List of top Mathematics Questions asked in WBJEE

Consider the function f(x) = (x−2)logx. Then the equation xlogx = 2−x has:
If for the series \(a_1, a_2, a_3, \ldots\), etc., \(a_{n+1} - a_n\) bears a constant ratio with \(a_n + a_{n+1}\), then \(a_1, a_2, a_3, \ldots\) are in:
Let A be the set of even natural numbers that are<8 and B be the set of prime integers that are<7. The number of relations from A to B is:
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 \( a_1, a_2, \dots, a_n \) are in A.P. with common difference \( \theta \), then the sum of the series:
\[ \sec a_1 \sec a_2 + \sec a_2 \sec a_3 + \dots + \sec a_{n-1} \sec a_n = k (\tan a_n - \tan a_1), \]
where \( k = ? \)
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:
Given an A.P. and a G.P. with positive terms, with the first and second terms of the progressions being equal. If \(a_n\) and \(b_n\) be the \(n\)-th term of A.P. and G.P. respectively, then:
Let \(y = f(x)\) be any curve on the X-Y plane and \(P\) be a point on the curve. Let \(C\) be a fixed point not on the curve. The length \(PC\) is either a maximum or a minimum. Then:
Let \(f : \mathbb{R} \to \mathbb{R}\) be given by \(f(x) = |x^2 - 1|\), then:
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: $$ \lim_{n \to \infty} \frac{1}{n^{k+1}} \left[ 2^k + 4^k + 6^k + \dots + (2n)^k \right]. $$ 
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:
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
If \(P(x) = ax^2 + bx + c\) and \(Q(x) = -ax^2 + dx + c\) where \(ac \neq 0\), then \(P(x) \cdot Q(x) = 0\) has:
The expression \(\cos^2 \theta + \cos^2 (\theta + \phi) - 2 \cos \theta \cos (\theta + \phi)\) is:
Two integers \(r\) and \(s\) are drawn one at a time without replacement from the set \(\{1, 2, \ldots, n\}\). Then \(P(r \leq k / s \leq k)\) is:
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 \(0 < \theta < \frac{\pi}{2}\) 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 \(\alpha, \beta\) are the roots of the equation \(ax^2 + bx + c = 0\), then:
\[ \lim_{x \to \beta} \frac{1 - \cos(ax^2 + bx + c)}{(x - \beta)^2} \]
In a plane, \(\vec{a}\) and \(\vec{b}\) are the position vectors of two points \(A\) and \(B\) respectively. A point \(P\) with position vector \(\vec{r}\) moves on that plane in such a way that
\[ |\vec{r} - \vec{a}| - |\vec{r} - \vec{b}| = c \quad (\text{real constant}). \]
The locus of \(P\) is a conic section whose eccentricity is:
If \( n \) is a positive integer, the value of:
\[ (2n + 1) \binom{n}{0} + (2n - 1) \binom{n}{1} + (2n - 3) \binom{n}{2} + \dots + 1 \cdot \binom{n}{n} \] is:
If 1000! = 3n × m, where m is an integer not divisible by 3, then n =?
In \(\mathbb{R}\), a relation \(p\) is defined as follows: For \(a, b \in \mathbb{R}\), \(apb\) holds if \(a^2 - 4ab + 3b^2 = 0\).
Then:
Let N be the number of quadratic equations with coefficients from {0,1,2,...,9} such that 0 is a solution of each equation. Then the value of N is: