Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The value of n C 0 . 2n C r – n C 1 . 2n – 2 C r + n C 2 . 2n – 4 C r +......... + (–1) nn C n 2n – 2n C n is -
A
B
C
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
A
We have
n C 0 . 2n C r – n C 1 . 2n–2 C r + n C 2 . 2n–4 C r + ....+ (–1) n n C n 2n–2n C n
= Coefficient of x r in [ n C 0 (1 + x) 2n – n C 1 (1 + x) 2n–2 + n C 2 (1 + x) 2n–4 – ….…+ (–1) n n C n (1 + x) 2n–2n ]
= Coefficient of x r in [(1 + x) 2 – 1] n
= Coefficient of x r in (2x + x 2 ) n
= Coefficient of x r–n in (2 + x) n
= 
Hence is correct answer.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems