2AB$, $E_a$ for forward and backward reaction are 180 and 200 kJ mol$^{-1}$ respectively. If catalyst lowers $E_a$ for both reaction by 100 kJ mol$^{-1}$. Which of the following statement is correct?

Accepted Answer

(A) Catalyst does not alter the Gibbs energy change of a reaction.

Answer

(B) Catalyst can cause non-spontaneous reactions to occur.

Answer

(C) The enthalpy change for the reaction is $+20$ kJ mol$^{-1}$.

Answer

(D) The enthalpy change for the catalysed reaction is different from that of uncatalysed reaction.

Question 57

Rate law for a reaction between A and B is given by $R=k[A]^n[B]^m$. If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction $\left(\dfrac{r_2}{r_1}\right)$ is:

Accepted Answer

(A) $2^{(n-m)}$

Answer

(B) $(n-m)$

Answer

(C) $(m+n)$

Answer

(D) $\dfrac{1}{2^{m+n}}$

Question 58

Number of stereoisomers possible for the complexes, $[CrCl_3(py)_3]$ and $[CrCl_2(ox)_2]^{3-}$ are respectively (py = pyridine, ox = oxalate)

Accepted Answer

(C) 2 & 3

Answer

(A) 3 & 3

Answer

(B) 2 & 2

Answer

(D) 1 & 2

Question 59

The major product (A) formed when nitrobenzene is treated with the following reagents in sequence — (i) Sn, HCl; (ii) Ac$_2$O, Pyridine; (iii) Br$_2$, AcOH; (iv) NaOH(aq) — is:

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 60

On charging the lead storage battery, the oxidation state of lead changes from $x_1$ to $y_1$ at the anode and from $x_2$ to $y_2$ at the cathode. The values of $x_1, y_1, x_2, y_2$ are respectively:

Accepted Answer

(B) $+2, 0, +2, +4$

Answer

(A) $+4, +2, 0, +2$

Answer

(C) $0, +2, +4, +2$

Answer

(D) $+2, 0, 0, +4$

Question 61

Given below are two statements:
Statement I: Nitrogen forms oxides with $+1$ to $+5$ oxidation states due to the formation of $p\pi-p\pi$ bond with oxygen.
Statement II: Nitrogen does not form halides with $+5$ oxidation state due to the absence of d-orbital in it. In the light of given statements, choose the correct answer from the options below:

Accepted Answer

(D) Both Statement I and Statement II are true

Answer

(A) Statement I is true but Statement II is false

Answer

(B) Both Statement I and Statement II are false

Answer

(C) Statement I is false but Statement II is true

Question 62

Benzene is treated with oleum to produce compound (X) which when further heated with molten sodium hydroxide followed by acidification produces compound (Y). The compound Y is treated with zinc metal to produce compound (Z). Identify the structure of compound (Z) from the following option.

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 63

Identify the pair of reactants that upon reaction, with elimination of HCl will give rise to the dipeptide Gly-Ala.

Accepted Answer

(A) $NH_2-CH_2-COCl$ and $NH_2-CH(CH_3)-COOH$

Answer

(B) $NH_2-CH_2-COCl$ and $\overset{\oplus}{N}H_3-CH(CH_3)-COCl$

Answer

(C) $NH_2-CH_2-COOH$ and $NH_2-CH(CH_3)-COCl$

Answer

(D) $NH_2-CH_2-COOH$ and $NH_2-CH(CH_3)-COOH$

Question 64

Given below are the pairs of group 13 elements showing their relation in terms of atomic radius. $(B<Al)$, $(Al<Ga)$, $(Ga<In)$ and $(In<Tl)$. Identify the elements present in the incorrect pair and in that pair find out the element (X) that has higher ionic radius ($M^{3+}$) than the other one. The atomic number of the element (X) is

Accepted Answer

(A) 31

Answer

(B) 49

Answer

(C) 13

Answer

(D) 81

JEE Main 4 April 2025 Shift 1 Question Paper with Answers

Physics — JEE Main 4 April 2025 Shift 1

Chemistry — JEE Main 4 April 2025 Shift 1

Mathematics — JEE Main 4 April 2025 Shift 1

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