Math for Computer science Questions and Answers 101 to 111

Math for Computer science

Questions  101 to 110

101.	Let a = bq + r, where a, b, q and r are integers. Which of the following statement is true? (a) g.c.d. (a,a) = g.c.d. (b,r) (b) g.c.d. (a,b) = g.c.d. (q,r) (c) g.c.d. (a,r) = g.c.d. (b,r) (d) g.c.d. (a,b) = g.c.d. (b,r) (e) g.c.d. (a) = g.c.d. (q).
102.	Pigeonhole principle can be stated as (a) If N+1 objects are placed into N boxes then there is one box with all the objects (b) If N+1 objects are placed into N boxes then there is one box with atmost 2 or more objects (c) If N+1 objects are placed into N boxes then there is exactly one box with 2 or more objects (d) If N+1 objects are placed into N boxes then there is atmost one box with 2 or more objects (e) If N+1 objects are placed into N boxes then there is atleast one box with 2 or more objects.
103.	How many license plates consisting of three letters followed by three digits contain no letter or digit twice? (a) 26 . 26 . 26 . 10 . 10 . 10 (b) 26 . 25 . 24 . 10 . 9 . 8 (c) 26 . 26 . 25 . 10 . 10 . 9 (d) 26 . 25 . 24 . 10 . 10 . 10 (e) 26 . 25 . 24. 10 . 8 . 9.
104.	The value of   is (a) (b) (c) (d) (e) .
105.	A Diagonal Relation defined on A is (a) {(x, y) / (x, y) = (y, x), x Î A, y Î A} (b) {(y, x) / (x, y) related to (y, x), x Î A, y Î A} (c) {(x, x) / x is an element belongs to the set A} (d) {(x, y) / x < y, x Î A, y Î A} (e) {(x, y) / x > y, x Î A, y Î A}.
106.	The symmetric closure of a relation is defined by (a) (b) (c) (d) (e) .
107.	Let a, b be two integers and m be a positive integer then a º b (mod m) means (a) m divides b – a (b) m divides a – b (c) m divides a + b (d) m divides a/b (e) m divides ab.
108.	A noun phrase is made up of (a) An adjective article noun (b) A noun article adjective (c) An article adjective noun (d) An article noun adjective (e) An adjective noun article.
109.	The rules that specify when we can replace a string with another string are called (a) Vocabulary (b) Productions (c) Terminals (d) Non-Terminals (e) Sentences.
110.	Which of the following statement is true? (a) Every production P must contain at least one non-terminal on its left side (b) Every production P must contain at most one non-terminal on its left side (c) Every production P must contain at least one terminal on its left side (d) Every production P must contain at most one terminal on its left side (e) Every production P must contain a production on its left side.

Answers

	101.		Answer : (d) Reason:  By Eucledian Algorithm a = bq + r then g.c.d. (a, b) = g.c.d. (b, r)
	102.		Answer : (e) Reason:  By definition of pigeonhole principle
	103.		Answer : (b) Reason:  L L L D D D        26 . 25 . 24 . 10 . 9 . 8
	104.		Answer : (a) Reason:  By Pascal’s identity
	105.		Answer : (c) Reason:  By definition of Diagonal relation
	106.		Answer : (c) Reason:  By definition of Symmetric Closure
	107.		Answer : (b) Reason:  a º b (mod m) Þ m divides a – b
	108.		Answer : (c) Reason:  Noun phrase ® An article adjective noun
	109.		Answer : (b) Reason:  By definition of productio
110.		Answer : (a) Reason : By conditions of production.