JEE Main 6 April 2026 Shift 2 Question Paper

Question 1

Let $f : \mathbb{R} 	o \mathbb{R}$ be defined as $f(x) = \frac{2x^{2} - 3x + 2}{3x^{2} + x + 3}$. Then $f$ is :

Accepted Answer

(D) neither one-one nor onto

Answer

(A) both one-one and onto

Answer

(B) one-one but not onto

Answer

(C) onto but not one-one

Question 2

Consider the quadratic equation $(n^{2} - 2n + 2)x^{2} - 3x + (n^{2} - 2n + 2)^{2} = 0$, $n \in \mathbb{R}$. Let α be the minimum value of the product of its roots and β be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is α and the common ratio is $\frac{\alpha}{\beta}$, is :

Accepted Answer

(C) $\frac{364}{243}$

Answer

(A) $\frac{61}{37}$

Answer

(B) $\frac{121}{81}$

Answer

(D) $\frac{1093}{729}$

Question 3

Let $S = \{z \in \mathbb{C} : z^{2} + \sqrt{6}\,iz - 3 = 0\}$. Then $\sum_{z \in S} z^{8}$ is equal to :

Accepted Answer

(A) 162

Answer

(B) 184

Answer

(C) 262

Answer

(D) 324

Question 4

The sum of all possible values of θ ∈ [0, 2π], for which the system of equations :
$x\cos 3	heta - 8y - 12z = 0$
$x\cos 2	heta + 3y + 3z = 0$
$x + y + 3z = 0$
has a non-trivial solution, is equal to :

Accepted Answer

(D) 4π

Answer

(A) π

Answer

(B) 2π

Answer

(C) 3π

Question 5

Let $A = \begin{bmatrix} 1 & 0 & 0 \ 3 & 1 & 0 \ 9 & 3 & 1 \end{bmatrix}$ and $B = [b_{ij}]$, $1 \leq i, j \leq 3$. If $B = A^{99} - I$, then the value of $\frac{b_{31} - b_{21}}{b_{32}}$ is :

Accepted Answer

(C) 149

Answer

(A) 99

Answer

(B) 199

Answer

(D) 159

Question 6

The sum $1 + \frac{1}{2}(1^{2} + 2^{2}) + \frac{1}{3}(1^{2} + 2^{2} + 3^{2}) + \ldots$ upto 10 terms is equal to :

Accepted Answer

(C) $\frac{315}{2}$

Answer

(A) 130

Answer

(B) 155

Answer

(D) $\frac{325}{2}$

Question 7

A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the $10^{	ext{th}}$ floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :

Accepted Answer

(C) 7056

Answer

(A) 2184

Answer

(B) 3064

Answer

(D) 11340

Question 8

Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14, α < β, be 8 and 16 respectively. Then the quadratic equation whose roots are 3α + 2 and 2β + 1 is :

Accepted Answer

(B) $x^{2} - 41x + 420 = 0$

Answer

(A) $x^{2} - 35x + 306 = 0$

Answer

(C) $x^{2} - 45x + 506 = 0$

Answer

(D) $x^{2} - 37x + 342 = 0$

Question 9

A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :

Accepted Answer

(C) $\frac{16}{231}$

Answer

(A) $\frac{63}{925}$

Answer

(B) $\frac{17}{231}$

Answer

(D) $\frac{64}{925}$

Question 10

Let $C$ be a circle having centre in the first quadrant and touching the $x$-axis at a distance of 3 units from the origin. If the circle $C$ has an intercept of length $6\sqrt{3}$ on $y$-axis, then the length of the chord of the circle $C$ on the line $x - y = 3$ is :

Accepted Answer

(C) $6\sqrt{2}$

Answer

(A) 8

Answer

(B) 6

Answer

(D) $8\sqrt{2}$

Question 11

The eccentricity of an ellipse $E$ with centre at the origin $O$ is $\frac{\sqrt{3}}{2}$ and its directrices are $x = \pm\frac{4\sqrt{6}}{3}$. Let $H : \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ be a hyperbola whose eccentricity is equal to the length of semi-major axis of $E$, and whose length of latus rectum is equal to the length of minor axis of $E$. Then the distance between the foci of $H$ is :

Accepted Answer

(D) $\frac{8}{7}$

Answer

(A) $\frac{4\sqrt{2}}{\sqrt{7}}$

Answer

(B) $\frac{4\sqrt{2}}{7}$

Answer

(C) $\frac{4}{\sqrt{7}}$

Question 12

Let $x = 9$ be a directrix of an ellipse $E$, whose centre is at the origin and eccentricity is $\frac{1}{3}$. Let $P(\alpha, 0)$, $\alpha > 0$, be a focus of $E$ and $AB$ be a chord passing through $P$. Then the locus of the mid point of $AB$ is :

Accepted Answer

(A) $9y^{2} = 8x(1 - x)$

Answer

(B) $3y^{2} = 4x(1 - x)$

Answer

(C) $9y^{2} = 8x(x - 1)$

Answer

(D) $3y^{2} = 4x(x - 1)$

Question 13

If $\sin(	an^{-1}(x\sqrt{2})) = \cot(\sin^{-1}\sqrt{1 - x^{2}})$, $x \in (0, 1)$, then the value of $x$ is :

Accepted Answer

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

Answer

(B) $\frac{1}{3}$

Answer

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

Answer

(D) $\frac{5}{8}$

Question 14

The shortest distance between the lines $\frac{x-4}{1} = \frac{y-3}{2} = \frac{z-2}{-3}$ and $\frac{x+2}{2} = \frac{y-6}{4} = \frac{z-5}{-5}$ is :

Accepted Answer

(C) $3\sqrt{5}$

Answer

(A) $\frac{5\sqrt{6}}{6}$

Answer

(B) $2\sqrt{5}$

Answer

(D) $4\sqrt{5}$

Question 15

Let $\vec{a} = 2\hat{i} + 3\hat{j} + 3\hat{k}$ and $\vec{b} = 6\hat{i} + 3\hat{j} + 3\hat{k}$. Then the square of the area of the triangle with adjacent sides determined by the vectors $(2\vec{a} + 3\vec{b})$ and $(\vec{a} - \vec{b})$ is :

Accepted Answer

(C) 1800

Answer

(A) 450

Answer

(B) 900

Answer

(D) 2400

Question 16

Let $\lim_{x 	o 2} \frac{(	an(x-2))(rx^{2} + (p-2)x - 2p)}{(x-2)^{2}} = 5$ for some $r, p \in \mathbb{R}$. If the set of all possible values of $q$, such that the roots of the equation $rx^{2} - px + q = 0$ lie in $(0, 2)$, be the interval $(\alpha, \beta]$, then $4(\alpha + \beta)$ equals :

Accepted Answer

(C) 17

Answer

(A) 11

Answer

(B) 13

Answer

(D) 21

Question 17

Let $A = \begin{bmatrix} 1 & 3 & -1 \ 2 & 1 & \alpha \ 0 & 1 & -1 \end{bmatrix}$ be a singular matrix. Let $f(x) = \int_{0}^{x} (t^{2} + 2t + 3)\, dt$, $x \in [1, \alpha]$. If $M$ and $m$ are respectively the maximum and the minimum values of $f$ in $[1, \alpha]$, then $3(M - m)$ is equal to :

Accepted Answer

(B) 68

Answer

(A) 64

Answer

(C) 72

Answer

(D) 76

Question 18

Let $f : \mathbb{R} 	o \mathbb{R}$ be such that $f(xy) = f(x)f(y)$, for all $x, y \in \mathbb{R}$ and $f(0) 
eq 0$. Let $g : [1, \infty) 	o \mathbb{R}$ be a differentiable function such that
$x^{2}g(x) = \int_{1}^{x} (t^{2}f(t) - tg(t))\, dt.$
Then $g(2)$ is equal to :

Accepted Answer

(C) $\frac{15}{32}$

Answer

(A) $\frac{13}{8}$

Answer

(B) $\frac{11}{16}$

Answer

(D) $\frac{17}{64}$

Question 19

The area of the region $\{(x, y) : x^{2} - 8x \le y \le -x\}$ is :

Accepted Answer

(A) $\frac{343}{6}$

Answer

(B) $\frac{637}{6}$

Answer

(C) $\frac{437}{6}$

Answer

(D) $\frac{523}{6}$

Question 20

The value of the integral $\int_{-1}^{1} \left( \frac{x^{3} + |x| + 1}{x^{2} + 2|x| + 1} \right) dx$ is equal to :

Accepted Answer

(B) $2\log_{e} 2$

Answer

(A) $3\log_{e} 2$

Answer

(C) $5\log_{e} 3$

Answer

(D) $3\log_{e} 3$

Question 21

Let $R = \{(x, y) \in \mathbb{N} 	imes \mathbb{N} : \log_{e}(x + y) \le 2\}$. Then the minimum number of elements, required to be added in $R$ to make it a transitive relation, is __________.

Accepted Answer

15

Question 22

If $(1 - x^{3})^{10} = \sum_{r=0}^{10} a_{r} x^{r} (1 - x)^{30-2r}$, then $\frac{9a_{9}}{a_{10}}$ is equal to __________.

Accepted Answer

30

Question 23

Let the line $x - y = 4$ intersect the circle $C : (x - 4)^{2} + (y + 3)^{2} = 9$ at the points $Q$ and $R$. If $P(\alpha, \beta)$ is a point on $C$ such that $PQ = PR$, then $(6\alpha + 8\beta)^{2}$ is equal to __________.

Accepted Answer

18

Question 24

Let the image of the point $P(0, -5, 0)$ in the line $\frac{x-1}{2} = \frac{y}{1} = \frac{z+1}{-2}$ be the point $R$ and the image of the point $Q\left(0, \frac{-1}{2}, 0\right)$ in the line $\frac{x-1}{-1} = \frac{y+9}{4} = \frac{z+1}{1}$ be the point $S$. Then the square of the area of the parallelogram $PQRS$ is __________.

Accepted Answer

162

Question 25

Let $f(x) = \begin{cases} x^{3} + 8; & x < 0 \ x^{2} - 4; & x \ge 0 \end{cases}$ and $g(x) = \begin{cases} (x - 8)^{1/3}; & x < 0 \ (x + 4)^{1/2}; & x \ge 0 \end{cases}$. Then the number of points, where the function $g \circ f$ is discontinuous, is __________.

Accepted Answer

3

Question 26

The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is __________.

Accepted Answer

(C) 6

Answer

(A) 1

Answer

(B) 2

Answer

(D) 8

Question 27

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 28

A solid sphere $(A)$ of mass $5m$ and a spherical shell $(B)$ of mass $m$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of $A$ and $B$, they start rolling without slipping with an acceleration of $a_{A}$ and $a_{B}$, respectively. The ratio of $a_{A}$ and $a_{B}$ is __________.

Accepted Answer

(A) 5 : 21

Answer

(B) 6 : 10

Answer

(C) 21 : 25

Answer

(D) 1 : 5

Question 29

A body of mass 1 kg moves along a straight line with a velocity $v = 2x^{2}$. The work done by the body during displacement from $x = 0$ to 5 m is __________ J.

Accepted Answer

(C) 1250

Answer

(A) 0

Answer

(B) 250

Answer

(D) 1000

Question 30

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V, T$. Heating is started from left side until pressure changes to $\frac{27P}{8}$. If initial volume of each compartment was 9 litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas $C_{P}/C_{V} = 1.5$)

Accepted Answer

(B) 4

Answer

(A) 3

Answer

(C) 14

Answer

(D) 9

Question 31

For an electromagnetic wave propagating through vacuum, $\vec{k}$, $\vec{E}$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by :

Accepted Answer

(B) $\frac{\vec{k} 	imes \vec{E}}{\omega}$

Answer

(A) $\frac{\vec{E} 	imes \vec{k}}{\omega}$

Answer

(C) $\omega(\vec{E} 	imes \vec{k})$

Answer

(D) $\omega(\vec{k} 	imes \vec{E})$

Question 32

Two identical bodies $A$ and $B$ of equal masses have initial velocities $\vec{v}_{1} = 4\hat{i}$ m/s and $\vec{v}_{2} = 4\hat{j}$ m/s respectively. The body $A$ has acceleration $\vec{a}_{1} = 6\hat{i} + 6\hat{j}$ m/s$^{2}$ while the acceleration of the other body $B$ is zero. The centre of mass of the two bodies moves in __________ path.

Accepted Answer

(C) straight line

Answer

(A) circular

Answer

(B) parabolic

Answer

(D) elliptical

Question 33

Figure represents the extension ($\Delta l$) of a wire of length 1 meter, suspended from the ceiling of the room at one end with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-5}$ m$^{2}$ then the Young's modulus of the wire is __________ N/m$^{2}$.

Accepted Answer

(C) $1.0 	imes 10^{10}$

Answer

(A) $1.0 	imes 10^{11}$

Answer

(B) $2.0 	imes 10^{10}$

Answer

(D) $2.0 	imes 10^{11}$

Question 34

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 dm$^{3}$ (dm : decimeter). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is __________ cm.

Accepted Answer

(B) $140\sqrt{2}$

Answer

(A) $120\sqrt{2}$

Answer

(C) $140\sqrt{3}$

Answer

(D) $120\sqrt{3}$

Question 35

If 2 mole of an ideal monoatomic gas at temperature $T$, is mixed with 6 mole of another ideal monoatomic gas at temperature $2T$ then the temperature of mixture is :

Accepted Answer

(D) $\frac{7}{4}T$

Answer

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

Answer

(B) $\frac{5}{4}T$

Answer

(C) $\frac{7}{2}T$

Question 36

A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g $= 10$ m/s$^{2}$)

Accepted Answer

(A) $\frac{5\sqrt{50}}{\pi}$ and $8 	imes 10^{-3}$

Answer

(B) $\frac{5\sqrt{50}}{\pi}$ and 8

Answer

(C) $10\sqrt{50}$ and $2 	imes 10^{-3}$

Answer

(D) $\frac{5\sqrt{50}}{\pi}$ and $16 	imes 10^{-3}$

Question 37

The electric potential as a function of $x, y$ is given by $V = 5(x^{2} - y^{2})$ V. The electric field at a point $(2, 3)$ m is __________ V/m.

Accepted Answer

(A) $(-20\hat{i} + 30\hat{j})$

Answer

(B) $(20\hat{i} - 30\hat{j})$

Answer

(C) $(20\hat{i} + 45\hat{j})$

Answer

(D) $(-4\hat{i} + 6\hat{j})$

Question 38

A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm. The magnetic field at the mid point between the two wires is __________ μT. $\left(\frac{\mu_{0}}{4\pi} = 10^{-7} 	ext{ N/A}^{2}ight)$

Accepted Answer

(B) 300

Answer

(A) 30

Answer

(C) 150

Answer

(D) 0.0

Question 39

A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as $B = 0.4\sin(300t)$ Tesla. The normal to the plane of loop makes an angle of 60° with the field. The maximum induced emf produced in the loop is __________ mV.

Accepted Answer

(D) 24

Answer

(A) 12

Answer

(B) 18

Answer

(C) 21

Question 40

A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha 	imes 10^{-7}$ J. The value of $\alpha$ is __________. (combined capacitance of spheres is 200 pF)

Accepted Answer

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

Answer

(A) 5

Answer

(C) $\frac{7}{2}$

Answer

(D) $\frac{9}{2}$

Question 41

The energy released if hydrogen atoms are combined to form ${}^{4}_{2}$He is __________ MeV. (Take binding energies per nucleon of ${}^{2}_{1}$H and ${}^{4}_{2}$He as 1.1 MeV and 7.2 MeV, respectively)

Accepted Answer

(B) 24.4

Answer

(A) 6.1

Answer

(C) 26.6

Answer

(D) 5

Question 42

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is __________.

Accepted Answer

(C) $\sqrt{2}$

Answer

(A) 1.5

Answer

(B) $\sqrt{3}$

Answer

(D) 1.65

Question 43

Refer to the logic circuit given below. For two inputs $(A = 1, B = 1)$ and $(A = 0, B = 1)$, output $(Y)$ will be __________.

Accepted Answer

(C) 0, 0 respectively

Answer

(A) 1, 0 respectively

Answer

(B) 0, 1 respectively

Answer

(D) 1, 1 respectively

Question 44

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is __________ m/s. Assume pulley is massless and string is light and inextensible. (Take g $= 10$ m/s$^{2}$)

Accepted Answer

(A) 7.74

Answer

(B) 7.20

Answer

(C) 6.55

Answer

(D) 4.50

Question 45

In a Young double slit experiment, the wavelength of incident light is 6000 Å, the separation between slits $S_{1}$ and $S_{2}$ is 5 cm and the distance between slits plane and screen is 50 cm, as shown in the figure below. If the resultant intensity at $P$ is equal to the intensity due to individual slits, the path difference between interfering waves is __________ Å.

Accepted Answer

Answer

(A) 4000

Answer

(B) 3000

Answer

(D) 1000

Question 46

A block takes $t$ time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time $\frac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\frac{\alpha}{100}\right)$. The value of $\alpha$ is __________.

Accepted Answer

75

Question 47

The de Broglie wavelength for an electron accelerated through the potential difference of $V_{1}$ volt is $\lambda_{1}$. When the potential difference is changed to $V_{2}$ volt, the associated de Broglie wavelength is increased by 50%. If $(V_{1}/V_{2}) = (9/\alpha)$, then the value of $\alpha$ is __________.

Accepted Answer

4

Question 48

A moving coil of galvanometer when shunted with 2 Ω resistance gives a full scale deflection for a current of 500 mA. When a resistance of 470 Ω is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is __________ Ω.

Accepted Answer

50

Question 49

Two cells of emfs 1 V and 2 V and internal resistance 2 Ω and 1 Ω, respectively connected in parallel, gave a current of 1 A through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be $\frac{\alpha}{5}$ A. The value of $\alpha$ is __________.

Accepted Answer

3

Question 50

A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is __________ cm.

Accepted Answer

10

Question 51

Which of the following contain the same number of atoms ? (Given : Molar mass in g mol$^{-1}$ of H, He, O and S are 1, 4, 16 and 32 respectively)
A. 2 g of $\mathrm{O_{2}}$ gas
B. 4 g of $\mathrm{SO_{2}}$ gas
C. 1400 mL of $\mathrm{O_{2}}$ at STP
D. 0.05 L of He at STP
E. 0.0625 mol of $\mathrm{H_{2}}$ gas
Choose the correct answer from the options given below :

Accepted Answer

(D) A, C and E only

Answer

(A) A and B only

Answer

(B) B and C only

Answer

(C) C and D only

Question 52

The Bohr radius of a hydrogen like species is 70.53 pm. The species and the stationary state $(n)$ are respectively (Given : Hydrogen atom Bohr radius is 52.9 pm)

Accepted Answer

(D) $\mathrm{Li^{2+}}$, 2

Answer

(A) $\mathrm{Li^{2+}}$, 3

Answer

(B) $\mathrm{He^{+}}$, 3

Answer

(C) $\mathrm{He^{+}}$, 2

Question 53

Given below are two statements :
Statement I : The number of compounds among $\mathrm{SO_{2}}$, $\mathrm{SO_{3}}$, $\mathrm{SF_{4}}$, $\mathrm{SF_{6}}$ and $\mathrm{H_{2}S}$ in which sulphur does not obey the Octet rule is 3.
Statement II : Among $[\mathrm{H_{2}O}$, $\mathrm{ClF_{3}}$, $\mathrm{SF_{4}}]$, $[\mathrm{NH_{3}}$, $\mathrm{BrF_{5}}$, $\mathrm{SF_{4}}]$, $[\mathrm{BrF_{5}}$, $\mathrm{ClF_{3}}$, $\mathrm{XeF_{4}}]$ and $[\mathrm{XeF_{4}}$, $\mathrm{ClF_{3}}$, $\mathrm{H_{2}O}]$, the number of sets in which all the molecules have one lone pair of electrons on the central atom is 1.
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 54

Match List - I (Isothermal process) with List - II (Expression). Given $V_{1}$ and $V_{2}$ are initial and final volumes respectively. Choose the correct answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 55

Given below are two statements :
Statement I : $\mathrm{H_{2}O}$ molecules move from the chamber 1 to chamber 2.
Statement II : The osmotic pressure of a solution prepared by dissolving 50 mg of potassium sulphate (molar mass = 174 g/mol) in 2 L of water (at 27 °C) is 0.0107 bar. (Given : R = 0.083 dm$^{3}$ bar K$^{-1}$ mol$^{-1}$ and assume complete dissociation of electrolyte)
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 56

Given is a concentrated solution of a weak electrolyte $A_{x}B_{y}$ of concentration 'c' and dissociation constant 'K'. The degree of dissociation is given by :

Accepted Answer

(B) $\left(\frac{K}{c^{x+y-1} x^{x} y^{y}}\right)^{\frac{1}{x+y}}$

Answer

(A) $\left[K 	imes c^{x+y-1} x^{x} y^{y}ight]^{x+y}$

Answer

(C) $\left(\frac{c^{x+y-1} x^{x} y^{y}}{K}\right)^{x+y}$

Answer

(D) $\left(\frac{c^{x+y-1} x^{x} y^{y}}{K}\right)^{\frac{1}{x+y}}$

Question 57

For a general redox reaction
Anode : $\mathrm{Red_{1}} \rightarrow \mathrm{Ox_{1}^{n_{1}^{+}}} + n_{1}e^{-}$
Cathode : $\mathrm{Ox_{2}} + n_{2}e^{-} \rightarrow \mathrm{Red_{2}^{n_{2}^{-}}}$
Which of the following statement is incorrect ?

Accepted Answer

(D) If the reaction is carried out reversibly, the electrical work done is equal to the ratio of charge and potential difference through which charge is moved.

Answer

(A) The overall reaction can be written as $n_{2}\mathrm{Red_{1}} + n_{1}\mathrm{Ox_{2}} \rightleftharpoons n_{2}\mathrm{Ox_{1}^{n_{1}^{+}}} + n_{1}\mathrm{Red_{2}^{n_{2}^{-}}}$

Answer

(B) The electrons do not appear in the overall reaction because electrons produced at the anode are consumed at the cathode.

Answer

(C) Here $n$ is the number of electrons transferred in redox reaction.

Question 58

In a period, the first ionisation enthalpy of the element at extreme left and the negative electron gain enthalpy of the extreme right element, except noble gases, are respectively.

Accepted Answer

(C) lowest and highest

Answer

(A) lowest and lowest

Answer

(B) highest and lowest

Answer

(D) highest and highest

Question 59

Given below are two statements :
Statement I : $\mathrm{F_{2}O} < \mathrm{H_{2}O} < \mathrm{Cl_{2}O}$ is the correct trend in terms of bond angle.
Statement II : $\mathrm{SiF_{4}}$, $\mathrm{SnF_{4}}$ and $\mathrm{PbF_{4}}$ are ionic in nature.
In the light of the above statements, choose the correct answer from the options given below :

Accepted Answer

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

Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

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

Question 60

The correct order of first $(\Delta_{i}H_{1})$ and second $(\Delta_{i}H_{2})$ ionisation enthalpy values of Cr and Mn are :
A. $\Delta_{i}H_{1}$ : Cr > Mn
B. $\Delta_{i}H_{2}$ : Cr > Mn
C. $\Delta_{i}H_{1}$ : Mn > Cr
D. $\Delta_{i}H_{2}$ : Mn > Cr
Choose the correct answer from the options given below :

Accepted Answer

(B) B and C only

Answer

(A) A and B only

Answer

(C) A and D only

Answer

(D) C and D only

Question 61

Which of the following sequences of hybridisation, geometry and magnetic nature are correct for the given coordination compounds ?
A. $[\mathrm{NiCl_{4}}]^{2-}$ − $\mathrm{sp^{3}}$, tetrahedral, paramagnetic
B. $[\mathrm{Ni(NH_{3})_{6}}]^{2+}$ − $\mathrm{sp^{3}d^{2}}$, octahedral, paramagnetic
C. $[\mathrm{Ni(CO)_{4}}]$ − $\mathrm{sp^{3}}$, tetrahedral, paramagnetic
D. $[\mathrm{Ni(CN)_{4}}]^{2-}$ − $\mathrm{dsp^{2}}$, square planar, diamagnetic
Choose the correct answer from the options given below :

Accepted Answer

(D) A, B and D only

Answer

(A) A, B, C and D

Answer

(B) B, C and D only

Answer

(C) A, C and D only

Question 62

Given below are two statements :
Statement I : A mixture of $\mathrm{C_{12}H_{22}O_{11}}$ (sugar) and NaCl can be separated by dissolving sugar in alcohol, due to differential solubility.
Statement II : Rose essence from rose petals is seperated by steam distillation due to its high volatility and insolubility in $\mathrm{H_{2}O}$.
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 63

Shown below is the structure of methyl acetate with three different α, β and γ carbon - oxygen bonds.
The correct order of bond lengths of these bonds is :

Accepted Answer

(B) $\alpha < \beta < \gamma$

Answer

(A) $\alpha > \beta > \gamma$

Answer

(C) $\alpha = \beta = \gamma$

Answer

(D) $\alpha < \beta = \gamma$

Question 64

'$x$' is the product which is obtained by the hydrolysis of prop-1-yne in the presence of mercuric sulphate under dilute acidic medium at 333 K. '$y$' is the product which is obtained by the reaction of ethane nitrile with methyl magnesium bromide in dry ether followed by hydrolysis. IUPAC name of product obtained from '$x$' and '$y$' in the presence of barium hydroxide followed by heating is :

Accepted Answer

(B) 4-Methylpent-3-en-2-one

Answer

(A) 2-Methylpent-4-en-3-one

Answer

(C) 4-Methylpent-1-ene

Answer

(D) 2-Methylpent-3-one

List - I	List - II
A.Boltzmann constant	I. $[M^{-1}L^{3}T^{-2}]$
B.Stefan's constant	II. $[ML^{2}T^{-1}]$
C.Planck's constant	III. $[ML^{2}T^{-2}K^{-1}]$
D.Gravitational constant	IV. $[ML^{0}T^{-3}K^{-4}]$

List - I (Isothermal process)	List - II (Expression)
A.Reversible expansion	I. $q = 0$
B.Free expansion	II. $q = nRT \ln \frac{V_{2}}{V_{1}}$
C.Irreversible Compression	III. $w = -p_{ext}(V_{1} - V_{2})$
D.Cyclic reversible	IV. $\frac{q_{rev}}{T} = 0$

JEE Main 6 April 2026 Shift 2 Question Paper with Answers

Physics — JEE Main 6 April 2026 Shift 2

Chemistry — JEE Main 6 April 2026 Shift 2

Mathematics — JEE Main 6 April 2026 Shift 2

Chapters tested in this paper

Attempt this paper under exam timing.