Chapter 1: Sets

NCERT Solutions for CBSE Class 10 Mathematics — 100 solved questions with detailed explanations.

100

Questions

Topics

Solved Questions

Q1. If A = {1,2,3,4} and B = {3,4,5,6}, then A ∩ B is:

{1,2}
{3,4}
{1,2,3,4,5,6}
{5,6}

Difficulty: Easy · Topic: Set Operations

Solution

A ∩ B = elements common to both = {3,4}.

Q2. The number of subsets of a set with n elements is:

n
2n
n²
2ⁿ

Difficulty: Easy · Topic: Subsets

Solution

A set with n elements has 2ⁿ subsets (each element either included or not).

Q3. The number of subsets of a set with 1 elements is:

Difficulty: Easy · Topic: Subsets

Solution

Number of subsets = 2^1 = 2.

Q4. The number of subsets of a set with 2 elements is:

Difficulty: Easy · Topic: Subsets

Solution

Number of subsets = 2^2 = 4.

Q5. The number of subsets of a set with 3 elements is:

Difficulty: Easy · Topic: Subsets

Solution

Number of subsets = 2^3 = 8.

Q6. The number of subsets of a set with 4 elements is:

Difficulty: Easy · Topic: Subsets

Solution

Number of subsets = 2^4 = 16.

Q7. The number of subsets of a set with 5 elements is:

Difficulty: Easy · Topic: Subsets

Solution

Number of subsets = 2^5 = 32.

Q8. The number of subsets of a set with 6 elements is:

Difficulty: Easy · Topic: Subsets

Solution

Number of subsets = 2^6 = 64.

Q9. The number of subsets of a set with 7 elements is:

Difficulty: Easy · Topic: Subsets

Solution

Number of subsets = 2^7 = 128.

Q10. The number of subsets of a set with 8 elements is:

Difficulty: Easy · Topic: Subsets

Solution

Number of subsets = 2^8 = 256.

Q11. Subsets of set with 1 elements:

Difficulty: Easy · Topic: Sets

Solution

2^1=2.

Q12. Subsets of set with 2 elements:

Difficulty: Easy · Topic: Sets

Solution

2^2=4.

Q13. Subsets of set with 3 elements:

Difficulty: Easy · Topic: Sets

Solution

2^3=8.

Q14. Subsets of set with 4 elements:

Difficulty: Easy · Topic: Sets

Solution

2^4=16.

Q15. Subsets of set with 5 elements:

Difficulty: Easy · Topic: Sets

Solution

2^5=32.

Q16. Subsets of set with 6 elements:

Difficulty: Easy · Topic: Sets

Solution

2^6=64.

Q17. Subsets of set with 7 elements:

Difficulty: Easy · Topic: Sets

Solution

2^7=128.

Q18. Subsets of set with 8 elements:

Difficulty: Easy · Topic: Sets

Solution

2^8=256.

Q19. Subsets of set with 9 elements:

Difficulty: Easy · Topic: Sets

Solution

2^9=512.

Q20. Subsets of set with 10 elements:

Difficulty: Easy · Topic: Sets

Solution

2^10=1024.

Q21. Subsets of set with 11 elements:

Difficulty: Easy · Topic: Sets

Solution

2^11=2048.

Q22. Subsets of set with 12 elements:

Difficulty: Easy · Topic: Sets

Solution

2^12=4096.

Q23. Subsets of set with 13 elements:

Difficulty: Easy · Topic: Sets

Solution

2^13=8192.

Q24. Subsets of set with 14 elements:

Difficulty: Easy · Topic: Sets

Solution

2^14=16384.

Q25. If n(A) = 20, n(B) = 30, n(A ∪ B) = 40, then n(A ∩ B) is:

Difficulty: Easy-Medium · Topic: Inclusion-Exclusion

Solution

n(A ∪ B) = n(A) + n(B) - n(A ∩ B). 40 = 20 + 30 - n(A ∩ B). n(A ∩ B) = 10.

Q26. If n(A)=15, n(B)=20, n(A∪B)=30, then n(A∩B) is:

Difficulty: Easy-Medium · Topic: Inclusion-Exclusion

Solution

n(A∩B) = n(A)+n(B)-n(A∪B) = 15+20-30 = 5.

Q27. If n(A)=25, n(B)=35, n(A∪B)=50, then n(A∩B) is:

Difficulty: Easy-Medium · Topic: Inclusion-Exclusion

Solution

n(A∩B) = n(A)+n(B)-n(A∪B) = 25+35-50 = 10.

Q28. If n(A)=10, n(B)=12, n(A∪B)=18, then n(A∩B) is:

Difficulty: Easy-Medium · Topic: Inclusion-Exclusion

Solution

n(A∩B) = n(A)+n(B)-n(A∪B) = 10+12-18 = 4.

Q29. If n(A)=30, n(B)=40, n(A∪B)=55, then n(A∩B) is:

Difficulty: Easy-Medium · Topic: Inclusion-Exclusion

Solution

n(A∩B) = n(A)+n(B)-n(A∪B) = 30+40-55 = 15.

Q30. If n(A)=20, n(B)=25, n(A∪B)=35, then n(A∩B) is:

Difficulty: Easy-Medium · Topic: Inclusion-Exclusion