Binomial Theore...

Find the coefficient of $$\cfrac { 1 }{ { y }^{ 2 } } $$ in $${ \left( y+\cfrac { { c }}{ { y }^{ 2 } }  \right)  }^{ 10 }$$.

If $${ x }^{ 4r }$$ occurs in the expansion of $${ \left( x+\cfrac { 1 }{ { x }^{ 2 } }  \right)  }^{ 4n }$$ , then its coefficient is 

Determine the value of $$x$$ in the expression of $${ ( 2+x) }^{ 5 }$$, if the second term in the expansion is $$240$$

Find the $$(n+1)^{th}$$ term from the end in the expansion of $${ \left( x-\cfrac { 1 }{ x }  \right)  }^{ 2n }$$

Find the middle term in the expansion of $${ \left( \cfrac { 2x }{ 3 } +\cfrac { 3 }{ 2x }  \right)  }^{ 10 }$$.

If $${ \left( 1+2x+x^{ 2 } \right)  }^{ n }=\sum _{ r=0 }^{ 2n }{ { a }_{ r }{ x }^{ r } } $$, then $${ a }_{ r }=$$

The middle term in the expansion of $${ \left( 1+x \right)  }^{ 2n }$$ is , $$n$$ being a positive integer is

If $$n>2$$, then find the value of $${ C }_{ 1 }{ \left( a-1 \right)  }^{ 2 }-{ C }_{ 2 }{ \left( a-2 \right)  }^{ 2 }+{ C }_{ 3 }{ \left( a-3 \right)  }^{ 2 }-.....+{ \left( -1 \right)  }^{ n-1 }{ C }_{ n }{ \left( a-n \right)  }^{ 2 }$$ where $${ C }_{ r }$$ stands for $$\quad { _{  }^{ n }{ C } }_{ r }$$

find the 7th term in the expansion of $${ \left( 4x-\frac { 1 }{ 2\sqrt { x }  }  \right)  }^{ 13 }$$

The $$8^{th}$$ term of $$\displaystyle { \left( 3x+\frac { 2 }{ 3{ x }^{ 2 } }  \right)  }^{ 12 }$$, when expanded ina scending power of $$x$$, is