List of top Mathematics Questions

If \( R_1 \) and \( R_2 \) be two equivalence relations on a set A, then prove that \( R_1 \cap R_2 \) be also an equivalence relation.
If P(A) = 0.12, P(B) = 0.15 and P(B/A) = 0.18, then find the value of P(A \( \cap \) B).
Prove that \(\displaystyle \frac{\sin A-\cos A+1}{\sin A+\cos A-1}=\frac{1}{\sec A-\tan A}\).

A relation R is defined in the set N as follows:
R = (x, y) : x = y - 3, y > 3
Then, which of the following is correct?

If  \(\begin{vmatrix} 2x & 3 \\ x & -8 \\ \end{vmatrix} = 0\), then the value of \(x\) is:

If radius of cone is 5 cm and its perpendicular height is 12 cm, then the slant height is ...................... .
In the following figure DE\(||\)BC, then: If DE = 4 cm, BC = 8 cm, A(\(\triangle\)ADE) = 25 cm\(^2\), find A(\(\triangle\)ABC).
If \( A = \begin{pmatrix} 2 & x + 9 \\ 1 & 2x \end{pmatrix} \) is invertible, then \( x \neq \):

What is the angle between the hour and minute hands at 4:30?

If point $Q(0,1)$ is equidistant from points $P(5,-3)$ and $R(x,6)$, find the values of $x$.
$\tan\left(\frac{2\pi}{7}\right)\tan\left(\frac{4\pi}{7}\right) + \tan\left(\frac{4\pi}{7}\right)\tan\left(\frac{\pi}{7}\right) + \tan\left(\frac{\pi}{7}\right)\tan\left(\frac{2\pi}{7}\right) =$
Find the direction cosines of a line joining two points \( (-2, 4, -5) \) and \( (1, 2, 3) \).
Let $ A(4, 3), B(2, 5) $ be two points. If $ P $ is a variable point on the same side of the origin as that of line $ AB $ and at most 5 units from the midpoint of $ AB $, then the locus of $ P $ is:
A box is formed by a 3 m x 8 m rectangular steel-sheet on cutting the squares of length x m from its each corner to form the box without cover. Then find the maximum volume of the box so formed.
Prove that \( \int_{0}^{\pi/2} \sqrt{\frac{1+\cos 4x}{2}} \, dx = 1 \).
Minimize Z = 3x + 2y by graphical method under the following constraints:
x + y \( \ge \) 8,
3x + 5y \( \le \) 15,
x \( \ge \) 0, y \( \ge \) 0
The equation of the normal drawn at the point \((\sqrt{2}+1, -1)\) to the ellipse \(x^2 + 2y^2 - 2x + 8y + 5 = 0\) is
Find the general solution of differential equation \( ydx + (x - y^2)dy = 0 \).
Let \( T \) denote the triangle in the \( xy \)-plane bounded by the \( x \)-axis and the lines \( y = x \) and \( x = 1 \). The value of the double integral (over \( T \)) \[ \iint_T (5 - y) \, dx \, dy \] is equal to ............. (rounded off to two decimal places).
The equation \((2p - 3)x^2 + 2pxy - y^2 = 0\) represents a pair of distinct lines
If \[ A = \begin{bmatrix} a & b & c \\ d & e & f \\ l & m & n \end{bmatrix} \] is a matrix such that $|A|>0$ and \[ Adj(A) = \begin{bmatrix} 0 & 4 & -6 \\ 10 & 8 & 0 \\ 2 & 4 & -4 \end{bmatrix}, \] then find the value of \[ \frac{cd}{fb} + \frac{ln}{em}. \]
Prove that the semi-vertical angle of a cone with given slant height and maximum volume is \( \tan^{-1}(\sqrt{2}) \).

Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.

Area of sector of angle $\theta$ of a circle with radius $r$ will be:
If $$ \int \frac{dx}{1 - \sin^4 x} = A \tan x + B \tan^{-1}(\sqrt{2} \tan x) + C, $$ then find $ A^2 - B^2 $.