JEE Main 6 April 2026 Shift 1 Question Paper

Question 1

Let [·] denote the greatest integer function. If the domain of the function $f(x) = \sin^{-1}\left(\frac{x + [x]}{3}\right)$ is [α, β), then α$^2$ + β$^2$ is equal to:

Accepted Answer

(B) 5

Answer

(A) 2

Answer

(C) 10

Answer

(D) 13

Question 2

Let one root of the quadratic equation in x: (k$^2$ − 15k + 27)x$^2$ + 9(k − 1)x + 18 = 0 be twice the other. Then the length of the latus rectum of the parabola y$^2$ = 6kx is equal to:

Accepted Answer

(D) 12

Answer

(A) 4

Answer

(B) 6

Answer

(C) 8

Question 3

Let e$_1$ and e$_2$ be two distinct roots of the equation x$^2$ − ax + 2 = 0. Let the sets
{a ∈ ℝ : e$_1$ and e$_2$ are the eccentricities of hyperbolas} = (α, β), and
{a ∈ ℝ : e$_1$ and e$_2$ are the eccentricities of an ellipse and a hyperbola, respectively} = (γ, ∞). Then α$^2$ + β$^2$ + γ$^2$ is equal to:

Accepted Answer

(C) 26

Answer

(A) 18

Answer

(B) 22

Answer

(D) 34

Question 4

Let the set of all values of k ∈ ℝ such that the equation $z(\bar{z} + 2 + i) + k(2 + 3i) = 0$, z ∈ ℂ, has at least one solution, be the interval [α, β]. Then 9(α + β) is equal to:

Accepted Answer

(A) −10

Answer

(B) −8

Answer

(C) 10√13

Answer

(D) 8√13

Question 5

The value of 1$^3$ − 2$^3$ + 3$^3$ − ... + 15$^3$ is:

Accepted Answer

(B) 1856

Answer

(A) 1706

Answer

Answer

(D) 2403

Question 6

The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is:

Accepted Answer

(A) $\frac{34}{9}$

Answer

(B) $\frac{34}{13}$

Answer

(C) $\frac{32}{9}$

Answer

(D) $\frac{32}{13}$

Question 7

The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:

Accepted Answer

(D) 3600

Answer

(A) 2670

Answer

(B) 2840

Answer

(C) 2920

Question 8

If the coefficients of the middle terms in the binomial expansions of (1 + αx)$^{26}$ and (1 − αx)$^{28}$, α ≠ 0, are equal, then the value of α is:

Accepted Answer

(D) $\frac{7}{27}$

Answer

(A) 1

Answer

(B) $\frac{14}{13}$

Answer

(C) $\frac{27}{7}$

Question 9

A data consists of 20 observations x$_1$, x$_2$, ..., x$_{20}$. If $\sum_{i=1}^{20}(x_i + 5)^2 = 2500$ and $\sum_{i=1}^{20}(x_i - 5)^2 = 100$, then the ratio of mean to standard deviation of this data is:

Accepted Answer

(B) 3 : 1

Answer

(A) 2 : 1

Answer

(C) 3 : 2

Answer

(D) 4 : 1

Question 10

A bag contains (N + 1) coins − N fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is $\frac{9}{16}$, then N is equal to:

Accepted Answer

(B) 7

Answer

(A) 5

Answer

(C) 8

Answer

(D) 9

Question 11

If the eccentricity e of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, passing through (6, 4√3), satisfies 15(e$^2$ + 1) = 34e, then the length of the latus rectum of the hyperbola $\frac{x^2}{b^2} - \frac{y^2}{2(a^2 + 1)} = 1$ is:

Accepted Answer

(A) 10

Answer

(B) 20

Answer

(C) 25

Answer

(D) 30

Question 12

Let chord PQ of length 3√13 of the parabola y$^2$ = 12x be such that the ordinates of points P and Q are in the ratio 1 : 2. If the chord PQ subtends an angle α at the focus of the parabola, then sin α is equal to:

Accepted Answer

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

Answer

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

Answer

(C) $\frac{5}{13}$

Answer

(D) $\frac{12}{13}$

Question 13

Let 0 < α < 1, $\beta = \frac{1}{3\alpha}$ and tan$^{-1}$(1 − α) + tan$^{-1}$(1 − β) = $\frac{\pi}{4}$. Then 6(α + β) is equal to:

Accepted Answer

(B) 7

Answer

(A) 6

Answer

(C) 8

Answer

(D) 9

Question 14

Let S = {θ ∈ (−2π, 2π) : cos θ + 1 = $\sqrt{3}$ sin θ}. Then $\sum_{	heta \in S} 	heta$ is equal to:

Accepted Answer

(B) $-\frac{4\pi}{3}$

Answer

(A) $-\frac{2\pi}{3}$

Answer

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

Answer

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

Question 15

Let the image of the point P(1, 6, a) in the line L : $\frac{x}{1} = \frac{y-1}{2} = \frac{z-a+1}{b}$, b > 0, be $\left(\frac{a}{3}, 0, a+c\right)$. If S(α, β, γ), α > 0, is the point on L such that the distance of S from the foot of perpendicular from the point P on L is $2\sqrt{14}$, then α + β + γ is equal to:

Accepted Answer

(C) 21

Answer

(A) 19

Answer

(B) 20

Answer

(D) 22

Question 16

Let a line L be perpendicular to both the lines L$_1$ : $\frac{x+1}{3} = \frac{y+3}{5} = \frac{z+5}{7}$ and L$_2$ : $\frac{x-2}{1} = \frac{y-4}{4} = \frac{z-6}{7}$. If θ is the acute angle between the lines L and L$_3$ : $\frac{x-\frac{8}{7}}{2} = \frac{y-\frac{4}{7}}{1} = \frac{z}{2}$, then tan θ is equal to:

Accepted Answer

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

Answer

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

Answer

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

Answer

(D) $\frac{4}{3}\sqrt{2}$

Question 17

The value of $\lim_{x 	o 0}\left(\frac{x^2 \sin^2 x}{x^2 - \sin^2 x}ight)$ is:

Accepted Answer

(B) 3

Answer

(A) 2

Answer

(C) 4

Answer

(D) 6

Question 18

The value of the integral $\int_{-\pi/4}^{\pi/4}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx$ is:

Accepted Answer

(B) 3π + 8

Answer

(A) 4π + 2

Answer

(C) 3π + 4

Answer

(D) 4π + 3

Question 19

The area of the region {(x, y) : 0 ≤ y ≤ 6 − x, y$^2$ ≥ 4x − 3, x ≥ 0} is:

Accepted Answer

(B) 9

Answer

(A) 8

Answer

(C) 12

Answer

(D) 15

Question 20

Let e be the base of natural logarithm and let f : {1, 2, 3, 4} → {1, e, e$^2$, e$^3$} and g : {1, e, e$^2$, e$^3$} → $\left\{1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\}$ be two bijective functions such that f is strictly decreasing and g is strictly increasing. If $\phi(x) = \left[f^{-1}\left\{g^{-1}\left(\frac{1}{2}\right)\right\}\right]^{x}$, then the area of the region R = {(x, y) : x$^2$ ≤ y ≤ φ(x), 0 ≤ x ≤ 1} is:

Accepted Answer

(A) $\frac{3 - \log_e(2)}{3\log_e(2)}$

Answer

(B) $\frac{1}{3\log_e(2)}$

Answer

(C) 3 + log$_e$(2)

Answer

(D) $\frac{3 + \log_e(2)}{2 + \log_e(3)}$

Question 21

Let A = $\begin{bmatrix} -1 & 1 & -1 \ 1 & 0 & 1 \ 0 & 0 & 1 \end{bmatrix}$ satisfy A$^2$ + α(adj(adj(A))) + β(adj(A)(adj(adj(A)))) = $\begin{bmatrix} 2 & -2 & 2 \ -2 & 0 & -1 \ 0 & 0 & -1 \end{bmatrix}$ for some α, β ∈ ℝ. Then (α − β)$^2$ is equal to ______

Accepted Answer

4

Question 22

Let the centre of the circle x$^2$ + y$^2$ + 2gx + 2fy + 25 = 0 be in the first quadrant and lie on the line 2x − y = 4. Let the area of an equilateral triangle inscribed in the circle be $27\sqrt{3}$. Then the square of the length of the chord of the circle on the line x = 1 is ______.

Accepted Answer

80

Question 23

If $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{b} = \hat{j} - \hat{k}$ and $\vec{c}$ be three vectors such that $\vec{a} 	imes \vec{c} = \vec{b}$ and $\vec{a} \cdot \vec{c} = 3$, then $\vec{c} \cdot (\vec{a} - 2\vec{b})$ is equal to ______.

Accepted Answer

3

Question 24

For the functions f(θ) = α tan$^2$ θ + β cot$^2$ θ, and g(θ) = α sin$^2$ θ + β cos$^2$ θ, α > β > 0, let $\min_{0< heta<\pi/2} f( heta) = \max_{0< heta<\pi} g( heta)$. If the first term of a G.P. is $\left(\frac{\alpha}{2\beta} ight)$, its common ratio is $\left(\frac{2\beta}{\alpha} ight)$ and the sum of its first 10 terms is $\frac{m}{n}$, gcd(m, n) = 1, then m + n is equal to ______.

Accepted Answer

1279

Question 25

Let y = y(x) be the solution of the differential equation $(x^2 - x\sqrt{x^2-1})dy + (y(x - \sqrt{x^2-1}) - x)dx = 0$, x ≥ 1. If y(1) = 1, then the greatest integer less than $y(\sqrt{5})$ is ______.

Accepted Answer

3

Question 26

The density ρ of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values of m, l and d are 97.42 ± 0.02 g, 8.35 ± 0.05 mm and 20.20 ± 0.02 mm, respectively. Calculated percentage fractional error in ρ is ________.

Accepted Answer

(B) 0.82%

Answer

(A) 0.63%

Answer

(C) 0.72%

Answer

(D) 0.25%

Question 27

The potential energy of a particle changes with distance x from a fixed origin as $V = \frac{A\sqrt{x}}{x + B}$, where A and B are constant with appropriate dimensions. The dimensions of AB are ________.

Accepted Answer

(D) $[M^{1}L^{7/2}T^{-2}]$

Answer

(A) $[M^{1}L^{5/2}T^{-2}]$

Answer

(B) $[M^{3/2}L^{5/2}T^{-2}]$

Answer

(C) $[M^{1}L^{2}T^{-2}]$

Question 28

The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of 5 m/s. The work done by the unknown resistive force is ________ J. (take g = 10 m/s²)

Accepted Answer

(D) −9.98

Answer

(A) −8.75

Answer

(B) −8.35

Answer

(C) −9.55

Question 29

Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (S), as shown in the figure below. Block P is positioned on the top surface which has no friction and block Q is in contact with side-surface, having coefficient friction μ. The cube (S) moves towards the right with acceleration of $\frac{g}{2}$, where g is gravitational acceleration. During this movement the block P and Q remain stationary. The value of μ is ________. (take g = 10 m/s²)

Accepted Answer

(B) 0.67

Answer

(A) 0.33

Answer

(C) 1

Answer

(D) 0.5

Question 30

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4 × 10$^{8}$ N/m² and its radius is 4 mm, then maximum acceleration the lift can take is ________ m/s². (take g = 10 m/s² and π = 3.14)

Accepted Answer

(A) 2.56

Answer

(B) 3.89

Answer

(C) 4.32

Answer

(D) 5.16

Question 31

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are ________ and ________ respectively.

Accepted Answer

(D) 0.0128π Nm, 100

Answer

(A) 0.128π Nm, 100

Answer

(B) 0.0128π Nm, 50

Answer

(C) 0.128π Nm, 50

Question 32

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height h as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height h = αR. The value of α is ________.

Accepted Answer

(B) 4

Answer

(A) 2

Answer

(C) 3

Answer

(D) 6

Question 33

The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point (p) of normal bisector, as shown in the figure is ________.

Accepted Answer

(A) $\left(\frac{\sqrt{3}}{4}, 1.25\right)$

Answer

(B) $\left(\frac{\sqrt{3}}{4}, 1.0\right)$

Answer

(C) (0, 0)

Answer

(D) (1.25, 0)

Question 34

The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire A and wire B is 20/11. When the joined wire is kept under certain tension the elongations in the wires A and B are equal. If the length of wire A is 2.2 m, then the length of wire B is ________ m.

Accepted Answer

(C) 1.21

Answer

(A) 1.1

Answer

(B) 2.22

Answer

(D) 4.44

Question 35

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is ________ kPa.

Accepted Answer

(A) 100

Answer

(B) 120

Answer

(C) 90

Answer

(D) 105

Question 36

In interference experiment the path difference between two interfering waves at a point A on the screen is λ/3, where λ is the wavelength of these waves, and at another point B the path difference is λ/6. The ratio of intensities at points A and B is ________.

Accepted Answer

(C) 1/3

Answer

(A) 3

Answer

(B) 4

Answer

(D) 1/4

Question 37

A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from x = A to $x = \frac{A}{\sqrt{2}}$ is ________ sec.

Accepted Answer

(C) 5/8

Answer

(A) 1/4

Answer

(B) 5/4

Answer

(D) 3/8

Question 38

A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of Q is ________ nC. (ε₀ = 8.85 × 10$^{-12}$ C²/Nm² and π = 3.14)

Accepted Answer

(A) 2.14

Answer

(B) 2.44

Answer

(C) 3.25

Answer

(D) 0.7

Question 39

The maximum rated power of the LED is 2 mW and it is used in the circuit with input voltage of 5 V as shown in the figure below. The current through resistance $R_S$ is 0.5 mA. The minimum value of the resistance of $R_S$, to ensure that the LED is not damaged is _______ kΩ.

Accepted Answer

(B) 2

Answer

(A) 6

Answer

(C) 4

Answer

(D) 5

Question 40

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L$ m, measures the intensity as $I_o$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as 45°. The measured intensity at new location will be _______.

Accepted Answer

(B) $I_o$

Answer

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

Answer

(C) $\frac{I_o}{\sqrt{2}}$

Answer

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

Question 41

A spherical interface lens of radius $R$ separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of $4R$ in front of spherical interface. The magnitude of the magnification of point source image is _______.

Accepted Answer

(A) 1.66

Answer

(B) 2.33

Answer

(C) 2.66

Answer

(D) 1.33

Question 42

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $\alpha 	imes 10^{-14}$ J. The value of $\alpha$ is _______. ($\mu_o = 4\pi 	imes 10^{-7}$ Tm/A, $\pi = 3.14$)

Accepted Answer

(A) 6.28

Answer

(B) $6.28 	imes 10^{-6}$

Answer

(C) 628

Answer

(D) $6.28 	imes 10^{-4}$

Question 43

An inductor of inductance 10 mH having resistance of 100 Ω is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is 2 mA and 4 mA is _______.

Accepted Answer

(A) 4/3

Answer

(B) 3/4

Answer

(C) 5/3

Answer

(D) 3/5

Question 44

The ratio of momentum of the photons of the 1$^{st}$ and 2$^{nd}$ line of Balmer series of Hydrogen atoms is $\alpha/\beta$. The possible values of $\alpha$ and $\beta$ are:-

Accepted Answer

(D) 20 and 27

Answer

(A) 27 and 20

Answer

(B) 3 and 16

Answer

(C) 5 and 36

Question 45

A LCR series circuit driven with $E_{rms} = 90$ V at frequency $f_d = 30$ Hz has resistance $R = 80$ Ω, an inductance with inductive reactance $X_L = 20.0$ Ω and capacitance with capacitive reactance $X_C = 80.0$ Ω. The power factor of the circuit is _______.

Accepted Answer

(A) 0.8

Answer

(B) 0.64

Answer

(C) 0.9

Answer

(D) 0.5

Question 46

Refer to the circuit diagram given below. The heat generated across the 6 Ω resistance in 100 second is $\frac{\alpha}{100}$ J. The value of $\alpha$ is _______. (Nearest integer)

Accepted Answer

3477

Question 47

An unpolarized light of intensity $I_o$ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is 0° and intensity of light emerged from analyser is $\frac{3}{8}I_o$, the angle of rotation of the light by the solution with respect to analyser is _______ degrees.

Accepted Answer

30

Question 48

The energy released when $\frac{7}{17.13}$ kg of $^{7}_{3}$Li is converted into $^{4}_{2}$He by proton bombardment is $\alpha 	imes 10^{32}$ eV. The value of $\alpha$ is _______. (Nearest integer) (Mass of $^{7}_{3}$Li = 7.0183 u, mass of $^{4}_{2}$He = 4.004 u, mass of proton = 1.008 u and 1 u = 931 MeV/c$^{2}$ and Avogadro number = $6.0 	imes 10^{23}$)

Accepted Answer

6

Question 49

A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2x\hat{i} + 3y^{2}\hat{j} + 4\hat{k}$ N/C. The work done in moving the charge is _______ J.

Accepted Answer

186

Question 50

A certain gas is isothermally compressed to $\left(\frac{1}{3}ight)^{rd}$ of its initial volume ($V_o = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3 	imes 10^{5}$ N/m$^{2}$, the magnitude of work done on the gas is _______ J.

Accepted Answer

989

Question 51

An oxide of iron contains 69.9% iron, its empirical formula, is: (Given: Molar mass of Fe and O are 56 and 16 g mol⁻¹ respectively.)

Accepted Answer

(B) Fe₂O₃

Answer

(A) FeO

Answer

(C) Fe₃O₄

Answer

(D) FeO₃

Question 52

If shortest wavelength of hydrogen atom in Lyman series is $x$, then longest wavelength in Balmer series of He⁺ is:

Accepted Answer

(A) $\frac{9x}{5}$

Answer

(B) $\frac{36x}{5}$

Answer

(C) $\frac{x}{4}$

Answer

(D) $\frac{5x}{9}$

Question 53

Match the LIST-I (Orbital) with LIST-II (Radial nodes and nodal plane)
Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 54

The pairs among A = [SO₃²⁻, CO₃²⁻], B = [O₂²⁻, F₂], C = [CN⁻, CO], D = [NH₃, H₃O⁺] and E = [MnO₄²⁻, CrO₄²⁻] that do not have similar Lewis dot structure are

Accepted Answer

(B) A and E

Answer

(A) A, B and E

Answer

(C) B, C and D

Answer

(D) C and D

Question 55

Arrange the following isothermal processes in order of the magnitude of the work $(p - V)$ involved between states 1 and 2.
A. Expansion in single stage $w_A$
B. Expansion in multi stages $w_B$
C. Compression in single stage $w_C$
D. Compression in multi stages $w_D$
Choose the correct option.

Accepted Answer

(C) $|w_C| > |w_D| > |w_B| > |w_A|$

Answer

(A) $|w_B| > |w_A| > |w_C| > |w_D|$

Answer

(B) $|w_C| > |w_D| > |w_A| > |w_B|$

Answer

(D) $|w_B| > |w_A| > |w_D| > |w_C|$

Question 56

When 0.25 moles of a non-volatile, non-ionizable solute was dissolved in 1 mole of a solvent the vapor pressure of solution was $x\%$ of vapor pressure of pure solvent. What is $x\%$?

Accepted Answer

(D) 80%

Answer

(A) 50%

Answer

(B) 60%

Answer

(C) 70%

Question 57

One mole each of He and A(g) are taken in a 10 L closed flask and heated to 400 K to establish the following equilibrium. A(g) ⇌ B(g). $K_c$ for this reaction at 400 K is 4.0. The partial pressures (in atm) of He and B(g) are respectively (at equilibrium) (Assume He, A(g) and B(g) behave as ideal gases) (Given: R = 0.082 L atm K⁻¹ mol⁻¹)

Accepted Answer

(A) 3.28, 2.624

Answer

(B) 2.624, 3.28

Answer

(C) 3.28, 0.656

Answer

(D) 0.656, 6.56

Question 58

Consider the following data.
BaSO₄ is sparingly soluble in water. If the conductivity of the saturated BaSO₄ solution is x S cm⁻¹ then the solubility product of BaSO₄ can be given as (Here Λm = Λ°m)

Accepted Answer

(A) $\frac{10^{6}x^{2}}{\alpha^{2}(x_1 + x_2 - 2x_3)^{2}}$

Answer

(B) $\frac{x^{2}}{(x_1 + x_2 - 2x_3)^{2}}$

Answer

(C) $\frac{\alpha^{2}(x_1 + x_2 - 2x_3)^{2}}{10^{6}x^{2}}$

Answer

(D) $\frac{x^{2}}{(x_1 + x_2 + 2x_3)^{2}}$

Question 59

Given below are two statements:
Statement I: Aluminium is more electropositive than thallium as the standard electrode potential value of $E^\circ_{Al^{3+}/Al}$ is negative and $E^\circ_{Tl^{3+}/Tl}$ is positive.
Statement II: The sum of first three ionization enthalpies of boron is very high when compared to that of aluminium. Due to this reason boron forms covalent compounds only and aluminium forms Al³⁺ ion.
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. Basic vanadium oxide is used in the manufacture of H₂SO₄.
B. The spin-only magnetic moment value of the transition metal halide employed in Ziegler-Natta polymerization is 2.84 BM.
C. The p-block metal compound employed in Ziegler-Natta polymerization has the metal in +3 oxidation state.
D. The number of electrons present in the outer most 'd' orbital of metal halide employed in Wacker process is 8.
Choose the correct answer from the options given below:

Accepted Answer

(C) C and D Only

Answer

(A) A and B Only

Answer

(B) A, C and D Only

Answer

(D) B, C and D Only

Question 61

Match the LIST-I (Electronic configuration of tetrahedral metal ion) with LIST-II (Crystal Field Stabilization Energy (Δₜ))
Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 62

Which of the following are true about the energy of the given d-orbitals of a tetrahedral complex?
A. $d_{xy} = d_{xz} > d_{x^2-y^2}$
B. $d_{xy} = d_{yz} > d_{z^2}$
C. $d_{x^2-y^2} > d_{z^2} > d_{xz}$
D. $d_{x^2-y^2} = d_{z^2} < d_{xz}$
Choose the correct answer from the given below:

Accepted Answer

(A) A, B and D only

Answer

(B) A and B only

Answer

(C) B and D only

Answer

(D) B, C and D only

Question 63

$R_f$ value for 2-methylpropene in a solvent system (Ethyl acetate + ether) is 0.42. 2-methylpropene is treated with dilute H₂SO₄ to give major organic product (X). $R_f$ value for (X) in the same solvent system under identical condition will be:

Accepted Answer

(D) 0.12

Answer

(A) 0.42

Answer

(B) 0.82

Answer

(C) 0.62

Question 64

Given below are two statements:
Statement I: 2,6-diethylcyclohexanone and 6-methyl-2-n-propylcyclohexanone are metamers.
Statement II: 2,2,6,6-tetramethylcyclohexanone exhibits keto-enol tautomerism.
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

List-I (Orbital)	List-II (Radial nodes and nodal plane)
A.2s	I.1 Radial node + two nodal planes
B.3s	II.1 Radial node + one nodal plane
C.3p	III.2 Radial nodes + No nodal plane
D.4d	IV.1 Radial node + No nodal plane

Electrolyte	Λ°m (S cm² mol⁻¹)
BaCl₂	x₁
H₂SO₄	x₂
HCl	x₃

List-I (Electronic configuration of tetrahedral metal ion)	List-II (Crystal Field Stabilization Energy (Δₜ))
A.d²	I.−0.6
B.d⁴	II.−0.8
C.d⁶	III.−1.2
D.d⁸	IV.−0.4

List-I (Deficiency Disease)	List-II (Vitamin)
A.Scurvy	I.Pyridoxine
B.Convulsions	II.Vitamin A
C.Cheilosis	III.Ascorbic Acid
D.Xerophthalmia	IV.Riboflavin

List-I (Amino acid)	List-II (Positive reaction/Test for functional group present in side chain of amino acid)
A.Glutamine	I.Hinsberg's test
B.Lysine	II.Neutral FeCl₃ test
C.Tyrosine	III.Ceric ammonium nitrate test
D.Serine	IV.Hoffman bromamide degradation

JEE Main 6 April 2026 Shift 1 Question Paper with Answers

Physics — JEE Main 6 April 2026 Shift 1

Chemistry — JEE Main 6 April 2026 Shift 1

Mathematics — JEE Main 6 April 2026 Shift 1

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