CGP Edu

Maths Binomial Theorem & Mathematical Induction Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

10 C 1 (x – 1) 2 – 10 C 2 (x – 2) 2 + 10 C 3 (x – 3) 2 + ……. – 10 C 10 (x – 10) 10 is equal to

(x 2 – 5) (x – 1)

x 2 – 1

x 2 + 1

x 2

Text Solution

Verified by Experts

The correct answer is:

S = 10 C 1 (x – 1) 2 – 10 C 2 (x – 2) 2 + 10 C 3 (x – 3) 2

+ ……… 10 C 10 (x – 10) 10

S = 10 C r (x – r) 2

= 10 C r (x 2 – 2x r + r 2 )

= 10 C r (x 2 ) – 2x 10 C r r

+ 10 C r r 2

= x 2 10 C r – 2x (0)

= x 2 ( 10 C 1 – 10 C 2 + 10 C 3 – 10 C 4 + ……….. – 10 C 10 )

= x 2 (1) = x 2

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