JEE Main 5 April 2026 Shift 2 Question Paper

Question 1

Let α, β be the roots of the equation $x^2 - x + p = 0$ and γ, δ be the roots the equation $x^2 - 4x + q = 0$; p, q ∈ Z. If α, β, γ, δ are in G.P., then $|p + q|$ equals :

Accepted Answer

(C) 34

Answer

(A) 16

Answer

(B) 32

Answer

(D) 38

Question 2

Let $z_1, z_2$ ∈ ℂ be the distinct solutions of the equation $z^2 + 4z - (1 + 12i) = 0$. Then $|z_1|^2 + |z_2|^2$ is equal to :

Accepted Answer

(D) 34

Answer

(A) 18

Answer

(B) 22

Answer

(C) 29

Question 3

If $f : \mathbf{N} 	o \mathbf{Z}$ is defined by
$f(n) = \begin{vmatrix} n & -1 & -5 \ -2n^2 & 3(2k+1) & 2k+1 \ -3n^3 & 3k(2k+1) & 3k(k+2)+1 \end{vmatrix}$, k ∈ N,
and $\sum_{n=1}^{k} f(n) = 98$, then k is equal to :

Accepted Answer

(A) 3

Answer

(B) 4

Answer

(C) 5

Answer

(D) 6

Question 4

Let M be a $3 	imes 3$ matrix such that $M \begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}$, $M \begin{pmatrix} 0 \ 1 \ 0 \end{pmatrix} = \begin{pmatrix} 0 \ 1 \ 2 \end{pmatrix}$ and $M \begin{pmatrix} 0 \ 0 \ 1 \end{pmatrix} = \begin{pmatrix} -1 \ 1 \ 1 \end{pmatrix}$. If $M \begin{pmatrix} x \ y \ z \end{pmatrix} = \begin{pmatrix} 1 \ 7 \ 11 \end{pmatrix}$, then $x + y + z$ equals :

Accepted Answer

(B) 5

Answer

(A) 4

Answer

(C) 7

Answer

(D) 11

Question 5

If the sum of the first 10 terms of the series $\frac{1}{1 + 1^4 	imes 4} + \frac{2}{1 + 2^4 	imes 4} + \frac{3}{1 + 3^4 	imes 4} + \frac{4}{1 + 4^4 	imes 4} + \ldots$ is $\frac{m}{n}$, gcd(m, n) = 1, then $m + n$ is equal to :

Accepted Answer

(C) 276

Answer

(A) 256

Answer

(B) 264

Answer

(D) 284

Question 6

Let $A_1, A_2, A_3, \ldots, A_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of $A_{25}, A_{28}, A_{31}$ and $A_{36}$ is equal to :

Accepted Answer

(D) 134

Answer

(A) 129

Answer

(B) 136

Answer

(C) 131.50

Question 7

The coefficient of $x^2$ in the expansion of $\left( 2x^2 + \frac{1}{x} ight)^{10}$, $x 
eq 0$, is :

Accepted Answer

(B) 3360

Answer

(A) 3240

Answer

(C) 3480

Answer

(D) 3600

Question 8

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4, respectively. If A is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected the captain, the probability that the team wins the tournament is 0.7. Then the probability, that the team wins the tournament, is :

Accepted Answer

(B) 0.76

Answer

(A) 0.74

Answer

(C) 0.72

Answer

(D) 0.78

Question 9

A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is :

Accepted Answer

(A) 4100

Answer

(B) 4140

Answer

(C) 4230

Answer

(D) 4290

Question 10

A variable X takes values $0, 0, 2, 6, 12, 20, \ldots, n(n - 1)$ with frequencies $^{n}C_0, ^{n}C_1, ^{n}C_2, ^{n}C_3, ^{n}C_4, ^{n}C_5, \ldots, ^{n}C_n$, respectively. If the mean of this data is 60, then its median is :

Accepted Answer

(A) 56

Answer

(B) 42

Answer

(C) 72

Answer

(D) 90

Question 11

Let the point P be the vertex of the parabola $y = x^2 - 6x + 12$. If a line passing through the point P intersects the circle $x^2 + y^2 - 2x - 4y + 3 = 0$ at the points R and S, then the maximum value of $(PR + PS)^2$ is :

Accepted Answer

(B) 20

Answer

(A) 10

Answer

(C) 25

Answer

(D) 5

Question 12

Let the directrix of the parabola $P : y^2 = 8x$, cut x-axis at the point A. Let $B(α, β)$, $α > 1$, be a point on P such that the slope of AB is 3/5. If BC is a focal chord of P, then six times the area of $	riangle ABC$ is :

Accepted Answer

(B) 160

Answer

(A) 80

Answer

(C) 174

Answer

(D) 192

Question 13

Let the eccentricity e of a hyperbola satisfy the equation $6e^2 - 11e + 3 = 0$. If the foci of the hyperbola are (3, 5) and (3, −4), then the length of its latus rectum is :

Accepted Answer

(C) $\frac{15}{2}$

Answer

(A) $\frac{11}{3}$

Answer

(B) $\frac{17}{3}$

Answer

(D) $\frac{17}{2}$

Question 14

Let a triangle PQR be such that P and Q lie on the line $\frac{x+3}{8} = \frac{y-4}{2} = \frac{z+1}{2}$ and are at a distance of 6 units from R(1, 2, 3). If (α, β, γ) is the centroid of △PQR, then α + β + γ is equal to :

Accepted Answer

(C) 6

Answer

(A) 4

Answer

(B) 5

Answer

(D) 8

Question 15

If the distance of the point (a, 2, 5) from the image of the point (1, 2, 7) in the line $\frac{x}{1} = \frac{y-1}{1} = \frac{z-2}{2}$ is 4, then the sum of all possible values of a is equal to :

Accepted Answer

(C) 6

Answer

(A) 11

Answer

(B) 9

Answer

(D) 4

Question 16

Let O be the origin, $\vec{OP} = \vec{a}$ and $\vec{OQ} = \vec{b}$. If R is the point on $\vec{OP}$ such that $\vec{OP} = 5\vec{OR}$, and M is the point such that $\vec{OQ} = 5\vec{RM}$, then $\vec{PM}$ is equal to :

Accepted Answer

(B) $\frac{1}{5}(\vec{b} - 4\vec{a})$

Answer

(A) $\frac{1}{5}(\vec{a} - 4\vec{b})$

Answer

(C) $\frac{1}{5}(-\vec{a} + 4\vec{b})$

Answer

(D) $\frac{1}{5}(-\vec{b} + 4\vec{a})$

Question 17

Let $f(x) = \lim_{y 	o 0} \frac{(1 - \cos(xy))	an(xy)}{y^{3}}$. Then the number of solutions of the equation f(x) = sin x, x ∈ ℝ is :

Accepted Answer

(C) 3

Answer

(A) 0

Answer

(B) 2

Answer

(D) 1

Question 18

Let $(2^{1-a} + 2^{1+a})$, f(a), $(3^{a} + 3^{-a})$ be in A.P. and α be the minimum value of f(a). Then the value of the integral $\int_{\log_e(\alpha-1)}^{\log_e(\alpha)} \frac{dx}{(e^{2x} - e^{-2x})}$ is :

Accepted Answer

(B) $\frac{1}{4}\log_e\left(\frac{4}{3}\right)$

Answer

(A) $\frac{1}{2}\log_e\left(\frac{4}{3}\right)$

Answer

(C) $\frac{1}{2}\log_e\left(\frac{8}{5}\right)$

Answer

(D) $\frac{1}{4}\log_e\left(\frac{8}{5}\right)$

Question 19

Let f : [1, ∞) → ℝ be a differentiable function defined as $f(x) = \int_{1}^{x} f(t)\, dt + (1 - x)(\log_e x - 1) + e$. Then the value of f(f(1)) is :

Accepted Answer

(A) $(1 + e^{e})$

Answer

(B) (1 + e)

Answer

(C) $(1 + e + e^{e})$

Answer

(D) 1 + 2e

Question 20

Let f(x) and g(x) be twice differentiable functions satisfying f''(x) = g''(x) for all x ∈ ℝ, f'(1) = 2g'(1) = 4 and g(2) = 3f(2) = 9. Then f(25) − g(25) is equal to :

Accepted Answer

(B) 40

Answer

(A) 20

Answer

(C) −20

Answer

(D) −40

Question 21

Let A = {1, 4, 7} and B = {2, 3, 8}. Then the number of elements, in the relation $R = \{((a_1, b_1), (a_2, b_2)) \in ((A 	imes B) 	imes (A 	imes B)) : a_1 + b_2 	ext{ divides } a_2 + b_1\}$ is _______.

Accepted Answer

18

Question 22

From the point (−1, −1), two rays are sent making angles of 45° with the line x + y = 0. These rays get reflected from the mirror x + 2y = 1. If the equations of the reflected rays are ax + by = 9 and cx + dy = 7, a, b, c, d ∈ ℤ, then the value of ad + bc is _______.

Accepted Answer

7

Question 23

If $S = \left\{	heta \in [-\pi, \pi] : \cos	heta \cos\frac{5	heta}{2} = \cos 7	heta \cos\frac{7	heta}{2}ight\}$, then n(S) is equal to _______.

Accepted Answer

19

Question 24

Let f : ℝ → ℝ be a function such that $f(x) + 3f\left(\frac{\pi}{2} - x\right) = \sin x$, x ∈ ℝ. Let the maximum value of f on ℝ be α. If the area of the region bounded by the curves $g(x) = x^{2}$ and $h(x) = \beta x^{3}$, β > 0, is $\alpha^{2}$, then $30\beta^{3}$ is equal to _______.

Accepted Answer

16

Question 25

Let y = y(x) be the solution of the differential equation $(	an x)^{1/2}\, dy = (\sec^{3} x - (	an x)^{3/2} y)\, dx$, $0 < x < \frac{\pi}{2}$, $y\left(\frac{\pi}{4}ight) = \frac{6\sqrt{2}}{5}$. If $y\left(\frac{\pi}{3}ight) = \frac{4}{5}\alpha$, then $\alpha^{4}$ equals _______.

Accepted Answer

48

Question 26

Match List-I with List-II.
where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) as fundamental units.
Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 27

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is ________ Ω.

Accepted Answer

(D) 0.18

Answer

(A) 0.25

Answer

(B) 2

Answer

(C) 2.5

Question 28

A mass of 1 kg is kept on an inclined plane with 30° inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 m/s. The work done by the frictional force in time 2 s is ________ J. (Take g = 10 m/s²)

Accepted Answer

(A) 20

Answer

(B) 25

Answer

(C) 30

Answer

(D) 10

Question 29

The velocity (v) versus time (t) plot of a particle is shown in the figure, for a time interval of 40 s. The total distance travelled by the particle and the average velocity during this period are, respectively ________.

Accepted Answer

(C) 100 m and zero

Answer

(A) 25 m and zero

Answer

(B) 50 m and zero

Answer

(D) 100 m and 2.5 m/s

Question 30

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle θ₁ and in the next 2 s it rotates through an angle θ₂. The ratio $\dfrac{	heta_{2}}{	heta_{1}}$ is ________.

Accepted Answer

(B) 3

Answer

(A) 6

Answer

(C) 4

Answer

(D) $\dfrac{1}{3}$

Question 31

An object of uniform density rolls up the curved path with the initial velocity v₀ as shown in the figure. If the maximum height attained by an object is $\dfrac{7v_{0}^{2}}{10g}$ (g = acceleration due to gravity), the object is a ________.

Accepted Answer

(D) solid sphere

Answer

(A) solid cylinder

Answer

(B) ring

Answer

(C) disc

Question 32

A body of mass m is taken from the surface of earth to a height equal to twice the radius of earth (R$_e$). The increase in potential energy will be ________.
(g is acceleration due to gravity at the surface of earth)

Accepted Answer

(D) $\dfrac{2}{3}mgR_{e}$

Answer

(A) $\dfrac{1}{2}mgR_{e}$

Answer

(B) $\dfrac{3}{4}mgR_{e}$

Answer

(C) $\dfrac{1}{4}mgR_{e}$

Question 33

Eight mercury drops, each of radius r, coalesce to form a bigger drop. The surface energy released in this process is ________. (S is the surface tension of mercury).

Accepted Answer

(B) 16πr²S

Answer

(A) 8πr²S

Answer

(C) 64πr²S

Answer

(D) 4πr²S

Question 34

An ideal gas at pressure P and temperature T is expanding such that PT³ = constant. The coefficient of volume expansion of the gas is ________.

Accepted Answer

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

Answer

(A) $\dfrac{2}{T}$

Answer

(B) $\dfrac{1}{T}$

Answer

(D) $\dfrac{3}{T}$

Question 35

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 36

A metal rod of length L rotates about one end at origin with a uniform angular velocity ω. The magnetic field radially falls off as B(r) = B₀e$^{-\lambda r}$; λ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

Accepted Answer

(A) $B_{0}\omega\left[\dfrac{1}{\lambda^{2}} - e^{-\lambda L}\left(\dfrac{1}{\lambda^{2}} + \dfrac{L}{\lambda}\right)\right]$

Answer

(B) $B_{0}\omega\left[\dfrac{1}{\lambda^{2}} + e^{-\lambda L}\left(\dfrac{1}{\lambda^{2}} + \dfrac{L}{\lambda}\right)\right]$

Answer

(C) $B_{0}\omega\left[\dfrac{4}{\lambda^{2}} - e^{-2\lambda L}\left(\dfrac{1}{\lambda^{2}} + \dfrac{2L}{\lambda}\right)\right]$

Answer

(D) $B_{0}\omega\left[\dfrac{3}{\lambda^{2}} - e^{-3\lambda L}\left(\dfrac{3}{\lambda^{2}} + \dfrac{L}{\lambda}\right)\right]$

Question 37

Under steady state condition the potential difference across the capacitor in the circuit is ________ V.

Accepted Answer

(A) 0.5

Answer

(B) 1.5

Answer

(C) 0

Answer

(D) 2

Question 38

A particle of charge q and mass m is projected from origin with an initial velocity $\vec{v} = \left(\dfrac{v_{0}}{\sqrt{2}}\hat{x} + \dfrac{v_{0}}{\sqrt{2}}\hat{y}\right)$. There exists a uniform magnetic field $\vec{B} = B_{0}\hat{z}$ and a space varying electric field $\vec{E} = E_{0}e^{-\lambda x}\hat{x}$ within the region 0 ≤ x ≤ L. After travelling a distance such that x-coordinate has changed from x = 0 to x = L, the change in the kinetic energy is ________.

Accepted Answer

(A) $\dfrac{qE_{0}}{\lambda}[1 - e^{-\lambda L}]$

Answer

(B) $\left(\dfrac{v_{0}qB_{0}}{2\lambda}\right)[2 - e^{-2\lambda L}]$

Answer

(C) $\dfrac{qE_{0}}{\lambda}[1 + e^{-\lambda L}]$

Answer

(D) $q\left(\dfrac{E_{0} + v_{0}B_{0}}{\lambda}\right)[1 - e^{-\lambda L/2}]$

Question 39

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.
Reason (R): There is no mass associated with the electromagnetic waves.
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) Both (A) and (R) are true and (R) is the correct explanation of (A)

Answer

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

Answer

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

Question 40

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

Accepted Answer

(A) behaves as concave lens if $|f_\mathrm{convex}| > |f_\mathrm{concave}|$

Answer

(B) behaves as concave lens if $|f_\mathrm{convex}| < |f_\mathrm{concave}|$

Answer

(C) behaves as convex lens if $|f_\mathrm{convex}| > |f_\mathrm{concave}|$

Answer

(D) Focal length of the lens system will change if the positions of two lenses are interchanged

Question 41

An object $AB$ is placed 15 cm on the left of a convex lens $P$ of focal length 10 cm. Another convex lens $Q$ is now placed 15 cm right of lens $P$. If the focal length of lens $Q$ is 15 cm, the final image is ________.

Accepted Answer

(B) real, formed at 7.5 cm right of lens $Q$, with a size same as that of $AB$

Answer

(A) virtual, formed at 7.5 cm right of lens $Q$, with a size bigger than that of $AB$

Answer

(C) formed at infinity.

Answer

(D) real, formed at 7 cm right of lens $Q$, with a size smaller than that of $AB$

Question 42

The maximum intensity in a Young's double slit experiment is $I_0$. Distance between the slits ($d$) is 5λ, where λ is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at $D = 10d$ is ________.

Accepted Answer

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

Answer

(A) $\frac{I_0}{4}$

Answer

(C) $I_0$

Answer

(D) $\frac{3I_0}{4}$

Question 43

An electron is travelling with a velocity $v$ in free space and when it enters a medium, its velocity is reduced by 20%. The de Broglie wavelength of electron in the medium is $\alpha\lambda_0$, where $\lambda_0$ is its de Broglie wavelength in free space. The value of $\alpha$ is ________.

Accepted Answer

(C) 1.25

Answer

(A) 1.20

Answer

(B) 1.0

Answer

(D) 0.75

Question 44

Assuming the experimental mass of $^{12}_{6}C$ as 12 u, the mass defect of $^{12}_{6}C$ atom is ________ MeV/$c^2$.
(Mass of proton $= 1.00727$ u, mass of neutron $= 1.00866$ u, 1 u $= 931.5$ MeV/$c^2$ and $c$ is the speed of the light in vacuum).

Accepted Answer

(B) 89.03

Answer

(A) 127.5

Answer

(C) 272.0

Answer

(D) 92.0

Question 45

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are 10$^{15}$ atoms/cm$^{3}$ and 10$^{18}$ atoms/cm$^{3}$, respectively. Which one of the following statements is true ?

Accepted Answer

(B) The depletion region width is more on p-side compared to that in n-side

Answer

(A) Widths of depletion region on either side of the interface are equal

Answer

(C) The depletion region width is more on n-side compared to that in p-side

Answer

(D) No depletion region forms because of unequal doping concentrations on p and n-sides

Question 46

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $600 	imes 10^{-6}$ m$^{3}$. The elastic potential energy stored in the wire in stretched condition would be ________ J.
(Given Young modulus of copper $= 1.1 	imes 10^{11}$ N/m$^{2}$)

Accepted Answer

33

Question 47

A series LCR circuit with $R = 20$ Ω, $L = 1.6$ H and $C = 40$ μF is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is ________ Ω.

Accepted Answer

200

Question 48

When an external resistance of 5 Ω is connected across terminals of a cell, a current of 0.25 A flows through it. When the 5 Ω resistor is replaced by a 2 Ω resistor, a current of 0.5 A flows through it. The internal resistance of the cell is ________ Ω.

Accepted Answer

1

Question 49

A circular loop of radius 20 cm and resistance 2 Ω is placed in a time varying magnetic field $\vec{B} = (2t^2 + 2t + 3)$ T. At $t = 0$, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t = 3$ s is $\frac{\alpha}{50}$ A. The value of $\alpha$ is ________.
(Take $\pi = 22/7$)

Accepted Answer

44

Question 50

What volume of hydrogen gas at STP would be liberated by action of 50 mL of H₂SO₄ of 50% purity (density = 1.3 g mL⁻¹) on 20 g of zinc ?
Given : Molar mass of H, O, S, Zn are 1, 16, 32, 65 g mol⁻¹ respectively.

Accepted Answer

(C) 6.892 L

Answer

(A) 5.824 L

Answer

(B) 7.428 L

Answer

(D) 8.375 L

Question 51

Which of the following statement(s) is/are true ?
A. If two orbitals have the same value of (n + l), the orbital with lower value of n will have lower energy.
B. Energies of the orbitals in the same subshell increase with increase in atomic number.
C. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital.
D. Among 5f, 6s, 4d, 5p and 5d orbitals, none of the orbitals have 2 radial nodes.
Choose the correct answer from the options given below :

Accepted Answer

(B) A and C only

Answer

(A) A, B and C only

Answer

(C) C and D only

Answer

(D) A only

Question 52

The covalent radii of atoms A and B are $r_A$ and $r_B$, respectively. The covalent bond length and total length of AB molecule are respectively

Accepted Answer

(A) $(r_A + r_B),\ 2(r_A + r_B)$

Answer

(B) $\frac{1}{2}(r_A + r_B),\ (r_A + r_B)$

Answer

(C) $(r_A + r_B),\ (r_A + r_B)$

Answer

(D) $2(r_A + r_B),\ \frac{1}{2}(r_A + r_B)$

Question 53

Consider the following data for the reaction
X₂(g) + Y₂(g) ⇌ 2XY(g)
at 600 K. The ΔrG° (in kJ mol⁻¹) for the reaction is :

Accepted Answer

(B) −10

Answer

(A) −21000

Answer

(C) −1000

Answer

(D) −9.012

Question 54

The correct order of molar heat capacities measured at 298 K and 1 bar is :

Accepted Answer

(B) Bromine(l) > Copper(s) > Helium(g)

Answer

(A) Copper(s) > Bromine(l) > Helium(g)

Answer

(C) Helium(g) > Bromine(l) > Copper(s)

Answer

(D) Helium(g) > Bromine(l) = Copper(s)

Question 55

The reaction A(g) ⇌ B(g) + C(g) was initiated with the amount 'a' of A(g). At equilibrium it is found that the amount of A(g) remaining is (a − x) at a total pressure of p.
The equilibrium constant $K_p$ of the reaction can be calculated from the expression :

Accepted Answer

(B) $\frac{x^{2}}{a^{2} - x^{2}} 	imes p$

Answer

(A) $\frac{x^{2}}{a^{2} + x^{2}} 	imes p$

Answer

(C) $\frac{a + x^{2}}{x^{2}} 	imes p$

Answer

(D) $\frac{a^{2} - x^{2}}{x^{2}} 	imes p$

Question 56

One half cell in a voltaic cell is constructed by dipping silver rod in AgNO₃ solution of unknown concentration, other half cell is Zn rod dipped in 1 molar solution of ZnSO₄. A voltage of 1.60 V is measured at 298 K for this cell. What is the concentration of Ag⁺ ions used in terms of log x (x = [Ag⁺]) ?
$E^{\circ}_{Zn^{2+}/Zn}$ = −0.76 V, $E^{\circ}_{Ag^{+}/Ag}$ = +0.80 V, $\frac{2.303RT}{F}$ = 0.059 V

Accepted Answer

(B) $\frac{4}{5.9}$

Answer

(A) $\frac{2}{3.9}$

Answer

(C) $\frac{2.9}{2}$

Answer

(D) $\frac{5.9}{4}$

Question 57

Given below are two statements :
Statement I: The number of pairs among [Al₂O₃, Cr₂O₃], [Cl₂O₇, Mn₂O₇], [Na₂O, V₂O₃] and [CO, N₂O] that contain oxides of same nature (acidic, basic, neutral or amphoteric) is 4.
Statement II: Among Na₂O, Al₂O₃, CO and Cl₂O₇, the most basic and acidic oxides are Na₂O and Cl₂O₇, respectively.
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 58

Given below are two statements :
Statement I: Aluminium upon reaction with NaOH forms [Al(OH)₆]³⁻ ion.
Statement II: The geometry of ICl₄⁻, ClO₃⁻ and IBr₂⁻ is square planar, pyramidal and linear respectively.
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 59

Given below are two statements :
Statement I: Presence of large number of unpaired electrons in transition metal atoms results in higher enthalpies of their atomisation.
Statement II: $d_{xy} = d_{xz} = d_{yz} < d_{x^{2}-y^{2}} = d_{z^{2}}$ and $d_{x^{2}-y^{2}} = d_{z^{2}} < d_{xy} = d_{xz} = d_{yz}$ are the d-orbital splittings in [Fe(H₂O)₆]³⁺ and [Ni(Cl)₄]²⁻ complex ions respectively.
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 correct

Answer

(B) Both Statement I and Statement II are incorrect

Answer

(C) Statement I is correct but Statement II is incorrect

Answer

(D) Statement I is incorrect but Statement II is correct

Question 60

Identify the correct statements from the following
A. [Fe(C₂O₄)₃]³⁻ is the most stable complex among [Fe(OH)₆]³⁻, [Fe(C₂O₄)₃]³⁻ and [Fe(SCN)₆]³⁻
B. The stability of [Cu(NH₃)₄]²⁺ is greater than that of [Cu(en)₂]²⁺
C. The hybridization of Fe in K₄[Fe(CN)₆] is d²sp³
D. [Fe(NO₂)₃Cl₃]³⁻ exhibits linkage isomerism
E. NO₂⁻ and SCN⁻ ligands are NOT ambidentate ligands
Choose the correct answer from the options given below :

Accepted Answer

(C) A, C and D only

Answer

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

Answer

(B) B, C and D only

Answer

(D) A, C and E only

Question 61

Match List-I (Purification technique) with List-II (Used to separate).
Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 62

IUPAC name of the some alkenes are given below. Find out the correct stability order.
A. 2-Methylbut-2-ene
B. cis-But-2-ene
C. 2,3-Dimethylbut-2-ene
D. Prop-1-ene
Choose the correct answer from the options given below :

Accepted Answer

(A) C > A > B > D

Answer

(B) C > A > D > B

Answer

(C) B > D > A > C

Answer

(D) A > B > C > D

Question 63

Identify the correct IUPAC name of hydrocarbon (x) containing three primary carbon atoms and with molar mass 72 g mol⁻¹.

Accepted Answer

(C) 2-Methylbutane

Answer

(A) 1,1-Dimethylcyclopropane

Answer

(B) 2,2-Dimethylpropane

Answer

(D) n-pentane

Question 64

Complete the following reaction sequence and give the name of major product 'P'.
CH₃ − CH₂ − C ≡ N $\xrightarrow[	ext{(ii) } H_3O^+]{	ext{(i) } OH^-/H_2O/\Delta}$ $\xrightarrow[	ext{(iv) } H_2O]{	ext{(iii) } Cl_2/	ext{Red P}}$ P (Major product)

Accepted Answer

(A) 2-Chloropropanoic acid

Answer

(B) 3-Chloropropanoic acid

Answer

(C) 1-Chloropropane

Answer

(D) 2-Chloropropane

List-I	List-II
A.Meter (L)	I. $\sqrt{\dfrac{hc}{G}}$
B.Second (S)	II. $\sqrt{\dfrac{Gh}{c^{5}}}$
C.Kilogram (M)	III. $\sqrt{\dfrac{K^{2}L^{2}c^{3}}{Gh}}$
D.Kelvin (K)	IV. $\sqrt{\dfrac{Gh}{c^{3}}}$

List-I	List-II
A.sin² ωt	I.Periodic with time period $T = \dfrac{\pi}{\omega}$ but not simple harmonic motion (SHM)
B.sin³(2ωt)	II.Periodic with time period $T = \dfrac{2\pi}{\omega}$ but Not SHM
C.sin(ωt) + cos(πωt)	III.Periodic with time period $T = \dfrac{\pi}{\omega}$ and SHM
D.cos ωt + cos 2ωt	IV.Non-periodic

List-I (Purification technique)	List-II (Used to separate)
A.Simple distillation	I.Steam volatile compound
B.Fractional distillation	II.Two liquids with large difference in boiling points
C.Steam distillation	III.Liquid decomposing at its boiling point
D.Distillation under reduced pressure	IV.Two liquids with close boiling points

JEE Main 5 April 2026 Shift 2 Question Paper with Answers

Physics — JEE Main 5 April 2026 Shift 2

Chemistry — JEE Main 5 April 2026 Shift 2

Mathematics — JEE Main 5 April 2026 Shift 2

Chapters tested in this paper

Attempt this paper under exam timing.

Compound	ΔfH°(600K) (kJ mol⁻¹)	S°(600K) (J mol⁻¹ K⁻¹)
XY(g)	42	200
X₂(g)	8	140
Y₂(g)	80	250