Qstnid -A-3-i-is {1, 2, 4, 16, 64} = {X : X Is A Factor Of 32} ? Give Reason. (Ii) Is {X : X Is A Factor Of 27} ≠ {3, 9, 27, 54}? Give Reason. (Iii) Write The Set Of Even Factors Of 124. (Iv) Write The Set Of Odd Factors Of 72. (V) Write The Set Of Prime Factors Of 3234. (Vi) Is {X : X2 - 7x + 12 = 0} = {3, 4} ? (Vii) Is {X : X2 - 5x - 6 = 0} = {2, 3} ? (Ii) Is {X : X Is A Factor Of 27} ≠ {3, 9, 27, 54}? Give Reason. (Iii) Write The Set Of Even Factors Of 124. (Iv) Write The Set Of Odd Factors Of 72. (V) Write The Set Of Prime Factors Of 3234. (Vi) Is {X : X2 - 7x + 12 = 0} = {3, 4} ? (Vii) Is {X : X2 - 5x - 6 = 0} = {2, 3} ? - 06: Sets Class 8 Maths

Home Learn Fast select Course

Show Unit/Chapter Change Unit Change Subject Last Menu

ICSE-VIII-Mathematics

06: Sets Class 8 Maths

with Solutions - page 2

Qstn# A-3-i Prvs-Qstn Next-Qstn

#3-i
Is {1, 2, 4, 16, 64} = {x : x is a factor of 32} ? Give reason. (ii) Is {x : x is a factor of 27} ≠ {3, 9, 27, 54}? Give reason. (iii) Write the set of even factors of 124. (iv) Write the set of odd factors of 72. (v) Write the set of prime factors of 3234. (vi) Is {x : x² - 7x + 12 = 0} = {3, 4} ? (vii) Is {x : x² - 5x - 6 = 0} = {2, 3} ? (ii) Is {x : x is a factor of 27} ≠ {3, 9, 27, 54}? Give reason. (iii) Write the set of even factors of 124. (iv) Write the set of odd factors of 72. (v) Write the set of prime factors of 3234. (vi) Is {x : x² - 7x + 12 = 0} = {3, 4} ? (vii) Is {x : x² - 5x - 6 = 0} = {2, 3} ?
Ans : No, {1, 2, 4, 16, 64} ≠ {x : x is a factor of 32}
Because 64 is not a factor of 32 (ii) Yes, { x : x is a factor of 27} + {3, 9, 27, 54}
Because 54 is not a factor of 27 (iii) 1 × 124 = 124
2 × 62 = 124
4 × 31 = 124
Factors of 124 = 1, 2, 4, 31, 62, 124
Set of even factors 124 = {2, 4, 62, 124} (iv) 1 × 172 = 72
2 × 36 = 72
3 × 24 = 72
4 × 18 = 72
6 ×12 = 72
8 × 9 = 72
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Set of odd factors of 72 = {1, 3, 9} (v)
3234 = 2 × 3 × 7 × 7 × 11
∴ Set of prime factors of 3234 = {2, 3, 7, 11} (vi) x² - 7x + 12 = 0
⇒ x² - 4x - 3x + 12 = 0
⇒ x(x - 4) - 3(x - 4) = 0
⇒ (x - 4)(x - 3) = 0
∴ Either x - 4 = 0 or x - 3 = 0
⇒ x = 4 ⇒ x = 3
∴ {x : x² - 7x + 12 = 0} = {3, 4} is true (vii) x² - 5x - 6 = 0
⇒ x² - 6x + x - 6 = 0
⇒ x(x - 6) + 1(x - 6) = 0
⇒ (x - 6)(x + 1) = 0
∴ Either x - 6 = 0 or x + 1 = 0
i.e., x = 6 i.e., x = -1
∴ {x : x² - 5x - 6 = 0} ≠ {2, 3}
In other words {x : x² - 5x - 6 = 0} = {2, 3} is not true (ii) Yes, { x : x is a factor of 27} + {3, 9, 27, 54}
Because 54 is not a factor of 27 (iii) 1 × 124 = 124
2 × 62 = 124
4 × 31 = 124
Factors of 124 = 1, 2, 4, 31, 62, 124
Set of even factors 124 = {2, 4, 62, 124} (iv) 1 × 172 = 72
2 × 36 = 72
3 × 24 = 72
4 × 18 = 72
6 ×12 = 72
8 × 9 = 72
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Set of odd factors of 72 = {1, 3, 9} (v)
3234 = 2 × 3 × 7 × 7 × 11
∴ Set of prime factors of 3234 = {2, 3, 7, 11} (vi) x² - 7x + 12 = 0
⇒ x² - 4x - 3x + 12 = 0
⇒ x(x - 4) - 3(x - 4) = 0
⇒ (x - 4)(x - 3) = 0
∴ Either x - 4 = 0 or x - 3 = 0
⇒ x = 4 ⇒ x = 3
∴ {x : x² - 7x + 12 = 0} = {3, 4} is true (vii) x² - 5x - 6 = 0
⇒ x² - 6x + x - 6 = 0
⇒ x(x - 6) + 1(x - 6) = 0
⇒ (x - 6)(x + 1) = 0
∴ Either x - 6 = 0 or x + 1 = 0
i.e., x = 6 i.e., x = -1
∴ {x : x² - 5x - 6 = 0} ≠ {2, 3}
In other words {x : x² - 5x - 6 = 0} = {2, 3} is not true

#3-ii
Is {x : x is a factor of 27} ≠ {3, 9, 27, 54}? Give reason.
Ans : Yes, { x : x is a factor of 27} + {3, 9, 27, 54}
Because 54 is not a factor of 27

#3-iii
Write the set of even factors of 124.
Ans : 1 × 124 = 124
2 × 62 = 124
4 × 31 = 124
Factors of 124 = 1, 2, 4, 31, 62, 124
Set of even factors 124 = {2, 4, 62, 124}

#3-iv
Write the set of odd factors of 72.
Ans : 1 × 172 = 72
2 × 36 = 72
3 × 24 = 72
4 × 18 = 72
6 ×12 = 72
8 × 9 = 72
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Set of odd factors of 72 = {1, 3, 9}

#3-v
Write the set of prime factors of 3234.
Ans :
3234 = 2 × 3 × 7 × 7 × 11
∴ Set of prime factors of 3234 = {2, 3, 7, 11}

#3-vi
Is {x : x² - 7x + 12 = 0} = {3, 4} ?
Ans : x² - 7x + 12 = 0
⇒ x² - 4x - 3x + 12 = 0
⇒ x(x - 4) - 3(x - 4) = 0
⇒ (x - 4)(x - 3) = 0
∴ Either x - 4 = 0 or x - 3 = 0
⇒ x = 4 ⇒ x = 3
∴ {x : x² - 7x + 12 = 0} = {3, 4} is true

#3-vii
Is {x : x² - 5x - 6 = 0} = {2, 3} ?
Ans : x² - 5x - 6 = 0
⇒ x² - 6x + x - 6 = 0
⇒ x(x - 6) + 1(x - 6) = 0
⇒ (x - 6)(x + 1) = 0
∴ Either x - 6 = 0 or x + 1 = 0
i.e., x = 6 i.e., x = -1
∴ {x : x² - 5x - 6 = 0} ≠ {2, 3}
In other words {x : x² - 5x - 6 = 0} = {2, 3} is not true