JEE Main2025Apr 7, Shift 1

JEE Main 2025 — Apr 7, Shift 1

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

Mathematics

Q1 $x \to 0^{+} lim \frac{tan ( 5 ( x ) ^{\frac{1}{3}} ) lo g _{e} ( 1 + 3 x ^{2} )}{( tan ^{- 1} 3 x ) ^{2} ( e ^{5 (x)^{\frac{4}{3}}} - 1 )}$ is equal to
Q2If the shortest distance between the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x}{1} = \frac{y}{α} = \frac{z - 5}{1}$ is $\frac{5}{6}$ , then the sum of all possible values of $α$ is
Q3 Let $x = - 1$ and $x = 2$ be the critical points of the function $\dots$
Q4The remainder when $((64)^{(64)})^{(64)}$ is divided by 7 is equal to
Q5 Let $P$ be the parabola, whose focus is $(- 2, 1)$ and directrix is $2 x + \dots$
Q6 Let $y = y (x)$ be the solution curve of the differential equation $x (x^{\dots}$
Q7 From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is …
Q8If for $θ \in [- \frac{π}{3}, 0]$ , the points $(x, y) = (3 tan (θ + \frac{π}{3}), 2 tan (θ + \frac{π}{6}))$ lie on $x y + α x + β y + γ = 0$ , then $α^{2} + β^{2} + γ^{2}$ is equal to :
Q9 Let $C_{1}$ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let $C^{\dots}$
Q10The integral $\int_{0}^{π} \frac{( x + 3 ) sin x}{1 + 3 cos ^{2} x} d x$ is equal to :
Q11 Among the statements $(S 1)$ : The set ${z \in C - {- i \dots$
Q12 The mean and standard deviation of 100 observations are 40 and 5.1, respectively, By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are $μ$ and $σ$ respectively, then $10 (μ + \dots$
Q13 Let $x_{1}, x_{\dots}$
Q14 Let the set of all values of $p \in R$ , for which both the roots of the equation $x^{2} \dots$
Q15Let $A$ be a $3 \times 3$ matrix such that $∣ adj (adj (adj A)) ∣ = 81$ . If $S = {n \in Z : (∣ adj (adj A) ∣)^{\frac{( n - 1 ) ^{2}}{2}} = ∣ A ∣^{(3 n^{2} - 5 n - 4)}}$ , then $n \in S \sum A^{(n^{2} + n)}$ is equal to
Q16If the area of the region bounded by the curves $y = 4 - \frac{x ^{2}}{4}$ and $y = \frac{x - 4}{2}$ is equal to $α$ , then $6 α$ equals
Q17 Let the system of equations : $2 x + 3 y + 5 z = \dots$
Q18 Let the line $L$ pass through $(1, 1, 1)$ and intersect the lines $\dots$
Q19 Let the angle $θ$ , $0 < θ < \dots$
Q20 Let $A B C$ be the triangle such that the equations of lines $A B$ and $A C$ be $3 \dots$
Q21The number of points of discontinuity of the function $f (x) = [\frac{x ^{2}}{2}] - [x]$ , $x \in [0, 4]$ , where $[\cdot]$ denotes the greatest integer function is _____
Q22 The number of relations on the set $A = {1, 2, 3}$ containing at most 6 elements including $(1,$
Q23 Consider the hyperbola $\frac{\dots}{a ^{2}}$
Q24The number of singular matrices of order 2, whose elements are from the set ${2, 3, 6, 9}$ is _____
Q25 For $n \geq 2$ , let $S_{n}$

JEE Main 2025 — Apr 7, Shift 1

Mathematics

Physics

Chemistry

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