JEE Main 24 January 2026 Shift 2 Question Paper

Question 1

Let $f(x) = \int \frac{7x^{10} + 9x^{8}}{(1 + x^{2} + 2x^{9})^{2}}dx$, $x > 0$, $\lim_{x 	o 0} f(x) = 0$ 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

Accepted Answer

(D) 4

Answer

(A) 2

Answer

(B) 3

Answer

(C) 1

Question 2

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

Accepted Answer

(C) 496

Answer

(A) 516

Answer

(B) 256

Answer

(D) 276

Question 3

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 $	heta_{1}$ and $	heta_{2}$. Then the value of $(	heta_{1} + 	heta_{2})$ is :

Accepted Answer

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

Answer

(A) $\frac{\pi}{12}$

Answer

(B) $\frac{\pi}{6}$

Answer

(D) $\frac{\pi}{3}$

Question 4

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

Accepted Answer

(C) 6

Answer

(A) 12

Answer

(B) 4

Answer

(D) 8

Question 5

$\left(\frac{1}{3} + \frac{4}{7}ight) + \left(\frac{1}{3^{2}} + \frac{1}{3} 	imes \frac{4}{7} + \frac{4^{2}}{7^{2}}ight) + \left(\frac{1}{3^{3}} + \frac{1}{3^{2}} 	imes \frac{4}{7} + \frac{1}{3} 	imes \frac{4^{2}}{7^{2}} + \frac{4^{3}}{7^{3}}ight)$ + ...... upto infinite terms is equal to -

Accepted Answer

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

Answer

(B) $\frac{7}{4}$

Answer

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

Answer

(D) $\frac{6}{5}$

Question 6

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 :

Accepted Answer

(B) 16

Answer

(A) 32

Answer

(C) 81

Answer

(D) 124

Question 7

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 :

Accepted Answer

(A) 1580

Answer

(B) 1578

Answer

(C) 1579

Answer

(D) 1581

Question 8

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

Accepted Answer

(D) 14

Answer

(A) 13

Answer

(B) 11

Answer

(C) 12

Question 9

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

Accepted Answer

(B) −6

Answer

(A) 8

Answer

(C) 6

Answer

(D) −8

Question 10

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

Accepted Answer

(C) 7

Answer

(A) 9

Answer

(B) 14

Answer

(D) 12

Question 11

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

Accepted Answer

(B) 4

Answer

(A) 2

Answer

(C) 3

Answer

(D) 5

Question 12

Let $X = \{x \in \mathbb{N} : 1 \le x \le 19\}$ and for some a, b $\in \mathbb{R}$, $Y = \{ax + b : x \in X\}$. 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

Accepted Answer

(D) 60

Answer

(A) 20

Answer

(B) 80

Answer

(C) 100

Question 13

Consider the following three statements for the function $f : (0, \infty) 	o \mathbb{R}$ 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.

Accepted Answer

(D) Only (I) and (III) are TRUE.

Answer

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

Answer

(B) Only (I) is TRUE.

Answer

(C) Only (II) and (III) are TRUE.

Question 14

Let $y = y(x)$ be a differentiable function in the interval $(0, \infty)$ such that $y(1) = 2$.
and $\lim\limits_{t 	o x} \left( \dfrac{t^{2} y(x) - x^{2} y(t)}{x - t} ight) = 3$ for each $x > 0$.
Then $2y(2)$ is equal to

Accepted Answer

(B) 23

Answer

(A) 18

Answer

(C) 27

Answer

(D) 12

Question 15

Let f be a function such that $3f(x) + 2f\left( \dfrac{m}{19x} ight) = 5x$, $x 
e 0$, where $m = \sum\limits_{i=1}^{9} (i)^{2}$. Then $f(5) - f(2)$ is equal to

Accepted Answer

(C) 18

Answer

(A) $-9$

Answer

(B) 36

Answer

(D) 9

Question 16

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

Accepted Answer

(D) 7

Answer

(A) 9

Answer

(B) 3

Answer

(C) 4

Question 17

Let $\vec{a} = 2\hat{i} - 5\hat{j} + 5k$ and $\vec{b} = \hat{i} - \hat{j} + 3k$. If $\vec{c}$ is a vector such that
$2(\vec{a} 	imes \vec{c}) + 3(\vec{b} 	imes \vec{c}) = \vec{0}$ and $(\vec{a} - \vec{b}) \cdot \vec{c} = -97$, then $\left| \vec{c} 	imes k ight|^{2}$ is equal to

Accepted Answer

(C) 218

Answer

(A) 193

Answer

(B) 233

Answer

(D) 205

Question 18

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

Accepted Answer

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

Answer

(A) $\dfrac{5}{8}$

Answer

(B) $\dfrac{9}{16}$

Answer

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

Question 19

If f(x) satisfies the relation $f(x) = e^{x} + \int\limits_{0}^{1} (y + xe^{x}) f(y)\, dy$, then $e + f(0)$ is equal to ________.

Accepted Answer

2

Question 20

Let (h, k) lie on the circle $C : x^{2} + y^{2} = 4$ and the point $(2h + 1, 3k + 2)$ lie on an ellipse with eccentricity e. Then the value of $\dfrac{5}{e^{2}}$ is equal to ________.

Accepted Answer

9

Question 21

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

Accepted Answer

5

Question 22

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 $P(S) 	imes P(S)$ such that $A \cap B = \varnothing$. If the probability of the event E is $\dfrac{3^{p}}{2^{q}}$, where p, q $\in \mathbb{N}$, then $p + q$ is equal to

Accepted Answer

15

Question 23

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

Accepted Answer

4

Question 24

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

Accepted Answer

(B) 1

Answer

(A) 2

Answer

(C) 1/2

Answer

(D) 0

Question 25

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.

Accepted Answer

(A) 0.002

Answer

(B) 0.05

Answer

(C) 0.02

Answer

(D) 0.005

Question 26

Five persons $P_1$, $P_2$, $P_3$, $P_4$ and $P_5$ recorded object distance (u) and image distance (v) using same convex lens having power $+5D$ as (25,96), (30,62), (35,37), (45,35) and (50,32) respectively. Identify correct statement

Accepted Answer

(B) Reading recorded by $P_3$ persons are incorrect

Answer

(A) Readings recorded by all persons are correct

Answer

(C) Reading recorded by $P_3$ and $P_2$ persons are incorrect

Answer

(D) Reading recorded by $P_4$ and $P_5$ persons are incorrect

Question 27

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

Accepted Answer

(A) $\frac{4}{5}r$

Answer

(B) $\frac{5}{8}r$

Answer

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

Answer

(D) $\frac{3}{5}r$

Question 28

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)

Accepted Answer

(B) $\sqrt{\frac{7}{2}gr}$

Answer

(A) $\sqrt{5gr}$

Answer

(C) $\sqrt{4gr}$

Answer

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

Question 29

A thin uniform rod (X) of mass M and length L is pivoted at a height $\left(\frac{L}{3}\right)$ 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 = gravitational acceleration)

Accepted Answer

(D) $\sqrt{\frac{3g}{L}}$

Answer

(A) $\sqrt{\frac{3}{2}\frac{g}{L}}$

Answer

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

Answer

(C) $\frac{1}{\sqrt{2}}\sqrt{\frac{g}{L}}$

Question 30

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 O. The net magnetic field at O is:

Accepted Answer

(D) $\frac{3\mu_o I}{4\sqrt{2}r}$ towards Q

Answer

(A) $\frac{3\mu_o I}{4\sqrt{2}r}$ toward P

Answer

(B) $\frac{\mu_o I}{4\sqrt{2}r}$ toward P

Answer

(C) $\frac{\mu_o I}{4\sqrt{2}r}$ towards Q

Question 31

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.
$(h = 6.63 	imes 10^{-34}\,	ext{J.s}, e = 1.6 	imes 10^{-19}\,	ext{C}, c = 3 	imes 10^{8}\,	ext{m/s})$

Accepted Answer

(D) $2.5 	imes 10^{-7}$

Answer

(A) $2.9 	imes 10^{-8}$

Answer

(B) $2.2 	imes 10^{-8}$

Answer

(C) $3.1 	imes 10^{-7}$

Question 32

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_______.

Accepted Answer

(B) 2

Answer

(A) 4

Answer

(C) 1

Answer

(D) 3

Question 33

Three parallel plate capacitors each with area A and separation d are filled with two dielectric ($k_1$ and $k_2$) in the following fashion. Which of the following is true? ($k_1 > k_2$)

Accepted Answer

(D) $C_A > C_C > C_B$

Answer

(A) $C_B > C_C > C_A$

Answer

(B) $C_C > C_B > C_A$

Answer

(C) $C_C > C_A > C_B$

Question 34

The binding energy for the following nuclear reactions are expressed in MeV.
$_2	ext{He}^3 + _0	ext{n}^1 ightarrow _2	ext{He}^4 + 20$ MeV
$_2	ext{He}^4 + _0	ext{n}^1 ightarrow _2	ext{He}^5 - 0.9$ MeV
If $X_3$, $X_4$, $X_5$ denote the stability of $_2	ext{He}^3$, $_2	ext{He}^4$ and $_2	ext{He}^5$, respectively, then the correct order is :

Accepted Answer

(A) $X_4 > X_5 > X_3$

Answer

(B) $X_4 = X_5 = X_3$

Answer

(C) $X_4 > X_5 < X_3$

Answer

(D) $X_4 < X_5 < X_3$

Question 35

A cubical block of density $\rho_b = 600$ kg/m$^3$ floats in a liquid of density $\rho_e = 900$ kg/m$^3$. If the height of block is $H = 8.0$ cm then height of the submerged part is ______ cm.

Accepted Answer

(D) 5.3

Answer

(A) 7.3

Answer

(B) 4.3

Answer

(C) 6.3

Question 36

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 ______ $\Omega$

Accepted Answer

(A) 25

Answer

(B) 10

Answer

(C) 0.5

Answer

(D) 2.5

Question 37

Identify the correct truth table of the given logical circuit.

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 38

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 _____.

Accepted Answer

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

Answer

(B) $\frac{1}{2}mg$

Answer

(C) $mg$

Answer

(D) $\sqrt{3}\,mg$

Question 39

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

Accepted Answer

(D) decrease by 4 times

Answer

(A) increase by 8 times

Answer

(B) increase by 64 times

Answer

(C) decrease by 8 times

Question 40

In the Young's double slit experiment the intensity produced by each one of the individual slits is $I_0$. The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is 6000 $	ext{\AA}$. The intensity of light on the screen in front of one of the slits is _____.

Accepted Answer

(B) $I_0$

Answer

(A) $2I_0$

Answer

(C) $\frac{I_0}{2}$

Answer

(D) $4I_0$

Question 41

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from $	ext{P}_1$ to $	ext{P}_2$ is $\alpha$ Joule ($	ext{P}_1 = 21.7$ Pa and $	ext{P}_2 = 30$ Pa, $	ext{C}_	ext{v} = 21$ J/K.mol, $R = 8.3$ J/mol.K). The value of $\alpha$ is _____.

Accepted Answer

(C) 21

Answer

(A) 24

Answer

(B) 15

Answer

(D) 28

Question 42

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

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 43

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

Accepted Answer

(D) $-15$

Answer

(A) $-15/2$

Answer

(B) $-10$

Answer

(C) $-20$

Question 44

A point charge q = 1 $\mu$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 $\frac{1}{4\pi\epsilon_0} = 9	imes10^{9}\,	ext{N.m}^{2}/	ext{C}^{2}$)

Accepted Answer

90

Question 45

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 ___ $\Omega$.

Accepted Answer

6

Question 46

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 _____.

Accepted Answer

162

Question 47

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 diameter 14 cm, then the value of x is ____.
($\pi = 22/7$)

Accepted Answer

11304

Question 48

Choose the INCORRECT statement

Accepted Answer

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

Answer

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

Answer

(C) Carbon cannot exceed its covalency more than four.

Answer

(D) $	ext{CO}_{2}$ is the most acidic oxide among the dioxides of group of 14 elements.

Question 49

The unsaturated ether on acidic hydrolysis produces carbonyl compounds as shown below:-
$	ext{CH}_{3}-	ext{CH}=	ext{CH}-	ext{O}-	ext{CH}=	ext{CH}_{2}$
$\downarrow 	ext{H}_{3}	ext{O}^{(+)}$
$	ext{CH}_{3}-	ext{CH}_{2}-	ext{CH}=	ext{O}$ and $	ext{O}=	ext{CH}-	ext{CH}_{3}$
Based on this, predict the solution / reagent that will help to distinguish “P” and “Q” obtained in the following reaction.
$	ext{CH}_{3}-	ext{CH}=	ext{CH}-	ext{O}-\overset{\overset{	ext{CH}_{3}}{|}}{	ext{C}}=	ext{CH}_{2} \xrightarrow[\Delta]{	ext{H}_{3}	ext{O}^{(+)}} 	ext{P} + 	ext{Q}$

Accepted Answer

(D) Fehling solution

Answer

(A) Lucas reagent

Answer

(B) 2,4-DNP reagent

Answer

(C) Saturated $	ext{NaHSO}_{3}$ solution

Question 50

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 :

Accepted Answer

(A) 6

Answer

(B) 3

Answer

(C) 4

Answer

(D) 8

Question 51

Two liquids A and B form an ideal solution at temperature T K. At T K , the vapour pressures of pure A and B are 55 and 15 $	ext{kNm}^{-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 ?

Accepted Answer

(A) 0.5217

Answer

(B) 0.480

Answer

(C) 0.663

Answer

(D) 0.340

Question 52

Consider the following gaseous equilibrium in a closed container of volume “V” at T(K).
$	ext{P}_{2}(	ext{g}) + 	ext{Q}_{2}(	ext{g}) ightleftharpoons 2	ext{PQ}(	ext{g})$
2 moles each of $	ext{P}_{2}(	ext{g})$, $	ext{Q}_{2}(	ext{g})$ and PQ (g) are present at equilibrium. Now one mole each of ‘$	ext{P}_{2}$’ and ‘$	ext{Q}_{2}$’ are added to the equilibrium keeping the temperature at T(K). The number of moles of $	ext{P}_{2}$, $	ext{Q}_{2}$ and PQ at the new equilibrium, respectively , are -

Accepted Answer

(A) 2.67, 2.67, 2.67

Answer

(B) 1.21, 2.24, 1.56

Answer

(C) 1.66, 1.66, 1.66

Answer

(D) 2.56, 1.62, 2.24

Question 53

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

Accepted Answer

(C) $	ext{O}_{2}^{+}, 	ext{N}_{2}^{-}$

Answer

(A) $	ext{O}_{2}^{+}, 	ext{N}_{2}^{2-}$

Answer

(B) $	ext{O}_{2}^{-}, 	ext{N}_{2}^{+}$

Answer

(D) $	ext{O}_{2}^{-}, 	ext{N}_{2}^{-}$

Question 54

The wavelength of light absorbed for the following complexes are in the order.
$	ext{[Co(NH}_{3}	ext{)}_{6}	ext{]}^{3+}$ (I) ; $	ext{[Co(H}_{2}	ext{O)}_{6}	ext{]}^{3+}$ (II) ; $	ext{[Co(CN)}_{6}	ext{]}^{3-}$ (III) ;
$	ext{[Co(NH}_{3}	ext{)}_{5}	ext{(H}_{2}	ext{O)]}^{3+}$ (IV) ; $	ext{[CoF}_{6}	ext{]}^{3-}$ (V)

Accepted Answer

(D) III < I < IV < II < V

Answer

(A) III < I < II < IV < V

Answer

(B) III < I < IV < V < II

Answer

(C) III < IV < I < II < V

Question 55

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

Accepted Answer

(C) 0.5 M , 0.5 M , 1 M

Answer

(A) 0.75 M , 0.75 M , 1 M

Answer

(B) 0.5 M , 0.5 M , 0.5 M

Answer

(D) 1 M , 1M , 1 M

Question 56

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

Accepted Answer

(A) 81.5%

Answer

(B) 97.5%

Answer

(C) 59.5%

Answer

(D) 72.5%

Question 57

Find out the statements which are not true.
A. Resonating structure with more number of covalent bonds and lesser charge separation 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 compounds.
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.

Accepted Answer

(D) B & D only

Answer

(A) A, D  & E only

Answer

(B) B, D & E only

Answer

(C) A, C & D only

Question 58

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

Accepted Answer

(C) C < N < F < O

Answer

(A) F < N < C < O

Answer

(B) C < O < N < F

Answer

(D) C < F < N < O

Question 59

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

Accepted Answer

(C) carbonate & carbonate

Answer

(A) sulphide & sulphide

Answer

(B) hydroxide & carbonate

Answer

(D) chromate & sulphide

Question 60

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

Accepted Answer

(D) $1.14 	imes 10^{-6}$ cm

Answer

(A) $2.28 	imes 10^{-7}$ cm

Answer

(B) $2.28 	imes 10^{-6}$ cm

Answer

(C) $1.14 	imes 10^{-7}$ cm

Question 61

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 forms a condensation product with acetophenone only.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

(A) Both Statement I and Statement II are false

Answer

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

Answer

(C) Both Statement I and Statement II are true

Answer

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

Question 62

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 $	ext{R}-\overset{	ext{O}}{\overset{\|}{	ext{C}}}-	ext{OH}$ .
Statement II : R-CN hydrolyses under acidic medium to produce a compound which on treatment with $	ext{SOCl}_{2}$, followed by the addition of $	ext{NH}_{3}$ gives another compound(x). This compound (x) on treatment with $	ext{NaOCl}/	ext{NaOH}$ gives a product, that on treatment with $	ext{CHCl}_{3}/	ext{KOH}/\Delta$ produces R-NC
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

(A) Both Statement I and Statement II are false

Answer

(B) Both Statement I and Statement II are true

Answer

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

Question 63

From the following, how many compounds contain at least one secondary alcohol ?
Choose the correct answer from the options given below :

Accepted Answer

(B) Three

Answer

(A) Five

Answer

(C) Four

Answer

(D) two

Question 64

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

Accepted Answer

(B) $\frac{	ext{N}_{	ext{A}}	ext{hc}}{250(4	ext{y}-6	ext{x})}$

Answer

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

Answer

(C) $\frac{	ext{N}_{	ext{A}}	ext{hc}}{250(	ext{y}-6	ext{x})}$

Answer

(D) $	ext{N}_{	ext{A}}	ext{hc}\left(	ext{y}-\frac{6	ext{x}}{4}ight)^{-1}$

JEE Main 24 January 2026 Shift 2 Question Paper with Answers

Physics — JEE Main 24 January 2026 Shift 2

Chemistry — JEE Main 24 January 2026 Shift 2

Mathematics — JEE Main 24 January 2026 Shift 2

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