| Assertion (A): \[\text{x}+\text{y}-\text{4}=0\]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) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
Correct Answer: B
Solution :
| [b] 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. |
| Reason does not give result of assertion. |
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