JEE Main 2026 Question Paper (04-Apr-2026) (Shift 2)

Question 1

For the function $f: [1,\infty) \rightarrow [1,\infty)$ defined by $f(x) = (x-1)^4 + 1$, among the two statements:
(I) The set $S = \{x \in [1,\infty) : f(x) = f^{-1}(x)\}$ contains exactly two elements, and
(II) The set $S = \{x \in [1,\infty) : f(x) = f^{-1}(x+1)\}$ is an empty set,

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

Let $S = \{z \in \mathbb{C} : z^2 + 4z + 16 = 0\}$. Then $\sum_{z \in S} |z + \sqrt{3}i|^2$ is equal to:

Accepted Answer

38

Answer

42

Answer

23

Answer

27

Question 3

If the system of equations:$x + y + z = 5$$x + 2y + 3z = 9$$x + 3y + \lambda z = \mu$has infinitely many solutions, then the value of $\lambda + \mu$ is:

Accepted Answer

18

Answer

16

Answer

19

Answer

21

Question 4

If $\alpha = 1$ and $\beta = 1 + i\sqrt{2}$, where $i = \sqrt{-1}$ are two roots of the equation $x^3 + ax^2 + bx + c = 0$, $a, b, c \in \mathbb{R}$, then $\int_{-1}^{1} (x^3 + ax^2 + bx + c) dx$ is equal to:

Accepted Answer

-8

Answer

-2

Answer

-4

Answer

-10

Question 5

If the quadratic equation $(\lambda + 2)x^2 - 3\lambda x + 4\lambda = 0$, $\lambda 
eq -2$, has two positive roots, then the number of possible integral values of $\lambda$ is:

Accepted Answer

2

Answer

1

Answer

3

Answer

4