List of top Mathematics Questions asked in Bihar Board Class XII

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

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

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

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

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

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

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

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

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

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

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

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

If \( n(A) = 4 \) and \( n(B) = 2 \), then \( n(A \times B) \) is?

If the operation 'o' is defined as \( (a \, o \, b) = a^3 + b^3 \), then what is \( 4 \, o \, (1 \, o \, 2) \)?

If \( f : A \to B \) is an onto function, then

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

If operation 'o' is defined as \( (a \, o \, b) = a^2 + b^2 - ab \), then \( (1 \, o \, 2) \, o \, 3 \) is?

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

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

\(\int_0^1 (x + 2x + 3x^2 + 4x^3) \, dx \)

\(\int_{-1}^1 \sin x \cos^3 x \, dx \)

\(\int_0^1 x^{99} \, dx \)

\(\int_1^9 \frac{dx}{\sqrt{x}} \)

\(\int \frac{dx}{x \log x} \)

\(\int_0^a e^x \, dx \)