Question

Consider the system of equations ax + by = 0; cx + dy = 0, where `a, b, c, d in {0,1}`)STATEMENT-1: The probability that the system of equations has a unique solution is 3/8 STATEMENT-2: The probability that the system of equations has a solution is 1 A. Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I B. Statement I is true,Statement II is also true, Statement II is not the correct explanation of Statement I C. Statement I is true, Statement II is false D. Statement I is false, Statement II is true Select the correct answer from above options

Answer 1

Correct Answer - B The number of all possible determinants of the form `|(a,b),(c,d)|=2^4=16` Out of which only 10 determinants given by `|(1,1),(1,1)|,|(0,0),(0,0)|,|(1,1),(0,0)|,|(0,0),(1,1)|,|(0,1),(0,1)|,|(1,0),(1,0)|,|(1,0),(0,0)|,|(0,1),(0,0)|,|(0,0),(1,0)|` Vanish and remaining six determinants have non-zero values . Hence, the required probility =`6/(16)=3/8` Statement I is true. Statement II is also true as the homogeneous equations have always a solution and Statement II is not the correct explanation of Statement I.