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Binomial Theore...

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  • Question 1
    1 / -0

    The coefficient of $$x^4$$ in the expansion of $$(1+x+x^2+x^3)^{11}$$ is 

  • Question 2
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    If the last term in the binomial expansion of $$\left(2^{1/3}-\dfrac {1}{\sqrt {2}}\right)^{n}$$ is $$\left(\dfrac {1}{3^{5/3}}\right)^{\log_{3}8}$$, then the $$5^{th}$$ terms form the beginning is:

  • Question 3
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    The co-efficient of $$x^{k}$$ in expansion of $$1+\left(1+x\right)+\left(1+x\right)^{2}++\left(1+x\right)^{n}$$ is : $$\left(n>k\right)$$

  • Question 4
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    For $$x\in R, x\neq -1$$ if $$(1+x)^{2016}+x(1+x)^{2015}+x(1+x)^{2014}+.+x^{2016}=\sum _{ i=0 }^{ 2016 }{ { a }_{ i }{ x }^{ i } }$$, then  $$a_{17}$$ is equal to 

  • Question 5
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    The coefficients of $$x^{10}$$ in the expansion of $$(1+x)^{15}+(1+x)^{16}+(1+x)^{17}+....+(1+x)^{30}$$ is 

  • Question 6
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    The sum of the coefficient in the expansion of $$(a+2b+c)^{11}$$ is-

  • Question 7
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    Coefficient of $$x^{11}$$ in the extension of $$(1+x^{2})^{4}(1+x^{3})^{7}(1+x^{4})^{12}$$ is 

  • Question 8
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    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 :-

  • Question 9
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    The coefficient of $$x^n$$ in the binomial expansion of $$(1-x)^{-2}$$, is

  • Question 10
    1 / -0

    The coefficient of $${x}^{n}$$ in the expansion of $$\dfrac { 1 }{ \left( 1-x \right) \left( 1-2x \right) \left( 1-3x \right)  }$$ is

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