JEE Main 2025 Question Paper (03-Apr-2025) (Shift-2)

Question 1

Let A = $\{-2, -1, 0, 1, 2, 3\}$. Let R be a relation on A defined by xRy if and only if y = max{x,1}. Let $l$ be the number of elements in R. Let n and $m$ 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

12

Answer

11

Answer

13

Answer

14

Question 2

If the domain of the function $f(x) = \log_7 (1-\log_4 (x^2-9x + 18))$ is $(\alpha, \beta)\cup(\gamma, \delta)$, then $\alpha + \beta + \gamma + \delta$ is equal to

Accepted Answer

18

Answer

15

Answer

16

Answer

17

Question 3

Let $f$ be a function such that $f (x)+3f (\frac{24}{x}) = 4x, x 
eq 0$. Then $f (3) + f (8)$ is equal to

Accepted Answer

11

Answer

10

Answer

12

Answer

13

Question 4

Let the equation $x(x + 2)(12-k) = 2$ have equal roots. Then the distance of the point $(k, \frac{k}{2})$ from the line $3x + 4y + 5 = 0$ is

Accepted Answer

15

Answer

$5\sqrt{3}$

Answer

12

Answer

$5\sqrt{5}$

Question 5

If $Z_1, Z_2, Z_3 \in C$ are the vertices of an equilateral triangle, whose centroid is $Z_0$, then $\sum_{k=1}^{3}(Z_k - Z_0)^2$ is equal to

Accepted Answer

0

Answer

1

Answer

$i$

Answer

-1