Consider the system of equations px + qy =0, rx + sy =0 where p , q , r , s ∈ -1,1 Statement-1 :- The probability that the system of equations has a unique solution is (1/2). Statement-2 :- The probability that the system of equations has no solution is zero.

Question

Consider the system of equations px + qy =0, rx + sy =0 where p , q , r , s ∈ -1,1 Statement-1 :- The probability that the system of equations has a unique solution is (1/2). Statement-2 :- The probability that the system of equations has no solution is zero. (A) Statement- 1 is true, statement- 2 is true and statement- 2 is correct explanation for statement- 1 . (B) Statement- 1 is true, statement- 2 is true and statement- 2 is NOT the correct explanation for statement- 1 . (C) Statement -1 is true, statement -2 is false. (D) Statement- 1 is false, statement- 2 is true.

Tardigrade Admin · Accepted Answer

Correct answer is (b) Statement- 1 is true, statement- 2 is true and statement- 2 is NOT the correct explanation for statement- 1 .

Q. Consider the system of equations px+qy=0,rx+sy=0 where p,q,r,s∈{−1,1} Statement-1 :- The probability that the system of equations has a unique solution is 21​. Statement-2 :- The probability that the system of equations has no solution is zero.

Statement- 1 is true, statement- 2 is true and statement- 2 is correct explanation for statement- 1 .

Statement- 1 is true, statement- 2 is true and statement- 2 is NOT the correct explanation for statement- 1 .

Statement -1 is true, statement -2 is false.

Statement- 1 is false, statement- 2 is true.

Correct answer is (b) Statement- 1 is true, statement- 2 is true and statement- 2 is NOT the correct explanation for statement- 1 .

Q. Consider the system of equations $p x + q y = 0, r x + sy = 0$ where $p, q, r, s \in {- 1, 1}$
Statement-1 :- The probability that the system of equations has a unique solution is $\frac{1}{2}$ .
Statement-2 :- The probability that the system of equations has no solution is zero.