NTA JEE Mains 2nd April Shift 1 2026

NTA JEE Mains 2nd April Shift 1 2026 - Question 1

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Let $$\alpha, \alpha + 2, \alpha \in \mathbb{Z}$$, be the roots of the quadratic equation $$x(x+2) + (x+1)(x+3) + (x+2)(x+4) + \ldots + (x+n-1)(x+n+1) = 4n$$ for some $$n \in \mathbb{N}$$. Then $$n + \alpha$$ is equal to :

A

$$0$$

B

$$1$$

C

$$2$$

D

$$3$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 2

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Let $$x$$ and $$y$$ be real numbers such that $$50\left(\frac{2x}{1+3i} - \frac{y}{1-2i}\right) = 31 + 17i$$, $$i = \sqrt{-1}$$. Then the value of $$10(x - 3y)$$ is :

A

$$20$$

B

$$31$$

C

$$35$$

D

$$75$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 3

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Let $$\alpha, \beta \in \mathbb{R}$$ be such that the system of linear equations
$$x + 2y + z = 5$$
$$2x + y + \alpha z = 5$$
$$8x + 4y + \beta z = 18$$
has no solution. Then $$\frac{\beta}{\alpha}$$ is equal to :

A

$$-4$$

B

$$4$$

C

$$8$$

D

$$-8$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 4

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Let $$A = \begin{bmatrix} 1 & 2 \\ 1 & \alpha \end{bmatrix}$$ and $$B = \begin{bmatrix} 3 & 3 \\ \beta & 2 \end{bmatrix}$$. If $$A^2 - 4A + I = O$$ and $$B^2 - 5B - 6I = O$$, then among the two statements : 

(S1): $$[(B-A)(B+A)]^T = \begin{bmatrix} 13 & 15 \\ 7 & 10 \end{bmatrix}$$ and 

(S2): $$\det(\text{adj}(A+B)) = -5$$,

A

only (S1) is correct

B

only (S2) is correct

C

both (S1) and (S2) are correct

D

both (S1) and (S2) are wrong

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NTA JEE Mains 2nd April Shift 1 2026 - Question 5

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Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in $$A \cap B$$, which are divisible by 3, is :

A

$$4$$

B

$$5$$

C

$$6$$

D

$$7$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 6

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The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is :

A

$$15400$$

B

$$17800$$

C

$$16800$$

D

$$29400$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 7

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The number of elements in the set $$S = \left\{(r, k) : k \in \mathbb{Z} \text{ and } {}^{36}C_{r+1} = \frac{6 \cdot {}^{35}C_r}{k^2 - 3}\right\}$$, is :

A

$$2$$

B

$$4$$

C

$$8$$

D

$$16$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 8

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If the mean of the data 

is 21, then k is one of the roots of the equation :

A

$$2x^2 - 23x - 10 = 0$$

B

$$4x^2 - 35x + 24 = 0$$

C

$$2x^2 - 19x - 10 = 0$$

D

$$2x^2 - 35x + 98 = 0$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 9

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Let the mid points of the sides of a triangle ABC be $$\left(\frac{5}{2}, 7\right)$$, $$\left(\frac{5}{2}, 3\right)$$ and $$(4, 5)$$. If its incentre is $$(h, k)$$, then $$3h + k$$ is equal to :

A

$$11$$

B

$$12$$

C

$$13$$

D

$$14$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 10

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Let an ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$, $$a < b$$, pass through the point $$(4, 3)$$ and have eccentricity $$\frac{\sqrt{5}}{3}$$. Then the length of its latus rectum is :

A

$$\frac{4\sqrt{5}}{3}$$

B

$$2\sqrt{5}$$

C

$$\frac{7\sqrt{5}}{3}$$

D

$$\frac{8\sqrt{5}}{3}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 11

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If $$\sin\left(\frac{\pi}{18}\right) \sin\left(\frac{5\pi}{18}\right) \sin\left(\frac{7\pi}{18}\right) = K$$, then the value of $$\sin\left(\frac{10K\pi}{3}\right)$$ is :

A

$$\frac{\sqrt{3}+1}{2\sqrt{2}}$$

B

$$\frac{\sqrt{3}-1}{\sqrt{2}}$$

C

$$\frac{\sqrt{3}}{2}$$

D

$$\frac{1}{2}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 12

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Let $$S = \{x \in [-\pi, \pi] : \sin x(\sin x + \cos x) = a, a \in \mathbb{Z}\}$$. Then $$n(S)$$ is equal to :

A

$$3$$

B

$$6$$

C

$$7$$

D

$$9$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 13

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If the point of intersection of the lines $$\frac{x+1}{3} = \frac{y+a}{5} = \frac{z+b+1}{7}$$ and $$\frac{x-2}{1} = \frac{y-b}{4} = \frac{z-2a}{7}$$ lies on the $$xy$$-plane, then the value of $$a + b$$ is :

A

$$2$$

B

$$5$$

C

$$7$$

D

$$9$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 14

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If $$\vec{a}$$ and $$\vec{b}$$ are two vectors such that $$|\vec{a}| = 2$$ and $$|\vec{b}| = 3$$, then the maximum value of $$3|3\vec{a} + 2\vec{b}| + 4|3\vec{a} - 2\vec{b}|$$ is :

A

$$30$$

B

$$36$$

C

$$60$$

D

$$72$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 15

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Let a line L passing through the point $$(1, 1, 1)$$ be perpendicular to both the vectors $$2\hat{i} + 2\hat{j} + \hat{k}$$ and $$\hat{i} + 2\hat{j} + 2\hat{k}$$. If P(a, b, c) is the foot of perpendicular from the origin on the line L, then the value of $$34(a + b + c)$$ is :

A

$$50$$

B

$$80$$

C

$$100$$

D

$$120$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 16

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If $$\lim_{x \to 2} \frac{\sin(x^3 - 5x^2 + ax + b)}{(\sqrt{x-1} - 1) \log_e(x-1)} = m$$, then $$a + b + m$$ is equal to :

A

$$5$$

B

$$6$$

C

$$8$$

D

$$10$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 17

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If the curve $$y = f(x)$$ passes through the point $$(1, e)$$ and satisfies the differential equation $$dy = y(2 + \log_e x) dx$$, $$x > 0$$, then $$f(e)$$ is equal to :

A

$$e^e$$

B

$$e^{e^2}$$

C

$$e^{2e}$$

D

$$e^{2^e}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 18

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The number of critical points of the function $$f(x) = \begin{cases} \left|\frac{\sin x}{x}\right|, & x \neq 0 \\ 1, & x = 0 \end{cases}$$ in the interval $$(-2\pi, 2\pi)$$ is equal to :

A

$$1$$

B

$$3$$

C

$$5$$

D

$$7$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 19

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Let $$[\cdot]$$ denote the greatest integer function. Then the value of $$\int_0^3 \left(\frac{e^x + e^{-x}}{[x]!}\right) dx$$ is :

A

$$e^2 + e^3 - \frac{1}{e^2} - \frac{1}{e^3}$$

B

$$\frac{1}{2}\left(e^2 + e^3 - \frac{1}{e^2} - \frac{1}{e^3}\right)$$

C

$$e^2 + e^3 - \frac{1}{2e^2} - \frac{1}{2e^3}$$

D

$$\frac{1}{2}(e^2 + e^3) - \frac{1}{e^2} - \frac{1}{e^3}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 20

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Let $$y = y(x)$$ be the solution curve of the differential equation $$(1 + \sin x)\frac{dy}{dx} + (y+1)\cos x = 0$$, $$y(0) = 0$$. If the curve $$y = y(x)$$ passes through the point $$\left(\alpha, \frac{-1}{2}\right)$$, then a value of $$\alpha$$ is :

A

$$\frac{\pi}{6}$$

B

$$\frac{\pi}{4}$$

C

$$\frac{\pi}{3}$$

D

$$\frac{\pi}{2}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 21

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If the domain of the function $$f(x)=\sqrt{\log_{0.6}\left(\left|\frac{2x-5}{x^2-4}\right|\right)}$$ is $$(-\infty, a] \cup \{b\} \cup [c, d) \cup (e, \infty)$$, then the value of $$a + b + c + d + e$$ is __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 22

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If $$\sum_{k=1}^{n} a_k = 6n^3$$, then $$\sum_{k=1}^{6} \left(\frac{a_{k+1} - a_k}{36}\right)^2$$ is equal to __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 23

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Let $$a, b, c \in \{1, 2, 3, 4\}$$. If the probability, that $$ax^2 + 2\sqrt{2}bx + c > 0$$ for all $$x \in \mathbb{R}$$, is $$\frac{m}{n}$$, $$\gcd(m, n) = 1$$, then $$m + n$$ is equal to __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 24

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Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line $$x + y = 1$$ is $$\sqrt{14}$$, then the square of the radius of C is __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 25

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If $$\alpha = \int_0^{2\sqrt{3}} \log_2(x^2 + 4) dx + \int_2^4 \sqrt{2^x - 4} \, dx$$, then $$\alpha^2$$ is equal to __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 26

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The dimensional formula of $$\frac{1}{2} \epsilon_0 E^2$$ ($$\epsilon_0$$ = permittivity of vacuum and E = electric field) is $$M^a L^b T^c$$. The value of $$2a - b + c$$ = __________.

A

$$0$$

B

$$1$$

C

$$-1$$

D

$$2$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 27

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The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is $$\alpha \times 10^9$$ N/m$$^2$$. The value of $$\alpha$$ is __________ . (Ignore the contribution of the load to Young's modulus error calculation)

A

$$1.3$$

B

$$1.65$$

C

$$0.13$$

D

$$0.25$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 28

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The velocity of a particle is given as $$\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k}$$ m/s. The magnitude of acceleration at point $$(1, 2, 4)$$ is __________ m/s$$^2$$.

A

$$\sqrt{6}$$

B

$$9$$

C

$$\sqrt{33}$$

D

$$0$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 29

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The position of an object having mass 0.1 kg as a function of time t is given as $$\vec{r} = \left(10t^2 \hat{i} + 5t^3 \hat{j}\right)$$ m. At $$t = 1$$ s, which of the following statements are correct? A. The linear momentum $$\vec{p} = \left(2\hat{i} + 1.5\hat{j}\right)$$ kg·m/s. B. The force acting on the object $$\vec{F} = \left(2\hat{i} + 3\hat{j}\right)$$ N. C. The angular momentum of the object about its origin $$\vec{L} = 15 \hat{k}$$ J·s. D. The torque acting on the object about its origin $$\vec{\tau} = 20 \hat{k}$$ N·m. Choose the correct answer from the options given below :

A

A, B and C only

B

B, C and D only

C

A, C and D only

D

A, B and D only

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NTA JEE Mains 2nd April Shift 1 2026 - Question 30

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A planet (P$$_1$$) is moving around the star of mass 2M in the orbit of radius R. Another planet (P$$_2$$) is moving around another star of mass 4M in a orbit of radius 2R. Ratio of time periods of revolution of P$$_2$$ and P$$_1$$ is __________.

A

$$\frac{1}{2}$$

B

$$2$$

C

$$4$$

D

$$\frac{1}{4}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 31

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A particle is rotating in a circular path and at any instant its motion can be described as $$\theta = \frac{5t^4}{40} - \frac{t^3}{3}$$. The angular acceleration of the particle after 10 seconds is __________ rad/s$$^2$$.

A

$$150$$

B

$$120$$

C

$$130$$

D

$$170$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 32

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A parallel plate air capacitor has a capacitance C. When it is half filled as shown in figure with a dielectric constant $$K = 5$$, the percentage increase in the capacitance is __________.

A

$$33.34$$

B

$$66.67$$

C

$$200$$

D

$$400$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 33

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Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $$\Delta Q : \Delta U : \Delta W$$ is __________.

A

$$2:3:5$$

B

$$5:3:2$$

C

$$2:5:7$$

D

$$7:5:2$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 34

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Two charged conducting spheres S$$_1$$ and S$$_2$$ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S$$_1$$ and S$$_2$$ spheres are E$$_{S1}$$ and E$$_{S2}$$ respectively. The value of $$\frac{E_{S1}}{E_{S2}}$$ is __________.

A

$$\frac{3}{2}$$

B

$$\frac{2}{3}$$

C

$$\frac{4}{9}$$

D

$$\frac{9}{4}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 35

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The equation of a plane progressive wave is given by $$y = 5 \cos \pi \left(200t - \frac{x}{150}\right)$$ where x and y are in cm and t is in second. The velocity of the wave is __________ m/s.

A

$$120$$

B

$$150$$

C

$$200$$

D

$$300$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 36

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Two short electric dipoles A and B having dipole moment p$$_1$$ and p$$_2$$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point x is making an angle of 60° with the line joining points O and x. The ratio of the dipole moments p$$_2$$/p$$_1$$ is __________.

A

$$\frac{\sqrt{3}}{2}$$

B

$$2\sqrt{3}$$

C

$$\frac{1}{\sqrt{3}}$$

D

$$\sqrt{3}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 37

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For the given circuit (shown in part (A)) the time dependent input voltage $$v_{in}(t)$$ and corresponding output $$v_o(t)$$ are shown in part (B) and part (C), respectively. Identify the components that are used in the circuit between points X and Y.

A

B

C

D

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NTA JEE Mains 2nd April Shift 1 2026 - Question 38

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When a coil is placed in a time dependent magnetic field the power dissipated in it is P. The number of turns, area of the coil and radius of the coil wire are N, A and r respectively. For a second coil number of turns, area of the coil and radius of the coil wire are 2N, 2A and 3r respectively. When the first coil is replaced with second coil the power dissipated in it is $$\sqrt{2} \alpha P$$. The value of $$\alpha$$ is __________.

A

$$36$$

B

$$128\sqrt{2}$$

C

$$16$$

D

$$64$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 39

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Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are B$$_1$$ and B$$_2$$ respectively, then the ratio $$\frac{B_1}{B_2}$$ is __________.

A

$$\frac{2+\pi}{1+\pi}$$

B

$$\frac{1+\pi}{1-\pi}$$

C

$$\frac{2+\pi}{1-\pi}$$

D

$$\frac{1+\pi}{2-\pi}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 40

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For a thin symmetric prism made of glass (refractive index 1.5), the ratio of incident angle and minimum deviation will be __________.

A

$$3:4$$

B

$$3:2$$

C

$$2:1$$

D

$$1:2$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 41

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Refer the figure given below. $$\mu_1$$ and $$\mu_2$$ are refractive indices of air and lens material. The height of image will be __________ cm.

A

$$1$$

B

$$0.5$$

C

$$1.2$$

D

$$0.25$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 42

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For a certain metal, when monochromatic light of wavelength $$\lambda$$ is incident, the stopping potential for photoelectrons is $$3V_0$$. When the same metal is illuminated by light of wavelength $$2\lambda$$, then the stopping potential becomes $$V_0$$. The threshold wavelength for photoelectric emission for the given metal is $$\alpha \lambda$$. The value of $$\alpha$$ is __________.

A

$$1$$

B

$$4$$

C

$$2$$

D

$$3$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 43

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An electromagnetic wave travelling in x-direction is described by field equation $$E_y = 300 \sin \omega \left(t - \frac{x}{c}\right)$$. If the electron is restricted to move in y-direction only with speed of $$1.5 \times 10^6$$ m/s then ratio of maximum electric and magnetic forces acting on the electron is __________.

A

$$200$$

B

$$150$$

C

$$400$$

D

$$300$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 44

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Angular momentum of an electron in a hydrogen atom is $$\frac{3h}{\pi}$$, then the energy of the electron is __________ eV.

A

$$-1.51$$

B

$$-0.85$$

C

$$-0.38$$

D

$$-0.28$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 45

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A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is $$\alpha \times 10^{-6}$$ J. The value of $$\alpha$$ is __________. (Take surface tension of liquid = 0.08 N/m)

A

$$10$$

B

$$7$$

C

$$8$$

D

$$11$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 46

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In single slit diffraction pattern, the wavelength of light used is 628 nm and slit width is 0.2 mm, the angular width of central maximum is $$\alpha \times 10^{-2}$$ degrees. The value of $$\alpha$$ is __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 47

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A vessel contains 0.15 m$$^3$$ of a gas at pressure 8 bar and temperature 140 °C with $$c_p = 3R$$ and $$c_v = 2R$$. It is expanded adiabatically till pressure falls to 1 bar. The work done during this process is __________ kJ. (R is gas constant)

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NTA JEE Mains 2nd April Shift 1 2026 - Question 48

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1 $$\mu$$C charge moving with velocity $$\vec{v} = \left(\hat{i} - 2\hat{j} + 3\hat{k}\right)$$ m/s in the region of magnetic field $$\vec{B} = \left(2\hat{i} + 3\hat{j} - 5\hat{k}\right)$$ T. The magnitude of force acting on it is $$\sqrt{\alpha} \times 10^{-6}$$ N. The value of $$\alpha$$ is __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 49

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A uniform wire of length $$l$$ of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at $$\frac{l}{3}$$ distance from the top is $$\left(\frac{W}{A} + \frac{2}{\gamma} \cdot \frac{w}{A}\right)$$, where A is the cross sectional area of the wire. The value of $$\gamma$$ is __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 50

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A tub is filled with water and a wooden cube 10 cm × 10 cm × 10 cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.87 cm. The mass of the metal coin is __________ gram. (Take water density as 1 g/cm$$^3$$ and density of wood = 0.4 g/cm$$^3$$)

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NTA JEE Mains 2nd April Shift 1 2026 - Question 51

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The mass of iron converted into Fe$$_3$$O$$_4$$ by the action of 18 g of steam is : (Given : Molar mass of H, O and Fe are 1, 16 and 56 g mol$$^{-1}$$ respectively) Assume iron is present in excess :

A

$$2.1$$ g

B

$$4.2$$ g

C

$$21$$ g

D

$$42$$ g

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NTA JEE Mains 2nd April Shift 1 2026 - Question 52

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What is the energy (in J atom$$^{-1}$$) required for the following process? $$\text{Li}^{2+}(g) \rightarrow \text{Li}^{3+}(g) + e^-$$ (Take the ionization energy for the H atom in the ground state as $$2.18 \times 10^{-18}$$ J atom$$^{-1}$$)

A

$$8.72 \times 10^{-18}$$

B

$$1.962 \times 10^{-18}$$

C

$$1.962 \times 10^{-17}$$

D

$$6.54 \times 10^{-17}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 53

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Given below are two statements : **Statement (I) :** The correct sequence of bond lengths in the following species is : $$O_2^+ < O_2 < O_2^- < O_2^{2-}$$ **Statement (II) :** The correct sequence of number of unpaired electrons in the following species is : $$O_2 > O_2^+ > O_2^- > O_2^{2-}$$ In the light of the above statements, choose the correct answer from the options given below :

A

Both Statement I and Statement II are true

B

Both Statement I and Statement II are false

C

Statement I is true but Statement II is false

D

Statement I is false but Statement II is true

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NTA JEE Mains 2nd April Shift 1 2026 - Question 54

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Consider the following data.
(i) 2Al(s) + 6HCl(aq) → Al$$_2$$Cl$$_6$$(aq) + 3H$$_2$$(g) + 1200 kJ/mol
(ii) H$$_2$$(g) + Cl$$_2$$(g) → 2HCl(g) + 164 kJ/mol.
(iii) HCl(g) + aq → HCl(aq) + 83 kJ/mol.
(iv) Al$$_2$$Cl$$_6$$(s) + aq → Al$$_2$$Cl$$_6$$(aq) + 663 kJ/mol
The enthalpy of formation of anhydrous solid Al$$_2$$Cl$$_6$$ is :

A

$$-648$$ kJ mol$$^{-1}$$

B

$$-1350$$ kJ mol$$^{-1}$$

C

$$-2002$$ kJ mol$$^{-1}$$

D

$$-1527$$ kJ mol$$^{-1}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 55

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19.5 g of fluoro acetic acid (molar mass = 78 g mol$$^{-1}$$) is dissolved in 500 g of water at 298 K. The depression in the freezing point was 1°C. What is K$$_a$$ of fluoro acetic acid? (For water, K$$_f$$ = 1.86 K kg mol$$^{-1}$$). Assume molarity and molality to have same values.

A

$$10^{-6}$$

B

$$4 \times 10^{-4}$$

C

$$3 \times 10^{-5}$$

D

$$3 \times 10^{-3}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 56

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The solubility product constants of Ag$$_2$$CrO$$_4$$ and AgBr are 32x and 4y respectively at 298 K. The value of $$\left(\frac{\text{molarity of Ag}_2\text{CrO}_4}{\text{molarity of AgBr}}\right)$$ can be expressed as :

A

$$\frac{2\sqrt[3]{x}}{y}$$

B

$$2\sqrt{\frac{x}{y}}$$

C

$$\sqrt{\frac{x}{y}}$$

D

$$\frac{\sqrt[3]{x}}{\sqrt{y}}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 57

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An electrochemical cell is constructed using half cells in the direction of spontaneous change
Fe(OH)$$_2$$(s) + 2e$$^-$$ → Fe(s) + 2OH$$^-$$(aq)       E$$^0$$ = −0.88 V
and AgBr(s) + e$$^-$$ → Ag(s) + Br$$^-$$(aq)                 E$$^0$$ = +0.07 V
Which of the following option is correct?

A

Overall reaction Fe(s)+2OH$$^-$$(aq)+2AgBr(s) ⇌ Fe(OH)$$_2$$(s)+2Ag(s)+2Br$$^-$$(aq)

B

$$E^0_{cell} = -0.95$$ V

C

Fe is reduced in the electrochemical cell

D

$$E^0_{cell}$$ is an extensive property

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NTA JEE Mains 2nd April Shift 1 2026 - Question 58

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$$t_{100\%}$$ is the time required for the 100% completion of the reaction while $$t_{1/2}$$ is the time required for 50% of the reaction to be completed. Which of the following option correctly represents the relation between $$t_{100\%}$$ and $$t_{1/2}$$ for zero and first order reactions respectively?

A

$$t_{100\%} = (t_{1/2})^2$$ and $$t_{100\%} = (t_{1/2})^{-\infty}$$

B

$$t_{100\%} = 2t_{1/2}$$ and $$t_{100\%} = (t_{1/2})^{\infty}$$

C

$$t_{100\%} = 2t_{1/2}$$ and $$t_{100\%} = (2t_{1/2})^2$$

D

$$t_{100\%} = (t_{1/2})^{\infty}$$ and $$t_{100\%} = 2t_{1/2}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 59

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Given below are two statements :

 Statement (I) : The first ionisation enthalpy of the elements Na, Mg, Cl and Ar follows the order Na > Mg > Cl > Ar.

 Statement (II) : Among Ca, Al, Fe and B, the third ionisation enthalpy is very high for Ca. In the light of the above statements, choose the correct answer from the options given below :

A

Both Statement I and Statement II are true

B

Both Statement I and Statement II are false

C

Statement I is true but Statement II is false

D

Statement I is false but Statement II is true

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NTA JEE Mains 2nd April Shift 1 2026 - Question 60

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Given below are two statements : 

Statement (I) : Oxidising power of halogens decreases in the order F$$_2$$ > Cl$$_2$$ > Br$$_2$$ > I$$_2$$, which is the basis of "Layer test". 

Statement (II) : "Layer test" to identify Br$$_2$$ and I$$_2$$ in aqueous solution involves the oxidation of bromide or iodide into Br$$_2$$ or I$$_2$$ respectively with Cl$$_2$$, which is a type of displacement redox reaction. 

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

A

Both Statement I and Statement II are true

B

Both Statement I and Statement II are false

C

Statement I is true but Statement II is false

D

Statement I is false but Statement II is true

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NTA JEE Mains 2nd April Shift 1 2026 - Question 61

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Which of the following sets includes all the species that will change the orange colour of K$$_2$$Cr$$_2$$O$$_7$$ in acidic medium?

A

Fe$$^{2+}$$, Sn$$^{2+}$$, I$$^-$$, S$$^{2-}$$

B

S$$^{2-}$$, Fe$$^{3+}$$, I$$^-$$, C$$_2$$O$$_4^{2-}$$

C

Fe$$^{2+}$$, NO$$_2^-$$, SO$$_2$$, Sn$$^{4+}$$

D

Fe$$^{3+}$$, SO$$_4^{2-}$$, S$$^{2-}$$, Sn$$^{4+}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 62

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Match List - I with List - II. 

Choose the correct answer from the options given below :

A

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

B

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

C

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

D

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

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NTA JEE Mains 2nd April Shift 1 2026 - Question 63

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Given below are two statements :
Statement (I) :1,2,3-Trihydroxypropane can be separated from water by simple distillation.
Statement (II) :An azeotropic mixture cannot be separated by fractional distillation.
In the light of the above statements, choose the correct answer from the options given below :

A

Both Statement I and Statement II are true

B

Both Statement I and Statement II are false

C

Statement I is true but Statement II is false

D

Statement I is false but Statement II is true

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NTA JEE Mains 2nd April Shift 1 2026 - Question 64

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Given below are two statements :
**Statement (I) :** Benzyl chloride reacts faster in S$$_N$$1 mechanism than ethyl chloride.
**Statement (II) :** Ethyl carbocation intermediate is less stabilized by hyperconjugation than benzyl carbocation by resonance.
In the light of the above statements, choose the correct answer from the options given below :

A

Both Statement I and Statement II are true

B

Both Statement I and Statement II are false

C

Statement I is true but Statement II is false

D

Statement I is false but Statement II is true

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NTA JEE Mains 2nd April Shift 1 2026 - Question 65

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In IUPAC nomenclature, the correct order of decreasing priority of functional group is :

A

$$-\text{CONH}_2, >\text{C=O}, -\text{CHO}, -\text{NH}_2, -\text{C} \equiv \text{C}-$$

B

$$-\text{CONH}_2, -\text{COOCH}_3, -\text{CHO}, -\text{NH}_2, -\text{OH}$$

C

$$-\text{CONH}_2, -\text{CHO}, >\text{C=O}, -\text{NH}_2, -\text{C} \equiv \text{C}-$$

D

$$-\text{CONH}_2, -\text{CHO}, -\text{CN}, -\text{NH}_2, -\text{C} \equiv \text{C}-$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 66

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For the given molecule, "x", the preferred site for the attack of the electrophile is :

A

Predominantly at "r"

B

"r" and "u"

C

"p" and "s"

D

Predominantly at "u"

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NTA JEE Mains 2nd April Shift 1 2026 - Question 67

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Match List - I with List - II. 

Choose the correct answer from the options given below :

A

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

B

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

C

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

D

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

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NTA JEE Mains 2nd April Shift 1 2026 - Question 68

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Consider the three aromatic molecules (P, Q and R) whose structures have been given below :

The correct order regarding the reactivity of these compounds with 

under optimum but slightly acidic medium is :

A

P > Q > R

B

R > P > Q

C

R > Q > P

D

P > R > Q

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NTA JEE Mains 2nd April Shift 1 2026 - Question 69

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Match List - I with List - II. 

Choose the correct answer from the options given below :

A

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

B

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

C

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

D

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

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NTA JEE Mains 2nd April Shift 1 2026 - Question 70

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A salt with few drops of conc. HCl gives apple green colour in flame test. The group precipitate of the salt is dissolved in acetic acid and treated with K$$_2$$CrO$$_4$$ to give yellow precipitate. When the sodium carbonate extract of the salt solution is heated with conc. HNO$$_3$$ and ammonium molybdate, it resulted a canary yellow precipitate. The cation and anion present in the salt are respectively,

A

Ca$$^{2+}$$ and SO$$_4^{2-}$$

B

Ba$$^{2+}$$ and PO$$_4^{3-}$$

C

Mn$$^{2+}$$ and PO$$_4^{3-}$$

D

Ba$$^{2+}$$ and SO$$_4^{2-}$$

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NTA JEE Mains 2nd April Shift 1 2026 - Question 71

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5.33 g of CrCl$$_3$$·6H$$_2$$O, which is a 1 : 3 electrolyte, is dissolved in water and is passed through a cation exchanger. The chloride ions in the eluted solution, on treatment with AgNO$$_3$$ results in 8.61 g of AgCl. The ratio of moles of complex reacted and moles of AgCl formed is __________ × 10$$^{-2}$$. (Nearest integer) [Molar mass in g mol$$^{-1}$$ Cr : 52, Ag : 108, Cl : 35.5, H : 1, O : 16]

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NTA JEE Mains 2nd April Shift 1 2026 - Question 72

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Consider the isomers of hydrocarbon with molecular formula C$$_5$$H$$_{10}$$. These isomers do not decolourise KMnO$$_4$$ solution. These isomers are subjected to chlorination with chlorine in presence of light to give monochloro compounds. The total number of monochloro compounds (structural isomers only) formed is __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 73

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One mole of an alkane (x) requires 8 mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (x) is __________.

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NTA JEE Mains 2nd April Shift 1 2026 - Question 74

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For reaction A → P, rate constant k = 1.5 × 10$$^3$$ s$$^{-1}$$ at 27°C. If activation energy for the above reaction is 60 kJ mol$$^{-1}$$, then the temperature (in °C) at which rate constant, k = 4.5 × 10$$^3$$ s$$^{-1}$$ is __________. (Nearest integer) Given : log 2 = 0.30, log 3 = 0.48, R = 8.3 J K$$^{-1}$$ mol$$^{-1}$$, ln 10 = 2.3

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NTA JEE Mains 2nd April Shift 1 2026 - Question 75

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At the transition temperature T, A ⇌ B and ΔG$$^0$$ = 105 − 35 log T where A and B are two states of substance X. The transition temperature in °C when pressure is 1 atm is __________. (Nearest integer)

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