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Question

Let x be a non-zero real number. A determinant is chosen from the set of all determinants of order 2 with entries x or x only. The probability that the value of the determinant is non-zero is

A
3/16
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B
1/4
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C
1/2
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D
1/8
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Solution

The correct options are
B 3/16
C 1/2
[abcd]=adbc
Each of the element can take two values, therefore total number of ways =16
But adbc0 if and only if ad=x2 and bc=x2 or ad=x2 and bc=x2
But ad=x2 and bc=x2 (a=d=x or a=d=x) and (b=x,c=x or b=x,c=x)
That is there are four ways
Similarly ad=x2 and bc=x2 in four ways
Thus, required probability =4+416=12

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