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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 1 of 12

Explore more Topics under Discrete Mathematics

Q1.
The last digit of the number ((\(\sqrt{51}\) + 1)51 – \(\sqrt{51}\) – 1)51 is _______

a.

32

b.

8

c.

51

d.

1

Discuss
Answer: (b).8
Q2.
How many even 4 digit whole numbers are there?

a.

1358

b.

7250

c.

4500

d.

3600

Discuss
Answer: (c).4500
Q3.
In a multiple-choice question paper of 15 questions, the answers can be A, B, C or D. The number of different ways of answering the question paper are ________

a.

65536 x 4⁷

b.

194536 x 4⁵

c.

23650 x 4⁹

d.

11287435

Discuss
Answer: (a).65536 x 4⁷
Q4.
How many words with seven letters are there that start with a vowel and end with an A? Note that they don’t have to be real words and letters can be repeated.

a.

45087902

b.

64387659

c.

12765800

d.

59406880

Discuss
Answer: (d).59406880
Q5.
Neela has twelve different skirts, ten different tops, eight different pairs of shoes, three different necklaces and five different bracelets. In how many ways can Neela dress up?

a.

50057

b.

14400

c.

34870

d.

56732

Discuss
Answer: (b).14400
Q6.
How many five-digit numbers can be made from the digits 1 to 7 if repetition is allowed?

a.

16807

b.

54629

c.

23467

d.

32354

Discuss
Answer: (a).16807
Q7.
For her English literature course, Ruchika has to choose one novel to study from a list of ten, one poem from a list of fifteen and one short story from a list of seven. How many different choices does Rachel have?

a.

34900

b.

26500

c.

12000

d.

10500

Discuss
Answer: (d).10500
Q8.
There are two different Geography books, five different Natural Sciences books, three different History books and four different Mathematics books on a shelf. In how many different ways can they be arranged if all the books of the same subjects stand together?

a.

353450

b.

638364

c.

829440

d.

768700

Discuss
Answer: (c).829440
Q9.
The code for a safe is of the form PPPQQQQ where P is any number from 0 to 9 and Q represents the letters of the alphabet. How many codes are possible for each of the following cases? Note that the digits and letters of the alphabet can be repeated.

a.

874261140

b.

537856330

c.

549872700

d.

456976000

Discuss
Answer: (d).456976000
Q10.
Amit must choose a seven-digit PIN number and each digit can be chosen from 0 to 9. How many different possible PIN numbers can Amit choose?

a.

10000000

b.

9900000

c.

67285000

d.

39654900

Discuss
Answer: (a).10000000
Page 1 of 12

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