JEE Main2025Jan 24, Shift 1

JEE Main 2025 — Jan 24, Shift 1

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

Mathematics

Q1 Let $a = \dots$
Q2In $I (m, n) = \int_{0}^{1} x^{m - 1} (1 - x)^{n - 1} d x$ , $m, n > 0$ , then $I (9, 14) + I (10, 13)$ is
Q3Let $f : R - {0} \to R$ be a function such that $f (x) - 6 f (\frac{1}{x}) = \frac{35}{3 x} - \frac{5}{2}$ . If $x \to 0 lim (\frac{1}{α x} + f (x)) = β$ ; $α, β \in R$ , then $α + 2 β$ is equal to
Q4 Let $S_{n} = \dots$
Q5Let $f (x) = \frac{2 ^{x + 2} + 16}{2 ^{2 x + 1} + 2 ^{x + 4} + 32}$ . Then the value of $8 (f (\frac{1}{15}) + f (\frac{2}{15}) + \dots + f (\frac{59}{15}))$ is equal to
Q6 If $α$ and $β$ are the roots of the equation $2 z^{2} \dots$
Q7 $x \to 0 lim cosec x (2 cos^{2} x + 3 cos x - cos^{2} x + sin x + 4)$ is
Q8 Let in a $△ A B C$ , the length of the side $A C$ be 6, the vertex $B$ be $(\dots$
Q9Let $y = y (x)$ be the solution of the differential equation $(x y - 5 x^{2} 1 + x^{2}) d x + (1 + x^{2}) d y = 0$ , $y (0) = 0$ . Then $y (3)$ is equal to
Q10 Let the product of the focal distances of the point $(3, \dots$
Q11 A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A throws a sum of 5. The probability, that A wins if A makes the first throw, is …
Q12 Consider the region $R = {(x, y) : x \leq \dots$
Q13The area of the region ${(x, y) : x^{2} + 4 x + 2 \leq y \leq ∣ x + 2∣}$ is equal to
Q14 For a statistical data $x_{1}, x_{\dots}$
Q15 Let circle $C$ be the image of $x^{2} + \dots$
Q16 For some $n \neq = 10$ , let the coefficients of the $5^{\dots}$
Q17The product of all the rational roots of the equation $(x^{2} - 9 x + 11)^{2} - (x - 4) (x - 5) = 3$ , is equal to :
Q18 Let the line passing through the points $(- 1, 2, 1)$ and parallel to the line $2 \dots$
Q19 Let the lines $3 x - 4 y - α = 0\dots$
Q20If the system of equations $2 x - y + z = 4$ $5 x + λ y + 3 z = 12$ $100 x - 47 y + μ z = 212$ , has infinitely many solutions, then $μ - 2 λ$ is equal to
Q21Let $f$ be a differentiable function such that $2 (x + 2)^{2} f (x) - 3 (x + 2)^{2} = 10 \int_{0}^{x} (t + 2) f (t) d t$ , $x \geq 0$ . Then $f (2)$ is equal to _____.
Q22If for some $α, β$ ; $α \leq β$ , $α + β = 8$ and $sec^{2} (tan^{- 1} α) + csc^{2} (cot^{- 1} β) = 36$ , then $α^{2} + β$ is ______.
Q23The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is
Q24 Let $A$ be a $3 \times 3$ matrix such that $X^{\dots}$
Q25 Let $S = {p_{1}, \dots$

JEE Main 2025 — Jan 24, Shift 1

Mathematics

Physics

Chemistry

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