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Welcome to the Counting Theory MCQs Page

Dive deep into the fascinating world of Counting Theory with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Counting Theory, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Counting Theory, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

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Check out the MCQs below to embark on an enriching journey through Counting Theory. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Counting Theory. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Counting Theory MCQs | Page 11 of 12

Explore more Topics under Discrete Mathematics

Q101.
Calculate the value of ⁸C₅.

a.

79

b.

43

c.

120

d.

56

Discuss
Answer: (d).56
Q102.
In how many ways can you select 9 cupcakes from a box containing 17 cupcakes?

a.

42769

b.

45398

c.

24310

d.

36214

Discuss
Answer: (c).24310
Q103.
How many 4-digit numbers can be formed by using 2, 4, 6, 8, 10, 12 without repetition of digits?

a.

15

b.

42

c.

70

d.

127

Discuss
Answer: (a).15
Q104.
What is the coefficient of x⁹ in the expansion of (x+5)¹⁴?

a.

5! * ¹⁴C₆

b.

¹⁴C₅

c.

54 * ¹⁴C₅

d.

34 * ¹¹C₅

Discuss
Answer: (c).54 * ¹⁴C₅
Q105.
Determine the independent term of x⁷ in the expansion of (3x² + 4)¹².

a.

220 * 4⁶

b.

230

c.

548* 3!

d.

220 * 3⁶ * 4⁶

Discuss
Answer: (d).220 * 3⁶ * 4⁶
Q106.
In a game, a fair coin is tossed 6 times. Each time the coin comes up tails, A will pay Rs. 15 but if each time heads come up, A will pay nothing. Determine the probability that A will win Rs. 45 by playing the game?

a.

5/16

b.

4/31

c.

3/7

d.

12/65

Discuss
Answer: (a).5/16
Q107.
Find the coefficient of x⁸ in the expansion of (x+2)¹¹.

a.

640

b.

326

c.

1320

d.

456

Discuss
Answer: (c).1320
Q108.
Determine the coefficient of the x⁵y⁷ term in the polynomial expansion of (m+n)¹².

a.

792

b.

439

c.

382

d.

630

Discuss
Answer: (a).792
Q109.
The independent term of x is 80000 in the expansion of (3x+b/x)⁶, where b is a positive constant. What the value of b?

a.

3.97

b.

6.87

c.

8.3

d.

5.2

Discuss
Answer: (d).5.2
Q110.
Consider the recurrence relation a₁=4, aₙ=5n+aₙ₋₁. The value of a₆₄ is _________

a.

10399

b.

23760

c.

75100

d.

53700

Discuss
Answer: (a).10399
Page 11 of 12

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