Binomial Theorem : Tutorial Problems II: IITJEE Mains practice

I. Find the $(r+1)6{th}$ term in each of the following expansions:

1. $(1+x)^{-\frac{1}{2}}$
2. $(1-x)^{-2}$
3. $(1+3x)^{\frac{1}{3}}$
4. $(1+x)^{-\frac{2}{3}}$
5. $latex(1+x^{2))^{-3}$
6. $(1-2x)^{-\frac{3}{2}}$
7. $(a+bx)^{-1}$
8. $(2-x)^{-2}$
9. $\sqrt[3]{a^{2}-x^{2}}$
10. $\frac{1}{\sqrt{1+2x}}$
11. $\frac{1}{\sqrt[3]{(1-3x)^{2}}}$
12. $\frac{1}{\sqrt[n]{(a^{n}-nx)}}$

Find the greatest term in each of the following expressions:

1. $(1+x)^{-r}$ when $x=\frac{4}{15}$
2. $(1+x)^{\frac{11}{2}}$ when $x=\frac{2}{3}$
3. $(1-7x)^{-\frac{11}{4}}$ when $x=\frac{1}{8}$
4. $(2x+5y)^{12}$​ when $x=8, y=3$
5. $(b-4x)^{-7}$ when $x=\frac{1}{2}$
6. $(3x^{2}=4y^{3})^{-n}$ when $x=9, y=2, n=15$

Find to five places of decimals the value of:

1. $\sqrt{98}$
2. $\sqrt[3]{998}$
3. $\sqrt[3]{1003}$
4. $\sqrt[4]{2400}$
5. $\frac{1}{\sqrt[3]{128}}$
6. $(\frac{601}{50})^{\frac{1}{3}}$
7. $(630)^{-\frac{2}{3}}$
8. $(3128)^{\frac{1}{4}}$

Regards,

Nalin Pithwa.

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