Permutations an...

If $$ n =  ^mC_2 $$, then the value of  $$ ^nC_2 $$ is given by

lf $$\displaystyle x,y\in(0,30)$$ such that $$ [ \dfrac{x}{3}]+[\dfrac{3x}{2}]+[\dfrac{y}{2}]+[\dfrac{3y}{4}]=\dfrac{11x}{6}+\dfrac{5y}{4} $$ (where [x] denote greatest integer $$ \le x $$) then the number of ordered pairs $$(x, y)$$ is

If $$_{  }^{ n+1 }{ { C }_{ r+1 } }$$: $$_{  }^{ n }{ { C }_{ r } }$$: $$_{  }^{ n-1 }{ { C }_{ r-1 } }=$$ 11: 6: 3 , then $$r=$$

 If $$ ^{n-1}C_r=(k^2-3 ) ^nC_{r+1} $$, then $$ k\in $$

In a test there were $$n$$ questions. In the test $$ 2^{n - i} $$ students gave wrong answers to at least $$i$$ questions $$i = 1, 2, 3 .... n$$. If the total number of wrong answers given is $$2047$$, then $$n$$ is

Which of the following is equal to $$\dfrac{1.3.5....(2n-1)}{2.4.6....(2n)}$$?

The value of $$\displaystyle \sum_{r=0}^{n-1} {\;}^nC_r / (^nC_r+^nC_{r+1})$$ equals

The value of $$x$$ in the equation $$3 \times ^{x+1}C_2 = 2\times ^{x+2}C_2, \space x\space \in N$$ is

How many different signals can be made by hoisting $$6$$ differently coloured flags one above the other, when any number of them may be hoisted at once?

The letters of word $$OUGHT$$ are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word $$TOUGH$$ in this dictionary.