JEE Main 4 April 2026 Shift 1 Question Paper

Question 1

Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x) = \cos^{-1}\left(\frac{4x + 2[x]}{3}\right)$ is $[\alpha, \beta]$, then $12(\alpha + \beta)$ is equal to:

Accepted Answer

(A) $6$

Answer

(B) $8$

Answer

(C) $9$

Answer

(D) $4$

Question 2

If the set of all solutions of $|x^2 + x - 9| = |x| + |x^2 - 9|$ is $[\alpha, \beta] \cup [\gamma, \infty)$, then $(\alpha^2 + \beta^2 + \gamma^2)$ is equal to:

Accepted Answer

(B) $18$

Answer

(A) $9$

Answer

(C) $36$

Answer

(D) $72$

Question 3

Let $z$ be a complex number such that $|z + 2| = |z - 2|$ and $\arg\left(\frac{z + 3}{z - i}\right) = \frac{\pi}{4}$. Then $|z|^2$ is equal to:

Accepted Answer

(A) $9$

Answer

(B) $4$

Answer

(C) $5$

Answer

(D) $1$

Question 4

The number of functions $f : \{1, 2, 3, 4\} 	o \{a, b, c\}$, which are not onto, is:

Accepted Answer

(B) $45$

Answer

(A) $48$

Answer

(C) $51$

Answer

(D) $35$

Question 5

Let $S = \left\{ A = \begin{bmatrix} a & b \ c & d \end{bmatrix} : a, b, c, d \in \{0, 1, 2, 3, 4\} 	ext{ and } A^2 - 4A + 3I = 0 ight\}$ be a set of $2 	imes 2$ matrices. Then the number of matrices in $S$, for which the sum of the diagonal elements is equal to 4, is:

Accepted Answer

(D) $19$

Answer

(A) $20$

Answer

(B) $17$

Answer

(C) $21$

Question 6

Let $A = \begin{bmatrix} 1 & 1 & 2 \ -2 & 0 & 1 \ 1 & 3 & 5 \end{bmatrix}$. Then the sum of all elements of the matrix $\mathrm{adj}(\mathrm{adj}(2(\mathrm{adj}A)^{-1}))$ is equal to:

Accepted Answer

(D) $-3$

Answer

(A) $3$

Answer

(B) $4$

Answer

(C) $-4$

Question 7

The first term of an A.P. of 30 non-negative terms is $\frac{10}{3}$. If the sum of this A.P. is the cube of its last term, then its common difference is:

Accepted Answer

(A) $\frac{5}{87}$

Answer

(B) $\frac{25}{83}$

Answer

(C) $\frac{15}{29}$

Answer

(D) $\frac{5}{29}$

Question 8

The number of ways of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:

Accepted Answer

(D) $4320$

Answer

(A) $5040$

Answer

(B) $3050$

Answer

(C) $3410$

Question 9

Let the smallest value of $k \in \mathbb{N}$, for which the coefficient of $x^3$ in $(1 + x)^3 + (1 + x)^4 + (1 + x)^5 + \ldots + (1 + x)^{99} + (1 + kx)^{100}$, $x 
eq 0$, is $\left(43n + \frac{101}{4}ight)\left({}^{100}C_3ight)$ for some $n \in \mathbb{N}$, be $p$. Then the value of $p + n$ is:

Accepted Answer

(B) $11$

Answer

(A) $10$

Answer

(C) $12$

Answer

(D) $13$

Question 10

Suppose that the mean and median of the non-negative numbers $21, 8, 17, a, 51, 103, b, 13, 67, (a > b)$, are 40 and 21, respectively. If the mean deviation about the median is 26, then $2a$ is equal to:

Accepted Answer

(D) $131$

Answer

(A) $109$

Answer

(B) $117$

Answer

(C) $161$

Question 11

Let the line $L_1 : x + 3 = 0$ intersect the lines $L_2 : x - y = 0$ and $L_3 : 3x + y = 0$ at the points $A$ and $B$, respectively. Let the bisector of the obtuse angle between the lines $L_2$ and $L_3$ intersect the line $L_1$ at the point $C$. Then $BC^2 : AC^2$ is equal to:

Accepted Answer

(A) $5 : 1$

Answer

(B) $1 : 5$

Answer

(C) $2 : 3$

Answer

(D) $3 : 2$

Question 12

Let the vertex $A$ of a triangle $ABC$ be $(1, 2)$, and the mid-point of the side $AB$ be $(5, -1)$. If the centroid of this triangle is $(3, 4)$ and its circumcenter is $(\alpha, \beta)$, then $21(\alpha + \beta)$ is equal to:

Accepted Answer

(C) $497$

Answer

(A) $309$

Answer

(B) $403$

Answer

(D) $524$

Question 13

Suppose that two chords, drawn from the point $(1, 2)$ on the circle $x^2 + y^2 + x - 3y = 0$ are bisected by the $y$-axis. If the other ends of these chords are $R$ and $S$, and the mid point of the line segment $RS$ is $(\alpha, \beta)$, then $6(\alpha + \beta)$ is equal to:

Accepted Answer

(B) $3$

Answer

(A) $1$

Answer

(C) $4$

Answer

(D) $6$

Question 14

A line with direction ratios $1, -1, 2$ intersects the lines $\frac{x}{2} = \frac{y}{3} = \frac{z+1}{3}$ and $\frac{x+1}{-1} = \frac{y-2}{1} = \frac{z}{4}$ at the points $P$ and $Q$, respectively. If the length of the line segment $PQ$ is $\alpha$, then $225\alpha^2$ is equal to:

Accepted Answer

(B) $1014$

Answer

(A) $1024$

Answer

(C) $1104$

Answer

(D) $1204$

Question 15

The square of the distance of the point $(-2, -8, 6)$ from the line $\frac{x-1}{1} = \frac{y-1}{2} = \frac{z}{-1}$ along the line $\frac{x+5}{1} = \frac{y+5}{-1} = \frac{z}{2}$ is equal to:

Accepted Answer

(B) $6$

Answer

(A) $3$

Answer

(C) $8$

Answer

(D) $12$

Question 16

If $y = 	an^{-1}\left(\frac{3\cos x - 4\sin x}{4\cos x + 3\sin x}ight) + 2	an^{-1}\left(\frac{x}{1+\sqrt{1-x^2}}ight)$, then $\frac{dy}{dx}$ at $x = \frac{\sqrt{3}}{2}$ is equal to:

Accepted Answer

(C) $1$

Answer

(A) $3$

Answer

(B) $-1$

Answer

(D) $2$

Question 17

Let $f$ be a real polynomial of degree $n$ such that $f(x) = f'(x)f''(x)$, for all $x \in \mathbb{R}$. If $f(0) = 0$, then $36\left(f'(2) + f''(2) + \int_0^2 f(x)\, dx\right)$ is equal to:

Accepted Answer

(C) $56$

Answer

(A) $42$

Answer

(B) $46$

Answer

(D) $66$

Question 18

The area of the region $\{(x, y) : y \leq \pi - |x|,\ y \leq |x \sin x|,\ y \geq 0\}$ is:

Accepted Answer

(B) $2 + \frac{\pi^2}{4}$

Answer

(A) $1 + \frac{\pi^2}{8}$

Answer

(C) $\frac{\pi^2}{8} - 1$

Answer

(D) $4 + \frac{\pi^2}{2}$

Question 19

Let $\int_{-2}^{2}\left(|\sin x| + [x \sin x]\right) dx = 2(3 - \cos 2) + \beta$, where $[\cdot]$ is the greatest integer function. Then $\beta \sin\left(\frac{\beta}{2}\right)$ equals:

Accepted Answer

(B) $2$

Answer

(A) $1$

Answer

(C) $4$

Answer

(D) $8$

Question 20

Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} = (1 + x + x^2)(1 - y + y^2)$, $y(0) = \frac{1}{2}$. Then $(2y(1) - 1)$ is equal to:

Accepted Answer

(C) $\sqrt{3} 	an\left(\frac{11\sqrt{3}}{12}ight)$

Answer

(A) $\sqrt{3} 	an\left(\frac{11\sqrt{3}}{6}ight)$

Answer

(B) $\frac{\sqrt{3}}{2} 	an\left(\frac{11\sqrt{3}}{12}ight)$

Answer

(D) $\frac{\sqrt{3}}{2} 	an\left(\frac{11\sqrt{3}}{6}ight)$

Question 21

A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is $p$, then $96p$ is equal to _______.

Accepted Answer

9

Question 22

Consider the parabola $P : y^2 = 4kx$ and the ellipse $E : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Let the line segment joining the points of intersection of $P$ and $E$, be their latus rectums. If the eccentricity of $E$ is $e$, then $e^2 + 2\sqrt{2}$ is equal to _______.

Accepted Answer

3

Question 23

If $A = \frac{\sin 3^\circ}{\cos 9^\circ} + \frac{\sin 9^\circ}{\cos 27^\circ} + \frac{\sin 27^\circ}{\cos 81^\circ}$ and $B = 	an 81^\circ - 	an 3^\circ$, then $\frac{B}{A}$ is equal to _______.

Accepted Answer

2

Question 24

Let $\vec{a}_k = (	an	heta_k)\hat{i} + \hat{j}$ and $\vec{b}_k = \hat{i} - (\cot	heta_k)\hat{j}$, where $	heta_k = \frac{2^{k-1}\pi}{2^n + 1}$, for some $n \in \mathbb{N}$, $n > 5$. Then the value of $\frac{\sum_{k=1}^{n} |\vec{a}_k|^2}{\sum_{k=1}^{n} |\vec{b}_k|^2}$ is _______.

Accepted Answer

3

Question 25

The number of points, at which the function $f(x) = \max\{6x, 2 + 3x^2\} + |x - 1|\left|\cos\left|x^2 - \frac{1}{4}\right|\right|$, $x \in (-\pi, \pi)$, is not differentiable, is _______.

Accepted Answer

9

Question 26

In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm. If the circular scale has 100 divisions, the least count of screw gauge is _____ mm.

Accepted Answer

(D) $5 	imes 10^{-3}$

Answer

(A) $1 	imes 10^{-2}$

Answer

(B) $1 	imes 10^{-3}$

Answer

(C) $5 	imes 10^{-2}$

Question 27

The increase in the pressure required to decrease the volume $(\Delta V)$ of water is $6.3 	imes 10^{7}$ N/m$^2$. The percentage decrease in the volume is _____. (Bulk modulus of water $= 2.1 	imes 10^{9}$ N/m$^2$.)

Accepted Answer

(B) $3\%$

Answer

(A) $2\%$

Answer

(C) $6\%$

Answer

(D) $4\%$

Question 28

The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is 50% more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at $45^\circ$ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is _____.

Accepted Answer

(C) $5/9$

Answer

(A) $3/4$

Answer

(B) $2/3$

Answer

(D) $4/9$

Question 29

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10 . If the binding energy per nucleon for the mass numbers 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process, $\Delta Mc^2 =$ _____ MeV.

Accepted Answer

(C) 2.2

Answer

(A) 6.9

Answer

(B) 7.9

Answer

(D) 4.3

Question 30

A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The smaller part having mass $M/8$ is converted into a sphere of radius $r$ and the larger part is converted into a circular disc of thickness $t$ and radius $2R$. If $I_1$ is moment of inertia of a sphere having radius $r$ about an axis through its centre and $I_2$ is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia $I_2/I_1 =$ _____.

Accepted Answer

(B) 70

Answer

(A) 35

Answer

(C) 140

Answer

(D) 210

Question 31

Two projectiles are projected with the same initial velocities at the $15^\circ$ and $30^\circ$ with respect to the horizontal. The ratio of their ranges is $1 : x$. The value of $x$ is:

Accepted Answer

(B) $\sqrt{3}$

Answer

(A) $\sqrt{2}$

Answer

(C) $2\sqrt{3}$

Answer

(D) $\frac{1}{\sqrt{2}}$

Question 32

The graph shows variation of stopping potential $V_o$ with the frequency $
u$ of the incident radiation for three photosensitive metals $X_1$, $X_2$ and $X_3$. Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation?

Accepted Answer

(A) $X_1$

Answer

(B) $X_2$

Answer

(C) $X_3$

Answer

(D) All the metals will give out photo electrons with same kinetic energies.

Question 33

A slit of width $a$ is illuminated by light of wavelength $\lambda$. The linear separation between $1^{st}$ and $3^{rd}$ minima in the diffraction pattern produced on a screen placed at a distance $D$ from the slit system is _____.

Accepted Answer

(C) $2\frac{D\lambda}{a}$

Answer

(A) $\frac{D\lambda}{a}$

Answer

(B) $1.5\frac{D\lambda}{a}$

Answer

(D) $3\frac{D\lambda}{a}$

Question 34

A string $A$ of length 0.314 m and Young's modulus $2 	imes 10^{10}$ N/m$^2$ is connected to another string $B$ of length and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is _____ mm. (radius of both the strings is 0.2 mm and acceleration due to gravity $= 10$ m/s$^2$) (Mass of both strings is to be neglected as compared to the mass of load)

Accepted Answer

(B) 2

Answer

(A) 3

Answer

(C) 1.9

Answer

(D) 1

Question 35

One gas of $n_1$ mole of molecules at temperature $T_1$, volume $V_1$, and pressure $P_1$, and another gas of $n_2$ mole of molecules at temperature $T_2$, volume $V_2$, and pressure $P_2$, are mixed resulting in pressure $P$ and volume $V$ of the mixture. The temperature of the mixture is _____.

Accepted Answer

(B) $T_1T_2PV/(T_2P_1V_1 + T_1P_2V_2)$

Answer

(A) $(T_1 + T_2)/2$

Answer

(C) $(T_2P_1V_1 + T_1P_2V_2)/(T_1T_2PV)$

Answer

(D) $|T_1 - T_2|/2$

Question 36

An ideal gas undergoes a process maintaining relation between pressure $(P)$ and volume $(V)$ as $P = P_o\left(1 + \left(\frac{V_o}{V}\right)^2\right)^{-1}$ , where $P_o$ and $V_o$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_o$ and $3V_o$ respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, $T_B - T_A$ is _____. ($R =$ gas constant)

Accepted Answer

(B) $\frac{11P_oV_o}{10R}$

Answer

(A) $\frac{9P_oV_o}{8R}$

Answer

(C) $\frac{7P_oV_o}{6R}$

Answer

(D) $\frac{13P_oV_o}{11R}$

Question 37

A voltmeter with internal resistance of $x$ $\Omega$ can be used to measure upto 20 V. In order to increase its measuring range to 30 V, the required modification is to _____.

Accepted Answer

(A) connect resistor of $\frac{x}{2}$ $\Omega$, in series with voltmeter.

Answer

(B) connect resistor of $\frac{x}{2}$ $\Omega$, in parallel to voltmeter.

Answer

(C) connect a resistor of $x$ $\Omega$ in series with voltmeter.

Answer

(D) connect resistor of $2x$ $\Omega$ in parallel to voltmeter.

Question 38

Two 4 bits binary numbers, $A = 1101$ and $B = 1010$ are given in the inputs of a logic circuit shown in figure below. The output $(Y)$ will be:

Accepted Answer

(A) $Y = 1101$

Answer

(B) $Y = 0010$

Answer

(C) $Y = 0111$

Answer

(D) $Y = 1000$

Question 39

A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is ______ cm.

Accepted Answer

(B) 5

Answer

(A) 2.5

Answer

(C) 7.5

Answer

(D) 7

Question 40

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed $v$. If $x$ is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to $x^{\alpha}$, where $\alpha$ is ______.

Accepted Answer

(A) $-2$

Answer

(B) $1$

Answer

(C) $-1$

Answer

(D) $2$

Question 41

An insulated wire is wound so that it forms a flat coil with $N = 200$ turns. The radius of the innermost turn is $r_1 = 3$ cm, and of the outermost turn $r_2 = 6$ cm. If 20 mA current flows in it then the magnetic moment will be $\alpha 	imes 10^{-2}$ A.m$^2$. The value of $\alpha$ is ______.

Accepted Answer

(B) 2.64

Answer

(A) 4.4

Answer

(C) 3.25

Answer

(D) 1.2

Question 42

Consider a circuit consisting of a capacitor ($20\ \mu$F), resistor ($100\ \Omega$) and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is $10\ \Omega$. The time constant of the circuit is $\alpha 	imes 10^{-3}$ s. The value of $\alpha$ is ______

Accepted Answer

(A) 2.2

Answer

(B) 2.0

Answer

(C) 2.1

Answer

(D) 2.4

Question 43

The voltage and the current between $A$ and $B$ points shown in the circuit are ______.

Accepted Answer

(B) 24 V, 4 A

Answer

(A) 24 V, 12 A

Answer

(C) 18 V, 12 A

Answer

(D) 27 V, 4 A

Question 44

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5 	imes 10^{-7}$ radian. The value of $R$ is ______ cm.

Accepted Answer

(B) 122

Answer

(A) 61

Answer

(C) 244

Answer

(D) 305

Question 45

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

Accepted Answer

(A) $(E_x\hat{i} + E_y\hat{j}) \sin(kx - kz - \omega t)$

Answer

(B) $(E_x\hat{i} + E_z\hat{k}) \sin(kx + ky - \omega t)$

Answer

(C) $(E_x\hat{j} + E_y\hat{k}) \sin(ky + kz - \omega t)$

Answer

(D) $(E_x\hat{i} + E_y\hat{j} + E_z\hat{k}) \sin(kx + ky - kz - \omega t)$

Question 46

A 1 kg block subjected to two simultaneous forces $(2\hat{i} + 3\hat{j} + 4\hat{k})$ N and $(3\hat{i} - \hat{j} - 2\hat{k})$ N is moved a distance of 25 m along $(3\hat{i} - 4\hat{j})$ direction. The work done in this process is ______ J.

Accepted Answer

35

Question 47

The surface tension of a soap solution is $3.5 	imes 10^{-2}$ N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is $\alpha 	imes 10^{-6}$ J. The value of $\alpha$ is ______. $(\pi = 22/7)$

Accepted Answer

264

Question 48

The velocity of a particle executing simple harmonic motion along $x$-axis is described as $v^2 = 50 - x^2$, where $x$ represents displacement. If the time period of motion is $\frac{x}{7}$ s, the value of $x$ is ______.

Accepted Answer

44

Question 49

A body of mass 2 kg begins to move under the influence of time dependent force $\vec{F} = (2t\hat{i} + 6t^2\hat{j})$ N, where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and $y$-axis respectively. The power produced by the force at $t = 2$ s is ______ W.

Accepted Answer

200

Question 50

An inductor of 10 mH, capacitor of $0.1\ \mu$F and a resistor of $100\ \Omega$ are connected in series across an $a.c$ power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitance reactance is $\sqrt{3}\alpha\ \Omega$. The value of $\alpha$ is ______.

Accepted Answer

100

Question 51

Number of moles and number of molecules in $1.4187$ L of $SO_2$ at STP respectively are:

Accepted Answer

(B) $0.0633; 3.812 	imes 10^{22}$

Answer

(A) $0.1266; 3.812 	imes 10^{22}$

Answer

(C) $0.1266; 7.6238 	imes 10^{22}$

Answer

(D) $0.0633; 7.6238 	imes 10^{22}$

Question 52

What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?

Accepted Answer

(B) $5 : 0.81$

Answer

(A) $5 : 1$

Answer

(C) $5 : 1.75$

Answer

(D) $5 : 27$

Question 53

Which of the following is correct set of 4 quantum numbers of $19^{th}$ electron in Chromium (Atomic number $= 24$) in accordance with Aufbau principle?

Accepted Answer

(D) $n = 4, l = 0, m = 0, s = +\frac{1}{2}$

Answer

(A) $n = 3, l = 2, m = +2, s = +\frac{1}{2}$

Answer

(B) $n = 3, l = 2, m = -2, s = +\frac{1}{2}$

Answer

(C) $n = 4, l = 1, m = 0, s = +\frac{1}{2}$

Question 54

Given below are two statements:
Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure.
Statement II: In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas.
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 true

Answer

(B) Both Statement I and Statement II are false

Answer

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

Question 55

At $T(K)$, the equilibrium constant of $A_2(g) + B_2(g) ightleftharpoons C(g)$ is $2.7 	imes 10^{-5}$. What is the equilibrium constant for $\frac{1}{3}A_2(g) + \frac{1}{3}B_2(g) ightleftharpoons \frac{1}{3}C(g)$ at the same temperature?

Accepted Answer

(D) $3 	imes 10^{-2}$

Answer

(A) $(2.7 	imes 10^{-5})^3$

Answer

(B) $6 	imes 10^{-2}$

Answer

(C) $\sqrt{2.7 	imes 10^{-5}}$

Question 56

In order to oxidise a mixture of 1 mole each of $FeC_2O_4$, $Fe_2(C_2O_4)_3$, $FeSO_4$ and $Fe_2(SO_4)_3$ in acidic medium, the number of moles of $KMnO_4$ required is

Accepted Answer

(B) 2

Answer

(A) 3

Answer

(C) 5

Answer

(D) 7

Question 57

Consider the first order reaction $R \rightarrow P$. The fraction of molecules decomposed in the given first order reaction can be expressed as

Accepted Answer

(D) $1 - e^{-k_1 t}$

Answer

(A) $1 - e^{k_1 t}$

Answer

(B) $1 + e^{k_1 t}$

Answer

(C) $1 + e^{-k_1 t}$

Question 58

A monoatomic anion $(A^-)$ has 45 neutrons and 36 electrons. Atomic mass, group in the periodic table and physical state at room temperature of the element $(A)$ respectively are

Accepted Answer

(A) $80, 17$, liquid

Answer

(B) $81, 16$, solid

Answer

(C) $80, 16$, gas

Answer

(D) $81, 15$, gas

Question 59

Given below are two statements:
Statement I: The covalency of oxygen is generally two but it can exceed upto four. The oxidation state of oxygen in $SO_2$ is $-2$ and in $OF_2$ it is $+2$.
Statement II: The anomalous behaviour of oxygen when compared to the other elements of group 16 is due to its small size and high electronegativity.
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 true but Statement II is false

Answer

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

Question 60

The correct statements among the following are,
A. $Mo(VI)$ and $W(VI)$ are less stable than $Cr(VI)$.
B. $Ce^{4+}$ and $Tb^{4+}$ are oxidant while $Eu^{2+}$ and $Yb^{2+}$ are reductant.
C. $Cm$ and $Am$ have seven unpaired electrons.
D. Actinoid contraction is greater from element to element than lanthanoid contraction.
Choose the correct answer from the options given below:

Accepted Answer

(C) B and D Only

Answer

(A) A and B Only

Answer

(B) C and D Only

Answer

(D) A and C Only

Question 61

Correct statements from the following are
A. Potassium dichromate is an oxidising agent and it oxidises $FeSO_4$ to $Fe_2(SO_4)_3$ in acidic medium.
B. Sodium dichromate can be used as primary standard in volumetric estimation.
C. $CrO_4^{2-}$ and $Cr_2O_7^{2-}$ are interconvertible in aqueous solution by varying the $pH$ of the solution.
D. $Cr	ext{-}O	ext{-}Cr$ bond angle in $Cr_2O_7^{2-}$ is $126^{\circ}$.
Choose the correct answer from the options given below:

Accepted Answer

(B) A, C and D Only

Answer

(A) A, B and C Only

Answer

(C) A and C Only

Answer

(D) B and D Only

Question 62

Match List-I (Complex ion) with List-II (Calculated spin only magnetic moment (BM)).
Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 63

Increasing order of electron withdrawing power of following functional groups is:
a. $-CN$
b. $-COOH$
c. $-NO_2$
d. $-I$

Accepted Answer

(C) $d < b < a < c$

Answer

(A) $c < b < d < a$

Answer

(B) $c < a < b < d$

Answer

(D) $a < b < c < d$

Question 64

Match List-I (Name of reaction) with List-II (Reagent or catalyst used).
Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

List-I (Complex ion)	List-II (Calculated spin only magnetic moment (BM))
A. $[Cr(H_2O)_6]^{2+}$	I. $3.87$
B. $[Co(H_2O)_6]^{2+}$	II. $5.92$
C. $[Cu(H_2O)_6]^{2+}$	III. $4.90$
D. $[Mn(H_2O)_6]^{2+}$	IV. $1.73$

List-I (Name of reaction)	List-II (Reagent or catalyst used)
A.Finkelstein reaction	I. $SbF_3$
B.Swarts reaction	II. $Na$ , dry ether
C.Sandmeyer's reaction	III. $NaI$
D.Fittig reaction	IV. $Cu_2Cl_2$

List-I (Name of amino acid)	List-II (One letter symbol/type)
A.Arginine	I.D/Non-essential
B.Aspartic acid	II.R/Essential
C.Lysine	III.E/Non-essential
D.Glutamic acid	IV.K/Essential

JEE Main 4 April 2026 Shift 1 Question Paper with Answers

Physics — JEE Main 4 April 2026 Shift 1

Chemistry — JEE Main 4 April 2026 Shift 1

Mathematics — JEE Main 4 April 2026 Shift 1

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