JEE Main2025Jan 23, Shift 1

JEE Main 2025 — Jan 23, Shift 1

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

Mathematics

Q1The value of $\int_{e^{2}}^{e^{4}} \frac{1}{x} (\frac{e ^{((l o g_{e} x)^{2} + 1)^{- 1}}}{e ^{((l o g_{e} x)^{2} + 1)^{- 1}} + e ^{((6 - l o g_{e} x)^{2} + 1)^{- 1}}}) d x$ is
Q2Let $I (x) = \int \frac{d x}{( x - 11 ) ^{11/13} ( x + 15 ) ^{15/13}}$ . If $I (37) - I (24) = \frac{1}{4} (\frac{1}{b ^{1/13}} - \frac{1}{c ^{1/13}})$ , $b, c \in N$ , then $3 (b + c)$ is equal to
Q3 If the function $f (x) = ⎩ \dots$
Q4 If the line $3 x - 2 y + 12 = 0$ intersects the …
Q5 Let a curve $y = f (x)$ pass through the points $(0, 5)$ and $\dots$
Q6Let $f (x) = lo g_{e} x$ and $g (x) = \frac{x ^{4} - 2 x ^{3} + 3 x ^{2} - 2 x + 2}{2 x ^{2} - 2 x + 1}$ . Then the domain of $f \circ g$ is
Q7 Let the arc AC of a circle subtend a right angle at the centre O. If the point B on the arc AC divides the arc AC such that $\frac{length of arc AB \dots}{length of arc BC}$
Q8 If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to …
Q9 Let P be the foot of the perpendicular from the point $Q (10, - 3, - 1)$ on the line $7 \dots$
Q10 Let $2 \dots$
Q11 Let $R = {(1, 2), (2, 3), (3, \dots$
Q12The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is
Q13 Let the area of a $△ P QR$ with vertices $P (5, 4)$ , $Q (- 2,\dots$
Q14If $\frac{π}{2} \leq x \leq \frac{3 π}{4}$ , then $cos^{- 1} (\frac{12}{13} cos x + \frac{5}{13} sin x)$ is equal to
Q15The value of $(sin 7 0^{\circ}) (cot 1 0^{\circ} cot 7 0^{\circ} - 1)$ is
Q16 Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is …
Q17 Let the position vectors of the vertices A, B and C of a tetrahedron ABCD be $\hat{i} + 2 \dots$
Q18If A, B and $(adj (A^{- 1}) + adj (B^{- 1}))$ are non-singular matrices of same order, then the inverse of $A (adj (A^{- 1}) + adj (B^{- 1}))^{- 1} B$ is equal to
Q19If the system of equations $(λ - 1) x + (λ - 4) y + λ z = 5$ $λ x + (λ - 1) y + (λ - 4) z = 7$ $(λ + 1) x + (λ + 2) y - (λ + 2) z = 9$ has infinitely many solutions, then $λ^{2} + λ$ is equal to
Q20 One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5, when both the dice are thrown together, is …
Q21If the area of the larger portion bounded between the curves $x^{2} + y^{2} = 25$ and $y = ∣ x - 1∣$ is $\frac{1}{4} (bπ + c)$ , $b, c \in N$ , then $b + c$ is equal to ________
Q22The sum of all rational terms in the expansion of $(1 + 2^{1/3} + 3^{1/2})^{6}$ is equal to _______
Q23 Let the circle C touch the line $x - y + 1 = 0$ , have the centre on the positive x-axis, and cut o…
Q24 If the set of all values of $a$ , for which the equation $5 x^{3} - 15 \dots$
Q25If the equation $a (b - c) x^{2} + b (c - a) x + c (a - b) = 0$ has equal roots, where $a + c = 15$ and $b = \frac{36}{5}$ , then $a^{2} + c^{2}$ is equal to ________

Physics

Chemistry

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