Assignment-2
Course: Discrete Mathematics (Math-206)
Marks: 5
Id. Number:______________________
Date of Submission: 18-11-2020 (Wednesday)
Name:_________________________________
Q1.Find the solution of the recurrence relation𝒂𝒏 = 𝟓𝒂𝒏
Q2.Solve the recurrence relation 𝒂𝒏 = 𝟏𝟎𝒂𝒏
𝟏
𝟏
− 𝟔𝒂𝒏 𝟐 where𝒂𝟎 = 𝟒and𝒂𝟏 = 𝟏.
− 𝟐𝟓𝒂𝒏 𝟐 where𝒂𝟎 = 𝟐 and 𝒂𝟏 = 𝟏𝟎.
Q3.(a).Find the sequence {𝒂𝒏 } having the generating function,𝑮(𝒙) =
𝟐𝒙
(𝟏 𝒙)𝟐
𝒌
+
𝟏
𝟏 𝟑𝒙
.
(b). Find the generating function for the sequence 𝟕𝒌(𝒌 + 𝟏) + 𝟐 .
Q4. If repetition is not permitted.
(a). How many three digit numbers can be formed from the digit 2, 3, 5, 6 and 9 ?
(b). How many three digit numbers are less than 400 can be formed from the digit 2, 3, 5, 6 and 9 ?
(c). Find the number of distinct permutations that can be formed from all the letters of the word
“PROPOSITION”.
Q5. (a). Find the value of 𝐶(6, 3).
(b). Show that, 𝐶(2𝑛, 2) = 2. 𝐶(𝑛, 2) + 𝑛 .
(c). Find the expansion of (𝑥 + 𝑦) .
(d). Find the coefficient of 𝑥 𝑦 in the expansion of (𝑥 + 𝑦) .