JEE Main 2025 Question Paper (02-Apr-2025) (Shift-2)

Question 1

If the domain of the function $f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}}$ is $(a, b)$, then $(1+a)^2+b^2$ is equal to :

Accepted Answer

26

Answer

25

Answer

29

Answer

30

Question 2

Let $A = \{1, 2, 3,...., 100\}$ and $R$ be a relation on $A$ such that $R = \{(a, b) : a=2b+1\}$. Let $(a_1, a_2), (a_2, a_3), (a_3, a_4), ...., (a_k, a_{k+1})$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer $k$, for which such a sequence exists, is equal to :

Accepted Answer

5

Answer

6

Answer

7

Answer

8

Question 3

Let $A$ be a $3	imes3$ real matrix such that $A^2(A-2I) - 4(A-I)=O$, where $I$ and $O$ are the identity and null matrices, respectively. If $A^5=\alpha A^2+\beta A+\gamma I$, where $\alpha$, $\beta$, and $\gamma$ are real constants, then $\alpha+ \beta + \gamma$ is equal to :

Accepted Answer

12

Answer

4

Answer

20

Answer

76

Question 4

If the system of equations $2x + \lambda y + 3z = 5$ $3x+2y-z=7$ $4x + 5y + \mu z = 9$ has infinitely many solutions, then $(\lambda^2+ \mu^2)$ is equal to :

Accepted Answer

26

Answer

18

Answer

22

Answer

30

Question 5

The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the A.P. is :

Accepted Answer

4

Answer

6

Answer

8

Answer

10