List of top Mathematics Questions asked in Bihar Board Class XII

Evaluate the following matrix multiplication: \[ \begin{pmatrix} -3 & 5 & 2 \end{pmatrix} \times \begin{pmatrix} 1 \\ 6 \\ -4 \end{pmatrix} \]

Solve the following expression: \[ \frac{x}{x - 1} \times \frac{x + 1}{x} \]

If the operation \(\ast\) is defined as \(a \ast b = 2a + b\), then \((2 \ast 3) \ast 4\) is:

The matrix \( A = [a_{ij}] \) of size \( m \times n \) is a square matrix if:

Evaluate the determinant of the following matrix: \[ \begin{vmatrix} 1 & 2 & 5 \\ 1 & 1 & 4 \\ -2 & -3 & -9 \end{vmatrix} \]

Evaluate the following matrix multiplication: \[ 5 \times \begin{pmatrix} 5 & 7 \\ 6 & 8 \end{pmatrix} \]

Evaluate the determinant of the following matrix: \[ \begin{vmatrix} 3 & 1 & 2 \\ -4 & -2 & 3 \\ 5 & 1 & 1 \end{vmatrix} \]

For a function \( f: A \to B \), the function will be onto if:

If the line \[ \frac{x - 3}{a} = \frac{y - 4}{b} = \frac{z - 5}{c} \] is parallel to the line \[ \frac{x}{5} = \frac{y}{3} = \frac{z}{2} \] then:

If the line \[ \frac{x - x_1}{a_1} = \frac{y - y_1}{b_1} = \frac{z - z_1}{c_1} \] is parallel to the plane \[ a_2 x + b_2 y + c_2 z + d = 0 \] then:

The distance of the plane \( x - 2y + 4z = 9 \) from the point \( (2, 1, -1) \) is:

If two planes \( 2x - 4y + 3z = 5 \) and \( x + 2y + \lambda z = 12 \) are mutually perpendicular to each other, then \(\lambda =\):

Evaluate the integral: \[ \int \frac{1 - \sin 2x}{dx} \]

If \[ \frac{x}{18} = \frac{6}{18} \] then \(x\) is equal to:

The angle between two planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \) is:

Given that \[ |\vec{a} + \vec{b}| = |\vec{a} - \vec{b}| \] which of the following is true?

The maximum value of \( Z = 3x + 2y \) subject to the constraints: \[ 3x + y \leq 15, \quad x \geq 0, \quad y \geq 0 \] is:

The minimum value of \( Z = 3x + 5y \) subject to the constraints: \[ x + y \leq 2, \quad x \geq 0, \quad y \geq 0 \] is:

The projection of the vector \[ \vec{a} = \hat{i} - 2\hat{j} + \hat{k} \] on the vector \[ \vec{b} = 4\hat{i} - 4\hat{j} + 7\hat{k} \] is:

The equation of the plane parallel to the plane \( 3x - 5y + 4z = 11 \) is:

The direction ratios of a straight line are \( 1, 3, 5 \). Then its direction cosines are:

The direction ratios of two straight lines are \( l, m, n \) and \( l_1, m_1, n_1 \). The lines will be perpendicular to each other if:

The angle between the vectors \[ \vec{a} = 2\hat{i} - 3\hat{j} + 2\hat{k} \quad \text{and} \quad \vec{b} = \hat{i} + 4\hat{j} + 5\hat{k} \] is:

If \[ \vec{a} = \hat{i} + \hat{j} + 2\hat{k}, \] then the corresponding unit vector \( \hat{a} \) in the direction of \( \vec{a} \) is:

Evaluate the integral: \[ \int \cot^2(x) \, dx \]