JEE Main2025Jan 22, Shift 1

JEE Main 2025 — Jan 22, Shift 1

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

Mathematics

Q1The number of non-empty equivalence relations on the set ${1, 2, 3}$ is :
Q2 Let $f : R \to R$ be a twice differentiable function such that $f (x \dots$
Q3 Let the triangle PQR be the image of the triangle with vertices $(1, 3)$ , $(3, 1)$ and $(2, \dots$
Q4 Let $z_{1}, z_{\dots}$
Q5 Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of $16 ((sec^{- 1} x) \dots$
Q6 A coin is tossed three times. Let X denote the number of times a tail follows a head. If $μ$ and $σ^{2}$ denote the mean and variance of X, then the value of $\dots$
Q7Let $a_{1}, a_{2}, a_{3}, \dots$ be a G.P. of increasing positive terms. If $a_{1} a_{5} = 28$ and $a_{2} + a_{4} = 29$ , the $a_{6}$ is equal to
Q8 Let $L_{1} : \dots$
Q9The product of all solutions of the equation $e^{5 (l o g_{e} x)^{2} + 3} = x^{8}$ , $x > 0$ , is :
Q10If $r = 1 \sum n T_{r} = \frac{( 2 n - 1 ) ( 2 n + 1 ) ( 2 n + 3 ) ( 2 n + 5 )}{64}$ , then $n \to \infty lim r = 1 \sum n (\frac{1}{T _{r}})$ is equal to :
Q11 From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is 'M', is : …
Q12Let $x = x (y)$ be the solution of the differential equation $y^{2} d x + (x - \frac{1}{y}) d y = 0$ . If $x (1) = 1$ , then $x (\frac{1}{2})$ is :
Q13 Let the parabola $y = x^{2} + \dots$
Q14 A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point $(2, 5)$ and intersects the circle C at exactly two points. If the set of all possible values of r is the interval $(α, β)$ , then $\dots$
Q15Let for $f (x) = 7 tan^{8} x + 7 tan^{6} x - 3 tan^{4} x - 3 tan^{2} x$ , $I_{1} = \int_{0}^{π /4} f (x) d x$ and $I_{2} = \int_{0}^{π /4} x f (x) d x$ . Then $7 I_{1} + 12 I_{2}$ is equal to :
Q16 Let $f (x)$ be a real differentiable function such that $f (0) = 1$ and
Q17Let $A = {1, 2, 3, \dots, 10}$ and $B = {\frac{m}{n} : m, n \in A, m < n and g cd (m, n) = 1}$ . Then $n (B)$ is equal to :
Q18The area of the region, inside the circle $(x - 23)^{2} + y^{2} = 12$ and outside the parabola $y^{2} = 23 x$ is
Q19 Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is $\frac{m \dots}{n}$
Q20Let the foci of a hyperbola be $(1, 14)$ and $(1, - 12)$ . If it passes through the point $(1, 6)$ , then the length of its latus-rectum is :
Q21 Let the function $f (x) = {- 3 a x \dots$
Q22If $r = 0 \sum 5 \frac{^{11} C _{2 r + 1}}{2 r + 2} = \frac{m}{n}$ , $g cd (m, n) = 1$ , then $m - n$ is equal to ______.
Q23Let A be a square matrix of order 3 such that $det (A) = - 2$ and $det (3 adj (- 6 adj (3 A))) = 2^{m + n} \cdot 3^{mn}$ , $m > n$ . Then $4 m + 2 n$ is equal to _____.
Q24 Let $L_{1} : \dots$
Q25 Let $c$ be the projection vector of $\dots$

JEE Main 2025 — Jan 22, Shift 1

Mathematics

Physics

Chemistry

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