Question

Assertion :Consider the system of equations $ax+by=0,cx+dy=0;$ where $a,b,c,dϵ\{0,1\}.$

STATEMENT-1: The probability that the system of equations has a unique solution is $\frac{3}{8},$ and

Reason: STATEMENT-2: The probability that the system of equations has a solution is 1.

• A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
• B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
• C. STATEMENT-1 is True, STATEMENT-2 is False.
• D. STATEMENT-1 is False, STATEMENT-2 is True.

Answer 1

The correct option is B STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.

For $ax+by=0$ and $cx+dy=0$
Then
$ad-bc\ne 0$. or determinant of $a,b,c,d$ should not be 0.
Considering element 1 and 0, there are 16 ways of constructing a determinant.
Out of which only 6 determinants give non-zero answers.
Hence the required probability is
$=\frac{6}{16}$
$=\frac{3}{8}$.

The statement-2 is not the correct explanation for the statement-1