CS and IT GATE 2016 Set-1 Questions with Answer

Ques 1 Aptitude

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.

40.00

46.02

60.01

92.02

Ques 2 Aptitude

Consider the following statements relating to the level of poker play of four players P, Q, R, and S.

I P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q

Which of the following can be logically inferred from the above statements?

(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set

(i) only

(ii) only

(i) and (ii)

neither (i) nor (ii)

Ques 3 Aptitude

Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of the nation’s diversity, nothing else is. Which of the following can be logically inferred from the above sentences?

India is a country of exactly seventeen languages.

Linguistic pluralism is the only indicator of a nation’s diversity.

Indian currency notes have sufficient space for all the Indian languages.

Linguistic pluralism is strong evidence of India’s diversity.

Ques 4 Aptitude

A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is __________.

Ques 5 Aptitude

If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’?

zentaga

tagafer

tagazen

relffer

Ques 6 Aptitude

Archimedes said, “Give me a lever long enough and a fulcrum on which to place it, and I will move the world.” The sentence above is an example of a ___________ statement.

figurative

collateral

literal

figurine

Ques 7 Aptitude

A rewording of something written or spoken is a ______________.

paraphrase

paradox

paradigm

paraffin

Ques 8 Aptitude

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.

I will not leave the place until the minister does not meet me.

I will not leave the place until the minister doesn’t meet me.

I will not leave the place until the minister meet me.

I will not leave the place until the minister meets me.

Ques 9 Automata

Let X be a recursive language and Y be a recursively enumerable but not recursive language. Let W and Z be two languages such that Y reduces to W, and Z reduces to X (reduction means the standard many-one reduction). Which one of the following statements is TRUE?

W can be recursively enumerable and Z is recursive.

W an be recursive and Z is recursively enumerable.

W is not recursively enumerable and Z is recursive.

W is not recursively enumerable and Z is not recursive

Ques 10 Automata

Consider the following context-free grammars:

G1: S → aS|B, B → b|bB
G2: S → aA|bB, A → aA|B|ε, B → bB|ε

Which one of the following pairs of languages is generated by G1 and G2, respectively?

{a^mbⁿ |m > 0 or n > 0} and {a^mbⁿ |m > 0 and n > 0}

{a^mbⁿ |m > 0 and n > 0} and {a^mbⁿ |m > 0 or n ≥ 0}

{a^mbⁿ |m ≥ 0 or n > 0} and {a^mbⁿ |m > 0 and n > 0}

{a^mbⁿ |m ≥ 0 and n > 0} and {a ^mbⁿ |m > 0 or n > 0}

Ques 11 Automata

Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive 0s and two consecutive 1s?

(0+1)*0011(0+1)* + (0+1)*1100(0+1)*

(0+1)* (00(0+1) *11+11(0+1)*00)(0+1)*

(0+1)*00(0+1) *+ (0+1) *11(0+1) *

00(0+1) *11+11(0+1)*00

Ques 12 Automata

Which of the following decision problems are undecidable?

I. Given NFAs N₁ and N₂, is L(N₁)∩L(N₂) = Φ?
II. Given a CFG G = (N,Σ,P,S) and a string x ∈ Σ*, does x ∈ L(G)?
III. Given CFGs G₁ and G₂, is L(G₁) = L(G₂)?
IV. Given a TM M, is L(M) = Φ?

I and IV only

II and III only

III and IV only

II and IV only

Ques 13 Automata

Which of the following languages is generated by the given grammar?

S → aS|bS| ε

{aⁿb^m | m,n >= 0}

{w∈{a,b}* | w has equal number of a's and b's}

{aⁿ | n>=0} U {aⁿbⁿ | n>=0}

{a,b}*

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CS and IT GATE 2016 Set-1 Questions with Answer