## Binomial Theorem Tutorial problems I: IITJEE mains practice

I. Expand up to 5 terms the following expressions:

1. $(1+x)^{\frac{1}{2}}$
2. $(1+x)^{\frac{7}{2}}$
3. $(1-x)^{\frac{2}{5}}$
4. $(1+x^{2})^{-2}$
5. $(1-3x)^{\frac{1}{3}}$
6. $(1-3x)^{\frac{-1}{2}}$
7. $(1+2x)^{-\frac{1}{2}}$
8. $(1+\frac{x}{3})^{-2}$
9. $(1+\frac{2x}{3})^{\frac{3}{2}}$
10. $(1+\frac{1}{2}a)^{-4}$
11. $(2+x)^{-2}$
12. $(9+2x)^{\frac{1}{2}}$
13. $(8+12a)^{\frac{3}{2}}$
14. $(9-6x)^{-\frac{3}{2}}$
15. $(4a-8x)^{-\frac{1}{2}}$

II. Write down and simplify:

1. The 8th term of $(1+2x)^{-\frac{1}{2}}$
2. The 11th term of $(1-2x^{3})^{\frac{11}{2}}$
3. The 16th term of $(1+3a^{2})^{\frac{16}{3}}$
4. The 6th term of $(3a-2b)^{-1}$
5. The $(r+1)^{th}$ term of $(1-x)^{-2}$
6. The $(r+1)^{th}$ term of $(1-x)^{-4}$
7. The $(r+1)^{th}$ term of $(1+x)^{\frac{1}{2}}$
8. The $(r+1)^{th}$ term of $(1+x)^{\frac{11}{3}}$
9. The 14th term of $(2^{10}-2^{7}x)^{\frac{13}{2}}$
10. The 7th term of $(3^{8}+6^{4}x)^{\frac{11}{4}}$

Regards,

Nalin Pithwa

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