JEE Main2026Jan 24, Shift 2

JEE Main 2026 — Jan 24, Shift 2

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

Mathematics

Q1 Let $f (x) = \int ( 1$
Q2 Let the length of the latus rectum of an ellipse $\frac{\dots}{a ^{2}}$
Q3 Let the angles made with the positive x-axis by two straight lines drawn from the point $P (2, 3)$ and meeting the line $x + y$
Q4 Let $a = 2 \dots$
Q5 Let $α_{1}, α_{\dots}$
Q6Let the image of parabola $x^{2} = 4 y$ , in the line $x - y = 1$ be $(y + α)^{2} = b (x - c)$ , $a, b, c \in N$ . Then $a + b + c$ is equal to
Q7 $(\frac{1}{3} + \frac{4}{7}) + (\frac{1}{3 ^{2}} + \frac{1}{3} \times \frac{4}{7} + \frac{4 ^{2}}{7 ^{2}}) + (\frac{1}{3 ^{3}} + \frac{1}{3 ^{2}} \times \frac{4}{7} + \frac{1}{3} \times \frac{4 ^{2}}{7 ^{2}} + \frac{4 ^{3}}{7 ^{3}}) + \dots$ upto infinite terms is equal to -
Q8 Let $P = [p_{ij} \dots$
Q9 The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is : …
Q10The largest value of $n$ , for which $4 0^{n}$ divides $60!$ , is
Q11The sum of all values of $α$ , for which the shortest distance between the lines $\frac{x + 1}{α} = \frac{y - 2}{- 1} = \frac{z - 4}{- α}$ and $\frac{x}{α} = \frac{y - 1}{2} = \frac{z - 1}{2 α}$ is $2$ , is
Q12Let $f (α)$ denote the area of the region in the first quadrant bounded by $x = 0$ , $x = 1$ , $y^{2} = x$ and $y = ∣ α x - 5∣ - ∣1 - α x ∣ + α x^{2}$ . Then $f (0) + f (1)$ is equal to
Q13If the domain of the function $f (x) = sin^{- 1} (\frac{1}{x ^{2} - 2 x - 2})$ , is $(- \infty, α] \cup [β, γ] \cup [δ, \infty)$ , then $α + β + γ + δ$ is equal to
Q14 Let $X = {x \in N : 1 \dots$
Q15 Consider the following three statements for the function $f : (0, \infty) \to R$ defined by $\dots$
Q16 Let $y = y (x)$ be a differentiable function in the interval $(0, \infty)$ such that $\dots$
Q17Let $f$ be a function such that $3 f (x) + 2 f (\frac{m}{19 x}) = 5 x$ , $x \neq = 0$ , where $m = i = 1 \sum 9 i^{2}$ . Then $f (5) - f (2)$ is equal to
Q18The smallest positive integral value of $a$ , for which all the roots of $x^{4} - a x^{2} + 9 = 0$ are real and distinct, is equal to
Q19Let $a = 2 \hat{i} - 5 \hat{j} + 5 \hat{k}$ and $b = \hat{i} - \hat{j} - 3 \hat{k}$ . If $c$ is a vector such that $2 (a \times c) + 3 (b \times c) = 0$ and $(a - b) \cdot c = - 97$ , then $∣ c \times \hat{k} ∣^{2}$ is equal to
Q20 Let $[t]$ denote the greatest integer less than or equal to $t$ . If the function $f (x) = \dots$
Q21If $f (x)$ satisfies the relation $f (x) = e^{x} + \int_{0}^{1} (y + x e^{x}) f (y) d y$ , then $e + f (0)$ is equal to ________.
Q22 Let $(h, k)$ lie on the circle $C : x^{\dots}$
Q23Let $z = (1 + i) (1 + 2 i) (1 + 3 i) \dots (1 + ni)$ , where $i = - 1$ . If $∣ z ∣^{2} = 44200$ , then $n$ is equal to ________.
Q24 Let S be a set of 5 elements and $P (S)$ denote the power set of S. Let E be an event of choosing an ordered pair $(A, B)$ from the set $\dots$
Q25The number of elements in the set ${x \in [0^{\circ}, 18 0^{\circ}] : tan (x + 10 0^{\circ}) = tan (x + 5 0^{\circ}) tan x tan (x - 5 0^{\circ})}$ is ________.

JEE Main 2026 — Jan 24, Shift 2

Mathematics

Physics

Chemistry

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