| 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] Pair of linear equations : |
| \[9x+3y+12=0\], \[18x+6y+24=0\]have infinitely many solutions. |
| Reason [R] Pair of linear equations |
| \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]have infinitely many solutions, if |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}.\] |
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: A
Solution :
| From the given equations, we have |
| \[\frac{9}{18}=\frac{3}{6}=\frac{12}{24}\] |
| \[\frac{1}{2}=\frac{1}{2}=\frac{1}{2}\] i.e., \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] |
| Both Assertion [A] and Reason [R] are true and Reason [R] is the correct explanation of Assertion [A]. |
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