In the expansion of a2-a - -a-a n the binomial coefficient of 3rd term is 36- The 7th term is -

The correct option is A 84a^3√(a) It is given that : ^nC_2=36 n(n 1)/2!=36 n(n 1)=72 n(n 1)=9(8) Hence n=9 Hence T_7= ^9C_6(a) ...

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Standard XII

Mathematics

Binomial Coefficients

In the expans...

Question

In the expansion of ${(a^{2} \sqrt{a} + \frac{\sqrt[3]{a}}{a})}^{n}$ the binomial coefficient of 3rd term is 36. The 7th term is :

84 a^{3} \sqrt{a}

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84 a^{2} \sqrt{a}

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84 a^{2}

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84 a^{3}

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Solution

The correct option is A $84 a^{3} \sqrt{a}$
It is given that :
$^{n} C_{2} = 36$
$\frac{n (n - 1)}{2!} = 36$
$n (n - 1) = 72$
$n (n - 1) = 9 (8)$
Hence $n = 9$
Hence
$T_{7} =^{9} C_{6} (a)^{\frac{15}{2}} a^{- 4}$
$=^{9} C_{3} a^{\frac{7}{2}}$
$= \frac{9.8.7}{3!} . (a^{3} \sqrt{a})$
$= 84 (a^{3} \sqrt{a})$

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In the expansion of (a2√a+3√aa)n the binomial coefficient of 3rd term is 36. The 7th term is :

The correct option is A 84a3√aIt is given that :nC2=36n(n−1)2!=36n(n−1)=72n(n−1)=9(8)Hence n=9HenceT7=9C6(a)152a−4=9C3a72=9.8.73!.(a3√a)=84(a3√a)

In the expansion of ${(a^{2} \sqrt{a} + \frac{\sqrt[3]{a}}{a})}^{n}$ the binomial coefficient of 3rd term is 36. The 7th term is :