JEE Main 2 April 2026 Shift 2 Question Paper

Question 1

Let $\alpha, \beta$ be the roots of the equation $x^2 - 3x + r = 0$, and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2 + 3x + r = 0$. If the roots of the equation $x^2 + 6x = m$ are $2\alpha + \beta + 2r$ and $\alpha - 2\beta - \frac{r}{2}$, then $m$ is equal to:

Accepted Answer

(D) $567$

Answer

(A) $-135$

Answer

(B) $-567$

Answer

(C) $135$

Question 2

Let the circles $C_1 : |z| = r$ and $C_2 : |z - 3 - 4i| = 5$, $z \in \mathbb{C}$, be such that $C_2$ lies within $C_1$. If $z_1$ moves on $C_1$, $z_2$ moves on $C_2$ and $\min |z_1 - z_2| = 2$, then $\max |z_1 - z_2|$ is equal to:

Accepted Answer

(C) $22$

Answer

(A) $12$

Answer

(B) $17$

Answer

(D) $24$

Question 3

If the system of equations
$x + 5y + 6z = 4$,
$2x + 3y + 4z = 7$,
$x + 6y + az = b$
has infinitely many solutions, then the point $(a, b)$ lies on the line

Accepted Answer

(B) $x - y = 3$

Answer

(A) $y - x = 3$

Answer

(C) $x + y = 11$

Answer

(D) $x + y = 12$

Question 4

Let $a_1, a_2, a_3, \ldots$ be an A.P. and $g_1 = a_1, g_2, g_3, \ldots$ be an increasing G.P. If $a_1 = a_2 + g_2 = 1$ and $a_3 + g_3 = 4$, then $a_{10} + g_5$ is equal to:

Accepted Answer

(D) $55$

Answer

(A) $81$

Answer

(B) $76$

Answer

(C) $62$

Question 5

The sum $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \cdots$ up to 8 terms, is:

Accepted Answer

(B) $71$

Answer

(A) $70$

Answer

(C) $72$

Answer

(D) $73$

Question 6

If for $3 \leq r \leq 30$, $\binom{30}{30-r} + 3\binom{30}{31-r} + 3\binom{30}{32-r} + \binom{30}{33-r} = \binom{m}{r}$, then $m$ equals:

Accepted Answer

(C) $33$

Answer

(A) $31$

Answer

(B) $32$

Answer

(D) $34$

Question 7

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-side regular polygon. If $p_{n+1} - p_n = 66$, then the sum of all distinct prime divisors of $n$ is:

Accepted Answer

(C) $5$

Answer

(A) $7$

Answer

(B) $8$

Answer

(D) $6$

Question 8

A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is $\frac{m}{n}$, $\gcd(m, n) = 1$, then $m + n$ is equal to:

Accepted Answer

(C) $107$

Answer

(A) $53$

Answer

(B) $55$

Answer

(D) $105$

Question 9

The mean and variance of $n$ observations are 8 and 16, respectively. If the sum of the first $(n - 1)$ observations is 48 and the sum of squares of the first $(n - 1)$ observations is 496, then the value of $n$ is:

Accepted Answer

(D) $7$

Answer

(A) $21$

Answer

(B) $16$

Answer

(C) $13$

Question 10

Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines $x + (k - 1)y + 3 = 0$ and $2x + k^2y - 4 = 0$. If the line $x - y + 2 = 0$ intersects the circle at the points A and B, then $(AB)^2$ is equal to:

Accepted Answer

(C) $18$

Answer

(A) $10$

Answer

(B) $27$

Answer

(D) $34$

Question 11

Let O be the origin, and P and Q be two points on the rectangular hyperbola $xy = 12$ such that the mid point of the line segment PQ is $\left(\frac{1}{2}, -\frac{1}{2}\right)$. Then the area of the triangle OPQ equals:

Accepted Answer

(C) $\frac{7}{2}$

Answer

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

Answer

(B) $\frac{5}{2}$

Answer

(D) $\frac{9}{2}$

Question 12

Let the parabola $y = x^2 + px + q$ passing through the point $(1, -1)$ be such that the distance between its vertex and the $x$-axis is minimum. Then the value of $p^2 + q^2$ is:

Accepted Answer

(B) $4$

Answer

(A) $2$

Answer

(C) $5$

Answer

(D) $8$

Question 13

Let $P = \{	heta \in [0, 4\pi] : 	an^2	heta 
eq 1\}$ and $S = \{a \in \mathbb{Z} : 2(\cos^8	heta - \sin^8	heta)\sec 2	heta = a^2, 	heta \in P\}$. Then $n(S)$ is:

Accepted Answer

(A) $0$

Answer

(B) $1$

Answer

(C) $2$

Answer

(D) $3$

Question 14

Let the vectors $\vec{a} = -\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = \hat{i} + 3\hat{j} + \hat{k}$. For some $\lambda, \mu \in \mathbb{R}$, let $\vec{c} = \lambda\vec{a} + \mu\vec{b}$. If $\vec{c} \cdot (3\hat{i} - 6\hat{j} + 2\hat{k}) = 10$ and $\vec{c} \cdot (\hat{i} + \hat{j} + \hat{k}) = -2$, then $|\vec{c}|^2$ is equal to:

Accepted Answer

(B) $12$

Answer

(A) $8$

Answer

(C) $14$

Answer

(D) $15$

Question 15

Let the point A be the foot of perpendicular drawn from the point $P(a, b, 0)$ on the line $\frac{x-1}{2} = \frac{y-2}{1} = \frac{z-\alpha}{3}$. If the midpoint of the line segment PA is $\left(0, \frac{3}{4}, \frac{-1}{4}\right)$, then the value of $a^2 + b^2 + \alpha^2$ is equal to:

Accepted Answer

(A) $1$

Answer

(B) $2$

Answer

(C) $6$

Answer

(D) $9$

Question 16

Two adjacent sides of a parallelogram PQRS are given by $\vec{PQ} = \hat{j} + \hat{k}$ and $\vec{PS} = \hat{i} - \hat{j}$. If the side PS is rotated about the point P by an acute angle $\alpha$ in the plane of the parallelogram so that it becomes perpendicular to the side PQ, then $\sin^2\left(\frac{5\alpha}{2}\right) - \sin^2\left(\frac{\alpha}{2}\right)$ is equal to:

Accepted Answer

(B) $\frac{\sqrt{3}}{2}$

Answer

(A) $\frac{1}{2}$

Answer

(C) $\frac{\sqrt{3}}{4}$

Answer

(D) $\frac{2\sqrt{3}}{5}$

Question 17

The value of $\int_0^{20\pi} (\sin^4 x + \cos^4 x)\, dx$ is equal to:

Accepted Answer

(C) $15\pi$

Answer

(A) $\frac{15\pi}{2}$

Answer

(B) $25\pi$

Answer

(D) $\frac{25\pi}{2}$

Question 18

Let $f(x)$ be a polynomial of degree 5, and have extrema at $x = 1$ and $x = -1$. If $\lim_{x 	o 0} \left(\frac{f(x)}{x^3}ight) = -5$, then $f(2) - f(-2)$ is equal to:

Accepted Answer

(D) $112$

Answer

(A) $0$

Answer

(B) $50$

Answer

(C) $92$

Question 19

Let $f(x) = \int \left(\frac{16x + 24}{x^2 + 2x - 15}\right) dx$. If $f(4) = 14 \log_e(3)$ and $f(7) = \log_e(2^{\alpha} \cdot 3^{\beta})$, $\alpha, \beta \in \mathbb{N}$, then $\alpha + \beta$ is equal to:

Accepted Answer

(C) $39$

Answer

(A) $31$

Answer

(B) $37$

Answer

(D) $41$

Question 20

Let $x = x(y)$ be the solution of the differential equation $2y^2 \frac{dx}{dy} - 2xy + x^2 = 0$, $y > 1$, $x(e) = e$. Then $x(e^2)$ is equal to:

Accepted Answer

(B) $\frac{2}{3}e^2$

Answer

(A) $\frac{3}{2}e^2$

Answer

(C) $e^2$

Answer

(D) $2e^2$

Question 21

Let $A = \{2, 3, 4, 5, 6\}$. Let R be a relation on the set $A 	imes A$ given by $(x, y)R(z, w)$ if and only if $x$ divides $z$ and $y \le w$. Then the number of elements in R is ________.

Accepted Answer

120

Question 22

Consider the matrices $A = \begin{bmatrix} 2 & -2 \ 4 & -2 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 9 \ 1 & 3 \end{bmatrix}$. If matrices P and Q are such that $PA = B$ and $AQ = B$, then the absolute value of the sum of the diagonal elements of $2(P + Q)$ is ________.

Accepted Answer

34

Question 23

Let A be the point $(3, 0)$ and circles with variable diameter AB touch the circle $x^2 + y^2 = 36$ internally. Let the curve C be the locus of the point B. If the eccentricity of C is $e$, then $72e^2$ is equal to ________.

Accepted Answer

18

Question 24

If the area of the region bounded by $16x^2 - 9y^2 = 144$ and $8x - 3y = 24$ is A, then $3(A + 6\log_e(3))$ is equal to ________.

Accepted Answer

24

Question 25

The number of points in the interval $[2, 4]$, at which the function $f(x) = \left[x^2 - x - \frac{1}{2}\right]$, where $[\cdot]$ denotes the greatest integer function, is discontinuous, is ________.

Accepted Answer

10

Question 26

Dimensions of universal gravitational constant $(G)$ in terms of Planck's constant $(h)$, distance $(L)$, mass $(M)$ and time $(T)$ are ______.

Accepted Answer

(B) $[hT^{-1}LM^{-2}]$

Answer

(A) $[hTLM^{-2}]$

Answer

(C) $[hTL^{2}M^{-2}]$

Answer

(D) $[h^{-1}T^{-1}LM^{-2}]$

Question 27

A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum's inner wall surface and mass is ______. (Take $g = 10$ m/s$^{2}$)

Accepted Answer

(A) 0.1

Answer

(B) 0.5

Answer

(C) 0.7

Answer

(D) 0.3

Question 28

Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in 2 s is ______ m. (Take $g = 10$ m/s$^{2}$)

Accepted Answer

(C) 2.22

Answer

(A) 3.33

Answer

(B) 3.12

Answer

(D) 1.42

Question 29

A particle having charge $10^{-9}$ C moving in $x$-$y$ plane in fields of $0.4\hat{j}$ N/C and $4 	imes 10^{-3}\hat{k}$ T experiences a force of $(4\hat{i} + 2\hat{j}) 	imes 10^{-10}$ N. The velocity of the particle at that instant is ______ m/s.

Accepted Answer

(A) $50\hat{i} + 100\hat{j}$

Answer

(B) $100\hat{i} + 50\hat{j}$

Answer

(C) $-50\hat{i} + 100\hat{j}$

Answer

(D) $50\hat{i} - 100\hat{j}$

Question 30

If $X$ and $Y$ are the inputs, the given circuit works as ______.

Accepted Answer

(D) NOR gate

Answer

(A) OR gate

Answer

(B) AND gate

Answer

(C) NAND gate

Question 31

If a body of mass 1 kg falls on the earth from infinity, it attains velocity $(v)$ and kinetic energy $(k)$ on reaching the surface of earth. The values of $v$ and $k$ respectively are ______. (Take radius of earth to be 6400 km and $g = 9.8$ m/s$^{2}$)

Accepted Answer

(A) 11.2 km/s; $6.27 	imes 10^{7}$ J

Answer

(B) 11.2 km/s; $12.54 	imes 10^{7}$ J

Answer

(C) 8.8 km/s; $6.27 	imes 10^{7}$ J

Answer

(D) 8.8 km/s; $12.54 	imes 10^{7}$ J

Question 32

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and $50^{	ext{th}}$ division of circular scale coincides with the reference line of main scale. The diameter of sphere is ______ mm.

Accepted Answer

(A) 5.045

Answer

(B) 5.055

Answer

(C) 5.450

Answer

(D) 5.550

Question 33

The surface tension of a soap bubble is 0.03 N/m. The work done in increasing the diameter of bubble from 2 cm to 6 cm is $\alpha\pi 	imes 10^{-4}$ J. The value of $\alpha$ is ______. (Take $\pi = 3.14$)

Accepted Answer

(C) 1.92

Answer

(A) 0.86

Answer

(B) 0.64

Answer

(D) 7.68

Question 34

A mixture of carbon dioxide and oxygen has volume 8310 cm$^{3}$, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ______. (Assume both carbon dioxide and oxygen gases behave like ideal gases) $[R = 8.31$ J/mol.K$]$

Accepted Answer

(C) 0.21 and 0.12

Answer

(A) 0.15 and 0.18

Answer

(B) 0.25 and 0.08

Answer

(D) 0.13 and 0.20

Question 35

If an air bubble of diameter 2 mm rises steadily through a liquid of density 2000 kg/m$^{3}$ at a rate of 0.5 cm/s, then the coefficient of viscosity of liquid is ______ Poise. (Take $g = 10$ m/s$^{2}$)

Accepted Answer

(B) 8.8

Answer

(A) 0.88

Answer

(C) 88.8

Answer

(D) 0.088

Question 36

A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is ______ N. (Take $g = 10$ m/s$^{2}$)

Accepted Answer

(B) 2020

Answer

(A) 1980

Answer

Answer

(D) 1000

Question 37

An electromagnetic wave travels in free space along the $x$-direction. At a particular point in space and time, $\vec{B} = 2 	imes 10^{-7}\hat{j}$ T is associated with this wave. The value of corresponding electric field $\vec{E}$ at this point is ______ V/m.

Accepted Answer

(B) $-60\hat{k}$

Answer

(A) $60\hat{k}$

Answer

(C) $30\hat{k}$

Answer

(D) $-600\hat{k}$

Question 38

Two resistors of $200\ \Omega$ and $400\ \Omega$ are connected in series with a battery of 100 V. A bulb rated at 200 V, 100 W is connected across the $400\ \Omega$ resistance. The potential drop across the bulb is ______ V.

Accepted Answer

(B) 50

Answer

(A) 25

Answer

(C) 66.6

Answer

(D) 100

Question 39

Two metal plates $(A, B)$ are kept horizontally with separation of $\left(\frac{12}{\pi}\right)$ cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 g/cm$^{3}$) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials $V_A$ and $V_B$ are required on plates A and B respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are ________.
(Neglect the air resistance to the droplets and take $g = 10$ m/s$^{2}$)

Accepted Answer

(A) $100\,V$ and $580\,V$

Answer

(B) $580\,V$ and $100\,V$

Answer

(C) $60\,V$ and $400\,V$

Answer

(D) $0\,V$ and $-200\,V$

Question 40

Two point charges $8\,\mu C$ and $-2\,\mu C$ are located at $x = 2$ cm and $x = 4$ cm, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is ________.

Accepted Answer

(C) $4 : 3$

Answer

(A) $4 : 1$

Answer

(B) $3 : 4$

Answer

(D) $4 : 5$

Question 41

One side of an equilateral prism is painted by a transparent material of refractive index $n_2$. The refractive index of prism is 1.6. The minimum value of $n_2$ required for total internal reflection from painted face is ________.

Accepted Answer

(D) $4\sqrt{3}/5$

Answer

(A) $3\sqrt{3}/1.6$

Answer

(B) $\sqrt{3}$

Answer

(C) $3.2/\sqrt{3}$

Question 42

The figure given below shows an $LCR$ series circuit with two switches $S_1$ and $S_2$. When switch $S_1$ is closed keeping $S_2$ open, the phase difference $(\phi)$ between the current and source voltage is $30^\circ$ and phase difference is $60^\circ$ when $S_2$ is closed keeping $S_1$ open. The value of $(3L_1 - L_2)$ is ________ H.

Accepted Answer

(B) $\frac{2}{9}$

Answer

(A) $\frac{9}{2}$

Answer

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

Answer

(D) $3$

Question 43

A circular current loop of radius $R$ is placed inside square loop of side length $L$ $(L >> R)$ such that they are co-planar and their centers coincide. The permeability of free space is $\mu_0$. The mutual inductance between circular loop and square loop is ________.

Accepted Answer

(D) $2\sqrt{2}\,\frac{\mu_0 R^2}{L}$

Answer

(A) $2\sqrt{2}\,\frac{\mu_0 L^2}{R}$

Answer

(B) $\sqrt{2}\,\frac{\mu_0 L^2}{R}$

Answer

(C) $\sqrt{2}\,\frac{\mu_0 R^2}{L}$

Question 44

The binding energy per nucleon of $^{209}_{83}Bi$ is ________ MeV.
$[$Take $m(^{209}_{83}Bi) = 208.980388\,u$, $m_p = 1.007825\,u$, $m_n = 1.008665\,u$, $1\,u = 931\,\mathrm{MeV}/c^2]$

Accepted Answer

(B) 7.84

Answer

(A) 7.48

Answer

(C) 8.79

Answer

(D) 6.94

Question 45

The equation of motion of a particle is given by $x = a \sin\left(50t + \frac{\pi}{3}\right)$ cm. The particle will come to rest at time $t_1$ and it will have zero acceleration at time $t_2$. The $t_1$ and $t_2$ respectively are ________.

Accepted Answer

(A) $\frac{\pi}{300}\,s$, $\frac{\pi}{75}\,s$

Answer

(B) $\frac{\pi}{75}\,s$, $\frac{\pi}{300}\,s$

Answer

(C) $\frac{\pi}{300}\,s$, $\frac{\pi}{25}\,s$

Answer

(D) $\frac{\pi}{50}\,s$, $\frac{\pi}{100}\,s$

Question 46

In a Young's double slit experiment, the intensity at some point on the screen is found to be $\frac{3}{4}$ times of the maximum of the interference pattern. The path difference between the interfering waves at this point is $\frac{\lambda}{x}$ where $\lambda$ is wavelength of the incident light. The value of $x$ is ________.

Accepted Answer

6

Question 47

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{nd}$ and $4^{th}$ orbits of hydrogen atom ________.

Accepted Answer

32

Question 48

5 moles of unknown gas is heated at constant volume from $10\,^\circ C$ to $20\,^\circ C$. The molar specific heat of this gas at constant pressure $c_p = 8$ cal/mol.$^\circ$C and $R = 8.36$ J/mol.$^\circ$C. The change in the internal energy of the gas is ________ calorie.

Accepted Answer

300

Question 49

If sunlight is focused on a paper using convex lens, it starts burning the paper in shortest time when the lens is kept at 30 cm above the paper. If the radius of curvature of the lens is 60 cm then the refractive index of the lens material is $\frac{\alpha}{10}$. The value of $\alpha$ is ________.

Accepted Answer

20

Question 50

Moment of inertia about an axis $AB$ for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius $R$ about an axis parallel to $AB$ axis with separation of 3 m as shown in figure below. The value of $R$ is given as $\sqrt{\frac{\alpha}{2}}$. The value of $\alpha$ is ________.

Accepted Answer

15

Question 51

The ratio of mass percentage (w/w) of C : H in a hydrocarbon is 12 : 1. It has two carbon atoms. The weight (in g) of $CO_2(g)$ formed when 3.38 g of this hydrocarbon is completely burnt in oxygen is : (Given : Molar mass in g mol$^{-1}$ C : 12, H : 1, O : 16)

Accepted Answer

(B) 11.44

Answer

(A) 5.68

Answer

(C) 22.74

Answer

(D) 17.05

Question 52

The first and second ionization constants of a weak dibasic acid $H_2A$ are $8.1 	imes 10^{-8}$ and $1.0 	imes 10^{-13}$ respectively. 0.1 mol of $H_2A$ was dissolved in 1 L of 0.1 M HCl solution. The concentration of $HA^-$ in the resultant solution is:

Accepted Answer

(C) $8.1 	imes 10^{-8}$ M

Answer

(A) 0.1 M

Answer

(B) $9.53 	imes 10^{-6}$ M

Answer

(D) $1.0 	imes 10^{-13}$ M

Question 53

$SF_4$ is isostructural with:
A. $BrF_4^{\ominus}$
B. $CH_4$
C. $IF_4^{\oplus}$
D. $XeF_4$
E. $XeO_2F_2$
Choose the correct answer from the options given below:

Accepted Answer

(B) C and E Only

Answer

(A) C Only

Answer

(C) A and D Only

Answer

(D) B and E Only

Question 54

Gas 'A' undergoes change from state 'X' to state 'Y'. In this process, the heat absorbed and work done by the gas is 10 J and 18 J respectively. Now gas is brought back to state 'X' by another process during which 6 J of heat is evolved. In the reverse process of 'Y' to 'X',

Accepted Answer

(D) 14 J of the work is done on the gas 'A' by the surrounding.

Answer

(A) 18 J of the work is done by the gas 'A'.

Answer

(B) 2 J of the work is done by the gas 'A'.

Answer

(C) 12 J of the work is done on the gas 'A' by the surrounding.

Question 55

Solution A is prepared by dissolving 1 g of a protein (molar mass = 50000 g mol$^{-1}$) in 0.5 L of water at 300 K. Its osmotic pressure is $x$ bar. Solution B is made by dissolving 2 g of same protein in 1 L of water at 300 K. Osmotic pressure of solution B is $y$ bar. Entire solution of A is mixed with entire solution of B at same temperature. The osmotic pressure of resultant solution is $z$ bar. $x, y$ and $z$ respectively are: $(R = 0.083$ L bar mol$^{-1}$ K$^{-1})$

Accepted Answer

(A) $9.96 	imes 10^{-4}$; $9.96 	imes 10^{-4}$; $9.96 	imes 10^{-4}$

Answer

(B) $9.96 	imes 10^{-4}$; $9.96 	imes 10^{-4}$; $19.92 	imes 10^{-4}$

Answer

(C) $4.98 	imes 10^{-4}$; $4.98 	imes 10^{-4}$; $9.96 	imes 10^{-4}$

Answer

(D) $4.98 	imes 10^{-4}$; $4.98 	imes 10^{-4}$; $4.98 	imes 10^{-4}$

Question 56

At $25^{\circ}C$, 20.0 mL of 0.2 M weak monoprotic acid HX is titrated against 0.2 M NaOH. The pH of the solution (a) at the start of the titration (when NaOH has not been added) and (b) when 10 mL of NaOH is added respectively, are:
Given: $K_a = 5 	imes 10^{-4}$, $pK_a = 3.3$, $\alpha << 1$

Accepted Answer

(B) (a) 2.0   (b) 3.3

Answer

(A) (a) 0.7   (b) 2.0

Answer

(C) (a) 1.1   (b) 2.2

Answer

(D) (a) 3.0   (b) 2.2

Question 57

Consider the reaction $aX ightarrow bY$, for which the rate constant at $30^{\circ}C$ is $1 	imes 10^{-3}$ mol$^{-1}$ L s$^{-1}$. Which of the following statements are true?
A. When concentration of 'X' is increased to four times, the rate of reaction becomes 16 times.
B. The reaction is a second order reaction.
C. The half-life period is independent of the concentration of X.
D. Decomposition of $N_2O_5$ is an example of the above reaction.
E. $\ln \frac{[R_o]}{[R]}$ vs time is valid for the above reaction.
Choose the correct answer from the options given below:

Accepted Answer

(A) A and B Only

Answer

(B) A, B and C Only

Answer

(C) A, B, D and E Only

Answer

(D) C and D Only

Question 58

The correct set that contains all kinds (basic, acidic, amphoteric and neutral) of oxides is:

Accepted Answer

(C) $K_2O$, $Cl_2O_7$, $As_2O_3$ and $NO$

Answer

(A) $Na_2O$, $K_2O$, $Al_2O_3$ and $As_2O_3$

Answer

(B) $Al_2O_3$, $As_2O_3$, $CO$ and $NO$

Answer

(D) $Na_2O$, $N_2O$, $Al_2O_3$ and $CO$

Question 59

Given below are two statements: Statement I: The second ionization enthalpy of B, Al and Ga is in the order of $B > Al > Ga$. Statement II: The correct order in terms of first ionization enthalpy is $Si < Ge < Pb < Sn$. In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(B) Both Statement I and Statement II are false

Answer

(A) Both Statement I and Statement II are true

Answer

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

Answer

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

Question 60

Given below are two statements:
Statement I: Among $Zn$, $Mn$, $Sc$ and $Cu$, the energy required to remove the third valence electron is highest for $Zn$ and lowest for $Sc$.
Statement II: The correct order of the following complexes in terms of CFSE is $[Co(H_2O)_6]^{2+} < [Co(H_2O)_6]^{3+} < [Co(en)_3]^{3+}$.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

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

Answer

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

Question 61

Which of the following complexes will show coordination isomerism?
A. $[Ag(NH_3)_2][Ag(CN)_2]$
B. $[Co(NH_3)_6][Cr(CN)_6]$
C. $[Co(NH_3)_6][Co(CN)_6]$
D. $[Fe(NH_3)_6][Co(CN)_6]$
E. $[Co(NH_3)_6][Fe(CN)_6]$
Choose the correct answer from the options given below:

Accepted Answer

(B) B, D and E Only

Answer

(A) B, C and D Only

Answer

(C) A, C and D Only

Answer

(D) C, D and E Only

Question 62

Complete combustion of $X$ g of an organic compound gave 0.25 g of $CO_2$ and 0.12 g of $H_2O$. If the % of carbon is 25% and of hydrogen is 4.89%, then $X = $ _____ $	imes 10^{-3}$ g. (Nearest integer) (Molar mass of C, H and O are $12, 1$ and 16 g mol$^{-1}$ respectively.)

Accepted Answer

(A) 273

Answer

(B) 27

Answer

(C) 2730

Answer

(D) 227

Question 63

Given below are two statements:
Statement I: In $O_2N	ext{-}C_6H_4	ext{-}CH^{\oplus}	ext{-}C_6H_4	ext{-}OCH_3$, the carbocation is stabilised by $+R$ effect of $-OCH_3$ group.
Statement II: In $O_2N	ext{-}C_6H_4	ext{-}CH^{\ominus}	ext{-}C_6H_4	ext{-}OCH_3$, the carbanion is stabilised by $-R$ effect of $-NO_2$ group.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

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

Answer

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

Question 64

The compound (X) on
(i) on heating in the presence of anhydrous $AlCl_3$ and HCl gas gives 2,4-dimethyl pentane
(ii) aromatization gives toluene and
(iii) cyclisation gives methyl cyclohexane
The correct name of compound (X) is:

Accepted Answer

(C) Heptane

Answer

(A) Hept-2-ene

Answer

(B) Hept-1,3,5-triene

Answer

(D) Hept-2,4,6-triene

JEE Main 2 April 2026 Shift 2 Question Paper with Answers

Physics — JEE Main 2 April 2026 Shift 2

Chemistry — JEE Main 2 April 2026 Shift 2

Mathematics — JEE Main 2 April 2026 Shift 2

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