Fourier Series, Numerical Methods And Complex Variables - MCQ Test 1


20 Questions MCQ Test Mock Test Series for Civil Engineering (CE) GATE 2020 | Fourier Series, Numerical Methods And Complex Variables - MCQ Test 1


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This mock test of Fourier Series, Numerical Methods And Complex Variables - MCQ Test 1 for Civil Engineering (CE) helps you for every Civil Engineering (CE) entrance exam. This contains 20 Multiple Choice Questions for Civil Engineering (CE) Fourier Series, Numerical Methods And Complex Variables - MCQ Test 1 (mcq) to study with solutions a complete question bank. The solved questions answers in this Fourier Series, Numerical Methods And Complex Variables - MCQ Test 1 quiz give you a good mix of easy questions and tough questions. Civil Engineering (CE) students definitely take this Fourier Series, Numerical Methods And Complex Variables - MCQ Test 1 exercise for a better result in the exam. You can find other Fourier Series, Numerical Methods And Complex Variables - MCQ Test 1 extra questions, long questions & short questions for Civil Engineering (CE) on EduRev as well by searching above.
QUESTION: 1

The Fourier series of a real periodic function has only 

P. cosine terms if it is even  

Q. sine terms if it is even  

R. cosine terms if it is odd  

S. sine terms if it is odd 

Which of the above statements are correct? 

Solution:

Because sine function is odd and cosine is even function. 

QUESTION: 2

For the function e–x, the linear approximation around x = 2 is 

Solution:

(neglecting higher power of x) 

QUESTION: 3

In the Taylor series expansion of exp(x) + sin(x) about the point x = π, the coefficient of (x – π)2 is  

Solution:

QUESTION: 4

The function x(t) is shown in the figure. Even and odd parts of a unit-step function u(t) are respectively,  

Solution:

QUESTION: 5

In the Taylor series expansion of ex about x = 2, the coefficient of (x - 2)4 is 

Solution:

Taylor series expansion of f(x) about a is given by

QUESTION: 6

The Fourier series expansion of a symmetric and even function, f(x) where 

 Will be 

Solution:

f(x) is symmetric and even, it’s Fourier series contain only cosine term.  Now.

QUESTION: 7

The Fourier series expansion    of the periodic signal shown below will contain the following nonzero terms  

Solution:

from the figure, we can say that   f(t) is an symmetric and even function of t.  as cost is even function so choice (b) is correct. 

QUESTION: 8

The Fourier series for the function f(x)=sin2x is  

Solution:

Here f(x ) = sin2 x is even function, hence f( x ) has no sine term. 

QUESTION: 9

X(t) is a real valued function of a real variable with period T. Its trigonometric Fourier Series expansion contains no terms of frequency ω = 2π (2k ) /T ; k = 1, 2,.... Also, no sine terms are present. Then x(t) satisfies the equation 

Solution:

No sine terms are present.

∴x(t ) is even function.

QUESTION: 10

 The residue of the function f(z) 

Solution:

QUESTION: 11

The residues of a complex function  ​ at its poles are   ​

Solution:

x(z) has simple poles at z = 0,1, 2.

QUESTION: 12

The value of the contour integral    in positive sense is  

Solution:

QUESTION: 13

The integral    evaluated around the unit circle on the complex plane for   

Solution:

QUESTION: 14

An analytic function of a complex variable z = x + iy is expressed as f(z) = u (x, y) + i v(x, y) where i =√−1 . If u = xy, the expression for v should be 

Solution:

Here u and v are  analytic  as f(z) is analytic. 

∴ u, v satisfy Cauchy-Riemann equation.

QUESTION: 15

The analytic function     has singularities at   

Solution:

QUESTION: 16

The value of the integral    (where C is a closed curve given by |z| = 1) is 

Solution:

QUESTION: 17

 Roots of the algebraic equation x3 +x2 +x+ 1 = 0 are 

Solution:

QUESTION: 18

The algebraic equation    

F (s ) = s5 − 3s4+ 5s3− 7s2 + 4s + 20 is given F ( s ) = 0 has  

Solution:

we can solve it by making Routh Hurwitz array.

We can replace 1st element of s1 by 10.

If we observe the 1st column, sign is changing two times.

So we have two poles on right half side of imaginary 

Axis and 5s2+20=0  

So, s =±2j and1 pole on left side of imaginary axis .

QUESTION: 19

The value of    where C is the contour z −i / 2=1 is

Solution:
QUESTION: 20

Let z3 = z, where z is a complex number not equal to zero. Then z is a solution of

Solution:

Now by hit and trial method we see the solution being 

Z4 = 1 

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