JEE Main2025Apr 4, Shift 2

JEE Main 2025 — Apr 4, Shift 2

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

Mathematics

Q1 Let $a > 0$ . If the function $f (x) = 6 \dots$
Q2 Let $f$ be a differentiable function on $R$ such that $f (2) = 1$ , $\dots$
Q3The sum of the infinite series $cot^{- 1} (\frac{7}{4}) + cot^{- 1} (\frac{19}{4}) + cot^{- 1} (\frac{39}{4}) + cot^{- 1} (\frac{67}{4}) + \dots$ is :-
Q4 Let $A = {- 3, - 2, - 1, 0, 1, \dots$
Q5 Let the product of $ω_{1} = (8 \dots$
Q6 Let the values of $p$ , for which the shortest distance between the lines $\frac{x \dots}{3}$
Q7 The axis of a parabola is the line $y = x$ and its vertex and focus are in the first quadrant at distances $2 \dots$
Q8 Let the domains of the functions $f (x) = lo g_{4}$
Q9 A line passing through the point $A (- 2, 0)$ , touches the parabola $P : y^{\dots}$
Q10 Let the sum of the focal distances of the point $P (4, 3)$ on the hyperbola $H : \dots$
Q11Let the matrix $A = 100101010$ satisfy $A^{n} = A^{n - 2} + A^{2} - I$ for $n \geq 3$ . Then the sum of all the elements of $A^{50}$ is :-
Q12 If the sum of the first 20 terms of the series $4 + 3 \cdot 1 ^{\dots}$
Q13If $1^{2} \cdot^{15} C_{1} + 2^{2} \cdot^{15} C_{2} + 3^{2} \cdot^{15} C_{3} + \dots + 1 5^{2} \cdot^{15} C_{15} = 2^{m} \cdot 3^{n} \cdot 5^{k}$ , where $m, n, k \in N$ , then $m + n + k$ is equal to :-
Q14 Let for two distinct values of $p$ the lines $y = x + p$ touch the ellipse $\dots$
Q15 Consider two sets $A$ and $B$ , each containing three numbers in A.P. Let the sum and the product of the elements of $A$ be 36 and $p$ respectively and the sum and the product of the elements of $\dots$
Q16 If a curve $y = y (x)$ passes through the point $(1, \dots$
Q17 The centre of a circle $C$ is at the centre of the ellipse $E : a ^{\dots}$
Q18Let $f (x) + 2 f (\frac{1}{x}) = x^{2} + 5$ and $2 g (x) - 3 g (\frac{1}{2}) = x, x > 0$ . If $α = \int_{1}^{2} f (x) d x$ and $β = \int_{1}^{2} g (x) d x$ , then the value of $9 α + β$ is :
Q19 Let $A$ be the point of intersection of the lines $L_{1} : \dots$
Q20 Let the mean and the standard deviation of the observation $2, 3, 3, 4, 5, 7, a, b$ be 4 and …
Q21If $α$ is a root of the equation $x^{2} + x + 1 = 0$ and $k = 1 \sum n (α^{k} + \frac{1}{α ^{k}})^{2} = 20$ , then $n$ is equal to ______
Q22If $\int \frac{( 1 + x ^{2} + x ) ^{10}}{( 1 + x ^{2} - x ) ^{9}} d x = \frac{1}{m} ((1 + x^{2} + x)^{n} (n 1 + x^{2} - x)) + C$ , where $C$ is the constant of integration and $m, n \in N$ , then $m + n$ is equal to
Q23 A card from a pack of 52 cards is lost. From the remaining 51 cards, $n$ cards are drawn and are found to be spades. If the probability of the lost card to be a spade is $\frac{11 \dots}{50}$
Q24Let $m$ and $n$ , ( $m < n$ ) be two 2-digit numbers. Then the total numbers of pairs $(m, n)$ , such that $g cd (m, n) = 6$ , is ______
Q25 Let the three sides of a triangle $A B C$ be given by the vectors $2 \hat{i} - \dots$

JEE Main 2025 — Apr 4, Shift 2

Mathematics

Physics

Chemistry

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