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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only.
The probability that the determinant chosen is non-zero is:
Solution
Total $2\times2$ matrices with entries $0$ or $1$: $2^4 = 16$Determinant: $ad - bc$
Non-zero determinant occurs in two cases.
Case 1: $ad = 1$ and $bc = 0$
$a = 1, d = 1$
$(b,c)$ can be $(0,0), (0,1), (1,0)$
→ 3 matrices
Case 2: $bc = 1$ and $ad = 0$
$b = 1,c = 1$
$(a,d)$ can be $(0,0), (0,1), (1,0)$
→ 3 matrices
Total non-zero determinants = $3 + 3 = 6$
$P(\text{non-zero determinants})=\dfrac{6}{16}=\dfrac{3}{8}$
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