JEE Main 2026 Question Paper (06-Apr-2026) (Shift 1)

Question 1

Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x) = \sin^{-1}\left(\frac{x + [x]}{3}\right)$ is $[\alpha, \beta)$, then $\alpha^2 + \beta^2$ is equal to:

Accepted Answer

5

Answer

2

Answer

10

Answer

13

Question 2

Let one root of the quadratic equation in x: $(k^2 - 15k + 27)x^2 + 9(k - 1)x + 18 = 0$ be twice the other. Then the length of the latus rectum of the parabola $y^2 = 6kx$ is equal to:

Accepted Answer

12

Answer

4

Answer

6

Answer

8

Question 3

Let $e_1$ and $e_2$ be two distinct roots of the equation $x^2 - ax + 2 = 0$. Let the sets
$\{a \in \mathbb{R} : e_1 \text{ and } e_2 \text{ are the eccentricities of hyperbolas}\} = (\alpha, \beta)$, and
$\{a \in \mathbb{R} : e_1 \text{ and } e_2 \text{ are the eccentricities of an ellipse and a hyperbola, respectively}\} = (\gamma, \infty)$.
Then $\alpha^2 + \beta^2 + \gamma^2$ is equal to:

Accepted Answer

26

Answer

18

Answer

22

Answer

34

Question 4

Let the set of all values of $k \in \mathbb{R}$ such that the equation $z(\bar{z} + 2 + i) + k(2 + 3i) = 0, z \in \mathbb{C}$, has at least one solution, be the interval $[\alpha, \beta]$. Then $9(\alpha + \beta)$ is equal to:

Accepted Answer

-10

Answer

-8

Answer

$10\sqrt{13}$

Answer

$8\sqrt{13}$

Question 5

The value of $1^3 - 2^3 + 3^3 - ... + 15^3$ is:

Accepted Answer

1856

Answer

1706

Answer

1982

Answer

2403