Recent questions tagged binomial-theorem

If $A$ and $B$ are coefficient of $x^n$ in the expansion of $(1+x)^{2n}$ and $(1+x)^{2n-1}$ respectively then $A/B$ equals

asked Jun 25, 2014 by sreemathi.v

1 answer

If the coefficient of $2^{nd},3^{rd}$ and $4^{th}$ terms in the expansion of $(1+x)^n$ are in $A.P$ then the value of $n$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

The coefficient of $x^n$ in the expansion of $(1+x)^{2n}$ and $(1+x)^{2n-1}$ are in the ratio

asked Jun 25, 2014 by sreemathi.v

1 answer

The two successive terms in the expansion of $(1+x)^{24}$ whose coefficients are in the ratio $ 1 : 4$ are

asked Jun 24, 2014 by sreemathi.v

1 answer

Given the integers $r > 1,n > 2$ and coefficients of $(3r)^{th}$ and $(r+2)^{nd}$ terms in the binomial expansion of $(1+x)^{2n}$ are equal then

asked Jun 24, 2014 by sreemathi.v

1 answer

The total number of terms in the expansion of $(x+a)^{100}+(x-a)^{100}$ after simplification is

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the term independent of $x$ in the expansion of $(1+x+2x^3)(\large\frac{3}{2}$$x^2-\large\frac{1}{3x})^9$

asked Jun 24, 2014 by sreemathi.v

1 answer

If $x^p$ occurs in the expansion of $(x^2+\large\frac{1}{x})^{2n}$.Prove that its coefficient is $\large\frac{2n!}{\Large\frac{4n-p}{3}!\frac{2n+p}{3}!}$

asked Jun 24, 2014 by sreemathi.v

1 answer

In the expansion of $(x+a)^n$ if the sum of odd terms is denoted by O and the sum of even term by E.Then prove that (ii) $4OE=(x+a)^{2n}-(x-a)^{2n}$

asked Jun 24, 2014 by sreemathi.v

1 answer

In the expansion of $(x+a)^n$ if the sum of odd terms is denoted by O and the sum of even term by E.Then prove that (i) $O^2-E^2=(x^2-a^2)^n$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find $n$ in the binomial $\big[\sqrt[3]{2} +\large\frac{1}{\sqrt[3]{3}} \big]^n$ if the ratio of $7^{th}$ term from the beginning to the $7^{th}$ term from the end is $\large\frac{1}{6}$

asked Jun 24, 2014 by sreemathi.v

1 answer

Show that the middle term in the expansion of $(x-\large\frac{1}{x})^{2n}$ is $\large\frac{1\times 3\times 5\times..... (2n-1)}{n!}$$\times (-2)^n$

asked Jun 24, 2014 by sreemathi.v

1 answer

If $p$ is a real number and if the middle term in the expansion of $(\large\frac{p}{2}$$+2)^8$ is 1120.Find $p$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the coefficient of $x^4$ in the expansion of $(1+x+x^2+x^3)^{11}$

asked Jun 24, 2014 by sreemathi.v

1 answer

If the coefficient of second,third and fourth terms in the expansion of $(1+x)^{2n}$ are in A.P.Show that $2n^2-9n+7=0$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the value of r if the coefficient of $(2r+4)^{th}$ and $(r-2)^{th}$ terms in the expansion of $(1+x)^{18}$ are equal.

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the sixth term of the expansion $(y^{\Large\frac{1}{2}}+x^{\Large\frac{1}{3}})^n$.If the binomial coefficient of the third term from the end is 45.

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the coefficient of $\large\frac{1}{x^{17}}$ in the expansion of $(x^4-\large\frac{1}{x^3})^{15}$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the coefficient of $x^{15}$ in the expression of $(x-x^2)^{10}$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the middle term in the expansion of $(3x-\large\frac{x^3}{6})^9$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the middle term in the expansion of $(\large\frac{x}{a}-\frac{a}{x})^{10}$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the term independent of $x$ in the expansion of $(3x-\large\frac{2}{x^2})^{15}$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the coefficient of $x$ in the expansion of $(1-3x+7x^2)(1-x)^{16}$

asked Jun 24, 2014 by sreemathi.v

1 answer

If the term free from $x$ in the expansion of $(\sqrt x-\large\frac{k}{x^2})^{10}$ is $405$,find the value of $k$.

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the term independent of $x,x\neq 0$ in the expansion of $\big(\large\frac{3x^2}{2}-\frac{1}{3x})^{15}$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the expansion of $(3x^2-2ax+3a^2)^3$ using Binomial theorem

asked Jun 24, 2014 by sreemathi.v

1 answer

Expand using Binomial theorem $(1+\large\frac{x}{2}-\frac{2}{x})^4$$\;\;x\neq 0$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find $x$ if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of $(4\sqrt 2+\large\frac{1}{4\sqrt 3})^n$ is $\sqrt 6 :1$

asked Jun 24, 2014 by sreemathi.v

1 answer

Find an approximation of $(0.99)^5$ using the first three terms of its expansion.

asked Jun 24, 2014 by sreemathi.v

1 answer

Find the value of $(a^2+\sqrt{a^2-1})^4+(a^2-\sqrt{a^2-1})^4$

asked Jun 24, 2014 by sreemathi.v

1 answer

Evaluate $(\sqrt 3+2)^6-(\sqrt 3-\sqrt 2)^6$

asked Jun 24, 2014 by sreemathi.v

1 answer

If $a$ and $b$ are distinct integers,prove that $a-b$ is a factor of $a^n-b^n$,whenever $n$ is a positive integer.

asked Jun 23, 2014 by sreemathi.v

1 answer

Find the coefficient of $x^5$ in the expansion of the product $(1+2x)^6(1-x)^7$

asked Jun 23, 2014 by sreemathi.v

1 answer

Find a if the coefficients of $x^2$ and $x^3$ in the expansion of $(3+ax)^9$ are equal.

asked Jun 23, 2014 by sreemathi.v

1 answer

Find $a,b$ and $n$ in the expansion of $(a+b)^n$ if the first three terms of the expansion are $729,7290$ and $30375$ respectively.

asked Jun 23, 2014 by sreemathi.v

1 answer

Find a positive value of m for which the coefficient of $x^2$ in the expansion of $(1+x)^m$ is $6$

asked Jun 23, 2014 by sreemathi.v

1 answer

Prove that the coefficient of $x^n$ in $(1+x)^{2n}$ is twice the coefficient of $x^n$ in $(1+x)^{2n-1}$

asked Jun 23, 2014 by sreemathi.v

1 answer

The coefficients of the $(r-1)^{th},r^{th}$ and $(r+1)^{th}$ terms in the expansion of $(x+1)^n$ are in the ratio of $1 : 3 : 5$. Find both $n$ and $r$.

asked Jun 23, 2014 by sreemathi.v

1 answer

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

asked Jun 23, 2014 by sreemathi.v

1 answer

Find the middle term in the expansion of $\big(\large\frac{3}{3}$$+9y\big)^{10}$

asked Jun 23, 2014 by sreemathi.v

1 answer

Find the middle term in the expansion of $(3-\large\frac{x^3}{6})^7$

asked Jun 23, 2014 by sreemathi.v

1 answer

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

asked Jun 23, 2014 by sreemathi.v

1 answer

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

asked Jun 23, 2014 by sreemathi.v

1 answer

Write the general term in the expansion of $(x^2-yx)^{12}$

asked Jun 23, 2014 by sreemathi.v

1 answer

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

asked Jun 23, 2014 by sreemathi.v

1 answer

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

asked Jun 23, 2014 by sreemathi.v

1 answer

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

asked Jun 23, 2014 by sreemathi.v

1 answer

Prove that $\sum\limits_{r=0}^n 3^{r-n}C_r=4^n$

asked Jun 23, 2014 by sreemathi.v

1 answer

Show that $9^{n+1}-8n-9$ is divisible by 64 whenever n is a positive integer.

asked Jun 23, 2014 by sreemathi.v

1 answer

Find $(x+1)^6+(x-1)^6$ Hence or otherwise evaluate $(\sqrt 2+1)^6+(\sqrt 2-1)^6$

asked Jun 23, 2014 by sreemathi.v

1 answer

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