List of top Mathematics Questions

Find the equation of the tangent to the curve \(y = x^2\) at the point (1,1).
What is the area of a circle with diameter 10 cm?
What is the value of \(\int \frac{1}{x^2 + 1} \, dx\)?
Solve the system of equations: \(x + y = 3\), \(x - y = 1\).
Find the angle between the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \).
A box contains 5 red balls and 3 blue balls. If two balls are drawn randomly without replacement, what is the probability that one of the balls is red and the other is blue?
Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \).
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
Find the angle between the vectors \( \mathbf{a} = (2, -1, 3) \) and \( \mathbf{b} = (1, 4, -2) \).
If \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \), find the determinant of \( A^2 \).
Find the value of the integral: \[ \int_0^\pi \sin^2(x) \, dx. \]
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 $.
The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
If $ y = \ln(x^2 + 1) $, then find $ \frac{dy{dx} $ at $ x = 1 $.
If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
If $ \tan \theta + \cot \theta = 4 $, then find the value of $ \tan^3 \theta + \cot^3 \theta $.
If $ f(x) = e^{2x} \sin x $, find $ f'(x) $.
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 value of $ \sin 75^\circ \cos 15^\circ + \cos 75^\circ \sin 15^\circ $.
The value of $ \sin^2 30^\circ + \cos^2 60^\circ $ is:
The area of a triangle with vertices at points $ A(1,2) $, $ B(4,6) $, and $ C(k, 8) $ is 5. Find the value of $ k $.
The sum of the infinite geometric series $ S = \frac{a}{1-r} $ is 24, and the sum of the first three terms is 21. Find $ a $ and $ r $.
Given the sets $ A = \{ x \mid |x - 2|<3 \} $ and $ B = \{ x \mid |x + 1| \leq 4 \} $, find $ A \cap B $.
The 5th term of an AP is 20 and the 12th term is 41. Find the first term.