GATE ECE 2025 PYQ

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

The identical MOSFETs and in the circuit given below are ideal and biased in the saturation region. and have a transconductance of 5 mS . The input signals (in Volts) are: The output signal (in Volts)

Which of the following statements is/are TRUE with respect to ideal MOSFET-based DC-coupled single-stage amplifiers having finite load resistors?

All the components in the bandpass filter given below are ideal. The lower frequency of the filter is 1 MHz . The upper frequency (in MHz , rounded off to the nearest integer) is __________ .

The diode in the circuit shown below is ideal. The input voltage (in Volts) is given by , where time t is in seconds. The time duration (in ms , rounded off to two decimal places) for which the diode

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

Which of the following statements is/are TRUE with respect to an ideal opamp?

In the circuit shown, the identical transistors Q1 and Q2 are biased in the active region with . The Zener diode is in the breakdown region with and . If and , then the values of and (in , rounded off

Consider a frequency-modulated (FM) signal , where and are, respectively, the amplitude and frequency (in Hz) of the carrier waveform. The frequency is in Hz, and assume that . The peak frequency devi

The Generator matrix of a binary linear block code is given by The minimum hamming distance between code words equals __________ (answer in integer).

Consider an additive white Gaussian noise (AWGN) channel with bandwidth and noise power spectral density . Let denote the average transmit power constraint. Which one of the following plots illustrate

Consider a real-valued random process , where and N is a positive integer. Here, for and 0 otherwise. The coefficients are pairwise independent, zero-mean unit-variance random variables. Read the foll

X and Y are Bernoulli random variables taking values in . The joint probability mass function of the random variables is given by: The mutual information is __________ (rounded off to two decimal plac

Consider a message signal which is bandlimited to , where W is in Hz . Consider the following two modulation schemes for the message signal: Double sideband-suppressed carrier (DSB-SC): Amplitude modu

The random variable takes values in with probabilities and , where . Let denote the entropy of (in bits), parameterized by . Which of the following statements is/are TRUE?

A source transmits symbol that takes values uniformly at random from the set . The receiver obtains , where is a zero-mean Gaussian random variable independent of . The receiver uses the maximum likel

The Nyquist plot of a system is given in the figure. Let and be the positive frequencies at the points and respectively. Which one of the following statements is TRUE?

Let be the transfer function of a secondorder system. A controller M(s) is connected to the system in the configuration shown below. Consider the following statements. (i) There exists no controller o

Consider a system represented by the block diagram shown below. Which of the following signal flow graphs represent(s) this system? Choose the correct option(s).

Consider the polynomial . Let be defined as follows. is the number of roots of with negative real parts. is the number of roots of that are purely imaginary. is the number of roots of with positive re

Consider the unity-negative-feedback system shown in Figure (i) below, where gain . The root locus of this system is shown in Figure (ii) below. For what value(s) of will the system in Figure (i) have

Consider a system where , and are three internal state signals and is the input signal. The differential equations governing the system are given by . Which of the following statements is/are TRUE?

A 4-bit weighted-resistor DAC with inputs , , and (MSB to LSB) is designed using an ideal opamp, as shown below. The switches are closed when the corresponding input bits are logic '1' and open otherw

A full adder and an XOR gate are used to design a digital circuit with inputs and , and output , as shown below. The input is connected to the carry-in input of the full adder. If the input is set to

A 3-input majority logic gate has inputs and . The output of the gate is logic '1' if two or more of the inputs are logic '1'. The output is logic '0' if two or more of the inputs are logic '0'. Which

A positive-edge-triggered sequential circuit is shown below. There are no timing violations in the circuit. Input P0 is set to logic '0' and P1 is set to logic '1' at all times. The timing diagram of

A 10-bit analog-to-digital converter (ADC) has a sampling frequency of 1 MHz and a full scale voltage of 3.3 V. For an input sinusoidal signal with frequency 500 kHz , the maximum SNR (in dB , rounded

In the circuit shown below, the AND gate has a propagation delay of 1 ns. The edge-triggered flipflops have a set-up time of 2 ns, a hold-time of 0 ns, and a clock-to-Q delay of 2 ns. The maximum cloc

A lossless transmission line is terminated with a load of . If the average incident power on the line is 10 mW , then the average power delivered to the load (in mW , rounded off to one decimal place)

An electric field of is applied along the length of a copper wire of circular cross-section with diameter 1 mm . Copper has a conductivity of . The current (in Amperes, rounded off to two decimal plac

A square metal sheet of is placed on the plane as shown in the figure below. If the surface charge density (in ) on the sheet is , then the total charge (in , rounded off to the nearest integer) on th

Two resistors are connected in a circuit loop of area , as shown in the figure below. The circuit loop is placed on the plane. When a time-varying magnetic flux, with fluxdensity (in Tesla), is applie

An ideal p-n junction germanium diode has a reverse saturation current of at 300 K . The voltage (in Volts, rounded off to two decimal places) to be applied across the junction to get a forward bias c

The ideal BJT in the circuit given below is biased in the active region with a of 100. If is , then (in Volts, rounded off to two decimal places) is __________ .

The intrinsic carrier concentration of a semiconductor is at 300 K. If the electron and hole mobilities are and , respectively, then the intrinsic resistivity of the semiconductor (in ) at 300 K is __

The electron mobility in a non-degenerate germanium semiconductor at 300 K is . The electron diffusivity at 300 K (in , rounded off to the nearest integer) is __________ . (Consider the Boltzmann cons

Which of the following can be used as an n-type dopant for silicon? Select the correct option(s).

In the circuit below, is an ideal AC voltmeter and is an ideal AC ammeter. The source voltage (in Volts) is . What should be the value of the variable capacitor C such that the RMS readings on and are

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

Let , and be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens (S). Which one of the following is TR

The Z-parameter matrix of a two-port network relates the port voltages and port currents as follows: The Z-parameter matrix (with each entry in ohms) of the network shown below is __________.

Consider the discrete-time system below with input and output . In the figure, and denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, is the unit impulse, and . Assuming , the

Consider a continuous-time, real-valued signal whose Fourier transform exists. Which one of the following statements is always TRUE?

Consider a continuous-time finite-energy signal whose Fourier transform vanishes outside the frequency interval , where is in rad/sec. The signal is uniformly sampled to obtain . Here, , with being th

Let be a discrete-time signal whose -transform is . Which of the following statements is/are TRUE?

Let be a periodic signal with fundamental period . Consider the signal , where . The Fourier series expansions of and are given by Which of following statement is/are TRUE?