List of top Mathematics Questions asked in WBJEE

Let \[ f(x) = \begin{vmatrix} \cos x & x & 1 \\ 2 \sin x & x^3 & 2x \\ \tan x & x & 1 \end{vmatrix}, \] then \[ \lim_{x \to 0} \frac{f(x)}{x^2} = ? \]
Consider the function
\[ f(x) = x(x - 1)(x - 2) \cdots (x - 100). \]
Which one of the following is correct?
Evaluate: $$ \lim_{n \to \infty} \frac{1}{n^{k+1}} \left[ 2^k + 4^k + 6^k + \dots + (2n)^k \right]. $$ 
The expression \(\cos^2 \theta + \cos^2 (\theta + \phi) - 2 \cos \theta \cos (\theta + \phi)\) is:
Let \( \Gamma \) be the curve \( y = b e^{-x/a} \) and \( L \) be the straight line:
\[ \frac{x}{a} + \frac{y}{b} = 1, \quad a, b \in \mathbb{R}. \]
Then:
If the quadratic equation \( ax^2 + bx + c = 0 \) (\( a > 0 \)) has two roots \( \alpha \) and \( \beta \) such that \( \alpha < -2 \) and \( \beta > 2 \), then:
If \(0 < \theta < \frac{\pi}{2}\) and \(\tan 30^\circ \neq 0\), then \(\tan \theta + \tan 2\theta + \tan 3\theta = 0\) if \(\tan \theta \cdot \tan 2\theta = k\), where \(k =\):
If \(z_1\) and \(z_2\) be two roots of the equation \(z^2 + az + b = 0, \, a^2 < 4b\), then the origin, \(z_1\) and \(z_2\) form an equilateral triangle if:
If a particle moves in a straight line according to the law \(x = a \sin(\sqrt{t} + b)\), then the particle will come to rest at two points whose distance is:
If \( A \) and \( B \) are acute angles such that \( \sin A = \sin^2 B \) and \( 2\cos^2 A = 3\cos^2 B \), then \( (A, B) \) is:
Five balls of different colors are to be placed in three boxes of different sizes. The number of ways in which we can place the balls in the boxes so that no box remains empty is:
The angle between two diagonals of a cube will be:
If \(x y' + y - e^x = 0, \, y(a) = b\), then
\[ \lim_{x \to 1} y(x) \text{ is} \]
If \(\int \frac{\log(x + \sqrt{1 + x^2})}{1 + x^2} \, dx = f(g(x)) + c\), then:
Choose the correct statement:
The coefficient of \(a^{10}b^7c^3\) in the expansion of \((bc + ca + ab)^{10}\) is:
Two smallest squares are chosen one by one on a chessboard. The probability that they have a side in common is:
If
\[ \begin{vmatrix} x^k & x^{k+2} & x^{k+3} \\ y^k & y^{k+2} & y^{k+3} \\ z^k & z^{k+2} & z^{k+3} \end{vmatrix} = (x - y)(y - z)(z - x)\left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right), \] then the value of \(k\) is:
If \( \triangle ABC \) is an isosceles triangle and the coordinates of the base points are \( B(1, 3) \) and \( C(-2, 7) \), the coordinates of \( A \) can be:
A line of fixed length a + b, moves so that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the line into two parts of length a and b is
A biased coin with probability \(p\) (where \(0 < p < 1\)) of getting head is tossed until a head appears for the first time. If the probability that the number of tosses required is even is \(\frac{2}{5}\), then \(p =\):
The function \(y=e^{kr}\) satisfies \((\frac{d^2y}{dx^2}+\frac{dy}{dx})(\frac{dy}{dx}-y)=y\frac{dy}{dx}\). It is valid for 
If I=∫\(\frac{x^2dx}{(x\,sin\,x+cos\,x)^2}\)=f(x)+tan x+c, then f(x) is
Let A and B be orthogonal and det A+det B=0. Then
Let f be a non-negative function defined on [\(0,\frac{\pi}{2}\)]. If \(\int_{0}^{x}(f'(t)-sin\,2t)dt=\int_{0}^{x}f(t)tan\,t\,dt\). \(f(0)=1\), then \(\int_{0}^{\frac{\pi}{2}}f(x)dx\) is