List of top Mathematics Questions

Find the value of $ \sin 75^\circ \cos 15^\circ + \cos 75^\circ \sin 15^\circ $.
A bag contains 5 red, 3 blue, and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both are red?
If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.
Solve the system of equations: \(x + y = 3\), \(x - y = 1\).
Find the angle between the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \).
If $ y = \ln(x^2 + 1) $, then find $ \frac{dy{dx} $ at $ x = 1 $.
Find the angle between the vectors \( \mathbf{a} = (2, -1, 3) \) and \( \mathbf{b} = (1, 4, -2) \).
If the roots of the quadratic equation \( 2x^2 - 5x + k = 0 \) are real and distinct, what is the range of values for \( k \)?
If $ f(x) = e^{2x} \sin x $, find $ f'(x) $.
If log$_{10}$(x + 1) = 2, what is the value of x?
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
In triangle $ ABC $, the length of sides are $ AB = 7 $, $ BC = 10 $, and $ AC = 5 $. What is the length of the median drawn from vertex $ B $?
Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \).
If \( \sin \theta + \cos \theta = 1 \), what is the value of \( \sin^2 \theta + \cos^2 \theta \)?
What is the value of \( \sin 30^\circ \)?
What is the area of a circle with diameter 10 cm?
What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
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 the roots of the quadratic equation \( x^2 - 6x + k = 0 \) are real and distinct, what is the range of values for \( k\)?
What is the value of \( \int_0^{\pi/2} \sin x \cos x \, dx\)?
If \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), find the determinant of \( A^2 \).
What is the sum of the first 10 terms of the arithmetic progression with first term 3 and common difference 2?
The area enclosed between the curve \(y = \log_e(x + e)\) and the coordinate axes is:
If the number of terms in the binomial expansion of \((2x + 3)^n\) is 22, then the value of \(n\) 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).