JEE Main2025Apr 2, Shift 2

JEE Main 2025 — Apr 2, Shift 2

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

Mathematics

Q1If the image of the point $P (1, 0, 3)$ in the line joining the points $A (4, 7, 1)$ and $B (3, 5, 3)$ is $Q (α, β, γ)$ , then $α + β + γ$ is equal to
Q2Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function. If $10 \int_{1}^{x} f (t) d t = 5 x f (x) - x^{5} - 9$ for all $x \geq 1$ , then the value of $f (3)$ is :
Q3 The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2} \dots$
Q4 Let $A = {1, 2, 3, \dots, 100}$ and $\dots$
Q5 If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is : …
Q6 The line $L_{1}$ is parallel to the vector $a \dots$
Q7 Let $(a, b)$ be the point of intersection of the curve $x^{2} = \dots$
Q8If the system of equation $2 x + λ y + 3 z = 5$ $3 x + 2 y - z = 7$ $4 x + 5 y + μ z = 9$ has infinitely many solutions, then $(λ^{2} + μ^{2})$ is equal to :
Q9If $θ \in [- \frac{7 π}{6}, \frac{4 π}{3}]$ , then the number of solutions of $3 cosec^{2} θ - 2 (3 - 1) cosec θ - 4 = 0$ , is equal to
Q10 Given three indentical bags each containing 10 balls, whose colours are as follows : A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is $p$ and if the balls is Green, the probability that it is from bag III is $q$ , then the value of $(\dots$
Q11If the mean and the variance of $6, 4, a, 8, b, 12, 10, 13$ are $9$ and $9.25$ respectively, then $a + b + ab$ is equal to :
Q12If the domain of the function $f (x) = \frac{1}{10 + 3 x - x ^{2}} + \frac{1}{x + ∣ x ∣}$ is $(a, b)$ , then $(1 + a)^{2} + b^{2}$ is equal to :
Q13 $4 \int_{0}^{1} (\frac{1}{3 + x ^{2} + 1 + x ^{2}}) d x - 3 lo g_{e} (3)$ is equal to :
Q14If $x \to 0 lim \frac{cos ( 2 x ) + a cos ( 4 x ) - b}{x ^{4}}$ is finite, then $(a + b)$ is equal to :
Q15If $r = 0 \sum 10 (\frac{1 0 ^{r + 1} - 1}{1 0 ^{r}})^{11} C_{r + 1} = \frac{α ^{11} - 1 1 ^{11}}{1 0 ^{10}}$ , then $α$ is equal to :
Q16 The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is : …
Q17 Let the point $P$ of the focal chord $P Q$ of the parabola $y^{\dots}$
Q18 Let $a = 2 \dots$
Q19 Let the area of the triangle formed by a straight line $L : x + b y + \dots$
Q20 Let $A$ be a $3 \times 3$ real matrix such that $A^{\dots}$
Q21 Let $y = y (x)$ be the solution of the differential equation $\dots$
Q22If the sum of the first 10 terms of the series $\frac{4 \cdot 1}{1 + 4 \cdot 1 ^{4}} + \frac{4 \cdot 2}{1 + 4 \cdot 2 ^{4}} + \frac{4 \cdot 3}{1 + 4 \cdot 3 ^{4}} + \dots$ is $\frac{m}{n}$ , where $g cd (m, n) = 1$ , then $m + n$ is equal to ________.
Q23If $y = cos (\frac{π}{3} + cos^{- 1} \frac{x}{2})$ , then $(x - y)^{2} + 3 y^{2}$ is equal to __________.
Q24 Let $A (4, - 2)$ , $B (1, 1)$ and $C \dots$
Q25 If the set of all $a \in R - {1}$ , for which the roots of the equation $(1 \dots$

JEE Main 2025 — Apr 2, Shift 2

Mathematics

Physics

Chemistry

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