GATE CS 1996


Question 1
Let A and B be sets and let Ac and Bc denote the complements of the sets A and B. The set (A−B)(B−A)(AB) is equal to a). A ∪ B b). A∪ Bc c). A ∩ B d). A∩ Bc
A
a
B
b
C
c
D
d
Set Theory & Algebra    GATE CS 1996    
Discuss it


Question 2
Let X= {2, 3, 6, 12, 24}, Let ≤ be the partial order defined by X ≤ Y if x divides y. Number of edges in the Hasse diagram of (X,≤) is
A
3
B
4
C
9
D
None of the above
Set Theory & Algebra    GATE CS 1996    
Discuss it


Question 3
Suppose X and Y are sets and |X| and |Y| are their respective cardinalities. It is given that there are exactly 97 functions from X to Y. From this one can conclude that
A
|X|=1,|Y|=97
B
|X|=97,|Y|=1
C
|X|=97,|Y|=97
D
None of the above
Set Theory & Algebra    GATE CS 1996    
Discuss it


Question 4
Which of the following statement is false?
A
The set of rational numbers is an abelian group under addition
B
The set of integers in an abelian group under addition
C
The set of rational numbers form an abelian group under multiplication
D
The set of real numbers excluding zero is an abelian group under multiplication
Set Theory & Algebra    GATE CS 1996    
Discuss it


Question 5
Two dice are thrown simultaneously. The probability  that at least one of them will have 6 facing up is
A
1/36
B
1/3
C
25/36
D
11/36
Probability    GATE CS 1996    
Discuss it


Question 5 Explanation: 
There can be two cases:
  • Case 1: Exactly one dice has 6 facing up and other dice can have any number from 1,2,3,4,5 facing up. There will be 5*2=10 such occurrences.
  • Case 2: Both of the dices having 6 coming up. Only one possible case exists for the same.
Thus total favorable cases = 10+1 = 11 While total cases = 6*6=36 Which gives the desired probability as: 11/36.
This explanation is contributed by Pradeep Pandey.
Question 6
The formula used to compute an approximation for the second derivative of a function f at a point X0 is opt              
A
a
B
b
C
c
D
d
Numerical Methods and Calculus    GATE CS 1996    
Discuss it


Question 7
Let Ax=b be a system of linear equations where A is an m×n matrix and b is a m×1 column vector and X is an n×1 column vector of unknowns. Which of the following is false?
A
The system has a solution if and only if, both A and the augmented matrix [Ab] have the same rank
B
If m
C
If m=n and b is a non-zero vector, then the system has a unique solution
D
The system will have only a trivial solution when m=n, b is the zero vector and rank(A) = n
Linear Algebra    GATE CS 1996    
Discuss it


Question 8
Which two of the following four regular expressions are equivalent? (ε is the empty string). (i). (00)*(ε+0) (ii). (00)* (iii). 0* (iv). 0(00)*
A
(i) and (ii)
B
(ii) and (iii)
C
(i) and (iii)
D
(iii) and (iv)
Regular languages and finite automata    GATE CS 1996    
Discuss it


Question 9
Which of the following statements is false?
A
The Halting Problem of Turing machines is undecidable
B
Determining whether a context-free grammar is ambiguous is undecidable
C
Given two arbitrary context-free grammars G1 and G2 it is undecidable whether L(G1)=L(G2)
D
Given two regular grammars G1 and G2 it is undecidable whether L(G1)=L(G2)
Undecidability    GATE CS 1996    
Discuss it


Question 10
Let L ⊆ ∑* where ∑ = {a, b}. Which of the following is true? a). L= { x | x has an equal number of a's and b's } is regular b). L= { anbn | n ≥ 1 } is regular c). L= { x | x has more a's than b's } is regular d). L= {ambn | m ≥ 1, n ≥ 1 } is regular
A
a
B
b
C
c
D
d
Regular languages and finite automata    GATE CS 1996    
Discuss it


There are 75 questions to complete.


My Personal Notes arrow_drop_up