List of top Mathematics Questions

Find the derivative of the function \(f(x) = \sqrt{3x^2 + 2x + 1}\).

If \( \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + 2\hat{j} - \hat{k} \), then the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \) is:
Two numbers are selected at random (without replacement) from the first 50 natural numbers. The probability that their sum is even is:
If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is:
The sum of the first 20 terms of an arithmetic progression is 610. If the first term is 7, what is the common difference?
The integral $ \int (3x^2 - 2x + 1) \, dx $ is:
If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) and \( A + B + C = \pi \), then which of the following is true?
If the roots of the quadratic equation \( x^2 - 6x + k = 0 \) have a difference of 2, find the value of \( k \).
If \( z = 1 + i \), find the modulus of \( z^2 \).
If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), find the inverse of matrix \( A \).
A box contains 4 white and 6 black balls. If 3 balls are drawn at random with replacement, what is the probability that at least one is white?
The mean of 5 numbers is 10, and their variance is 16. If one number is increased by 5, what is the new mean?
Find the area of the triangle with vertices at (0, 0), (3, 0), and (0, 4).
If $ \log_2(x + 1) = 3 $, what is the value of $ x $?

If \(\sin \theta = \frac{3}{5}\) and $ \theta $ is in the first quadrant, what is $ \tan \theta $?

The equation of the circle with center at $ (2, -3) $ and radius $ 5 $ is:
A box contains 5 red balls and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?
If the roots of the quadratic equation $ 2x^2 - 3x + 1 = 0 $ are $ \alpha $ and $ \beta $, what is the value of $ \alpha^2 + \beta^2 $?
Let \( f(x) = 2x^3 - 3x \neq 4 \). Then the inverse function \( f^{-1}(x) \) is:
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
Let a circle pass through the point \( (1, 2) \) and touch the \( x \)-axis at \( (3, 0) \). Then the equation of the circle is:
If \( \tan \theta = \frac{3}{4} \) and \( \theta \) is in the first quadrant, find the value of \( \sin \theta + \cos \theta \).
If \( A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \), find the determinant of \( A \).
Evaluate \( \int_{0}^{1} (2x + 1) \, dx \).
Given the linear equation \(2x + 3y – 8 = 0\), write another linear equation in two variables such that the geometrical representation of the pair so formed is: (i) intersecting lines (ii) parallel lines (iii) coincident lines