JEE Main - Fundamental principle of counting Online Test (MCQ Quiz)

1. What is the fundamental principle of counting also known as?

A) The Pigeonhole Principle B) The Principle of Mathematical Induction C) The Multiplication Principle D) The Addition Principle

2. If an event can occur in 'm' different ways and another independent event can occur in 'n' different ways, in how many ways can both events occur in succession?

A) m + n B) m - n C) m * n D) m / n

3. A restaurant offers 4 appetizers and 6 main courses. How many different meal combinations are possible if a meal consists of one appetizer and one main course?

A) 10 B) 24 C) 20 D) 12

4. In how many ways can a student choose a subject from Physics, Chemistry, and Biology if there are 3, 4, and 5 different courses available in each subject respectively?

A) 12 B) 15 C) 9 D) 7

5. Consider the task of forming a two-digit number using the digits 1, 2, 3, 4, and 5 without repetition. How many such numbers can be formed?

A) 10 B) 25 C) 20 D) 15

6. A person has 3 shirts and 2 pairs of trousers. How many different outfits can be created by wearing one shirt and one pair of trousers?

A) 5 B) 6 C) 3 D) 2

7. How many ways are there to select one fruit from a basket containing 5 apples and 4 oranges?

A) 9 B) 20 C) 5 D) 4

8. If there are 5 routes from city A to city B and 3 routes from city B to city C, how many distinct routes are there from city A to city C via city B?

A) 8 B) 15 C) 2 D) 5

9. A code word is to be formed by selecting one consonant and one vowel from the English alphabet. If there are 21 consonants and 5 vowels, how many such code words can be formed?

A) 26 B) 105 C) 16 D) 21

10. How many three-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if repetition of digits is allowed?

A) 60 B) 125 C) 15 D) 75

11. Suppose there are 6 roads connecting town X to town Y, and 7 roads connecting town Y to town Z. How many ways can one travel from X to Z through Y?

A) 13 B) 42 C) 1 D) 6

12. A painter has 5 different colors of paint. How many ways can she choose 2 different colors to mix?

A) 10 B) 25 C) 5 D) 2

13. How many possible outcomes are there when flipping a coin and rolling a standard six-sided die simultaneously?

A) 8 B) 6 C) 12 D) 2

14. An office has 10 employees. In how many ways can a president and a vice-president be selected if one person cannot hold both positions?

A) 100 B) 90 C) 20 D) 10

15. A committee of 2 members is to be formed from a group of 4 men and 3 women. How many different committees can be formed if the committee must consist of one man and one woman?

A) 7 B) 12 C) 10 D) 6

16. How many ways can the letters of the word 'CAT' be arranged?

A) 3 B) 6 C) 9 D) 1

17. A person wants to buy a car. There are 3 models available, and each model comes in 4 different colors. How many different choices does the person have?

A) 7 B) 12 C) 3 D) 4

18. How many possible outcomes are there when drawing one card from a standard deck of 52 playing cards?

A) 4 B) 13 C) 52 D) 26

19. A survey asks individuals to choose one option from 'Yes', 'No', or 'Maybe'. How many possible responses are there for each individual?

A) 1 B) 2 C) 3 D) 0

20. Consider the task of painting a house with 3 rooms. If there are 5 different colors available for each room, and each room must be painted a different color, how many ways can the house be painted?

A) 125 B) 60 C) 15 D) 10

21. How many ways can a person choose a main course from a menu with 8 options and a dessert from a menu with 5 options?

A) 13 B) 40 C) 8 D) 5

22. A lock has a 3-digit combination using digits 0-9. How many possible combinations are there if repetition of digits is not allowed?

A) 1000 B) 720 C) 270 D) 90

23. In how many ways can a student answer a multiple-choice question with 4 options, where only one option is correct?

A) 1 B) 4 C) 3 D) 0

24. A factory produces 3 types of products. Each product can be either defective or non-defective. How many possible outcomes are there for a batch of 3 products?

A) 6 B) 9 C) 27 D) 8

25. How many ways can a president, vice-president, and treasurer be selected from a club of 10 members, assuming no member can hold more than one position?

A) 1000 B) 720 C) 30 D) 120

26. A bakery offers 7 types of cookies. How many ways can a customer choose 2 different types of cookies?

A) 14 B) 49 C) 42 D) 21

27. Consider a scenario where you need to choose an outfit from 5 shirts and 3 pants. How many different outfits can you create?

A) 8 B) 15 C) 5 D) 3

28. How many ways are there to arrange the letters of the word 'GO'?

A) 1 B) 2 C) 3 D) 4

29. A person has 4 pairs of shoes and 6 pairs of socks. How many different combinations of shoes and socks can be worn?

A) 10 B) 24 C) 4 D) 6

30. How many possible outcomes are there when rolling two distinct six-sided dice?

A) 12 B) 36 C) 6 D) 1

31. A company has 8 employees. In how many ways can a team of 3 employees be selected for a project?

A) 24 B) 56 C) 336 D) 8

32. How many different signals can be made by using flags of different colors, choosing at least one flag at a time, if 5 different flags are available?

A) 5 B) 15 C) 31 D) 32

33. Consider a menu with 5 appetizers, 10 main courses, and 7 desserts. How many different meals consisting of one appetizer, one main course, and one dessert can be ordered?

A) 22 B) 350 C) 50 D) 70

34. How many ways can a person choose a password of length 4 using digits 0-9 if repetition is allowed?

A) 10000 B) 256 C) 10 D) 40

35. A library has 10 fiction books and 8 non-fiction books. How many ways can a reader choose one fiction book and one non-fiction book?

A) 18 B) 80 C) 10 D) 8

36. How many ways can you travel from point A to point B if there are 3 different bus routes and 2 different train routes?

A) 5 B) 6 C) 3 D) 2

37. If a number can be formed by choosing a digit from {1, 2, 3} for the tens place and a digit from {4, 5} for the units place, how many such two-digit numbers can be formed?

A) 5 B) 6 C) 3 D) 2

38. How many ways can a person choose a shirt from 5 options and a pair of pants from 4 options?

A) 9 B) 20 C) 5 D) 4

39. A coin is tossed 3 times. How many possible sequences of outcomes are there?

A) 6 B) 8 C) 9 D) 3

40. In how many ways can a committee of 3 people be selected from a group of 7 people?

A) 21 B) 35 C) 7 D) 3

41. How many different paths are there from city A to city B if there are 4 roads connecting them?

A) 1 B) 4 C) 16 D) 8

42. A painter has 6 colors. How many ways can she choose 3 different colors to paint a picture, where the order of colors matters?

A) 20 B) 120 C) 18 D) 6

43. How many ways can a student choose one mathematics book and one physics book from a shelf containing 5 mathematics books and 7 physics books?

A) 12 B) 35 C) 5 D) 7

44. Consider the task of forming a 3-letter word using the letters A, B, C, D, E, where repetition is not allowed. How many such words can be formed?

A) 15 B) 60 C) 125 D) 20

45. A person wants to buy a pen. There are 3 brands, and each brand offers 2 ink colors. How many different pen choices does the person have?

A) 5 B) 6 C) 3 D) 2

46. How many odd numbers can be formed using the digits 1, 2, 3, 4, 5, 6 without repetition, considering only 3-digit numbers?

A) 100 B) 60 C) 80 D) 120

47. If there are 5 choices for a shirt, 4 choices for pants, and 3 choices for shoes, how many different outfits can be created?

A) 12 B) 60 C) 20 D) 15

48. How many ways can a student select one course from a list of 10 elective courses?

A) 1 B) 10 C) 0 D) 100

49. A restaurant offers 4 types of sandwiches and 3 types of drinks. How many different lunch combinations are possible if a lunch consists of one sandwich and one drink?

A) 7 B) 12 C) 4 D) 3

50. How many distinct permutations are there of the letters in the word 'BOOK'?

A) 24 B) 12 C) 6 D) 4

Fundamental principle of counting - Online Test

Test Results