List of top Questions asked in Bihar Board XII

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 integral of \( e^x \) from 0 to 2.

Evaluate the integral: \[ \int_{\alpha}^{\beta} \varphi(x) \, dx + \int_{\beta}^{\alpha} \varphi(x) \, dx \]

Find the derivative of \[ \frac{d}{dx} \left\{ \left| x \right|^2 \right\}. \]

Find the derivative of \[ \frac{d}{dx} \left( \log_3 x \cdot \log_x 3 \right). \]

Find the derivative of \[ \frac{d}{dx} \left( \log x^{100} \right). \]

Addition theorem of probability is.

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

Multiplication theorem of probability is.

Find \( \frac{d}{dx} \left(e^{3-2x}\right) \).

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

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

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?

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

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

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

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

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