GATE Instrumentation Mock Test - 2 - GATE Instrumentation MCQ

Below are three statements along with four conclusions derived from those statements.

Statement 1: Some engineers are also writers.
Statement 2: No writer is an actor.
Statement 3: All actors are engineers.
Conclusion I: Some engineers are writers.
Conclusion II: All engineers are actors.
Conclusion III: No actor is a writer.
Conclusion IV: Some writers are actors.

Which of the following conclusions can be logically deduced?

Which of the following combinations of pieces can be arranged to create a square featuring a single circular hole positioned near the center? The pieces must not overlap.

A control system with unity-gain negative feedback has a loop-gain L(s) represented by

A function f(x) that is periodic with a period of 2 is defined as  

What does the Fourier series of this function contain_______.

The diagram illustrates a Chromel-Alumel thermocouple, where the junction A is maintained at a temperature of T_A, and a thermal emf E₁ is detected using an ideal voltmeter between the open terminals B1 and B2, both at temperature T_B. Two identical copper wires are connected between B1-C1 and B2-C2 as depicted in the diagram. When C1 and C2 are kept at a temperature T_C, the voltmeter indicates a thermal emf E₂. Therefore, ________

A signal x(t) is confined within the frequency range of 100 Hz to 200 Hz.

A signal y(t) is defined in relation to x(t) as follows:

y(t) = x(2t - 5)

The assertion that is always valid is______

A beam of unpolarised light is initially directed through a linear polariser and subsequently through a quarter-wave plate. What is the nature of the resulting beam?

The unit step function u(t) is defined as:

Consider the discrete-time system illustrated below.

x[n] → h[n] → y[n]
y[n] ↔ y[z], with y[n] being absolutely summable
x[n] ↔ x[z], with x[n] being absolutely summable
h[n] ↔ H[z]

The pole-zero plots for x(z) and Y(z) are depicted in Figures (A) and (B), respectively.

Which of the following illustrates the pole-zero plot of H(z)?

Let A be a 3×3 matrix with eigenvalues 1, -1, and 0.What will be the determinant of I + A¹⁰⁰?

Which of the following represents the root locus plot for the loop gain

The output F of the logic block depicted is given by _____

The system's input x(t) is connected to its output y(f) through the relationship shown below:

In this equation, u(t) denotes a unit-step function. 
What is the transfer function of this system?

What is the result of (55)₁₀ – (55)₁₆ when represented in 6-bit 2's complement format?

Given the JK flip-flop shown below with K set to 1. If the flip-flop starts in a cleared state and is clocked for 7 pulses, what will be the resulting sequence at the Q output?

The frequency of resonance (in Hz) for the Wein bridge oscillator depicted in the circuit shown is _____. (Round your answer to two decimal places)

In the circuit depicted below, what is the resonant frequency f₀ (in MHz)? Please provide your answer rounded to two decimal places.

A voltage signal V_in(t) displayed is applied to the circuit from t = 0 ms to t = 6 ms. The initial voltage across the capacitor is 0.3 V, and it is assumed that the diode is ideal. What is the open circuit voltage V_out(t) at t = 5 ms?

The signal x(t) = (t - 1)²u(t - 1), where u(t) denotes the unit-step function, possesses the Laplace transform X(S). What is the value of X(1)?

A digital-to-analog converter (DAC) constructed with a resistor ladder receives a digital input, resulting in the state represented in the figure. For this particular digital input, determine the Thevenin voltage, V_th, and Thevenin resistance, R_th, observed at the output node are ______

Two positive numbers x and y, both of which do not exceed 2, are selected randomly. What is the probability that xy ≤ 1 and y/x ≤ 2?

The output of a first-order measurement system in response to a unit step input is given by 1 - e^-t, where t represents time in seconds. If an input of 0.2 units per second is applied to this system, what is the error in the measured value once the transient effects have subsided? (Provide your answer rounded to one decimal place)

A sine-wave generator operating at 1 kHz with an internal resistance of 50 Ω produces an open-circuit voltage of 10 V_p-p. When a capacitor is connected across its output terminals, the voltage decreases to 8 V_p-p. Calculate the capacitance of the capacitor (in microfarads), rounding off to two decimal places.

In the circuit depicted in the figure, the voltage v₁ (in V) is equal to _______ (Provide your answer rounded to the nearest integer)

What is the gain margin of the system that has the open loop transfer function shown below?

In the regulator circuit illustrated below, the following parameters are provided:
V₂ = 6.3 V
I₂T = 40 mA
R_z = 2 Ω
V_s = 12 V to 18 V
Minimum load current = 0 mA
Minimum Zener diode current = 1 mA

To ensure that the power dissipation P_z(max) of the Zener diode does not exceed 750 mW at 25°C, what is the maximum allowable value of Zener current iz(max) (rounded to the nearest integer, in mA)?

In a 220 kV power system, the reactance and capacitance at the circuit breaker location are 16Ω and 0.05 μF, respectively. A resistance of 1200Ω is connected across the circuit breaker's contacts.
[Given ω = 2π 50 rad/sec]
What will be the natural frequency of oscillation? (Provide your answer in kHz, rounded to two decimal places)