List of top Mathematics Questions asked in WBJEE

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 $I$ 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
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
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
$AB$ 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
Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on
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?
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
Domain of $y = \sqrt{\log_{10} \left( \frac{3x - x^2}{2} \right)}$ is
$I = \int \cos(\ln x) \, dx$. Then $I =$
If $x$ satisfies the inequality $\log_2 5x^2 + (\log_5 x)^2<2$, then $x$ belongs to
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
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]
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
Let $f(x) = (x - 2)^{17} (x + 5)^{24}$. Then
The solution of $\cos y \frac{dy}{dx} = e^x + \sin y + x^2 e^{\sin y}$ is $f(x) + e^{-\sin y} = C$ (where $C$ is an arbitrary real constant), where $f(x)$ is equal to
$PQ$ 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
The maximum value of $f(x) = e^{\sin x} + e^{\cos x}$, where $x \in \mathbb{R}$, 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
$\lim_{x \to 0} \left( \frac{1}{x} \ln \left( \frac{\sqrt{1 + x}}{\sqrt{1 - x}} \right) \right)$ 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
$\lim_{x \to \infty} \left[ \frac{x^2 + 1}{x + 1} - ax - b \right], \, (a, b \in \mathbb{R}) = 0$. 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
If $|z - 25i| \leq 15$, the maximum $\arg(z) -$ minimum $\arg(z)$ is equal to