List of top Questions asked in WBJEE- 2022

$A$ 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
There are $n$ white and $n$ black balls marked $1, 2, 3, \ldots, n$. The number of ways in which we can arrange these balls in a row so that neighboring balls are of different colors is
If the transformation $z = \log \tan \frac{x}{2}$ reduces the differential equation $\frac{d^2y}{dx^2} + \cot x \frac{dy}{dx} + 4y \csc^2 x = 0$ into the form $\frac{d^2y}{dz^2} + ky = 0$, then $k$ 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
Consider the equation $y - y_1 = m(x - x_1)$. If $m$ and $x_1$ are fixed, and different lines are drawn for different values of $y_1$, then
The maximum value of $f(x) = e^{\sin x} + e^{\cos x}$, where $x \in \mathbb{R}$, is
The value of $\int_0^{\pi/2} \frac{(\cos x)\sin x}{(\cos x)\sin x + (\sin x)\cos x} \, dx$ is
Let $f$ be a non-negative function defined in $[0, \pi/2]$, $f'$ exists and is continuous for all $x$, and $\int_0^x \sqrt{1 - (f'(t))^2} dt = \int_0^x f(t) dt$ and $f(0) = 0$. Then
If $I$ is the greatest of $I_1 = \int_0^1 e^{-x} \cos^2 x \, dx$, $I_2 = \int_0^1 e^{-x^2} \cos^2 x \, dx$, $I_3 = \int_0^1 e^{-x^2} \, dx$, $I_4 = \int_0^1 e^{-\frac{x^2}{2}} \, dx$, then
The area of the figure bounded by the parabola $y^2 + 8x = 16$ and $y^2 - 24x = 48$ 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 $|z - 25i| \leq 15$, the maximum $\arg(z) -$ minimum $\arg(z)$ is equal to
Let $z_1$ and $z_2$ be two non-zero complex numbers. Then
If $x$ satisfies the inequality $\log_2 5x^2 + (\log_5 x)^2<2$, then $x$ belongs to
Let $f(x) = (x - 2)^{17} (x + 5)^{24}$. Then
Let $p(x_0)$ be a polynomial with real coefficients, $p(0) = 1$ and $p'(x)>0$ for all $x \in \mathbb{R}$. Then
The number of zeros at the end of $\angle 100$ 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
From a balloon rising vertically with uniform velocity $v$ ft/sec, a piece of stone is let go. The height of the balloon above the ground when the stone reaches the ground after 4 sec is [g = 30 ft/sec²]
A line passes through the point $(-1, 1)$ and makes an angle $\sin^{-1} \left( \frac{3}{5} \right)$ with the positive direction of the $x$-axis. If this line meets the curve $x^2 = 4y - 9$ at $A$ and $B$, then $|AB|$ is equal to
Two circles $S_1 = px^2 + py^2 + 2g'x + 2f'y + d = 0$ and $S_2 = x^2 + y^2 + 2gx + 2fy + d' = 0$ have a common chord $PQ$. The equation of $PQ$ is
If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus is
Let $P$ be a point on $(2, 0)$ and $Q$ be a variable point on $(y - 6)^2 = 2(x - 4)$. Then the locus of the midpoint of $PQ$ is
If the equation of one tangent to the circle with center at $(2, -1)$ from the origin is $3x + y = 0$, then the equation of the other tangent through the origin is
A straight line meets the coordinate axes at $A$ and $B$. A circle is circumscribed about the triangle $OAB$, with $O$ being the origin. If $m$ and $n$ are the distances of the tangent from the origin to the points $A$ and $B$ respectively, the diameter of the circle is