JEE Main2025Apr 3, Shift 2

JEE Main 2025 — Apr 3, Shift 2

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

Mathematics

Q1 Let $f : R \to R$ be a function defined by $f (x) \dots$
Q2 Each of the angles $β$ and $γ$ that a given line makes with the positive y- and z-axes, respectively, is half of the angle that this line makes with the positive x-axes. Then the sum of all possible values of the angle $β$ is …
Q3If the four distinct points $(4, 6)$ , $(- 1, 5)$ , $(0, 0)$ and $(k, 3 k)$ lie on a circle of radius $r$ , then $10 k + r^{2}$ is equal to
Q4 Let the Mean and Variance of five observations $x_{1} = 1$ , $\dots$
Q5 Consider the lines $x (3 λ + 1) + y (7 λ + \dots$
Q6 Let $A = {- 2, - 1, 0, 1, 2, 3 \dots$
Q7Let the equation $x (x + 2) (12 - k) = 2$ have equal roots. Then the distance of the point $(k, \frac{k}{2})$ from the line $3 x + 4 y + 5 = 0$ is
Q8 Line $L_{1}$ of slope $2$ and line $\dots$
Q9The integral $\int_{0}^{π} \frac{8 x d x}{4 cos ^{2} x + sin ^{2} x}$ is equal to
Q10Let $f$ be a function such that $f (x) + 3 f (\frac{24}{x}) = 4 x$ , $x \neq = 0$ . Then $f (3) + f (8)$ is equal to
Q11The area of the region ${(x, y) : ∣ x - y ∣ \leq y \leq 4 x}$ is
Q12If the domain of the function $f (x) = lo g_{7} (1 - lo g_{4} (x^{2} - 9 x + 18))$ is $(α, β) \cup (γ, δ)$ , then $α + β + γ + δ$ is equal to
Q13 If the probability that the random variable $X$ takes the value $x$ is given by $P (X = x)\dots$
Q14Let $y = y (x)$ be the solution of the differential equation $\frac{d y}{d x} + 3 (tan^{2} x) y + 3 y = sec^{2} x$ , $y (0) = \frac{1}{3} + e^{3}$ . Then $y (\frac{π}{4})$ is equal to
Q15If $z_{1}, z_{2}, z_{3} \in C$ are the vertices of an equilateral triangle, whose centroid is $z_{0}$ , then $k = 1 \sum 3 (z_{k} - z_{0})^{2}$ is equal to
Q16The number of solutions of equation $(4 - 3) sin x - 23 cos^{2} x = \frac{- 4}{1 + 3}$ , $x \in [- 2 π, \frac{5 π}{2}]$ is
Q17 Let $C$ be the circle of minimum area enclosing the ellipse $E : a ^{\dots}$
Q18The shortest distance between the curves $y^{2} = 8 x$ and $x^{2} + y^{2} + 12 y + 35 = 0$ is:
Q19The distance of the point $(7, 10, 11)$ from the line $\frac{x - 4}{1} = \frac{y - 4}{0} = \frac{z - 2}{3}$ along the line $\frac{x - 9}{2} = \frac{y - 13}{3} = \frac{z - 17}{6}$ is
Q20The sum $1 + \frac{1 + 3}{2 !} + \frac{1 + 3 + 5}{3 !} + \frac{1 + 3 + 5 + 7}{4 !} + \dots$ upto $\infty$ terms, is equal to
Q21 Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $A = \dots$
Q22Let $(1 + x + x^{2})^{10} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{20} x^{20}$ . If $(a_{1} + a_{3} + a_{5} + \dots + a_{19}) - 11 a_{2} = 121 k$ , then $k$ is equal to ______.
Q23If $x \to 0 lim (\frac{tan x}{x})^{1/ x^{2}} = p$ , then $96 lo g_{e} p$ is equal to ____
Q24Let $a = \hat{i} + 2 \hat{j} + \hat{k}$ , $b = 3 \hat{i} - 3 \hat{j} + 3 \hat{k}$ , $c = 2 \hat{i} - \hat{j} + 2 \hat{k}$ and $d$ be a vector such that $b \times d = c \times d$ and $a \cdot d = 4$ . Then $∣ (a \times d) ∣^{2}$ is equal to ______.
Q25If the equation of the hyperbola with foci $(4, 2)$ and $(8, 2)$ is $3 x^{2} - y^{2} - α x + β y + γ = 0$ , then $α + β + γ$ is equal to ______.

JEE Main 2025 — Apr 3, Shift 2

Mathematics

Physics

Chemistry

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