NTA JEE Main 2025 April 3rd Shift 1

NTA JEE Main 2025 April 3rd Shift 1 - Question 1

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Let A be a matrix of order $$3 \times 3$$ and $$|A| = 5$$. If $$|2\text{adj}(3A \text{adj}(2A))| = 2^{\alpha} \cdot 3^{\beta} \cdot 5^{\gamma}$$, $$\alpha, \beta, \gamma \in \mathbb{N}$$ then $$\alpha + \beta + \gamma$$ is equal to

A

$$25$$

B

$$26$$

C

$$27$$

D

$$28$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 2

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Let a line passing through the point $$(4, 1, 0)$$ intersect the line $$L_1 : \frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$$ at the point $$A(\alpha, \beta, \gamma)$$ and the line $$L_2 : x - 6 = y = -z + 4$$ at the point $$B(a, b, c)$$. Then $$\begin{vmatrix} 1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c \end{vmatrix}$$ is equal to

A

$$8$$

B

$$16$$

C

$$12$$

D

$$6$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 3

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Let $$\alpha$$ and $$\beta$$ be the roots of $$x^2 + \sqrt{3}x - 16 = 0$$, and $$\gamma$$ and $$\delta$$ be the roots of $$x^2 + 3x - 1 = 0$$. If $$P_n = \alpha^n + \beta^n$$ and $$Q_n = \gamma^n + \delta^n$$, then $$\frac{P_{25} + \sqrt{3}P_{24}}{2P_{23}} + \frac{Q_{25} - Q_{23}}{Q_{24}}$$ is equal to

A

$$3$$

B

$$4$$

C

$$5$$

D

$$7$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 4

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The sum of all rational terms in the expansion of $$(2 + \sqrt{3})^8$$ is

A

$$16923$$

B

$$3763$$

C

$$33845$$

D

$$18817$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 5

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Let $$A = \{-3, -2, -1, 0, 1, 2, 3\}$$. Let R be a relation on A defined by $$xRy$$ if and only if $$0 \leq x^2 + 2y \leq 4$$. Let $$l$$ be the number of elements in R and $$m$$ be the minimum number of elements required to be added in R to make it a reflexive relation. Then $$l + m$$ is equal to

A

$$19$$

B

$$20$$

C

$$17$$

D

$$18$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 6

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A line passing through the point $$P(\sqrt{5}, \sqrt{5})$$ intersects the ellipse $$\frac{x^2}{36} + \frac{y^2}{25} = 1$$ at A and B such that $$(PA) \cdot (PB)$$ is maximum. Then $$5(PA^2 + PB^2)$$ is equal to :

A

$$218$$

B

$$377$$

C

$$290$$

D

$$338$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 7

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The sum $$1 + 3 + 11 + 25 + 45 + 71 + \ldots$$ upto 20 terms, is equal to

A

$$7240$$

B

$$7130$$

C

$$6982$$

D

$$8124$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 8

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If the domain of the function $$f(x) = \log_e\left(\frac{2x - 3}{5 + 4x}\right) + \sin^{-1}\left(\frac{4 + 3x}{2 - x}\right)$$ is $$[\alpha, \beta)$$, then $$\alpha^2 + 4\beta$$ is equal to

A

$$5$$

B

$$4$$

C

$$3$$

D

$$7$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 9

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If $$\sum_{r=1}^{9} \left(\frac{r+3}{2^r}\right) \cdot \,^{9}C_r = \alpha\left(\frac{3}{2}\right)^9 - \beta$$, $$\alpha, \beta \in \mathbb{N}$$, then $$(\alpha + \beta)^2$$ is equal to

A

$$27$$

B

$$9$$

C

$$81$$

D

$$18$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 10

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The number of solutions of the equation $$2x + 3\tan x = \pi$$, $$x \in [-2\pi, 2\pi] - \left\{\pm\frac{\pi}{2}, \pm\frac{3\pi}{2}\right\}$$ is

A

$$6$$

B

$$5$$

C

$$4$$

D

$$3$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 11

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If $$y(x) = \begin{vmatrix} \sin x & \cos x & \sin x + \cos x + 1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{vmatrix}$$, $$x \in \mathbb{R}$$, then $$\frac{d^2y}{dx^2} + y$$ is equal to

A

$$-1$$

B

$$28$$

C

$$27$$

D

$$1$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 12

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Let g be a differentiable function such that $$\int_0^x g(t)\,dt = x - \int_0^x tg(t)\,dt$$, $$x \geq 0$$ and let $$y = y(x)$$ satisfy the differential equation $$\frac{dy}{dx} - y\tan x = 2(x+1)\sec x \cdot g(x)$$, $$x \in \left[0, \frac{\pi}{2}\right)$$. If $$y(0) = 0$$, then $$y\left(\frac{\pi}{3}\right)$$ is equal to

A

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

B

$$\frac{4\pi}{3}$$

C

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

D

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

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NTA JEE Main 2025 April 3rd Shift 1 - Question 13

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A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $$L_1 : 2x + y + 6 = 0$$ and $$L_2 : 4x + 2y - p = 0$$, $$p \gt 0$$, at the points A and B, respectively. If $$AB = \frac{9}{\sqrt{2}}$$ and the foot of the perpendicular from the point A on the line $$L_2$$ is M, then $$\frac{AM}{BM}$$ is equal to

A

$$5$$

B

$$4$$

C

$$2$$

D

$$3$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 14

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Let $$z \in \mathbb{C}$$ be such that $$\frac{z^2 + 3i}{z - 2 + i} = 2 + 3i$$. Then the sum of all possible values of $$z^2$$ is

A

$$19 - 2i$$

B

$$-19 - 2i$$

C

$$19 + 2i$$

D

$$-19 + 2i$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 15

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Let $$f(x) = \int x^3\sqrt{3 - x^2}\,dx$$. If $$5f(\sqrt{2}) = -4$$, then $$f(1)$$ is equal to

A

$$-\frac{2\sqrt{2}}{5}$$

B

$$-\frac{8\sqrt{2}}{5}$$

C

$$-\frac{4\sqrt{2}}{5}$$

D

$$-\frac{6\sqrt{2}}{5}$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 16

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Let $$a_1, a_2, a_3, \ldots$$ be a G.P. of increasing positive numbers. If $$a_3 a_5 = 729$$ and $$a_2 + a_4 = \frac{111}{4}$$, then $$24(a_1 + a_2 + a_3)$$ is equal to

A

$$131$$

B

$$130$$

C

$$129$$

D

$$128$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 17

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Let the domain of the function $$f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2)$$ be $$(a, b)$$. If $$\int_0^{b-a} [x^2]\,dx = p - \sqrt{q} - \sqrt{r}$$, $$p, q, r \in \mathbb{N}$$, $$\gcd(p, q, r) = 1$$, then $$p + q + r$$ is equal to

A

$$10$$

B

$$8$$

C

$$11$$

D

$$9$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 18

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The radius of the smallest circle which touches the parabolas $$y = x^2 + 2$$ and $$x = y^2 + 2$$ is

A

$$\frac{7\sqrt{2}}{2}$$

B

$$\frac{7\sqrt{2}}{16}$$

C

$$\frac{7\sqrt{2}}{4}$$

D

$$\frac{7\sqrt{2}}{8}$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 19

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Let $$f(x) = \begin{cases} (1 + ax)^{1/x}, & x \lt 0 \\ 1 + b, & x = 0 \\ \frac{(x+4)^{1/2} - 2}{(x+c)^{1/3} - 2}, & x \gt 0 \end{cases}$$ be continuous at $$x = 0$$. Then $$e^a bc$$ is equal to

A

$$64$$

B

$$72$$

C

$$48$$

D

$$36$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 20

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Line $$L_1$$ passes through the point $$(1, 2, 3)$$ and is parallel to z-axis. Line $$L_2$$ passes through the point $$(\lambda, 5, 6)$$ and is parallel to y-axis. Let for $$\lambda = \lambda_1, \lambda_2$$, $$\lambda_2 \lt \lambda_1$$, the shortest distance between the two lines be 3. Then the square of the distance of the point $$(\lambda_1, \lambda_2, 7)$$ from the line $$L_1$$ is

A

$$40$$

B

$$32$$

C

$$25$$

D

$$37$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 21

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All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $$n$$ be denoted by $$W_n$$. Let the probability $$P(W_n)$$ of choosing the word $$W_n$$ satisfy $$P(W_n) = 2P(W_{n-1})$$, $$n \gt 1$$. If $$P(CDBEA) = \frac{2^{\alpha}}{2^{\beta} - 1}$$, $$\alpha, \beta \in \mathbb{N}$$, then $$\alpha + \beta$$ is equal to __________.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 22

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Let the product of the focal distances of the point $$P(4, 2\sqrt{3})$$ on the hyperbola $$H : \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ be 32. Let the length of the conjugate axis of H be p and the length of its latus rectum be q. Then $$p^2 + q^2$$ is equal to __________.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 23

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Let $$\vec{a} = \hat{i} + \hat{j} + \hat{k}$$, $$\vec{b} = 3\hat{i} + 2\hat{j} - \hat{k}$$, $$\vec{c} = \lambda\hat{j} + \mu\hat{k}$$ and $$\hat{d}$$ be a unit vector such that $$\vec{a} \times \hat{d} = \vec{b} \times \hat{d}$$ and $$\vec{c} \cdot \hat{d} = 1$$. If $$\vec{c}$$ is perpendicular to $$\vec{a}$$, then $$|3\lambda\hat{d} + \mu\vec{c}|^2$$ is equal to __________.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 24

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If the number of seven-digit numbers, such that the sum of their digits is even, is $$m \cdot n \cdot 10^n$$; $$m, n \in \{1, 2, 3, \ldots, 9\}$$, then $$m + n$$ is equal to __________.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 25

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The area of the region bounded by the curve $$y = \max\{|x|, x|x-2|\}$$, then x-axis and the lines $$x = -2$$ and $$x = 4$$ is equal to __________.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 26

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During the melting of a slab of ice at 273 K at atmospheric pressure :

A

Internal energy of ice-water system remains unchanged.

B

Positive work is done by the ice-water system on the atmosphere.

C

Internal energy of the ice-water system decreases.

D

Positive work is done on the ice-water system by the atmosphere.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 27

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Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m$$^2$$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : $$(g = 10\,\text{m/s}^2)$$

A

$$3$$ m/s

B

$$5$$ m/s

C

$$2$$ m/s

D

$$4$$ m/s

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NTA JEE Main 2025 April 3rd Shift 1 - Question 28

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Choose the correct logic circuit for the given truth table having inputs A and B.

A

B

C

D

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NTA JEE Main 2025 April 3rd Shift 1 - Question 29

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The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2m away from it, is :

A

$$1.5 \times 10^{-8}$$ Pascals

B

$$0$$

C

$$6 \times 10^{-8}$$ Pascals

D

$$3 \times 10^{-8}$$ Pascals

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NTA JEE Main 2025 April 3rd Shift 1 - Question 30

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A wire of length 25 m and cross-sectional area 5 mm$$^2$$ having resistivity of $$2 \times 10^{-6}\,\Omega$$ m is bent into a complete circle. The resistance between diametrically opposite points will be

A

$$12.5\,\Omega$$

B

$$50\,\Omega$$

C

$$100\,\Omega$$

D

$$2.5\,\Omega$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 31

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Two blocks of masses m and M, $$(M \gt m)$$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then ($$\mu$$ = coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is $$T = 2\pi\sqrt{\frac{m+M}{k}}$$
(B) The acceleration of the blocks is $$a = \frac{kx}{M+m}$$
(C) The magnitude of the frictional force on upper block is $$\frac{m\mu|x|}{M+m}$$
(D) The maximum amplitude of the upper block, if it does not slip, is $$\frac{\mu(M+m)g}{k}$$
(E) Maximum frictional force can be $$\mu(M+m)g$$.

Choose the correct answer from the options given below :

A

A, B, D Only

B

B, C, D Only

C

C, D, E Only

D

A, B, C Only

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NTA JEE Main 2025 April 3rd Shift 1 - Question 32

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Which of the following curves possibly represent one-dimensional motion of a particle ?

Choose the correct answer from the options given below :

A

A, B and D only

B

A, B and C only

C

A and B only

D

A, C and D only

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NTA JEE Main 2025 April 3rd Shift 1 - Question 33

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A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant $$\varepsilon_1$$ and $$\varepsilon_2$$, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are $$C_1$$ and $$C_2$$ respectively, then $$\frac{C_1}{C_2}$$ is :

A

$$\frac{\varepsilon_1 \varepsilon_2^2}{(\varepsilon_1 + \varepsilon_2)^2}$$

B

$$\frac{4\varepsilon_1 \varepsilon_2}{(\varepsilon_1 + \varepsilon_2)^2}$$

C

$$\frac{\varepsilon_1 \varepsilon_2}{\varepsilon_1 + \varepsilon_2}$$

D

$$\frac{\varepsilon_0(\varepsilon_1 + \varepsilon_2)}{2}$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 34

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Match the LIST-I with LIST-II.

Choose the correct answer from the options given below :

A

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

B

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

C

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

D

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

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NTA JEE Main 2025 April 3rd Shift 1 - Question 35

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A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

A

$$3.5$$ m/s$$^2$$

B

$$0.35$$ m/s$$^2$$

C

$$2.5$$ m/s$$^2$$

D

$$0.25$$ m/s$$^2$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 36

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A piston of mass M is hung from a massless spring whose restoring force law goes as $$F = -kx^3$$, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with 'n' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $$L_0$$ to $$L_1$$, the total energy delivered by the filament is (Assume spring to be in its natural length before heating)

A

$$3nRT\ln\left(\frac{L_1}{L_0}\right) + 2Mg(L_1 - L_0) + \frac{k}{3}(L_1^3 - L_0^3)$$

B

$$nRT\ln\left(\frac{L_1^2}{L_0^2}\right) + \frac{Mg}{2}(L_1 - L_0) + \frac{k}{4}(L_1^4 - L_0^4)$$

C

$$nRT\ln\left(\frac{L_1}{L_0}\right) + Mg(L_1 - L_0) + \frac{k}{4}(L_1^4 - L_0^4)$$

D

$$nRT\ln\left(\frac{L_1}{L_0}\right) + Mg(L_1 - L_0) + \frac{3k}{4}(L_1^4 - L_0^4)$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 37

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A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 cm$$^3$$ and temperature 27°C. The change in temperature when the gas is adiabatically compressed to 200 cm$$^3$$ is :
(Take $$\gamma = 1.5$$ : $$\gamma$$ is the ratio of specific heats at constant pressure and at constant volume)

A

$$327$$ K

B

$$600$$ K

C

$$522$$ K

D

$$300$$ K

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NTA JEE Main 2025 April 3rd Shift 1 - Question 38

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Match the 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-III, B-I, C-II, D-IV

C

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

D

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

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NTA JEE Main 2025 April 3rd Shift 1 - Question 39

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The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell, respectively, are :

A

120V, 120V, 80V

B

40V, 40V, 80V

C

0V, 0V, 80V

D

0V, 120V, 40V

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NTA JEE Main 2025 April 3rd Shift 1 - Question 40

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The work function of a metal is $$3 eV$$. The color of the visible light that is required to cause emission of photoelectrons is

A

Green

B

Blue

C

Red

D

Yellow

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NTA JEE Main 2025 April 3rd Shift 1 - Question 41

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A particle is released from height S above the surface of the earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

A

$$\frac{S}{2}, \sqrt{\frac{3gS}{2}}$$

B

$$\frac{S}{2}, \frac{3gS}{2}$$

C

$$\frac{S}{4}, \frac{3gS}{2}$$

D

$$\frac{S}{4}, \sqrt{\frac{3gS}{2}}$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 42

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A person measures mass of 3 different particles as 435.42 g, 226.3 g and 0.125 g. According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be.

A

$$661.845$$ g

B

$$662$$ g

C

$$661.8$$ g

D

$$661.84$$ g

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NTA JEE Main 2025 April 3rd Shift 1 - Question 43

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The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm. The refractive index of the lens material is

A

$$1.2$$

B

$$1.4$$

C

$$1.5$$

D

$$1.8$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 44

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The angle of projection of a particle is measured from the vertical axis as $$\phi$$ and the maximum height reached by the particle is $$h_m$$. Here $$h_m$$ as function of $$\phi$$ can be presented as

A

B

C

D

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NTA JEE Main 2025 April 3rd Shift 1 - Question 45

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Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.

Choose the correct answer from the options given below.

A

A, C and D Only

B

B, C and D Only

C

A, B and E Only

D

B, D and E Only

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NTA JEE Main 2025 April 3rd Shift 1 - Question 46

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Three identical spheres of mass m, are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time $$T = 4$$ seconds. If the sides of the triangle are increased to length 2a and also the masses of the spheres are made 2m, then they will collide after _________ seconds.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 47

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A 4.0 cm long straight wire carrying a current of 8A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is _________ mN.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 48

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Two coherent monochromatic light beams of intensities $$4I$$ and $$9I$$are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is $$xI$$. The value of x is __________.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 49

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A loop ABCDA, carrying current $$I = 12$$ A, is placed in a plane, consists of two semi-circular segments of radius $$R_1 = 6\pi$$ m and $$R_2 = 4\pi$$ m. The magnitude of the resultant magnetic field at center O is $$k \times 10^{-7}$$ T. The value of k is __________.
(Given $$\mu_0 = 4\pi \times 10^{-7}$$ Tm A$$^{-1}$$)

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NTA JEE Main 2025 April 3rd Shift 1 - Question 50

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In the figure shown below, a resistance of 150.4 $$\Omega$$ is connected in series to an ammeter A of resistance 240 $$\Omega$$. A shunt resistance of 10 $$\Omega$$ is connected in parallel with the ammeter. The reading of the ammeter is _________ mA.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 51

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Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of an atom ?

A

An atom in a stationary state does not emit electromagnetic radiation as long as it stays in the same state

B

An atom can take only certain distinct energies $$E_1, E_2, E_3$$, etc. These allowed states of constant energy are called the stationary states of atom

C

When an electron makes a transition from a higher energy stationary state to a lower energy stationary state, then it emits a photon of light

D

The electron in a H atom's stationary state moves in a circle around the nucleus

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NTA JEE Main 2025 April 3rd Shift 1 - Question 52

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Given below are two statements :
Statement I : The N-N single bond is weaker and longer than that of P-P single bond
Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions.
In the light of the above statements, choose the correct answer from the options given below

A

Statement I is true but Statement II is false

B

Both Statement I and Statement II are false

C

Statement I is false but Statement II is true

D

Both Statement I and Statement II are true

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NTA JEE Main 2025 April 3rd Shift 1 - Question 53

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Given below are two statements
Statement I : A catalyst cannot alter the equilibrium constant $$(K_c)$$ of the reaction, temperature remaining constant
Statement II : A homogeneous catalyst can change the equilibrium composition of a system temperature remaining constant
In the light of the above statements, choose the correct answer from the options given below

A

Statement I is false but Statement II is true

B

Both Statement I and Statement II are true

C

Both Statement I and Statement II are false

D

Statement I is true but Statement II is false

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NTA JEE Main 2025 April 3rd Shift 1 - Question 54

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The metal ions that have the calculated spin only magnetic moment value of 4.9 B.M. are
A. $$Cr^{2+}$$
B. $$Fe^{2+}$$
C. $$Fe^{3+}$$
D. $$Co^{2+}$$
E. $$Mn^{3+}$$

Choose the correct answer from the options given below

A

A, C and E only

B

A, D and E only

C

B and E only

D

A, B and E only

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NTA JEE Main 2025 April 3rd Shift 1 - Question 55

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In a reaction $$A + B \to C$$, initial concentrations of A and B are related as $$[A]_0 = 8[B]_0$$. The half lives of A and B are 10 min and 40 min respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?

A

$$60$$ min

B

$$80$$ min

C

$$20$$ min

D

$$40$$ min

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NTA JEE Main 2025 April 3rd Shift 1 - Question 56

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Which of the following is the correct structure of L-fructose ?

A

B

C

D

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NTA JEE Main 2025 April 3rd Shift 1 - Question 57

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Identify the correct statements from the following

Choose the correct answer from the options given below

A

C & D only

B

B & C only

C

A & B only

D

A, B & C only

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NTA JEE Main 2025 April 3rd Shift 1 - Question 58

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Among $$10^{-9}$$ g (each) of the following elements, which one will have the highest number of atoms?
Element : Pb, Po, Pr and Pt

A

Po

B

Pr

C

Pb

D

Pt

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NTA JEE Main 2025 April 3rd Shift 1 - Question 59

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Which of the following statements are correct?
A. The process of the addition of an electron to a neutral gaseous atom is always exothermic
B. The process of removing an electron from an isolated gaseous atom is always endothermic
C. The 1st ionization energy of the boron is less than that of the beryllium
D. The electronegativity of C is 2.5 in $$CH_4$$ and $$CCl_4$$
E. Li is the most electropositive among elements of group I

Choose the correct answer from the options given below

A

B and C only

B

A, C and D only

C

B and D only

D

B, C and E only

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NTA JEE Main 2025 April 3rd Shift 1 - Question 60

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Which of the following properties will change when system containing solution 1 will become solution 2 ?

A

Molar heat capacity

B

Density

C

Concentration

D

Gibbs free energy

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NTA JEE Main 2025 April 3rd Shift 1 - Question 61

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Number of molecules from below which cannot give iodoform reaction is :
Ethanol, Isopropyl alcohol, Bromoacetone, 2-Butanol, 2-Butanone, Butanal, 2-Pentanone, 3-Pentanone, Pentanal and 3-Pentanol

A

$$5$$

B

$$4$$

C

$$3$$

D

$$2$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 62

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Identify [A], [B], and [C], respectively in the following reaction sequence :

A

B

C

D

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NTA JEE Main 2025 April 3rd Shift 1 - Question 63

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In the following reactions, which one is NOT correct?

A

B

C

D

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NTA JEE Main 2025 April 3rd Shift 1 - Question 64

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The correct order of the complexes $$[Co(NH_3)_4(H_2O)]^{3+}$$ (A), $$[Co(NH_3)_6]^{3+}$$ (B), $$[Co(CN)_6]^{3-}$$ (C) and $$[CoCl(NH_3)_5]^{2+}$$ (D) in terms of wavelength of light absorbed is :

A

$$D \gt A \gt B \gt C$$

B

$$C \gt B \gt D \gt A$$

C

$$D \gt C \gt B \gt A$$

D

$$C \gt B \gt A \gt D$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 65

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2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is :
(Given : Ebullioscopic constant of water = 0.52 K kg mol$$^{-1}$$)

A

$$379.2$$ K

B

$$377.3$$ K

C

$$375.3$$ K

D

$$277.3$$ K

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NTA JEE Main 2025 April 3rd Shift 1 - Question 66

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Which compound would give 3-methyl-6-oxoheptanal upon ozonolysis ?

A

B

C

D

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NTA JEE Main 2025 April 3rd Shift 1 - Question 67

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Match the LIST-I with LIST-II.

Choose the correct answer from the options given below :

A

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

B

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

C

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

D

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

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NTA JEE Main 2025 April 3rd Shift 1 - Question 68

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The least acidic compound, among the following is:

A

D

B

A 

C

B 

D

C 

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NTA JEE Main 2025 April 3rd Shift 1 - Question 69

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Correct order of limiting molar conductivity for cations in water at 298 K is :

A

$$H^+ \gt Na^+ \gt K^+ \gt Ca^{2+} \gt Mg^{2+}$$

B

$$H^+ \gt Ca^{2+} \gt Mg^{2+} \gt K^+ \gt Na^+$$

C

$$Mg^{2+} \gt H^+ \gt Ca^{2+} \gt K^+ \gt Na^+$$

D

$$H^+ \gt Na^+ \gt Ca^{2+} \gt Mg^{2+} \gt K^+$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 70

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During estimation of nitrogen by Dumas' method of compound X (0.42 g) :

_________ mL of $$N_2$$ gas will be liberated at STP. (nearest integer)
(Given molar mass in g mol$$^{-1}$$ : C : 12, H : 1, N : 14)

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NTA JEE Main 2025 April 3rd Shift 1 - Question 71

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0.5 g of an organic compound on combustion gave 1.46 g of $$CO_2$$ and 0.9 g of $$H_2O$$. The percentage of carbon in the compound is _________. (Nearest integer)
[Given : Molar mass (in g mol$$^{-1}$$) C : 12, H : 1, O : 16]

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NTA JEE Main 2025 April 3rd Shift 1 - Question 72

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The number of optical isomers exhibited by the iron complex (A) obtained from the following reaction is _________.
$$FeCl_3 + KOH + H_2C_2O_4 \to A$$

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NTA JEE Main 2025 April 3rd Shift 1 - Question 73

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Given :
$$\Delta H^{\ominus}_{\text{sub}}[C(\text{graphite})] = 710$$ kJ mol$$^{-1}$$
$$\Delta_{C-H} H^{\ominus} = 414$$ kJ mol$$^{-1}$$
$$\Delta_{H-H} H^{\ominus} = 436$$ kJ mol$$^{-1}$$
$$\Delta_{C=C} H^{\ominus} = 611$$ kJ mol$$^{-1}$$

The $$\Delta H_f^{\ominus}$$ for $$CH_2=CH_2$$ is _________ kJ mol$$^{-1}$$
(nearest integer value)

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NTA JEE Main 2025 April 3rd Shift 1 - Question 74

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Consider the following reactions
$$A + NaCl + H_2SO_4 \to CrO_2Cl_2 + \text{Side Products}$$ (Little amount)
$$CrO_2Cl_{2(Vapour)} + NaOH \to B + NaCl + H_2O$$
$$B + H^+ \to C + H_2O$$

The number of terminal 'O' present in the compound 'C' is _________.

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NTA JEE Main 2025 April 3rd Shift 1 - Question 75

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In the following system,
$$PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$$ at equilibrium, upon addition of xenon gas at constant T & p, the concentration of

A

$$PCl_5$$ will increase

B

$$Cl_2$$ will decrease

C

$$PCl_5$$, $$PCl_3$$ & $$Cl_2$$ remain constant

D

$$PCl_3$$ will increase

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