List of top Mathematics Questions

The value of \( (1 + i)^4 \) is:

The relation \( R \) defined on the set \( A = \{1, 2, 3, 4, 5\} \) by \( R = \{(x, y) : |x^2 - y^2|<16 \} \) is given by:

\[ \int \frac{2dx}{(e^x + e^{-x})^2} = ? \]

If \( \mathbf{a} = 2i - 2j + k \) and \( \mathbf{c} = -i + 2k \), then \( \mathbf{a} \times \mathbf{c} \) is equal to:

If \( (-4, 5) \) is one vertex and \( 7x - y + 8 = 0 \) is one diagonal of a square, then the equation of second diagonal is:

\( P = Q \) can also be written as:

Let \[ \int \frac{x^{1/2}}{\sqrt{1 - x^3}} \, dx = \frac{3}{3} \, g(x) + C \] then

Which of the following is an infinite set?

The domain of the function \[ \sqrt{2x - 5x^2 + 6} + \sqrt{2x + 8 - x^2} \] is:

The value of \( c \) in Rolle’s Theorem for the function \( f(x) = e^x \sin x, x \in [0, \pi] \) is:

The equations \( 2x + 3y + 4 = 0 \), \( 3x + 4y + 6 = 0 \), and \( 4x + 5y + 8 = 0 \) are:

The shortest distance between the lines \( x = y + 2 \), \( z = 6x - 6 \) and \( x + 1 = 2y = -12z \) is:

If the tangent at \( P(1, 1) \) on \( y^2 = x(2 - x) \) meets the curve again at \( Q \), then \( Q \) is:

If \( f(x) = \frac{x}{1 + x^2} + \frac{x}{(1 + x^2)^2} + \cdots \) to infinity, then at \( x = 0, f(x) \)

Radius of the circle \( (x + 5)^2 + (y - 3)^2 = 36 \) is:

If \( A = \begin{pmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{pmatrix} \) and \( M = A + A^2 + A^3 + \cdots + A^{20} \), then the sum of all the elements of the matrix \( M \) is equal to ________.

Let \( f : [0, \infty) \rightarrow [0, 3] \) be a function defined by
\[ f(x) = \begin{cases} \max\{\sin t : 0 \le t \le x\}, & 0 \le x \le \pi \\ 2 + \cos x, & x > \pi \end{cases} \] Then which of the following is true ?

Let the mean and variance of the frequency distribution be 6 and 6.8 respectively.
x : \( x_1 = 2,\; x_2 = 6,\; x_3 = 8,\; x_4 = 9 \)
f : \( 4,\; 4,\; \alpha,\; \beta \)
If \( x_3 \) is changed from 8 to 7, then the mean for the new data will be:

If $\int_0^\pi (\sin^3 x) e^{-\sin^2 x} dx = \alpha - \frac{\beta}{e} \int_0^1 \sqrt{t} e^t dt$, then $\alpha+\beta$ is equal to ________.

The number of real roots of the equation $e^{4x} - e^{3x} - 4e^{2x} - e^x + 1 = 0$ is equal to ________.

The distance of the point P(3, 4, 4) from the point of intersection of the line joining the points Q(3, -4, -5) and R(2, -3, 1) and the plane $2x+y+z=7$, is equal to ________.

Let n be a non-negative integer. Then the number of divisors of the form "4n+1" of the number $(10)^{10} \cdot (11)^{11} \cdot (13)^{13}$ is equal to ________.

Let $A = \{n \in \mathbb{N} | n^2 \le n+10000\}$, $B = \{3k+1 | k \in \mathbb{N}\}$ and $C = \{2k | k \in \mathbb{N}\}$. Then the sum of all the elements of the set $A \cap (B-C)$ is equal to ________.

If the real part of the complex number $z = \frac{3+2i\cos\theta}{1-3i\cos\theta}$, $\theta \in (0, \frac{\pi}{2})$ is zero, then the value of $\sin^2 3\theta + \cos^2 \theta$ is equal to ________.

For real numbers $\alpha$ and $\beta \neq 0$, if the point of intersection of the straight lines
$\frac{x-\alpha}{1} = \frac{y-1}{2} = \frac{z-1}{3}$ and $\frac{x-4}{\beta} = \frac{y-6}{3} = \frac{z-7}{3}$
lies on the plane $x+2y-z=8$, then $\alpha-\beta$ is equal to :