Recent questions tagged general-and-middle-terms

In the expansion of $(1 + a)^{m+n}$, prove that coefficients of $a^m$ and $a^n$ are equal.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the middle terms in the expansions of $\; \large ( \frac{x}{3}$$+9y \large)$$^{10}$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the middle terms in the expansions of $\;\large ($$ 3 $$- \large\frac{x^3}{6})^7$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the $13th$ term in the expansion of $\large ($$9x$$-\large \frac{1}{3\sqrt x})^{\normalsize 18}$$, x\neq 0$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the $4th$ term in the expansion of $(x - 2y)^{12}$.

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Write the general term in the expansion of $ (x^2 - yx)^{12},\; x\neq 0$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Write the general term in the expansion of $ (x^2 - y)^6$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the coefficient of $a^5b^7$ in $ (a-2b)^{12}$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

Find the coefficient of $x^5$ in $(x+3)^8$

asked Apr 10, 2014 by balaji.thirumalai

1 answer

The ratio of the coefficient of $x^{10}$ in $(1-x^2)^{10}$ and the term independent of $x$ in $(x-\large\frac{2}{x}$$)^{10}$ is ?

asked Jan 21, 2014 by rvidyagovindarajan_1

1 answer

The term independent of $x$ in the expansion $\bigg(\large\frac{x+1}{x^{\large\frac{2}{3}}-x^{\large\frac{1}{3}}+1}-\frac{x-1}{x-\sqrt x}\bigg)^{10}$ is ?

asked Dec 1, 2013 by rvidyagovindarajan_1

1 answer

If the sum of $5^{th}\:and\:6^{th}$ terms in the expansion of $(a-b)^n$, $n\geq5$, is 0, then $\large\frac{a}{b}$ = ?

asked Nov 24, 2013 by rvidyagovindarajan_1

1 answer

Coeff. of $x^{50}$ in $(1+x)^{1000}$ + $x(1+x)^{999}$ + $x^2(1+x)^{998}$ + .... + $x^{1000}$ is

asked Nov 23, 2013 by rvidyagovindarajan_1

1 answer

If the $4^{th}$ term in the expansion of $\big(x^2-\large\frac{1}{x^3}\big)^n$ is independent of $x$, then $n=?$

asked Oct 26, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of the term independent of $x$ in the expansion of $\bigg[\large\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-\sqrt x}\bigg]^{\normalsize 10}$ is ?

asked Oct 22, 2013 by rvidyagovindarajan_1

1 answer

If the last term in the expansion of $\bigg(2^{\large\frac{1}{3}}-\frac{1}{\sqrt{ 2}}\bigg)^n $ is $\bigg(\large\frac{1}{3^{\large\frac{5}{3}}}\bigg)^{log_38}$, then the $5^{th} $ term from the beginning is ?

asked Oct 20, 2013 by rvidyagovindarajan_1

1 answer

If the sum of the coefficients of $1^{st},\:2^{nd}$ and $3^{rd}$ terms in the expansion of $(x^2+\large\frac{1}{x})$$^n $ is $46$, then the coefficient of the term independent of $x$ = ?

asked Oct 20, 2013 by rvidyagovindarajan_1

1 answer

The coeff. of $x^n$ in the expansion of $(1+x)(1-x)^n$ is ?

asked Oct 14, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of the term independent of $x$ in the expansion of

$(1+x+2x^3)\bigg(\large\frac{3}{2}$$x^2-\large\frac{1}{3x}$$\bigg)^9$ is

asked Oct 12, 2013 by rvidyagovindarajan_1

1 answer

If the sum of the coefficients in the expansion of $(x+y)^n $ is 4096, then the greatest coefficient in the expansion is ?

asked Oct 12, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of $x^m$ in the expansion 1 + $(1+x)$ + $(1+x)^2$ + ..... + $(1+x)^n$ is

asked Oct 12, 2013 by rvidyagovindarajan_1

1 answer

If $\large\frac{T_2}{T_3}$ in the expansion of $(a+b)^n$ and $\large\frac{T_3}{T_4}$ in the expansion of $(a+b)^{n+3}$ are equal, then $n=?$

asked Sep 26, 2013 by rvidyagovindarajan_1

1 answer

The coefficients of $x^p$, and $x^q$ in the expansion of $(1+x)^{p+q}$ are

asked Sep 26, 2013 by rvidyagovindarajan_1

1 answer

In the binomial expansion of $(1+ax)^n$, the first three terms are $1+12x+64x^2$, then $n=?$

asked Sep 26, 2013 by rvidyagovindarajan_1

1 answer

If the third term in the expansion of $\bigg(\large\frac{1}{x}$$+ x^{log_{10}x}\bigg)^5$ is 1000, then $x$ = ?

asked Sep 23, 2013 by rvidyagovindarajan_1

1 answer

If the coefficient of $x^2$ and $x^3$ in the expansion of $(3+ax)^9$ are same, then the value of $a$ is ?

asked Sep 19, 2013 by rvidyagovindarajan_1

1 answer

The $5^{th}$ term from the end in the expansion of $\bigg(\large\frac{x^3}{2}-\frac{2}{x}\bigg)^{12}$ is ?

asked Sep 19, 2013 by rvidyagovindarajan_1

1 answer

The middle term in the expansion $(1+x)^{2n}$ is ?

asked Sep 19, 2013 by rvidyagovindarajan_1

1 answer

The term independent of $x$ in the expansion $(2x-\large\frac{1}{3x})^6$ is ?

asked Sep 17, 2013 by rvidyagovindarajan_1

1 answer

If $x=\large\frac{1}{3}$, the greatest term in the expansion of $(1+4x)^8$ is ?

asked Sep 17, 2013 by rvidyagovindarajan_1

1 answer

If the coefficient of middle terms in $(1+\alpha x)^4$ and $(1-\alpha x)^6$ is same then $\alpha =?$

asked Sep 17, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of $x^7$ in the expansion $(1-x-x^2+x^3)^6$ is ?

asked Sep 17, 2013 by rvidyagovindarajan_1

1 answer

In the binomial expansion of $(a-b)^n,\:n\geq 5$ the sum of $5^{th}$ and $6^{th}$ term is $0$, then $\large\frac{a}{b}$=?

asked Sep 16, 2013 by rvidyagovindarajan_1

1 answer

If the coefficient of $x^7$ in $\big(ax^2+\large\frac{1}{bx}\big)^{11}$ is equal to coefficient of $x^{-7}$ in $\big(ax-\large\frac{1}{bx^2}\big)^{11}$, then $a$ and $b$ satisfy the relation

asked Sep 15, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of $x^n$ in the expansion $(1+x)(1-x)^n$ is

asked Sep 15, 2013 by rvidyagovindarajan_1

1 answer

Ask Questions, Get Answers