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Recent questions and answers in Binomial Theorem
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CBSE XI
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Math
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Binomial Theorem
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.
cbse
math
class11
ch8
binomial-theorem
exemplar
q8
sec-b
medium
answered
Feb 8, 2018
by
rohit0112004
1
answer
The number of terms in the expansion of $(a+b+c)^{10}$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q33
sec-b
medium
answered
Jun 26, 2014
by
sreemathi.v
1
answer
$49^n+16n-1$ is divisible by
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q32
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q31
sec-a
easy
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q30
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q29
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q28
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q27
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q26
sec-b
medium
answered
Jun 26, 2014
by
sreemathi.v
1
answer
The coefficient of $x^5$ in the expansion of $(x+3)^6$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q25
sec-a
easy
answered
Jun 26, 2014
by
sreemathi.v
1
answer
Coefficient of $x^6$ in the expansion $(x+\large\frac{1}{x^2})^6$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q24
sec-b
medium
answered
Jun 26, 2014
by
sreemathi.v
1
answer
The least (positive) remainder when $17^{30}$ is divided by $5$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q23
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q22
sec-a
easy
answered
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 $r=$
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q21
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q20
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q19
sec-a
easy
answered
Jun 26, 2014
by
sreemathi.v
1
answer
If $n$ is even,then the greatest coefficient in the expansion of $(x+a)^n$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q18
sec-a
easy
answered
Jun 26, 2014
by
sreemathi.v
1
answer
The digit at units place in the number $17^{1995}+11^{1995}-7^{1995}$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q17
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q16
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q15
sec-a
easy
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q14
sec-b
medium
answered
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 $ab=$
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q13
sec-c
difficult
answered
Jun 25, 2014
by
sreemathi.v
1
answer
If the $6^{th}$ term in the expansion of $\big(\large\frac{1}{x^{8/3}}+$$x^2\log _{10} x\big)^{8}$ is 5600 then the value of $x$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q12
sec-b
medium
answered
Jun 25, 2014
by
sreemathi.v
1
answer
The sum of the coefficients of the polynomial $(1+x-3x^2)^{2143}$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q11
sec-a
easy
answered
Jun 25, 2014
by
sreemathi.v
1
answer
If the third term in the binomial expansion if $(1+x)^m$ is $-\large\frac{1}{8}$$x^2$ then the rational value of m is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q10
sec-a
easy
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q9
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q8
sec-a
easy
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q7
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q6
sec-b
medium
answered
Jun 25, 2014
by
sreemathi.v
1
answer
The value of $13C_2+13C_3+13C_4+....13C_{13}$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q5
sec-b
medium
answered
Jun 25, 2014
by
sreemathi.v
1
answer
$(\sqrt 3+1)^4+(\sqrt 3-1)^4$ is equal to
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q4
sec-b
medium
answered
Jun 25, 2014
by
sreemathi.v
1
answer
The coefficient if $x^n$ in the expansion of $(1+x+x^2+...)^{-n}$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q3
sec-a
easy
answered
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
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q2
sec-a
easy
answered
Jun 25, 2014
by
sreemathi.v
1
answer
The middle term in the expansion of $\big(x+\large\frac{1}{x}\big)^{10}$ is
cbse
math
class11
ch8
binomial-theorem
additionalproblem
q1
sec-b
medium
answered
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 $n$.
cbse
math
class11
ch8
binomial-theorem
exemplar
q40
sec-a
easy
answered
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 $2$
cbse
math
class11
ch8
binomial-theorem
exemplar
q39
sec-a
easy
answered
Jun 25, 2014
by
sreemathi.v
1
answer
The last two digits of the numbers $3^{400}$ are $01$
cbse
math
class11
ch8
binomial-theorem
exemplar
q38
sec-a
easy
answered
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 $2n-1C_n$.
cbse
math
class11
ch8
binomial-theorem
exemplar
q37
sec-a
easy
answered
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 $8$
cbse
math
class11
ch8
binomial-theorem
exemplar
q36
sec-a
easy
answered
Jun 25, 2014
by
sreemathi.v
1
answer
True or False :The expression $7^9+9^7$ is divisible by $64$.
cbse
math
class11
ch8
binomial-theorem
exemplar
q35
sec-a
easy
answered
Jun 25, 2014
by
sreemathi.v
1
answer
True or False:The sum of series $\sum \limits_{r=0}^{10} 20C_r$ is $2^{19}+\large\frac{20C_{10}}{2}$
cbse
math
class11
ch8
binomial-theorem
exemplar
q34
sec-a
easy
answered
Jun 25, 2014
by
sreemathi.v
1
answer
If $25^{15}$ is divided by 13 the remainder is ___________
cbse
math
class11
ch8
binomial-theorem
exemplar
q33
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
exemplar
q32
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
exemplar
q31
sec-a
easy
answered
Jun 25, 2014
by
sreemathi.v
1
answer
Middle term in the expansion of $(a^3+ba)^{28}$ is ______
cbse
math
class11
ch8
binomial-theorem
exemplar
q30
sec-b
medium
answered
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
cbse
math
class11
ch8
binomial-theorem
exemplar
q29
sec-b
medium
answered
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 _____
cbse
math
class11
ch8
binomial-theorem
exemplar
q28
sec-b
medium
answered
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 ________
cbse
math
class11
ch8
binomial-theorem
exemplar
q27
sec-b
medium
answered
Jun 25, 2014
by
sreemathi.v
1
answer
The number of terms in the expansion of $(x+y+z)^n$ ________
cbse
math
class11
ch8
binomial-theorem
exemplar
q26
sec-b
medium
answered
Jun 25, 2014
by
sreemathi.v
1
answer
The largest coefficient in the expansion of $(1+x)^{30}$ is __________
cbse
math
class11
ch8
binomial-theorem
exemplar
q25
sec-a
easy
answered
Jun 25, 2014
by
sreemathi.v
1
answer
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