List of top Mathematics Questions asked in WBJEE

The acceleration \( f \) (in ft/sec\(^2\)) of a particle after a time \( t \) seconds starting from rest is given by:
\[ f = 6 - \sqrt{1.2t}. \]
Then the maximum velocity \( v \) and the time \( T \) to attain this velocity are:

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:

Choose the correct statement:

The points of extremum of \[ \int_{0}^{x^2} \frac{t^2 - 5t + 4}{2 + e^t} \, dt \] are:

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:

The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = e^x + e^{-x} \) 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:

If \( a_i, b_i, c_i \in \mathbb{R} \) (\( i = 1, 2, 3 \)) and \( x \in \mathbb{R} \), and
\[ \begin{vmatrix} a_1 + b_1x & a_1x + b_1 & c_1 \\ a_2 + b_2x & a_2x + b_2 & c_2 \\ a_3 + b_3x & a_3x + b_3 & c_3 \end{vmatrix} = 0, \]
then:

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:

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:

If \[ y = \tan^{-1} \left[ \frac{\log_e\left(\frac{e}{x}\right)}{\log_e(e x^2)} \right] + \tan^{-1} \left[ \frac{3 + 2\log_e x}{1 - 6\cdot\log_e x} \right], \]
then \( \frac{d^2y}{dx^2} = ? \)

The angle between two diagonals of a cube will be:

Let
\[ A = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \end{bmatrix}. \]
Which of the following is true?

The locus of the midpoint of the system of parallel chords parallel to the line \( y = 2x \) to the hyperbola \( 9x^2 - 4y^2 = 36 \) is:

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:

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 1000! = 3ⁿ × m, where m is an integer not divisible by 3, then n =?

If two circles which pass through the points \( (0, a) \) and \( (0, -a) \) and touch the line \( y = mx + c \) cut orthogonally, then:

In a plane, \(\vec{a}\) and \(\vec{b}\) are the position vectors of two points \(A\) and \(B\) respectively. A point \(P\) with position vector \(\vec{r}\) moves on that plane in such a way that
\[ |\vec{r} - \vec{a}| - |\vec{r} - \vec{b}| = c \quad (\text{real constant}). \]
The locus of \(P\) is a conic section whose eccentricity 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:

Consider the function
\[ f(x) = x(x - 1)(x - 2) \cdots (x - 100). \]
Which one of the following is correct?

Let
\[ A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 2 \\ 1 \\ 7 \end{bmatrix}. \]
For the validity of the result \(AX = B\), \(X\) is:

Let
\[ I(R) = \int_0^R e^{-R \sin x} \, dx, \quad R > 0. \]
Which of the following is correct?

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 \( k = ? \)