JEE Main2026Apr 5, Shift 1

JEE Main 2026 — Apr 5, Shift 1

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

Mathematics

Q1Let $a, b \in C$ . Let $α, β$ be the roots of the equation $x^{2} + a x + b = 0$ . If $β - α = 11$ and $β^{2} - α^{2} = 3 i 11$ , then $(β^{3} - α^{3})^{2}$ is equal to :
Q2Let the sum of the first n terms of an A.P. be $3 n^{2} + 5 n$ . Then the sum of squares of the first 10 terms of the A.P. is :
Q3 Let $A$ be a $3 \times 3$ matrix such that $A^{\dots}$
Q4 Consider the system of linear equations in $x, y, z$ : $x + 2 y\dots$
Q5 $n = 1 \sum 10 (\frac{528}{n ( n + 1 ) ( n + 2 )})$ is equal to :
Q6Let $tan A, tan B$ , where $A, B \in (- \frac{π}{2}, \frac{π}{2})$ , be the roots of the quadratic equation $x^{2} - 2 x - 5 = 0$ . Then $20 sin^{2} (\frac{A + B}{2})$ is equal to :
Q7 A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is : …
Q8The mean deviation about the mean for the data is equal to :
Q9 Let a focus of the ellipse $E : a ^{2}$
Q10 Let $P$ be a moving point on the circle $x^{2} + \dots$
Q11 In an equilateral triangle $P QR$ , let the vertex $P$ be at $(3, 5)$ and the side $\dots$
Q12The sum of all the integral values of $p$ such that the equation $3 sin^{2} x + 12 cos x - 3 = p$ , $x \in R$ , has at least one solution, is :
Q13The square of the distance of the point $P (5, 6, 7)$ from the line $\frac{x - 2}{2} = \frac{y - 5}{3} = \frac{z - 2}{4}$ is equal to :
Q14Let $a = 7 \hat{i} + \hat{j} - \hat{k}$ and $b = \hat{j} + 2 \hat{k}$ . If $r$ is a vector such that $r \times a + a \times b = 0$ and $r \cdot a = 0$ , then $∣3 r ∣^{2}$ is equal to :
Q15 The square of the distance of the point of intersection of the lines $r = (\dots$
Q16The area of the region $R = {(x, y) : x y \leq 27, 1 \leq y \leq x^{2}}$ is equal to :
Q17The product of all possible values of $α$ , for which $x \to 0 lim (\frac{1 - cos ( α x ) cos (( α + 1 ) x ) cos (( α + 2 ) x )}{sin ^{2} (( α + 1 ) x )}) = 2$ , is :
Q18The value of the integral $\int_{0}^{\infty} \frac{lo g _{e} ( x )}{x ^{2} + 4} d x$ is :
Q19 Let $f : R \to R$ be a differentiable function such that $f \dots$
Q20The value of the integral $\int_{π /6}^{π /3} (\frac{4 - csc ^{2} x}{cos ^{4} x}) d x$ is :
Q21Let $A = {1, 2, 3, 4, 5, 6}$ . The number of one-one functions $f : A \to A$ such that $f (1) \geq 3$ , $f (3) \leq 4$ and $f (2) + f (3) = 5$ , is _________.
Q22 Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is _______. …
Q23If the sum of the coefficients of $x^{7}$ and $x^{14}$ in the expansion of $(\frac{1}{x ^{3}} - x^{4})^{n}$ , $x \neq = 0$ , is zero, then the value of $n$ is _______.
Q24If $\frac{π}{4} + p = 1 \sum 11 tan^{- 1} (\frac{2 ^{p - 1}}{1 + 2 ^{2 p - 1}}) = α$ , then $tan α$ is equal to ________.
Q25 Let $y = y (x)$ be the solution of the differential equation $x sin \dots$

JEE Main 2026 — Apr 5, Shift 1

Mathematics

Physics

Chemistry

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