List of top Questions asked in WBJEE- 2025

If \( \vec{a}, \vec{b}, \vec{c} \) are non-coplanar vectors and \( \lambda \) is a real number, then the vectors \( \vec{a} + 2\vec{b} + 3\vec{c} \), \( \lambda \vec{b} + 4\vec{c} \), and \( (2\lambda - 1)\vec{c} \) are non-coplanar for:
Suppose \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 + qx + r = 0 \) (with \( r \neq 0 \)) and they are in A.P. Then the rank of the matrix \( \begin{pmatrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{pmatrix} \) is:
The value of the expression \( {}^{47} C_4 + \sum_{j=1}^{5} {}^{52-j} C_3 \) is:
The function \( f(x) = 2x^3 - 3x^2 - 12x + 4 \), \( x \in \mathbb{R} \) has:
The set of points of discontinuity of the function \( f(x) = x - [x], x \in \mathbb{R} \) is:
An \( n \times n \) matrix is formed using 0, 1 and -1 as its elements. The number of such matrices which are skew symmetric is:
If \( E \) and \( F \) are two independent events with \( P(E) = 0.3 \) and \( P(E \cup F) = 0.5 \), then \( P(E \mid F) - P(F \mid E) \) equals:
Let \( \vec{a}, \vec{b}, \vec{c} \) be vectors of equal magnitude such that the angle between \( \vec{a} \) and \( \vec{b} \) is \( \alpha \), the angle between \( \vec{b} \) and \( \vec{c} \) is \( \beta \), and the angle between \( \vec{c} \) and \( \vec{a} \) is \( \gamma \). Then the minimum value of \( \cos \alpha + \cos \beta + \cos \gamma \) is:
Evaluate the limit \[ \lim_{x \to 0} \frac{\tan \left( -\pi^2 x^2 - x^2 \tan \left( -\pi^2 \right) \right)}{\sin^2 x} \] is:
If \( a, b, c \) are positive real numbers each distinct from unity, then the value of the determinant \[ \left| \begin{matrix} 1 & \log_a b & \log_a c \\ \log_b a & 1 & \log_b c \\ \log_c a & \log_c b & 1 \end{matrix} \right| \] is:
The sum of the first four terms of an arithmetic progression is 56. The sum of the last four terms is 112. If its first term is 11, then the number of terms is:
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:
A function \( f : \mathbb{R} \to \mathbb{R} \), satisfies \[ \frac{f(x+y)}{3} = \frac{f(x) + f(y) + f(0)}{3} \quad \text{for all} \, x, y \in \mathbb{R}. \] If the function \( f \) is differentiable at \( x = 0 \), then \( f \) 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:
If \( \cos^{-1} \alpha + \cos^{-1} \beta + \cos^{-1} \gamma = 3\pi \), then the value of \( \alpha(\beta+\gamma) + \beta(\gamma+\alpha) + \gamma(\alpha+\beta) \) is:
The value of \( \displaystyle \int_0^{1.5} \left\lfloor x^2 \right\rfloor \, dx \) is:
The expression \( 2^{4n} - 15n - 1 \), where \( n \in \mathbb{N} \) (the set of natural numbers), is divisible by:
The straight line \[ \frac{x-3}{3} = \frac{y-2}{1} = \frac{z-1}{0} \] is:
If \( f \) is the inverse function of \( g \) and \( g'(x) = \frac{1}{1+x^n} \), then the value of \( f'(x) \) is:
If the matrix \[ \begin{pmatrix} 0 & a & a\\ 2b & b & -b\\ c & -c & c \end{pmatrix} \] is orthogonal, then the values of \( a, b, c \) are:
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:
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:
The value of the integral \( \int_{0}^{\pi/2} \log\left(\frac{4 + 3\sin x}{4 + 3\cos x}\right) dx \) is:
If \( x = -1 \) and \( x = 2 \) are extreme points of \( f(x) = \alpha \log|x| + \beta x^2 + x \), \( x \neq 0 \), then:
A function \( f \) is defined by \( f(x) = 2 + (x - 1)^{2/3} \) on \( [0, 2] \). Which of the following statements is incorrect?