question_answer

If \[\left( a+1 \right)\,\,\left( a+2 \right)\,\,\left( a+3 \right)\,\,\left( a+m \right)+1\] is a perfect square where a and m are any natural numbers, then find the value of \[\left( m+\text{1} \right)\,\,\left( m+2 \right)\,\,\left( m+3 \right)\,\,\left( m+4 \right)\].

A)  3024               

B)  1680

C)  360                             

D)  24

E)  None of these