JEE Main 2025 Question Paper (04-Apr-2025) (Shift-2)

Question 1

Let the domains of the functions $f(x) = \log_4\log_3\log_7 (8-\log_2(x^2+4x+5))$ and $g(x) = \sin^{-1} \left(\frac{7x + 10}{x-2}\right)$ be $(\alpha, \beta)$ and $[\gamma, \delta]$, respectively. Then $\alpha^2+\beta^2+\gamma^2+\delta^2$ is equal to:

Accepted Answer

15

Answer

13

Answer

14

Answer

16

Question 2

Let $A = \{-3, -2, -1, 0, 1, 2, 3\}$ and $R$ be a relation on $A$ defined by $xRy$ if and only if $2x-y \in \{0, 1\}$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric relations, respectively. Then $l+m+n$ is equal to :

Accepted Answer

17

Answer

15

Answer

16

Answer

18

Question 3

Let the product of $\omega_1 = (8 + i)\sin	heta + (7+4i) \cos	heta$ and $\omega_2 = (1 + 8i)\sin	heta + (4+7i) \cos	heta$ be $\alpha + i\beta$, $i = \sqrt{-1}$. Let $p$ and $q$ be the maximum and the minimum values of $\alpha + \beta$ respectively. Then $p + q$ is equal to :

Accepted Answer

130

Answer

140

Answer

150

Answer

160

Question 4

Let the matrix $A = \begin{pmatrix} 1 & 0 & 0 \ 1 & 0 & 1 \ 0 & 1 & 0 \end{pmatrix}$ satisfy $A^n = A^{n-2}+A^2-I$ for $n \ge 3$. Then the sum of all the elements of $A^{50}$ is :

Accepted Answer

53

Answer

52

Answer

44

Answer

39

Question 5

If the sum of the first 20 terms of the series$ \frac{4\cdot1}{4+3\cdot1^2+1^4} + \frac{4\cdot2}{4+3\cdot2^2+2^4} + \frac{4\cdot3}{4+3\cdot3^2+3^4} + \frac{4\cdot4}{4+3\cdot4^2+4^4} + \dots $ is $ \frac{m}{n} $, where $m$ and $n$ are coprime, then $m + n$ is equal to :

Accepted Answer

421

Answer

420

Answer

422

Answer

423