List of top Mathematics Questions asked in WBJEE

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 number of solutions of \( \sin^{-1} x + \sin^{-1} (1 - x) = \cos^{-1} x \) is:
The probability that a non-leap year selected at random will have 53 Sundays or 53 Saturdays is:
The maximum number of common normals of \( y^2 = 4ax \) and \( x^2 = 4by \) is equal to:
If \( |z_1| = |z_2| = |z_3| = 1 \) and \( z_1 + z_2 + z_3 = 0 \), then the area of the triangle whose vertices are \( z_1, z_2, z_3 \) is:
The number of common tangents to the circles \( x^2 + y^2 - 4x - 6y - 12 = 0 \) and \( x^2 + y^2 + 6x + 18y + 26 = 0 \) is:
If \( \cos(\theta + \phi) = \frac{3}{5} \) and \( \sin(\theta - \phi) = \frac{5}{13} \), \( 0<\theta, \phi<\frac{\pi}{4} \), then \( \cot(2\theta) \) has the value:
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 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:
Let \( f(x) \) be continuous on \( [0, 5] \) and differentiable in \( (0, 5) \). If \( f(0) = 0 \) and \( |f'(x)| \leq \frac{1}{5} \) for all \( x \) in \( (0, 5) \), then for all \( x \) in \( [0, 5] \):
If \( z_1, z_2 \) are complex numbers such that \( \frac{z_1}{3z_2} \) is a purely imaginary number, then the value of \( \left| \frac{z_1 - z_2}{z_1 + z_2} \right| \) is:
The value of the integral \( \int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9 - x} + \sqrt{x}} \, dx \) is:
The value of the expression \( {}^{47} C_4 + \sum_{j=1}^{5} {}^{52-j} C_3 \) is:
If \( \text{adj } B = \lambda I \) where \( |\lambda| = 1 \), then \( \text{adj} ((Q^{-1} B P^{-1})) \) =
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:
The set of points of discontinuity of the function \( f(x) = x - [x], x \in \mathbb{R} \) is:
An \( n \times n \) matrix is formed using 0, 1 and -1 as its elements. The number of such matrices which are skew symmetric is:
If \( E \) and \( F \) are two independent events with \( P(E) = 0.3 \) and \( P(E \cup F) = 0.5 \), then \( P(E \mid F) - P(F \mid E) \) equals:
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:
The function \( f(x) = 2x^3 - 3x^2 - 12x + 4 \), \( x \in \mathbb{R} \) has:
Let \( \vec{a}, \vec{b}, \vec{c} \) be vectors of equal magnitude such that the angle between \( \vec{a} \) and \( \vec{b} \) is \( \alpha \), the angle between \( \vec{b} \) and \( \vec{c} \) is \( \beta \), and the angle between \( \vec{c} \) and \( \vec{a} \) is \( \gamma \). Then the minimum value of \( \cos \alpha + \cos \beta + \cos \gamma \) is:
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:
The value of \( \displaystyle \int_0^{1.5} \left\lfloor x^2 \right\rfloor \, dx \) is:
The expression \( 2^{4n} - 15n - 1 \), where \( n \in \mathbb{N} \) (the set of natural numbers), is divisible by:
A function \( f : \mathbb{R} \to \mathbb{R} \), satisfies \[ \frac{f(x+y)}{3} = \frac{f(x) + f(y) + f(0)}{3} \quad \text{for all} \, x, y \in \mathbb{R}. \] If the function \( f \) is differentiable at \( x = 0 \), then \( f \) is: