BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI
K K BIRLA GOA CAMPUS, GOA
DISCRETE MATHEMATICS
(MATH F 213)
(1st Semester-2017-18)
Last Date for Submission: 11/11/2017 (before 5pm)
INSTRUCTIONS:
• Attempt all questions.
• Describe each step clearly for complete credit.
1. A grain elevator company receives 200 tons of corn per week from farmers once harvest
starts. The elevator operators plan to ship out 30% of the corn on hand each week once
the harvest season begins. If the company has 600 tons of corn on hand at the beginning
of harvest, what recurrence relation describes the amount of corn on hand at the end of
each week throughout the the harvest season?
2. The Thompsons are purchasing a new house costing $2000, 000, with a down payment
of $25000 and a 30-year mortgage. Interest on the unpaid balance of the mortgage is to
be compounded at the monthly rate of 1%, and the monthly payments will be $1800.
Find a recurrence relation to determine that how much will the Thompsons owe after n
months of payments?
3. Ram and Shyam have agrees to bet one dollar on reach flip of a fair coin and to continue
playing until one of the them wins all of other’s money. Use recurrence relation to find
the probability that Ram will win all of Shyam’s money if Ram starts with a dollars and
Shyam starts with b dollars.
4. An embassy communicates with its home country in code words consisting of a string
of n decimal digits. In order to catch errors in transmission, it is agreed that the total
number of 3s and 7s in each word should always be odd. Use recurrence relation to find
the number of code words are possible.
***** BEST OF LUCK *******
1
K K BIRLA GOA CAMPUS, GOA
DISCRETE MATHEMATICS
(MATH F 213)
(1st Semester-2017-18)
Last Date for Submission: 11/11/2017 (before 5pm)
INSTRUCTIONS:
• Attempt all questions.
• Describe each step clearly for complete credit.
1. A grain elevator company receives 200 tons of corn per week from farmers once harvest
starts. The elevator operators plan to ship out 30% of the corn on hand each week once
the harvest season begins. If the company has 600 tons of corn on hand at the beginning
of harvest, what recurrence relation describes the amount of corn on hand at the end of
each week throughout the the harvest season?
2. The Thompsons are purchasing a new house costing $2000, 000, with a down payment
of $25000 and a 30-year mortgage. Interest on the unpaid balance of the mortgage is to
be compounded at the monthly rate of 1%, and the monthly payments will be $1800.
Find a recurrence relation to determine that how much will the Thompsons owe after n
months of payments?
3. Ram and Shyam have agrees to bet one dollar on reach flip of a fair coin and to continue
playing until one of the them wins all of other’s money. Use recurrence relation to find
the probability that Ram will win all of Shyam’s money if Ram starts with a dollars and
Shyam starts with b dollars.
4. An embassy communicates with its home country in code words consisting of a string
of n decimal digits. In order to catch errors in transmission, it is agreed that the total
number of 3s and 7s in each word should always be odd. Use recurrence relation to find
the number of code words are possible.
***** BEST OF LUCK *******
1
