List of top Mathematics Questions

If \( \mathbf{a} \) and \( \mathbf{b} \) are two non-zero vectors such that the angle between them is \( 60^\circ \), what is the probability that the dot product \( \mathbf{a} \cdot \mathbf{b} \) is positive?
A die is rolled once. What is the probability of rolling a number greater than 4?
In the word "UNIVERSITY", find the probability that the two "I"s do not come together.
Find the value of the following expression: \[ \tan^2(\sec^{-1}4) + \cot(\csc^{-1}3) \]
Given that: \[ x = a \sin(2t) (1 + \cos(2t)), \quad y = a \cos(2t) (1 - \cos(2t)) \] Find \(\frac{dy}{dx}\).
Find the value of \( \log_3 81 \).
Find the value of \( x \) if \( \sin(2x) = 1 \).
Find the sum of the first 20 terms of the arithmetic progression: \( 2, 5, 8, 11, \dots \).
Solve the system of equations: \[ x + y = 10 \] \[ 3x - y = 5 \]
Find the length of the diagonal of a rectangle with length 6 cm and breadth 8 cm.
If \( \log_2 x = 5 \), what is the value of \( x \)?
Solve the system of equations: \[ x + y = 5 \] \[ 2x - y = 4 \]
Find the value of the determinant \( \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix} \).
Find the derivative of the function \( f(x) = 3x^2 - 5x + 7 \).
Solve for \( x \): \( \log_2 (x-1) = 3 \).
Find the area of a triangle with vertices \( A(2, 3) \), \( B(5, 11) \), and \( C(8, 7) \).
Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).
Find the area of a circle with radius 7 cm.
Solve for $ x $ in the equation $ 2x - 3 = 5x + 12 $.
If $ f(x) = 2x^2 - 3x + 5 $, find $ f(3) $.
Find the area of a triangle with base 8 cm and height 6 cm.
Find the sum of the roots of the quadratic equation $ 2x^2 - 5x + 3 = 0 $.
If $ x = 2 $, what is the value of $ 3x^2 - 5x + 7 $?
Find the area of a triangle with base 12 cm and height 5 cm.
Solve for $ x $ in the equation $ \frac{1}{x+3} + \frac{1}{x+5} = \frac{1}{6} $.