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 B3/16 C1/2 [abcd]=ad−bc Each of the element can take two values, therefore total number of ways =16 But ad−bc≠0 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