Electronics and Communication Gate 2017 Set-1 Questions with Answer

Ques 53 GATE 2017 SET-1

The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 μs, then the number of T-states needed for executing the instruction is

Ques 54 GATE 2017 SET-1

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

(1) is the correct answer.

Ques 55 GATE 2017 SET-1

The figure shows an RLC circuit excited by the sinusoidal voltage 100cos(3t) Volts, where t is in seconds.

The ratio amplitude of V₂/amplitude of V₁ is

(2.6) is the correct answer.

Ques 56 GATE 2017 SET-1

In the circuit shown, the voltage V_IN(t) is described by:

where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is

(0.35) is the correct answer.

Ques 57 GATE 2017 SET-1

Let (X₁,X₂) be independent random variables. X₁ has mean 0 and variance 1, while X₂ has mean 1 and variance 4. The mutual information I(X₁;X₂) between X₁ and X₂ in bits is

(0) is the correct answer.

Ques 58 GATE 2017 SET-1

Let X(t) be a wide sense stationary random process with the power spectral density S_X(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal lowpass filter with the frequency response

as shown in Figure (b). The output of the lowpass filter is Y(t).

Let E be the expectation operator and consider the following statements:
I. E(X(t))=E(Y(t))
II. E(X²(t))=E(Y²(t))
III. E(Y²(t))=2
Select the correct option:

only I is true

only II and III are true

only I and II are true

only I and III are true

(a) is the correct answer.

Ques 59 GATE 2017 SET-1

A continuous time signal x(t)=4cos(200πt)+8cos(400πt)., where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response h(t)=2sin(300πt)/(πt), t≠0 and 600, t=0. Let y(t) be the output of this filter. The maximum value of |y(t)| is

(8) is the correct answer.

Ques 60 GATE 2017 SET-1

Consider the following statements for continuous-time linear time invariant (LTI) systems.
I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.
Which one among the following is correct?

Both I and II are true

Both I and II are not true

Only I is true

Only II is true

(d) is the correct answer.

Ques 61 GATE 2017 SET-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

], otherwise. Which one of the following statements is true about the system?

It is causal and stable

It is causal but not stable

It is not causal but stable

It is neither causal nor stable

(a) is the correct answer.

Ques 62 GATE 2017 SET-1

A periodic signal x(t) has a trigonometric Fourier series expansion x(t)=a₀+∑_n=1^∞(a_ncos nω₀t+b_nsin nω₀t) If x(t)=-x(-t)=-x(t-π/ω₀). we can conclude that

a_n are zero for all n and b_n are zero for n even

a_n are zero for all n and b_n are zero for n odd

a_n are zero for n even and b_n are zero for n odd

a_n are zero for n odd and b_n are zero for n even

(a) is the correct answer.

Ques 63 GATE 2017 SET-1

Let x(t) be a continuous time periodic signal with fundamental period T=1 seconds. Let {a_k} be the complex Fourier series coefficients of x(t) where k is integer valued. Consider the following statements about x(3t)
I. The complex Fourier series coefficients of x(3t) are {a_k} where k is integer valued
II. The complex Fourier series coefficients of x(3t) are {3a_k} where k is integer valued
III. The fundamental angular frequency of x(3t) is 6π rad/s
For the three statements above, which one of the following is correct?

only II and III are true

only I and III are true

only III is true

only I is true

(b) is the correct answer.

Ques 64 GATE 2017 SET-1

Two discrete-time signals x[n] and h[n] are both non-zero only for n=0,1,2, and are zero otherwise. It is given that x[0]=1, x[1]=2, x[2]=1, h[0]=1. Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1]=3 and y[2]=4, the value of the expression (10y[3]+y[4]) is

(31) is the correct answer.

Ques 65 GATE 2017 SET-1

Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by h[0]=1/3, h[1]=1/3, h[2]=1/3; and h[n]=0 for n<0 and n>2. Let H(ω) be the discrete-time Fourier transform (DTFT) of h[n], where ω is the normalized angular frequency in radians. Given that H(ω₀)=0 and 0<ω₀<π. the value of ω₀ (in radians) is equal to

(2.09) is the correct answer.

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