question_answer

The value of the determinant  is

A) \[5(\sqrt{6}-5)\]          

B)   \[5\sqrt{3}(\sqrt{6}-5)\]

C) \[5(\sqrt{6}-\sqrt{3})\]

D)   \[\sqrt{2}(\sqrt{7}-\sqrt{5})\]

Correct Answer: B

Solution :

Take \[\sqrt{5}\] common from each of \[{{C}_{2}}\] and \[{{C}_{3}}\] and rearrange the elements of first column Split into two determinants the first of which will vanish. Take \[\sqrt{13}\] common from \[{{\Delta }_{1}}\]and \[\sqrt{3}\]from \[{{\Delta }_{2}}\]. Apply \[{{C}_{1}}\to {{C}_{1}}-{{C}_{2}}\]we get