JEE Main2025Apr 4, Shift 1

JEE Main 2025 — Apr 4, Shift 1

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

Mathematics

Q1Let $f, g : (1, \infty) \to R$ be defined as $f (x) = \frac{2 x + 3}{5 x + 2}$ and $g (x) = \frac{2 - 3 x}{1 - x}$ . If the range of the function $f \circ g : [2, 4] \to R$ is $[α, β]$ , then $\frac{1}{β - α}$ is equal to
Q2 Consider the sets $A = {(x, y) \in R \times \dots$
Q3Let $A = {1, 6, 11, 16, \dots}$ and $B = {9, 16, 23, 30, \dots}$ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then $n (A \cup B)$ is
Q4 For an integer $n \geq 2$ , if the arithmetic mean of all coefficients in the binomial expansion of $(x + y \dots$
Q5 The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is: …
Q6Let the shortest distance between the lines $\frac{x - 3}{3} = \frac{y - α}{- 1} = \frac{z - 3}{1}$ and $\frac{x + 3}{- 3} = \frac{y + 7}{2} = \frac{z - β}{4}$ be $330$ . Then the positive value of $5 α + β$ is
Q7If $x \to 1^{+} lim \frac{( x - 1 ) ( 6 + λ cos ( x - 1 )) + μ sin ( 1 - x )}{( x - 1 ) ^{3}} = - 1$ , where $λ, μ \in R$ , then $λ + μ$ is equal to
Q8 Let $f : [0, \infty) \to R$ be differentiable function such that $\dots$
Q9 Let $A$ and $B$ be two distinct points on the line $L : \dots$
Q10 Let $f : R \to R$ be a continuous function satisfying $f (0) \dots$
Q11 $1 + 3 + 5^{2} + 7 + 9^{2} + \dots$ upto 40 terms is equal to
Q12 In the expansion of $(3 2 \dots$
Q13Considering the principal values of the inverse trigonometric functions, $sin^{- 1} (\frac{3}{2} x + \frac{1}{2} 1 - x^{2}), - \frac{1}{2} < x < \frac{1}{2}$ , is equal to
Q14 Consider two vectors $u = 3 \dots$
Q15 Let the three sides of a triangle are on the lines $4 x - 7 y + 10 = 0\dots$
Q16The value of $\int_{- 1}^{1} \frac{( 1 + ∣ x ∣ - x ) e ^{x} + ( ∣ x ∣ - x ) e ^{- x}}{e ^{x} + e ^{- x}} d x$ is equal to
Q17The length of the latus-rectum of the ellipse, whose foci are $(2, 5)$ and $(2, - 3)$ and eccentricity is $\frac{4}{5}$ , is
Q18 Consider the equation $x^{2} + 4 x - \dots$
Q19 A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is …
Q20If $10 sin^{4} θ + 15 cos^{4} θ = 6$ , then the value of $\frac{27 csc ^{6} θ + 8 sec ^{6} θ}{16 sec ^{8} θ}$ is:
Q21If the area of the region ${(x, y) : ∣ x - 5∣ \leq y \leq 4 x}$ is $A$ , then $3 A$ is equal to ____.
Q22 Let $A = \dots$
Q23Let $A = {z \in C : ∣ z - 2 - i ∣ = 3}$ , $B = {z \in C : Re (z - i z) = 2}$ and $S = A \cap B$ . Then $z \in S \sum ∣ z ∣^{2}$ is equal to ____.
Q24 Let $C$ be the circle $x^{2} + (\dots$
Q25 Let $m$ and $n$ be the number of points at which the function $f (x) = max {x \dots$

JEE Main 2025 — Apr 4, Shift 1

Mathematics

Physics

Chemistry

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