Indian Institute of Technology Mumbai (IIT-M) 2005 M.E Information Technology GATE IT - Question Paper

(D) TCP for congestion control
30. A HTML form is to be designed to enable purchase of office stationery. needed items are
to be opted (checked). Credit card details are to be entered and then the submit button is
to be pressed. Which 1 of the subsequent choices would be improper for sending the data to
the server? presume that security is handled in a way that is transparent to the form design.
(A) only GET
(B) only POST
(C) either of GET or POST
(D) neither gET not POST
Q.31 - Q.80 Carry 2 Marks every.
31. Let f be a function from a set A to a set B, g a function from B to C, and h a function from
A to C, such that h(a) = g(f (a))for all a E A. Which of the subsequent statements is always actual
for all such functions f and g?
(A) g is onto h is onto
(B) h is onto f is onto
(C) h is onto g is onto
(D) h is onto f and g are onto
32. Let A be a set with n elements. Let C be a collection of distinct subsets of A such that for
any 2 subsets S1 and S2 in C, either S1 S or two S1. What is the maximum cardinality of C?
(A) n
(B) n+1
(C) 2fh+1
(D)n!
33. An unbiased coin is tossed repeatedly until the result of 2 successive tosses is the
same. Assuming that the trials are independent, the expected number of
tosses is:
(A) 3
(B) 4
(C) 5
(D)6
34. Let n = p2q,where p and q are distinct prime numbers. How many numbers m satisfy one m
nand gcd(m,n) = 1? Note that gcd(m,n) is the greatest common divisor of m and n.
(A) p(q—i)
(C) (p2 —i)(q—i)
35. What is the value of [(x — r)3 (sin x) dx
(A) -1 (B) 0
(B) pq
(D) p(p—i)(q—i)
(C) one (D)t
36. Let P(x) and Q(x) be arbitrary predicates. Which of the subsequent statements is always
TRUE?
(A) ((vxP (x) v Q (x))) ((vx ( (x) v (vxQ (x)))
(B) (vx(P (x) Q(x))) ((vx(P (x) (vxQ(x)))
(C) (vx(P(x)) (vxQ(x))) ((vx(P(x) Q(x)))
(D) (vx(P(x))) (vxQ(x)))
37. Consider the non-deterministic finite automation (NFA) shown in the figure.

Earning:   Approval pending.