JEE Main 2026 Question Paper (06-Apr-2026) (Shift 2)

Question 1

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $f(x) = \frac{2x^2 - 3x + 2}{3x^2 + x + 3}$. Then $f$ is :

Accepted Answer

neither one-one nor onto

Answer

both one-one and onto

Answer

one-one but not onto

Answer

onto but not one-one

Question 2

Consider the quadratic equation $(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0, n \in \mathbf{R}$. Let $\alpha$ be the minimum value of the product of its roots and $\beta$ be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is $\alpha$ and the common ratio is $\frac{\alpha}{\beta}$, is :

Accepted Answer

$\frac{364}{243}$

Answer

$\frac{61}{37}$

Answer

$\frac{121}{81}$

Answer

$\frac{1093}{729}$

Question 3

Let $S=\{z \in \mathbf{C} : z^2 + \sqrt{6} iz - 3 = 0\}$. Then $\sum_{z \in S} z^8$ is equal to :

Accepted Answer

162

Answer

184

Answer

262

Answer

324

Question 4

The sum of all possible values of $	heta \in [0, 2\pi]$, for which the system of equations : $x\cos3	heta - 8y - 12z = 0$ $x\cos2	heta + 3y + 3z = 0$ $x + y + 3z = 0$ has a non-trivial solution, is equal to :

Accepted Answer

$4\pi$

Answer

$\pi$

Answer

$2\pi$

Answer

$3\pi$

Question 5

Let $A = \begin{bmatrix} 1 & 0 & 0 \ 3 & 1 & 0 \ 9 & 3 & 1 \end{bmatrix}$ and $B=[b_{ij}], 1 \le i, j \le 3$. If $B = A^{99} - I$, then the value of $\frac{b_{31} - b_{21}}{b_{32}}$ is :

Accepted Answer

149

Answer

99

Answer

199

Answer

159