| 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] The value of k for which the system of equations\[kx-y=2\], \[6x-2y=3\]has a unique solution is 3. |
| Reason [R] The system of linear equations |
| \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] has a unique solutions, if \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\]. |
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: D
Solution :
| Given system of linear equations has a unique solution, if |
| \[\frac{k}{6}\ne \frac{-1}{-2}\] |
| \[\frac{k}{6}\ne \frac{1}{2}\] |
| \[k\ne 3\] |
| So, Assertion is false and Reason is true. |
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