JEE Main2026Jan 22, Shift 2

JEE Main 2026 — Jan 22, Shift 2

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

Mathematics

Q1 Let $n$ be the number obtained on rolling a fair die. If the probability that the system $x - n y + z\dots$
Q2If the mean deviation about the median of the numbers $k, 2 k, 3 k, \dots, 1000 k$ is 500, then $k^{2}$ is equal to :
Q3The number of elements in the relation $R = {(x, y) : 4 x^{2} + y^{2} < 52, x, y \in Z}$ is
Q4Let $S = {z \in C : 4 z^{2} + \overset{z}{ˉ} = 0}$ . Then $z \in S \sum ∣ z ∣^{2}$ is equal to :
Q5If $x \to 0 lim \frac{e ^{(a - 1) x} + 2 cos b x + ( c - 2 ) e ^{- x}}{x cos x - lo g _{e} ( 1 + x )} = 2$ , then $a^{2} + b^{2} + c^{2}$ is equal to :
Q6 If $y = y (x)$ satisfies the differential equation $16 (\dots$
Q7 Among the statements (S1) : If $A (5, - 1)$ and $B (- 2, 3)$ are two vertices of a triangle, whose orthocentre is $\dots$
Q8 Let $a = 2 \dots$
Q9If $X = x y z$ is a solution of the system of equations $A X = B$ , where $adj A = 422 - 505 1 - 23$ and $B = 402$ , then $∣ x + y + z ∣$ is equal to :
Q10 Let $L$ be the line $\frac{x + \dots}{2}$
Q11 Let $P (10, 2 15 \dots$
Q12The area of the region $A = {(x, y) : 4 x^{2} + y^{2} \leq 8 and y^{2} \leq 4 x}$ is :
Q13Let $α, β$ be the roots of the quadratic equation $12 x^{2} - 20 x + 3 λ = 0$ , $λ \in Z$ . If $\frac{1}{2} \leq ∣ β - α ∣ \leq \frac{3}{2}$ , then the sum of all possible values of $λ$ is :
Q14Let the domain of the function $f (x) = lo g_{3} lo g_{5} (7 - lo g_{2} (x^{2} - 10 x + 85)) + sin^{- 1} (\frac{3 x - 7}{17 - x})$ be $(α, β]$ . Then $α + β$ is equal to :
Q15 Let $[∙]$ denote the greatest integer function, and let $f (x) = min {\dots$
Q16 Let $S$ and $S^{'}$ be the foci of the ellipse $\dots$
Q17 Let the locus of the mid-point of the chord through the origin $O$ of the parabola $y^{2} = \dots$
Q18Let $f (x) = [x]^{2} - [x + 3] - 3$ , $x \in R$ where $[∙]$ is the greatest integer function. Then
Q19 Let $f$ and $g$ be functions satisfying $f (x + \dots$
Q20 Let $C_{r}$ denote the coefficient of $x^{\dots}$
Q21 Let a vector $a = \dots$
Q22Let $[∙]$ be the greatest integer function. If $α = \int_{0}^{64} (x^{1/3} - [x^{1/3}]) d x$ , then $\frac{1}{π} \int_{0}^{α π} (\frac{sin ^{2} θ}{sin ^{6} θ + cos ^{6} θ}) d θ$ is equal to ______.
Q23 Let $cos (α + β) = - \dots$
Q24Suppose $a, b, c$ are in A.P. and $a^{2}, 2 b^{2}, c^{2}$ are in G.P. If $a < b < c$ and $a + b + c = 1$ , then $9 (a^{2} + b^{2} + c^{2})$ is equal to ______.
Q25 Let $S$ be the set of the first 11 natural numbers. Then the number of elements in $A = {B \subseteq S \dots$

JEE Main 2026 — Jan 22, Shift 2

Mathematics

Physics

Chemistry

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