JEE Main2026Apr 8, Shift 2

JEE Main 2026 — Apr 8, Shift 2

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

Mathematics

Q1 Consider the relation $R$ on the set ${- 2, - 1, 0, 1, 2}$ defined by $\dots$
Q2The number of values of $z \in C$ , satisfying the equations $∣ z - (4 + 8 i) ∣ = 10$ and $∣ z - (3 + 5 i) ∣ + ∣ z - (5 + 11 i) ∣ = 45$ , is :
Q3If the system of linear equations : $x + y + z = 6$ , $x + 2 y + 5 z = 10$ , $2 x + 3 y + λ z = μ$ . has infinitely many solutions, then the value of $λ + μ$ equals.
Q4Let $A = α 12 230045$ and $B = 100 0 - 5 α 0 04 α - 2 α + adj (A)$ . If $det (B) = 66$ , then $det (adj (A))$ equals :
Q5Let $α = 3 + 4 + 8 + 9 + 13 + 14 + \dots$ upto $40$ terms. If $(tan β)^{α /1020}$ is a root of the equation $x^{2} + x - 2 = 0$ , $β \in (0, \frac{π}{2})$ , then $sin^{2} β + 3 cos^{2} β$ is equal to :
Q6 A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabilities of the candidate going by bus, scooter and car, respectively, are $\frac{2 \dots}{5}$
Q7 A set of four observations has mean $1$ and variance $13$ . Another set of six observations has mean $2$ and variance $1$ . Then, the variance of all these $10$ observations is equal to : …
Q8If $26 (\frac{2 ^{3}}{3}^{13} C_{2} + \frac{2 ^{5}}{5}^{12} C_{4} + \frac{2 ^{7}}{7}^{12} C_{6} + \dots + \frac{2 ^{13}}{13}^{12} C_{12}) = 3^{13} - α$ , then $α$ is equal to :
Q9 A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is …
Q10 If a straight line drawn through the point of intersection of the lines $4 x + 3 y - 1 = \dots$
Q11 Let $O$ be the vertex of the parabola $y^{2} = \dots$
Q12 Let $α = 3 sin^{- 1} \dots$
Q13 For the function $f (x) = e^{s i n \dots}$
Q14Let $a = 4 \hat{i} - \hat{j} + 3 \hat{k}$ , $b = 10 \hat{i} + 2 \hat{j} - \hat{k}$ and a vector $c$ be such that $2 (a \times b) + 3 (b \times c) = 0$ . If $a \cdot c = 15$ , then $c \cdot (\hat{i} + \hat{j} - 3 \hat{k})$ is equal to :
Q15 Let the foot of perpendicular from the point $(λ, 2, 3)$ on the line $1 \dots$
Q16The value of the integral $\int_{0}^{2} \frac{x ( x ^{2} + x + 1 )}{( x + 1 ) ( x ^{4} + x ^{2} + 1 )} d x$ is equal to :
Q17Let $y = y (x)$ be the solution of the differential equation $x 1 - x^{2} d y + (y 1 - x^{2} - x cos^{- 1} x) d x = 0$ , $x \in (0, 1)$ , $x \to 1^{-} lim y (x) = 1$ . Then $y (\frac{1}{2})$ equals :
Q18 Let $f : (1, \infty) \to R$ be function defined as $\dots$
Q19Let $f (x) = ⎩ ⎨ ⎧ \frac{1}{3}, x \leq \frac{π}{2} \frac{b ( 1 - sin x )}{( π - 2 x ) ^{2}}, x > \frac{π}{2}$ . If $f$ is continuous at $x = π /2$ , then the value of $\int_{0}^{3 b - 6} ∣ x^{2} + 2 x - 3∣ d x$ is :
Q20 Let $f ( a ^{2} + \dots$
Q21The sum of squares of all real solution of the equation $lo g_{(x + 1)} (2 x^{2} + 5 x + 3) = 4 - lo g_{(2 x + 3)} (x^{2} + 2 x + 1)$ is equal to _______.
Q22If $\int_{π /6}^{π /4} [cot (x - \frac{π}{3}) cot (x + \frac{π}{3}) + 1] d x = α lo g_{e} (3 - 1)$ , then $9 α^{2}$ is equal to _______.
Q23 Let a line $L_{1}$ pass through the origin and be perpendicular to the lines $L_{\dots}$
Q24 Consider the circle $C : x^{2} + \dots$
Q25 Let $f$ be a polynomial function such that $lo g_{2} (\dots$

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