GATE Instrumentation Mock Test - 1 - GATE Instrumentation MCQ

If n is defined as 1 x, where x represents the product of four consecutive positive integers, which of the following statements is/are correct?

• A. n is odd
• B. n is prime
• C. n is a perfect square

The total of n terms from the series is

Rice is a crucial and affordable source of carbohydrates, forming an essential part of diets globally. The impact of climate change, leading to severe weather events, threatens the consistent supply of rice. Researchers are engaged in the development of Green Super Rice (GSR), which is designed to withstand extreme weather while ensuring higher sustainable yields.

Which of the following represents the CORRECT logical conclusion derived from the information provided in the passage above?

The solution to the differential equation (cos x)    is

The unilateral Laplace transform of f(t) is expressed as log (S² S 1). What is the unilateral Laplace transform of t f(t)?

Consider a counterclockwise path C in the z-plane defined by |z 2| = 1. What is the value of ?
(Give your answer as a single-digit number.)

A resistor of 1500Ω rated at 3W and another resistor of 1200Ω rated at 2W are connected in series. What is the maximum continuous DC voltage that can be applied to this series circuit without exceeding the power ratings of either resistor?

In the circuit shown, if the power dissipated across the 6 ohm resistor is zero, what is the value of the current I?

In the circuit shown in the figure, the switch S is closed at time t = 0, with initial conditions of i_L(0) = 0 and V_C(0) = 0. What is the value of V_C in the steady state?

The diagram presented illustrates a circuit with an initial current of i_L(0^-) = 1 A flowing through the inductor, and the initial voltage across the capacitor is v_C(0^-) = -1 V. Given the input v(t) = u(t), determine the Laplace transform of the current i(t) for t ≥ 0 as shown in the following image:

A strain gauge bridge is utilized to measure the strain in a cantilever where the gauge is permanently attached. Given that the strain E causes the gauge resistance to rise from 220Ω to 220.50Ω, and the gauge factor is 2, what will be the strain in the cantilever?

A voltage waveform that is periodic and displayed on an oscilloscope across a load is depicted. A permanent magnet moving coil (PMMC) meter connected to the same load indicates

A diagnostic screening is performed to identify a specific disease. It has been observed that 15% of the positive outcomes and 20% of the negative outcomes are erroneous. Given that the likelihood of a person receiving a positive outcome is 0.02, what is the probability of an individual receiving an incorrect report? (Provide your answer up to three decimal points)

An analog-to-digital converter with a resolution of 0.01 V transforms analog signals ranging from 0 V to 10 V into an unsigned binary output. The smallest number of bits (in integer) required for the output is _________

Consider a scenario where 24 voice signals are being transmitted without any delay via time-division multiplexing. Each signal is sampled at a rate of 12 kHz and represented using an 8-bit word. Calculate the bit-duration (in microseconds) and round your answer to two decimal places.

The Newton-Raphson technique is utilized to find the root of the equation f(x) = 0, where f(x) = x - cos(x). Given that the initial approximation of the root is x₀ = 0, what is the value of the subsequent approximation x₁? Please round your answer to two decimal places.

Consider two 4-ray signal constellations displayed. It is specified that φ₁ and φ₂ form an orthonormal basis for these constellations. Assume the four symbols in each constellation have equal probability. Let N₀/2 represent the power spectral density of white Gaussian noise.

If these constellations are employed for digital communication over an AWGN channel, which of the following statements is accurate?

Given the complex number where a > 0 and b > 0, which of the following statement(s) is/are correct?

A monochromatic light source with a wavelength of 532 nm is utilized to determine the absorption coefficient of a substance using a UV-Visible Spectrophotometer. After passing through a sample of the material that is 1 cm thick, the intensity of the transmitted light is measured at 0.414 mW/cm². When the thickness of the sample is increased to 2 cm, the intensity of the transmitted light is recorded as 0.186 mW/cm². Calculate the absorption coefficient (in cm^-1) of the material, rounding your answer to two decimal places.

A conducting semi-circular loop with a radius of R = 0.1 m, positioned such that its diameter is centered at the origin, rotates in the x-y plane around the origin at a constant angular velocity of ω = 20 rad/s, as illustrated. A magnetic field with a magnitude of B = 2 T, oriented perpendicular to the x-y plane, is present in the region where x ≥ 0 as depicted. Given that the loop has a resistance of 2 Ω and negligible inductance, calculate the peak-to-peak current (in milliamperes) flowing through the loop, rounding off to one decimal place. 

The depicted bridge reaches a balanced state when R₁ = 100 Ω, R₂ = 210 Ω, C₂ = 2.9 µF, and R₄ = 50 Ω. A sine-wave generator operating at 2 kHz provides a voltage of 10 V_p-p. What is the value of L₃ (in millihenry)? Please round your answer to two decimal places. 

The circuit depicted is supplied with a sinusoidal input voltage, V_in, which leads to the output voltage, V_out. What is the frequency (in kilohertz) at which the voltage gain equals 0 dB? (Round your answer to two decimal places.)

A capacitor is designed using two concentric spherical surfaces with air serving as the dielectric medium (permittivity of air = 8.854 × 10^-12 F/m). The inner sphere has a radius of a = 10 cm, while the outer sphere has a radius of b = 15 cm. What is the capacitance (in picofarads) of this configuration? Please round your answer to 2 decimal places.

What is the value of the load impedance (in ohms) that will enable the maximum power transfer to occur to the load in the given network diagram?

The Fourier transform of the function f(t) is given by where a > 0. What is the value of f(0)? (Please provide your answer rounded to two decimal places)

An 80 KVA transformer experiences a core loss of 800 W and a copper loss at full load of 1600 W. What is the percentage of full load at maximum efficiency (rounded to one decimal place)?

The gain margin (in dB) for the given transfer function will be _____.