Class 11 Mathematics

1. The value of 0! is equal to:

• A. 1
• B. 0
• C. Infinity
• D. Not defined

2. Compute the value of 7! / 5! :

• A. 42
• B. 35
• C. 49
• D. 21

3. If 1/8! + 1/9! = x/10!, then x is equal to:

• A. 100
• B. 90
• C. 81
• D. 10

4. The value of ⁿPᵣ is given by the formula:

• A. n! / (n - r)!
• B. n! / [r! (n - r)!]
• C. (n - r)! / n!
• D. n! / r!

5. The value of ⁿCᵣ is given by the formula:

• A. n! / [r! (n - r)!]
• B. n! / (n - r)!
• C. n! / r!
• D. r! / (n - r)!

6. The relation between ⁿPᵣ and ⁿCᵣ is:

• A. ⁿPᵣ = r! × ⁿCᵣ
• B. ⁿCᵣ = r! × ⁿPᵣ
• C. ⁿPᵣ = ⁿCᵣ / r!
• D. ⁿPᵣ = n! × ⁿCᵣ

7. If ⁿC₈ = ⁿC₂, then the value of n is:

• A. 10
• B. 6
• C. 16
• D. 8

8. If ⁿC₈ = ⁿC₂, then the value of ⁿC₂ is:

• A. 45
• B. 90
• C. 10
• D. 20

9. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4, 5 if repetition of digits is allowed?

• A. 125
• B. 60
• C. 24
• D. 120

10. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4, 5 if repetition of digits is not allowed?

• A. 60
• B. 125
• C. 120
• D. 20

11. How many 4-digit code numbers can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

• A. 5040
• B. 10000
• C. 210
• D. 720

12. Find the number of permutations of the letters of the word 'ALLAHABAD':

• A. 7560
• B. 9!
• C. 362880
• D. 15120

13. In how many ways can a committee of 3 persons be chosen from a group of 2 men and 3 women?

• A. 10
• B. 12
• C. 15
• D. 20

14. The value of ⁿC₀ + ⁿC₁ + ⁿC₂ + ... + ⁿCₙ is equal to:

• A. 2ⁿ
• B. 2ⁿ - 1
• C. n²
• D. 2n

15. The value of ⁿCₙ is always:

• A. 1
• B. n
• C. 0
• D. n!

16. The value of ⁿC₁ is always:

• A. n
• B. 1
• C. 0
• D. n!

17. Pascal's identity states that ⁿCᵣ + ⁿCᵣ₋₁ is equal to:

• A. ⁿ⁺¹Cᵣ
• B. ⁿ⁺¹Cᵣ₊₁
• C. ⁿCᵣ₊₁
• D. ⁿ⁺²Cᵣ

18. The number of diagonals in a polygon of 'n' sides is:

• A. n(n - 3) / 2
• B. n(n - 1) / 2
• C. n(n - 2) / 2
• D. n(n + 1) / 2

19. How many diagonals are there in a hexagon (6 sides)?

• A. 9
• B. 12
• C. 15
• D. 6

20. The number of ways to arrange n distinct objects in a circle is:

• A. (n - 1)!
• B. n!
• C. (n + 1)!
• D. n! / 2

21. In how many ways can 5 people sit around a circular table?

• A. 24
• B. 120
• C. 60
• D. 12

22. What is the value of ⁿP₀?

• A. 1
• B. 0
• C. n
• D. n!

23. What is the value of ⁿPₙ?

• A. n!
• B. 1
• C. n
• D. 0

24. If ⁿP₅ = 42 × ⁿP₃ (n > 4), then n is:

• A. 10
• B. 12
• C. 9
• D. 8

25. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

• A. 25200
• B. 210
• C. 2400
• D. 5040

26. How many chords can be drawn through 21 points on a circle?

• A. 210
• B. 420
• C. 105
• D. 21

27. How many 3-digit even numbers can be made using digits 1, 2, 3, 4, 6, 7 if no digit is repeated?

• A. 60
• B. 120
• C. 30
• D. 90

28. The number of ways in which 5 boys and 3 girls can be seated in a row so that no two girls are together is:

• A. 14400
• B. 7200
• C. 2880
• D. 1200

29. The total number of sub-sets of a set containing 5 elements is:

• A. 32
• B. 25
• C. 16
• D. 64

30. Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour:

• A. 2000
• B. 1000
• C. 500
• D. 2500