List of top Mathematics Questions asked in Bihar Board Class XII

Find the integral of \( \frac{(\sqrt{x+1})^2}{x\sqrt{x + 2x + \sqrt{x}}} \).
Find \( \tan^{-1} (\sqrt{3}) - \cot^{-1} (-\sqrt{3}) \).
Find \( \sin \left( \sin^{-1} \frac{2}{3} \right) + \tan^{-1} \left( \tan \frac{3\pi}{4} \right) \).
Find \( \tan^{-1} \left( \frac{1}{2} \right) + \tan^{-1} \left( \frac{1}{3} \right) \).
If \( \sin \left( \sin^{-1} \frac{1}{5} \right) + \cos^{-1} x = 1 \), find \( x \).
Multiply the matrices: \[ \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \]
If \( A = \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \), find \( A^{100} \).

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

Multiply the matrices: \[ \left[ \begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix} \right] \left[ \begin{matrix} 4 & 0 \\ 0 & 4 \end{matrix} \right] \]
Multiply the matrices: \[ \left[ \begin{matrix} 2 & 5 \\ 3 & 7 \end{matrix} \right] \left[ \begin{matrix} 2 & 5 \end{matrix} \right] \] \\
Find the product of the matrices: \[ \left[ \begin{matrix} 3 & -2 \\ -1 & -1 \end{matrix} \right] \]
Multiply the matrix: \[ \left[ \begin{matrix} 4 & -2 \\ \end{matrix} \right] \] \[ \left[ \begin{matrix} -1 \\ -1 \end{matrix} \right] \]
Find the adjoint of the matrix: \[ \left[ \begin{matrix} 2 & 3 \\ 5 & 4 \end{matrix} \right] \]
Find the integral: \[ \int e^{3x} \, dx \]
Find the derivative: \[ \frac{d}{dx} \left[ \left| \frac{x}{4} \right| \right] \]
Find the integral: \[ \int x^m \cdot x^n \, dx \]
Find the derivative: \[ \frac{d}{dx} \left[ \sin^{-1}\left( 2x \sqrt{1 - x^2} \right) \right] \]
Evaluate the integral: \[ \int e^{2x} \, dx \]
Find the derivative of \[ \frac{d}{dx} \left( \lim_{n \to 1} \frac{x^n - 1}{n+1} \right). \]
Find the derivative of \[ \frac{d}{dx} \left( \log_3 x \cdot \log_x 3 \right). \]
Find the derivative of \[ \frac{d}{dx} \left( \log x^{100} \right). \]
Find the derivative of \[ \frac{d}{dx} \left\{ \left| x \right|^2 \right\}. \]
Find the integral of \( e^x \) from 0 to 2.
Evaluate the integral: \[ \int_{\alpha}^{\beta} \varphi(x) \, dx + \int_{\beta}^{\alpha} \varphi(x) \, dx \]
If odds in favor of event \( E \) are \( a : b \), then \( P(E) = \).