JEE Main 8 April 2025 Shift 2 Question Paper

Question 1

Let the values of $\lambda$ for which the shortest distance between the lines $\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$ and $\dfrac{x-\lambda}{3}=\dfrac{y-4}{4}=\dfrac{z-5}{5}$ is $\dfrac{1}{\sqrt6}$ be $\lambda_1$ and $\lambda_2$. Then the radius of the circle passing through the points $(0,0)$, $(\lambda_1,\lambda_2)$ and $(\lambda_2,\lambda_1)$ is:

Accepted Answer

(A) $\dfrac{5\sqrt2}{3}$

Answer

(B) $4$

Answer

(C) $\dfrac{\sqrt2}{3}$

Answer

(D) $3$

Question 2

Let $\alpha$ be a solution of $x^2+x+1=0$, and for some $a$ and $b$ in $\mathbb{R}$, $\begin{bmatrix}4 & a & b\end{bmatrix}\begin{bmatrix}1 & 16 & 13\ -1 & -1 & 2\ -2 & -14 & -8\end{bmatrix}=\begin{bmatrix}0 & 0 & 0\end{bmatrix}$. If $\dfrac{4}{\alpha^4}+\dfrac{m}{\alpha^a}+\dfrac{n}{\alpha^b}=3$, then $m+n$ is equal to ___

Accepted Answer

(B) $11$

Answer

(A) $3$

Answer

(C) $7$

Answer

(D) $8$

Question 3

Let the function $f(x)=\dfrac{x}{3}+\dfrac{3}{x}+3,\ x
e0$ be strictly increasing in $(-\infty,\alpha_1)\cup(\alpha_2,\infty)$ and strictly decreasing in $(\alpha_3,\alpha_4)\cup(\alpha_4,\alpha_5)$. Then $\sum_{i=1}^{5}\alpha_i^2$ is equal to:

Accepted Answer

(D) $36$

Answer

(A) $48$

Answer

(B) $28$

Answer

(C) $40$

Question 4

If $A$ and $B$ are two events such that $P(A)=0.7$, $P(B)=0.4$ and $P(A\cap\bar B)=0.5$, where $\bar B$ denotes the complement of $B$, then $P\big(B\,|\,(A\cup\bar B)\big)$ is equal to:

Accepted Answer

(A) $\dfrac{1}{4}$

Answer

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

Answer

(C) $\dfrac{1}{6}$

Answer

(D) $\dfrac{1}{3}$

Question 5

If $\dfrac{1}{1^4}+\dfrac{1}{2^4}+\dfrac{1}{3^4}+\ldots\infty=\dfrac{\pi^4}{90}$, $\dfrac{1}{1^4}+\dfrac{1}{3^4}+\dfrac{1}{5^4}+\ldots\infty=\alpha$, $\dfrac{1}{2^4}+\dfrac{1}{4^4}+\dfrac{1}{6^4}+\ldots\infty=\beta$, then $\dfrac{\alpha}{\beta}$ is equal to:

Accepted Answer

(C) $15$

Answer

(A) $23$

Answer

(B) $18$

Answer

(D) $14$

Question 6

The sum of the squares of the roots of $|x+2|^2+|x-2|-2=0$ and the squares of the roots of $x^2-2|x-3|-5=0$, is:

Accepted Answer

(B) $36$

Answer

(A) $26$

Answer

(C) $30$

Answer

(D) $24$

Question 7

Let $a$ be the length of a side of a square $OABC$ with $O$ being the origin. Its side $OA$ makes an acute angle $\alpha$ with the positive x-axis and the equations of its diagonals are $(\sqrt3+1)x+(\sqrt3-1)y=0$ and $(\sqrt3-1)x-(\sqrt3+1)y+8\sqrt3=0$. Then $a^2$ is equal to:

Accepted Answer

(A) $48$

Answer

(B) $32$

Answer

(C) $16$

Answer

(D) $24$

Question 8

Let $f(x)$ be a positive function and $I_1=\displaystyle\int_{-1/2}^{1}2x\,f\big(2x(1-2x)\big)\,dx$ and $I_2=\displaystyle\int_{-1}^{2}f\big(x(1-x)\big)\,dx$. Then the value of $\dfrac{I_2}{I_1}$ is equal to ___

Accepted Answer

(D) $4$

Answer

(A) $9$

Answer

(B) $6$

Answer

(C) $12$

Question 9

Let $\vec a=\hat i+2\hat j+\hat k$ and $\vec b=2\hat i+\hat j-\hat k$. Let $\hat c$ be a unit vector in the plane of the vectors $\vec a$ and $\vec b$ and be perpendicular to $\vec a$. Then such a vector $\hat c$ is:

Accepted Answer

(D) $\dfrac{1}{\sqrt2}(-\hat i+\hat k)$

Answer

(A) $\dfrac{1}{\sqrt2}(\hat j-2\hat k)$

Answer

(B) $\dfrac{1}{\sqrt3}(-\hat i-\hat j-\hat k)$

Answer

(C) $\dfrac{1}{\sqrt3}(\hat i-\hat j+\hat k)$

Question 10

Let the ellipse $3x^2+py^2=4$ pass through the centre $C$ of the circle $x^2+y^2-2x-4y-11=0$ of radius $r$. Let $f_1,f_2$ be the focal distances of the point $C$ on the ellipse. Then $6f_1f_2-r$ is equal to:

Accepted Answer

(C) $70$

Answer

(A) $74$

Answer

(B) $68$

Answer

(D) $78$

Question 11

The integral $\displaystyle\int_{-1}^{3/2}\big(\,|\pi^2 x\sin(\pi x)|\,\big)\,dx$ is equal to:

Accepted Answer

(C) $1+3\pi$

Answer

(A) $3+2\pi$

Answer

(B) $4+\pi$

Answer

(D) $2+3\pi$

Question 12

A line passing through the point $P(a,0)$ makes an acute angle $\alpha$ with the positive x-axis. Let this line be rotated about the point $P$ through an angle $\dfrac{\alpha}{2}$ in the clock-wise direction. If in the new position, the slope of the line is $2-\sqrt3$ and its distance from the origin is $\dfrac{1}{\sqrt2}$, then the value of $3a^2	an^2\alpha-2\sqrt3$ is:

Accepted Answer

(A) $4$

Answer

(B) $6$

Answer

(C) $5$

Answer

(D) $8$

Question 13

There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is:

Accepted Answer

(D) $210$

Answer

(A) $230$

Answer

(B) $220$

Answer

(C) $200$

Question 14

Let $A=\left\{	heta\in[0,2\pi]:1+10\,\mathrm{Re}\left(\dfrac{2\cos	heta+i\sin	heta}{\cos	heta-3i\sin	heta}ight)=0ight\}$. Then $\sum_{	heta\in A}	heta^2$ is equal to:

Accepted Answer

(A) $\dfrac{21}{4}\pi^2$

Answer

(B) $8\pi^2$

Answer

(C) $\dfrac{27}{4}\pi^2$

Answer

(D) $6\pi^2$

Question 15

Let $A=\{0,1,2,3,4,5\}$. Let $R$ be a relation on $A$ defined by $(x,y)\in R$ if and only if $\max\{x,y\}\in\{3,4\}$. Then among the statements $(S_1)$: The number of elements in $R$ is 18, and $(S_2)$: The relation $R$ is symmetric but neither reflexive nor transitive:

Accepted Answer

(C) only $(S_2)$ is true

Answer

(A) both are true

Answer

(B) both are false

Answer

(D) only $(S_1)$ is true

Question 16

The number of integral terms in the expansion of $\left(5^{1/2}+7^{1/8}\right)^{1016}$ is:

Accepted Answer

(D) $128$

Answer

(A) $127$

Answer

(B) $130$

Answer

(C) $129$

Question 17

Let $f(x)=x-1$ and $g(x)=e^x$ for $x\in\mathbb{R}$. If $\dfrac{dy}{dx}=\left(e^{-2\sqrt x}\,g\big(f(f(x))\big)-\dfrac{y}{\sqrt x}\right)$, $y(0)=0$, then $y(1)$ is:

Accepted Answer

(C) $\dfrac{e-1}{e^4}$

Answer

(A) $\dfrac{1-e^2}{e^4}$

Answer

(B) $\dfrac{2e-1}{e^3}$

Answer

(D) $\dfrac{1-e^3}{e^4}$

Question 18

The value of $\cot^{-1}\left(\dfrac{\sqrt{1+	an^2(2)}-1}{	an(2)}ight)-\cot^{-1}\left(\dfrac{\sqrt{1+	an^2\left(	frac12ight)}+1}{	an\left(	frac12ight)}ight)$ is equal to:

Accepted Answer

(A) $\pi-\dfrac{5}{4}$

Answer

(B) $\pi-\dfrac{3}{2}$

Answer

(C) $\pi+\dfrac{3}{2}$

Answer

(D) $\pi+\dfrac{5}{2}$

Question 19

Let $A=\begin{bmatrix}2 & 2+p & 2+p+q\ 4 & 6+2p & 8+3p+2q\ 6 & 12+3p & 20+6p+3q\end{bmatrix}$. If $\det\big(\mathrm{adj}(\mathrm{adj}(3A))\big)=2^m\cdot3^n$, $m,n\in\mathbb{N}$, then $m+n$ is equal to:

Accepted Answer

(B) $24$

Answer

(A) $22$

Answer

(C) $26$

Answer

(D) $20$

Question 20

Given below are two statements:
Statement I: $\lim\limits_{x	o0}\dfrac{	an^{-1}x+\log_e\sqrt{\dfrac{1+x}{1-x}}-2x}{x^5}=\dfrac{2}{5}$.
Statement II: $\lim\limits_{x	o1}x^{\frac{2}{1-x}}=\dfrac{1}{e^2}$.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(D) Both Statement I and Statement II are true

Answer

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

Answer

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

Answer

(C) Both Statement I and Statement II are false

Question 21

Let the area of the bounded region $\{(x,y):0\le9x\le y^2,\ y\ge3x-6\}$ be $A$. Then $6A$ is equal to ___

Accepted Answer

15

Question 22

Let the domain of the function $f(x)=\cos^{-1}\left(\dfrac{4x+5}{3x-7}\right)$ be $[\alpha,\beta]$ and the domain of $g(x)=\log_2\big(2-6\log_{27}(2x+5)\big)$ be $(\gamma,\delta)$. Then $\big|7(\alpha+\beta)+4(\gamma+\delta)\big|$ is equal to ___

Accepted Answer

96

Question 23

Let the area of the triangle formed by the lines $x+2=y-1=z$, $\dfrac{x-3}{5}=\dfrac{y}{-1}=\dfrac{z-1}{1}$ and $\dfrac{x}{-3}=\dfrac{y-3}{3}=\dfrac{z-2}{1}$ be $A$. Then $A^2$ is equal to ___

Accepted Answer

56

Question 24

The product of the last two digits of $(1919)^{1919}$ is ___

Accepted Answer

63

Question 25

Let $r$ be the radius of the circle, which touches x-axis at point $(a,0)$, $a<0$ and the parabola $y^2=9x$ at the point $(4,6)$. Then $r$ is equal to ___

Accepted Answer

30

Question 26

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.
Reason R: Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

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

Answer

(A) A is true but R is false

Answer

(C) A is false but R is true

Answer

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

Question 27

A rod of linear mass density '$\lambda$' and length '$L$' is bent to form a ring of radius '$R$'. Moment of inertia of ring about any of its diameter is:

Accepted Answer

(D) $\dfrac{\lambda L^3}{8\pi^2}$

Answer

(A) $\dfrac{\lambda L^3}{16\pi^2}$

Answer

(B) $\dfrac{\lambda L^3}{12}$

Answer

(C) $\dfrac{\lambda L^3}{4\pi^2}$

Question 28

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young’s modulus. The value of Young’s modulus of the wire as per this experiment is $P	imes10^{10}\ Nm^{-2}$, where the value of $P$ is: (Take $g=3\pi\ m/s^2$)

Accepted Answer

(A) $5$

Answer

(B) $10$

Answer

(C) $25$

Answer

(D) $2.5$

Question 29

Electric charge is transferred to an irregular metallic disk as shown in figure. If $\sigma_1$, $\sigma_2$, $\sigma_3$ and $\sigma_4$ are charge densities at given points then, choose the correct answer from the options given below: (A) $\sigma_1>\sigma_3$ ; $\sigma_2=\sigma_4$ (B) $\sigma_1>\sigma_2$ ; $\sigma_3>\sigma_4$ (C) $\sigma_1>\sigma_3>\sigma_2=\sigma_4$ (D) $\sigma_1<\sigma_3<\sigma_2=\sigma_4$ (E) $\sigma_1=\sigma_2=\sigma_3=\sigma_4$

Accepted Answer

(A) A, B and C Only

Answer

(B) A and C Only

Answer

(C) D and E Only

Answer

(D) B and C Only

Question 30

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take $g=10\ m/s^2$, specific heat of water $=4200\ J/(kg\cdot K)$)

Accepted Answer

(D) $0.48\ K$

Answer

(A) $0.23\ K$

Answer

(B) $0.36\ K$

Answer

(C) $0.14\ K$

Question 31

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be:

Accepted Answer

(D) $\dfrac{600}{11}$ cm

Answer

(A) $\dfrac{500}{11}$ cm

Answer

(B) $\dfrac{800}{11}$ cm

Answer

(C) $\dfrac{700}{11}$ cm

Question 32

An infinitely long wire has uniform linear charge density $\lambda=2\ nC/m$. The net flux through a Gaussian cube of side length $\sqrt3$ cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $x\ Nm^2C^{-1}$, where $x$ is: [Neglect any edge effects and use $\dfrac{1}{4\pi\varepsilon_0}=9	imes10^9$ SI units]

Accepted Answer

(D) $2.16\pi$

Answer

(A) $0.72\pi$

Answer

(B) $1.44\pi$

Answer

(C) $6.48\pi$

Question 33

The output voltage in the following circuit is (Consider ideal diode case):

Accepted Answer

(B) $0$ V

Answer

(A) $10$ V

Answer

(C) $+5$ V

Answer

(D) $-5$ V

Question 34

Two metal spheres of radius $R$ and $3R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\dfrac{\sigma_1}{\sigma_2}$ is:

Accepted Answer

(D) $3$

Answer

(A) $\dfrac{1}{9}$

Answer

(B) $9$

Answer

(C) $\dfrac{1}{3}$

Question 35

A quantity $Q$ is formulated as $X^{-2}Y^{3/2}Z^{-2/5}$. $X$, $Y$ and $Z$ are independent parameters which have fractional errors of 0.1, 0.2 and 0.5, respectively in measurement. The maximum fractional error of $Q$ is:

Accepted Answer

(C) $0.7$

Answer

(A) $0.1$

Answer

(B) $0.8$

Answer

(D) $0.6$

Question 36

A monoatomic gas having $\gamma=\dfrac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to $\left(\dfrac{1}{8}\right)^{th}$ of its initial volume. The ratio of final pressure and initial pressure is: ($\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume)

Accepted Answer

(C) $32$

Answer

(A) $16$

Answer

(B) $40$

Answer

(D) $28$

Question 37

A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is ___

Accepted Answer

(D) $15$

Answer

(A) $30$

Answer

(B) $45$

Answer

(C) $\dfrac{60}{7}$

Question 38

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section $R$ is $v_1$ and that in the other string having radius of cross section $R/2$ is $v_2$. Then $\dfrac{v_2}{v_1}=$

Accepted Answer

(B) $2$

Answer

(A) $\sqrt2$

Answer

(C) $8$

Answer

(D) $4$

Question 39

Figure shows a current carrying square loop ABCD of edge length is '$a$' lying in a plane. If the resistance of the ABC part is $r$ and that of ADC part is $2r$, then the magnitude of the resultant magnetic field at centre of the square loop is:

Accepted Answer

(C) $\dfrac{\sqrt2\,\mu_0 I}{3\pi a}$

Answer

(A) $\dfrac{3\pi\mu_0 I}{\sqrt2\,a}$

Answer

(B) $\dfrac{\mu_0 I}{2\pi a}$

Answer

(D) $\dfrac{2\mu_0 I}{3\pi a}$

Question 40

A body of mass 2 kg moving with velocity $\vec v_{in}=3\hat i+4\hat j\ ms^{-1}$ enters into a constant force field of 6 N directed along positive z-axis. If the body remains in the field for a period of $\dfrac{5}{3}$ seconds, then velocity of the body when it emerges from force field is:

Accepted Answer

(B) $3\hat i+4\hat j+5\hat k$

Answer

(A) $4\hat i+3\hat j+5\hat k$

Answer

(C) $3\hat i+4\hat j-5\hat k$

Answer

(D) $3\hat i+4\hat j+\sqrt5\,\hat k$

Question 41

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. $T_1$ and $T_2$ are the total flying times of first and second ball, respectively, then the ratio of $T_1$ and $T_2$ is:

Accepted Answer

(A) $2\sqrt2:1$

Answer

(B) $2:1$

Answer

(C) $\sqrt2:1$

Answer

(D) $4:1$

Question 42

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $y_1(x,t)=4\sin(kx-\omega t)$ and $y_2(x,t)=2\sin\left(kx-\omega t+\dfrac{2\pi}{3}\right)$, are: (Take the angular frequency of initial waves same as $\omega$)

Accepted Answer

(D) $\left[2\sqrt3,\dfrac{\pi}{6}\right]$

Answer

(A) $\left[6,\dfrac{2\pi}{3}\right]$

Answer

(B) $\left[6,\dfrac{\pi}{3}\right]$

Answer

(C) $\left[\sqrt3,\dfrac{\pi}{6}\right]$

Question 43

In a Young’s double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case (1) There shall be an interference pattern for red distinct from that for green. (2) There shall be no interference fringes. (3) There shall be alternate interference fringes of red and greens. (4) There shall be an interference pattern, where each fringe’s pattern center is green and outer edges is red.

Accepted Answer

(B) There shall be no interference fringes.

Answer

(A) There shall be an interference pattern for red distinct from that for green.

Answer

(C) There shall be alternate interference fringes of red and greens.

Answer

(D) There shall be an interference pattern, where each fringe’s pattern center is green and outer edges is red.

Question 44

For a nucleus of mass number $A$ and radius $R$, the mass density of nucleus can be represented as:

Accepted Answer

(D) Independent of $A$

Answer

(A) $A^{3}$

Answer

(B) $A^{1/3}$

Answer

(C) $A^{2/3}$

Question 45

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring’s natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance $x$ m ($x<2$) from the wall, the speed of the block will be:

Accepted Answer

(B) $10[1-(2-x)^2]^{1/2}\ m/s$

Answer

(A) $10[1-(2-x)]^{3/2}\ m/s$

Answer

(C) $10[1-(2-x)^2]\ m/s$

Answer

(D) $10[1-(2-x)^2]^{2}\ m/s$

Question 46

An electron is released from rest near an infinite non-conducting sheet of uniform charge density '$-\sigma$'. The rate of change of de-Broglie wave length associated with the electron varies inversely as $n^{th}$ power of time. The numerical value of $n$ is ___

Accepted Answer

2

Question 47

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of $0.8\ cm^3$. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ___ litre. (Take 1 atm $=10^5$ Pa)

Accepted Answer

4

Question 48

Space between the plates of a parallel plate capacitor of plate area $4\ cm^2$ and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ___ pF. (Given $\varepsilon_0=8.85	imes10^{-12}$ F/m)

Accepted Answer

15

Question 49

A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of $25\pi$ Nm for 40 s, the speed increases to 2100 rpm. The diameter of the disk is ___ m.

Accepted Answer

40

Question 50

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is $1\ gm/cm^3$.) The unknown mass is ___ kg.

Accepted Answer

3

Question 51

In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $t_1$ and $t_2$ (s), respectively. The ratio $\dfrac{t_1}{t_2}$ will:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 52

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

Accepted Answer

(D) A-III, B-IV, C-I, D-II

Answer

(A) A-IV, B-II, C-III, D-I

Answer

(B) A-II, B-III, C-I, D-IV

Answer

(C) A-III, B-IV, C-II, D-I

Question 53

$A\xrightarrow{	ext{(i) NaOH (ii) }H_3O^+}B\xrightarrow{	ext{(i) EtOH (ii) }H_2SO_4,\,\Delta}C$. 'A' shows positive Lassaigne's test for N and its molar mass is 121. 'B' gives effervescence with aq. $NaHCO_3$. 'C' gives fruity smell. Identify A, B and C from the following:

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 54

Choose the correct set of reagents for the following conversion: Ethyl benzene $\rightarrow$ (product shown in figure)

Accepted Answer

(A) $Br_2/Fe$; $Cl_2,\Delta$; alc. KOH

Answer

(B) $Cl_2/Fe$; $Br_2/$anhy.$AlCl_3$; aq. KOH

Answer

(C) $Br_2/$anhy.$AlCl_3$; $Cl_2,\Delta$; aq. KOH

Answer

(D) $Cl_2/$anhy.$AlCl_3$; $Br_2/Fe$; alc. KOH

Question 55

1,2-dibromocyclooctane $\xrightarrow{	ext{(i) KOH (alc.) (ii) }NaNH_2	ext{ (iii) }Hg^{2+}/H^+	ext{ (iv) Zn-Hg}/H^+}P$ (Major product). 'P' is:

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 56

Given below are two statements:
Statement I: A homoleptic octahedral complex, formed using monodentate ligands, will not show stereoisomerism.
Statement II: cis- and trans- platin are heteroleptic complexes of Pd.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(D) Statement I is true but Statement II is false.

Answer

(A) Both statement I and Statement II are true.

Answer

(B) Statement I is false but Statement II is true.

Answer

(C) Both statement I and Statement II are false.

Question 57

The atomic number of the element from the following with lowest $1^{st}$ ionisation enthalpy is:

Accepted Answer

(C) $87$

Answer

(A) $32$

Answer

(B) $35$

Answer

(D) $19$

Question 58

Which of the following binary mixture does not show the behaviour of minimum boiling azeotropes?

Accepted Answer

(B) $C_2H_5OH+C_2H_5NH_2$

Answer

(A) $H_2O+CH_3COC_2H_5$

Answer

(C) $CS_2+CH_3COCH_3$

Answer

(D) $CH_3OH+CHCl_3$

Question 59

$HA(aq)\rightleftharpoons H^+(aq)+A^-(aq)$. The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is $0.20^\circ C$. The dissociation constant for the acid is: Given: $K_f(H_2O)=1.8\ K\,kg\,mol^{-1}$, molality $=$ molarity.

Accepted Answer

(A) $1.38	imes10^{-3}$

Answer

(B) $1.1	imes10^{-2}$

Answer

(C) $1.90	imes10^{-3}$

Answer

(D) $1.89	imes10^{-1}$

Question 60

What is the correct IUPAC name of the following compound?

Accepted Answer

(D) 4-Ethylcyclopent-2-en-1-ol

Answer

(A) 4-Ethyl-1-hydroxycyclopent-2-ene

Answer

(B) 1-Ethyl-3-hydroxycyclopent-2-ene

Answer

(C) 1-Ethylcyclopent-2-en-3-ol

Question 61

The correct decreasing order of spin only magnetic moment (BM) of $Cu^+$, $Cu^{2+}$, $Cr^{2+}$ and $Cr^{3+}$ ions is:

Accepted Answer

(C) $Cr^{2+}>Cr^{3+}>Cu^{2+}>Cu^+$

Answer

(A) $Cu^+>Cu^{2+}>Cr^{2+}>Cr^{3+}$

Answer

(B) $Cu^{2+}>Cu^+>Cr^{2+}>Cr^{3+}$

Answer

(D) $Cr^{3+}>Cr^{2+}>Cu^{2+}>Cu^+$

Question 62

Which one of the following reactions will not lead to the desired ether formation in major proportion? (iso-Bu $\Rightarrow$ isobutyl, sec-Bu $\Rightarrow$ sec-butyl, nPr $\Rightarrow$ n-propyl, $^tBu\Rightarrow$ tert-butyl, Et $\Rightarrow$ ethyl)

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 63

On combustion 0.210 g of an organic compound containing C, H and O gave 0.127 g $H_2O$ and 0.307 g $CO_2$. The percentages of hydrogen and oxygen in the given organic compound respectively are:

Accepted Answer

(B) $6.72,\ 53.41$

Answer

(A) $53.41,\ 39.6$

Answer

(C) $7.55,\ 43.85$

Answer

(D) $6.72,\ 39.87$

Question 64

For the amino acid shown in the figure, $A$ and $B$ represent its structures at $pH=2$ and $pH=10$, respectively. Choose the correct option for structures of A and B respectively:

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

LIST-I	LIST-II
A.Carbocation	I.Species that can supply a pair of electrons.
B.C-Free radical	II.Species that can receive a pair of electrons.
C.Nucleophile	III. $sp^2$ hybridized carbon with empty p-orbital.
D.Electrophile	IV. $sp^2/sp^3$ hybridized carbon with one unpaired electron.

LIST-I (Reagent)	LIST-II (Functional Group detected)
A.Sodium bicarbonate solution	I.double bond/unsaturation
B.Neutral ferric chloride	II.carboxylic acid
C.ceric ammonium nitrate	III.phenolic - OH
D.alkaline $KMnO_4$	IV.alcoholic - OH

LIST-I (Complex/Species)	LIST-II (Shape & magnetic moment)
A. $[Ni(CO)_4]$	I.Tetrahedral, 2.8 BM
B. $[Ni(CN)_4]^{2-}$	II.Square planar, 0 BM
C. $[NiCl_4]^{2-}$	III.Tetrahedral, 0 BM
D. $[MnBr_4]^{2-}$	IV.Tetrahedral, 5.9 BM

JEE Main 8 April 2025 Shift 2 Question Paper with Answers

Physics — JEE Main 8 April 2025 Shift 2

Chemistry — JEE Main 8 April 2025 Shift 2

Mathematics — JEE Main 8 April 2025 Shift 2

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