Single Choice

The total number of irrational terms in the binomial expansion of $$(7^\frac 15 - 3^\frac1{10})^{60}$$ is :

A$$55$$
B$$49$$
C$$48$$
D$$54$$
Correct Answer

Solution

Given $$(7^\frac 15 - 3^\frac1{10})^{60}$$ has $$61$$ terms

General term $$T_{r+1} = ^{60}C_r \ 7^{\tfrac{60-r}{5}} \ 3^{\tfrac{r}{10}}$$

$$\therefore$$ for rational term, $$r = 0, 10, 20, 30, 40, 50, 60 $$\Rightarrow $$ no of rational terms $$= 7$$

$$\therefore$$ number of irrational terms$$=61-7= 54$$

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Prove that $$ ( 2 +\sqrt {x})^4 +(2 - \sqrt {x} )^4 = 2 (16 +24x +x^2 ) $$.

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