List of top Mathematics Questions

The angle between the lines \( \frac{x}{1} = \frac{y}{1} = \frac{z}{1} \) and \( \frac{x}{0} = \frac{y}{1} = \frac{z}{-1} \) is:
If \( \left( \frac{1 - i}{1 + i} \right)^{10} = a + ib \), then the values of \( a \) and \( b \) are, respectively:
The second term of a G.P. is 4, then the product of the first three terms is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
The numbers \( a, b, c, d \) are in G.P. with common ratio \( r \). If \( \frac{1}{a^3 + b^3} + \frac{1}{b^3 + c^3} + \frac{1}{c^3 + d^3} \) are also in G.P., then the common ratio is:
If \( B = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a \( 3 \times 3 \) matrix \( A \) and \( |A| = 4 \), then the value of \( \alpha \) is:
If the determinant of the matrix \( \begin{bmatrix} |x| & 1 & 2 \\ 4 & 1 & x \\ 1 & -1 & 3 \end{bmatrix} \) equals -10, then the values of \( x \) are:
If the points \( (2, -3), (\lambda, -1) \) and \( (0, 4) \) are collinear, then the value of \( \lambda \) is equal to:
The minimum value of \( f(x) = 7x^4 + 28x^3 + 31 \) is:
Let \( f(x) = x - \lfloor x \rfloor \), where \( \lfloor \cdot \rfloor \) denotes the greatest integer function and \( x \in (-1, 2) \). The number of points at which the function is not continuous is:
Let \( \vec{a} = \hat{i} - \hat{j} \), \( \vec{b} = \hat{j} - \hat{k} \), and \( \vec{c} = \hat{k} - \hat{i} \), then the value of \( \vec{b} \cdot (\vec{a} + \vec{c}) \) is:
A ray of light passing through the point \( (1, 2) \) is reflected on the \( x \)-axis at a point \( P \) and passes through the point \( (5, 6) \). Then the abscissa of the point \( P \) is:
If \( f(x) = \cos x - \sin x \), and \( x \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right) \), then \( f' \left( \frac{\pi}{3} \right) \) is equal to:
The differential equation \( \frac{dy}{dx} + x = A \) (where A is constant) represents:
If \( f(x) = \sin^{-1}(\cos x) \), then \( \frac{d^2 y}{dx^2} \) at \( x = \frac{\pi}{4} \) is:
If \( y = \tan^{-1} \left( \frac{\cos x - \sin x}{\cos x + \sin x} \right) \), \( \frac{-\pi}{2}<x<\frac{\pi}{2} \), then \( \frac{dy}{dx} \) is:
If \( f(x) = \begin{cases} x^2 & \text{for } x < 0 \\ 5x - 3 & \text{for } 0 \leq x \leq 2 \\ x^2 + 1 & \text{for } x > 2 \end{cases} \), then the positive value of \( x \) for which \( f(x) = 2 \) is:
The maximum value of \( y = 12 - |x - 12| \) in the range \( -11 \leq x \leq 11 \) is:

If 

then the value of \( x - y \) is:

Let \( A = (a_{ij}) \) be a square matrix of order 3 and let \( M_{ij} \) be the minors of \( a_{ij} \). If \( M_{11} = -40, M_{12} = -10, M_{13} = 35 \), and \( a_{11} = 1, a_{12} = 3, a_{13} = -2 \), then the value of \( |A| \) is equal to:
Evaluate \( \int x e^{x^2} \, dx \):
If \( y = \frac{x^2}{x - 1} \), then \( \frac{dy}{dx} \) at \( x = -1 \) is:
The equation of the line passing through the point \( (1, 2) \) and perpendicular to the line \( x + y + 1 = 0 \) is:
If \( _nP_r = 480 \) and \( _nC_r = 20 \), then the value of \( r \) is equal to:
The function \( f(x) = 2x^3 + 9x^2 + 12x - 1 \) is decreasing in the interval: