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Recent questions tagged binomial-theorem

The number of terms in the expansion of $(a+b+c)^{10}$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

$49^n+16n-1$ is divisible by

asked Jun 26, 2014 by sreemathi.v

1 answer

The $10^{th}$ term in the expansion of $(x-1)^{11}$ (in decreasing power of $x$) is

asked Jun 26, 2014 by sreemathi.v

1 answer

If the sum of the coefficients in the expansion of $(x+y)^n$ is $1024$,then the value of the greatest coefficient in the expansion is

asked Jun 26, 2014 by sreemathi.v

1 answer

If the coefficients of $x^2$ and $x^3$ in the expansion of $(3+kx)^9$ are equal then the value of $k$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

If the expansion of $(x^2+\large\frac{2}{x})^n$ for positive integer n has $13^{th}$ term independent of $x$ then n is

asked Jun 26, 2014 by sreemathi.v

1 answer

If the $r^{th}$ term in the expansion of $(\large\frac{x}{3}-\frac{2}{x^2})^{10}$ contains $x^4$ then $r$ is equal to

asked Jun 26, 2014 by sreemathi.v

1 answer

If the sum of coefficients in the expansion of $(a+b)^n$ is $4096$ then the greatest coefficient in the expansion is

asked Jun 26, 2014 by sreemathi.v

1 answer

The coefficient of $x^5$ in the expansion of $(x+3)^6$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

Coefficient of $x^6$ in the expansion $(x+\large\frac{1}{x^2})^6$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

The least (positive) remainder when $17^{30}$ is divided by $5$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

The coefficient of $x^{32}$ in the expansion of $(x^4-\large\frac{1}{x^3})^{15}$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

The coefficient of $r^{th}$ and $(r+1)^{th}$ terms in the expansion of $(1+x)^{20}$ are in the ratio 1 : 2 then $r=$

asked Jun 26, 2014 by sreemathi.v

1 answer

The coefficient of $x^{17}$ in the expansion of $(x-1)(x-2)\times (x-3)$.......$(x-18)$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

Let $S_p$ and $S_q$ be the coefficient of $x6p$ and $x^q$ respectively in $(1+x)^{p+q}$ then

asked Jun 26, 2014 by sreemathi.v

1 answer

If $n$ is even,then the greatest coefficient in the expansion of $(x+a)^n$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

The digit at units place in the number $17^{1995}+11^{1995}-7^{1995}$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

If the second ,third and fourth term in the expansion of $(x+a)^n$ and $240,720$ and $1080$ respectively,then the value of $n$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

The coefficient of $x^2$ in the expansion of $(1+4x+x^2)^{\Large\frac{1}{2}}$ is

asked Jun 26, 2014 by sreemathi.v

1 answer

If there is a term containing $x^{2r}$ in $(x+\large\frac{1}{x^2})^{n-3}$ then

asked Jun 25, 2014 by sreemathi.v

1 answer

If the coefficient of $x^7$ in the expansion of $(a^2x+b^{-1}x^{-1})^{11}$ is equal to the coefficient of $x^{-7}$ in $(ax-b^{-1}x^{-2})^{11}$ then $ab=$

asked Jun 25, 2014 by sreemathi.v

1 answer

If the $6^{th}$ term in the expansion of $\big(\large\frac{1}{x^{8/3}}+$$x^2\log _{10} x\big)^{8}$ is 5600 then the value of $x$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

The sum of the coefficients of the polynomial $(1+x-3x^2)^{2143}$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

If the third term in the binomial expansion if $(1+x)^m$ is $-\large\frac{1}{8}$$x^2$ then the rational value of m is

asked Jun 25, 2014 by sreemathi.v

1 answer

The coefficient of the third term in the expansion of $(x^2-\large\frac{1}{4})^n$,when expanded in descending powers of $x$ is $31$.Then n is equal to

asked Jun 25, 2014 by sreemathi.v

1 answer

If A and B are coefficients of $x^r$ and $x^{n-r}$ respectively in the expansion of $(1+x)^n$ then

asked Jun 25, 2014 by sreemathi.v

1 answer

The co-efficient of $x$ in the expansion of $(x^2+\large\frac{\lambda}{x})^2$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

The power of x occuring in the $7^{th}$ term in the expansion of $\big(\large\frac{4x}{5}-\frac{8}{5x}\big)^9$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

The value of $13C_2+13C_3+13C_4+....13C_{13}$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

$(\sqrt 3+1)^4+(\sqrt 3-1)^4$ is equal to

asked Jun 25, 2014 by sreemathi.v

1 answer

The coefficient if $x^n$ in the expansion of $(1+x+x^2+...)^{-n}$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

The coefficient of $x^7$ in the expansion of $(\large\frac{x^2}{2}-\frac{2}{x})^9$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

The middle term in the expansion of $\big(x+\large\frac{1}{x}\big)^{10}$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

True or False :Number of terms in the expansion of $(a+b)^n$ where $n\in N$ is one less than the power $n$.

asked Jun 25, 2014 by sreemathi.v

1 answer

True or False :If the expression of $(x-\large\frac{1}{x^2})^{2n}$ contains a term independent of $x$,then $n$ is a multiple of $2$

asked Jun 25, 2014 by sreemathi.v

1 answer

The last two digits of the numbers $3^{400}$ are $01$

asked Jun 25, 2014 by sreemathi.v

1 answer

True or False : The sum of coefficients of the two middle terms in the expansion of $(1+x)^{2n-1}$ is equal to $2n-1C_n$.

asked Jun 25, 2014 by sreemathi.v

1 answer

True or False :The number of terms in the expansion of $[(2x+y^3)^4]^7$ is $8$

asked Jun 25, 2014 by sreemathi.v

1 answer

True or False :The expression $7^9+9^7$ is divisible by $64$.

asked Jun 25, 2014 by sreemathi.v

1 answer

True or False:The sum of series $\sum \limits_{r=0}^{10} 20C_r$ is $2^{19}+\large\frac{20C_{10}}{2}$

asked Jun 25, 2014 by sreemathi.v

1 answer

If $25^{15}$ is divided by 13 the remainder is ___________

asked Jun 25, 2014 by sreemathi.v

1 answer

The position of the term independent of $x$ in the expansion of $\big(\sqrt{\large\frac{x}{3}}+\large\frac{3}{2x^2}\big)^{10}$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

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

asked Jun 25, 2014 by sreemathi.v

1 answer

Middle term in the expansion of $(a^3+ba)^{28}$ is ______

asked Jun 25, 2014 by sreemathi.v

1 answer

The coefficient of $a^{-6}b^4$ in the expansion of $\big(\large\frac{1}{a}-\frac{2b}{3}\big)^{10}$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

If the seventh terms from the beginning and the end in the expansion of $\big(\sqrt[3]{2} +\large\frac{1}{\sqrt[3]{3}} \big)^n$ are equal then n equals _____

asked Jun 25, 2014 by sreemathi.v

1 answer

In the expansion of $(x^2-\large\frac{1}{x^2})^{16}$ the value of the constant term is ________

asked Jun 25, 2014 by sreemathi.v

1 answer

The number of terms in the expansion of $(x+y+z)^n$ ________

asked Jun 25, 2014 by sreemathi.v

1 answer

The largest coefficient in the expansion of $(1+x)^{30}$ is __________

asked Jun 25, 2014 by sreemathi.v

1 answer

If the middle term of $(\large\frac{1}{x}$$+x\sin x)^{10}$ is equal to $7\large\frac{7}{8}$ then value of $x$ is

asked Jun 25, 2014 by sreemathi.v

1 answer

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