JEE Main2026Apr 4, Shift 2

JEE Main 2026 — Apr 4, Shift 2

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

Mathematics

Q1 For the function $f : [1, \infty) \to [1, \infty)\dots$
Q2Let $S = {z \in C : z^{2} + 4 z + 16 = 0}$ . Then $z \in S \sum ∣ z + 3 i ∣^{2}$ is equal to:
Q3If the system of equations: $x + y + z = 5$ $x + 2 y + 3 z = 9$ $x + 3 y + λ z = μ$ has infinitely many solutions, then the value of $λ + μ$ is:
Q4If $α = 1$ and $β = 1 + i 2$ , where $i = - 1$ , are two roots of the equation $x^{3} + a x^{2} + b x + c = 0$ , $a, b, c \in R$ , then $\int_{- 1}^{1} (x^{3} + a x^{2} + b x + c) d x$ is equal to:
Q5If the quadratic equation $(λ + 2) x^{2} - 3 λ x + 4 λ = 0$ , $λ \neq = - 2$ , has two positive roots, then the number of possible integral values of $λ$ is:
Q6 Let $A = \dots$
Q7 Let $α = \frac{1 \dots}{4}$
Q8For 10 observations $x_{1}, x_{2}, \dots, x_{10}$ , if $i = 1 \sum 10 (x_{i} + 2)^{2} = 180$ and $i = 1 \sum 10 (x_{i} - 1)^{2} = 90$ , then their standard deviation is:
Q9In the expansion of $(9 x - \frac{1}{3 x})^{18}$ , $x > 0$ , if the term independent of $x$ is $(221) k$ , then $k$ is equal to:
Q10 Let $P (3 cos α, 2 sin α)$ , $α \dots$
Q11 Let $H : a ^{2} \dots$
Q12 $0 \leq x \leq π max (16 sin (\frac{x}{2}) cos^{3} (\frac{x}{2}))$ is equal to:
Q13The shortest distance between the lines $r = (\frac{1}{3} \hat{i} + 2 \hat{j} + \frac{8}{3} \hat{k}) + λ (2 \hat{i} - 5 \hat{j} + 6 \hat{k})$ and $r = (- \frac{2}{3} \hat{i} - \frac{1}{3} \hat{k}) + μ (\hat{j} - \hat{k})$ , $λ, μ \in R$ , is:
Q14If $(2 α + 1, α^{2} - 3 α, \frac{α - 1}{2})$ is the image of $(α, 2 α, 1)$ in the line $\frac{x - 2}{3} = \frac{y - 1}{2} = \frac{z}{1}$ , then the possible value(s) of $α$ is(are):
Q15Let $\overset{u}{^}$ and $\overset{v}{^}$ be unit vectors inclined at an acute angle such that $∣ \overset{u}{^} \times \overset{v}{^} ∣ = \frac{3}{2}$ . If $A = λ \overset{u}{^} + \overset{v}{^} + (\overset{u}{^} \times \overset{v}{^})$ . Then $λ$ is equal to:
Q16 Let for some $α \in R$ , $f : R \to \dots$
Q17Let $A = {(a, b, c) : a, b, c are non-negative integers and a + b + 2 c = 22}$ . The $n (A)$ is equal to:
Q18The area of the region bounded by the curves $x + 3 y^{2} = 0$ and $x + 4 y^{2} = 1$ is equal to:
Q19 Let $y = y (x)$ be the solution of the differential equation:
Q20The integral $\int_{0}^{1} cot^{- 1} (1 + x + x^{2}) d x$ is equal to:
Q21 From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to $\frac{a}{b} \dots$
Q22 Let $f (x) = {e^{\dots}$
Q23 Let $A$ , $B$ be points on the two half-lines $x - \dots$
Q24 Let $A$ , $B$ and $C$ be the vertices of a variable right angled triangle inscribed in the parabola $y^{\dots}$
Q25 Let $f$ be a twice differentiable function such that $f (x) = \int_{\dots}$

JEE Main 2026 — Apr 4, Shift 2

Mathematics

Physics

Chemistry

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