>
WBJEE
>
Mathematics
List of top Mathematics Questions asked in WBJEE
Let \(f : \mathbb{R} \to \mathbb{R}\) be given by \(f(x) = |x^2 - 1|\), then:
WBJEE - 2024
WBJEE
Mathematics
Limits
\(f(x) = \cos x - 1 + \frac{x^2}{2!}, \, x \in \mathbb{R}\)
Then \(f(x)\) is:
WBJEE - 2024
WBJEE
Mathematics
Limits
Let \(f : \mathbb{R} \to \mathbb{R}\) be a differentiable function and \(f(1) = 4\). Then the value of
\[ \lim_{x \to 1} \int_{4}^{f(x)} \frac{2t}{x - 1} \, dt \]
WBJEE - 2024
WBJEE
Mathematics
Integration
If \(\int \frac{\log(x + \sqrt{1 + x^2})}{1 + x^2} \, dx = f(g(x)) + c\), then:
WBJEE - 2024
WBJEE
Mathematics
Integration
The equation \(2x^5 + 5x = 3x^3 + 4x^4\) has:
WBJEE - 2024
WBJEE
Mathematics
Quadratic Equation
For every real number \(x \neq -1\), let \(f(x) = \frac{x}{x+1}\). Write \(f_1(x) = f(x)\) and for \(n \geq 2\), \(f_n(x) = f(f_{n-1}(x))\). Then \(f_1(-2), f_2(-2), \ldots, f_n(-2)\) must be:
WBJEE - 2024
WBJEE
Mathematics
Relations and Functions
The area bounded by the curves \(x = 4 - y^2\) and the Y-axis is:
WBJEE - 2024
WBJEE
Mathematics
Integration
If \(x y' + y - e^x = 0, \, y(a) = b\), then
\[ \lim_{x \to 1} y(x) \text{ is} \]
WBJEE - 2024
WBJEE
Mathematics
Differential Equations
Let \(f\) be a differential function with
\[ \lim_{x \to \infty} f(x) = 0. \text{ If } y' + y f'(x) - f(x) f'(x) = 0, \lim_{x \to \infty} y(x) = 0 \text{ then,} \]
WBJEE - 2024
WBJEE
Mathematics
Differential Equations
For any integer \(n\),
\[ \int_{0}^{\pi} e^{\cos^2 x} \cdot \cos^3(2n + 1)x \, dx \text{ has the value.} \]
WBJEE - 2024
WBJEE
Mathematics
Integration
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:
WBJEE - 2024
WBJEE
Mathematics
Straight lines
Choose the correct statement:
WBJEE - 2024
WBJEE
Mathematics
Trigonometry
The points of extremum of \[ \int_{0}^{x^2} \frac{t^2 - 5t + 4}{2 + e^t} \, dt \] are:
WBJEE - 2024
WBJEE
Mathematics
Integration
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:
WBJEE - 2024
WBJEE
Mathematics
Binomial theorem
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:
WBJEE - 2024
WBJEE
Mathematics
Quadratic Equation
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:
WBJEE - 2024
WBJEE
Mathematics
Straight lines
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:
WBJEE - 2024
WBJEE
Mathematics
Limits
The angle between two diagonals of a cube will be:
WBJEE - 2024
WBJEE
Mathematics
Vectors
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:
WBJEE - 2024
WBJEE
Mathematics
Relations and Functions
If two circles which pass through the points \( (0, a) \) and \( (0, -a) \) and touch the line \( y = mx + c \) cut orthogonally, then:
WBJEE - 2024
WBJEE
Mathematics
Circle
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:
WBJEE - 2024
WBJEE
Mathematics
Trigonometry
Let
\[ A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}. \]
Which of the following is true?
WBJEE - 2024
WBJEE
Mathematics
Matrices and Determinants
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 \( k = ? \)
WBJEE - 2024
WBJEE
Mathematics
Sequence and series
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:
WBJEE - 2024
WBJEE
Mathematics
Probability
Consider the function
\[ f(x) = x(x - 1)(x - 2) \cdots (x - 100). \]
Which one of the following is correct?
WBJEE - 2024
WBJEE
Mathematics
Limits
Prev
1
2
3
4
...
23
Next