JEE Main 23 January 2026 Shift 1 Question Paper

Question 1

Let the domain of the function $f(x) = \log_3\log_5\log_7 (9x - x^2 - 13)$ be the interval (m, n). Let the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ have eccentricity $\frac{n}{3}$ and the length of the latus rectum $\frac{8m}{3}$. Then $b^2 - a^2$ is equal to :

Accepted Answer

(D) 7

Answer

(A) 5

Answer

(B) 11

Answer

(C) 9

Question 2

Let $f(x) = \int \frac{(2-x^2).e^x}{\left(\sqrt{1+x}\right)(1-x)^{3/2}} dx$ . If $f(0) - 0$, then $f\left(\frac{1}{2}\right)$ is equal to :

Accepted Answer

(A) $\sqrt{3e} - 1$

Answer

(B) $\sqrt{2e} + 1$

Answer

(C) $\sqrt{2e} - 1$

Answer

(D) $\sqrt{3e} + 1$

Question 3

Let $\vec{a} = -\hat{i} + \hat{j} + 2\hat{k}$, $\vec{b} = \hat{i} - \hat{j} - 3\hat{k}$, $\vec{c} = \vec{a} 	imes \vec{b}$ and $\vec{d} = \vec{c} 	imes \vec{a}$. Then $\left(\vec{a} - \vec{b}ight) \cdot \vec{d}$ is equal to :

Accepted Answer

(C) -2

Answer

(A) 4

Answer

(B) -4

Answer

(D) 2

Question 4

A rectangle is formed by the lines x = 0, y = 0, x = 3 and y = 4. Let the line L be perpendicular to 3x + y + 6 = 0 and divide the area of the rectangle into two equal parts. Then the distance of the point $\left(\frac{1}{2}, -5\right)$ from the line L is equal to :

Accepted Answer

(D) $2\sqrt{10}$

Answer

(A) $2\sqrt{5}$

Answer

(B) $3\sqrt{10}$

Answer

(C) $\sqrt{10}$

Question 5

Let the line y - x = 1 intersect the ellipse $\frac{x^2}{2} + \frac{y^2}{1} = 1$ at the points A and B. Then the angle made by the line segment AB at the center of the ellipse is :

Accepted Answer

(B) $\frac{\pi}{2} + 	an^{-1}\left(\frac{1}{4}ight)$

Answer

(A) $\pi - 	an^{-1}\left(\frac{1}{4}ight)$

Answer

(C) $\frac{\pi}{2} + 2	an^{-1}\left(\frac{1}{4}ight)$

Answer

(D) $\frac{\pi}{2} - 	an^{-1}\left(\frac{1}{4}ight)$

Question 6

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

Accepted Answer

(C) 33

Answer

(A) 32

Answer

(B) 34

Answer

(D) 35

Question 7

Let y = y(x) be the solution of the differential equation $x^4 dy + (4x^3 y + 2\sin x)dx = 0$, $x > 0$, $y\left(\frac{\pi}{2}\right) = 0$. Then $\pi^4 y\left(\frac{\pi}{3}\right)$ is equal to :

Accepted Answer

(A) 81

Answer

(B) 92

Answer

(C) 64

Answer

(D) 72

Question 8

If $\alpha$ and $\beta$ ($\alpha < \beta$) are the roots of the equation $\left(-2 + \sqrt{3}\right)\left(\left|\sqrt{x} - 3\right|\right) + \left(x - 6\sqrt{x}\right) + \left(9 - 2\sqrt{3}\right) = 0$, $x \ge 0$, then $\sqrt{\frac{\beta}{\alpha}} + \sqrt{\alpha\beta}$ is equal to :

Accepted Answer

(C) 10

Answer

(A) 8

Answer

(B) 9

Answer

(D) 11

Question 9

Let $f(x) = \begin{cases} \frac{ax^2 + 2ax + 3}{4x^2 + 4x - 3}, & x 
e -\frac{3}{2}, \frac{1}{2} \ b, & x = -\frac{3}{2}, \frac{1}{2} \end{cases}$ be continuous at $x = -\frac{3}{2}$. If $fof(x) = \frac{7}{5}$, then x is equal to :

Accepted Answer

(B) 1

Answer

(A) 2

Answer

(C) 0

Answer

(D) 1.4

Question 10

The value of the integral $\int_{\frac{\pi}{24}}^{\frac{5\pi}{24}} \frac{dx}{1 + \sqrt[3]{	an 2x}}$ is :

Accepted Answer

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

Answer

(B) $\frac{\pi}{18}$

Answer

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

Answer

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

Question 11

Among the statements :
I : If $\begin{vmatrix} 1 & \cos\alpha & \cos\beta \ \cos\alpha & 1 & \cos\gamma \ \cos\beta & \cos\gamma & 1 \end{vmatrix} = \begin{vmatrix} 0 & \cos\alpha & \cos\beta \ \cos\alpha & 0 & \cos\gamma \ \cos\beta & \cos\gamma & 0 \end{vmatrix}$, then $\cos^2\alpha + \cos^2\beta + \cos^2\gamma = \frac{3}{2}$, and
II : If $\begin{vmatrix} x^2 + x & x + 1 & x - 2 \ 2x^2 + 3x - 1 & 3x & 3x - 3 \ x^2 + 2x + 3 & 2x - 1 & 2x - 1 \end{vmatrix} = px + q$, then $p^2 = 196q^2$,

Accepted Answer

(A) both are false

Answer

(B) only II is true

Answer

(C) both are true

Answer

(D) only I is true

Question 12

The value of $\frac{^{100}C_{50}}{51} + \frac{^{100}C_{51}}{52} + \ldots + \frac{^{100}C_{100}}{101}$ is :

Accepted Answer

(D) $\frac{2^{100}}{101}$

Answer

(A) $\frac{2^{101}}{100}$

Answer

(B) $\frac{2^{100}}{100}$

Answer

(C) $\frac{2^{101}}{101}$

Question 13

Let the mean and variance of 8 numbers -10, -7, -1, x, y, 9, 2, 16 be $\frac{7}{2}$ and $\frac{293}{4}$, respectively. Then the mean of 4 numbers x, y, x + y + 1, |x - y| is:

Accepted Answer

(A) 11

Answer

(B) 9

Answer

(C) 10

Answer

(D) 12

Question 14

The sum of all possible values of $n \in N$, so that the coefficients of $x$, $x^{2}$ and $x^{3}$ in the expansion of $(1 + x^{2})^{2} (1 + x)^{n}$, are in arithmetic progression is :

Accepted Answer

(D) 9

Answer

(A) 3

Answer

(B) 7

Answer

(C) 12

Question 15

The vertices B and C of a triangle ABC lie on the line $\frac{x}{1} = \frac{1-y}{-2} = \frac{z-2}{3}$. The coordinates of A and B are (1, 6, 3) and (4, 9, $\alpha$) respectively and C is at a distance of 10 units from B. The area (in sq. units) of $\Delta ABC$ is:

Accepted Answer

(A) $5\sqrt{13}$

Answer

(B) $15\sqrt{13}$

Answer

(C) $20\sqrt{13}$

Answer

(D) $10\sqrt{13}$

Question 16

Number of solutions of $\sqrt{3}\ \cos 2	heta + 8 \cos	heta + 3\sqrt{3} = 0$, $	heta \in [-3\pi, 2\pi]$ is:

Accepted Answer

(B) 5

Answer

(A) 0

Answer

(C) 3

Answer

(D) 4

Question 17

Let $S = \{z : 3 \le | 2z - 3(1 + i)| \le 7\}$ be a set of complex numbers. Then $\underset{z \in S}{\mathrm{Min}}\ \left|\left(z + \frac{1}{2}(5 + 3i)\right)\right|$ is equal to :

Accepted Answer

(B) $\frac{3}{2}$

Answer

(A) $\frac{1}{2}$

Answer

(C) 2

Answer

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

Question 18

Let $\alpha$ and $\beta$ respectively be the maximum and the minimum values of the function $f(	heta) = 4\left(\sin^{4}\left(\frac{7\pi}{2} - 	hetaight) + \sin^{4}(11\pi + 	heta)ight) - 2\left(\sin^{6}\left(\frac{3\pi}{2} - 	hetaight) + \sin^{6}(9\pi - 	heta)ight)$, $	heta \in \mathbf{R}$. Then $\alpha + 2\beta$ is equal to :

Accepted Answer

(B) 5

Answer

(A) 4

Answer

(C) 3

Answer

(D) 6

Question 19

A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in:

Accepted Answer

(D) 36 days

Answer

(A) 24 days

Answer

(B) 42 days

Answer

(C) 30 days

Question 20

Let the direction cosines of two lines satisfy the equations : $4\ell + m - n = 0$ and $2mn + 10n\ell + 3\ell m = 0$. Then the cosine of the acute angle between these lines is :

Accepted Answer

(D) $\frac{10}{3\sqrt{38}}$

Answer

(A) $\frac{10}{\sqrt{38}}$

Answer

(B) $\frac{20}{3\sqrt{38}}$

Answer

(C) $\frac{10}{7\sqrt{38}}$

Question 21

Let $|A| = 6$, where A is a $3 	imes 3$ matrix. If $|\mathrm{adj}(3\mathrm{adj}(A^{2} \cdot \mathrm{adj}(2A)))| = 2^{m} \cdot 3^{n}$, $m, n \in \mathbf{N}$, then $m + n$ is equal to __________.

Accepted Answer

62

Question 22

Let the area of the region bounded by the curve $y = \max\ \{\sin x, \cos x\}$, lines $x = 0$, $x = \frac{3\pi}{2}$, and the x-axis be A. Then, $A + A^{2}$ is equal to

Accepted Answer

12

Question 23

Let f be a twice differentiable non-negative function such that $(f(x))^{2} = 25 + \int\limits_{0}^{x}\left((f(t))^{2} + (f'(t))^{2}\right) dt$. Then the mean of $f(\log_{e}(1))$, $f(\log_{e}(2))$, ....., $f(\log_{e}(625))$ is equal to _________ .

Accepted Answer

1565

Question 24

From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that $a - b \ge 10$ is $\frac{m}{n}$, gcd (m, n) = 1, then $m + n$ is equal to _______.

Accepted Answer

311

Question 25

The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is _______ .

Accepted Answer

1422

Question 26

A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is _______.

Accepted Answer

(C) 4°

Answer

(A) 4.5°

Answer

(B) 6°

Answer

(D) 5°

Question 27

A small both A of mass m is attached to a massless rigid rod of length 1m pivoted at point P and kept at an angle of 60° with vertical as shown in figure. At distance of 1m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by bob A, then radius R is _______m.

Accepted Answer

(B) $\frac{1}{5}$

Answer

(A) $\frac{3}{5}$

Answer

(C) $\frac{2+\sqrt{3}}{5}$

Answer

(D) $\frac{2-\sqrt{3}}{5}$

Question 28

Match List-I (Relation) with List-II (Law).
Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 29

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is :

Accepted Answer

(C) 0.06

Answer

(A) 0.24

Answer

(B) 0.18

Answer

(D) 0.08

Question 30

The de Broglie wavelength of an oxygen molecule at 27°C is $x 	imes 10^{-12}$ m. The value of x is (take Planck's constant $= 6.63 	imes 10^{-34}$ J.s, Boltzmann constant $= 1.38 	imes 10^{-23}$ J/K, mass of oxygen. Molecule $= 5.31 	imes 10^{-26}$ kg).

Accepted Answer

(A) 26

Answer

(B) 24

Answer

(C) 30

Answer

(D) 20

Question 31

A simple pendulum of string length 30 cm performs 20 oscillations in 10s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is ______cm. [Assume that the mass of the pendulum remains same.]

Accepted Answer

(C) 7.5

Answer

(A) 120

Answer

(B) 0.75

Answer

(D) 15

Question 32

Two blocks with masses 100g and 200g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E. The energy stored in B, when spring constants $k_A$, $k_B$ of A and B, respectively satisfy the relation $4k_A = 3k_B$, is :

Accepted Answer

(C) 3E

Answer

(A) 4E

Answer

(B) 2E

Answer

(D) $\frac{4}{3}E$

Question 33

The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L (R < L) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M) :

Accepted Answer

(D) $\frac{3}{8}MR^2 + \frac{1}{6}ML^2$

Answer

(A) $\frac{3}{8}MR^2 + \frac{7}{12}ML^2$

Answer

(B) $\frac{3}{4}MR^2 + \frac{1}{6}ML^2$

Answer

(C) $\frac{3}{4}MR^2 + \frac{7}{12}ML^2$

Question 34

A wire of uniform resistance λΩ/m is bent into a circle of radius r and another piece of wire with length 2r is connected between points A and B (AOB) as shown in figure. The equivalent resistance between points A and B is ______Ω.

Accepted Answer

(C) $\frac{6\pi\lambda r}{3\pi + 16}$

Answer

(A) $\frac{3\pi\lambda r}{8}$

Answer

(B) $(\pi + 1)\,2r\lambda$

Answer

(D) $2\pi\lambda r$

Question 35

The strain-stress  plot for materials A,B,C and D is shown in the figure. Which material has the largest Young's modulus ?

Accepted Answer

(A) C

Answer

(B) D

Answer

(C) A

Answer

(D) B

Question 36

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are $2.4 	imes 10^8$ m/s and $2.7 	imes 10^8$ m/s respectively, then the value of critical angle is :

Accepted Answer

(C) $	an^{-1}\left(\frac{8}{\sqrt{17}}ight)$

Answer

(A) $\cot^{-1}\left(\frac{3}{\sqrt{13}}\right)$

Answer

(B) $\sin^{-1}\left(\frac{9}{8}\right)$

Answer

(D) $\cos^{-1}\left(\frac{8}{9}\right)$

Question 37

In hydrogen atom spectrum, (R → Rydberg's constant)
A. the maximum wavelength of the radiation of Lyman series is $\frac{4}{3R}$
B. the Balmer series lies in the visible region of the spectrum
C. the minimum wavelength of the radiation of Paschen series is $\frac{9}{R}$
D. the minimum wavelength of Lyman series is $\frac{5}{4R}$
Choose the correct answer from the options given below :

Accepted Answer

(B) A, B and C Only

Answer

(A) B, D Only

Answer

(C) A, B and D Only

Answer

(D) A, B Only

Question 38

An object is projected with kinetic energy K from a point A at an angle 60° with the horizontal. The ratio of the difference in kinetic energies points B and C to that at point A (see figure), in the absence of air friction is :

Accepted Answer

(D) $3 : 4$

Answer

(A) $1 : 2$

Answer

(B) $2 : 3$

Answer

(C) $1 : 4$

Question 39

Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :

Accepted Answer

(D) $\frac{3q}{4\varepsilon_0}$

Answer

(A) $\frac{3q}{\varepsilon_0}$

Answer

(B) $\frac{q}{\varepsilon_0}$

Answer

(C) $\frac{3q}{2\varepsilon_0}$

Question 40

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity (g = 10 m/s$^2$) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire it travells a vertical distance of 200 m is ______ mV.

Accepted Answer

(B) $20\sqrt{10}$

Answer

(A) $0.2\sqrt{10}$

Answer

(C) $2\sqrt{10}$

Answer

(D) $200\sqrt{10}$

Question 41

Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is :

Accepted Answer

(A) $\frac{3}{2}\frac{L}{md^2}$

Answer

(B) $\frac{2L}{md^2}$

Answer

(C) $\frac{4}{3}\frac{L}{md^2}$

Answer

(D) $\frac{2L}{5md^2}$

Question 42

In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 m/s and 30 m/s, respectively, strike each other and stick together. The rise in temperature (in °C), if all the heat produced during the collision is retained by these spheres, is :
(specific heat of sphere material 31 cal/kg. °C and 1 cal = 4.2 J)

Accepted Answer

(B) $1.44$

Answer

(A) $1.75$

Answer

(C) $1.15$

Answer

(D) $1.95$

Question 43

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is ______ mm.
[Assume least count is 0.01 mm]

Accepted Answer

(C) $1.54$

Answer

(A) $1.50$

Answer

(B) $1.48$

Answer

(D) $1.51$

Question 44

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Consider a ferromagnetic material :
Assertion (A) : The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains.
Reason (R) : At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

(B) Both (A) and (R) are true but (R) is not the correct explanation of (A)

Answer

(A) (A) is true but (R) is false

Answer

(C) Both (A) and (R) are true and (R) is the correct explanation of (A)

Answer

(D) (A) is false but (R) is true

Question 45

A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of 60° with vertical, then maximum induced EMF between the point of suspension and point of oscillation is ______ mV. (Take g = 10 m/s$^2$)

Accepted Answer

100

Question 46

The equation of the electric field of an electromagnetic wave propagating through free space is given by :
$E = \sqrt{377}\ \sin(6.27 	imes 10^{3}t - 2.09 	imes 10^{-5}x)$ N/C
he average power of the electromagnetic wave is $\left(\frac{1}{\alpha}ight)$ W/m$^2$. The value of $\alpha$ is ______
$\left(	ext{Take } \sqrt{\frac{\mu_0}{\varepsilon_0}} = 377 	ext{ in SI units}ight)$

Accepted Answer

2

Question 47

Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for V=5sin(100t). The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ______ μF.

Accepted Answer

50

Question 48

In two separate Young's double-slit experimental set-ups, two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slit separations and that of the wavelengths of light used are 2 : 1 and 1 : 2 respectively. The corresponding ratio of the distances between the slits and the respective screens ($D_1 / D_2$) is ______.

Accepted Answer

4

Question 49

The space between the plates of a parallel-plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants $K_1 = 2$, $K_2 = 3$, and $K_3 = 5$ (as shown in the figure). If new capacitance is $\frac{n}{3}C$ then the value of n is ______.

Accepted Answer

8

Question 50

Which of the following statements regarding the energy of the stationary state is true in the following one-electron system ?

Accepted Answer

(D) $-2.18 	imes 10^{-18}$ J for third orbit of Li$^{2+}$ ion

Answer

(A) $-1.09 	imes 10^{-18}$ J for second orbit of H atom.

Answer

(B) $+2.18 	imes 10^{-18}$ J for second orbit of He$^+$ ion

Answer

(C) $+8.72 	imes 10^{-18}$ J for first orbit of He$^+$ ion

Question 51

Which one of the following graphs accurately represents the plot of partial pressure of CS$_2$ vs its mole fraction in a mixture of acetone and CS$_2$ at constant temperature ?

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 52

The correct trend in the first ionization enthalpies of the elements in the 3$^{rd}$ period of periodic table is:

Accepted Answer

(A) Al < Si < S < P < Cl

Answer

(B) Al < S < P < Si < Cl

Answer

(C) Si < S < Al < P < Cl

Answer

(D) S < Si < Al < P < Cl

Question 53

The correct sequence of reagents for the above conversion of X to Y is :

Accepted Answer

(D) (i) NaOEt (ii) B$_2$H$_6$/H$_2$O$_2$ (iii) Jones reagent

Answer

(A) (i) NaOH (aq) (ii) Jones reagent (iii) H$_3$O$^+$

Answer

(B) B$_2$H$_6$/H$_2$O$_2$ (ii) NaOEt (iii) Jones reagent

Answer

(C) (i) Jones reagent (ii) NaOEt (iii) Hot KMnO$_4$/KOH

Question 54

'x' is the product which is obtained from propanenitrile and stannous chloride in the presence of hydrochloric acid followed by hydrolysis. 'y' is the product which is obtained from the but-2-ene by the ozonolysis followed by hydrolysis. From the following, which product is not obtained when one mole of 'x' and one mole of 'y' react with each other in the presence of alkali followed by heating ?

Accepted Answer

(D) 3-Methylbut-2-enal

Answer

(A) 2-Methylbut-2-enal

Answer

(B) Pent-2-enal

Answer

(C) 2-Methylpent-2-enal

Question 55

Consider the following sequence of reactions.
4-Nitrotoluene
Assuming that the reaction proceeds to completion, then 137 mg of 4-nitrotoluene will produce ______mg of B.
(Given molar mass in g mol$^{-1}$ H : 1, C : 12, N :14, O :16, Br : 80)

Accepted Answer

(C) 228

Answer

(A) 301

Answer

(B) 146

Answer

(D) 208

Question 56

A cup of water at 5$^\circ$C (system) is placed in a microwave oven and the oven is turned on for one minute during which, the water begins to boil. Which of the following option is true ?

Accepted Answer

(B) q = +ve, w = -ve, $\Delta$U = +ve

Answer

(A) q = +ve, w = 0, $\Delta$U = -ve

Answer

(C) q = -ve, w = -ve, $\Delta$U = -ve

Answer

(D) q = +ve, w = -ve, $\Delta$U = -ve

Question 57

Given below are two statements :
Statement I : [CoBr$_4$]$^{2-}$ ion will absorb light of lower energy than [CoCl$_4$]$^{2-}$ ion.
Statement II : In [CoI$_4$]$^{2-}$ ion, the energy separation between the two set of d-orbitals is more than [CoCl$_4$]$^{2-}$ ion.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

(A) Both Statement I and Statement II are false

Answer

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

Answer

(D) Both Statement I and Statement II are true

Question 58

But-2-yne and hydrogen (one mole each) are separately treated with (i) Pd/C and (ii) Na/liq. NH$_3$ to give the products X and Y respectively.
Identify the incorrect statements.
A. X and Y are stereoisomers.
B. Dipole moment of X is zero
C. Boiling point of X is higher than Y.
D. X and Y react with O$_3$/Zn + H$_2$O to give different products.
Choose the correct answer from the options given below :

Accepted Answer

(B) B and D only

Answer

(A) B and C only

Answer

(C) A and B only

Answer

(D) A and C only

Question 59

Given,
(A) n = 5, m$_l$ = $-1$
(B) n = 3, l = 2, m$_l$ = $-1$, m$_s$ = $+\frac{1}{2}$
The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are :

Accepted Answer

(D) 8 and 1

Answer

(A) 26 and 1

Answer

(B) 4 and 1

Answer

(C) 2 and 4

Question 60

Consider the following compounds
Arrange these compounds in the increasing order of reactivity with nitrating mixture.

Accepted Answer

(D) b < a < c

Answer

(A) c < a < b

Answer

(B) b < c < a

Answer

(C) c < b < a

Question 61

The statements that are incorrect about the nickel (II) complex of dimethylglyoxime are :
A. It is red in colour
B. It has a high solubility in water at pH = 9
C. The Ni ion has two unpaired d-electrons
D. The N - Ni - N bond angle is almost close to 90$^\circ$
E. The complex contains four five-membered metallacycles (metal containing rings)
Choose the correct answer from the options given below :

Accepted Answer

(C) B, C and E only

Answer

(A) C and E only

Answer

(B) A, D and B only

Answer

(D) C and D only

Question 62

From the given following (A to D) cyclic structures, those which will not react with Tollen's reagent are :

Accepted Answer

(D) B and C

Answer

(A) B and D

Answer

(B) A and D

Answer

(C) A and B

Question 63

Identify the molecule(X) with maximum number of lone pairs of electrons (obtained using Lewis dot structure) among HNO$_3$, H$_2$SO$_4$, NF$_3$ and O$_3$. Choose the correct bond angle made by the central atom of the molecule (X).

Accepted Answer

(C) 102°

Answer

(A) 120°

Answer

(B) 107°

Answer

(D) 116°

Question 64

Match List-I (Functional group (detection)) with List-II (Change observed during detection).
Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

List-I (Relation)	List-II (Law)
A. $\oint \vec{E} \cdot \vec{dl} = -\frac{d}{dt}\oint \vec{B} \cdot \vec{da}$	I.Ampere's circuital law.
B. $\oint \vec{B} \cdot \vec{dl} = \mu_0\left(1 + \in_0 \frac{d\phi_E}{dt}\right)$	II.Faraday's laws of electromagnetic induction.
C. $\oint \vec{E} \cdot \vec{da} = \frac{1}{\in_0}\int \rho dv$	III.Ampere-Maxwell law
D. $\oint \vec{B} \cdot \vec{dl} = \mu_0 I$	IV.Gauss's law of electrostatics

List-I (Functional group (detection))	List-II (Change observed during detection)
A.Unsaturation (Baeyer's test)	I.Red colour Appears
B.Alcoholic group (Ceric ammonium nitrate test)	II.Silver mirror appears
C.Aldehyde group (Tollen's reagent)	III.Violet colour appears
D.Phenolic group (FeCl $_3$ test)	IV.Discharge of pink colour

JEE Main 23 January 2026 Shift 1 Question Paper with Answers

Physics — JEE Main 23 January 2026 Shift 1

Chemistry — JEE Main 23 January 2026 Shift 1

Mathematics — JEE Main 23 January 2026 Shift 1

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