List of top Mathematics Questions asked in WBJEE

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
$AB$ 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
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
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
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
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
$f: X \to \mathbb{R}, X = \{x | 0<x<1\}$ is defined as $f(x) = \frac{2x - 1}{1 - |2x - 1|}$. Then
If $x$ satisfies the inequality $\log_2 5x^2 + (\log_5 x)^2<2$, then $x$ belongs to
Let $f$ be derivable in $[0, 1]$, then
From the point $(-1, -6)$, two tangents are drawn to $y^2 = 4x$. Then the angle between the two tangents is
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
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?
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
Let $f(x) = (x - 2)^{17} (x + 5)^{24}$. 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
If $A= \begin{bmatrix} 1 & 1 \\ 0 & i \end{bmatrix}$ and $A^{2018} = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$, then $(a + d)$ equals
$AB$ is a variable chord of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. If $AB$ subtends a right angle at the origin $O$, then $\frac{1}{OA^2} + \frac{1}{OB^2}$ equals to
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?
$\lim_{x \to 0} \left( \frac{1}{x} \ln \left( \frac{\sqrt{1 + x}}{\sqrt{1 - x}} \right) \right)$ is
$\lim_{x \to \infty} \left[ \frac{x^2 + 1}{x + 1} - ax - b \right], \, (a, b \in \mathbb{R}) = 0$. Then
Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on
The values of $a, b, c$ for which the function $f(x) = \begin{cases} \sin((a + 1)x) + \sin x, & x<0 \\ c, & x = 0 \\ \frac{(\sqrt{x + bx^2}) - \sqrt{x}}{bx^{1/2}}, & x > 0 \end{cases}$ is continuous at $x = 0$, are
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
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