List of top Mathematics Questions asked in WBJEE

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
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:
A square with each side equal to \( a \) lies above the \( x \)-axis and has one vertex at the origin. One of the sides passing through the origin makes an angle \( \alpha \) (\( 0 < \alpha < \frac{\pi}{4} \)) with the positive direction of the \( x \)-axis. The equation of the diagonals of the square is:
Let \(f\) be a differential function with
\[ \lim_{x \to \infty} f(x) = 0. \text{ If } y' + y f'(x) - f(x) f'(x) = 0, \lim_{x \to \infty} y(x) = 0 \text{ then,} \]
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:
If \((1 + x + x^2 + x^3)^5 = \sum_{k=0}^{15} a_k x^k\), then \(\sum_{k=0}^{7} (-1)^k \cdot a_{2k}\) is equal to:
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:
Consider the function
\[ f(x) = x(x - 1)(x - 2) \cdots (x - 100). \]
Which one of the following is correct?
The equation \(r \cos \theta = 2a \sin^2 \theta\) represents the curve:
The numbers \(1, 2, 3, \ldots, m\) are arranged in random order. The number of ways this can be done, so that the numbers \(1, 2, \ldots, r \, (r < m)\) appear as neighbours is:
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:
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:
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 \(k =\):
The expression \(\cos^2 \theta + \cos^2 (\theta + \phi) - 2 \cos \theta \cos (\theta + \phi)\) is:
The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = e^x + e^{-x} \) is:
If \(x y' + y - e^x = 0, \, y(a) = b\), then
\[ \lim_{x \to 1} y(x) \text{ is} \]
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:
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 \(p =\):
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:
With origin as a focus and x = 4 as the corresponding directrix, a family of ellipses are drawn. Then the locus of an end of the minor axis is:
In \(\triangle ABC\), coordinates of \(A\) are \((1, 2)\), and the equations of the medians through \(B\) and \(C\) are \(x + y = 5\) and \(x = 4\), respectively. Then the midpoint of \(BC\) is:
If (1,5) is the midpoint of the segment of a line between the lines 5x −y −4 = 0 and 3x +4y −4=0,then the equation of the line will be:
Consider the function f(x) = (x−2)logx. Then the equation xlogx = 2−x has:
The angle between two diagonals of a cube will be:
Chords AB CD of a circle intersect at right angle at the point P. If the lengths of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is: