JEE Main2025Apr 8, Shift 2

JEE Main 2025 — Apr 8, Shift 2

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

Mathematics

Q1 Let the values of $λ$ for which the shortest distance between the lines $\frac{x - \dots}{2}$
Q2 Let $α$ be a solution of $x^{2} + x \dots$
Q3 Let the function $f (x) = 3$
Q4If A and B are two events such that $P (A) = 0.7$ , $P (B) = 0.4$ and $P (A \cap \overline{B}) = 0.5$ , where $\overline{B}$ denotes the complement of B, then $P (B ∣ (A \cup \overline{B}))$ is equal to:
Q5If $\frac{1}{1 ^{4}} + \frac{1}{2 ^{4}} + \frac{1}{3 ^{4}} + \dots = \frac{π ^{4}}{90}$ , $\frac{1}{1 ^{4}} + \frac{1}{3 ^{4}} + \frac{1}{5 ^{4}} + \dots = α$ , $\frac{1}{2 ^{4}} + \frac{1}{4 ^{4}} + \frac{1}{6 ^{4}} + \dots = β$ , then $\frac{α}{β}$ is equal to
Q6The sum of the squares of the roots of $∣ x + 2 ∣^{2} + ∣ x - 2∣ - 2 = 0$ and the squares of the roots of $x^{2} - 2∣ x - 3∣ - 5 = 0$ , is
Q7 Let $a$ be the length of a side of a square $O A B C$ with $O$ being the origin. Its side $O \dots$
Q8Let $f (x)$ be a positive function and $I_{1} = \int_{- 1/2}^{1} 2 x f (2 x (1 - 2 x)) d x$ and $I_{2} = \int_{- 1}^{2} f (x (1 - x)) d x$ . Then the value of $\frac{I _{2}}{I _{1}}$ is equal to ____
Q9 Let $a = \dots$
Q10 Let the ellipse $3 x^{2} + p y^{\dots}$
Q11The integral $\int_{- 1}^{3/2} π^{2} x sin (π x) d x$ is equal to:
Q12 A line passing through the point $P (a, 0)$ makes an acute angle $α$ with the positive x-axis. Let this line be rotated about the point $P$ through an angle $\dots$
Q13 There are 12 points in a plane, no three of which are in the same straight line, except 5 points which are collinear. Then the total number of triangles that can be formed with the vertices at any three of these 12 points is …
Q14Let $A = {θ \in [0, 2 π] : 1 + 10 Re (\frac{2 cos θ + i sin θ}{cos θ - 3 i sin θ}) = 0}$ . Then $θ \in A \sum θ^{2}$ is equal to
Q15 Let $A = {0, 1, 2, 3, 4, 5}$ . Let …
Q16The number of integral terms in the expansion of $(5^{1/2} + 7^{1/8})^{1016}$ is
Q17Let $f (x) = x - 1$ and $g (x) = e^{x}$ for $x \in R$ . If $\frac{d y}{d x} = (e^{- 2 x} g (f (f (x))) - \frac{y}{x})$ , $y (0) = 0$ , then $y (1)$ is:
Q18The value of $cot^{- 1} (\frac{1 + tan ^{2} ( 2 ) - 1}{tan ( 2 )}) - cot^{- 1} \frac{1 + tan ^{2} ( \frac{1}{2} ) + 1}{tan ( \frac{1}{2} )}$ is equal to
Q19Let $A = 22 + p 2 + p + q 46 + 2 p 8 + 3 p + 2 q 612 + 3 p 20 + 6 p + 3 q$ . If $det (adj (adj (3 A))) = 2^{m} \cdot 3^{n}$ , $m, n \in N$ , then $m + n$ is equal to
Q20 Given below are two statements: Statement I: $x \to 0 lim \dots$
Q21Let the area of the bounded region ${(x, y) : 0 \leq 9 x \leq y^{2}, y \geq 3 x - 6}$ be $A$ . Then $6 A$ is equal to ______
Q22 Let the domain of the function $f (x) = cos^{- 1} \dots$
Q23Let the area of the triangle formed by the lines $x + 2 = y - 1 = z$ , $\frac{x - 3}{5} = \frac{y}{- 1} = \frac{z - 1}{1}$ and $\frac{x}{- 3} = \frac{y - 3}{3} = \frac{z - 2}{1}$ be $A$ . Then $A^{2}$ is equal to ______
Q24The product of the last two digits of $(1919)^{1919}$ is ______
Q25 Let $r$ be the radius of the circle, which touches x-axis at point $(a, 0)$ , $a …

JEE Main 2025 — Apr 8, Shift 2

Mathematics

Physics

Chemistry

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