JEE Main 2026 Question Paper (05-Apr-2026) (Shift 1)

Question 1

Let $a, b \in \mathbb{C}$. Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$. If $\beta - \alpha = \sqrt{11}$ and $\beta^2 - \alpha^2 = 3i\sqrt{11}$, then $(\beta^3 - \alpha^3)^2$ is equal to:

Accepted Answer

176

Answer

160

Answer

194

Answer

187

Question 2

Let the sum of the first $n$ terms of an A.P. be $3n^2 + 5n$. Then the sum of squares of the first 10 terms of the A.P. is:

Accepted Answer

15220

Answer

10220

Answer

12860

Answer

19780

Question 3

Let A be a $3 	imes 3$ matrix such that$A^T \begin{bmatrix} 1 \ 0 \ 1 \end{bmatrix} = \begin{bmatrix} 5 \ 2 \ 2 \end{bmatrix}$, $A^T \begin{bmatrix} 0 \ 0 \ 1 \end{bmatrix} = \begin{bmatrix} 3 \ 1 \ 1 \end{bmatrix}$, $A \begin{bmatrix} 1 \ 0 \ 1 \end{bmatrix} = \begin{bmatrix} 3 \ 4 \ 4 \end{bmatrix}$ and $A \begin{bmatrix} 0 \ 0 \ 1 \end{bmatrix} = \begin{bmatrix} 1 \ 3 \ 1 \end{bmatrix}$.If $	ext{det}(A) = 1$, then $	ext{det}(	ext{adj}(A^2 + A))$ is equal to:

Accepted Answer

64

Answer

16

Answer

25

Answer

49

Question 4

Consider the system of linear equations in $x, y, z$:
$x + 2y + tz = 0$,
$6x + y + 5tz = 0$,
$3x + t^2y + f(t)z = 0$,
where $f: \mathbb{R} \to \mathbb{R}$ is a differentiable function. If this system has infinitely many solutions for all $t \in \mathbb{R}$, then $f$

Accepted Answer

is strictly increasing on $\mathbb{R}$

Answer

is a constant function

Answer

is strictly decreasing on $\mathbb{R}$

Answer

has two critical points

Question 5

$\sum_{n=1}^{10} \left( \frac{528}{n(n+1)(n+2)} \right)$ is equal to:

Accepted Answer

130

Answer

65

Answer

220

Answer

440