Binomial Theorem : Tutorial Problems II: IITJEE Mains practice « Mathematics Hothouse

Binomial Theorem : Tutorial Problems II: IITJEE Mains practice

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

$(1+x)^{-\frac{1}{2}}$
$(1-x)^{-2}$
$(1+3x)^{\frac{1}{3}}$
$(1+x)^{-\frac{2}{3}}$
$latex(1+x^{2))^{-3}$
$(1-2x)^{-\frac{3}{2}}$
$(a+bx)^{-1}$
$(2-x)^{-2}$
$\sqrt[3]{a^{2}-x^{2}}$
$\frac{1}{\sqrt{1+2x}}$
$\frac{1}{\sqrt[3]{(1-3x)^{2}}}$
$\frac{1}{\sqrt[n]{(a^{n}-nx)}}$

Find the greatest term in each of the following expressions:

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

Find to five places of decimals the value of:

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

Regards,

Nalin Pithwa.

This entry was written by Nalin Pithwa, posted on April 27, 2020 at 9:17 am, filed under IITJEE Foundation Math IITJEE Main and Advanced Math and RMO/INMO of (TIFR and Homibhabha). Bookmark the permalink. Follow any comments here with the RSS feed for this post. Post a comment or leave a trackback: Trackback URL.

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