List of top Mathematics Questions

Find the area of the triangle with vertices at (0, 0), (3, 0), and (0, 4).
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?
If $ \log_2(x + 1) = 3 $, what is the value of $ x $?
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 \(\sin \theta = \frac{3}{5}\) 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:
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
Which of the following is correct for A - B?
For the matrix \(A=\begin{bmatrix}1&1&1\\ 1&2&-3\\ 2&-1&3\end{bmatrix}\)show that \(A^3−6A^2+5A+11I=O\).Hence,find A−1.
The coefficient of $ {{a}^{5}}{{b}^{6}}{{c}^{7}} $ in the expansion of $ {{(bc+ca+ab)}^{9}} $ is
Let A = [1, 2, 3, 4, 5], m be the number of relations such as 4x ≤ 5y XRY and n be the minimum number of elements to be added from A × A to make a symmetric relation. Then the value of n + m.
Let $q$ be the maximum integral value of $p$ in $[0,10]$ for which the roots of the equation $x^2-p x+\frac{5}{4} p=0$ are rational Then the area of the region $\left\{(x, y): 0 \leq y \leq(x-q)^2, 0 \leq x \leq q\right\}$ is
Compute the indicated products \((i)\begin{bmatrix}a&b\\-b&a\end{bmatrix}\begin{bmatrix}a&-b\\b&a\end{bmatrix}\)\((ii)\begin{bmatrix}1\\2\\3\end{bmatrix}\begin{bmatrix}2&3&4\end{bmatrix}\)\((iii)\begin{bmatrix}1&-2\\2&3\end{bmatrix}\begin{bmatrix}1&2&3\\2&3&1\end{bmatrix}\)\((iv)\begin{bmatrix}2&3&4\\ 3&4&5\\ 4&5&6\end{bmatrix}\begin{bmatrix}1&-3&5\\ 0&2&4\\ 3&0&5\end{bmatrix}\)
\((v)\begin{bmatrix}2&1\\3&2\\-1&1\end{bmatrix}\begin{bmatrix}2&-3\\1&0\\3&1\end{bmatrix}\)\((vi)\begin{bmatrix}3&-1&3\\-1&0&2\end{bmatrix}\begin{bmatrix}2&-3\\1&0\\3&1\end{bmatrix}\)
The value of $ ^{49}C_3 ^{48}C_3 ^{47}C_3 ^{46}C_3 ^{45}C_3 ^{45}C_4 $ is
Using the number line write the integer which is :
(a) 3 more than 5
(b) 5 more than –5
(c) 6 less than 2
(d) 3 less than –2