
In the given circuit, we have two diodes \( D_1 \) and \( D_2 \). The voltage across the diodes and the resistor is affected by the direction in which the diodes are connected and their characteristics.
- \( D_1 \) is forward-biased because its anode is connected to +5V, and the cathode is connected to the node where \( V_o \) is measured.
- \( D_2 \) is reverse-biased because its anode is connected to the node \( V_o \), and its cathode is connected to ground.
Since \( D_2 \) is reverse-biased, it will not conduct, and \( D_1 \) will conduct. Therefore, the output voltage \( V_o \) will be zero because the voltage drop across the conducting diode \( D_1 \) is almost zero in a forward-biased condition.
Thus, the output voltage is zero.
Therefore, the correct answer is (2) Zero.
Current passing through a wire as function of time is given as $I(t)=0.02 \mathrm{t}+0.01 \mathrm{~A}$. The charge that will flow through the wire from $t=1 \mathrm{~s}$ to $\mathrm{t}=2 \mathrm{~s}$ is:
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process.
In the light of the above statements, choose the correct answer from the options given below:

For the circuit shown above, the equivalent gate is:
Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \[ (\sin x \cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x \sin y)(f(2x + 2y) + f(2x - 2y)), \] for all \( x, y \in \mathbb{R}. \)
If \( f'(0) = \frac{1}{2} \), then the value of \( 24f''\left( \frac{5\pi}{3} \right) \) is: