10th Maths Unit 1 Important 5 Mark Questions

Lay a flawless foundation for your board exam preparation with this curated list of 10th Maths Unit 1 Important 5 Mark Questions. Centered entirely on Relations and Functions, this chapter offers some of the most reliable and high-scoring long-answer problems in the syllabus. This strategic guide isolates highly repeated textbook examples and exercise problems, with a strong focus on verifying the composition of functions, mapping arrow diagrams, and solving multi-part function equations. Practice these high-yield problems to perfect your step-by-step working, understand the structural blueprint, and secure full marks right from the very first section of your math paper!

UNIT - 1 (RELATIONS AND FUNCTIONS)

IMPORTANT FIVE MARKS

1. Let A = {x ∈ ℕ | 1 < x < 4}, B = {x ∈ W | 0 ≤ x < 2}, and C = {x ∈ ℕ | x < 3}. Then verify that,
A × (B ∪ C) = (A × B) ∪ (A × C)

2. Let A = {x ∈ ℕ | 1 < x < 4}, B = {x ∈ W | 0 ≤ x < 2}, and C = {x ∈ ℕ | x < 3}. Then verify that,
A × (B ∩ C) = (A × B) ∩ (A × C)

3. Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime numbers. Verify that (A ∩ B) × C = (A × C) ∩ (B × C).

4. Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime numbers. Verify that A × (B - C) = (A × B) - (A × C).

5. Let A = {1, 2, 3, 7} and B = {3, 0, -1, 7} which of the following are relations from A to B?
(i) R₁ = {(2, 1), (7, 1)}
(ii) R₂ = {(-1, 1)}
(iii) R₃ = {(2, -1), (7, 7), (1, 3)}
(iv) R₄ = {(7, -1), (0, 3), (3, 3), (0, 7)}

6. Represent each of the given relations by (a) an arrow diagram, (b) a graph and (c) a set in roster form, wherever possible.
(i) {(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}}
(ii) {(x, y) | y = x + 3, x, y are natural numbers < 10}

7. Let A = {1, 2, 3, 4} and B = {2, 5, 8, 11, 14} be two sets. Let f: A → B be a function given by f(x) = 3x - 1. Represent this function:
(i) by arrow diagram
(ii) as a set of ordered pairs
(iii) in a table form
(iv) in a graphical form.

8. Let f be a function f: ℕ → ℕ be defined by f(x) = 3x + 2, x ∈ ℕ
(i) find the images of 1, 2, 3
(ii) identify the type of function
(iii) find the pre-images of 29, 53

9. If the function f: ℝ → ℝ is defined by

f(x) =
  • 2x + 7, x < -2
  • x² - 2, -2 ≤ x < 3
  • 3x - 2, x ≥ 3

find: (i) f(4) (ii) f(-2) (iii) f(4) + 2f(1) (iv) ^{[f(1) - 3f(4)]}/_f(-3)

10. Let f: A → B be a function given by f(x) = ^x/₂ - 1 where A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}. Represent f by (i) set of ordered pairs (ii) a table (iii) an arrow diagram (iv) a graph.

11. A function f is defined by f(x) = 2x - 3
(i) find ^{[f(0) + f(1)]}/₂
(ii) find x such that f(x) = 0
(iii) find x such that f(x) = x
(iv) find x such that f(x) = f(1 - x)

12. If the function f is defined by

f(x) =
  • x + 2, x > 1
  • 2, -1 ≤ x ≤ 1
  • x - 1, -3 < x < -1

find (i) f(3) (ii) f(0) (iii) f(-1.5) (iv) f(2) + f(-2)

13. A function f: [-5, 9] → ℝ is defined as follows:

f(x) =
  • 6x + 1, -5 ≤ x < 2
  • 5x² - 1, 2 ≤ x < 6
  • 3x - 4, 6 ≤ x ≤ 9

find: (i) f(-3) + f(2) (ii) f(7) - f(1) (iii) 2f(4) + f(8) (iv) ^{[2f(-2) - f(6)]}/_{[f(4) + f(-2)]}

14. The function 't' which maps temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F = ⁹/₅C + 32. Find:
(i) t(0)
(ii) t(28)
(iii) t(-10)
(iv) the value of C when t(C) = 212
(v) the temperature when the Celsius value is equal to the Fahrenheit value.