JEE Main2025Jan 28, Shift 2

JEE Main 2025 — Jan 28, Shift 2

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

Mathematics

Q1 Bag $B_{1}$ contains 6 white and 4 blue balls, Bag $B_{\dots}$
Q2 Let A, B, C be three points in xy-plane, whose position vector are given by $3 \dots$
Q3 If the components of $a = α \dots$
Q4If $α + i β$ and $γ + i δ$ are the roots of $x^{2} - (3 - 2 i) x - (2 i - 2) = 0$ , $i = - 1$ , then $α γ + β δ$ is equal to :
Q5If the midpoint of a chord of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ is $(2, \frac{4}{3})$ , and the length of the chord is $\frac{2 α}{3}$ , then $α$ is :
Q6 Let $S$ be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set $S$ , one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is : …
Q7 Let $f$ be a real valued continuous function defined on the positive real axis such that $g (x) = \int_{\dots}$
Q8The square of the distance of the point $(\frac{15}{7}, \frac{32}{7}, 7)$ from the line $\frac{x + 1}{3} = \frac{y + 3}{5} = \frac{z + 5}{7}$ in the direction of the vector $\hat{i} + 4 \hat{j} + 7 \hat{k}$ is :
Q9The area of the region bounded by the curves $x (1 + y^{2}) = 1$ and $y^{2} = 2 x$ is :
Q10 Let $A = \dots$
Q11If $f (x) = \int \frac{1}{x ^{1/4} ( 1 + x ^{1/4} )} d x$ , $f (0) = - 6$ , then $f (1)$ is equal to :
Q12 Let $f : R \to R$ be a twice differentiable function such that $f (2)\dots$
Q13For positive integers $n$ , if $4 a_{n} = (n^{2} + 5 n + 6)$ and $S_{n} = k = 1 \sum n (\frac{1}{a _{k}})$ , then the value of $507 S_{2025}$ is :
Q14 Let $f : [0, 3] \to A$ be defined by
Q15Let $[x]$ denote the greatest integer less than or equal to $x$ . Then domain of $f (x) = sec^{- 1} (2 [x] + 1)$ is :
Q16If $r = 1 \sum 13 ⎩ ⎨ ⎧ \frac{1}{sin ( \frac{π}{4} + ( r - 1 ) \frac{π}{6} ) sin ( \frac{π}{4} + r \frac{π}{6} )} ⎭ ⎬ ⎫ = a 3 + b$ , $a, b \in Z$ , then $a^{2} + b^{2}$ is equal to :
Q17 Two equal sides of an isosceles triangle are along $- x + 2 y = 4$ and $x \dots$
Q18 Let the coefficients of three consecutive terms $T_{r}$ , $T^{\dots}$
Q19 If $A$ and $B$ are the points of intersection of the circle $x^{2} + \dots$
Q20 Let $f : R - {0} \to (\dots$
Q21The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is _____.
Q22Let $f (x) = n \to \infty lim r = 0 \sum n (\frac{tan ( x / 2 ^{r + 1} ) + tan ^{3} ( x / 2 ^{r + 1} )}{1 - tan ^{2} ( x / 2 ^{r + 1} )})$ . Then $x \to 0 lim \frac{e ^{x} - e ^{f (x)}}{( x - f ( x ))}$ is equal to ____.
Q23 The interior angles of a polygon with $n$ sides, are in an A.P. with common difference $6°$ . If the largest interior angle of the polygon is $219°$ , then $n$ is equal to _____. …
Q24 Let $A$ and $B$ be the two points of intersection of the line $y + 5 = \dots$
Q25 If $y = y (x)$ is the solution of the differential equation $\dots$

JEE Main 2025 — Jan 28, Shift 2

Mathematics

Physics

Chemistry

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