JEE Main 23 January 2026 Shift 2 Question Paper

Question 1

If $f(x)=\begin{cases} \dfrac{a|x|+x^2-2(\sin|x|)(\cos|x|)}{x} & ,\ x \neq 0 \[6pt] b & ,\ x = 0 \end{cases}$
is continuous at $x = 0$, then $a + b$ is equal to :

Accepted Answer

(B) 2

Answer

(A) 1

Answer

(C) 0

Answer

(D) 4

Question 2

Let $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$, $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$, $\vec{c} = \lambda\hat{i} + \hat{j} + \hat{k}$ and $\vec{v} = \vec{a} 	imes \vec{b}$. If $\vec{v}.\vec{c} = 11$ and the length of the projection of $\vec{b}$ on $\vec{c}$ is p, then $9p^2$ is equal to :

Accepted Answer

(D) 12

Answer

(A) 9

Answer

(B) 6

Answer

(C) 4

Question 3

Let A(1, 2) and C(−3, −6) be two diagonally opposite vertices of a rhombus, whose sides AD an BC are parallel to the line $7x - y = 14$. If B ($\alpha$, $\beta$) and D($\gamma$, $\delta$) are the other two vertices, then $|\alpha + \beta + \gamma + \delta|$ is equal to :

Accepted Answer

(C) 6

Answer

(A) 9

Answer

(B) 3

Answer

(D) 1

Question 4

Consider two sets A = $\{x \in z : |(|x - 3| - 3)| \leq 1\}$ and B= $\left\{ x \in \mathbb{R} - \{1,2\} : \dfrac{(x-2)(x-4)}{x-1}\log_e(|x-2|) = 0 \right\}$. Then the number of onto functions $f$ : A→B is equal to :

Accepted Answer

(A) 62

Answer

(B) 79

Answer

(C) 32

Answer

(D) 81

Question 5

The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has

Accepted Answer

(B) infinitely many solutions for $a = 8$ and $b = 14$

Answer

(A) unique solution for $a = 8$ and $b = 16$

Answer

(C) infinitely many solutions for $a = 8$ and $b = 16$

Answer

(D) unique solution for $a = 8$ and $b = 14$

Question 6

The sum of all the real solutions of the equation $\log_{(x+3)}(6x^2 + 28x + 30) = 5 - 2\log_{(6x+10)}(x^2 + 6x + 9)$ is equal to :

Accepted Answer

(C) 0

Answer

(A) 2

Answer

(B) 1

Answer

(D) 4

Question 7

Let PQ be a chord of the hyperbola $\dfrac{x^2}{4} - \dfrac{y^2}{b^2} = 1$, perpendicular to the x-axis such that OPQ is an equilateral triangle, O being the centre of the hyperbola. If the eccentricity of the hyperbola is $\sqrt{3}$, then the area of the triangle OPQ is :

Accepted Answer

(B) $\dfrac{8\sqrt{3}}{5}$

Answer

(A) $2\sqrt{3}$

Answer

(C) $\dfrac{11}{5}$

Answer

(D) $\dfrac{9}{5}$

Question 8

Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $\vec{a} 	imes \vec{b} = 2(\vec{a} 	imes \vec{c})$. If $|\vec{a}| = 1, |\vec{b}| = 4$, $|\vec{c}| = 2$, and the angle between $\vec{b}$ and $\vec{c}$ is 60°, then $|\vec{a}.\vec{c}|$ is :

Accepted Answer

(D) 1

Answer

(A) 2

Answer

(B) 4

Answer

(C) 0

Question 9

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is $\dfrac{p}{q}$, gcd(p, q) = 1, then $p + q$ is equal to

Accepted Answer

(B) 23

Answer

(A) 22

Answer

(C) 24

Answer

(D) 21

Question 10

The area of the region enclosed between the circles $x^2 + y^2 = 4$ and $x^2 + (y-2)^2 = 4$ is :

Accepted Answer

(D) $\dfrac{2}{3}(4\pi - 3\sqrt{3})$

Answer

(A) $\dfrac{2}{3}(2\pi - 3\sqrt{3})$

Answer

(B) $\dfrac{4}{3}(2\pi - 3\sqrt{3})$

Answer

(C) $\dfrac{4}{3}(2\pi - \sqrt{3})$

Question 11

The least value of $(\cos^2	heta - 6\sin	heta\ \cos	heta + 3\sin^2	heta + 2)$ is

Accepted Answer

(C) $4 - \sqrt{10}$

Answer

(A) −1

Answer

(B) $4 + \sqrt{10}$

Answer

(D) 1

Question 12

Let $I(x) = \int \frac{3dx}{(4x+6)(\sqrt{4x^2+8x+3})}$ and $I(0) = \frac{\sqrt{3}}{4}+20$. If $I\left(\frac{1}{2}\right) = \frac{a\sqrt{2}}{b}+c$, where a, b, c ∈ N, gcd(a,b) = 1, then a + b + c is equal to :

Accepted Answer

(C) 31

Answer

(A) 29

Answer

(B) 28

Answer

(D) 30

Question 13

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

Accepted Answer

(D) 455

Answer

(A) 429

Answer

(B) 384

Answer

(C) 403

Question 14

If $z = \frac{\sqrt{3}}{2} + \frac{i}{2}, i = \sqrt{-1}$, then $(z^{201} - i)^{8}$ is equal to

Accepted Answer

(D) 256

Answer

(A) –1

Answer

(B) 0

Answer

(C) 1

Question 15

If the mean and the variance of the data
Class | 4–8 | 8–12 | 12–16 | 16–20
Frequency | 3 | $\lambda$ | 4 | 7
are µ and 19 respectively, then the value of λ + µ is

Accepted Answer

(D) 19

Answer

(A) 18

Answer

(B) 21

Answer

(C) 20

Question 16

An equilateral triangle OAB is inscribed in the parabola $y^2 = 4x$ with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having AB as a diameter from the origin is

Accepted Answer

(A) $4(3 - \sqrt{3})$

Answer

(B) $2(8 - 3\sqrt{3})$

Answer

(C) $4(6 + \sqrt{3})$

Answer

(D) $2(3 + \sqrt{3})$

Question 17

Let $\sum_{k=1}^{n} a_k = \alpha n^2 + \beta n$. If $a_{10} = 59$ and $a_6 = 7a_1$ then
α + β is equal to

Accepted Answer

(C) 5

Answer

(A) 12

Answer

(B) 3

Answer

(D) 7

Question 18

If the solution curve y = f(x) of the differential equation $(x^2 - 4)y' - 2xy + 2x(4 - x^2)^2 = 0$ x > 2, passes through the point (3, 15), then the local maximum value of f is ………

Accepted Answer

16

Question 19

If the image of the point P(a, 2, a) in the line $\frac{x}{2} = \frac{y+a}{1} = \frac{z}{1}$ is Q and the of image of Q in the line $\frac{x-2b}{2} = \frac{y-a}{1} = \frac{z+2b}{-5}$ is P, then a + b is equal to………..

Accepted Answer

3

Question 20

The number of elements in the set $S = \left\{ x : x \in [0,100] 	ext{ and } \int_{0}^{x} t^2 \sin(x-t)dt = x^2 ight\}$ is.....

Accepted Answer

16

Question 21

Let $A = \begin{bmatrix} 0 & 2 & -3 \ -2 & 0 & 1 \ 3 & -1 & 0 \end{bmatrix}$ and B be a matrix such that $B(I - A) = I + A$. Then the sum of the diagonal elements of $B^{T}B$ is equal to______.

Accepted Answer

3

Question 22

Let S denote the set of 4-digit numbers abcd such that a > b > c > d and P denote the set of 5-digit numbers having product of its digits equal to 20. Then n(S) + n(P) is equal to…………

Accepted Answer

260

Question 23

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of 17 cm$^{2}$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by 4 °C, then the piston will move______cm.
(atmospheric pressure = $10^{5}$ Pa)

Accepted Answer

(C) 15.5

Answer

(A) 14.5

Answer

(B) 1.55

Answer

(D) 1.45

Question 24

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment is_____m/s.

Accepted Answer

(B) $12\sqrt{2}$

Answer

(A) $10\sqrt{2}$

Answer

(C) 12

Answer

(D) $24\sqrt{2}$

Question 25

A block is sliding down on an inclined plane of slope θ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$. The distance $(S)$ travelled by the block before its velocity become zero, is______.
(g = gravitational acceleration)

Accepted Answer

(A) $\frac{u^{2}}{4g\sin	heta}$

Answer

(B) $\frac{2u^{2}}{g\cos	heta}$

Answer

(C) $\frac{u^{2}}{\sqrt{2}g\cos	heta}$

Answer

(D) $\frac{u^{2}}{2g\cos	heta}$

Question 26

The current passing through a conducting loop in the form of equilateral triangle of side $4\sqrt{3}$ cm is 2A. The magnetic field at its centroid is $\alpha 	imes 10^{-5}$ T. The value of $\alpha$ is ______.
(Given : $\mu_{o} = 4\pi 	imes 10^{-7}$ SI units)

Accepted Answer

(C) $3\sqrt{3}$

Answer

(A) $2\sqrt{3}$

Answer

(B) $\sqrt{3}$

Answer

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

Question 27

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with 3 m/s$^{2}$. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the aeroplane is_____m.
(g = 10 m/s$^{2}$)

Accepted Answer

(B) 92.5

Answer

(A) 62.5

Answer

(C) 20

Answer

(D) 82.5

Question 28

Two shorts dipoles $(A, B)$, $A$ having charges ± 2μC and length 1 cm and $B$ having charges ± 4μC and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point $P$, equi-distant from the centres of both dipoles is_____N/C.

Accepted Answer

(D) $\frac{9}{16}\sqrt{2}	imes 10^{4}$

Answer

(A) $\frac{9}{16}\sqrt{2}	imes 10^{5}$

Answer

(B) $4.5\sqrt{2}	imes 10^{4}$

Answer

(C) $9\sqrt{2}	imes 10^{4}$

Question 29

Two charges 7μC and −2 μC are placed at (−9, 0, 0) cm and (9, 0, 0) cm respectively in an external field $E = \frac{A}{r^{2}}\hat{r}$ , where $A = 9 	imes 10^{5}$ N/C.m$^{2}$.
Considering the potential at infinity is 0, the electrostatic energy of the configuration is_____J.

Accepted Answer

(C) 49.3

Answer

(A) 1.4

Answer

(B) −90.7

Answer

(D) 24.3

Question 30

A bead $P$ sliding on a frictionless semi-circular string $(ACB)$ and it is at point $S$ at t = 0 and at this instant the horizontal component of its velocity is $v$. Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at t = 0 along the horizontal string $AB$, with the speed $v$, friction between the beads and the respective strings may be neglected in both cases. Let $t_{p}$ and $t_{Q}$ be the respective times taken by beads $P$ and $Q$ to reach the point $B$, then the relation between $t_{p}$ and $t_{Q}$ is

Accepted Answer

(B) $t_{p} < t_{Q}$

Answer

(A) $t_{P} > t_{Q}$

Answer

(C) $t_{p} > 1.25 t_{Q}$

Answer

(D) $t_{p} = t_{Q}$

Question 31

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25% more charge from the battery. The dielectric constant of mica is____.

Accepted Answer

(B) 2.0

Answer

(A) 2.5

Answer

(C) 1.5

Answer

(D) 1.0

Question 32

An air bubble of volume 2.9 cm$^{3}$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is 17 °C. The volume of the bubble when it reaches the surface, where the water temperature is 27 °C, is____ cm$^{3}$.
(g = 10 m/s$^{2}$, density of water = $10^{3}$ kg/m$^{3}$, and 1 atm pressure is $10^{5}$ Pa)

Accepted Answer

(D) 4.5

Answer

(A) 4.2

Answer

(B) 2.0

Answer

(C) 3.0

Question 33

Which of the following pair of nuclei are isobars of the element ?

Accepted Answer

(D) $^{3}_{1}\mathrm{H}$ and $^{3}_{2}\mathrm{H}$

Answer

(A) $^{2}_{1}\mathrm{H}$ and $^{3}_{1}\mathrm{H}$

Answer

(B) $^{236}_{92}\mathrm{U}$ and $^{238}_{92}\mathrm{U}$

Answer

(C) $^{198}_{80}\mathrm{Hg}$ and $^{197}_{79}\mathrm{Au}$

Question 34

For the given logic gate circuit, which of the following is the correct truth table?

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 35

One mole of an ideal diatomic gas expands from volume V to 2V isothermally at a temperature 27°C and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from 27°C doing the same amount of work W, then its final temperature will be (close to) __________ °C.

Accepted Answer

(B) −56

Answer

(A) −189

Answer

(C) −30

Answer

(D) −117

Question 36

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ___________ mV.

Accepted Answer

(D) 1.32

Answer

(A) 6.6

Answer

(B) 13.2

Answer

(C) 8.25

Question 37

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I$ = 10 sin (ωt) A, where ω = 1000 rad./s. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed v = 1 cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is $\alpha/\sqrt{2}$ μA. The value of α is __________.
[Resistance of the loop = 10 Ω]

Accepted Answer

(A) 197

Answer

(B) 80

Answer

(C) 280

Answer

(D) 100

Question 38

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k = 3 and permeability of $\mu = 2\mu_0$, is
($\mu_0$ = permeability of vacuum)

Accepted Answer

(D) $\sqrt{6}$ : 1

Answer

(A) 36 : 1

Answer

(B) 3 : 2

Answer

(C) 6 : 1

Question 39

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is ________.
($	an^{-1}$ (1.52) = 57.7°, refractive indices of air and glass are 1.00 and 1.52, respectively)

Accepted Answer

(B) 32.3°

Answer

(A) 39.6°

Answer

(C) 42.6°

Answer

(D) 36.3°

Question 40

A small metallic sphere of diameter 2 mm and density 10.5 g/cm$^{3}$ is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm$^{3}$ respectively. The terminal velocity attained by the sphere is ________ cm/s.
($\pi = \frac{22}{7}$ and g = 10 m/s$^{2}$)

Accepted Answer

(A) 2.0

Answer

(B) 1.0

Answer

(C) 3.0

Answer

(D) 1.5

Question 41

The average energy released per fission for the nucleus of $^{235}_{92}$U is 190 MeV. When all the atoms of 47 g pure $^{235}_{92}$U undergo fission process, the energy released is $\alpha 	imes 10^{23}$ MeV. The value of α is ________.
(Avogadro Number = $6 	imes 10^{23}$ per mole)

Accepted Answer

228

Question 42

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ________ cm.

Accepted Answer

16

Question 43

A ball of radius r and density ρ dropped through a viscous liquid of density σ and viscosity η attains its terminal velocity at time t, given by t = A $\rho^{a}$ $r^{b}$ $\eta^{c}$ $\sigma^{d}$, where A is a constant and a, b c and d are integers. The value of $\frac{b+c}{a+d}$ is ______.

Accepted Answer

1

Question 44

Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by $\frac{x}{256}$ M$r^{2}$. The value of x is __________.

Accepted Answer

109

Question 45

The velocity of sound in air is doubled when the temperature is raised from 0°C to α°C. The value of α is _______.

Accepted Answer

819

Question 46

Given above is the concentration vs time plot for a dissociation reaction : A → nB.
Based on the data of the initial phase of the reaction (initial 10 min), the value of n is ________.

Accepted Answer

(B) 3

Answer

(A) 4

Answer

(C) 2

Answer

(D) 5

Question 47

Consider the above electrochemical cell where a metal electrode (M) is undergoing redox reaction by forming M$^{+}$ (M → M$^{+}$ + e). The cation M$^{+}$ is present in two different concentrations c$_{1}$ and c$_{2}$ as shown above. Which of the following statement is correct for generating a positive cell potential?

Accepted Answer

(C) If c$_{1}$ is present at cathode, then c$_{1}$ > c$_{2}$

Answer

(A) If c$_{1}$ is present at anode, then c$_{1}$ = c$_{2}$

Answer

(B) If c$_{1}$ is present at cathode, then c$_{1}$ < c$_{2}$

Answer

(D) If c$_{1}$ is present at anode, then c$_{1}$ > c$_{2}$

Question 48

Both human DNA and RNA are chiral molecules. The chirality in DNA and RNA arises due to the presence of

Accepted Answer

(C) D-sugar component

Answer

(A) Base unit

Answer

(B) Chiral phosphate unit

Answer

(D) L-sugar component

Question 49

Identify the CORRECT set of details from the following :
A. [Co(NH$_{3}$)$_{6}$]$^{3+}$ : Inner orbital complex ; d$^{2}$sp$^{3}$ hybridized
B. [MnCl$_{6}$]$^{3-}$ Outer orbital complex; sp$^{3}$d$^{2}$ hybridized
C. [CoF$_{6}$]$^{3-}$ : Outer orbital complex ; d$^{2}$sp$^{3}$ hybridized
D. [FeF$_{6}$]$^{3-}$ : Outer orbital complex: sp$^{3}$d$^{2}$ hybridized
E. [Ni(CN)$_{4}$]$^{2-}$ : Inner orbital complex ; sp$^{3}$ hybridized
Choose the correct answer from the options given below:

Accepted Answer

(B) A, B & D only

Answer

(A) C & D only

Answer

(C) A, C & E only

Answer

(D) A, B, C, D & E

Question 50

Elements X and Y belong to Group 15. The difference between the electronegativity values of ‘X’ and phosphorus is higher than that of the difference between phosphorus and ‘Y’. ‘X’ & ‘Y’ are respectively

Accepted Answer

(A) N & As

Answer

(B) As & Bi

Answer

(C) Bi & N

Answer

(D) As & Sb

Question 51

Given below are two statements:
Statement I: $\left(\mathrm{CH_{3}}\right)_{3}\overset{\oplus}{\mathrm{C}}$ is more stable than $\overset{\oplus}{\mathrm{C}}\mathrm{H_{3}}$ as nine hyperconjugation interactions are possible in $\left(\mathrm{CH_{3}}\right)_{3}\overset{\oplus}{\mathrm{C}}$.
Statement II: $\overset{\oplus}{\mathrm{C}}\mathrm{H_{3}}$ is less stable than $\left(\mathrm{CH_{3}}\right)_{3}\overset{\oplus}{\mathrm{C}}$ as only three hyperconjugation interactions are possible in $\overset{\oplus}{\mathrm{C}}\mathrm{H_{3}}$.
In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

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

Answer

(B) Both Statement I and Statement II are true

Answer

(C) Both Statement I and Statement II are false

Answer

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

Question 52

Iodoform test can differentiate between
A. Methanol and Ethanol
B. CH$_{3}$COOH and CH$_{3}$CH$_{2}$COOH
C. Cyclohexene and cyclohexanone
D. Diethyl ether and Pentan-3-one
E. Anisole and acetone
Choose the correct answer from the options given below:

Accepted Answer

(A) A & E only

Answer

(B) A & D only

Answer

(C) A, B & E only

Answer

(D) B, C & E only

Question 53

Given below are two statements :
Statement I : The second ionisation enthalpy of Na is larger than the corresponding ionisation enthalpy of Mg.
Statement II : The ionic radius of O$^{2-}$ is larger than that of F$^{-}$.
In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

(A) Both statement I and statement II are true

Answer

(B) Both statement I and statement II are false

Answer

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

Answer

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

Question 54

Identify (P)

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 55

Observe the following reactions at T(K)
I. A → products.
II. 5Br$^{-}$ (aq) + BrO$_{3}^{-}$ (aq) + 6H$^{+}$(aq) → 3Br$_{2}$(aq) + 3H$_{2}$O($l$)
Both the reactions are started at 10.00 am. The rates of these reactions at 10.10 am are same. The value of $-\frac{\Delta[\mathrm{Br}^{-}]}{\Delta \mathrm{t}}$ at 10.10 am is 2 × 10$^{-4}$ mol L$^{-1}$ Min$^{-1}$. The concentration of A at 10.10 am is 10$^{-2}$ mol L$^{-1}$. What is the first order rate constant (in min$^{-1}$) of reaction I?

Accepted Answer

(D) 4 × 10$^{-3}$

Answer

(A) 2 × 10$^{-3}$

Answer

(B) 10$^{-3}$

Answer

(C) 10$^{-2}$

Question 56

Which of the following statements are TRUE about Haloform reaction?
A. Sodium hypochlorite reacts with KI to give KOI.
B. KOI is a reducing agent.
C. α, β-unsaturated methylketone $\left(\mathrm{CH_{3}-CH=CH-}\overset{	ext{O}}{\overset{\|}{\mathrm{C}}}\mathrm{-CH_{3}}ight)$ will give iodoform reaction.
D. Isopropyl alcohol will not give iodoform test.
E. Methanoic acid will give positive iodoform test.
Choose the correct answer from the options given below:

Accepted Answer

(C) A & C only

Answer

(A) A, C & E only

Answer

(B) A, B & C only

Answer

(D) B, D & E only

Question 57

Which statements are NOT TRUE about XeO$_{2}$F$_{2}$?
A. It has a see-saw shape.
B. Xe has 5 electron pairs in its valence shell in XeO$_{2}$F$_{2}$.
C. The O–Xe–O bond angle is close to 180°.
D. The F–Xe–F bond angle is close to 180°
E. Xe has 16 valence electrons in XeO$_{2}$F$_{2}$.
Choose the correct answer from the options given below.

Accepted Answer

(A) B, C and E only

Answer

(B) B and D only

Answer

(C) A and D only

Answer

(D) B, D and E only

Question 58

Identify the INCORRECT statements from the following:
A. Notation $_{12}^{24}$Mg represents 24 protons and 12 neutrons.
B. Wavelength of a radiation of frequency 4.5 × 10$^{15}$ s$^{-1}$ is 6.7 × 10$^{-8}$ m.
C. One radiation has wavelength = $\lambda_{1}$(900 nm) and energy = E$_{1}$. Other radiation has wavelength = $\lambda_{2}$(300 nm) and energy = E$_{2}$.E$_{1}$ : E$_{2}$ = 3 : 1.
D. Number of photons of light of wavelength 2000 pm that provides 1 J of energy is 1.006 × 10$^{16}$.
Choose the correct answer from the options given below:

Accepted Answer

(B) A and C only

Answer

(A) A and D only

Answer

(C) A and B only

Answer

(D) B and C only

Question 59

In Carius method 0.2425 g of an organic compounds gave 0.5253 g silver chloride. The percentage of chlorine in the organic compound is

Accepted Answer

(A) 53.58%

Answer

(B) 87.65%

Answer

(C) 37.57%

Answer

(D) 34.79%

Question 60

A mixed ether (P), when heated with excess of hot concentrated hydrogen iodide produces two different alkyl iodides which when treated with aq. NaOH give compounds (Q) and (R). Both (Q) and (R) give yellow precipitate with NaOI. Identify the mixed ether (P):

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 61

The oxidation state of chromium in the final product formed in the reaction between KI and acidified K$_{2}$Cr$_{2}$O$_{7}$ solution is:

Accepted Answer

(B) +3

Answer

(A) +4

Answer

(C) +2

Answer

(D) +6

Question 62

The work functions of two metals (M$_{A}$ and M$_{B}$) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of M$_{A}$ : M$_{B}$ is in the ratio of 2.642 : 1. The work functions (in eV) of M$_{A}$ and M$_{B}$ are respectively.

Accepted Answer

(B) 2.3, 4.6

Answer

(A) 3.1, 6.2

Answer

(C) 1.4, 2.8

Answer

(D) 1.5, 3.0

Question 63

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

Accepted Answer

(C) Both Statement I and Statement II are true

Answer

(A) Both Statement I and Statement II are false

Answer

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

Answer

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

Question 64

A student has been given a compound “x” of molecular formula – C$_{6}$H$_{7}$N. ‘x’ is sparingly soluble in water. However, on addition of dilute mineral acid , ‘x’ becomes soluble in water. ‘x’ when treated with CHCl$_{3}$ and KOH (alc.) ‘y’ is produced. ‘y’ has a specific unpleasant smell. On treatment with benzenesulphonyl chloride, ‘x’ gives a compound ‘z’ which is soluble in alkali. The number of different “H” atoms present in ‘z’ is:-

Accepted Answer

(D) 7

Answer

(A) 5

Answer

(B) 8

Answer

(C) 4

JEE Main 23 January 2026 Shift 2 Question Paper with Answers

Physics — JEE Main 23 January 2026 Shift 2

Chemistry — JEE Main 23 January 2026 Shift 2

Mathematics — JEE Main 23 January 2026 Shift 2

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