# Math for Computer science Questions and Answers 41 to 50

## Math for Computer science

### Questions 41 to 50

 41 Find gof if f(x) = ax + b and g(x) = cx + d when a,b,c,d are constants.    (a) ac + bc + d      (b) ac + bcx + d        (c) acx + bc + d            (d) ac + bc + dx (e) ax + bc + d. 42 To show The statement p(1) is true for a fixed +ve integer ‘1’, is called     (a) Inductive step           (b) Inductive hypothesis (c) Basic Step (d) Strong induction                   (e) Rule of inference. 43 The difference of A and B denoted by A – B contains (a)        Those elements in both A and B (b)        Those elements in either A or B (c)        Those elements purely in A but not B (d)        Those elements in Set A, but not in universal set (e)        Those elements in Set B, but not in set A. 44 A fair coin has been tossed for 3 times. What is the probability that all three times head will be outcome. (a) 3/8     (b) 1/3     (c) 1/8           (d) 3/3   (e) 0. 45 Let G be grammar with Vocabulary V = {s, 0,1}, Set of terminals T = {0,1} starting symbol s, and production p = {s ®1s1, s® 0} then the language of the grammar, [L(G)] is (a)        {0, 110, 11110, 1011101, …………} (b)        {0, 110, 11101, 1111110, ……….} (c)        {0, 101, 11011, 1110111, …………} (d)        {0, 110, 11110, 1111101, …………} (e)        {0, 110, 11110, 1111110, ……….}. 46 Let V = { S, A, a, b} and T = {a, b} Let G = {V,T,S,P}. The language of G, L(G) is given by L(G) = {bb, ba}then the production is given by (a) P = {S ®a AB, A®Bb, B ® l }         (b) P = {S ®A, A®B, B ® l } (c) P = {S ®b B, B®b, B ® a }  (d) P = {S ®A Ba, AB®a} (e) P = {S ®b A, A®B, B ® a }. 47 Which of the following statements is true? (a)        Sentence ® Noun Verb (b)        Sentence ® Noun Pronoun (c)        Sentence ® Noun Phrase Verb Phrase (d)        Sentence ® Verb Phrase Noun Phrase (e)        Sentence ® Noun Phrase Noun Phrase. 48 Let R be a relation from C to A and S be a relation from B to C. Then RoS defined by (a) { (b, c) / b Î B, c Î C }          (b) { (c, a) / c Î C, a Î A } (c) { (a, b) / a Î A, b Î B }          (d) { (a, c) / a Î A, c Î C } (e) { (b, a) / b Î B, aÎA }. 49 Let R = { (1,1), (1,2), (2,2), (2,3),(2,4), (3,1), (3,2), (3,3), (3,4) } then R-1 is given by (a)        { (1,1), (1,2), (2,2), (2,3), (3,1), (3,2), (3,3),(2,4), (4,3)} (b)        ( (1,1), (2,1), (2,2), (3,2), (1,3), (2,3), (3,3),(4,2), (4,3)} (c)        { (1,1), (2,1), (2,2), (3,2), (2,3), (3,1), (3,3), (4,2),(3,4)} (d)        { (1,1), (1,2), (2,2), (2,3),(2,4) (3,1), (3,2), (3,3), (4,3)} (e)        { (1,1), (4,1), (4,2), (3,2), (1,3), (2,3), (3,3), (3,4),(4,2) }. 50 From a deck of well shuffled pack of cards 4 cards are drawn. What is the probability that all four are aces?   (a) 5/52C4      (b) 2/52C4            (c) 1/52C4         (d) 4/52C4         (e) 3/52C4.