A) 0
B) - 6
C) 6
D) 1
Correct Answer: C
Solution :
Ans. For infinite solutions \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] Here, \[{{a}_{1}}=K,\,\,{{b}_{1}}=3,\] \[{{a}_{2}}=12,\,\,{{b}_{2}}=K\] \[{{C}_{1}}=-K+3\] and \[{{c}_{2}}=-K\] \[\Rightarrow \] \[\frac{{{K}_{1}}}{12}=\frac{3}{K}=\frac{-K+3}{-K}\] \[\Rightarrow \] \[{{K}^{2}}=36\] \[\therefore \] \[K=\sqrt{36}=6\]
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