JEE Main 2026 Question Paper (02-Apr-2026) (Shift 1)

Question 1

Let $\alpha, \alpha+2, \alpha \in \mathbf{Z}$, be the roots of the quadratic equation
$x(x+2) + (x+1)(x+3) + (x+2)(x+4) + \dots + (x+n-1)(x+n+1) = 4n$ for some $n \in \mathbf{N}$.
Then $n+\alpha$ is equal to :

Accepted Answer

2

Answer

0

Answer

1

Answer

3

Question 2

Let $x$ and $y$ be real numbers such that $50\left(\frac{2x}{1+3i} - \frac{y}{1-2i}\right) = 31 + 17i$, $i = \sqrt{-1}$. Then the value of $10(x-3y)$ is :

Accepted Answer

75

Answer

20

Answer

31

Answer

35

Question 3

Let $\alpha, \beta \in \mathbf{R}$ be such that the system of linear equations$x+2y+z=5$$2x+y+\alpha z=5$$8x+4y+\beta z=18$has no solution. Then $\frac{\beta}{\alpha}$ is equal to :

Accepted Answer

4

Answer

$-4$

Answer

8

Answer

$-8$

Question 4

Let $A = \begin{bmatrix} 1 & 2 \ 1 & \alpha \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 3 \ \beta & 2 \end{bmatrix}$. If $A^2 - 4A + I = O$ and $B^2 - 5B - 6I = O$, then among the two statements :(S1): $[(B-A)(B+A)]^T = \begin{bmatrix} 13 & 15 \ 7 & 10 \end{bmatrix}$and(S2): $\det(	ext{adj}(A+B)) = -5$,

Accepted Answer

only (S2) is correct

Answer

only (S1) is correct

Answer

both (S1) and (S2) are correct

Answer

both (S1) and (S2) are wrong

Question 5

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in A $\cap$ B, which are divisible by 3, is :

Accepted Answer

5

Answer

4

Answer

6

Answer

7