Discrete Mathematics Week 9 NPTEL

                     

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−x2)
b. 1/(1+x2)
c. 7/(1−x2)
d. 7/(1+x2)

Answer: c. 7/(1−x2)


Q2. What is the coefficient of x2 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?

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

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