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

• 1/(1-x² )

• 1/(1-x² )

• 7/(1-x² )

• 7/(1-x² )

Correct Answer :7/(1-x² )

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

• 70

• 126

• 56

• 84

Correct Answer : 70

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

• 5, 10, 15, 20,...

• 1, 1, 5, 10, 15, 20,...

• 0, 5, 0, 10, 0, 15, 0, 20,...

• 0, 0, 5, 10, 15, 20,...

Correct Answer : 0, 0, 5, 10, 15, 20,...

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

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

• (1+x+x² +x³ +x⁴ +....)

• Derivative of the function (x+2x² +3x³ +4x⁴ +....)

• (1+x+4x² +8x³ +16x⁴ +....)

Correct Answer :Derivative of the function (1+x+x² +x³ +x⁴ +....)

5. 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?

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

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

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

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

Correct Answer :The coefficient of x²⁰⁰ in (x⁷ + x⁸ + x⁹ +x¹⁰ +x¹¹ + x¹²)⁷

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

• 3

• 6

• 8

• 4

Correct Answer : 6

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?

• 495

• 165

• 330

• 32

Correct Answer : 165

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

• 1/(1-x )

• 1/(1-11x )

• 1/(1-21x )

• 1/(1-2x )

Correct Answer : 1/(1-11x )

9. State whether true/false:

(1+x)⁶ is the generating function for the sequence:

• True

• False

Correct Answer :True

10. The sequence generated by the function x+1/(1-x)²

• 1,−1,1,−1,1,−1,...

• 1, 2, 4, 8, 16,…

• 1² , 2² , 3² , 4² , 5²

• (-1)² , (-2)² , (-3)² , (-4)² , (-5)²

Correct Answer :1² , 2² , 3² , 4² , 5²

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