# Math for Computer science Questions and Answers 31 to 40

## 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 r-combination from a set with “n” elements when repetitions of elements are not allowed is (a) C(n+r+1, r)        (b) C(n+r-1, r)                        (c) C(n, r) (d) C(n+r-1, 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}.

 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:  2|246        2|123-0           2|61-1        2|30-1        2|15-0        2|7-1        2|3-1        2|1-1        (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}