List of top Mathematics Questions asked in WBJEE

If \( x = \int_0^y \frac{1}{\sqrt{1+9t^2}} \, dt \) and \( \frac{d^2y}{dx^2} = ay \), then the value of \( a \) is:
If \( \theta \) is the angle between two vectors \( \vec{a} \) and \( \vec{b} \) such that \( |\vec{a}| = 7 \), \( |\vec{b}| = 1 \) and \( |\vec{a} \times \vec{b}|^2 = k^2 - (\vec{a} \cdot \vec{b})^2 \), then the values of \( k \) and \( \theta \) are:
The expression \( 2^{4n} - 15n - 1 \), where \( n \in \mathbb{N} \) (the set of natural numbers), is divisible by:
If \( (1 + x - 2x^2)^6 = 1 + a_1x + a_2x^2 + \ldots + a_{12}x^{12} \), then the value of \( a_2 + a_4 + a_6 + \ldots + a_{12} \) is:
If \( f \) is the inverse function of \( g \) and \( g'(x) = \frac{1}{1+x^n} \), then the value of \( f'(x) \) is:
The straight line \[ \frac{x-3}{3} = \frac{y-2}{1} = \frac{z-1}{0} \] is:
The value of the integral \( \int_{0}^{\pi/2} \log\left(\frac{4 + 3\sin x}{4 + 3\cos x}\right) dx \) is:
Let \( p(x) \) be a real polynomial of least degree which has a local maximum at \( x = 1 \) and a local minimum at \( x = 3 \). If \( p(1) = 6 \) and \( p(3) = 2 \), then \( p'(0) \) is equal to:
If \( x = -1 \) and \( x = 2 \) are extreme points of \( f(x) = \alpha \log|x| + \beta x^2 + x \), \( x \neq 0 \), then:
The line \( y - \sqrt{3}x + 3 = 0 \) cuts the parabola \( y^2 = x + 2 \) at the points \( P \) and \( Q \). If the co-ordinates of the point \( X \) are \( (\sqrt{3}, 0) \), then the value of \( XP \cdot XQ \) is:
For what value of \( 'a' \), the sum of the squares of the roots of the equation \( x^2 - (a - 2)x - a + 1 = 0 \) will have the least value?
A function \( f \) is defined by \( f(x) = 2 + (x - 1)^{2/3} \) on \( [0, 2] \). Which of the following statements is incorrect?
The line parallel to the x-axis passing through the intersection of the lines \( ax + 2by + 3b = 0 \) and \( bx - 2ay - 3a = 0 \) where \( (a, b) \neq (0, 0) \) is:
If \( \vec{\alpha} = 3\hat{i} - \hat{j} + \hat{k} \), \( |\vec{\beta}| = \sqrt{5} \) and \( \vec{\alpha} \cdot \vec{\beta} = 3 \), then the area of the parallelogram for which \( \vec{\alpha} \) and \( \vec{\beta} \) are adjacent sides is:
Let \( f(x) = |1 - 2x| \), then:
Consider three points \( P(\cos \alpha, \sin \beta) \), \( Q(\sin \alpha, \cos \beta) \) and \( R(0, 0) \), where \( 0<\alpha, \beta<\frac{\pi}{4} \). Then:
Let \( \vec{a}, \vec{b}, \vec{c} \) be unit vectors. Suppose \( \vec{a} \cdot \vec{b} = \vec{a} \cdot \vec{c} = 0 \) and the angle between \( \vec{b} \) and \( \vec{c} \) is \( \frac{\pi}{6} \). Then \( \vec{a} \) is:
Let \( \omega (\neq 1) \) be a cubic root of unity. Then the minimum value of the set \( \{ |a + b\omega + c\omega^2|^2 : a, b, c \) are distinct non-zero integers \( \} \) equals:
The number of reflexive relations on a set \( A \) of \( n \) elements is equal to:
Let $f(x)$ be a second degree polynomial. If $f(1) = f(-1)$ and $p, q, r$ are in A.P., then $f'(p), f'(q), f'(r)$ are
Let \( f \) be a function which is differentiable for all real \( x \). If \( f(2) = -4 \) and \( f'(x) \geq 6 \) for all \( x \in [2, 4] \), then:
Let \( f_n(x) = \tan\left(\frac{x}{2}\right)(1+\sec x)(1+\sec 2x)\dotsm(1+\sec 2^{n}x) \), then which of the following is true?
If the sum of the squares of the roots of the equation $x^2 - (a-2)x - (a+1) = 0$ is least for an appropriate value of the variable parameter $a$, then that value of $a$ will be
Let \( \phi(x) = f(x) + f(2a - x) \), \( x \in [0, 2a] \) and \( f'(x)>0 \) for all \( x \in [0, a] \). Then \( \phi(x) \) is:
Evaluate the integral \( \int_{-1}^{1} \frac{x^2 + |x| + 1}{x^2 + 2|x| + 1} \, dx \):