Permutations an...

 $\left( ^ { 2 n } C _ { 0 } \right) ^ { 2 } - \left( ^ { 2 n } C _ { 1 } \right) ^ { 2 } + \left( ^ { 2 n } C _ { 2 } \right) ^ { 2 } - \ldots + ( - 1 ) ^ { 2 n } \left( ^ { 2 n } C _ { 2 n } \right) ^ { 2 }$  equals to

If $${C_r} = {\,^n}{C_r}\,\,and\,\,\left( {{C_0} + {C_1}} \right)\,\,\left( {{C_1} + {C_2}} \right)......$$
$\left( {{C_{n - 1}} + {C_n}} \right) = k\frac{{{{\left( {n + 1} \right)}^n}}}{{n!}}$ then the value of k is 

If $^{35}C_{n+7}=^{35}C_{4n-2}$, then the value of $n$ is

In a conference hall 10  executive are to be seated on 10 chairs placed left to right. Executive $E_1$ wants to sit to the right of $E_2$ Also, $E_4$ wants to sit the left of $E_1$ and $E_5$ wants to sits to the left of ways $E_4$ Number of ways the executives can be seated on the 10 chairs, is 

Total number of four-digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are

What is the hundreds digits of ( 20 !-15!) ? 

If $n$ and $r$ are positive integers such that $r < n$ then $^{n}C_{r}+^{n}C_{r-1}$ is equal to

The number of five digit numbers in which digits decrease from left to  right, is 

If $x\epsilon N and C^{x-1_{4}}-C^{X-1}_{3}-\frac{5}{4}P^{x-2}_{2}< 0$ then x is equal to 

If  $m$  and  $n$  are positive integers more than or equal to  $2 , m > n ,$  then  $( m n ) !$  is divisible by