Math for Computer science
Questions 31 to 40
31.

Let f(x) = ëx2/2û. Find f(s) if S= {1, 2, 3, 4}
(a) {1, 2, 4, 4, 8} (b) {1, 2, 5, 8} (c) {0, 2, 4, 8} (d)
{0, 2, 5, 8} (e) {0, 2, 4, 9}.

32.

Which of the
following statements is false?
(a) fÎ{f} (b)
fÎ{f, {f}} (c)
{f}Î{f}
(d) {f}Î{{f}} (e)
{f} Ì{{f}, {f}}.

33.

From the
following, choose the decimal expansion of the integer that has (101011010)2
as its binary expansion.
(a) 338 (b) 344 (c) 346 (d) 330 (e) 340.

34.

From the
following, choose the binary expansion of 246.
(a) 1111 0011 (b) 1111 0110 (c) 1111 0101 (d)
1111 1100 (e) 1111 1001.

35.

The
rcombination from a set with “n” elements when repetitions of elements are not
allowed is
(a) C(n+r+1, r) (b) C(n+r1, r) (c) C(n, r)
(d) C(n+r1, r 1) (e) C(n+r+1, r+1).

36.

Which of the
following statements is true in a year?
(a) Among any
group of 366 people there must be at least one with the same birthday.
(b) Among any
group of 366 people there must be at least two with the same birthday
(c) Among any
group of 366 people there must be at most one with the same birthday
(d) Among any
group of 366 people there must be at most none with the same birthday
(e) Among any
group of 366 people there must be exactly 2 with the same birthday.

37.

What is the
probability that a card selected from a deck is a king?
(a) 1/4 (b) 1/52 (c) 4/52 (d) 2/52 (e) 3/52.

38.

What is the
probability that a positive integer less than 100 selected at random is
divisible by 25?
(a) 3/100 (b) 4/100 (c) 2/100 (d) 5/100 (e) 1/100.

39.

What is the
probability that a positive integer selected at random from the set of
positive integers not exceeding 21 is divisible by 5 or 3?
(a) 11/20 (b) 10/20 (c) 11/21 (d) 10/21 (e) 12/21.

40.

Let A = {0,11}
and B = {1,10,101} then AB is given by [concatenation of A and B is AB]
(a) {01, 010,
0110, 110, 1110, 11110}
(b) {01, 010,
0111, 111, 1110, 11110}
(c) {01, 010,
0101, 111, 1110, 11101}
(d) {01, 010,
0111, 111, 1110, 11111}
(e) {01, 010,
0110, 111, 1110, 11010}.

Answers
31.

Answer : (c)
Reason: Let
f(x) = ëx2/2û if S= {1,2,3,4}
f(s)
= f({1,2,3,4})
f(1)
= ë12/2û = ë1/2û = ë0.5û = 0
f(2)
= ë22/2û = ë4/2û = ë2û = 2
f(3)
= ë32/2û = ë9/2û = ë4. 5û = 4
f(4)
= ë42/2û = ë16/2û = ë8û = 8
\ f(s) = {0,2,4,8}

32.

Answer : (c)
Reason: by
definition

33.

Answer : (c)
Reason: (1010
11010)2
=
1x28+ 0x27 + 1x26 + 0x25 + 1x24 + 1x23 + 0x22 + 1x21 +0x20
=
256 +0 +64+ 0 + 16 +8 +0 +2 +0
=
346

34.

Answer : (b)
Reason: 2246
21230
2611
2301
2150
271
231
211
(11110110)2

35.

Answer : (c)
Reason: by
definition

36.

Answer : (b)
Reason: In
a year there are 365 days, if we distribute every day one pessons birthday
then at least two with the same birthday.

37.

Answer : (c)
Reason: E:
Selecting a king

38.

Answer : (a)
Reason: E:
A positive integer less than 100 in divisible by 25

39.

Answer : (d)
Reason: Positive
integer not exceeding 21 divisible by 5 or 3

40.

Answer : (c)
Reason: A={0,11}
B={1, 10, 101}
AB
= {01, 010, 0101, 111, 1110, 11101}

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