question_answer

If x is a positive integer, then  is equal to

A)  \[2\left( x! \right)\left( x4-1 \right)!\]   

B)        \[2\left( x! \right)\left( x4-1 \right)!\left( x+2 \right)!\]

C)  \[2\left( x! \right)\left( x+3 \right)!\]    

D)  None of these

Correct Answer: B

Solution :

[b]: Applying \[{{R}_{1}}\to {{R}_{2}}-{{R}_{1}},{{R}_{2}}\to {{R}_{3}}-{{R}_{2}}\] we get \[=2(x!)(x+1)!(x+2)!\](Expanding along \[{{C}_{1}}\]).