Binomial Theore...

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

Number of irrational terms in the expansion of $$(\sqrt {2}+\sqrt {3})^{15}$$ are 

The coefficient of $$x^{n}$$ in $$\dfrac {x+1}{(x-1)^{2}(x-2)}$$ is

If the coefficient of $${ x }^{ 2 }{ y }^{ 3 }{ z }^{ 4 }$$ in $$\left( x+y+z \right) ^{ n }$$ is A, then the coefficient of $${ x }^{ 4 }{ y }^{ 4 }{ z }$$ 

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:-

The 4th term in the expansion of $${ \left( \sqrt { x } +\frac { 1 }{ x }  \right)  }^{ 2 }$$ is

In how many terms in the expansion of $$(x^{1/5}+y^{1/10})^{55}$$ do not have fractional power of the variable :

In the expansion of $$(a-b)^{n},n\ge 5$$, if the sum of the $$5^{th}$$ and $$6^{th}$$ terms is zero, then $$a/b$$=

The value of the sum $$\sum _{ j=0 }^{ 8 }{8 \choose j}{ \frac { 1 }{ (j+1)(j+2) }  }  $$ is

Find the number of terms in the expression $$5x^ {2}-x^ {2}y+2xy+7$$