WBJEE 2026 Mathematics Question Paper (24-May-2026)

Question 1

Given $P(x) = x^4 + ax^3 + bx^2 + cx + d$ such that $x=0$ is the only real root of $P'(x) = 0$. If $P(-1) < P(1)$, then in the interval $[-1, 1]$

Accepted Answer

$P(-1)$ is the minimum but $P(1)$ is not the maximum of $P$

Answer

$P(-1)$ is not minimum but $P(1)$ is the maximum of $P$

Answer

neither $P(-1)$ is the minimum nor $P(1)$ is the maximum of $P$

Answer

$P(-1)$ is the minimum and $P(1)$ is the maximum of $P$

Question 2

If $\alpha$, $\beta$ are the roots of the equation $x^2 - px + q = 0$ and $\alpha > 0$, $\beta > 0$, then $\alpha^{\frac{1}{4}} + \beta^{\frac{1}{4}} = \left(p + 6\sqrt{p} + 4q^{\frac{1}{4}}\sqrt{p+2\sqrt{q}}\right)^K$, where $K$ is

Accepted Answer

$\frac{1}{4}$

Answer

$\frac{3}{2}$

Answer

$\frac{1}{3}$

Answer

$1$

Question 3

If $\sum_{r=1}^{\infty} 	an^{-1}\left(\frac{1}{2r^2}ight) = a$, then $	an a$ is equal to

Accepted Answer

$1$

Answer

$0$

Answer

$\sqrt{3}$

Answer

$\frac{\pi}{4}$

Question 4

Consider a function $f(x)$ which has exactly two roots at $x=a$. If $\lim_{x 	o a}\left(\frac{\lambda f'(x)}{f(x)} - \frac{1}{x-a}ight) = m \, (
eq 0)$, then the value of $\lambda$ is

Accepted Answer

$2$

Answer

$1$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{4}$

Question 5

A vector given by $\vec{P} = f(t)\hat{i} + g(t)\hat{j} + \hat{k}$ moves in such a way that it is always parallel to the vector $\vec{Q} = -f''(t)\hat{i} + f'(t)\hat{j} + \hat{k}$. The magnitude of $\vec{P}$ is

Accepted Answer

constant

Answer

a linear function of time

Answer

a quadratic function of time

Answer

a cubic function of time