JEE Main 2026 Question Paper (08-Apr-2026) (Shift 2)

Question 1

Consider the relation R on the set $\{-2, -1, 0, 1, 2\}$ defined by $(a, b) \in R$ if and only if $1 + ab > 0$. Then, among the statements :
I. The number of elements in R is 17
II. R is an equivalence relation

Accepted Answer

Only I is true

Answer

Only II is true

Answer

Both I and II are true

Answer

Neither I nor II is true

Question 2

The number of values of $z \in \mathbb{C}$, satisfying the equations $|z - (4 + 8i)| = \sqrt{10}$ and $|z - (3 + 5i)| + |z - (5 + 11i)| = 4\sqrt{5}$, is :

Accepted Answer

2

Answer

0

Answer

1

Answer

4

Question 3

If the system of linear equations : $x + y + z = 6$, $x + 2y + 5z = 10$, $2x + 3y + \lambda z = \mu$ has infinitely many solutions, then the value of $\lambda + \mu$ equals :

Accepted Answer

22

Answer

12

Answer

16

Answer

28

Question 4

Let $A = \begin{bmatrix} \alpha & 1 & 2 \ 2 & 3 & 0 \ 0 & 4 & 5 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 & 0 \ 0 & -5\alpha & 0 \ 0 & 4\alpha & -2\alpha \end{bmatrix} + 	ext{adj}(A)$. If $\det(B) = 66$, then $\det(	ext{adj}(A))$ equals :

Accepted Answer

441

Answer

289

Answer

361

Answer

529

Question 5

Let $\alpha = 3 + 4 + 8 + 9 + 13 + 14 + \dots$ upto 40 terms. If $(	an\beta)^{\frac{\alpha}{1020}}$ is a root of the equation $x^2 + x - 2 = 0$, $\beta \in \left(0, \frac{\pi}{2}ight)$, then $\sin^2\beta + 3\cos^2\beta$ is equal to :

Accepted Answer

2

Answer

$\frac{7}{4}$

Answer

$\frac{5}{2}$

Answer

$\frac{3}{2}$