List of top Mathematics Questions asked in Bihar Board Class XII

Find the integral of \( \sin^{13} x \cos^{12} x \).

If odds in favor of event \( E \) are \( a : b \), then \( P(E) = \).

Find the integral of \( 2x + 1 \).

Multiplication theorem of probability is.

Addition theorem of probability is.

The maximum value of \( Z = 2x + y \) subject to the constraints \[ x + y \leq 35, \quad x \geq 0, \quad y \geq 0 \] is.

The chance of getting a doublet in a throw of 2 dice is.

The maximum value of \( Z = 3x - y \) subject to the constraints \[ x + y \leq 8, \quad x \geq 0, \quad y \geq 0 \text{ is}. \]

Find the value of \( (k \times j) \cdot i \).

Find the dot product of \( (i - 2j + 5k) \cdot (-2i + 4j + 2k) \).

Evaluate the expression \( (i \times j) + (i \times i) \).

Which of the following is an objective function?

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

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

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

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

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 \( \log(x^9) \).

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

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

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

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