List of top Mathematics Questions

Equation of a plane parallel to the plane \( 9x - 8y + 7z = 10 \) is:

Find the magnitude of the vector \[ \left| \mathbf{i} - \mathbf{j} - 3 \mathbf{k} \right|. \]

Find the square of the vector \[ (4\mathbf{i} + 3\mathbf{j})^2. \]

Find the derivative of \( \log(x^9) \).

Given that \( \frac{x - 19}{13} = \frac{y - 17}{11} = \frac{z - 15}{9} \), find the values of \( x, y, z \).

If the direction ratios of two parallel lines are 2, 7, 9, then the value of x is:

If the direction ratios of two parallel lines are \( a, b, c \) and \( x, y, z \), then \( az = \dots \)?

If the direction ratios of two mutually perpendicular lines are 5, 2, 4 and 4, 8, x, then the value of x is:

Through which of the following points does the line \[ \frac{x-11}{12} = \frac{y-12}{13} = \frac{z+13}{14} \text{ pass?} \]

If \( A = [1 \ 2 \ 3] \), find \( A' \).

Find the product of the matrices: \[ \left[ \begin{matrix} 5 & -1 \\ 6 & -7 \end{matrix} \right] \times \left[ \begin{matrix} 2 & 1 \\ 3 & 4 \end{matrix} \right] \]

Multiply the matrices: \[ \left[ \begin{matrix} 5 & 1 & 2 \\ 3 & 4 \end{matrix} \right] \]

Evaluate the determinant: \[ \left| \begin{matrix} 3 & \sqrt{3} & \sqrt{3} \\ 4 & 0 & 0 \\ 0 & 0 & 0 \\ \end{matrix} \right| \]

Find \( \frac{d}{dx} \left( \log 5x \right) \).

Find the determinant of the matrix: \[ \left| \begin{matrix} 21 & 11 & 10 \\ 25 & 15 & 10 \\ 64 & 27 & 37 \end{matrix} \right| \]

Find the determinant of the matrix: \[ \left| \begin{matrix} 10 & 4 \\ 13 & 5 \end{matrix} \right| \]

Solve for \( x \) in the determinant equation: \[ \left| \begin{matrix} x & 15 \\ 4 & 15 \end{matrix} \right| = 0 \]

What is \( \cos^{-1} x + \sec^{-1} 1 \)?

Find \( \cot^{-1} \left( \tan \frac{\pi}{7} \right) \).

What is \( \tan \left( \frac{1}{2} \left( \tan^{-1} x + \tan^{-1} \frac{1}{x} \right) \right) \)?

Find \( \cos^{-1} \left( \cos \frac{8\pi}{5} \right) \).

Find \( \tan^{-1} (-\sqrt{3}) \).

\(\int \frac{x-3}{x^2-9} \, dx\)

Let \( A = \{ 1, 2, 3, ..., n \} \), how many bijective functions \( f: A \to A \) can be defined?

If \( f: \mathbb{R} \to \mathbb{R} \) such that \( f(x) = 3x - 4 \), then which of the following is \( f^{-1}(x) \)?