Complex Analysis - General Aptitude - General Aptitude (GA) Previous Year Questions

1

2012 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2012

If \(x = \sqrt{-1}\), then the value of \(x^x\) is

A

\(e^{-\pi/2}\)

B

\(e^{\pi/2}\)

C

\(x\)

D

1

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2

2012 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2012

Given \[f(z) = \frac{1}{z+1} - \frac{2}{z+3}\] If C is a counterclockwise path in the z-plane such that \(|z+1| = 1\), the value of \[\frac{1}{2\pi j} \oint_C f(z) dz\] is

A

-2

B

-1

C

1

D

2

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3

2012 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2012

A system with transfer function \[G(s) = \frac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}\] is excited by \(\sin(\omega t)\). The steady-state output of the system is zero at

A

\(\omega = 1\) rad/s

B

\(\omega = 2\) rad/s

C

\(\omega = 3\) rad/s

D

\(\omega = 4\) rad/s

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4

2012 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2012

If \(x[n] = (1/3)^{|n|} - (1/2)^n u[n]\), then the region of convergence (ROC) of its Z-transform in the Z-plane will be

A

\(\frac{1}{3} < |z| < 3\)

B

\(\frac{1}{3} < |z| < \frac{1}{2}\)

C

\(\frac{1}{2} < |z| < 3\)

D

\(\frac{1}{3} < |z|\)

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5

2012 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2012

The open loop transfer function of a unity gain negative feedback control system is given by G(s) = (s² + 4s + 8) / (s(s + 2)(s + 8)). The angle θ, at which the root locus approaches the zeros of the system, satisfies

A

|θ| = π - tan^-1(1/4)

B

|θ| = 3π/4 - tan^-1(1/3)

C

|θ| = π/2 - tan^-1(1/4)

D

|θ| = π/4 - tan^-1(1/3)

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6

2012 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2012

The phase of the above lead compensator is maximum at

A

√2 rad/s

B

√3 rad/s

C

√6 rad/s

D

1/√3 rad/s

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7

2015 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2015

The filter whose transfer function is of the form \(G(s) = \frac{s^2 - bs + c}{s^2 + bs + c}\) is

A

a high-pass filter

B

a low-pass filter

C

an all-pass filter

D

a band-reject filter

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8

2015 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2015

Let \(3 + 4j\) be a zero of a fourth order linear-phase FIR filter. The complex number which is NOT a zero of this filter is

A

\(3 - 4j\)

B

\(\frac{3}{25} + \frac{4}{25}j\)

C

\(\frac{3}{25} - \frac{4}{25}j\)

D

\(\frac{1}{3} - \frac{1}{4}j\)

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9

2015 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2015

The z-transform of $x[n] = a^{|n|}$, $0 < |a| < 1$, is $X(z)$. The region of convergence of $X(z)$ is

A

$|a| < |z| < \frac{1}{|a|}$

B

$|z| > a$

C

$|z| > \frac{1}{|a|}$

D

$|z| < \min \left[ |a|, \frac{1}{|a|} \right]$

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10

2015 · General Aptitude (GA) · General Aptitude · Complex Analysis

Instrumentation Engineering (IN) 2015

The open loop transfer function of a system is \( G(s) = \frac{s^2 + 6s + 10}{s^2 + 2s + 2} \). The angles of arrival of its root loci are

A

\(\pm \frac{\pi}{4} \)

B

\(\pm \frac{\pi}{3} \)

C

\(\pm \frac{\pi}{2} \)

D

\(\pm \frac{5\pi}{6} \)

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