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RD Chapter 4 Algebraic Identities Ex MCQS Solutions

Question - 1 : -

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Question - 3 : -

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Question - 8 : -
If a + b + c = 9 and  ab + bc + ca = 23, then a2 + b2 + c2 =
(a) 35
(b) 58
(c) 127
(d) none of these

Answer - 8 : -

a + b + c = 9, ab + bc + ca = 23
Squaring,
(a + b+ c) = (9)2
a2 + b2 + c2 + 2 (ab + bc+ ca) = 81
⇒ a2 +b2 + c2 + 2 x 23 = 81
⇒ a2 + b2+ c2 + 46 = 81
⇒ a2 + b2+ c2 = 81 – 46 = 35  (a)

Question - 9 : - (a – b)3 + (b – c)3 +(c – a)3 =
(a) (a + b + c) (a2 + b2 + c2 –ab – bc – ca)
(d) (a -b)(b- c) (c – a)
(c) 3(a – b) (b – c) (c – a)
(d) none of these

Answer - 9 : -

(a – b)3 + (b- c)3 + (c- a)3
∵ a – b+ b – c + c – a = 0
∴ (a – b)3 +(b – c)3 +(c – a)3
= 3 (a-b)(b- c) (c – a)        (c)

Question - 10 : -

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