JEE Main2026Jan 22, Shift 1

JEE Main 2026 — Jan 22, Shift 1

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

Mathematics

Q1 Let $A B = 2 \dots$
Q2 Let the relation R on the set $M = {1, 2, 3, \dots, 16}$ be given by …
Q3Let the line $x = - 1$ divide the area of the region ${(x, y) : 1 + x^{2} \leq y \leq 3 - x}$ in the ratio $m : n$ , $g cd (m, n) = 1$ . Then $m + n$ is equal to
Q4Two distinct numbers a and b are selected at random from 1, 2, 3, …, 50. The probability, that their product ab is divisible by 3, is
Q5Let $f (x) = x^{2025} - x^{2000}, x \in [0, 1]$ and the minimum value of the function $f (x)$ in the interval $[0, 1]$ be $(80)^{80} (n)^{- 81}$ . Then n is equal to
Q6 Let $P (α, β, γ)$ be the point on the line
Q7If a random variable x has the probability distribution $x 01234567 p (x) 02 k k 3 k 2 k^{2} 2 k k^{2} + k 7 k^{2}$ then $P (3 < x \leq 6)$ is equal to
Q8The number of distinct real solutions of the equation $x ∣ x + 4∣ + 3∣ x + 2∣ + 10 = 0$ is
Q9Let $f : [1, \infty) \to R$ be a differentiable function. If $6 \int_{1}^{x} f (t) d t = 3 x f (x) + x^{3} - 4$ for all $x \geq 1$ , then the value of $f (2) - f (3)$ is
Q10If the line $α x + 2 y = 1$ , where $α \in R$ , does not meet the hyperbola $x^{2} - 9 y^{2} = 9$ , then a possible value of $α$ is :
Q11If the image of the point $P (1, 2, a)$ in the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{7 - z}{2}$ is $Q (5, b, c)$ , then $a^{2} + b^{2} + c^{2}$ is equal to
Q12 Let the set of all values of $r$ , for which the circles $(x + 1)^{2 \dots}$
Q13If $A = [2335]$ , then the determinant of the matrix $(A^{2025} - 3 A^{2024} + A^{2023})$ is
Q14If the domain of the function $f (x) = sin^{- 1} (\frac{5 - x}{3 + 2 x}) + \frac{1}{lo g _{e} ( 10 - x )}$ is $(- \infty, α] \cup [β, γ) - {δ}$ , then $6 (α + β + γ + δ)$ is equal to
Q15The value of $\int_{- π /2}^{π /2} (\frac{1}{[ x ] + 4}) d x$ , where $[\cdot]$ denotes the greatest integer function, is
Q16The coefficient of $x^{48}$ in $(1 + x) + 2 (1 + x)^{2} + 3 (1 + x)^{3} + \dots + 100 (1 + x)^{100}$ is equal to :
Q17 If the chord joining the points $P_{1} (x_{\dots}$
Q18The number of solutions of $tan^{- 1} (4 x) + tan^{- 1} (6 x) = \frac{π}{6}$ , where $- \frac{1}{2 6} < x < \frac{1}{2 6}$ is equal to
Q19Let the solution curve of the differential equation $x d y - y d x = x^{2} + y^{2} d x, x > 0, y (1) = 0$ , be $y = y (x)$ . Then $y (3)$ is equal to
Q20If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is
Q21Let $α = \frac{- 1 + i 3}{2}$ and $β = \frac{- 1 - i 3}{2}$ , $i = - 1$ . If $(7 - 7 α + 9 β)^{20} + (9 + 7 α - 7 β)^{20} + (- 7 + 9 α + 7 β)^{20} + (14 + 7 α + 7 β)^{20} = m^{10}$ , then m is _________.
Q22 Let A be a $3 \times 3$ matrix such that $A + A^{\dots}$
Q23 If $\int (sin x)^{- 11/2} (cos x)^{\dots}$
Q24If $\frac{cos ^{2} 48 d e g ; - sin ^{2} 12 d e g ;}{sin ^{2} 24 d e g ; - sin ^{2} 6 d e g ;} = \frac{α + β 5}{2}$ , where $α, β \in N$ , then $α + β$ is equal to _____.
Q25 Let ABC be a triangle. Consider four points $p_{1}, p$

JEE Main 2026 — Jan 22, Shift 1

Mathematics

Physics

Chemistry

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