JEE Main2026Apr 4, Shift 1

JEE Main 2026 — Apr 4, 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 $f (x) = cos^{- 1} (\frac{4 x + 2 [ x ]}{3})$ is $[α, β]$ , then $12 (α + β)$ is equal to :
Q2If the set of all solutions of $∣ x^{2} + x - 9∣ = ∣ x ∣ + ∣ x^{2} - 9∣$ is $[α, β] \cup [γ, \infty)$ , then $(α^{2} + β^{2} + γ^{2})$ is equal to :
Q3Let $z$ be a complex number such that $∣ z + 2∣ = ∣ z - 2∣$ and $ar g (\frac{z + 3}{z - i}) = \frac{π}{4}$ . Then $∣ z ∣^{2}$ is equal to :
Q4The number of functions $f : {1, 2, 3, 4} \to {a, b, c}$ , which are not onto, is :
Q5 Let $S = {A = [\dots$
Q6Let $A = 112 - 201 135$ . Then the sum of all elements of the matrix $adj (adj (2 (adj A)^{- 1}))$ is equal to :
Q7 The first term of an A.P. of $30$ non-negative terms is $\frac{10 \dots}{3}$
Q8The number of ways, of forming a queue of $4$ boys and $3$ girls such that all the girls are not together, is:
Q9 Let the smallest value of $k \in N$ , for which the coefficient of $x^{3}$ in …
Q10 Suppose that the mean and median of the non-negative numbers $21, 8, 17, a, 51, 103, b, 13, \dots$
Q11 Let the line $L_{1} : x + \dots$
Q12 Let the vertex $A$ of a triangle $A B C$ be $(1, 2)$ , and the mid-point of the side $\dots$
Q13 Suppose the two chords, drawn from the point $(1, 2)$ on the circle $x^{2} + \dots$
Q14 A line with direction ratios $1, - 1, 2$ intersects the lines $2 \dots$
Q15The square of the distance of the point $(- 2, - 8, 6)$ from the line $\frac{x - 1}{1} = \frac{y - 1}{2} = \frac{z}{- 1}$ along the line $\frac{x + 5}{1} = \frac{y + 5}{- 1} = \frac{z}{2}$ is equal to:
Q16If $y = tan^{- 1} (\frac{3 cos x - 4 sin x}{4 cos x + 3 sin x}) + 2 tan^{- 1} (\frac{x}{1 + 1 - x ^{2}})$ , then $\frac{d y}{d x}$ at $x = \frac{3}{2}$ is equal to :
Q17Let $f$ be a real polynomial of degree $n$ such that $f (x) = f^{'} (x) f^{''} (x)$ , for all $x \in R$ . If $f (0) = 0$ , then $36 (f^{'} (2) + f^{''} (2) + \int_{0}^{2} f (x) d x)$ is equal to :
Q18The area of the region ${(x, y) : y \leq π - ∣ x ∣, y \leq ∣ x sin x ∣, y \geq 0}$ is :
Q19Let $\int_{- 2}^{2} (∣ sin x ∣ + [x sin x]) d x = 2 (3 - cos 2) + β$ , where $[\cdot]$ is the greatest integer function. Then $β sin (\frac{β}{2})$ equals.
Q20Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} = (1 + x + x^{2}) (1 - y + y^{2})$ , $y (0) = \frac{1}{2}$ . Then $(2 y (1) - 1)$ is equal to
Q21 A coin is tossed $8$ times. If the probability that exactly $4$ heads appear in the first six tosses and exactly $3$ heads appear in the last five tosses is $p$ , then $96 \dots$
Q22 Consider the parabola $P : y^{2} =$
Q23If $A = \frac{sin 3 ^{\circ}}{cos 9 ^{\circ}} + \frac{sin 9 ^{\circ}}{cos 2 7 ^{\circ}} + \frac{sin 2 7 ^{\circ}}{cos 8 1 ^{\circ}}$ and $B = tan 8 1^{\circ} - tan 3^{\circ}$ , then $\frac{B}{A}$ is equal to _______.
Q24 Let $a_{\dots}$
Q25The number of points, at which the function $f (x) = max {6 x, 2 + 3 x^{2}} + ∣ x - 1∣ cos x^{2} - \frac{1}{4}, x \in (- π, π)$ , is not differentiable, is _____.

JEE Main 2026 — Apr 4, Shift 1

Mathematics

Physics

Chemistry

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