List of top Mathematics Questions asked in WBJEE

If \(\int \frac{\log(x + \sqrt{1 + x^2})}{1 + x^2} \, dx = f(g(x)) + c\), then:

The angle between two diagonals of a cube will 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

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 \( k = ? \)

The equation \(2x^5 + 5x = 3x^3 + 4x^4\) has:

For the real numbers \( x \) and \( y \), we write \( x \, P \, y \) iff \( x - y + \sqrt{2} \) is an irrational number.
Then the relation \( P \) is:

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 \(P(x) = ax^2 + bx + c\) and \(Q(x) = -ax^2 + dx + c\) where \(ac \neq 0\), then \(P(x) \cdot Q(x) = 0\) has:

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:

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:

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:

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:

If \(U_n (n = 1, 2)\) denotes the \(n\)-th derivative (\(n = 1, 2\)) of \(U(x) = \frac{Lx + M}{x^2 - 2Bx + C}\) (\(L, M, B, C\) are constants), then \(PU_2 + QU_1 + RU = 0\) holds for:

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:

Let \(f : \mathbb{R} \to \mathbb{R}\) be a function defined by \(f(x) = \frac{e^{|x|} - e^{-x}}{e^x + e^{-x}}\), then: