# 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
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.

101.
Reason:  By Eucledian Algorithm a = bq + r then g.c.d. (a, b) = g.c.d. (b, r)

102.
Reason:  By definition of pigeonhole principle

103.
Reason:
 L L L D D D
26 . 25 . 24 . 10 . 9 . 8

104.
Reason:  By Pascal’s identity

105.
Reason:  By definition of Diagonal relation

106.
Reason:  By definition of Symmetric Closure

107.
Reason:  a º b (mod m) Þ m divides a – b

108.
Reason:  Noun phrase ® An article adjective noun

109.
Reason:  By definition of productio

110.