# Discrete Mathematics | Week 9

## Quiz

1. What is the closed-form expression of the generating function for the sequence: 7,0,7,0,7,0……?

c. 7/ (1-x2)

Explanation

2. What is the coefficient of 𝑥4 in (1−x)-5?

a. 70

Explanation

3. What is the sequence in the generating series for the expression 5x2+10x3+15x4+20x5+⋯?

d. 0, 0, 5, 10, 15, 20,…

Explanation

4. What is the generating function of the sequence 0, 1, 2, 3, 4, ……….?

a. Derivative of the function (1+x+x2+x3+x4+⋯)

Explanation

5. In how many ways can 200 players be distributed among 10 teams, so that each team gets at least 7 players and not more than 12?

d. The coefficient of 𝑥200 in (x7+x8+x9+x10+x11+x12)10

Explanation

6. How many 5 lettered words can be formed from the following words, given that you have to pick one letter per line?

b. 6

Explanation

7. A bag contains several blue, green, purple and yellow candies, in how many ways can Amit eat 8 candies from these blue, green, purple and yellow-colored candies?

b. 165

Explanation

8. Find the closed form expression of the generating function for the sequence: 1, 11, 121, 1331, 14641……?

b. 1/(1−11x)

Explanation

9. State whether true/false:
(1+𝑥)6 is the generating function for the sequence:
(6/0), (6/1), (6/2), …, (6/5), (6/6),0,0,
0,

a. True

Explanation

10. The sequence generated by the function (x+1)/(1−x)3 .

c. 12, 22, 32, 42, 52 ,…

Explanation 0 