If in the expansion of a -2 b n- the sum of 5th and 6th terms is 0 - then the value of a - b is equal toA- 5-n-4-5B- j-2n-4C- n-4-5D- 2 n -4-5

The correct option is D 2(n 4)5Given: T_6+T_5=0 ⇒T_6T_5= 1 ⇒T_6T_5= ^nC_5 a^n 5·( 2b)^5 ^nC_4 a^n 4·( 2b)^4 ∴ nbsp;T_6T_5= (n 4)· b · ( 2)5· a= 1 ⇒ab=2(n 4)5 ...

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Byju's Answer

Standard XII

Mathematics

General Term of Binomial Expansion

If in the exp...

Question

If in the expansion of $(a - 2 b)^{n}$ , the sum of $5^{th}$ and $6^{th}$ terms is $0$ , then the value of $\frac{a}{b}$ is equal to

\frac{n - 4}{5}

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\frac{2 (n - 4)}{5}

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\frac{5}{n - 4}

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\frac{5}{2 (n - 4)}

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Solution

The correct option is B $\frac{2 (n - 4)}{5}$
Given: $T_{6} + T_{5} = 0 \Rightarrow \frac{T_{6}}{T_{5}} = - 1$
$\Rightarrow \frac{T_{6}}{T_{5}} = \frac{^{n} C_{5} a^{n - 5} \cdot (- 2 b)^{5}}{^{n} C_{4} a^{n - 4} \cdot (- 2 b)^{4}}$
$∴ \frac{T_{6}}{T_{5}} = \frac{(n - 4) \cdot b \cdot (- 2)}{5 \cdot a} = - 1$
$\Rightarrow \frac{a}{b} = \frac{2 (n - 4)}{5}$

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General Term of Binomial Expansion

Standard XII Mathematics

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If in the expansion of (a−2b)n, the sum of 5th and 6th terms is 0, then the value of ab is equal to

The correct option is B 2(n−4)5Given: T6+T5=0⇒T6T5=−1 ⇒T6T5= nC5 an−5⋅(−2b)5 nC4 an−4⋅(−2b)4 ∴T6T5=(n−4)⋅b⋅(−2)5⋅a=−1 ⇒ab=2(n−4)5

If in the expansion of $(a - 2 b)^{n}$ , the sum of $5^{th}$ and $6^{th}$ terms is $0$ , then the value of $\frac{a}{b}$ is equal to