Electronics and Communication Gate 2017 Set-1 Questions with Answer

Ques 27 GATE 2017 SET-1

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?

Ques 28 GATE 2017 SET-1

An n⁺-n Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of N_D1=1×10¹⁸cm^-3 and N_D2=1×10¹⁵cm^-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 n_i=1×10¹⁰cm^-3 What is the magnitude of the built-in potential of this device?

Ques 29 GATE 2017 SET-1

For a narrow base PNP BJT, the excess minority carrier concentrations (Δn_E for emitter. Δp_B for base. Δn_c for collector) normalized to equilibrium minority carrier concentrations (n_E0 for emitter, p_B0 for base, n_c0 for collector) in the quasi-neutral emitter, base and collector regions are shown below.

Ques 30 GATE 2017 SET-1

The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of n=1×10¹⁶cm^-3 and electronic charge q=1.6×10^-19 C.

Ques 31 GATE 2017 SET-1

As shown, a uniformly doped Silicon (Si) bar of length L=0.1μm with a donor concentration N_D=10¹⁶cm^-3 is illuminated at x=0 such that electron and hole pairs are generated at the rate of G_L=G_L0(1-x/L), 0≤x≤L where G_L0=10¹⁷cm^-3s^-1. Hole lifetime is 10^-4 s, electronic charge q=1.6×10^-19 C. hole diffusion coefficient D_p=100 cm²/s and low level injection condition prevails. Assuming a linearly decaying steady state excess hole concentration that goes to 0 at x=L the magnitude of the diffusion current density at x=L/2 in A/cm² is

Ques 32 GATE 2017 SET-1

As shown, two Silicon (Si) abrupt p-n junction diodes are fabricated with uniform donor doping concentrations of N_D1=10¹⁴cm^-3 and N_D2=10¹⁶cm^-3 in the n-regions of the diodes, and uniform acceptor doping concentrations of N_A1=10¹⁴cm^-3 and N_A2=10¹⁶cm^-3 in the p-regions of the diodes, respectively. Assuming that the reverse bias voltage is >> built-in potentials of the diodes, the ratio C₂/C₁ of their reverse bias capacitances for the same applied reverse bias, is

Ques 33 GATE 2017 SET-1

Consider the 5×5 matrix A

Ques 34 GATE 2017 SET-1

The rank of the matrix is

Ques 35 GATE 2017 SET-1

Consider the following statements about the linear dependence of the real valued functions y₁=1, y₂=x and y₃=x² over the field of real numbers.
I. y₁, y₂ and y₃ are linearly independent on -1≤x≤0
II. y₁, y₂ and y₃ are linearly dependent on 0≤x≤1
III. y₁, y₂ and y₃ are linearly independent on 0≤x≤1
IV. y₁, y₂ and y₃ are linearly dependent on -1≤x≤0
Which one among the following is correct?

Ques 36 GATE 2017 SET-1

Let f(x)=e^x+x2 for real x. From among the following, choose the Taylor series approximation of f(x) around x=0 which includes all powers of x less than or equal to 3.

Ques 37 GATE 2017 SET-1

A three dimensional region R of finite volume is described by x²+y²≤z³; 0≤z≤1, where x, y, z are real. The volume of R (up to two decimal places) is

Ques 38 GATE 2017 SET-1

Let I=∫_C(2z dx+2y dy+2x dz) where x, y, z are real, and let C be the straight line segment from point A: (0,2, 1) to point B: (4, 1, -1). The value of I is

Ques 39 GATE 2017 SET-1

Which one of the following is the general solution of the first order differential equation dy/dx=(x+y-1)² , where x, y are real?