JEE Main2025Jan 29, Shift 1

JEE Main 2025 — Jan 29, Shift 1

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

Mathematics

Q1 Let the line $x + y = 1$ meet the circle $x^{\dots}$
Q2 Let $M$ and $m$ respectively be the maximum and the minimum values of $f (x) = \dots$
Q3 Two parabolas have the same focus $(4, 3)$ and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at the points $A$ and $B$ , then $\dots$
Q4 Let $A B C$ be a triangle formed by the lines $7 x - 6 y + \dots$
Q5Let $a = 2 \hat{i} - \hat{j} + 3 \hat{k}$ , $b = 3 \hat{i} - 5 \hat{j} + \hat{k}$ and $c$ be a vector such that $a \times c = c \times b$ and $(a + c) \cdot (b + c) = 168.$ Then the maximum value of $∣ c ∣^{2}$ is :
Q6 Let $P$ be the set of seven digit numbers with sum of their digits equal to $11$ . If the numbers in $P$ are formed by using the digits $1, 2$ and $\dots$
Q7Let the area of the region ${(x, y) : 2 y \leq x^{2} + 3, y + ∣ x ∣ \leq 3, y \geq ∣ x - 1∣}$ be $A$ . Then $6 A$ is equal to:
Q8The least value of $n$ for which the number of integral terms in the Binomial expansion of $(37 + 1211)^{n}$ is $183$ , is :
Q9The number of solutions of the equation $(\frac{9}{x} - \frac{9}{x} + 2) (\frac{2}{x} - \frac{7}{x} + 3) = 0$ is :
Q10 Let $y = y (x)$ be the solution of the differential equation $cos x (lo\dots$
Q11Define a relation $R$ on the interval $[0, \frac{π}{2})$ by $x R y$ if and only if $sec^{2} x - tan^{2} y = 1.$ Then $R$ is :
Q12 Let the ellipse $E_{1} : \dots$
Q13 Consider an A.P. of positive integers, whose sum of the first three terms is $54$ and the sum of the first twenty terms lies between $1600$ and $1800.$ Then its $1 1^{\dots}$
Q14 Let $a = \dots$
Q15The value of $n \to \infty lim (k = 1 \sum n \frac{k ^{3} + 6 k ^{2} + 11 k + 5}{( k + 3 )!})$ is :
Q16The integral $80 \int_{0}^{π /4} \frac{sin θ + cos θ}{9 + 16 sin 2 θ} d θ$ is equal to :
Q17 Let $L_{1} : \dots$
Q18 Let $x_{1}, x_{\dots}$
Q19Let $∣ z_{1} - 8 - 2 i ∣ \leq 1$ and $∣ z_{2} - 2 + 6 i ∣ \leq 2, z_{1}, z_{2} \in C .$ Then the minimum value of $∣ z_{1} - z_{2} ∣$ is :
Q20 Let $A = [a_{ij}] \dots$
Q21 Let $f : (0, \infty) \to R$ be a twice differentiable function. If for some $\dots$
Q22Let $S = {m \in Z : A^{m^{2}} + A^{m} = 3 I - A^{- 6}}$ , where $A = [2 - 1 10] .$ Then $n (S)$ is equal to ______.
Q23 Let $[t]$ be the greatest integer less than or equal to $t .$ Then the least value of $p \in N$ for which $\dots$
Q24 The number of $6$ -letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is ______. …
Q25Let $S = {x : cos^{- 1} x = π + sin^{- 1} x + sin^{- 1} (2 x + 1)} .$ Then $x \in S \sum (2 x - 1)^{2}$ is equal to ______.

JEE Main 2025 — Jan 29, Shift 1

Mathematics

Physics

Chemistry

Attempt this as a full mock test