List of top Questions asked in WBJEE

A body of mass $m$ is thrown vertically upward with speed $\sqrt{3}v_e^2$, where $v_e$ is the escape velocity of a body from earth surface. The final velocity of the body is
A body of mass $m$ is thrown with velocity $u$ from the origin of a coordinate axes at an angle with the horizon. The magnitude of the angular momentum of the particle about the origin at time $t$ when it is at the maximum height of the trajectory is proportional to
Three particles, each of mass $m$ grams situated at the vertices of an equilateral $\Delta ABC$ of side $a$ cm (as shown in the figure). The moment of inertia of the system about a line $AX$ perpendicular to $AB$ and in the plane of $\Delta ABC$ in $g$-cm² units will be:
Three particles, each of mass
Let $f(x) = x^2 + x \sin x - \cos x$. Then
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]
Let $z_1$ and $z_2$ be two non-zero complex numbers. Then
Let $\Delta = \left| \begin{matrix} \sin \theta \cos \varphi & \sin \theta \sin \varphi & \cos \theta \\ \cos \theta \cos \varphi & \cos \theta \sin \varphi & -\sin \theta \\ -\sin \theta \sin \varphi & \sin \theta \cos \varphi & 0 \end{matrix} \right|$. 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
Twenty meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle be, if the area of the flower bed is greatest?
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 line $y = x + 5$ touches
Let $R$ and $S$ be two equivalence relations on a non-void set $A$. Then
The maximum value of $f(x) = e^{\sin x} + e^{\cos x}$, where $x \in \mathbb{R}$, is
If $\alpha$ is a unit vector, $\beta = \hat{i} + \hat{j} - \hat{k}$, $\gamma = \hat{i} + \hat{k}$, then the maximum value of $|\alpha \beta \gamma|$ is
Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on
The solution of $\det(A - \lambda I_2) = 0$ is $4$ and $8$, and $A = \begin{pmatrix} 2 & 3 \\ x & y \end{pmatrix}$. Then
If $x$ satisfies the inequality $\log_2 5x^2 + (\log_5 x)^2<2$, then $x$ belongs to
From the point $(-1, -6)$, two tangents are drawn to $y^2 = 4x$. Then the angle between the two tangents is
The value of $a$ for which the sum of the squares of the roots of the equation $x^2 - (a - 2)x - (a - 1) = 0$ assumes the least value 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
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
$\lim_{x \to \infty} \left[ \frac{x^2 + 1}{x + 1} - ax - b \right], \, (a, b \in \mathbb{R}) = 0$. Then
$PQ$ is a double ordinate of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ such that $\triangle OPQ$ is an equilateral triangle, with $O$ being the center of the hyperbola. Then the eccentricity $e$ of the hyperbola satisfies
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