JEE Main & Advanced
Sample Paper
JEE Main - Mock Test - 21
question_answer
If a, b, c are positive integers, then the determinant is divisible by
A)\[{{x}^{3}}\]
B)\[{{x}^{2}}\]
C)\[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\]
D) None of these
Correct Answer:
B
Solution :
[b]: Clearly, (Applying\[{{R}_{1}}\to {{R}_{1}}+{{R}_{2}}+{{R}_{3}}\]) \[={{x}^{2}}({{a}^{2}}+{{b}^{2}}+{{c}^{2}}+x)\] Hence \[\Delta \]is divisible by \[{{x}^{2}}\] as well as by x.