List of top Mathematics Questions

The sum of the ages of a father and his son is 60 years. The father is three times as old as the son. What is the son's age?
Find the value of \( \sin 30^\circ + \cos 60^\circ \).
The area of a triangle with base 12 cm and height 5 cm is?
If the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are \( p \) and \( q \), then what is the value of \( p + q \)?
If ∫ (2x + 3)/((x - 1)(x^2 + 1)) dx = log_x {(x - 1)^(5/2)(x^2 + 1)^a} - (1/2) tan^(-1)x + C, then the value of a is:
Find the value of the integral: ∫ (2x + 3)/((xy)(x^2 + 1)) dx
If \( y = x^x + x^x \), then find \( \frac{dy}{dx} \):
Given \( f'(1) = 3 \), \( f(1) = 1 \), and
\[ y = f\left(f(f(x))\right) + \left(f(x)\right)^2, \] then find \( \frac{dy}{dx} \) at \( x = 1 \).
Evaluate the expression: \[ f\left(f(f(x))\right) + \left(f(f(x))\right)^2 \quad \text{if} \quad x = 1 \]
Evaluate the determinant of the matrix: \[ \left| \begin{array}{cc} 1 & \tan x
-\tan x & 1 \end{array} \right| \]
Evaluate the integral: \( \int \sin^5 x \, dx \)
The feasible region of the linear programming problem is determined by the system of inequalities: \[ x + y \leq 6, \quad x \geq 0, \quad y \geq 0. \] What is the maximum value of \( x + y \) in the feasible region?
In how many ways can 5 people be arranged in a row?
If the roots of the quadratic equation \( x^2 - 7x + 12 = 0 \) are \( \alpha \) and \( \beta \), then the value of \( \alpha + \beta \) is:
If \( \tan \theta = 2 \), then the value of \( \sec^2 \theta \) is:
A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls drawn are red?
The distance between the points \( A(3, 4) \) and \( B(-1, -2) \) is:
The value of the definite integral \( \int_0^{\pi} \sin^2 x \, dx \) is:
What is the sum of the first 10 terms of the arithmetic progression with first term 3 and common difference 2?
If \( \sin \theta + \cos \theta = \sqrt{2} \), what is the value of \( \sin \theta \cos \theta \)?
What is the value of \( \int_0^{\pi/2} \sin x \cos x \, dx\)?
If the roots of the quadratic equation \( x^2 - 6x + k = 0 \) are real and distinct, what is the range of values for \( k\)?
If \( \sin \theta + \cos \theta = 1 \), what is the value of \( \sin^2 \theta + \cos^2 \theta \)?
The sum of the first 30 terms of an arithmetic progression is 930. If the first term is 2, what is the common difference of the progression?
If log$_{10}$(x + 1) = 2, what is the value of x?