Electronics and Communication Gate 2020 Questions with Answer

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Ques 40 GATE 2020

For a vector field A, which one of the following is FALSE?

A→ is solenoidal if ∇·A→=0.

∇×A→ is another vector field.

A→ is irrotational if ∇²A→=0.

∇×(∇×A→)=∇(∇·A→)-∇²A→

Ques 41 GATE 2020

The partial derivative of the function
f(x,y,z)=e^{1-x cos y}+xze^-1/(1+y²)
with respect to x at the point (1, 0, e) is

(A) -1

(B) 0

(D) 1/e

(b) is the correct answer.

Ques 42 GATE 2020

The general solution of d²y/dx² - 6dy/dx + 9y = 0 is

y=C₁e³x+C₂e-³x

y=(C₁+C₂x)e-³x

y=(C₁+C₂x)e³x

y=C₁e³x

Ques 43 GATE 2020

Consider the following system of linear equations.
x₁+2x₂=b₁;
2x₁+4x₂=b₂;
3x₁+7x₂=b₃;
3x₁+9x₂=b₄;
Which one of the following conditions ensures that a solution exists for the above system?

b₂=2b₁ and 6b₁-3b₃+b₄=0

b₃=2b₁ and 6b₁-3b₃+b₄=0

b₂=2b₁ and 3b₁-6b₃+b₄=0

b₃=2b₁ and 3b₁-6b₃+b₄=0

(a) is the correct answer.

Ques 44 GATE 2020

Which one of the following options contains two solutions of the differential equation dy/dx=(y-1)x ?

ln|y-1|=0.5x²+C and y=1

ln|y-1|=2x²+C and y=1

ln|y-1|=0.5x²+C and y=-1

ln|y-1|=2x²+C and y=-1

(a) is the correct answer.

Ques 45 GATE 2020

For the solid S shown below, the value of ∫∫∫S xdxdydz (rounded off to two decimal places) is

(2.25) is the correct answer.

Ques 46 GATE 2020

The untimely loss of life is a cause of serious global concern as thousands of people get killed ______ accidents every year while many other die ______ diseases like cardio vascular disease, cancer, etc.

in, of

from, of

during, from

from, from

(a) is the correct answer.

Ques 47 GATE 2020

He was not only accused of theft ______ of conspiracy.

rather

but also

but even

rather than

(b) is the correct answer.

Ques 48 GATE 2020

Select the word that fits the analogy:
Explicit: Implicit :: Express:

Impress

Repress

Compress

Suppress

(b) is the correct answer.

Ques 49 GATE 2020

The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements in English lasting 15 seconds, as opposed to informal 5 second messages in French.
The French-speaking couple were upset at __________.

the in-flight announcements being made in English.

the English announcements being clearer than the French ones.

the English announcements being longer than the French ones.

equal importance being given to English and French.

Ques 50 GATE 2020

A superadditive function f(·) satisfies the following property
f(x₁+x₂)≥ f(x₁)+f(x₂)
Which of the following functions is a superadditive function for x>1?

e^x

√x

1/x

e^-x

(a) is the correct answer.

Ques 51 GATE 2020

The global financial crisis in 2008 is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in USA in 2007. The sub-prime lending crisis led to the banking crisis in 2008 with the collapse of Lehman Brothers in 2008. The sub-prime lending refers to the provision of loans to those borrowers who may have difficulties in repaying loans, and it arises because of excess liquidity following the East Asian crisis.
Which one of the following sequences shows the correct precedence as per the given passage?

East Asian crisis → subprime lending crisis → banking crisis → global financial crisis.

Subprime lending crisis → global financial crisis → banking crisis → East Asian crisis.

Banking crisis → subprime lending crisis → global financial crisis → East Asian crisis.

Global financial crisis → banking crisis → East Asian crisis → subprime lending crisis.

(a) is the correct answer.

Ques 52 GATE 2020

It is quarter past three in your watch.
The angle between the hour hand and the minute hand is

0°

7.5°

15°

22.5°

(b) is the correct answer.

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