List of top Questions asked in Bihar Board XII

Find the dot product of the vectors \[ (7\mathbf{i} - 8\mathbf{j} + 9\mathbf{k}) \cdot (\mathbf{i} - \mathbf{j} + \mathbf{k}). \]

Evaluate the following expression: \[ \mathbf{i} \cdot \mathbf{i} + \mathbf{i} \cdot \mathbf{j} + \mathbf{j} \cdot \mathbf{j} + \mathbf{j} \cdot \mathbf{k} + \mathbf{k} \cdot \mathbf{k} \]

Find the dot product of the vectors \[ (11\mathbf{i} + \mathbf{j} + \mathbf{k}) \cdot (\mathbf{i} + \mathbf{j} + 11\mathbf{k}). \]

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 \( x, y, z \).

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

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:

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

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

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

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

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

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

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

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

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

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

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

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