The largest value of a third order determinant whose elements are 0 or 1, is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$Let Δ = |\begin{array}{lll} a_{1} b_{1} c_{1} \\ a_{2} b_{2} c_{2} \\ a_{3} b_{3} c_{3} \end{array}|$ be a determinant of order 3.

Then,

$\begin{array}{l} Δ = a_{1} b_{2} c_{3} + a_{3} b_{1} c_{2} + a_{2} b_{3} c_{1} - a_{1} b_{3} c_{2} - a_{2} b_{1} c_{3} - a_{3} b_{2} c_{1} \\ Δ = (a_{1} b_{2} c_{3} + a_{3} b_{1} c_{2} + a_{2} b_{3} c_{1}) - (a_{1} b_{3} c_{2} + a_{2} b_{1} c_{3} + a_{3} b_{2} c_{1}) \end{array}$

Since each element of $∆$ is either 1 or 0. Therefore, the value of the determinant cannot exceed 3. Clearly, the value of $∆$ is maximum when the value of each term in first bracket is 1 and the value of each term in the second bracket is zero. But $a_{1} b_{2} c_{3} = a_{3} b_{1} c_{2} = a_{2} b_{3} c_{1} = 1$