CS and IT GATE 2016 Set-2 Questions with Answer

Ques 1 Aptitude

All hill-stations have a lake. Ooty has two lakes. Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?

(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.

Ques 2 Aptitude

Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required. Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph?

(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions

Ques 3 Aptitude

Among 150 faculty members in an institute, 55 are connected with each other through Facebook ® and 85 are connected through WhatsApp ® . 30 faculty members do not have Facebook ® or WhatsApp ® accounts. The number of faculty members connected only through Facebook ® accounts is ______________.

Ques 4 Aptitude

Pick the odd one from the following options.

Ques 5 Aptitude

Find the odd one in the following group of words.

mock, deride, praise, jeer

Ques 6 Aptitude

Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia.

Choose the option which is closest in meaning to the underlined phrase in the above sentence.

Ques 7 Aptitude

The man who is now Municipal Commissioner worked as ______________.

Ques 8 Automata

The number of states in the minimum sized DFA that accepts the language defined by the regular expression

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


is __________________

Ques 9 Automata

A student wrote two context-free grammars G1 and G2 for generating a single C-like array declaration. The dimension of the array is at least one. For example,

int a[10][3];
The grammars use D as the start symbol, and use six terminal symbols int ; id [ ] num.

Grammar G1
D → int L;
L → id [E
E → num]
E → num] [E

Grammar G2
D → int L;
L → id E
E → E[num]
E → [num]

Which of the grammars correctly generate the declaration mentioned above?

Ques 10 Automata

Which one of the following grammars is free from left recursion?

Ques 11 Automata

Consider the following languages.

L₁ = {(M) | M takes at least 2016 steps on some input},
L₂ = {(M) | M takes at least 2016 steps on all inputs} and
L₃ = {(M) | M accepts ε},

where for each Turing machine M, denotes a specific encoding of M. Which one of the following is TRUE?

Ques 12 Automata

Consider the following languages:

L₁= {aⁿb^mc^n+m : m, n >= 1}
L₂= {aⁿbⁿc²ⁿ : n >= 1}

Which one of the following is TRUE?

Ques 13 Automata

Consider the following two statements:

I. If all states of an NFA are accepting states then the language accepted by the NFA is Σ* .
II. There exists a regular language A such that for all languages B, A ∩ B is regular.

Which one of the following is CORRECT?