NTA JEE Mains 24th Jan 2026 Shift 2

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 1

Report

Let $$f$$ be a function such that $$3f(x)+2f \left(\frac{m}{19x}\right) = 5x, x\neq 0$$, where $$m= \sum_{i=1}^9 i^{2}$$. Then $$f(5) - f(2)$$ is equal to

A

36

B

9

C

-9

D

18

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 2

Report

Lety = y (x) be a differentiable function in the interval $$(0, \infty)$$ such that y(l) = 2, and $$\lim_{t \rightarrow x} \left( \frac{t^{2}y(x)-x^{2}y(t)}{x-t} \right) = 3$$ for each x > 0. Then 2){2) is equal to

A

27

B

12

C

23

D

18

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 3

Report

Let f(a) denote the area of the region in the first quadrant bounded by x = 0, x = 1, $$y^{2}=x$$ and y = |ax - 5| - |1 - ax| + $$ax^{2}$$. Then (f(0) + f(1)) is equal

A

9

B

14

C

7

D

12

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 4

Report

Let the image of parabola $$x^{2}=4y$$, in the line x - y = 1 be $$(y+a)^{2}$$ = b(x-c), $$a,b,c \in N.$$ Then a + b + c is equal to

A

12

B

6

C

4

D

8

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 5

Report

Let $$\overrightarrow{a}= 2\widehat{i}-\widehat{j}-\widehat{k}, \overrightarrow{b}=\widehat{i}+ 3\widehat{j}-\widehat{k}$$ and $$\overrightarrow{c} = 2\widehat{i}+\widehat{j}+3\widehat{k}.$$ Let $$\overrightarrow{\nu}$$ be the vector in the plane of the vectors $$\overrightarrow{a}$$ and $$\overrightarrow{b}$$, such that the length of its projection on the vector $$\overrightarrow{C}$$ is $$\frac{1}{\sqrt{14}}$$. Then $$\mid \overrightarrow{\nu} \mid$$ is euqal to

A

$$\frac{\sqrt{21}}{2}$$

B

7

C

13

D

$$\frac{\sqrt{35}}{2}$$

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 6

Report

Let $$\overrightarrow{a}= 2\widehat{i}-5\widehat{j}+5\widehat{k}$$ and $$\overrightarrow{b}= \widehat{i}-\widehat{j}+3\widehat{k}$$. If $$\overrightarrow{C}$$ is a vector such that $$2(\overrightarrow{a}\times\overrightarrow{c})+3(\overrightarrow{b}\times\overrightarrow{c})= \overrightarrow{0}$$ and $$(\overrightarrow{a}-\overrightarrow{b})\cdot\overrightarrow{c}=-97,$$ then $$\mid \overrightarrow{c}\times\widehat{k} \mid^{2}$$ is equal to

A

233

B

205

C

218

D

193

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 7

Report

The sum of all values of $$\alpha$$, for which the shortest distance between the lines
$$\frac{x+1}{\alpha}=\frac{y-2}{-1}=\frac{z-4}{-\alpha}$$ and $$\frac{x}{\alpha}=\frac{y-1}{2}=\frac{z-1}{2\alpha}$$ is $$\sqrt{2}$$, is

A

6

B

-8

C

8

D

-6

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 8

Report

Let $$a_{1},a_{2},a_{3},a_{4}$$ be an A.P. of four terms such that each term of the A.P. and its common difference $$l$$ are integers. If $$a_{1} +a_{2}+a_{3}+a_{4}= 48$$ and $$a_{1} a_{2}a_{3}a_{4} + l^{4} = 361,$$ then the largest term of the A.P. is equal to

A

21

B

27

C

24

D

23

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 9

Report

The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is

A

1580

B

1581

C

1578

D

1579

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 10

Report

Let the length of the latus rectum of an ellipse $$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$$ (where a > b) be 30. If its eccentricity is the maximum value of the function $$f(t) = -\frac{3}{4} + 2t - t^{2}$$, then the value of $$(a^{2} + b^{2})$$ is equal to:

A

516

B

256

C

496

D

276

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 11

Report

$$\left(\dfrac{1}{3}+\dfrac{4}{7}\right)+\left( \dfrac{1}{3^{2}}+\dfrac{1}{3}\times\dfrac{4}{7}+\dfrac{4^{2}}{7^{2}} \right)+\left(\dfrac{1}{3^{3}}+\dfrac{1}{3^{2}}\times\dfrac{4}{7}+\dfrac{1}{3}\times\dfrac{4^{2}}{7^{2}}+\dfrac{4^{3}}{7^{3}} \right)+......$$ upto infinite term, is equal to

A

$$\frac{6}{5}$$

B

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

C

$$\frac{5}{2}$$

D

$$\frac{7}{4}$$

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 12

Report

Let [t] denote the greatest integer less than or equal to t. If the function $$f(x) = \begin{cases} b^2 \sin\!\left(\dfrac{\pi}{2}\left[\dfrac{\pi}{2}(\cos x + \sin x)\cos x\right]\right), & x < 0 \\[10pt] \dfrac{\sin x - \dfrac{1}{2}\sin 2x}{x^3}, & x > 0 \\[10pt] a, & x = 0 \end{cases}$$ is continuous at x = 0,then $$a^{2} + b^{2}$$ is equal to

A

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

B

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

C

$$\frac{9}{16}$$

D

$$\frac{5}{8}$$

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 13

Report

The smallest positive integral value of a, for which all the roots of $$x^{4} - ax^{2} + 9 = 0$$ are real and distinct, is equal to

A

9

B

7

C

4

D

3

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 14

Report

Let $$f(x)=\int_{}^{} \frac{7x^{10}+9x^{8}}{(1+x^{2}+2x^{9})^{2}}dx, x>0, \lim_{x \rightarrow 0}f(x)=0$$ and $$f(1)=\frac{1}{4.}$$ If $$A= \begin{bmatrix}0 & 0 & 1 \\ \frac{1}{4} & f'(1) & 1 \\ \alpha^{2} & 4 & 1 \end{bmatrix}$$ and B = adj(adj A) be such that |B| = 81 , then $$\alpha^{2}$$ is equal to

A

1

B

3

C

4

D

2

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 15

Report

If the domain of the function f(x) = $$\sin^{-1}\frac{1}{x^{2}-2x-2}$$, is $$\left[-\infty, \alpha\right] \cup \left[\beta,\gamma\right]\cup \left[\delta,\infty\right],$$ then $$\alpha+\beta+\gamma+\delta$$ is equal to

A

5

B

4

C

2

D

3

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 16

Report

Consider the following three statements for the function $$f: (0, \infty ) \rightarrow \mathbb R$$ defined by
$$f(x)= |\log_{e}{x}|-|x-1|:$$
(I)f is differentiable at all x > 0.
(II)f is increasing in (0, 1).
(III)f is decreasing in (1, $$\infty$$).
Then.

A

Only (I) and (III) are TRUE.

B

Only (II) and (III) are TRUE.

C

All (I), (II) and (III) are TRUE.

D

Only (I) is TRUE.

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 17

Report

Let the angles made with the positive x-axis by two straight lines drawn from the point P(2, 3) and meeting the line x + y = 6 at a distance $$\sqrt{\frac{2}{3}}$$ from the point P be $$\theta_{1}$$ and $$\theta_{2}$$. Then the value of $$(\theta_{1}+\theta_{2})$$ is :

A

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

B

$$\frac{\pi}{12}$$

C

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

D

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

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 18

Report

Let $$P=[p_{ij}]$$ and $$Q=[q_{ij}]$$ be two square matrices of order 3 such that $$q_{ij}= 2^{(i+j-1)}p_{ij}$$ and $$\det (Q)=2^{10}.$$ Then the value of det(adj(adj P)) is:

A

124

B

32

C

81

D

16

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 19

Report

Let $$X= \left\{x\in N:1\leq x\leq19 \right\}$$ and for some $$a,b \in \mathbb R, Y = \left\{ax+b:x\in X\right\}.$$ If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b is

A

20

B

100

C

60

D

80

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 20

Report

The largest value of n, for which $$40^{n}$$ divides 60! , is

A

13

B

11

C

14

D

12

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 21

Report

If f(x) satisfies the relation $$f(x)=e^{x}+\int_{0}^{1}\left(y+xe^{x}\right)f(y)dy,$$ then e + f(0) is equal to ______.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 22

Report

Let (h, k) lie on the circle $$C: x^{2}+y^{2}=4$$ and the point (2h + l , 3k + 2) lie on an ellipse with eccentricity e. Then the value of $$\frac{5}{e^{2}}$$ is equal to __________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 23

Report

The number of elements in the set $$\left\{x \in [0,180^{\circ}]:\tan (x+100^{\circ}) = \tan (x+50^{\circ}) \tan x \tan(x-50^{\circ})\right\}$$ is ___________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 24

Report

Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the set P(S) x P(S) such that $$A\cap B=\phi.$$ If
the probability of the event E is $$\frac{3^{p}}{2^{q}}$$, where p,q $$\in$$ N, then p + q is equal to __________

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 25

Report

Let z = (1 + i) (1 + 2i) (1 + 3i) .... (1 + ni), where i = $$\sqrt{-1}$$. If $$|z|^{2}$$ = 44200, then n is equal to __

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 26

Report

In the Young's double slit experiment the intensity produced by each one of the individual slits is $$I_{o}.$$ The distance between two slits is 2 mm . The distance of
screen from slits is 10 m. The wavelength of light is $$6000_A^\circ$$. The intensity of light on the screen in front of one of the slits is __________.

A

$$2I_{\circ}$$

B

$$\frac{I_{\circ}}{2}$$

C

$$I_{\circ}$$

D

$$4I_{\circ}$$

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 27

Report

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V. If a second light having wavelength twice of first light is used, the stopping potential drops to 0. 7 V. The wavelength of first light is ___ m.
$$(h= 6.63\times10^{-34}J.s,e=1.6\times10^{-19}C,c=3\times10^{8}m/s)$$

A

$$2.2\times10^{-8}$$

B

$$2.5\times10^{-7}$$

C

$$2.9\times10^{-8}$$

D

$$3.1\times10^{-7}$$

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 28

Report

A cubical block of density $$\rho_{b}= 600kg/m^{3}$$ floats in a liquid of density $$\rho_{e}= 900kg/m^{3}$$. If the height of block is H = 8.0 cm then height of the submerged part is ________ cm.

A

6.3

B

4.3

C

7.3

D

5.3

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 29

Report

The binding energy for the following nuclear reactions are expressed in MeV.
$$ _{2}He^{3}+ _{0}n^{1} \rightarrow {}_{2}He^{4}+20$$ MeV
$$ _{2}He^{4}+ _{0}n^{1} \rightarrow {}_{2}He^{5}-0.9$$ MeV
If $$X_{3}$$, $$X_{4}$$, $$X_{5}$$ denote the stability of $${}_{2}He^{3}, {}_{2}He^{4}$$ and $${}_{2}He^{5},$$ respectively, then the correct order is :

A

$$X_{4} > X_{5} > X_{3}$$

B

$$X_{4} > X_{5} < X_{3}$$

C

$$X_{4} < X_{5} < X_{3}$$

D

$$X_{4}=X_{5}=X_{3}$$

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 30

Report

Identify the correct truth table of the given logic circuit.

A

B

C

D

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 31

Report

A regular hexagon is fonned by six wires each of resistance $$r \Omega$$ and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and and leaves at. the opposite corner,the equivalent. resistance of the hexagon between the two opposite corners will be

A

$$\frac{4}{5}r$$

B

$$\frac{5}{8}r$$

C

$$\frac{3}{5}r$$

D

$$\frac{3}{4}r$$

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 32

Report

The reading of the ammeter (A) in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is ___ A.

A

1/2

B

0

C

2

D

1

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 33

Report

10 mole of an ideal gas is undergoing the process showu in the figure. The heat involved in the process from $$P_{1}$$ to $$P_{2}$$ is $$\alpha$$ Joule(P_{1}= 21.7Pa and $$P_{2} = 30$$ Pa, $$C_{v}=21J/K.mol, R=8.3 J/mol.K.$$) The value of $$\alpha$$ is _________.

A

28

B

15

C

24

D

21

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 34

Report

Three parallel plate capacitors each with area A and separation dare filled with two dielectric $$(k_{1} \text{and} k_{2})$$ in the following fashion. Which of the following is true? $$(k_{1}>  k_{2})$$

A

$$C_{A} > C_{C} > C_{B}$$

B

$$C_{C} > C_{B} > C_{A}$$

C

$$C_{B} > C_{C} > C_{A}$$

D

$$C_{C} > C_{A} > C_{B}$$

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 35

Report

A thin uniform rod X of mass M and length L is pivoted at a height $$(\frac{L}{3})$$ as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is __________.
(g is the acceleration due to gravity)

A

$$\frac{1}{\sqrt{2}}\sqrt{\frac{g}{L}}$$

B

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

C

$$\sqrt{\frac{3g}{L}}$$

D

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

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 36

Report

Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The current through P and Q are I and 4I respectively in clockwise direction as seen from 0 . The net magnetic field at O is:

A

$$\frac{\mu_{0}I}{4\sqrt{2}r}$$ towards Q

B

$$\frac{3\mu_{0}I}{4\sqrt{2}r}$$ towards Q

C

$$\frac{\mu_{0}I}{4\sqrt{2}r}$$ towards P

D

$$\frac{3\mu_{0}I}{4\sqrt{2}r}$$ towards P

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 37

Report

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will

A

decrease by 4 times

B

increase by 64 times

C

increase by 8 times

D

decrease by 8 times

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 38

Report

A flexible chain of mass m hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is $$30^{\circ}$$. Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is __________.

A

$$\sqrt{3}mg$$

B

mg

C

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

D

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

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 39

Report

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division= 0.05 mm, then the least count of the vernier callipers is__________ mm.

A

0.05

B

0.02

C

0.002

D

0.005

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 40

Report

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x is ______.

A

1

B

3

C

2

D

4

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 41

Report

In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle $$30^{\circ}$$ shown in figure, the velocity at the bottom point (A) of the circular path is
(g = gravitational acceleration)

A

$$\sqrt{4gr}$$

B

$$\sqrt{5gr}$$

C

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

D

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

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 42

Report

The velocity (v) - Distance (x) graph is shown in figure. Which graph represents accderation(a) versus distance (x) variation of this system?

A

B

C

D

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 43

Report

Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is ___ cm.

A

-10

B

-15

C

-15/2

D

-20

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 44

Report

A moving coil galvanometer of resistance $$100\Omega$$ shows a full scale deflection for a current of 1 mA. The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA, is ____ $$\Omega$$

A

0.5

B

2.5

C

25

D

10

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 45

Report

Five persons $$P_{1},P_{2},P_{3},P{4}, \text{and} P_{5}$$ recorded object distance (u) and image distance (v) using same convex lens having powei· +5D as (25,96), (30,62), (35,37), (45,35)
and (50,32) respectively. Identify correct statement

A

Readings recorded by all persons are correct

B

Readings recorded by $$P_{4}$$ and $$P_{5}$$ persons are incorrect

C

Readings recorded by $$P_{3}$$ and $$P_{2}$$ perso11S are incorrect

D

Readings recorded by $$P_{3}$$ person are incorrect

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 46

Report

When 300 J of heat given to an ideal gas with $$C_{p}= \frac{7}{2}R$$ its temperature raises from $$20^{\circ}C$$ to $$50^{\circ}C$$ keeping its volume constant. The millimoles of the gas is (approximately) __ . (R = 8.314 J/mol.K)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 47

Report

A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to $$I_{1}$$. A small co-centric cylinder of length L/2 and radius R/3 carved from this cylinder has moment of inertia about its axis equals to $$I_{2}$$. The ratio $$I_{1}/I_{2}$$ is __________.

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 48

Report

A soap bubble of surface tension 0.04 N/m is blown to a diameter of 7 cm. If (15000 - x) $$\mu J$$ of work is done in blowing it further to make its diameterl4 cm, then the value of x is_____.
$$\left(\pi=22/7\right)$$

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 49

Report

A point charge q = l $$\mu C$$ is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 $$\mu C$$, distributed uniformly along its length, as shown in figure. Force between q and wire is __ N.
(Use: $$\frac{1}{4\pi\epsilon_{0}}=9 \times10^{9} N.m^{2}/C^{2}$$)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 50

Report

In a meter bridge experiment to determine the value of unknown resistance, first the resistances $$2\Omega$$ and $$3\Omega$$ are connected in the left and right gaps of the bridge and the null point is obtained at a distance l cm from the left. Now when an unknown resistance $$x\Omega$$ is connected in parallel to $$3\Omega$$ resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance x is __________ $$\Omega$$ .

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 51

Report

The wavelength of spectral line obtained in the spectrum of $$Li^{2+}$$ ion, when the transition takes place between two levels whose sum is 4 and difference is 2, is

A

$$1.14 \times 10^{-7}cm$$

B

$$2.28 \times 10^{-6}cm$$

C

$$1.14 \times 10^{-6}cm$$

D

$$2.28 \times 10^{-7}cm$$

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 52

Report

Find out the statements which are not true.
A. Resonating structures with more number of covalent bonds and lesser charge separntion are more stable.
B. In electromeric effect, an unsaturated system shows +E effect with nucleophile and -E effect with electrophile.
C. Inductive effect is responsible for high melting point, boiling point and dipole moment of polar compotmds.
D. The greater the number of alkyl groups attached to the doubly bonded carbon atoms, higher is the heat of hydrogenation.
E. Stability of carbanion increases with the increase in s - character of the carbon carrying the negative charge.

Choose the correct answer from the options given below:

A

A, C &amp; D only

B

B, D &amp; E only

C

A, D &amp; E only

D

B &amp; D only

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 53

Report

"X" is an oxoanion of the lightest element of group 7 (in the periodic table). The metal is in +6 oxidation state in "X". The color of the potassium salt of X is

A

purple

B

yellow

C

orange

D

green

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 54

Report

Consider the following gaseous equilibrimn in a closed container of volume 'V' at T(K).
$$P_{2}(g)+Q_{2}(g)\rightleftharpoons 2PQ(g)$$
2 moles each of $$P_{2}(g)$$, $$Q_{2}(g)$$ and PQ(g) are present at equilibrium. Now one mole each of'$$P_{2}$$' and '$$Q_{2}$$' are added to the equilibrium keeping the temperature at T(K). The number of moles of $$P_{2}$$, $$Q_{2}$$ and PQ at the new equilibrium, respectively, are

A

2.67, 2.67, 2.67

B

1.21, 2.24, 1.56

C

1.66, 1.66, 1.66

D

2.56, 1.62, 2.24

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 55

Report

A student has planned to prepare acetanilide from aniline using acetic anhydride. The student has started from 9.3 g of aniline. However, the student has managed to obtain 11 g of dry acetanilide.
The % yield of this reaction is :-

A

72.5%

B

81.5%

C

97.5%

D

59.5%

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 56

Report

From the following, how many compounds contain at least one secondary alcohol?

Choose the correct answer from the options given below:

A

Five

B

Three

C

Four

D

Two

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 57

Report

Given below are two statements:
Statement I: The dipole moment of R-CN is greater than R-NC and R-NC can undergo hydrolysis under acidic medium to produce $$O\\||\\R-C-OH$$.

Statement II: R-CN hydrolyses under acidic medium to produce a compound which on treatment with $$SOCl_{2}$$, followed by the addition of $$NH_{3}$$ gives another compound(x). This compound (x) on treatment with NaOCl/NaOH gives a product, that on treatment with $$CHCl_{3}/KOH/ \Delta$$ produces R-NC

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 hue

B

Both Statement I and Statement II are true

C

Statement I is true but Statement II is false

D

Both Statement I and Statement II are false

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 58

Report

The heat of atomisation of methane and ethane are 'x' kJ $$mol^{-1}$$ and 'y' kJ $$mol^{-1}$$ respectively. The longest wavelength ($$\lambda$$) of light capable of breaking the C-C bond
can be expressed in SI unit as:

A

$$\frac{N_{A}hc}{250(y-6x)}$$

B

$$N_{A}hc\left(y-\frac{6x}{4}\right)^{-1}$$

C

$$\frac{N_{A}hc}{250(4y-6x)}$$

D

$$\frac{hc}{1000}\left(\frac{y-6x}{4}\right)^{-1}$$

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 59

Report

At 298 K, the mole percentage of $$N_{2}$$(g) in air is 80%. Water is in equilibrium with air at a pressure of 10 atm. What is the mole fraction of $$N_{2}$$(g) in water at 298 K?
($$K_{H}$$ for $$N_{2}$$ is $$6.5 \times 10^{7}$$ mm Hg)

A

$$1.17 \times 10^{-4}$$

B

$$9.35 \times 10^{5}$$

C

$$9.35 \times 10^{-5}$$

D

$$1.23 \times 10^{-7}$$

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 60

Report

Choose the INCORRECT statement

A

Carbon cannot exceed its covalency more than four.

B

Carbon exhibits negative oxidation states along with +4 and +2.

C

Among the isotopes of carbon, $$^{13}C$$ is a radioactive isotope.

D

$$CO_{2}$$ is the most acidic oxide among the dioxides of group of 14 elements.

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 61

Report

One mole of $$Cl_{2}(g)$$ was passed into 2 L of cold 2M KOH solution. After the reaction, the concentrations of $$Cl^{-}$$ , $$ClO^{-}$$ and $$OH^{-}$$ are respectively (assume volume remains constant)

A

0.5M, 0.5M, lM

B

0.75M, 0.75M, lM

C

0.5M, 0.5M, 0.5M

D

lM, lM, 1M

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 62

Report

Given below are two statements:
Statement I: Cross aldol condensation between two different aldehydes will always produce four different products.
Statement II: When semicarbazide reacts with a mixture of benzaldehyde and acetophenone under optimum pH, it fonns a condensation product with acetophenone only.
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

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 63

Report

Pair of species among the following having same bond order as well as paramagnetic character will be-

A

$${O_{2}}^{+},{N_{2}}^{2-}$$

B

$${O_{2}}^{+},{N_{2}}^{-}$$

C

$${O_{2}}^{-},{N_{2}}^{-}$$

D

$${O_{2}}^{-},{N_{2}}^{+}$$

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 64

Report

Given below are two statements:
Statement I: There are several conformers for n-butane. Out of those conformers,

is the least stable and most stable conformer is

Statement II: As the dihedral angle increases, torsional strain decreases from (X) to (Y).
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

Statement I is true but Statement II is false

D

Both Statement I and Statement II are false

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 65

Report

In the Group analysis of cations, $$Ba^{2+}$$ &amp; $$Ca^{2+}$$ are precipitated respectively as

A

chromate &amp; sulphide

B

hydroxide &amp; carbonate

C

sulphide &amp; sulphide

D

carbonate &amp; carbonate

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 66

Report

The number of possible tripeptides formed involving alanine (ala), glycine (gly) and valine (val), where no amino acid has been used more than once is:

A

4

B

8

C

3

D

6

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 67

Report

Two liquids A and B form an ideal solution at temperature TK. At TK, the vapour pressures of pure A and B are 55 and 15 kN $$m^{-2}$$ respectively. What is the mole fraction of A in solution of A and B in equilibrium with a vapour in which the mole fraction of A is 0.8?

A

0.663

B

0.480

C

0.340

D

0.5217

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 68

Report

The wavelength of light absorbed for the following complexes are in the order
(I)$$\left[Co{(NH_{3})}_{6}\right]^{3+}$$
(II)$$\left[Co{(H_{2}O)}_{6}\right]^{3+}$$
(III)$$\left[Co{(CN)}_{6}\right]^{3-}$$
(IV)$$\left[Co(NH_{3})_{5}(H_{2}O)\right]^{3+}$$
(V)$$\left[CoF_{6}\right]^{3-}$$

A

III < IV < I < II < IV

B

III < I < IV < V < II

C

III < I < IV < II <V

D

III < I < II < IV < V

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 69

Report

The unsaturated ether On acidic hydrolysis produces carbonyl compom1ds as shown below:-

Based On this, predict the solution/reagent that will help to distillguish "P" and "Q" obtained in the following reaction:-

A

2, 4 - DNP reagent

B

Fehling solution

C

Saturated $$NaHSO_{3}$$ solution

D

Lucas reagent

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 70

Report

The correct order of C, N, 0 and F in terms of second ionisation potential is

A

C &lt; O &lt; N &lt; F

B

F &lt; N &lt; C &lt; O

C

C &lt; N &lt; F &lt; O

D

C &lt; F &lt; N &lt; O

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 71

Report

0.25 g of an organic compound &quot;A&quot; containing carbon, hydrogen and oxygen was analysed using the combustion method. There was an increase in mass of $$CaCl_{2}$$ tube and potash tube at the end of the experiment. The amount was found to be 0.15 g and 0.1837 g, respectively. The percentage of oxygen in compound A is __ %. (Nearest integer)
(Given: molar massing $$mol^{-1}$$ H : 1, C : 12, O : 16)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 72

Report

Molar conductivity of a weak acid HQ of concentration 0.18 M was found to be 1/30 of the molar conductivity of another weak acid HZ with concentration of 0.02M. If $$\lambda^{\circ}{}_{Q}-$$ happened to be equal with $$\lambda^{\circ}{}_{Z}-$$, then the difference of the $$pK_{a}$$ values of the two weak acids $$(pK_{a}(HQ) - pK_{a}(HZ))$$ is ___ (Nearest integer).
[Given: degree of dissociation ($$\alpha$$) << 1 for both weak acids, $$\lambda^{\circ}$$ : limiting molar conductivity of ions]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution Video Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 73

Report

A chromium complex with a formula $$CrCl_{3}.6H_{2}O$$ has a spin only magnetic moment value of 3.87 BM and its solution conductivity corresponds to 1:2 electrolyte. 2.75 g of the complex solution was initially passed through a cation exchanger. The solution obtained after the process was reacted with excess of $$AgNO_{3}$$. The amount of AgCI formed in the above process is __ g. (Nearest
integer)
[Given: Molar massing $$mol^{-1}$$ Cr:52; Cl:35.5, Ag:108, 0:16, H:1]

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 74

Report

Grignard reagent RMgBr (P) reacts with water and forms a gas (Q). One gram of Q occupies $$1.4 dm^{3}$$ at STP.(P) on reaction with dry ice in dry ether followed by $$H_{3}O^{+}$$ fonns a compound (Z). 0.1 mole of(Z) will weigh ____ g. (Nearest integer)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution

NTA JEE Mains 24th Jan 2026 Shift 2 - Question 75

Report

The half-life of $${}^{65}Zn$$ is 245 days. After x days, 75% of original activity remained. The value of x in days is ___ . (Nearest integer)
(Given: log 3 = 0.4771 and log 2 = 0.3010)

Backspace
789
456
123
0.-
Clear All

Submit

View Solution