GATE EC 2017 Question Paper (05-Feb-2017) (Shift 1)

Consider a single input single output discrete-time system with x[n] as input and y[n] as output. Where the two are related as

y≤ft[ n ] = ≤ft\{ {*20c n≤ft| x≤ft[ n ] |, \\ x≤ft[ n ] - x≤ft[ n - 1 ], } .*20c for 0 ≤ n ≤ 10\\ otherwise.

Which one of the following statements is true about the system?

In the circuit shown, the positive angular frequency ω (in radians per second) at which the magnitude of the phase difference between the voltages V₁ and V₂ equals π /4 radians, is _____.

A periodic signal x(t) has a trigonometric Fourier series expansion

$x\left(t\right)=a_0+\sum _{n=1}^{\infty }(a_{n}cosn{\omega }_{0}t+b_n\sin n{\omega }_{0}t)$

If x(t) = -x (- t) = -x (t - π/ω₀), we can conclude that

A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true?

An n⁺- n Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of N${}_{D1}$ = 1 × 10¹⁸ cm⁻³ and N${}_{D2}$ = 1 × 10¹⁵ cm⁻³ corresponding to the n⁺ and n regions respectively. At the operational temperature T, assume complete impurity ionization, kT/q = 25 mV, and intrinsic carrier concentration to be nᵢ = 1 × 10¹⁰ cm⁻³. What is the magnitude of the built – in potential of this device?