List of top Mathematics Questions

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 \( (1, 2, 3) \).
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 $.
Cards numbered 10, 11, 12, ..., 30 are kept in a box and shuffled thoroughly. Rahit draws a card at random from the box. The probability that the number on the card is a multiple of 6 or 5 is:
If the operation 'o' is defined as \( (a \, o \, b) = a^3 + b^3 \), then what is \( 4 \, o \, (1 \, o \, 2) \)?
If \( f(x) = \begin{cases} -2 & \text{if } x \le -1 \\ 2x & \text{if } -1 < x \le 1 \\ 2 & \text{if } x > 1 \end{cases} \), then test the continuity of the function at \( x = -1 \) and at \( x = 1 \).

Evaluate:
\[ I = \int_2^4 \left( |x - 2| + |x - 3| + |x - 4| \right) dx \]

If sum of first 9 terms of an $A.P.$ is $81$ and the sum of first $17$ terms is $289$, find its first term and the common difference.
If \( 2P(A) = P(B) = \frac{5}{13} \) and \( P(A|B) = \frac{2}{5} \), then find \( P(A \cup B) \).
What is the value of \( \csc 31^\circ \sec 59^\circ \)?
$\cot(90^\circ - \theta) = ?$
The value of \( 1 + \sec 19^\circ \sin 71^\circ \) is: