| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion [A] \[x+y-4=0\] and \[2x+ky-3=0\] has no solution if k = 2. |
| Reason [R] \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] are consistent, if |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{k}_{1}}}{{{k}_{2}}}\]. |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is False.
D) A is false; R is true.
Correct Answer: B
Solution :
| For assertion, given equation has no solution if |
| \[\frac{1}{2}=\frac{1}{k}\ne \frac{-4}{-3}\] i.e. \[\frac{4}{3}\] |
| \[k=2\left[ \frac{1}{2}\ne \frac{4}{3}holds \right]\] |
| Assertion is true. |
| Both Assertion [A] and Reason [R] are true but Reason [R] is not the correct explanation of Assertion [A]. |
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