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 \( M \)?





In the given circuit with ideal diodes, the current-voltage relationship will change depending on the input voltage (\(V_I\)). The behavior of the circuit can be broken down into the following steps:
Step 1: Diode behavior when \(V_I\) is negative
When \(V_I\) is negative, the diodes will be reverse biased and no current will flow through the circuit. Therefore, the output voltage \(V_o\) will be 0 for negative \(V_I\), and the plot will be flat from \(-M\) to 0.
Step 2: Diode behavior when \(V_I\) is positive
When \(V_I\) is positive, the diodes will conduct and the output voltage will increase linearly with \(V_I\). This results in a linear relationship between \(V_o\) and \(V_I\) for positive \(V_I\). The correct plot is (A) for the output voltage and (D) for the current \(I_I\) in the circuit, where the current increases as \(V_I\) increases.

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).
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).

Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.
Who all are left in the game after the 4th round?

The identical MOSFETs \( M_1 \) and \( M_2 \) in the circuit given below are ideal and biased in the saturation region. \( M_1 \) and \( M_2 \) have a transconductance \( g_m \) of 5 mS. The input signals (in Volts) are: \[ V_1 = 2.5 + 0.01 \sin \omega t, \quad V_2 = 2.5 - 0.01 \sin \omega t. \] The output signal \( V_3 \) (in Volts) is _________.

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration n' is:

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the \( 3\,\Omega \) resistor are as indicated.
The voltage (in Volts) at node \( X \) is _________.
