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Question: If the binomial coefficient of the third term in the expansion of \(\left( 9x - \frac{1}{\sqrt{3x}} ...

If the binomial coefficient of the third term in the expansion of (9x−13x)m\left( 9x - \frac{1}{\sqrt{3x}} \right)^{m}is 105, then the third term in the expansion is –

A

35 · 913 · x12

B

24 · 913 · x12

C

35 · 913 · x9

D

None of these

Answer

35 · 913 · x12

Explanation

Solution

We have, t3 = mC2 (9x)m–2 · (−13x)2\left( - \frac{1}{\sqrt{3x}} \right)^{2}

Also from questions mC2 = 105

\ m(m – 1) = 210 or m2 – m – 210 = 0 ;

or m = 15, – 14 (absurd).

\ t3 = 15C2 · (9x)13 · (−13x)2\left( - \frac{1}{\sqrt{3x}} \right)^{2}

= 15⋅142\frac{15 \cdot 14}{2}· 913 · x13 · 13x\frac{1}{3x} = 35 · 913 · x12.