Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If n is odd, then C 0 2 – C 1 2 + C 2 2 – C 3 2 +……….(–1) n C n 2 equals –
A
0
B
1
C
∞
D
Text Solution
Verified by ExpertsThe correct answer is:
A
(1 + x) n = C 0 + C 1 x + C 2 x 2 +…….C n x n ––––(i)
(x–1) n = C 0 x n – C 1 x n–1 + C 2 x n–2 ……..(–1) n n C n –(ii)
Multiplying (i) & (ii) and equating the coeff of x n , we get,
C 0 2 – C 1 2 + C 2 2 …………(–1) n C n 2 = n C n/2 (–1) n/2 (x 2 ) n/2
Above is possible only when 
is an integer i.e. n is even and in case n is odd, then term x n will not occur
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