List of practice Questions

The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by \[ V_I = 10 \sin(100\pi t), \quad {where time} \, t \, {is in seconds.} \] The time duration (in ms, rounded off to two decimal places) for which the diode is forward biased during one period of the input is (answer in ms).


 

All the diodes in the circuit given below are ideal. Which of the following plots is/are correct when \( V_I \) (in Volts) is swept from \( -M \) to \( M \)?

Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable \( X \) denote the sum of the outcomes obtained. The expectation of \( X \) is _________ (rounded off to two decimal places).

Consider the vectors \[ a = \begin{bmatrix} 1 \\ 1 \end{bmatrix}, \quad b = \begin{bmatrix} 0 \\ 3\sqrt{2} \end{bmatrix}. \] For real-valued scalar variable \( x \), the value of \[ \min_x \|a x - b\|_2 \text{ is} \quad \text{(rounded off to two decimal places)}. \] \( \| \cdot \|_2 \text{ denotes the Euclidean norm, i.e., for } y = \begin{bmatrix} y_1 \\ y_2 \end{bmatrix}, \quad \|y\|_2 = \sqrt{y_1^2 + y_2^2}. \)
Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable \( X \) denote the sum of the outcomes obtained. The expectation of \( X \) is _________ (rounded off to two decimal places).
Consider the vectors
\[ a = \begin{bmatrix} 1 \\ 1 \end{bmatrix}, \quad b = \begin{bmatrix} 0 \\ 3\sqrt{2} \end{bmatrix}. \] For real-valued scalar variable \( x \), the value of
\[ \min_x \|a x - b\|_2 \text{ is} \quad \text{(rounded off to two decimal places)}. \] \( \| \cdot \|_2 \text{ denotes the Euclidean norm, i.e., for } y = \begin{bmatrix} y_1 \\ y_2 \end{bmatrix}, \quad \|y\|_2 = \sqrt{y_1^2 + y_2^2}. \)

The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by \[ V_I = 10 \sin(100\pi t), \quad {where time} \, t \, {is in seconds.} \] The time duration (in ms, rounded off to two decimal places) for which the diode is forward biased during one period of the input is (answer in ms).