Permutations an...

If $$^nC_{12} = ^nC_8$$ then is equal to

If different words are formed with all the letters of the word 'AGAIN' and are arranged alphabetically among themselves as in a dictionary, the word at the 50th place will be

Out of $$15$$ points in a plane, n points are in the same straight line, $$445$$ triangles can be formed by joining these points. What is the value of n?

The number of six-digit numbers which have sum of their digits as an odd integer, is

The value of $$\left( \dfrac { ^{ 50 }{ C }_{ 0 } }{ 1 } +\dfrac {^{ 50 }{ C }_{ 2 } }{ 3 } +...+\dfrac {^{ 50 }{ C }_{ 50 } }{ 51 }  \right) $$ is

If $$^nC_{r-1}=10, ^nC_r=45$$ and $$^nC_{r+1}=120$$, then $$r$$ equals to

If $$\quad { _{  }^{ n }{ C } }_{ 2 }+{ _{  }^{ n }{ C } }_{ 3 }={ _{  }^{ 6 }{ C } }_{ 3 }$$ and $${ _{  }^{ n }{ C } }_{ x }={ _{  }^{ n }{ C } }_{ 3 },x\neq 3$$ then the value of $$x$$ is

The number of positive integers satisfying the inequality $${ _{  }^{ n+1 }{ C } }_{ n-2 }-{ _{  }^{ n+1 }{ C } }_{ n-1 }\le 50$$ is

Find the term independent of $$x$$ in $${ \left( \cfrac { 3 }{ 2 } { x }^{ 2 }-\cfrac { 1 }{ 3x }  \right)  }^{ 9 }$$.