Recent questions tagged binomial-theorem

The sum of the coefficients of integral powers of $x$ in the expansion of $(1+\sqrt x)^{40}$ is

asked Oct 22, 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

$\sum ^{n}_{r=0} r^2.\:^nC_r$ = ?

asked Oct 22, 2013 by rvidyagovindarajan_1

1 answer

$\sum^{n} _ {r=0} r. \: ^nCr$ = ?

asked Oct 22, 2013 by rvidyagovindarajan_1

1 answer

$\sum^{n} _ {r=0} r. ^nCr$=?

asked Oct 22, 2013 by rvidyagovindarajan_1

0 answers

The number of dissimilar terms in the expansion of $(x_1+x_2+.....x_n)^3$ is ?

asked Oct 22, 2013 by rvidyagovindarajan_1

1 answer

If $x\in R,$ then the value of $S=1-^nC_1.\large\frac{1+x}{1+nx}$$+^nC_2.\large\frac{1+2x}{(1+nx)^2}$$-^nC_3.\large\frac{1+3x}{(1+nx)^3}$$+..............(n+1) $terms = ?

asked Oct 21, 2013 by rvidyagovindarajan_1

1 answer

The coefficient if $x^{10}$ in the expansion $(1+x^2-x^3)^8$ is ?

asked Oct 21, 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 sum of rational terms in the expansion of $(2^{\large\frac{1}{5}}$$+\sqrt 3)^{20}$ is

asked Oct 19, 2013 by rvidyagovindarajan_1

1 answer

The sum of last $30$ coefficients in the expansion of $(1+x)^{59}$ when expanded in ascending power of $x$ is ?

asked Oct 19, 2013 by rvidyagovindarajan_1

1 answer

The interval in which $x$ must lie so that the greatest term in the expansion of $(1+x)^{2n}$, ($x>0$) has greatest coefficient is

asked Oct 16, 2013 by rvidyagovindarajan_1

1 answer

$(1+x)^n-nx-1$ is divisible by ?

asked Oct 16, 2013 by rvidyagovindarajan_1

1 answer

The remainder when $2^{2003}$ is divided by $17$ is ?

asked Oct 16, 2013 by rvidyagovindarajan_1

1 answer

Sum of $(n+1)$ terms of the series $\large\frac{^nC_0}{2}$ - $\frac{^nC_1}{3}$ + $\frac{^nC_2}{4}$ - ...... = ?

asked Oct 16, 2013 by rvidyagovindarajan_1

1 answer

If $n\in N$, then the value of $\displaystyle\sum_{r=0} ^{n} (-1)^r \large\frac{^nC_r}{^{r+2}C_r}$ is

asked Oct 15, 2013 by rvidyagovindarajan_1

1 answer

The expression $P(x)$ = $\big(\sqrt {x^5-1}+x\big)^7$ - $\big(\sqrt {x^5-1}-x\big)^7$ is a polynomial of what degree?

asked Oct 15, 2013 by rvidyagovindarajan_1

1 answer

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

asked Oct 14, 2013 by rvidyagovindarajan_1

1 answer

The coefficient of $x^5$ in the expansion of $(1+x)^{21}$ + $(1+x)^{22}$ + ...... + $(1+x)^{30}$ is

asked Oct 14, 2013 by rvidyagovindarajan_1

1 answer

If $P_n$ denotes the product of binomial coeff. in the expansion of $(1+x)^n$, then $\large\frac{P_{n+1}}{P_n}$=?

asked Oct 14, 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

$^nC_0^2$ + $^nC_1^2$ + $^nC_2^2$ + ...... + $^nC_n^2$ = ?

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 value of $^nC_0-^nC_1$ + $^nC_2-......$ + $(-1)^n$ $^n C_n$ = ?

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

In the expansion of $(1+x)^m.(1-x)^n, $ the coefficients of $x$ and $x^2$ are $3$ and $-6$ respectively, then $m=?$

asked Oct 12, 2013 by rvidyagovindarajan_1

1 answer

The number of integral terms in the expansion of $(5^{\large\frac{1}{2}}$$+7^{\large\frac{1}{8}}$$)^{1024}$ is ?

asked Oct 5, 2013 by rvidyagovindarajan_1

1 answer

If $t_n=\bigg(1+\large\frac{1}{n}\bigg)$$^n$ for $n\in N$, then $t_n$ lies in the interval?

asked Oct 1, 2013 by rvidyagovindarajan_1

1 answer

$8^n-7n-1$ is divisible by ? where $n\in N$

asked Oct 1, 2013 by rvidyagovindarajan_1

1 answer

If the coefficients of $2^{nd},3^{rd}\:and\:4^{th}$ terms in the expansion of $(1+x)^{2n} $ are in A.P., then $n=?$

asked Sep 26, 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

$^nC_0$ - $\large\frac{^nC_1}{2}$ + $\frac{^nC_2}{3}$ - ...... = ?

asked Sep 26, 2013 by rvidyagovindarajan_1

1 answer

$^nC_1$ + $2.^nC_2$ + $3.^nC_3$ + ..... + $n.^nC_n$ = ?

asked Sep 24, 2013 by rvidyagovindarajan_1

1 answer

The sum of coefficients of odd powers of $x$ in the expansion $(1+x)^{50}$ is ?

asked Sep 24, 2013 by rvidyagovindarajan_1

1 answer

If the sum of odd numbered terms and even numbered terms in the expansion of $(x+a)^n$ are $A,B$, then $(x^2-a^2)^n=?$

asked Sep 24, 2013 by rvidyagovindarajan_1

1 answer

The no. of terms in the expansion $(x+y+z)^{10}$ is ?

asked Sep 24, 2013 by rvidyagovindarajan_1

1 answer

If the coefficient of $(2r+4)^{th}$ and $(r-2)^{th}$ terms in the expansion of $(1+x)^{18} $ are equal, then $r=?$

asked Sep 24, 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

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