List of top Mathematics Questions asked in WBJEE

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 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
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 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
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
$AB$ 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
From the point $(-1, -6)$, two tangents are drawn to $y^2 = 4x$. Then the angle between the two tangents is
A curve passes through the point $(3, 2)$ for which the segment of the tangent line contained between the coordinate axes is bisected at the point of contact. The equation of the curve 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]
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
Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on
The maximum value of $f(x) = e^{\sin x} + e^{\cos x}$, where $x \in \mathbb{R}$, is
The number of zeros at the end of $\angle 100$ is
Let $P(3\sec\theta, 2\tan\theta)$ and $Q(3\sec\phi, 2\tan\phi)$ be two points on $\frac{x^2}{9} - \frac{y^2}{4} = 1$ such that $\theta + \phi = \frac{\pi}{2}$. Then the ordinate of the intersection of the normals at $P$ and $Q$ 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?
$PQ$ 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 $z_1$ and $z_2$ be two non-zero complex numbers. Then
The value of $\int_0^{\pi/2} \frac{(\cos x)\sin x}{(\cos x)\sin x + (\sin x)\cos x} \, dx$ is
The side $AB$ of $\triangle ABC$ is fixed and is of length $2a$ units. The vertex $C$ moves in the plane such that the vertical angle is always constant and is $\alpha$. Let the $x$-axis be along $AB$ and the origin be at $A$. Then the locus of the vertex is
$\lim_{x \to 0} \left( \frac{1}{x} \ln \left( \frac{\sqrt{1 + x}}{\sqrt{1 - x}} \right) \right)$ is
$f: X \to \mathbb{R}, X = \{x | 0<x<1\}$ is defined as $f(x) = \frac{2x - 1}{1 - |2x - 1|}$. Then
Domain of $y = \sqrt{\log_{10} \left( \frac{3x - x^2}{2} \right)}$ is
$\lim_{x \to \infty} \left[ \frac{x^2 + 1}{x + 1} - ax - b \right], \, (a, b \in \mathbb{R}) = 0$. Then
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.
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