CS and IT GATE 2020 Questions with Answer

Ques 1 Aptitude

Two straight lines are drawn perpendicular to each other in X−Y plane. If α and β are the acute angles the straight lines make with the X- axis, then α+β is ________ .

120

180

Ques 2 Aptitude

If P=3, R=27, T=243, then Q+S = ________ .

110

Ques 3 Aptitude

The dawn of the 21st century witnessed the melting glaciers oscillating between giving too much and too little to billions of people who depend on them for fresh water. The UN climate report estimates that without deep cuts to man-made emissions, at least 30% of the northern hemisphere’s surface permafrost could melt by the end of the century. Given this situation of imminent global exodus of billions of people displaced by rising seas, nation-states need to rethink their carbon footprint for political concerns, if not for environmental ones.

Which one of the following statements can be inferred from the given passage ?

Nation-states do not have environmental concerns.

Nation-states are responsible for providing fresh water to billions of people.

Billions of people are responsible for man-made emissions.

Billions of people are affected by melting glaciers.

Ques 4 Aptitude

Select the word that fits the analogy:
Cook : Cook :: Fly : _______

Flyer

Flying

Flew

Flighter

Ques 5 Aptitude

His knowledge of the subject was excellent but his classroom performance was _______ .

extremely poor

good

desirable

praiseworthy

Ques 6 Aptitude

Raman is confident of speaking English _______ six months as he has been practising regularly _______ the last three weeks.

during, for

for, since

for, in

within, for

Ques 7 Automata

Consider the following languages.

L₁ = { wxyx ∣ w,x,y ∈ (0+1)⁺ }
L₂ = { xy ∣ x,y ∈ (a+b)*, ∣x∣=∣y∣, x≠y }

Which one of the following is TRUE ?

L1 is regular and L2 is context- free

L1 context- free but not regular and L2 is context-free

Neither L1 nor L2 is context- free

L1 context- free but L2 is not context-free

Ques 8 Automata

Which of the following languages are undecidable? Note that ⟨M⟩ indicates encoding of the Turing machine M.

L₁ = { ⟨M⟩ ∣ L(M)=∅ }
L₂ = { ⟨M,w,q⟩ ∣ M on input w reaches state q in exactly 100 steps }
L₃ = { ⟨M⟩ ∣ L(M) is not recursive }
L₄ = { ⟨M⟩ ∣ L(M) contains at least 21 members }

L₁, L₃, and L₄ only

L₁, and L₃ only

L₂, and L₃ only

L₂, L₃ and L₄ only

Ques 9 Automata

Consider the language L = { aⁿ ∣ n≥0 }∪{ aⁿbⁿ∣ n≥0 } and the following statements.
I. L is deterministic context-free.
II. L is context-free but not deterministic context-free.
III. L is not LL(k) for any k.
Which of the above statements is/are TRUE ?

Ⅰ only

Ⅱ only

Ⅰ and Ⅲ only

Ⅲ only

Ques 10 Automata

Consider the following statements
I. If L1∪L2 is regular, then both L1 and L2 must be regular.
II. The class of regular languages is closed under infinite union.
Which of the above statements is/are TRUE ?

Ⅰ only

Ⅱ only

Both Ⅰ and Ⅱ

Neither Ⅰ nor Ⅱ

Ques 11 Automata

Which one of the following regular expressions represents the set of all binary strings with an odd number of 1′s ?

((0+1)*1(0+1)*1)*10*

(0*10*10*)*0*1

10*(0*10*10*)*

None

Ques 12 Automata

Consider the following language.

L = { x∈{a,b}* ∣ number of a’s in x divisible by 2 but not divisible by 3 }

The minimum number of states in DFA that accepts L is _________ .

6 is the correct answer.

Ques 13 Automata

Consider the following language.
L = { x∈{a,b}* ∣ number of a’s in x divisible by 2 but not divisible by 3 }
The minimum number of states in DFA that accepts L is _________ .

6 is the correct answer.

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CS and IT GATE 2020 Questions with Answer