JEE Main2026Apr 5, Shift 2

JEE Main 2026 — Apr 5, Shift 2

75 questions with step-by-step solutions. All free.

Mathematics

Q1 Let $α, β$ be the roots of the equation $x^{2} - \dots$
Q2Let $z_{1}, z_{2} \in C$ be the distinct solutions of the equation $z^{2} + 4 z - (1 + 12 i) = 0$ . Then $∣ z_{1} ∣^{2} + ∣ z_{2} ∣^{2}$ is equal to:
Q3If $f : N \to Z$ is defined by $f (n) = n - 1 - 5 - 2 n^{2} 3 (2 k + 1) 2 k + 1 - 3 n^{3} 3 k (2 k + 1) 3 k (k + 2) + 1, k \in N$ , and $n = 1 \sum k f (n) = 98$ , then $k$ is equal to:
Q4Let $M$ be a $3 \times 3$ matrix such that $M 100 = 123, M 010 = 012$ and $M 001 = - 1 11$ . If $M x y z = 1711$ , then $x + y + z$ equals:
Q5If the sum of the first 10 terms of the series $\frac{1}{1 + 1 ^{4} \cdot 4} + \frac{2}{1 + 2 ^{4} \cdot 4} + \frac{3}{1 + 3 ^{4} \cdot 4} + \frac{4}{1 + 4 ^{4} \cdot 4} + \dots$ is $\frac{m}{n}$ , $g cd (m, n) = 1$ , then $m + n$ is equal to:
Q6Let $A_{1}, A_{2}, A_{3}, \dots, A_{39}$ 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:
Q7The coefficient of $x^{2}$ in the expansion of $(2 x^{2} + \frac{1}{x})^{10}$ , $x \neq = 0$ , is:
Q8 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 t…
Q9A 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:
Q10 A variable $X$ takes values $0, 0, 2, 6, 12, 20, \dots\dots$
Q11 Let the point $P$ be the vertex of the parabola $y = x^{2}$
Q12 Let the directrix of the parabola $P : y^{2} = \dots$
Q13 Let the eccentricity $e$ of a hyperbola satisfy the equation $6 e^{2} - 11 \dots$
Q14 Let a triangle $P QR$ be such that $P$ and $Q$ lie on the line $\dots$
Q15 If the distance of the point $(a, 2, 5)$ from the image of the point $(1, 2, 7)$ in the line $\dots$
Q16 Let $O$ be the origin, $O P \dots$
Q17Let $f (x) = y \to 0 lim \frac{( 1 - cos ( x y )) tan ( x y )}{y ^{3}}$ . Then the number of solutions of the equation $f (x) = sin x$ , $x \in R$ is:
Q18 Let $(2^{1 - a} + 2^{\dots}$
Q19Let $f : [1, \infty) \to R$ be a differentiable function defined as $f (x) = \int_{1}^{x} f (t) d t + (1 - x) (lo g_{e} x - 1) + e$ . Then the value of $f (f (1))$ is:
Q20 Let $f (x)$ and $g (x)$ be twice differentiable functions satisfying $f^{\dots}$
Q21 Let $A = {1, 4, 7}$ and $B = \dots$
Q22 From the point $(- 1, - 1)$ , two rays are sent making angles of $45°$ with the line $x +$
Q23If $S = {θ \in [- π, π] : cos θ cos \frac{5 θ}{2} = cos 7 θ cos \frac{7 θ}{2}}$ , then $n (S)$ is equal to ______.
Q24 Let $f : R \to R$ be a function such that $f (x) \dots$
Q25 Let $y = y (x)$ be the solution of the differential equation $(tan x)^{\dots}$

JEE Main 2026 — Apr 5, Shift 2

Mathematics

Physics

Chemistry

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