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.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: