List of top Questions asked in WBJEE

Let the tangent and normal at any point $P(at^2, 2at), (a>0)$, on the parabola $y^2 = 4ax$ meet the axis of the parabola at $T$ and $G$ respectively. Then the radius of the circle through $P$, $T$, and $G$ is

If $P_1P_2$ and $P_3P_4$ are two focal chords of the parabola $y^2 = 4ax$, then the chords $P_1P_3$ and $P_2P_4$ intersect on the

$A$ is a set containing elements. $P$ and $Q$ are two subsets of $A$. Then the number of ways of choosing $P$ and $Q$ such that $P \cap Q = \emptyset$ is

Let $a_n = (1^2 + 2^2 + \cdots + n^2)$ and $b_n = n^n (n!)$. Then

If $\mathbf{a} = \hat{i} + \hat{j} - \hat{k}$, $\mathbf{b} = \hat{i} - \hat{j} + \hat{k}$, and $\mathbf{c}$ is a unit vector perpendicular to $\mathbf{a}$ and coplanar with $\mathbf{a}$ and $\mathbf{b}$, then the unit vector $\mathbf{d}$ perpendicular to both $\mathbf{a}$ and $\mathbf{c}$ is

If $z = x - iy$ and $z^{1/3} = p + iq$ ($x, y, p, q \in \mathbb{R}$), then $\frac{\left( \frac{x}{p} + \frac{y}{q} \right)}{p^2 + q^2}$ is equal to

If $a$, $b$, and $c$ are in GP, and $\log a - \log 2b$, $\log 2b - \log 3c$, $\log 3c - \log a$ are in A.P., then $a$, $b$, and $c$ are the lengths of the sides of a triangle which is

The area of the figure bounded by the parabola $y^2 + 8x = 16$ and $y^2 - 24x = 48$ is

A particle moving in a straight line starts from rest, and the acceleration at any time $t$ is $a - kt^2$, where $a$ and $k$ are positive constants. The maximum velocity attained by the particle is

Let $f(x) = (x - 2)^{17} (x + 5)^{24}$. Then

The point of contact of the tangent to the parabola $y^2 = 9x$ which passes through the point $(4, 10)$ and makes an angle $\theta$ with the positive side of the axis of the parabola, where $\tan \theta>2$, is

Let $\lim_{\varepsilon \to 0^+} \int_\varepsilon^x \frac{b t \cos 4t - a \sin 4t}{t^2} \, dt = \frac{a \sin 4x}{x} - 1,\quad (0<x<\frac{\pi}{4})$. Then $a$ and $b$ are given by

If $x \frac{dy}{dx} + y = x \frac{f(xy)}{f'(xy)}$, then $|f(xy)|$ is equal to