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Binomial Theorem

Integral terms in binomial expansion

nta_pyq_2025_apr

Grade 12

Question:

The number of integral terms in the expansion of (5 1 1 1016$2 + 78$) is

$127$

$130$

$129$

$128$

Step-by-Step Solution

Key Concept: Use the general term of the binomial expansion for integral terms$i_n$binomial expansion and impose the required coefficient or exponent condition.

$Tr = 1016$Cr (5) 2 78 (4) $\Rightarrow$$r = 0$, 8, 16, 24,$\ldots$. , 1016$1016 = 0 + (n - 1)8$1016 $\Rightarrow$$n - 1$= = 127 8 So,$n = 128.$

Correct Answer: 4