List of top Mathematics Questions

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:

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:

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

If ΔABC is right angled at C, then the value of tan A + tan B is

Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?

If \[ A = \begin{bmatrix} \cos\theta & \sin\theta & 0
-\sin\theta & \cos\theta & 0
0 & 0 & 1 \end{bmatrix} \] and \( A_{11}, A_{12}, A_{13} \) are the cofactors of \( a_{11}, a_{12}, a_{13} \) respectively, then the value of \( a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13} \) is:

A wire of length 20 units is divided into two parts such that the product of one part and the cube of the other part is maximum. The product of these parts is: