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Chapter 1: Relations & Functions

NCERT Solutions for CBSE Class 10 Mathematics — 21 solved questions with detailed explanations.

21

Questions

0

Topics

Solved Questions

Q1. A relation R on set A is an equivalence relation if it is:

Reflexive and symmetric
Symmetric and transitive
Reflexive, symmetric, and transitive
Reflexive and transitive

Difficulty: Easy · Topic: Equivalence Relations

Solution

Equivalence relation must be reflexive (aRa), symmetric (aRb ⇒ bRa), and transitive (aRb, bRc ⇒ aRc).

Q2. If f(x) = 2x+3 and g(x) = x², then (g∘f)(2) is:

49
19
7
14

Difficulty: Easy · Topic: Composition

Solution

f(2) = 2(2)+3 = 7. g(f(2)) = g(7) = 7² = 49.

Q3. The number of one-one functions from {1,2,3} to {a,b,c,d} is:

Difficulty: Easy-Medium · Topic: Injective Functions

Solution

⁴P₃ = 4!/(4-3)! = 4×3×2 = 24.

Q4. A relation that is reflexive, symmetric, and transitive is:

empty relation
partial order
function
equivalence relation

Difficulty: Easy-Medium · Topic: Relations & Functions

Solution

equivalence relation.

Q5. The number of bijections from set of n elements to itself is:

n!
n²
2ⁿ
n

Difficulty: Easy-Medium · Topic: Relations & Functions

Solution

n!.

Q6. Number of functions from set of 2 elements to set of 2 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 2^2 = 4.

Q7. Number of functions from set of 2 elements to set of 3 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 3^2 = 9.

Q8. Number of functions from set of 2 elements to set of 4 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 4^2 = 16.

Q9. Number of functions from set of 2 elements to set of 5 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 5^2 = 25.

Q10. Number of functions from set of 3 elements to set of 2 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 2^3 = 8.

Q11. Number of functions from set of 3 elements to set of 3 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 3^3 = 27.

Q12. Number of functions from set of 3 elements to set of 4 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 4^3 = 64.

Q13. Number of functions from set of 3 elements to set of 5 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 5^3 = 125.

Q14. Number of functions from set of 4 elements to set of 2 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 2^4 = 16.

Q15. Number of functions from set of 4 elements to set of 3 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 3^4 = 81.

Q16. Number of functions from set of 4 elements to set of 4 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 4^4 = 256.

Q17. Number of functions from set of 4 elements to set of 5 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 5^4 = 625.

Q18. Number of functions from set of 5 elements to set of 2 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 2^5 = 32.

Q19. Number of functions from set of 5 elements to set of 3 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 3^5 = 243.

Q20. Number of functions from set of 5 elements to set of 4 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 4^5 = 1024.

Q21. Number of functions from set of 5 elements to set of 5 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 5^5 = 3125.

Other Chapters in Mathematics

Ch 2: Inverse Trig Functions Ch 3: Matrices Ch 4: Determinants Ch 5: Continuity & Differentiability Ch 6: Applications of Derivatives Ch 7: Integrals Ch 8: Applications of Integrals Ch 9: Differential Equations Ch 10: Vector Algebra Ch 11: Three Dimensional Geometry Ch 12: Linear Programming Ch 13: Probability

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