JEE Main2025Jan 24, Shift 2

JEE Main 2025 — Jan 24, Shift 2

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

Mathematics

Q1The equation of the chord, of the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1$ , whose mid-point is $(3, 1)$ is :
Q2The function $f : (- \infty, \infty) \to (- \infty, 1)$ , defined by $f (x) = \frac{2 ^{x} - 2 ^{- x}}{2 ^{x} + 2 ^{- x}}$ is :
Q3If $α > β > γ > 0$ , then the expression $cot^{- 1} {β + \frac{( 1 + β ^{2} )}{( α - β )}} + cot^{- 1} {γ + \frac{( 1 + γ ^{2} )}{( β - γ )}} + cot^{- 1} {α + \frac{( 1 + α ^{2} )}{( γ - α )}}$ is equal to:
Q4 Let $f : (0, \infty) \to R$ be a function which is differentiable at all points of its domain and satisfies the condition $\dots$
Q5Let $A = {x \in (0, π) - {\frac{π}{2}} : lo g_{(2/ π)} ∣ sin x ∣ + lo g_{(2/ π)} ∣ cos x ∣ = 2}$ and $B = {x \geq 0 : x (x - 4) - 3∣ x - 2∣ + 6 = 0}$ . Then $n (A \cup B)$ is equal to:
Q6 Let the position vectors of three vertices of a triangle be $4 p + \dots$
Q7 Let $[x]$ denote the greatest integer function, and let $m$ and $n$ respectively be the numbers of the points, where the function $f (x) \dots$
Q8 Let the points $(\frac{11}{2}, \dots$
Q9In an arithmetic progression, if $S_{40} = 1030$ and $S_{12} = 57$ , then $S_{30} - S_{10}$ is equal to:
Q10If $7 = 5 + \frac{1}{7} (5 + α) + \frac{1}{7 ^{2}} (5 + 2 α) + \frac{1}{7 ^{3}} (5 + 3 α) + \dots \infty$ , then the value of $α$ is:
Q11If the system of equations $x + 2 y - 3 z = 2$ $2 x + λ y + 5 z = 5$ $14 x + 3 y + μ z = 33$ has infinitely many solutions, then $λ + μ$ is equal to:
Q12 Let $(2, 3)$ be the largest open interval in which the function $f (x) = 2 lo\dots$
Q13 Suppose $A$ and $B$ are the coefficients of $3 0^{th}$ and …
Q14Let $a = 3 \hat{i} - \hat{j} + 2 \hat{k}$ , $b = a \times (\hat{i} - 2 \hat{k})$ and $c = b \times \hat{k}$ . Then the projection of $c - 2 \hat{j}$ on $a$ is:
Q15For some $a, b$ , let $f (x) = a + \frac{sin x}{x} 1 b a 1 + \frac{sin x}{x} b a 1 b + \frac{sin x}{x}$ , $x \neq = 0$ , $x \to 0 lim f (x) = λ + μ a + ν b$ . Then $(λ + μ + ν)^{2}$ is equal to:
Q16 Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to: …
Q17The area of the region enclosed by the curves $y = e^{x}$ , $y = ∣ e^{x} - 1∣$ and the y-axis is:
Q18The number of real solution(s) of the equation $x^{2} + 3 x + 2 = min {∣ x - 3∣, ∣ x + 2∣}$ is :
Q19 Let $A = [a_{ij}] \dots$
Q20If the equation of the parabola with vertex $V (\frac{3}{2}, 3)$ and the directrix $x + 2 y = 0$ is $α x^{2} + β y^{2} - γ x y - 30 x - 60 y + 225 = 0$ , then $α + β + γ$ is equal to:
Q21Number of functions $f : {1, 2, \dots, 100} \to {0, 1}$ , that assign $1$ to exactly one of the positive integers less than or equal to $98$ , is equal to ______.
Q22 Let $P$ be the image of the point $Q (7, - 2, 5)$ in the line $L : \dots$
Q23 Let $y = y (x)$ be the solution of the differential equation $2 cos x \dots$
Q24 Let $H_{1} : \dots$
Q25 If $\int x ^{\dots}$

JEE Main 2025 — Jan 24, Shift 2

Mathematics

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Chemistry

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