List of top Mathematics Questions asked in WBJEE

Let $f(x) = (x - 2)^{17} (x + 5)^{24}$. Then
Let $\int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{2}{3} \, g(f(x)) + c$; then
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
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 $f(x) = a_0 + a_1|x| + a_2|x^2| + a_3|x^3|$, where $a_0, a_1, a_2, a_3$ are real constants. Then $f(x)$ is differentiable at $x = 0$
The maximum value of $f(x) = e^{\sin x} + e^{\cos x}$, where $x \in \mathbb{R}$, 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
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
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
The value of $\int_0^{\pi/2} \frac{(\cos x)\sin x}{(\cos x)\sin x + (\sin x)\cos x} \, dx$ 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
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
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 $y = e^{\tan^{-1} x}$, then
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
Let $f(x) = x^2 + x \sin x - \cos x$. Then
$f: X \to \mathbb{R}, X = \{x | 0<x<1\}$ is defined as $f(x) = \frac{2x - 1}{1 - |2x - 1|}$. 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
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
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 the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by
A candidate is required to answer 6 out of 12 questions which are divided into two parts A and B, each containing 6 questions and he/she is not permitted to attempt more than 4 questions from any part. In how many different ways can he/she make up his/her choice of 6 questions ?
General solution of $\left(x+y\right)^{2} \frac{dy}{dx} = a^{2}, a \ne 0$ is (c is an arbitrary constant)
The general value of the real angle $\theta$, which satisfies the equation, (cos$\theta$ + i sin$\theta$) (cos2$\theta$ + i sin2$\theta$)........ (cosn$\theta$ + i sinn$\theta$) = 1 is given by, (assuming k is an integer)