JEE Main2025Apr 3, Shift 1

JEE Main 2025 — Apr 3, Shift 1

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

Mathematics

Q1Let $A$ be a matrix of order $3 \times 3$ and $∣ A ∣ = 5$ . If $∣2 adj (3 A adj (2 A)) ∣ = 2^{α} \cdot 3^{β} \cdot 5^{γ}$ , $α, β, γ \in N$ , then $α + β + γ$ is equal to
Q2 Let a line passing through the point $(4, 1, 0)$ intersect the line $L_{1}$
Q3 Let $α$ and $β$ be the roots of $x^{2} \dots$
Q4The sum of all rational terms in the expansion of $(2 + 3)^{8}$ is
Q5 Let $A = {- 3, - 2, - 1, 0, 1, \dots$
Q6 A line passing through the point $P (5,$
Q7The sum $1 + 3 + 11 + 25 + 45 + 71 + \dots$ upto 20 terms, is equal to
Q8If the domain of the function $f (x) = lo g_{e} (\frac{2 x - 3}{5 + 4 x}) + sin^{- 1} (\frac{4 + 3 x}{2 - x})$ is $[α, β)$ , then $α^{2} + 4 β$ is equal to
Q9If $r = 1 \sum 9 (\frac{r + 3}{2 ^{r}})^{9} C_{r} = α (\frac{3}{2})^{9} - β$ , $α, β \in N$ , then $(α + β)^{2}$ is equal to
Q10The number of solutions of the equation $2 x + 3 tan x = π$ , $x \in [- 2 π, 2 π] - {\pm \frac{π}{2}, \pm \frac{3 π}{2}}$ is
Q11If $y (x) = sin x cos x sin x + cos x + 1 272827111, x \in R$ , then $\frac{d ^{2} y}{d x ^{2}} + y$ is equal to
Q12 Let $g$ be a differentiable function such that $\int_{0}^{x}$
Q13 A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $L_{1} : 2 \dots$
Q14Let $z \in C$ be such that $\frac{z ^{2} + 3 i}{z - 2 + i} = 2 + 3 i$ . Then the sum of all possible values of $z^{2}$ is
Q15Let $f (x) = \int x^{3} 3 - x^{2} d x$ . If $5 f (2) = - 4$ , then $f (1)$ is equal to
Q16Let $a_{1}, a_{2}, a_{3}, \dots$ be a G.P. of increasing positive numbers. If $a_{3} a_{5} = 729$ and $a_{2} + a_{4} = \frac{111}{4}$ , then $24 (a_{1} + a_{2} + a_{3})$ is equal to
Q17 Let the domain of the function $f (x) = lo g_{2}$
Q18The radius of the smallest circle which touches the parabolas $y = x^{2} + 2$ and $x = y^{2} + 2$ is
Q19Let $f (x) = ⎩ ⎨ ⎧ (1 + a x)^{1/ x}, x < 0 1 + b, x = 0 \frac{( x + 4 ) ^{1/2} - 2}{( x + c ) ^{1/3} - 2}, x > 0$ be continuous at $x = 0$ . Then $e^{a} b c$ is equal to
Q20 Line $L_{1}$ passes through the point $(1, 2, \dots$
Q21 All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by $W_{n} \dots$
Q22 Let the product of the focal distances of the point $P (4, 2 3 \dots$
Q23 Let $a = \dots$
Q24If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 1 0^{n}$ ; $m, n \in {1, 2, 3, \dots, 9}$ , then $m + n$ is equal to _____
Q25The area of the region bounded by the curve $y = max {∣ x ∣, x ∣ x - 2∣}$ , the x-axis and the lines $x = - 2$ and $x = 4$ is equal to ______.

JEE Main 2025 — Apr 3, Shift 1

Mathematics

Physics

Chemistry

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