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Questions >> JEEMAIN and NEET >> Mathematics >> Class11 >> Bionomial Theorem and Simple Applications

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

answered Apr 11, 2018 by vijayalakshmi.r

1 answer

The total no. of terms in the expansion $(x+y)^{100}+(x-y)^{100}$ is ?

answered Nov 19, 2016 by devanshugarg200ce

2 answers

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 ?

answered Jan 23, 2014 by rvidyagovindarajan_1

1 answer

$\displaystyle\sum_ {i=o} ^{{m} ^{10}} C_i ^{20}C_{m-i}$ is maximum when $m=?$

answered Jan 23, 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 ?

answered Dec 1, 2013 by rvidyagovindarajan_1

1 answer

If in the expansion of $(x+a)^{15},$ the $11^{th}$ term is $G.M.$ of $8^{th}$ & $12^{th}$ terms, then which term is the greatest term?

answered Nov 24, 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 $\large\frac{a}{b}$ = ?

answered Nov 24, 2013 by rvidyagovindarajan_1

1 answer

If the sum of the coefficients of $(1+x)^n=4096$ , then the largest coefficient is ?

answered Nov 24, 2013 by rvidyagovindarajan_1

1 answer

The value of $^nC_0.^{2n}C_r$ - $^nC_1^{2-2}C_r$ + $^nC_2.^{2n-4}C_r$ - ...., if $r \lt n$ is

answered 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

answered Nov 23, 2013 by rvidyagovindarajan_1

1 answer

$53^{53} - 33^{33}$ is divisible by

answered Nov 22, 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

answered Nov 7, 2013 by pady_1

1 answer

A student is allowed to select at the most n books from a collection of $2n+1$ books. The no. of ways in which he can select at least one book is 63, then $n$ = ?

answered Oct 28, 2013 by rvidyagovindarajan_1

1 answer

$^nC_0.^nC_1$ + $^nC_1.^nC_2$ + $....^nC_{n-1}.^nC_n$ = ?

answered Oct 27, 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 $n=?$

answered Oct 26, 2013 by rvidyagovindarajan_1

1 answer

The remainder when $5^{99}$ is divided by $13$ is

answered Oct 26, 2013 by rvidyagovindarajan_1

1 answer

$\large\frac{^8C_0}{6}$ - $^8C_1$ + $^8C_2.6$ + $....$ + $^8C_8.6^7$ = ?

answered Oct 26, 2013 by rvidyagovindarajan_1

1 answer

If $(1+\sqrt 2)^n=x_n+y_n\sqrt 2$ , where $x_n,y_n$ are integers, then

answered Oct 23, 2013 by rvidyagovindarajan_1

1 answer

If the sum of the coefficients in the expansion of $(b+c)^{20}[1+(a-2)x]^{20}$ is square of the sum of the coefficients in the expansion $[2bcx-(b+c)y]^{10}$ where $a,b,c$ are positive constants, then $a,b,c$ satisfies the equation?

answered Oct 23, 2013 by rvidyagovindarajan_1

1 answer

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

answered 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 ?

answered Oct 22, 2013 by rvidyagovindarajan_1

1 answer

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

answered Oct 22, 2013 by rvidyagovindarajan_1

1 answer

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

answered Oct 22, 2013 by rvidyagovindarajan_1

1 answer

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

asked Oct 22, 2013 by rvidyagovindarajan_1

0 answers

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 = ?

answered Oct 22, 2013 by rvidyagovindarajan_1

1 answer

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

answered Oct 22, 2013 by rvidyagovindarajan_1

1 answer

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

answered 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 ?

answered 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 $x$ = ?

answered 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

answered 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 ?

answered Oct 19, 2013 by rvidyagovindarajan_1

1 answer

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

answered Oct 16, 2013 by rvidyagovindarajan_1

1 answer

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

answered Oct 16, 2013 by rvidyagovindarajan_1

1 answer

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

answered 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

answered 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?

answered Oct 15, 2013 by rvidyagovindarajan_1

1 answer

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

answered 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

answered 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 $\large\frac{P_{n+1}}{P_n}$ =?

answered Oct 14, 2013 by rvidyagovindarajan_1

1 answer

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

answered Oct 14, 2013 by rvidyagovindarajan_1

1 answer

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

answered 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

answered Oct 14, 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 ?

answered Oct 12, 2013 by rvidyagovindarajan_1

1 answer

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

answered 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

answered 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 $m=?$

answered Oct 12, 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?

answered Oct 8, 2013 by rvidyagovindarajan_1

1 answer

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

answered 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 $n=?$

answered Oct 1, 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 $n=?$

answered Sep 26, 2013 by rvidyagovindarajan_1

1 answer

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