List of top Mathematics Questions

If \[ 7 \cos^2 x + 3 \sin^2 x = 6, \] then the value of \( \cos 2x \) is equal to
Let \[ \sum_{k=1}^{15} \sin (t_k) = 0 \quad {and} \quad \sum_{k=1}^{15} \sin (3t_k) = \frac{-24}{5}, \] where \( t_1, t_2, t_3, \dots \) are real numbers. Then the value of the sum \[ \sum_{k=1}^{15} \sin^3 (t_k) \] is equal to
The value of \[ \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{2}{3} \right) + \cot^{-1} \left( \frac{9}{7} \right) \] is equal to
The value of \( \sin \left( 2 \cos^{-1} \left( \frac{5}{12} \right) + \sin^{-1} \left( \frac{5}{12} \right) \right) \) is equal to
If \( \sin t + \cos t = \sqrt{2} \), then \( \tan t + \cot t \) is equal to
The value of \( \tan \left( \cos^{-1} \left( \frac{-24}{25} \right) \right) \) is equal to

Simplify: \( \tan x - \cot x + \csc x \sec x \)

Let \( A \) and \( B \) be two events. If \( P(A) = 0.49 \), \( P(B) = 0.3 \) and \( P(A | B^c) = 0.4 \), then \( P(A | B) \) is equal to
If two dice are rolled simultaneously, then the probability that the difference of the numbers on the two dice equals to zero is
The standard deviation of a data set \( x_1, x_2, \dots, x_6 \) (\( x_i>0 \)) is 2. If \[ \sum_{i=1}^{9} x_i^2 = 360, \] then the mean of the data set is
The means of two samples of size 30 and 40 are 35 and 42 respectively. Then the mean of the combined sample of size 70 is
If \[ A = \begin{bmatrix} -7 & 3 \\ 3 & -1 \end{bmatrix} \] then \( \det(A^5) \) is equal to:
Let \( A \) be a \( 3 \times 3 \) matrix with \( |A| = 7 \). If \( B = 3A \), then the value of \[ \left| \frac{{adj } A}{B} \right| \] is equal to
The value of the sum \[ \sum_{k=0}^{48} \frac{1}{(k + 1)(k + 2)} \] is equal to
The relation \( R \) in the set of integers \( \mathbb{Z} \) is given by \( R = \{(a, b) : b = 2a + 3 \} \). Then the relation \( R \) is:
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
The sum of the first 20 terms of the G.P. \( \sqrt{3} + \frac{-1}{\sqrt{3}} + \frac{1}{3\sqrt{3}} + \cdots \) is equal to
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
If the complex number \( \frac{2 + i}{\lambda + i} \) lies on the line \( y = x \) of the first quadrant, then the value of \( \lambda \) is equal to
Let \( f(x) = 6x^2 + 9x + 10 \) and \( g(x) = x^2 - 9x - 9 \). Then the value of \( (f \circ g)(10) \) is
If \( x \) satisfies the inequality \( -3<\frac{1}{2} + \frac{-3x}{2} \leq 6 \), then \( x \) lies in the interval
The range of the function \( f(x) = 8 + \sqrt{x - 5} \) is:

Let \( f(x) = \sqrt{4 - x^2} \), \( g(x) = \sqrt{x^2 - 1} \). Then the domain of the function \( h(x) = f(x) + g(x) \) is equal to:

Differentiate \( y = x^x + (\cos x)^{\tan x} \) with respect to \( x \).

The probabilities of solving a question by \( A \) and \( B \) independently are \( \frac{1}{2} \) and \( \frac{1}{3} \) respectively. If both of them try to solve it independently, find the probability that: