JEE Main2025Jan 22, Shift 2

JEE Main 2025 — Jan 22, Shift 2

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

Mathematics

Q1 Let $α$ , $β$ , $γ$ and $δ$ be the coefficients of
Q2 In a group of 3 girls and 4 boys, there are two boys $B_{1}$ and $B_{\dots}$
Q3 Let $P (4, 4 3 \dots$
Q4 For a $3 \times 3$ matrix $M$ , let trace $(M)$ denote the sum of all the diagonal elements of $\dots$
Q5 Suppose that the number of terms in an A.P. is $2 k$ , $k \in N$ . If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then $\dots$
Q6 Let a line pass through two distinct points $P (- 2, - 1, 3)$ and $Q$ , and be parallel to the vector $3 \dots$
Q7If $x \to \infty lim ((\frac{e}{1 - e}) (\frac{1}{e} - \frac{x}{1 + x}))^{x} = α$ , then the value of $\frac{lo g _{e} α}{1 + lo g _{e} α}$ equals :
Q8Let $f (x) = \int_{0}^{x^{2}} \frac{t ^{2} - 8 t + 15}{e ^{t}} d t$ , $x \in R$ . Then the numbers of local maximum and local minimum points of $f$ , respectively, are :
Q9The perpendicular distance, of the line $\frac{x - 1}{2} = \frac{y + 2}{- 1} = \frac{z + 3}{2}$ from the point $P (2, - 10, 1)$ , is :
Q10If $x = f (y)$ is the solution of the differential equation $(1 + y^{2}) + (x - 2 e^{t a n^{- 1} y}) \frac{d y}{d x} = 0$ , $y \in (- \frac{π}{2}, \frac{π}{2})$ with $f (0) = 1$ , then $f (\frac{1}{3})$ is equal to :
Q11If $\int e^{x} (\frac{x sin ^{- 1} x}{1 - x ^{2}} + \frac{sin ^{- 1} x}{( 1 - x ^{2} ) ^{3/2}} + \frac{x}{1 - x ^{2}}) d x = g (x) + C$ , where $C$ is the constant of integration, then $g (\frac{1}{2})$ equals :
Q12 Let $α_{θ}$ and $β_{\dots}$
Q13Let $A = {1, 2, 3, 4}$ and $B = {1, 4, 9, 16}$ . Then the number of many-one functions $f : A \to B$ such that $1 \in f (A)$ is equal to :
Q14 If the system of linear equations : $x + y + 2 z = 6\dots$
Q15 Let $a$ and $\dots$
Q16 Let $E : a ^{2} \dots$
Q17 If $A$ and $B$ are two events such that $P (A \cap B) \dots$
Q18The sum of all values of $θ \in [0, 2 π]$ satisfying $2 sin^{2} θ = cos 2 θ$ and $2 cos^{2} θ = 3 sin θ$ is
Q19Let the curve $z (1 + i) + \overset{z}{ˉ} (1 - i) = 4$ , $z \in C$ , divide the region $∣ z - 3∣ \leq 1$ into two parts of areas $α$ and $β$ . Then $∣ α - β ∣$ equals :
Q20The area of the region enclosed by the curves $y = x^{2} - 4 x + 4$ and $y^{2} = 16 - 8 x$ is :
Q21 Let $y = f (x)$ be the solution of the differential equation $\dots$
Q22 Let $A (6, 8)$ , $B (10 cos α, - 10 \dots$
Q23 Let the distance between two parallel lines be 5 units and a point $P$ lie between the lines at a unit distance from one of them. An equilateral triangle $P QR$ is formed such that $Q$ lies on one of the parallel lines, while $\dots$
Q24If $r = 1 \sum 30 \frac{r ^{2} ( r 30 ) ^{2}}{( r - 1 30 )} = α \times 2^{29}$ , then $α$ is equal to ______.
Q25Let $A = {1, 2, 3}$ . The number of relations on $A$ , containing $(1, 2)$ and $(2, 3)$ , which are reflexive and transitive but not symmetric, is ______.

JEE Main 2025 — Jan 22, Shift 2

Mathematics

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Chemistry

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