List of top Questions asked in WBJEE

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
Let $p(x_0)$ be a polynomial with real coefficients, $p(0) = 1$ and $p'(x)>0$ for all $x \in \mathbb{R}$. Then
$A$ 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
If the algebraic sum of the distances from the points $(2, 0)$, $(0, 2)$, and $(1, 1)$ to a variable straight line is zero, then the line passes through the fixed point.
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
Under which of the following condition(s) does(do) the system of equations $\begin{bmatrix} 1 & 2 & 4 \\ 2 & 1 & 2 \\ 1 & 2 & a-4 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ a \end{bmatrix}$ possess(possess) a unique solution?
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 $I$ 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
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
$f: X \to \mathbb{R}, X = \{x | 0<x<1\}$ is defined as $f(x) = \frac{2x - 1}{1 - |2x - 1|}$. Then
The value of $\int_0^{\pi/2} \frac{(\cos x)\sin x}{(\cos x)\sin x + (\sin x)\cos x} \, dx$ is
$AB$ is a chord of a parabola $y^2 = 4ax$, $(a > 0)$ with vertex $A$, $BC$ is drawn perpendicular to $AB$ meeting the axis at $C$. The projection of $BC$ on the axis of the parabola is
Let $R$ and $S$ be two equivalence relations on a non-void set $A$. Then
Let $f$ be derivable in $[0, 1]$, then
If $x \frac{dy}{dx} + y = x \frac{f(xy)}{f'(xy)}$, then $|f(xy)|$ is equal to
If $|z - 25i| \leq 15$, the maximum $\arg(z) -$ minimum $\arg(z)$ is equal to
From the point $(-1, -6)$, two tangents are drawn to $y^2 = 4x$. Then the angle between the two tangents is
The equation of the plane through the intersection of the planes $x + y + z = 1$ and $2x + 3y - z + 4 = 0$ and parallel to the $x$-axis 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
$I = \int \cos(\ln x) \, dx$. Then $I =$
If $(\cot \alpha_1)(\cot \alpha_2) \cdots (\cot \alpha_n) = 1$, with $0<\alpha_1, \alpha_2, \ldots, \alpha_n<\frac{\pi}{2}$, then the maximum value of $(\cos \alpha_1)(\cos \alpha_2) \cdots (\cos \alpha_n)$ is
A determinant is chosen at random from the set of all determinants of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is
A, B, C are mutually exclusive events such that $P(A) = \frac{3x + 1}{3}$, $P(B) = \frac{1 - x}{4}$, and $P(C) = \frac{1 - 2x}{2}$. Then the set of possible values of $x$ are in
Let $f(x) = x^2 + x \sin x - \cos x$. Then