JEE Main 2025 Question Paper (02-Apr-2025) (Shift-1)

Question 1

Let the focal chord PQ of the parabola $y^2=4x$ make an angle of $60^\circ$ with the positive x-axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y-axis at the point (0, $\alpha$), then $5\alpha^2$ is equal to :

Accepted Answer

15

Answer

20

Answer

25

Answer

30

Question 2

Let z be a complex number such that $|z|=1$. If $\frac{2 + k^2z}{k+z} = kz$, $k \in R$, then the maximum distance of $k + ik^2$ from the circle $|z -(1+2i)|=1$ is:

Accepted Answer

$\sqrt{5}+1$

Answer

$\sqrt{3}+1$

Answer

2

Answer

3

Question 3

If $	heta \in [ - 2\pi, 2\pi]$, then the number of solutions of $2\sqrt{2}\cos^2	heta+(2-\sqrt{6}) \cos	heta-\sqrt{3}=0$, is equal to:

Accepted Answer

8

Answer

6

Answer

10

Answer

12

Question 4

If S and S' are the foci of the ellipse $\frac{x^2}{18} + \frac{y^2}{9} = 1$ and P be a point on the ellipse, then min $(SP \cdot S'P)$ + max $(SP \cdot S'P)$ is equal to :

Accepted Answer

27

Answer

$3(1+\sqrt{2})$

Answer

$3(6+\sqrt{2})$

Answer

9

Question 5

Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be 5, 6 and 7 square units respectively. Then the area (in square units) of the $	riangle BCD$ is equal to :

Accepted Answer

$\sqrt{110}$

Answer

$7\sqrt{3}$

Answer

12

Answer

$\sqrt{340}$