First slide

Binomial theorem for positive integral Index

Question

If the sum of the coefficients in the expansion of (x - 2y + 3 z)ⁿ is 128, then the greatest coefficient in the expansion of(1 + x)ⁿ is

Moderate

A

35
B

20
C

10
D

None of these

Solution

Sum of the coefficients in the expansion of
$(x - 2 y + 3 z)^{n} is (1 - 2 + 3)^{n} = 2^{n} (put x = y = z = 1) ∴ 2^{n} = 128 \Rightarrow n = 7$
Therefore, the greatest coefficient in the expansion of
$(1 + x)^{7} {is}^{7} C_{3} {or}^{7} C_{4}$ because both are equal to 35.

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