GATE-CS-2014-(Set-2)

Question 51

If the associativity of a processor cache is doubled while keeping the capacity and block size unchanged, which one of the following is guaranteed to be NOT affected?

• Width of tag comparator

• Width of set index decoder

• Width of way selection multiplexer

• Width of processor to main memory data bus

Question 52

The value of a float type variable is represented using the single-precision 32-bit floating point format IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of −14.25. The representation of X in hexadecimal notation is

• C1640000H
• 416C0000H
• 41640000H
• C16C0000H

Question 53

In the Newton-Raphson method, an initial guess of x0 = 2 is made and the sequence x0, x1, x2 … is obtained for the function

0.75x3 – 2x2 – 2x + 4 = 0

Consider the statements
(I) x3 = 0.
(II) The method converges to a solution in a finite number of iterations. 

Which of the following is TRUE?

• Only I
• Only II
• Both I and II
• Neither I nor II

Question 54

The product of the non-zero eigenvalues of the matrix

1 0 0 0 1
0 1 1 1 0
0 1 1 1 0
0 1 1 1 0
1 0 0 0 1

is ______

• 4

• 5

• 6

• 7

Question 55

The number of distinct positive integral factors of 2014 is _________________________

• 7
• 8
• 9
• 10

Question 56

Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U. Consider the following two statements:

S1: There is a subset of S that is larger than every other subset.
S2: There is a subset of S that is smaller than every other subset. 

Which one of the following is CORRECT?

• Both S1 and S2 are true

• S1 is true and S2 is false

• S2 is true and S1 is false

• Neither S1 nor S2 is true

Question 57

A cycle on n vertices is isomorphic to its complement. The value of n is _____.

• 2
• 4
• 6
• 5

Question 58

The number of distinct minimum spanning trees for the weighted graph below is ____

• 4
• 5
• 6
• 7

Question 59

Which one of the following Boolean expressions is NOT a tautology? 

• C
  

• D
  

• B
  

• A
  

Question 60

SQL allows tuples in relations, and correspondingly defines the multiplicity of tuples in the result of joins. Which one of the following queries always gives the same answer as the nested query shown below:

    select * from R where a in (select S.a from S) 

• select R.* from R, S where R.a=S.a (D)
• select distinct R.* from R,S where R.a=S.a
• select R.* from R,(select distinct a from S) as S1 where R.a=S1.a
• select R.* from R,S where R.a=S.a and is unique R