A) \[\left( 0,\frac{1}{2} \right)\]
B) \[\left( 3,\,\infty \right)\]
C) \[\left( \frac{1}{2},3 \right)\]
D) \[\left( -3,-\frac{1}{2} \right)\]
Correct Answer: C
Solution :
[c] Given lines \[{{L}_{1}}:x-2y=0\] \[{{L}_{2}}:3x-y=0\] Points A and P lie on opposite Side of line \[x-2y=0.\] \[{{L}_{1}}(1,0)=1-2(0)>0\] \[\therefore a-2{{a}^{2}}<0\] Or \[a(2a-1)>0\] Or \[a>1/2\] ...(i) Points A and P lie on same side of line \[3x-y=0\] \[{{L}_{2}}(1,0)=3-0>0\] \[\therefore 3a-{{a}^{2}}>0\] Or \[a(a-3)<0\] Or \[0<a<3\] ...(ii) From (i) and (ii), \[1/2<a<3\]You need to login to perform this action.
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