Math for Computer science Questions and Answers 231 to 240

Math for Computer science

Questions 231 to 240

231.	A drawer contains 4 red pens, 5 blue pens and 2 black pens. If you reach into the drawer without looking and pull out a pen for you and a pen for your work partner to own them, what is the probability that the first pen will be blue and the second pen will be black? (a) 1/121 (b) 2/121 (c) 11/40 (d) 7/11 (e) 1/11.
232.	You and 5 friends go on a roller coaster in which each car holds a pair. How many different pairs can you and your friends create for the ride? (a) 10 (b) 12 (c) 15 (d) 30 (e) 36.
233.	A pair of dice is thrown. What is the probability of both the faces not having the same number throwing a double? (a) 1 (b) 5/6 (c) 1/6 (d) 5/36 (e) 1/36.
234.	You and a group of 9 friends are playing basketball in a local park. At the end of the game, if each player shakes hands with every other player, how many handshakes will there be? (a)    9! Ways (b)   36 Ways (c)   45 Ways (d)   81 Ways (e) 100 Ways.
235.	A simple theorem used in the proofs of the other theorems (a) Axiom (b) Postulate (c) Lemma (d) Corollary (e) Conjecture.
236.	Let A = {1, 2, 3}, B = {2, 3, 4} and U = {1, 2, 3, 4, 5, 6, 7}. What is the value of (a) {1, 5, 6, 7} (b) {1, 2, 5, 7} (c) {1, 3, 5, 6, 7} (d) {2, 5, 6, 7} (e) {5, 6, 7}.
237.	If two sets A and B, A is a subset of B and A ≠  B then A is called –––––––––– of B. (a) Disjoint set (b) Power set (c) Proper subset (d) Unequal set (e) Super set.
238.	The inductive step for strong induction is (a) To show P(k) →  P(k + 1) is true for every positive integer k (b) To show [P(1) ∧ P(2) ∧ …∧ P (k)] → P(k + 1) is true for every positive integer k (c) To show [P(1) ∨ P(2) ∨ …∨ P (k)] → P(k + 1) is true for every positive integer k (d) To show P(1) →  P(k + 1) is true for every positive integer k (e) To show P(1) →  P(k) is true for every positive integer k.
239.	Which of the following relations is antisymmetric on the set of positive integers? (a) Divides (b) Equal to (c) Greater than (d) Not equal to (e) Less than.
240.	If f: z→z is defined by f(x) = 1 if x is even, f(x) =  –1 if x is odd, f(x) = 1, if x = 0, then f is a mapping. What is the codomain and range of f respectively. (a) z, z (b) {1, –1} (c) {1, –1}{1, –1} (d) z, {–1, 1} (e) {–1,1}, z.

Answers

231.	Answer : (e) Reason:  drawing a blue pen is 5/11 drawing a black pen is after not replacing the blue pen is 2/10 drawing both is 5/11*2/10=1/11
232.	Answer : (c) Reason:  total there are 6 people including you so the total number of ways  pairs  can be formed is gieven by   6C2 = 15
233.	Answer : (b) Reason:  The probability of throwing a diouble is 6/36. The probability of not  throwing a diouble is 1- 6/36 = 30/36 = 5/6
234.	Answer : (c) Reason:  along with you there are 10 people, out of tehm hand shaking must be done, so two people shakes the hands. total number of ways hand shaking takes place is given by 10C2 = 45 ways.
235.	Answer : (c) Reason:  by definition of lemma
236.	Answer : (a) Reason:  Bc  = {1,5,6,7 } Ac  = { 4,5,6,7 } B - Ac   =  {  2,3,} Bc – (B-Ac) =  {1,5,6,7 }
237.	Answer : (c) Reason:  by the definition of proper subset
238.	Answer : (b) Reason:  by the definition of strong induction
239.	Answer : (b) Reason:  by the definition of antisymmetric
240.	Answer : (d) Reason:  as the function is defined on z to z so the codomain is z (integers) and  the only integers which are mapped by the function are -1, 1 so the range is  {-1,1 }.