List of top Questions asked in WBJEE

Let \( \phi(x) = f(x) + f(2a - x) \), \( x \in [0, 2a] \) and \( f'(x)>0 \) for all \( x \in [0, a] \). Then \( \phi(x) \) is:
Let $f(x)$ be a second degree polynomial. If $f(1) = f(-1)$ and $p, q, r$ are in A.P., then $f'(p), f'(q), f'(r)$ are
If the sum of the squares of the roots of the equation $x^2 - (a-2)x - (a+1) = 0$ is least for an appropriate value of the variable parameter $a$, then that value of $a$ will be
Evaluate the limit \[ \lim_{x \to 0} \frac{\tan \left( -\pi^2 x^2 - x^2 \tan \left( -\pi^2 \right) \right)}{\sin^2 x} \] is:
If \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar vectors and \( \lambda \) is a real number, then the vectors \( \vec{a} + 2\vec{b} + 3\vec{c} \), \( \lambda \vec{b} + 4\vec{c} \), and \( (2\lambda - 1)\vec{c} \) are non-coplanar for:
Let \( f(x) = |x - \alpha| + |x - \beta| \), where \( \alpha, \beta \) are the roots of the equation \( x^2 - 3x + 2 = 0 \). Then the number of points in \( [\alpha, \beta] \) at which \( f \) is not differentiable is:
The set of points of discontinuity of the function \( f(x) = x - [x], x \in \mathbb{R} \) is:
If \( 0 \leq a, b \leq 3 \) and the equation \( x^2 + 4 + 3\cos(ax + b) = 2x \) has real solutions, then the value of \( (a + b) \) is:
If \( g(f(x)) = |\sin x| \) and \( f(g(x)) = (\sin \sqrt{x})^2 \), then:
If \( f(x) = \frac{3x - 4}{2x - 3} \), then \( f(f(f(x))) \) will be:
The sum of the first four terms of an arithmetic progression is 56. The sum of the last four terms is 112. If its first term is 11, then the number of terms is:
Let \( f(x) = \max\{x + |x|, x - |x|, x - [x]\} \), where \( [x] \) stands for the greatest integer not greater than \( x \). Then \( \int_{-3}^{3} f(x) \, dx \) has the value:
If \( f(x) \) and \( g(x) \) are two polynomials such that \( \phi(x) = f(x^3) + xg(x^3) \) is divisible by \( x^2 + x + 1 \), then:
Let \( u + v + w = 3 \), \( u, v, w \in \mathbb{R} \) and \( f(x) = ux^2 + vx + w \) be such that \( f(x + y) = f(x) + f(y) + xy \) for all \( x, y \in \mathbb{R} \). Then \( f(1) \) is equal to:
If \( f \) is the inverse function of \( g \) and \( g'(x) = \frac{1}{1+x^n} \), then the value of \( f'(x) \) is:
If the sum of \( n \) terms of an A.P. is \( 3n^2 + 5n \) and its \( m^{th} \) term is \( 164 \), then the value of \( m \) is:
Evaluate the integral \( \int_{-1}^{1} \frac{x^2 + |x| + 1}{x^2 + 2|x| + 1} \, dx \):
If \( \text{adj } B = \lambda I \) where \( |\lambda| = 1 \), then \( \text{adj} ((Q^{-1} B P^{-1})) \) =
Let \( f(\theta) = \begin{vmatrix} 1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1 \end{vmatrix} \). Suppose \( A \) and \( B \) are respectively the maximum and minimum values of \( f(\theta) \). Then \( (A, B) \) is equal to:
The straight line \[ \frac{x-3}{3} = \frac{y-2}{1} = \frac{z-1}{0} \] is:
Let \( f \) be a function which is differentiable for all real \( x \). If \( f(2) = -4 \) and \( f'(x) \geq 6 \) for all \( x \in [2, 4] \), then:
The solution set of the equation \( \tan(\pi \tan x) = \cot(\pi \cot x) \), \( x \in \left(0, \frac{\pi}{2}\right) \), is:
Let \( f(x) = x^2 \), \( x \in [-1, 1] \). Then which of the following are correct?
A diode is connected in parallel with a resistance as shown in Figure. The most probable current (\( I \)) - voltage (\( V \)) characteristic is:
The minimum wavelength of Lyman series lines is \( P \), then the maximum wavelength of the Lyman series lines is: