JEE Main2026Jan 21, Shift 2

JEE Main 2026 — Jan 21, Shift 2

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

Mathematics

Q1 The positive integer n, for which the solutions of the equation $x (x + 2) + (x + \dots$
Q2 Let $f : R \to R$ be a twice differentiable function such that $f^{\dots}$
Q3Let $f (x) = x^{3} + x^{2} f^{'} (1) + 2 x f^{''} (2) + f^{'''} (3)$ , $x \in R$ . Then the value of $f^{'} (5)$ is :
Q4 In the line $α x + 4 y = \dots$
Q5 Let $y^{2} = 12 x$ be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x-axis such that $\dots$
Q6 Let one end of a focal chord of the parabola $y^{2} = 16 x$ be $(\dots$
Q7 Let the line L pass through the point $(- 3, 5, 2)$ and make equal angles with the positive coordinate axes. If the distance of L from the point $(- 2, r, \dots$
Q8 Let the line $L_{1}$ be parallel to the vector $- 3 \dots$
Q9Let $α$ and $β$ be the roots of equation $x^{2} + 2 a x + (3 a + 10) = 0$ such that $α < 1 < β$ . Then the set of all possible values of a is :
Q10 A random variable X takes values 0, 1, 2, 3 with probabilities $\frac{2 a + 1 \dots}{30}$
Q11If the area of the region ${(x, y) : 1 - 2 x \leq y \leq 4 - x^{2}, x \geq 0, y \geq 0}$ is $\frac{α}{β}, α, β \in N, g cd (α, β) = 1$ , then the value of $(α + β)$ is :
Q12Let $a_{1}, \frac{a _{2}}{2}, \frac{a _{3}}{2 ^{2}}, \dots, \frac{a _{10}}{2 ^{9}}$ be a G.P. of common ratio $\frac{1}{2}$ . If $a_{1} + a_{2} + \dots + a_{10} = 62$ , then $a_{1}$ is equal to :
Q13Let $A = {x : ∣ x^{2} - 10∣ \leq 6}$ and $B = {x : ∣ x - 2∣ > 1}$ . Then
Q14For the matrices $A = [3 - 4 1 - 1]$ and $B = [- 2949 - 1318]$ , if $(A^{15} + B) [x y] = [00]$ , then among the following which one is true?
Q15 For a triangle ABC, let $p = \dots$
Q16Let $y = y (x)$ be the solution of the differential equation $sec x \frac{d y}{d x} - 2 y = 2 + 3 sin x, x \in (- \frac{π}{2}, \frac{π}{2})$ , $y (0) = - \frac{7}{4}$ . Then $y (\frac{π}{6})$ is equal to:
Q17 Let $A = {2, 3, 5, 7, 9}$ . Let R be the relation on A defined by $\dots$
Q18If the system of equations $3 x + y + 4 z = 3$ $2 x + α y - z = - 3$ $X + 2 y + z = 4$ has no solution, then the value of $α$ is equal to:
Q19Let z be the complex number satisfying $∣ z - 5∣ \leq 3$ and having maximum positive principal argument. Then $34 \frac{5 z - 12}{5 i z + 16}^{2}$ is equal to:
Q20The largest $n \in N$ , for which $7^{n}$ divides $101!$ , is :
Q21Let $[\cdot]$ denote the greatest integer function and $f (x) = n \to \infty lim \frac{1}{n ^{3}} k = 1 \sum n [\frac{k ^{2}}{3 ^{x}}]$ . Then $12 j = 1 \sum \infty f (j)$ is equal to ________.
Q22If $\int_{0}^{1} 4 cot^{- 1} (1 - 2 x + 4 x^{2}) d x = a tan^{- 1} (2) - b lo g_{e} (5)$ , where $a, b \in N$ , then $(2 a + b)$ is equal to _______.
Q23Let the maximum value of $(sin^{- 1} x)^{2} + (cos^{- 1} x)^{2}$ for $x \in [- \frac{3}{2}, \frac{1}{2}]$ be $\frac{m}{n} π^{2}$ , where $g cd (m, n) = 1$ . Then $m + n$ is equal to _______.
Q24If $(\frac{1}{^{15} C _{0}} + \frac{1}{^{15} C _{1}}) (\frac{1}{^{15} C _{1}} + \frac{1}{^{15} C _{2}}) \dots (\frac{1}{^{15} C _{12}} + \frac{1}{^{15} C _{13}}) = \frac{α ^{13}}{^{14} C _{0} \cdot ^{14} C _{1} \dots ^{14} C _{12}}$ , then $30 α$ is equal to _____.
Q25 If P is a point on the circle $x^{2} + y^{\dots}$

Physics

Chemistry

Attempt this as a full mock test

Timed paper, instant score, all-India rank prediction on Fundamenthol.

Take this mock test →