JEE Main & Advanced
Sample Paper
JEE Main - Mock Test - 18
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