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Ratio and Proportion

Binomial coef...

Question

Binomial coefficient of $7^{t h}$ term of the expansion $(2 x - 3 y)^{20}$ is/are

A

^{19} C_{6} +^{20} C_{5}

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B

^{20} C_{6}

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C

^{19} C_{6} +^{19} C_{5}

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D

^{19} C_{6}

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Solution

The correct options are
B $^{20} C_{6}$
C $^{19} C_{6} +^{19} C_{5}$
Given : $(2 x - 3 y)^{20}$
$T_{7} = T_{6 + 1} =^{20} C_{6} (2 x)^{14} (- 3 y)^{6}$
$∴$ Binomial coefficient of $7^{t h}$ term $=^{20} C_{6}$
and $^{20} C_{6} =^{19} C_{6} +^{19} C_{5}$
$(∵^{n + 1} C_{r} =^{n} C_{r} +^{n} C_{r - 1})$

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Ratio and Proportion

Standard IX Mathematics

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