JEE Main 2026 Question Paper (02-Apr-2026) (Shift 2)

Question 1

Let $\alpha, \beta$ be the roots of the equation $x^2 - 3x + r = 0$, and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2 + 3x + r = 0$.
If the roots of the equation $x^2 + 6x = m$ are $2\alpha + \beta + 2r$ and $\alpha - 2\beta - \frac{r}{2}$, then $m$ is equal to :

Accepted Answer

567

Answer

-135

Answer

-567

Answer

135

Question 2

Let the circles $C_1 : |z| = r$ and $C_2 : |z - 3 - 4i| = 5$, $z \in \mathbb{C}$, be such that $C_2$ lies within $C_1$. If $z_1$ moves on $C_1$, $z_2$ moves on $C_2$ and $\min|z_1 - z_2| = 2$, then $\max|z_1 - z_2|$ is equal to :

Accepted Answer

22

Answer

12

Answer

17

Answer

24

Question 3

If the system of equations$x + 5y + 6z = 4,$$2x + 3y + 4z = 7,$$x + 6y + az = b$has infinitely many solutions, then the point (a, b) lies on the line

Accepted Answer

$x - y = 3$

Answer

$y - x = 3$

Answer

$x + y = 11$

Answer

$x + y = 12$

Question 4

Let $a_1, a_2, a_3, \dots$ be an A.P. and $g_1 = a_1, g_2, g_3, \dots$ be an increasing G.P. If $a_1 = a_2 + g_2 = 1$ and $a_3 + g_3 = 4$, then $a_{10} + g_5$ is equal to :

Accepted Answer

55

Answer

81

Answer

76

Answer

62

Question 5

The sum $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \dots$ up to 8 terms, is :

Accepted Answer

71

Answer

70

Answer

72

Answer

73