GATE CS 1999

Question 21

The maximum gate delay for any output to appear in an array multiplier for multiplying two n bit number is:

• O(n^2)
• O(n)
• O(log n)
• O(1)

Question 22

The main memory of a computer has 2 cm blocks while the cache has 2c blocks. If the cache uses the set associative mapping scheme with 2 blocks per set, then the block k of main memory maps to the set:

• (k mod m) of the cache
• (k mod c) of the cache
• (k mod 2c) of the cache
• (k mod 2cm) of the cache

Question 23

The Newton-Raphson method is to be used to find the root of the equation f(x)=0 where x₀ is the initial approximation and f \' is the derivative of f.   The method converges:  

• Always
• Only if f is a polynomial
• Only if f(x0) <0
  
• None of the above

Question 24

Let R = ( A, B, C, D, E, F ) be a relation scheme with the following dependencies: C→F, E→A, EC→D, A→B. Which of the following is a key of R?

• CD
• EC
• AE
• AC

Question 25

Consider two events E1 and E2 such that probability of E1, Pr[E1]=1/2, probability of E2, Pr[E2]=1/3, and probability of E1 and E2, Pr[E1 and E2]=1/5, Which of the following statement is/are True?

• Pr[E1 and E2] is 2/3
• Events E1 and E2 are independent.
• Events E1 and E2 are not independent.
• Pr[E1/E2]= 4/5

Question 26

Two girls have picked 10 roses, 15 sunflowers and 14 daffodils. What is the number of ways they can divide the flowers amongst  themselves?

• 1638
• 2100
• 2640
• None of the above

Question 27

Let L be a set with relation R which is transitive, anti-symmetric and reflexive and for any two elements a,b ∈ L let the least upper bound lub(a,b) and greatest lower bound glb(a,b) exist. Which of the following is/are true? a.  L is a poset. b.  L is a boolean algebra. c.  L is a lattice. d.  None of the above.

• a, b
• a, c
• only c
• only b

Question 28

If L1 is a context free language and L2 as a regular language, which of the following is/are False? a.  L1-L2 is not context free b.  L1 ∩ L2 is context free c.  ~L1 is context free d.  ~L2 is regular

• Only b
• Only c
• Both a and c
• Both b and c

Question 29

Given the programming constructs i)assignment  ii)for loops where the loop parameter cannot be changed within the loop  iii)if-then-else  iv)forward  go to v)arbitrary go to  vi)non-recursive procedure call vii)recursive procedure/function call  viii)repeat loop, which constructs will you not include in a programming language such that it should be possible to program the terminates (i.e. halting) function in the same programming language.

• ii), iii), iv)
• v), vii), viii)
• vi), vii), viii)
• iii), v), viii)

Question 30

For the schedule given below, which of the following is Correct?

1   Read A
2                               Read B
3   Write A
4                               Read A
5                               Write A
6                               Write B
7   Read B
8   Write B 

• This schedule is serialisable and can occur in a scheme using 2PL protocol.
• This schedule is serialisable but cannot occur in a scheme using 2PL protocol.
• This schedule is not serialisable but can occur in a scheme using 2PL protocol.
• This schedule is not serialisable and cannot occur in a scheme using 2PL protocol.