Electronics and Communication Gate 2015 Set-2 Questions with Answer

Ques 27 GATE 2015 SET-2

The value of the integral ∫_−∞^∞ 12 cos(2πt) ^sin(4πt)⁄_4πt dt is __________.

(3) is the correct answer.

Ques 28 GATE 2015 SET-2

If C denotes the counterclockwise unit circle, the value of the contour integral ¹⁄_2πj ∮_C Re{z} dz is __________.

(0.5) is the correct answer.

Ques 29 GATE 2015 SET-2

Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is __________.

(6) is the correct answer.

Ques 30 GATE 2015 SET-2

An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is

¹⁄_2π√LC

¹⁄_2π√LC√(1 − R² ^C⁄_L)

¹⁄_2π√LC√(1 − ^L⁄_R²C)

¹⁄_2π√LC(1 − R² ^C⁄_L)

(b) is the correct answer.

Ques 31 GATE 2015 SET-2

In the circuit shown, the Norton equivalent resistance (in Ω) across terminals a-b is __________.

(1.33) is the correct answer.

Ques 32 GATE 2015 SET-2

In the circuit shown, the initial voltages across the capacitors C₁ and C₂ are 1 V and 3 V, respectively. The switch is closed at time t=0. The total energy dissipated (in Joules) in the resistor R until steady state is reached, is __________.

(1.5) is the correct answer.

Ques 33 GATE 2015 SET-2

A DC voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a length of 1 cm as shown in figure. The donor doping concentration N_D and the mobility of electrons μ_n are 10¹⁶ cm⁻³ and 1000 cm² V⁻¹ s⁻¹ respectively. The average time (in μs) taken by the electrons to move from one end of the bar to other end is __________.

(100) is the correct answer.

Ques 34 GATE 2015 SET-2

In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness is 100 nm. The permittivities of the semiconductor and the oxide layer are ε_s and ε_ox respectively. Assuming ε_s / ε_ox = 3, the ratio of the maximum capacitance to the minimum capacitance of this MOS capacitor is __________.

(4.33) is the correct answer.

Ques 35 GATE 2015 SET-2

The energy band diagram and the electron density profile n(x) in a semiconductor are shown in the figures. Assume that n(x) = 10¹⁵ e^{(qαx / kT)} cm⁻³, with α = 0.1 V/cm and x expressed in cm. Given D_n = 36 cm²s⁻¹, and ^kT⁄_q = 0.026 V, ^D⁄_μ = ^kT⁄_q. The electron current density (in A/cm²) at x=0 is

−4.4 × 10⁻²

−2.2 × 10⁻²

2.2 × 10⁻²

Ques 36 GATE 2015 SET-2

A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as F(X,Y,Z) = ∑(1,2,5,6,7). Which one of the product of sums given below is equal to the function F(X,Y,Z)?

(A) (X+Y+Z) · (X+Y+Z) · (X+Y+Z)

(B) (X+Y+Z) · (X+Y+Z) · (X+Y+Z)

(D) (X+Y+Z) · (X+Y+Z) · (X+Y+Z) · (X+Y+Z) · (X+Y+Z)

(b) is the correct answer.

Ques 37 GATE 2015 SET-2

The figure shows a binary counter with synchronous clear input. With the decoding logic shown, the counter works as a

mod-2 counter

mod-4 counter

mod-5 counter

mod-6 counter

(d) is the correct answer.

Ques 38 GATE 2015 SET-2

A 1-to-8 demultiplexer with data input D_in, address inputs S₀, S₁, S₂ (with S₀ as the LSB) and Y₀ to Y₇ as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with enable input E and address inputs A₀ and A₁) as shown in the figure. D_in, S₀, S₁ and S₂ are to be connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P, Q, R, and S terminals should be

S₂, D_in, S₀, S₁

S₁, D_in, S₀, S₂

D_in, S₀, S₁, S₂

D_in, S₂, S₀, S₁

(d) is the correct answer.

Ques 39 GATE 2015 SET-2

The diode in the circuit given below has V_ON = 0.7 V but is ideal otherwise. The current (in mA) in the 4 kΩ resistor is __________.

(0.6) is the correct answer.

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