# Discrete Mathematics Week 9 NPTEL

**These are the solution of Discrete Mathematics Week 9 NPTEL Assignment 9 Solution Answers**

**These are the solution of Discrete Mathematics Week 9 NPTEL Assignment 9 Solution Answers**

Course name: Discrete Mathematics

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**Q1. What is the closed-form expression of the generating function for the sequence: 7,0,7,0,7,0……?**

a. 1/(1−x^{2})

b. 1/(1+x^{2})

c. 7/(1−x^{2})

d. 7/(1+x^{2})

**Answer: c. 7/(1−x ^{2})**

**Q2. What is the coefficient of x ^{2} in (1−x)^{-5}?**

a. 70

b. 126

c. 56

d. 84

**Answer: a. 70**

**These are the solution of Discrete Mathematics Week 9 NPTEL Assignment 9 Solution Answers**

**Q3. What is the sequence in the generating series for the expression 5×2+10×3+15×4+20×5+⋯?**

a. 5, 10, 15, 20,…

b. 1, 1, 5, 10, 15, 20,…

c. 0, 5, 0, 10, 0, 15, 0, 20,…

d. 0, 0, 5, 10, 15, 20,…

**Answer: d. 0, 0, 5, 10, 15, 20,…**

**Q4. What is the generating function of the sequence 0, 1, 2, 3, 4, ……….?**

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

b. (1+x+x2+x3+x4+⋯)

c. Derivative of the function (x+2×2+3×3+4×4+⋯)

d. (1+x+4×2+8×3+16×4+⋯)

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

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**Q5. In how many ways can 200 players be distributed among 10 teams, so that each team gets atleast 7 players and not more than 12?**

a. The coefficient of x200 in (x7+x8+x9+x10+x11+x12)12

b. The coefficient of x200 in (x7+x8+x9+x10+x11+x12)7

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

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

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

**These are the solution of Discrete Mathematics Week 9 NPTEL Assignment 9 Solution Answers**

**Q6. How many 5 lettered words can be formed from the following words, given that you have to pick one letter per line?**

a. 3

b. 6

c. 8

d. 4

**Answer: b. 6**

**Q7. 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?**

a. 495

b. 165

c. 330

d. 32

**Answer: b. 165**

**These are the solution of Discrete Mathematics Week 9 NPTEL Assignment 9 Solution Answers**

**Q8. Find the closed form expression of the generating function for the sequence: 1, 11, 121, 1331, 14641……?**

a. 1/1−x

b. 1/1−11x

c. 1/1−21x

d. 1/1−2x

**Answer: b. 1/1−11x**

**Q9. State whether true/false:(1+x)6(1+𝑥)6 is the generating function for the sequence:(60),(61),(62),…,(65)(66),0,0,0,…**

a. True

b. False

**Answer: a. True**

**Q10. The sequence generated by the function x+1/(1−x)3.**

a. 1,−1,1,−1,1,−1,…

b. 1, 2, 4, 8, 16,…

c. 12,22,32,42,52,…

d. (−1)2,(2)2,(−3)2,(4)2,(−5)2,…

**Answer: c. 12,22,32,42,52,…**

**These are the solution of Discrete Mathematics Week 9 NPTEL Assignment 9 Solution Answers**

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