JEE Main2026Apr 6, Shift 1

JEE Main 2026 — Apr 6, Shift 1

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

Mathematics

Q1Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f (x) = sin^{- 1} (\frac{x + [ x ]}{3})$ is $[α, β)$ , then $α^{2} + β^{2}$ is equal to:
Q2 Let one root of the quadratic equation in $x$ : $(k^{2} - \dots$
Q3 Let $e_{1}$ and $e_{\dots}$
Q4 Let the set of all values of $k \in R$ such that the equation $z (\overline{z}$
Q5The value of $1^{3} - 2^{3} + 3^{3} - \dots + 1 5^{3}$ is:
Q6 The sum of the first ten terms of an A.P. is $160$ and the sum of the first two terms of a G.P. is $8$ . If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is: …
Q7 The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is: …
Q8If the coefficients of the middle terms in the binomial expansions of $(1 + α x)^{26}$ and $(1 - α x)^{28}$ , $α \neq = 0$ , are equal, then the value of $α$ is:
Q9 A data consists of $20$ observations $x_{1}, x^{\dots}$
Q10 A bag contains $(N + 1)$ coins $-$ $N$ fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If …
Q11 If the eccentricity $e$ of the hyperbola $a ^{2} \dots$
Q12 Let chord PQ of length $313$ of the parabola $\dots$
Q13Let $0 < α < 1$ , $β = \frac{1}{3 α}$ and $tan^{- 1} (1 - α) + tan^{- 1} (1 - β) = \frac{π}{4}$ . Then $6 (α + β)$ is equal to:
Q14Let $S = {θ \in (- 2 π, 2 π) : cos θ + 1 = 3 sin θ}$ . Then $θ \in S \sum θ$ is equal to:
Q15 Let the image of the point $P (1, 6, a)$ in the line $L : \dots$
Q16 Let a line $L$ be perpendicular to both the lines $L_{1} : \dots$
Q17The value of $x \to 0 lim (\frac{x ^{2} sin ^{2} x}{x ^{2} - sin ^{2} x})$ is:
Q18The value of the integral $\int_{- π /4}^{π /4} (\frac{32 cos ^{4} x}{1 + e ^{s i n x}}) d x$ is:
Q19The area of the region ${(x, y) : 0 \leq y \leq 6 - x, y^{2} \geq 4 x - 3, x \geq 0}$ is:
Q20 Let $e$ be the base of natural logarithm and let $f : {1, 2, 3, 4 \dots$
Q21 Let $A = \dots$
Q22 Let the centre of the circle $x^{2} + y^{\dots}$
Q23If $a = \hat{i} + \hat{j} + \hat{k}$ , $b = \hat{j} - \hat{k}$ , and $c$ be three vectors such that $a \times c = b$ and $a \cdot c = 3$ , then $c \cdot (a - 2 b)$ is equal to __________.
Q24 For the functions $f (θ) = α tan^{2 \dots}$
Q25 Let $y = y (x)$ be the solution of the differential equation $(x^{\dots}$

JEE Main 2026 — Apr 6, Shift 1

Mathematics

Physics

Chemistry

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