List of top Mathematics Questions asked in WBJEE

The value of $\int_0^{\pi/2} \frac{(\cos x)\sin x}{(\cos x)\sin x + (\sin x)\cos x} \, dx$ is
$\lim_{x \to 0} \left( \frac{1}{x} \ln \left( \frac{\sqrt{1 + x}}{\sqrt{1 - x}} \right) \right)$ is
If $y = e^{\tan^{-1} x}$, 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 $z = x - iy$ 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
For the mapping $f: \mathbb{R} \setminus \{1\} \to \mathbb{R} \setminus \{2\}$ given by $f(x) = \frac{2x}{x - 1}$, which of the following is correct?
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
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
Let $f(x) = \int \cos x \sin x \, e^{-t^2} dt$. Then $f' \left( \frac{\pi}{4} \right)$ equals
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
$f: X \to \mathbb{R}, X = \{x | 0<x<1\}$ is defined as $f(x) = \frac{2x - 1}{1 - |2x - 1|}$. Then
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
If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus is
If $\Delta(x)= \begin{vmatrix} x - 2 & (x - 1)^2 & x^3 \\ x - 1 & x^2 & (x + 1)^3 \\ x & (x + 1)^2 & (x + 2)^3 \end{vmatrix}$, then coefficient of $x$ in $\Delta(x)$ is
If $p = \begin{bmatrix} 1 & a & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of the $3 \times 3$ matrix $A$ and $\det A = 4$, then $A$ is equal to
If $|z - 25i| \leq 15$, the maximum $\arg(z) -$ minimum $\arg(z)$ is equal to
The solution of $\det(A - \lambda I_2) = 0$ is $4$ and $8$, and $A = \begin{pmatrix} 2 & 3 \\ x & y \end{pmatrix}$. 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
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?
Let $R$ and $S$ be two equivalence relations on a non-void set $A$. Then
$I = \int \cos(\ln x) \, dx$. Then $I =$
Let $f$ be derivable in $[0, 1]$, then
The area of the figure bounded by the parabola $y^2 + 8x = 16$ and $y^2 - 24x = 48$ is
If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by