JEE Main 2025 Question Paper (07-Apr-2025) (Shift-2)

Question 1

Let $A = \{(\alpha, \beta) \varepsilon R	imes R: |\alpha-1|\leq 4$ and $|\beta-5|\leq6\}$ and $B = \{(\alpha, \beta) \in R 	imes R : 16(\alpha-2)^2+9(\beta-6)^2 \leq 144 \}$.Then

Accepted Answer

B ⊂ A

Answer

A ⊂ B

Answer

A ∪ B = {(x, y) : -4 ≤ x ≤ 4, -1 ≤ y ≤ 11}

Answer

neither A ⊂ B nor B ⊂ A

Question 2

If the range of the function $f(x) = \frac{5-x}{x^2-3x + 2}$ , $x 
eq 1, 2$, is $(-\infty, \alpha] \cup [\beta, \infty)$, then $\alpha^2 + \beta^2$is equal to :

Accepted Answer

194

Answer

188

Answer

190

Answer

192

Question 3

The number of real roots of the equation $x |x-2|+3|x-3|+1=0$ is:

Accepted Answer

1

Answer

2

Answer

3

Answer

4

Question 4

If the locus of $z \in C$, such that Re $\left(\frac{z-1}{2z + i}\right)$+Re $\left(\frac{\bar{z}-1}{2\bar{z}-i}\right)$ = 2, is a circle of radius r andcenter (a, b), then $\frac{15ab}{r^2}$ is equal to :

Accepted Answer

18

Answer

12

Answer

16

Answer

24

Question 5

Let the system of equations : $x+5y-z=1$, $4x+3y-3z=7$ , $24x + \lambda y + \lambda z = \mu$$\lambda, \mu \in R$, have infinitely many solutions. Then the number of the solutions of this system,if x, y, z are integers and satisfy $7\leq x+y+z\leq77$, is :

Accepted Answer

3

Answer

4

Answer

5

Answer

6