List of top Questions asked in WBJEE

Two integers $r$ and $s$ are drawn one at a time without replacement from the set $\{1, 2, \ldots, n\}$. Then $P(r \leq k / s \leq k)$ is:

Let $f : \mathbb{R} \to \mathbb{R}$ be a function defined by $f(x) = \frac{e^{|x|} - e^{-x}}{e^x + e^{-x}}$, then:

Let A be the set of even natural numbers that are<8 and B be the set of prime integers that are<7. The number of relations from A to B is:

If
$$\begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix} \cdot A \cdot \begin{pmatrix} -3 & 2 \\ 5 & -3 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix},$$
then $A$ is:

Let $$f(x) = \begin{vmatrix} \cos x & x & 1 \\ 2 \sin x & x^3 & 2x \\ \tan x & x & 1 \end{vmatrix},$$ then $$\lim_{x \to 0} \frac{f(x)}{x^2} = ?$$

If
$$\begin{vmatrix} x^k & x^{k+2} & x^{k+3} \\ y^k & y^{k+2} & y^{k+3} \\ z^k & z^{k+2} & z^{k+3} \end{vmatrix} = (x - y)(y - z)(z - x)\left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right),$$ then the value of $k$ is:

If $$A = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}$$ and $\theta = \frac{2\pi}{7}$, then $A^{100} = A \times A \times \ldots$ (100 times) is equal to:

The coefficient of $a^{10}b^7c^3$ in the expansion of $(bc + ca + ab)^{10}$ is:

If $P(x) = ax^2 + bx + c$ and $Q(x) = -ax^2 + dx + c$ where $ac \neq 0$, then $P(x) \cdot Q(x) = 0$ has:

Let N be the number of quadratic equations with coefficients from {0,1,2,...,9} such that 0 is a solution of each equation. Then the value of N is:

If $\cos\theta + i \sin\theta, \, \theta \in \mathbb{R}$, is a root of the equation
$$a_0 x^n + a_1 x^{n-1} + \cdots + a_{n-1}x + a_n = 0, \, a_0, a_1, \ldots, a_n \in \mathbb{R}, \, a_0 \neq 0$$
then the value of $a_1 \sin\theta + a_2 \sin 2\theta + \cdots + a_n \sin n\theta$ is:

If a particle moves in a straight line according to the law $x = a \sin(\sqrt{t} + b)$, then the particle will come to rest at two points whose distance is: