JEE Main2026Apr 2, Shift 2

JEE Main 2026 — Apr 2, Shift 2

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

Mathematics

Q1 Let $α, β$ be the roots of the equation $x^{2} - \dots$
Q2 Let the circle $C_{1} : ∣ z ∣ \dots$
Q3If the system of equations $x + 5 y + 6 z = 4$ , $2 x + 3 y + 4 z = 7$ , $x + 6 y + a z = b$ has infinitely many solutions, then the point $(a, b)$ lies on the line
Q4Let $a_{1}, a_{2}, a_{3}, \dots$ be an A.P. and $g_{1} = a_{1}, g_{2}, g_{3}, \dots$ be an increasing G.P. If $a_{1} = a_{2} + g_{2} = 1$ and $a_{3} + g_{3} = 4$ , then $a_{10} + g_{5}$ is equal to :
Q5The sum $\frac{1 ^{3}}{1} + \frac{1 ^{3} + 2 ^{3}}{1 + 3} + \frac{1 ^{3} + 2 ^{3} + 3 ^{3}}{1 + 3 + 5} + \dots$ up to $8$ terms, is :
Q6If for $3 \leq r \leq 30$ , $(^{30} C_{30 - r}) + 3 (^{30} C_{31 - r}) + 3 (^{30} C_{32 - r}) + (^{30} C_{33 - r}) =^{m} C_{r}$ , then $m$ equals :
Q7 Let $p_{n}$ denote the total number of triangles formed by joining the vertices of an $n$ -side regular polygon. If $\dots$
Q8 A man throws a fair coin repeatedly. He gets $10$ points for each head he throws and $5$ points for each tail he throws. If the probability that he gets exactly $30$ points is $\dots$
Q9 The mean and variance of $n$ observations are $8$ and $16$ , respectively. If the sum of the first $(n - \dots$
Q10 Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines $x + (k - 1) y + \dots$
Q11 Let $O$ be the origin, and $P$ and $Q$ be two points on the rectangular hyperbola $x y = \dots$
Q12 Let the parabola $y = x^{2} + \dots$
Q13Let $P = {θ \in [0, 4 π] : tan^{2} θ \neq = 1}$ and $S = {a \in Z : 2 (cos^{8} θ - sin^{8} θ) sec 2 θ = a^{2}, θ \in P}$ . Then $n (S)$ is :
Q14 Let the vectors $a = - \dots$
Q15 Let the point $A$ be the foot of perpendicular drawn from the point $P (a, b, 0)$ on the line $\dots$
Q16 Two adjacent sides of a parallelogram $P QR S$ are given by $\overset{\dots}{P Q}$
Q17The value of $\int_{0}^{20 π} (sin^{4} x + cos^{4} x) d x$ is equal to:
Q18Let $f (x)$ be a polynomial of degree $5$ , and have extrema at $x = 1$ and $x = - 1$ . If $x \to 0 lim (\frac{f ( x )}{x ^{3}}) = - 5$ , then $f (2) - f (- 2)$ is equal to :
Q19Let $f (x) = \int (\frac{16 x + 24}{x ^{2} + 2 x - 15}) d x$ . If $f (4) = 14 lo g_{e} (3)$ and $f (7) = lo g_{e} (2^{α} \cdot 3^{β})$ , $α, β \in N$ , then $α + β$ is equal to:
Q20Let $x = x (y)$ be the solution of the differential equation $2 y^{2} \frac{d x}{d y} - 2 x y + x^{2} = 0$ , $y > 1$ , $x (e) = e$ . Then $x (e^{2})$ is equal to:
Q21 Let $A = {2, 3, 4, 5, 6}$ . Let
Q22 Consider the matrices $A = [2 - 2 \dots$
Q23 Let $A$ be the point $(3, 0)$ and circles with variable diameter $A B$ touch the circle $x \dots$
Q24If the area of the region bounded by $16 x^{2} - 9 y^{2} = 144$ and $8 x - 3 y = 24$ is $A$ , then $3 (A + 6 lo g_{e} (3))$ is equal to______.
Q25 The number of points in the interval $[2, 4]$ , at which the function $f (x) = [\dots$

JEE Main 2026 — Apr 2, Shift 2

Mathematics

Physics

Chemistry

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