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.

Answers


41.
Answer :  (c)
Reason:  f(x) = ax+b g(x) = cx+d
       (gof) (x) = g[f(x)]
                            = g[ax+b]
                            = C(ax+b) +d 
                     = acx+bc+d
42.
Answer :  (c)
Reason:  by definition
43.
Answer :  (c)
Reason:  by definition
44.
Answer :  (c)
Reason:  Let E : getting all three times head
       A fair con is tossed for three times so the
       Total no. of cases are 23 = 8
       These will be only one case favorable to E.
      
45.
Answer :  (c)
       L (G) = {0, 101, 11011, 1110111, …..}
46.
Answer :  (c)
Reason:  L(G) = {bb, ba}
      
47.
Answer :  (c)
Reason:  Sentence Noun phrase verb phrase
48.
Answer :  (c)
49.
Answer :  (b)
Reason:  R-1 = {(1,1) (2,1) (2,2) (3,2) (4,2) (1,3) (2,3) (3,3) (4,3)}
50.
Answer :  (c)
Reason:  In a pack of cards these are 4 aces so all four aces can be selected in only one way.
From the deck of well shuffled pack of cards 4 cards are drawn, which can be selected in 52
       E : getting 4 aces
      




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