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?
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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