Electrical Engineering Gate Yearwise 




Electrical Engineering GATE 2016 Set-1 Questions with Answer

Ques 27 Electromagnetics

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by φ = f(r,z), where f is a continuous function of r and z. Let E⃗ be the resulting electric field. Then the magnitude of ∇ x E⃗

A

increases with r.

B

is 0.

C

is 3.

D

decreases with z.



Ques 28 Electromagnetics

A soft-iron toroid is concentric with a long straight conductor carrying a direct current I. If the relative permeability μr of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is ________.


100 is the correct answer.


Ques 29 Electromagnetics

Two electric charges q and -2q are placed at (0,0) and (6,0) on the x-y plane. The equation of the zero equipotential curve in the x-y plane is

A

x = -2

B

y = 2

C

x2+y2 = 2

D

(x+2)2+y2 = 16



Ques 30 Engineering Mathematics

The maximum value attained by the function f(x) = x(x-1)(x-2) in the interval [1, 2] is ________.


0.3849 is the correct answer.


Ques 31 Engineering Mathematics

Consider a 3x3 matrix with every element being equal to 1. Its only non-zero eigenvalue is ________.


3 is the correct answer.


Ques 32 Engineering Mathematics

The Laplace Transform of f(t) = e2tsin(5t)u(t) is

A

5 / (s2 - 4s + 29)

B

5 / (s2 + 5)

C

(s-2) / (s2 - 4s + 29)

D

5 / (s+5)



Ques 33 Engineering Mathematics

A function y(t), such that y(0)=1 and y(1)=3e-1, is a solution of the differential equation d2y/dt2 + 2(dy/dt) + y = 0. Then y(2) is

A

5e-1

B

5e-2

C

7e-1

D

7e-2



Ques 34 Engineering Mathematics

The value of the integral ∫c (2z+5)/((z-1/2)(z2-4z+5)) dz over the contour |z|=1, taken in the anti-clockwise direction, would be

A

(24πi)/13

B

(48πi)/13

C

24/13

D

12/13



Ques 35 Engineering Mathematics

Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is ________.


0.0625 is the correct answer.


Ques 36 Engineering Mathematics

Let S = Σn=0∞ nαn where |α|<1. The value of α in the range 0 < α < 1, such that S = 2α is ________.


0.2928 is the correct answer.


Ques 37 Engineering Mathematics

Let the eigenvalues of a 2x2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A2 - 3A + 4I would, respectively, be

A

2, 14; x1, x2

B

2, 14; x1+x2, x1-x2

C

2, 0; x1, x2

D

2, 0; x1+x2, x1-x2



Ques 38 Engineering Mathematics

Let A be a 4x3 real matrix with rank 2. Which one of the following statement is TRUE?

A

Rank of ATA is less than 2.

B

Rank of ATA is equal to 2.

C

Rank of ATA is greater than 2.

D

Rank of ATA can be any number between 1 and 3.



Ques 39 General Aptitude

The man who is now Municipal Commissioner worked as

A

the security guard at a university

B

a security guard at the university

C

a security guard at university

D

the security guard at the university



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