List of top Mathematics Questions

The radius of the circle \( x^2 + y^2 - 2x - 4y - 4 = 0 \) is:
The area of the triangle formed by the coordinate axes and a line whose perpendicular from the origin makes an angle of 45° with the x-axis is 50 square units. Then the equation of the line is:
If \( \vec{a} = 2\vec i + 4\vec j + 7\vec k \) and \( \vec {b} = 4\vec i + 7\vec j + 2\vec k \), then the angle between \( \vec{a} + \vec{b} \) and \( \vec{a} - \vec{b} \) is equal to:
If \( \tan \left( \frac{\pi}{12} + 2x \right) = \cot 3x \), where \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
If \( 3 \tan^{-1}(x) + \cot^{-1}(x) = \pi \), then \( \sin^{-1}(x) \) is:
If \( z = 1 + i \), then the maximum value of \( |z + 12 + 9i| \) is
If a continuous function \( f \) is defined as \[ f(x) = \left\{ \begin{array}{ll} ax + 1, & x < 2 \\ x^2 + 7, & x \geq 2 \end{array} \right. \] then the value of \( a \) is:
If \( A \) and \( B \) are two independent events such that \( P(A) = 0.4 \) and \( P(A \cup B) = 0.7 \), then \( P(B) \) is equal to:
Let \( f(x) = \cos^{-1} \left( \frac{1 - \tan^2 x}{1 + \tan^2 x} \right) \). Then \( f\left( \frac{\pi}{2} \right) \) is equal to:
The integral \( \int \sqrt{1 + \sin 2x} \, dx \) is equal to:
The value of \( \int_{-1}^{1} x^2 \sin x \, dx \) is equal to:
If \( \sin x = \frac{3}{5} \), then the value of \( \sec x + \tan x \) is equal to:
The value of \( \int_0^1 x(1 - x)^{10} \, dx \) is equal to:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
If \( \cos x - \sin x = 0 \), \( 0 \leq x \leq \pi \), then the value(s) of \( x \) is/are:
If \( A = \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \), then \( A^2 (\text{adj} A) \) is:
The value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) is:
If \( \cos \theta + \sin \theta = \sqrt{2} \), then \( \cos \theta - \sin \theta \) is equal to:
The common ratio of a G.P. is 10. Then the ratio between its 11th term and its 6th term is:
The value of \( \lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1} \) is:
Equation of the line parallel to the line \( \frac{x-2}{2} = \frac{y-2}{3} = \frac{z-1}{-2} \) and passing through the point \( (3, 2, -1) \) is:
If \( f(x) = \int_0^{x^3} (t + 4)^2 \, dt \), then \( f'(2) \) is equal to:
The function \( f(x) = (x - 4)^2 (1 + x)^3 \) attains a local extremum at the point:
If \( f(x) = x|x| \), then \( f'(-1) + f'(1) \) is equal to:
The derivative of \( t^2 + t \) with respect to \( t-1 \) at \( t = -2 \), is equal to: