GATE IN 2022 Question Paper (06-Feb-2022) (Shift 2)

A sinusoidal carrier wave with amplitude A${}_c$ and frequency f${}_c$ is amplitude modulated with a message signal 𝑚(𝑡) having frequency 0 < f${}_m$ << f${}_c$ to generate the modulated wave 𝑠(𝑡) given by

s(t) = A${}_c$ [1 + m(t)] cos (2πf${}_c$ t)

The message signal that can be retrieved completely using envelope detection is _______

A Hall sensor is based on the principle of ________

A signal 𝑥(𝑡) is band-limited between 100 Hz and 200 Hz.

A signal 𝑦(𝑡) is related to 𝑥(𝑡) as follows:

𝑦(𝑡) = 𝑥(2𝑡 − 5)

The statement that is always true is______

The figure shows a Chromel-Alumel thermocouple, where the junction A is held at temperature T${}_A$, and a thermal emf E₁ is measured using an ideal voltmeter between the open ends B1 and B2, both held at temperature T${}_B$. Two identical copper wires are introduced between B1-C1 and B2-C2 as shown in the figure. When C1 and C2 are held at temperature T${}_C$, the voltmeter reads a thermal emf E₂. Then, _______

The resistance of a pure copper wire of length 10 cm and diameter 1 mm is to be measured. The most suitable method from amongst the choices given below is ________