GATE EC 2025 Question Paper (15-Feb-2025) (Shift 2)

A simplified small-signal equivalent circuit of a BJT-based amplifier is given below. The small-signal voltage gain $V_o/V_s$ (in V/V) is ________.

The ideal BJT in the circuit given below is biased in the active region with a $\beta$ of 100. If $I_B$ is $10\mu A$, then $V_{CE}$ (in Volts, rounded off to two decimal places) is ________.

A 3-input majority logic gate has inputs X, Y and Z. The output F of the gate is logic '1' if two or more of the inputs are logic ‘1’. The output F is logic '0' if two or more of the inputs are logic '0'. Which one of the following options is a Boolean expression of the output F?

A full adder and an XOR gate are used to design a digital circuit with inputs X, Y, and Z, and output F, as shown below. The input Z is connected to the carry-in input of the full adder. If the input Z is set to logic ‘1', then the circuit functions as __________ with X and Y as inputs.

Consider the function $f:\mathbb{R}\to \mathbb{R}$ defined as $f(x)=2x^3-3x^2-12x+1$ Which of the following statements is/are correct?
(Here, $\mathbb{R}$ is the set of real numbers.)