List of top Mathematics Questions

The integral \( \int_5^{10} \left\lfloor x \right\rfloor dx \) is equal to (where \( \left\lfloor x \right\rfloor \) denotes the greatest integer function):
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
The direction ratios of the line joining the points \( (2, 3, 4) \) and \( (-1, 4, -3) \) is:
If \( P(-3, 4) \) and \( Q(3, 1) \) are points on a straight line, then the slope of the straight line perpendicular to PQ is:
If \( A = \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \), then \( A^2 (\text{adj} A) \) is:
The value of \( \lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1} \) 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:
The function \( f(x) = (x - 4)^2 (1 + x)^3 \) attains a local extremum at the point:
If \( \cos x - \sin x = 0 \), \( 0 \leq x \leq \pi \), then the value(s) of \( x \) is/are:
If \( \vec{a} \) and \( \vec{b} \) are non-collinear unit vectors and \( |\vec{a} + \vec{b}|^2 = 3 \), then \( (3\vec{a} + 2\vec{b}) \cdot (3\vec{a} - \vec{b}) \) is equal to:
If \( x + iy = \frac{3 + 4i}{5 - 12i} \), then \( x + y \) 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:
Let \( \alpha, \beta, \gamma \) be the direction cosines of a vector \( \vec{a} = x \hat{i} + y \hat{j} + z \hat{k} \), where \( z<0 \). If \( \alpha = \frac{-4}{\sqrt{105}} \) and \( \beta = \frac{\sqrt{5}}{\sqrt{21}} \), then \( \gamma \) is equal to
Let \( A(0,3,-3) \), \( B(1,1,1) \) and \( C(2,0,3) \) be three points in space. Then the projection of \( \overrightarrow{AB} \) on \( \overrightarrow{AC} \) is equal to
If \( \vec{a} = 5\hat{i} - 7\hat{j} + 9\hat{k} \) and \( \vec{b} = -5\hat{i} + 7\hat{j} - 9\hat{k} \), then \( \vec{a} \cdot (\vec{a} \times \vec{b}) + (\vec{a} + \vec{b}) \cdot \hat{b} \) is equal to
The angle between the vectors \( \vec{a} \) and \( \vec{b} \) is \( \frac{\pi}{3} \). If \( | \vec{a} \cdot \vec{b} |^2 = 15 \), then \( | \vec{a} \times \vec{b} |^2 \) is equal to
If \( \sin t + \cos t = \sqrt{2} \), then \( \tan t + \cot t \) is equal to
If \[ 7 \cos^2 x + 3 \sin^2 x = 6, \] then the value of \( \cos 2x \) is equal to
The range of the function \( f(x) = 7\cos(10x + 4\pi) \) is
Evaluate the integral: \[ \int \frac{\sin \theta \sin 2\theta}{1 - \cos 2\theta} d\theta. \]
If the complex number \( 2 + i \) is rotated through an angle \( 90^\circ \) in the anti-clockwise direction about the origin in the complex plane, then the resulting complex number is
For the curve \[ y = \alpha x^2 + \cos y + \beta, \] the value of \( \frac{dy}{dx} \) at \( (1,0) \) is 2. Then the value of \( \alpha \beta \) is equal to
Let \( \alpha \) and \( \beta \) be real numbers such that \( f(x) \) is defined as: \[ f(x) = \begin{cases} 2x^2 + 4x + \alpha, & \text{if } x < 1 \\ \beta x^2 + 5, & \text{if } x \geq 1 \end{cases} \] and is differentiable at \( x = 1 \). Then \( \alpha + \beta \) is equal to:
Let \( A = \{ 1, 3, 5, 7, \dots, 21 \} \). The number of ways 4 numbers, containing always 11, can be selected from the set A is equal to