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Recent questions and answers in Bionomial Theorem and Simple Applications
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JEEMAIN and NEET
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Mathematics
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Class11
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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 ?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
difficult
answered
Apr 11, 2018
by
vijayalakshmi.r
1
answer
The total no. of terms in the expansion $(x+y)^{100}+(x-y)^{100} $ is ?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
easy
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 ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
easy
mock
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=?$
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
medium
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 ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
difficult
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?
jeemain
math
class11
ch8
binomial-theorem
properties-and-application
medium
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}$ = ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
easy
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 ?
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
easy
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
jeemain
math
class11
ch8
binomial-theorem
properties-and-application
difficult
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
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
difficult
answered
Nov 23, 2013
by
rvidyagovindarajan_1
1
answer
$53^{53} - 33^{33}$ is divisible by
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
medium
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
jeemain
math
class11
ch8
binomial-theorem
properties-and-application
medium
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$ = ?
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
medium
answered
Oct 28, 2013
by
rvidyagovindarajan_1
1
answer
$^nC_0.^nC_1$ + $^nC_1.^nC_2$ + $....^nC_{n-1}.^nC_n$ = ?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
easy
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=?$
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
easy
answered
Oct 26, 2013
by
rvidyagovindarajan_1
1
answer
The remainder when $5^{99}$ is divided by $13$ is
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
easy
answered
Oct 26, 2013
by
rvidyagovindarajan_1
1
answer
$\large\frac{^8C_0}{6}$ - $^8C_1$ + $^8C_2.6$ + $....$ + $^8C_8.6^7$ = ?
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
easy
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
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
medium
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?
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
difficult
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
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
medium
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 ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
medium
answered
Oct 22, 2013
by
rvidyagovindarajan_1
1
answer
$\sum ^{n}_{r=0} r^2.\:^nC_r$ = ?
jeemain
math
class11
ch6
binomial-theorem
medium
answered
Oct 22, 2013
by
rvidyagovindarajan_1
1
answer
$\sum^{n} _ {r=0} r. \: ^nCr$ = ?
jeemain
math
class11
ch6
binomial-theorem
easy
answered
Oct 22, 2013
by
rvidyagovindarajan_1
1
answer
$\sum^{n} _ {r=0} r. ^nCr$=?
jeemain
math
class11
ch6
binomial-theorem
easy
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 = ?
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
medium
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 ?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
easy
answered
Oct 22, 2013
by
rvidyagovindarajan_1
1
answer
The coefficient if $x^{10}$ in the expansion $(1+x^2-x^3)^8$ is ?
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
easy
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 ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
difficult
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})$$^n $ is $46$, then the coefficient of the term independent of $x$ = ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
medium
answered
Oct 20, 2013
by
rvidyagovindarajan_1
1
answer
The sum of rational terms in the expansion of $(2^{\large\frac{1}{5}}$$+\sqrt 3)^{20}$ is
jeemain
math
class11
binomial-theorem
ch8
properties-and-applications
medium
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 ?
jeemain
math
class11
binomial-theorem
ch8
positive-integral-index
easy
answered
Oct 19, 2013
by
rvidyagovindarajan_1
1
answer
$(1+x)^n-nx-1$ is divisible by ?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
easy
answered
Oct 16, 2013
by
rvidyagovindarajan_1
1
answer
The remainder when $2^{2003}$ is divided by $17$ is ?
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
easy
answered
Oct 16, 2013
by
rvidyagovindarajan_1
1
answer
Sum of $(n+1)$ terms of the series $\large\frac{^nC_0}{2}$ - $\frac{^nC_1}{3}$ + $\frac{^nC_2}{4}$ - ...... = ?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
difficult
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
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
difficult
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?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
medium
answered
Oct 15, 2013
by
rvidyagovindarajan_1
1
answer
The digit at unit place in the number $17^{1995}+11^{1995}-7^{1995}$ is ?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
medium
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
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
medium
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 $\large\frac{P_{n+1}}{P_n}$=?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
difficult
answered
Oct 14, 2013
by
rvidyagovindarajan_1
1
answer
The coeff. of $x^n$ in the expansion of $(1+x)(1-x)^n$ is ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
easy
answered
Oct 14, 2013
by
rvidyagovindarajan_1
1
answer
$^nC_0^2$ + $^nC_1^2$ + $^nC_2^2$ + ...... + $^nC_n^2$ = ?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
medium
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
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
difficult
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 ?
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
medium
answered
Oct 12, 2013
by
rvidyagovindarajan_1
1
answer
The value of $^nC_0-^nC_1$ + $^nC_2-......$ + $(-1)^n$ $^n C_n$ = ?
jeemain
math
class11
ch8
binomial-theorem
positive-integral-index
easy
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
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
difficult
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 $m=?$
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
medium
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?
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
difficult
answered
Oct 8, 2013
by
rvidyagovindarajan_1
1
answer
$8^n-7n-1$ is divisible by ? where $n\in N$
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
easy
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 $n=?$
jeemain
math
class11
ch8
binomial-theorem
properties-and-applications
medium
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 $n=?$
jeemain
math
class11
ch8
binomial-theorem
general-and-middle-terms
medium
answered
Sep 26, 2013
by
rvidyagovindarajan_1
1
answer
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