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Class 9 | Maths | Revision-1 Solutions | SEBA.

 


1. Find the value of √2 up to two decimal places using square root.

Answer:
√2 ≈ 1.41

2. Write two irrational numbers whose sum and product are rational.

Answer:
 Let the two irrational numbers be √2 and −√2

  • Sum = √2 − √2 = 0 (rational)
  • Product = √2 × (−√2) = −2 (rational)

3. Write all integers between −5 and 5 with the help of number line.

Answer:
Integers: −4, −3, −2, −1, 0, 1, 2, 3, 4

4. Show that a⁰ = 1 using aᵐ ÷ aⁿ = aᵐ⁻ⁿ (taking m = n).

Answer:
aᵐ ÷ aᵐ = aᵐ⁻ᵐ = a⁰
But aᵐ ÷ aᵐ = 1
∴ a⁰ = 1

5. Show that a⁻ⁿ = 1/aⁿ using aᵐ ÷ aⁿ = aᵐ⁻ⁿ (taking m = 0).

Answer:
a⁰ ÷ aⁿ = a⁰⁻ⁿ = a⁻ⁿ
But a⁰ = 1
∴ 1 ÷ aⁿ = a⁻ⁿ
∴ a⁻ⁿ = 1/aⁿ

6. Find LCM and HCF using prime factorisation

(i) 321, 396

321 = 3 × 107
396 = 2² × 3² × 11
HCF = 3
LCM = 2² × 3² × 11 × 107 = 42372

(ii) 455, 42

455 = 5 × 7 × 13
42 = 2 × 3 × 7
HCF = 7
LCM = 2 × 3 × 5 × 7 × 13 = 2730

(iii) 408, 170

408 = 2³ × 3 × 17
170 = 2 × 5 × 17
HCF = 2 × 17 = 34
LCM = 2³ × 3 × 5 × 17 = 2040

7. Write two rational numbers between 2/11 and 1/6

Answer:
2/11 = 12/66
1/6 = 11/66

Numbers between: 13/66, 14/66

8. Simplify √10 × √5 and find approximate value (√2 = 1.41)

√10 × √5 = √50 = √(25×2) = 5√2
≈ 5 × 1.41 = 7.05

9. Express in p/q form

(i) 0.81 (repeating 1)


= 73/90

(ii) 0.18 (repeating 8)

= 17/90

(iii) 2.47 (repeating 7)

= 223/90

(iv) 2.4431 (repeating 31)

= 242/99

10. Simplify

(i) (√3 − √2)²

= 3 + 2 − 2√6
= 5 − 2√6

(ii) (2√3 + √5)(2√3 − √5)

= (2√3)² − (√5)²
= 12 − 5 = 7

(iii) (8 + √3)(2 + √3)

= 16 + 8√3 + 2√3 + 3
= 19 + 10√3

(iv) 1 / (1 + √2)

Rationalize:
= (1 − √2)/(1 − 2)
= √2 − 1

(v) 4 / (√7 + √3)

= 4(√7 − √3)/(7 − 3)
= √7 − √3

(vi) (7 + √3)/(7 − √3)

= (7 + √3)²/(49 − 3)
= (49 + 14√3 + 3)/46
= (52 + 14√3)/46 = (26 + 7√3)/23


13. Express in decimal

(i) 7/25 = 0.28
(ii) 3/40 = 0.075
(iii) 3/100 = 0.03
(iv) 23/(5²×2³) = 23/200 = 0.115
(v) 14/175 = 2/25 = 0.08

14. Express percentages in fractions

(i) 53% = 53/100
(ii) 50% = 1/2
(iii) ½% = 1/200
(iv) 100% = 1
(v) 0.01% = 1/10000

15. Express in percentages

(i) 1/2 = 50%
(ii) 50 = 5000%
(iii) 1/4 = 25%
(iv) 3/20 = 15%
(v) 42/125 = 33.6%
(vi) 0.25 = 25%
(vii) 1.25 = 125%


16. An object is sold at a profit of 10%. What is the ratio of its cost price to sale price?



17. The cost price of 30 eggs is equal to the sale price of 20 eggs. What is the percentage of profit?



18. The cost price of an object is Rs. 2100. What is the sale price if it is sold with a profit of 10%?



19. Lemons are sold with 20% profit after buying 4 in Re. 1. What is the sale price of 1 lemon?



20. If an object is sold at Rs. 500, there is a loss of 5%. At what price it should be sold to gain a profit of 5%?



21. To attract customers a businessman offers discounts of 10%, 10% and 5%. What is equivalent discount?




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