Math for Computer science Questions and Answers 281 to 290

Math for Computer science

Questions 281 to 290

281.	What is the 5th term of (3 + x)8 ? (a)  C(8, 4) 34 x4                                      (b)  C(8, 5) 33 x5       (c)  C(8, 4) 34 x5 (d)  C(8, 4) 35 x4                                     (e)  C(7, 4) 34 x4.
282.	How many different strings can be made by reordering the letters of the word ABRACADABRA (a)  8 ! / 5!2!2!         (b)  11! / 5!2!2!         (c)  5!2!2! / 11!         (d)  5!2!2! / 8!          (e)  11!.
283.	What is the value of k after the following code has been executed. k := 0           for i1 := 1 to n1               for  i2 := 1 to n2               for i2 := 1 to n2               :               :                 for  im := 1 to nm                      k := k + 1 (a)  n1 + n2 + n3 +….nm                           (b)  n1.n2.n3…………nm                     (c)  C(n+m-1, m) (d)  C(n,m)                                             (e)  P(n,m).
284.	GCD of 24.35.72 and 24.32 is (a)  22.35.72              (b)  24.35.72              (c)  25.34.72              (d)  24.32.70              (e)  22.35.74.
285.	How many solutions are there to the equation x1 + x2 +x3+x4 = 17 (a)  C(20,17)                                          (b)  C(20 , 3)                                          (c)  1140                        (d)  All the above                                   (e)  none of the above.
286.	Fermat’s theorem states that If  p is prime and a is an integer not divisible by p, then (a)  ap–1  1 (mod p)                                                             (b)  ap  1 (mod p)                    (c)  ap–1  0 (mod p) (d)  ap–1  1 (mod p–1)                            (e)  ap  1 (mod p–1).
287.	Warshall’s algorithm is used for finding the __________ of a relation. (a)  reflexive closure                                                             (b)  symmetric closure              (c)  transitive closure (d)  transpose                                        (e)  inverse.
288.	Suppose that A is a subset if V*. Then the set consisting of concatenations of arbitrarily many strings from A represented by A* is called (a)  Symmetric closure                           (b)  Reflexive closure                   (c)  Kleene closure (d)  Finite closure                                   (e)  Finite state closure.
289.	The finite-state machine with no output is called _________ (a)  Kleene machine                               (b)  Finite machine                (c)  Output-free machine (d)  Finite-state automata                        (e)  Moore machine.
290.	Type 2 grammars are also called ­__________ (a)  Context-sensitive grammars             (b)  Regular grammars            c)  Context-free grammars (d)  Context less grammars                    (e)  Irregular grammars.

Answers

281.	Answer : (a) Reason : For finding the 5th term use the general term formula tr+1 = C(x, y)xn–r yr. Here you have to find the term tr+1.
282.	Answer : (b) Reason : This is a problem of permutations with repetitions. If n be the total number of letters and r1 letters are of same type and r2 letters are of same type then the number of different strings by reordering the letters of the word is n!/r1! × r2!
283.	Answer : (b) Reason : By the definition of product rule.
284.	Answer : (d) Reason : Gcd of 24.35.72 and 24.32 is 2 min(4,4) 3 min(5,2) 7 min(2,0) = 24.32.70
285.	Answer : (d) Reason : This is combinations with indistinguishable objects. Here n=4 and r=17. The number of solutions is equal to the number of 17-combinations with repletion allowed from  a set with 4 elements. Therefore the answer is C(4+17-1,17) = C(20,17) = C(20,3).
286.	Answer : (a) Reason : Definition of Fermat’s theorem
287.	Answer : (c) Reason : Warshall’s algorithm is one of the algorithms for finding the transitive closure of the relation.
288.	Answer : (c) Reason : Definition of the kleene’s closure
289.	Answer : (d) Reason : Definition of finite-state automata
290.	Answer : (c) Reason : Type 2 grammars are also called context-free grammars.