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

Consider 24 voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at 12 kHz and represented by an 8-bit word, the bit-duration (in microseconds) is ________ (round off to two decimal places)

A photodiode is made of a semiconductor with a bandgap of 1.42 eV. Given that Planck’s constant is 6.626 × 10⁻³⁴ Js, the speed of light in vacuum is 3 × 10⁸ m/s, and 1 eV = 1.6 × 10⁻¹⁹ J, the cut-off wavelength (in nanometers) of the photodiode is ________ (round off to one decimal place)

The global minimum of x³e${}^{-|x|}$ for x ∈ (−∞, ∞) occurs at 𝑥 = ________ (round off to one decimal place)

A 440 V, 8 kW, 4-pole, 50 Hz, star-connected induction motor has a full load slip of 0.04. The rotor speed (in rpm) at full load is _________ (round off to one decimal place)

The transfer function of a system is:

$\frac{(\mathrm{s}+1)(\mathrm{s}+3)}{(\mathrm{s}+5)(\mathrm{s}+7)(\mathrm{s}+9)}$

In the state-space representation of the system, the minimum number of state variables (in integer) necessary is _____