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Chapter 2: Relations & Functions

NCERT Solutions for CBSE Class 10 Mathematics — 22 solved questions with detailed explanations.

22

Questions

0

Topics

Solved Questions

Q1. A function f: A → B is one-one (injective) if:

f(a₁) = f(a₂) implies a₁ = a₂
Every element of B has a preimage
f is a polynomial
f(a) = a for all a

Difficulty: Easy · Topic: Types of Functions

Solution

Injective: distinct inputs give distinct outputs. f(a₁) = f(a₂) ⇒ a₁ = a₂.

Q2. The domain of f(x) = √(x-2) is:

x > 2
x ≥ 2
x < 2
All real numbers

Difficulty: Easy · Topic: Domain

Solution

For √(x-2) to be defined, x-2 ≥ 0, so x ≥ 2. Domain = [2, ∞).

Q3. The range of f(x) = |x - 3| is:

[0, ∞)
(-∞, ∞)
[3, ∞)
(0, ∞)

Difficulty: Easy-Medium · Topic: Range

Solution

Absolute value is always ≥ 0. Minimum value is 0 (at x=3). Range = [0, ∞).

Q4. A function that is both one-one and onto is called

bijective
injective
neither
surjective

Difficulty: Easy-Medium · Topic: Relations & Functions

Solution

bijective.

Q5. If f(x)=x², the function is

neither
both
odd
even

Difficulty: Easy-Medium · Topic: Relations & Functions

Solution

even.

Q6. The composition f∘g means

f(x)×g(x)
f(x)+g(x)
f(g(x))
g(f(x))

Difficulty: Easy-Medium · Topic: Relations & Functions

Solution

f(g(x)).

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

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 2^2 = 4.

Q8. Number of functions from set of 2 elements to set of 3 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 3^2 = 9.

Q9. Number of functions from set of 2 elements to set of 4 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 4^2 = 16.

Q10. Number of functions from set of 2 elements to set of 5 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 5^2 = 25.

Q11. Number of functions from set of 3 elements to set of 2 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 2^3 = 8.

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

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 3^3 = 27.

Q13. Number of functions from set of 3 elements to set of 4 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 4^3 = 64.

Q14. Number of functions from set of 3 elements to set of 5 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 5^3 = 125.

Q15. Number of functions from set of 4 elements to set of 2 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 2^4 = 16.

Q16. Number of functions from set of 4 elements to set of 3 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 3^4 = 81.

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

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 4^4 = 256.

Q18. Number of functions from set of 4 elements to set of 5 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 5^4 = 625.

Q19. Number of functions from set of 5 elements to set of 2 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 2^5 = 32.

Q20. Number of functions from set of 5 elements to set of 3 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 3^5 = 243.

Q21. Number of functions from set of 5 elements to set of 4 elements:

Difficulty: Easy-Medium · Topic: Functions

Solution

n^m = 4^5 = 1024.

Q22. 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 1: Sets Ch 3: Trigonometric Functions Ch 4: Principle of Mathematical Induction Ch 5: Complex Numbers Ch 6: Linear Inequalities Ch 7: Permutations & Combinations Ch 8: Binomial Theorem Ch 9: Sequences & Series Ch 10: Straight Lines Ch 11: Conic Sections Ch 12: Intro to 3D Geometry Ch 13: Limits & Derivatives Ch 14: Mathematical Reasoning Ch 15: Statistics Ch 16: Probability

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