BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI
K K BIRLA GOA CAMPUS, GOA
Discrete Mathematics
(MATH F 213)
(1st Semester-2013-14) Test-II(Open Book)
Date:28-10-2013 (12Noon–1PM) Max. Marks:40
INSTRUCTIONS:
• Attempt all questions and marks are displayed against each question.
• Describe each steps clearly for complete credit.
• Make a page-index.
1. Use GIEP to find the number of permutations of 1, 2, . . . , n that are not derange-
ments. [7]
2. Let gn be denote the maximum number of non overlapping regions formed inside
a circle by joining n distinct points on it. Find the recurrence relation for gn and
solved it. [10]
3. Amar and Nitu have agreed to to bet one dollar on each flip of a fair coin and
to continue playing until one of them wins all of other’s money. Write a recur-
rence relation to analyze the game. Also find the probability that Amar will win
all of Nitu’s money if Amar starts with a dollars and Nitu starts with b dollars. [7]
4. Solve the recurrence relation nan + (n − 1)an−1 = 2n , where a0 = 1. [6]
5.
***** BEST OF LUCK *******
1
K K BIRLA GOA CAMPUS, GOA
Discrete Mathematics
(MATH F 213)
(1st Semester-2013-14) Test-II(Open Book)
Date:28-10-2013 (12Noon–1PM) Max. Marks:40
INSTRUCTIONS:
• Attempt all questions and marks are displayed against each question.
• Describe each steps clearly for complete credit.
• Make a page-index.
1. Use GIEP to find the number of permutations of 1, 2, . . . , n that are not derange-
ments. [7]
2. Let gn be denote the maximum number of non overlapping regions formed inside
a circle by joining n distinct points on it. Find the recurrence relation for gn and
solved it. [10]
3. Amar and Nitu have agreed to to bet one dollar on each flip of a fair coin and
to continue playing until one of them wins all of other’s money. Write a recur-
rence relation to analyze the game. Also find the probability that Amar will win
all of Nitu’s money if Amar starts with a dollars and Nitu starts with b dollars. [7]
4. Solve the recurrence relation nan + (n − 1)an−1 = 2n , where a0 = 1. [6]
5.
***** BEST OF LUCK *******
1
