CBSE Questions for Class 11 Engineering Maths Binomial Theorem Quiz 13 - MCQExams.com

Coefficient of $$x^{11}$$ in the extension of $$(1+x^{2})^{4}(1+x^{3})^{7}(1+x^{4})^{12}$$ is 
  • 1051
  • 1106
  • 1113
  • 1120
If the variable takes the values 0,1,2,....., n with frequericies proportional to the binomial coefficients $$C\left( n,0 \right) ,C\left( n,1 \right) ,C\left( n,2 \right) ...,C\left( n,n \right) $$ respectively, then the variance of the distribution is :-
  • n
  • $$\frac { \sqrt { n } }{ 2 } $$
  • $$\frac { n }{ 2 } $$
  • $$\frac { n }{ 4 } $$
In the expansion of $$(\dfrac{1+x}{1-x})^2$$ , the coefficient of $$x^n$$ will be 
  • $$4n$$
  • $$4n - 3$$
  • $$4n - 1$$
  • none of these
Coefficient of $${ t }^{ 12 }$$ in $$({ 1+t }^{ 2 }{ ) }^{ 6 }{ (1+t }^{ 6 }){ (1+t }^{ 12 })$$ is:
  • 24
  • 21
  • 22
  • 23
The coefficient of $$x^n$$ in the binomial expansion of $$(1-x)^{-2}$$, is
  • $$\dfrac{2^n}{2!}$$
  • $$n+1$$
  • n
  • $$2n$$
The coefficient of $${x}^{24}$$ in the expansion of $$ { \left( 1+{ x }^{ 2 } \right)  }^{ 12 }\left( 1+{ x }^{ 12 } \right) \left( 1+{ x }^{ 24 } \right)$$ is
  • $$^{12}{C}_{6}$$
  • $$^{12}{C}_{6}+2$$
  • $$^{12}{C}_{6}+4$$
  • $$^{12}{C}_{6}+6$$
The term independent of $x$ in the expansion of $$\left( \sqrt { \left( \frac { x } { 3 } \right) } + \sqrt { \left( \frac { 3 } { 2 x ^ { 2 } } \right) } \right) ^ { 10 }$$ is:-
  • $$5$$$$/ 12$$
  • $$^ { 10 } C _ { 1 }$$
  • $$1$$
  • none of these
If $${ x }^{ m }$$ occurs in the expansion of $$(x+\frac { 1 }{ { x }^{ 2 } } )^{ 2n }$$, the coefficient of $${ x }^{ m }$$, is 
  • $$\frac { (2n)! }{ m!(2n-m)! } $$
  • $$\frac { (2n)!3!3! }{ (2n-m)! } $$
  • $$\frac { (2n)! }{ (\frac { 2n-m }{ 3 } )!(\frac { 4n+m }{ 3 } )! } $$
  • none of these
The coefficient of $$a^{3}b^{4}c$$ in the expansion of $$(1+a+b-c)^{9}$$ is 
  • $$2\;^{9}C_{7}\cdot ^{7}C_{4}$$
  • $$-2\;^{9}C_{7}\cdot ^{7}C_{3}$$
  • $$^{9}C_{7}\cdot ^{7}C_{3}$$
  • $$-^{9}C_{7}\cdot ^{7}C_{3}$$
The 4th term in the expansion of $${ \left( \sqrt { x } +\frac { 1 }{ x }  \right)  }^{ 2 }$$ is
  • $$110{ x }^{ \frac { 3 }{ 2 } }$$
  • $$220{ x }^{ \frac { 3 }{ 2 } }$$
  • $$220{ x }^{ 2 }$$
  • $$110{ x }^{ 2 }$$
In how many terms in the expansion of $$(x^{1/5}+y^{1/10})^{55}$$ do not have fractional power of the variable :
  • $$6$$
  • $$7$$
  • $$8$$
  • $$10$$
The coefficient of $$x^{4}$$ in $$\dfrac{3x^{2}+2x}{(x^{2}+2)(x-3)}$$ is
  • $$\dfrac{11}{27}$$
  • $$\dfrac{77}{324}$$
  • $$-\dfrac{77}{324}$$
  • $$\dfrac{11}{27}$$
In the expansion of $$\left( \dfrac { x+1 }{ { x }^{ 2/3 }-{ x }^{ 1/3 }+1 } -\dfrac { x-1 }{ x-x^{ -1/2 } }  \right) ^{ 10 },$$ the term which does not contain x is
  • $$^{ 10 }{ { C }_{ 0 } }$$
  • $$^{ 10 }{ { C }_{ 7 } }$$
  • $$^{ 10 }{ { C }_{ 4 } }$$
  • none
The coefficient of $$x^{-2}$$ in $$(1+3x^2+x^4)\left(1+\dfrac{1}{x}\right)^8$$ is
  • $$266$$
  • $$161$$
  • $$162$$
  • none of these
$$ {1 \choose 0} ^2 + {2 \choose 1}^2 + {3 \choose 2}^2 + ... + { n+1 \choose n}^2 = $$
  • $$(n+1){{2n}\choose{n}}$$
  • $$(\frac{n+2}{2}){{2n}\choose{n}}$$
  • $$(n+2).2^{n-1}$$
  • $$(n){{2n}\choose{n}}$$
Number of irrational terms in the expansion of $$(\sqrt {2}+\sqrt {3})^{15}$$ are 
  • $$9$$
  • $$7$$
  • $$16$$
  • $$10$$
Coefficient of $$x^8$$ in $$(x-1)(x-2)(x-3)..(x-10)$$ is?
  • $$980$$
  • $$1395$$
  • $$1320$$
  • None of these
The sum of the coefficient in the expansion of $$(x+y)^{n}$$ is $$4096$$. The greatest coefficient in the expansion is-
  • $$1024$$
  • $$924$$
  • $$824$$
  • $$724$$
The coefficient of $$x^{n}$$ in $$\dfrac {x+1}{(x-1)^{2}(x-2)}$$ is
  • $$1-2n-\dfrac {3}{2^{n+1}}$$
  • $$1-2n-\dfrac {3}{2^{n-1}}$$
  • $$1+2n+\dfrac {3}{2^{n+1}}$$
  • $$1+2n-\dfrac {3}{2^{n-1}}$$
The coefficient of the middle term in the binomial expansion in power of $$x$$ of $$(1+\alpha x)^{4}$$ and of $$(1-\alpha x)^{6}$$ is the same if $$\alpha$$ equals-
  • $$-\dfrac{5}{3}$$
  • $$\dfrac{10}{3}$$
  • $$\dfrac{-3}{10}$$
  • $$\dfrac{3}{5}$$
The number of terms which are free from radical signs in the expansion of $$(y^{1/5} + x^{1/10})^{55}$$ is
  • $$5$$
  • $$6$$
  • $$7$$
  • None of these
The number of irrational terms in the expansion of  $$\left( 5 ^ { 1 / 6 } + 2 ^ { 1 / 8 } \right) ^ { 100 }$$  is :
  • $$96$$
  • $$97$$
  • $$98$$
  • $$99$$
The value of the sum $$\sum _{ j=0 }^{ 8 }{8 \choose j}{ \frac { 1 }{ (j+1)(j+2) }  }  $$ is
  • $$\frac { 1003 }{ 90 } $$
  • $$\frac { 1013 }{ 90 } $$
  • $$\frac { 1023 }{ 90 } $$
  • $$\frac { 1033 }{ 90 } $$
Find the number of terms in the expression $$5x^ {2}-x^ {2}y+2xy+7$$
  • $$3$$
  • $$4$$
  • $$1$$
  • $$2$$
The coefficient of $$x^2$$ in expansion of the product
(2 $$x^2$$).($$(1 + 2x + 3x^2)^6$$ + $$(1 4x^2)^6$$) is :
  • 107
  • 106
  • 108
  • 155
The sum of the co-efficients of all odd degree terms in the expansion of $${ \left( x+\sqrt { { x }^{ 3 }-1 }  \right)  }^{ 5 }+{ \left( x-\sqrt { { x }^{ 3 }-1 }  \right)  }^{ 5 }$$, $$\left(x>1\right)$$
  • $$2$$
  • $$-1$$
  • $$0$$
  • $$1$$
$$^{26}C_{0}+^{26}C_{1}+^{26}C_{2}+...+^{26}C_{13}$$ is equal to
  • $$2^{25}$$
  • $$2^{25}+\dfrac {1}{2}^{26}C_{13}$$
  • $$2^{13}$$
  • $$2^{13}+\dfrac {1}{2}^{26}C_{13}$$
Number of terms which are rational in the expansion of $$(\sqrt[4]{5}+\sqrt[3]{4})^{100}$$ is 
  • $$10$$
  • $$8$$
  • $$9$$
  • $$11$$
If $$| x | < 2 / 3$$ then the fourth term in the expansion of $$\left( 1 + \frac { 3 } { 2 } x \right) ^ { 1 / 2 }$$ is
  • $$\frac { 27 } { 128 } x ^ { 3 }$$
  • $$-\frac { 27 } { 128 } x ^ { 3 }$$
  • $$\frac { 81 } { 256 } x ^ { 3 }$$
  • $$-\frac { 81 } { 256 } x ^ { 3 }$$
If $${ (1+x-{ 2x }^{ 2 }) }^{ 6 }=1+{ C }_{ 1 }x+{ C }_{ 2 }{ x }^{ 2 }+{ C }_{ 3 }{ x }^{ 3 }+...+{ C }_{ 12 }{ x }^{ 12 }$$, then the value of $${ C }_{ 2 }+{ C }_{ 4 }+{ C }_{ 6 }+...+{ C }_{ 12 }$$ is
  • 30
  • 32
  • 31
  • None of these
The sum of the coefficients in the expansion (6a-5b) when n is a positive integer, is 
  • $${ 10 }^{ \circ }$$
  • 1
  • $${ 11 }^{ n }$$
  • 0
Coefficient of $${ x }^{ 2009 }in(1+x+{ x }^{ 2 }+{ x }^{ 3 }+{ x }^{ 4 }{ ) }^{ 1001 }{ \left( 1-x \right)  }^{ 1002 }$$ IS...
  • $${ 4. }^{ 1001 }{ c }_{ 501 }$$
  • - 2009
  • 0
  • None of these
The number of terms which are free from radical signs in the expansion of $$\left( \frac { 1 }{ { y }^{ 4 } } +\frac { 1 }{ { y }^{ 8 } }  \right) $$ is:
  • 5
  • 6
  • 7
  • non of these
If sum of the coefficient in the expression of $${ (-3{ x }^{ 2 }+\frac { 2 }{ x } ) }^{ 2n+1 }$$ is 'a' then the values of 'b' for which roots of the equation $${ x }^{ 2 }+bx+6a=0$$ are integral
  • {-7,-5,5,7}
  • {-7,-1,1,7}
  • {-5,-1,1,5}
  • none of these
If $$\left | x \right |$$ < 1, then the coefficient of $$x^n$$ in the expansion of $$(1 + x + x^2 + x^3 + .....)^2$$ is
  • n
  • n 1
  • n + 2
  • n + 1
If the number of terms in the expansion of $${ \left( 1-\dfrac { 2 }{ X } +\dfrac { 4 }{ { X }^{ 2 } }  \right)  }^{ n },x\neq 0,$$ is 28, then sum coefficients of all the terms in this expansion,is:
  • 2187
  • 243
  • 729
  • 64
Coefficient of $$x^ {15}$$ in $$(1+x+x^ {3}+x^ {4})$$^ {n} is
  • $$\displaystyle \sum _{ r=0 }^{ 5 }{ ^{ n } } { C }_{ 5-r }.^{ n }{ C }_{ 3r }$$
  • $$\displaystyle \sum _{ r=0 }^{ 5 }{ ^{ n } } { C }_{ 5r }$$
  • $$\displaystyle \sum _{ r=0 }^{ 5 }{ ^{ n } } { C }_{ 2r }$$
  • $$\displaystyle \sum _{ r=0 }^{ 3 }{ ^{ n } } { C }_{ 3-r }.^{ n }{ C }_{ 5r }$$
The 11$$^{th}$$ term from last, in expansion of (2x+$$\frac{1}{^{x2}}$$ is
  • $$^{25}C_{15}$$$$\frac{2^{10}}{x^{20}}$$
  • $$^{-25}C_{15}\frac{2^{10}}{x^{20}}$$
  • $$^{25}C_{14}\frac{2^{11}}{x^{11}}$$
  • $$^{25}C_{15}\frac{2^{10}}{x^{20}}$$
The sum of rational terms in $$(\sqrt{2}+\sqrt[3] {3} +\sqrt[6] {5})^{10}$$
  • $$12632$$
  • $$1260$$
  • $$126$$
  • none of these
The number of distinct terms in the expansion of $${ \left( { x+y }^{ 2 } \right)  }^{ 13 }+{ \left( { x }^{ 2 }+y \right)  }^{ 14 }$$ is...
  • 29
  • 28
  • 25
  • 27
The number of terms whose values depend on $$x$$ in the expansion of $$\left( x ^ { 2 } - 2 + \frac { 1 } { x ^ { 2 } } \right) ^ { n }$$ is 
  • $$2 n + 1$$
  • 2$$n$$
  • $$n$$
  • None of these
Find the middle terms of the equation of $$\left(x^4 - \dfrac{1}{x^3}\right)^{11}$$.
  • $$-462\ x^9, 462\ x^2$$
  • $$-462\ x^8, 462\ x^4$$
  • $$462\ x^7, -462\ x^3$$
  • None of these
The coefficient of $$  x^{5}  $$ in the expansion of $$ \left(x^{2}-x-2\right)^{5}  $$ is
  • $$-83$$
  • $$-82$$
  • $$-81$$
  • $$0$$
In the expansion of $$ \left(1+3 x+2 x^{2}\right)^{6}  $$ the coefficient of $$  x^{11}  $$ is
  • $$144$$
  • $$288$$
  • $$216$$
  • $$576$$
The coefficient of $${ x }^{ 1 }$$ in the expansion of $$\left( 1-2x \right) ^{ -1/2 }$$ is 
  • $$\dfrac { \left( 2r \right) ! }{ \left( r! \right) ^{ 2 } } $$
  • $$\dfrac { \left( 2r \right) ! }{ { 2 }^{ r }\left( r! \right) ^{ 2 } } $$
  • None of these
  • $$\dfrac { \left( 2r \right) ! }{ { 2 }^{ r }\left( r+1 \right) !\left( c-1 \right) ! } $$
The coefficient of  $$x^m$$ in the expansion of  $$(1+)^{m+n}$$ is -
  • $$\frac { m!n! }{ (m+n)! } $$
  • $$(m+n)!$$
  • $$\frac { (m+n)! }{ m!n! } $$
  • none of these
The fifth term of $$\left(1 - \dfrac{2x}{3}\right)^{3/4}$$ is
  • $$\dfrac{-5x^4}{1152}$$
  • $$\dfrac{5x^4}{1152}$$
  • $$-\dfrac{5x^4}{1052}$$
  • $$\dfrac{5x^4}{1052}$$
If the middle term in the expansion of $${ \left( { x }^{ 2 }+\dfrac { 1 }{ x }  \right)  }^{ n }$$ is $$924{ x }^{ 6 }$$ then n=
  • 10
  • 12
  • 14
  • None of these
the number of terms in the expansion of $${\left( {x + y - x} \right)^3}$$ is  
  • 4
  • 6
  • 9
  • 10
The value of $$  x,  $$ for which the $$6 th$$ term in the expansion of $$ \int 2^{\log 2 \sqrt{\left(9^{x-1}+7\right)}}+\frac{1}{_{0}^{(1 / 5) \log _{2}\left(3^{x-1}+1\right)}} )^{7}  $$ is 84 is equal to
  • $$4$$,$$3$$
  • $$0$$,$$3$$
  • $$0$$,$$2$$
  • $$1$$,$$2$$
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