question_answer

If the point (1, a) lies between the straight lines  \[x+y=1\] and \[2(x+y)=3\]then a lies in interval     JEE Main Online Paper (Held On 12 May 2012)

A) \[\left( \frac{3}{2},\infty  \right)\]                           

B)                        \[\left( 1,\frac{3}{2} \right)\]

C)                        \[\left( -\infty ,0 \right)\]                            

D)                        \[\left( 0,\frac{1}{2} \right)\]

Correct Answer: D

Solution :

            Since, (1, a) lies between \[x+y=1\]and \[2(x+y)=3\] \[\therefore \]Put \[x=1\]in \[\text{2(x}+\text{y)}=\text{3}.\] We get the range of y. Thus, \[2(1+y)=3\Rightarrow y=\frac{3}{2}-1=\frac{1}{2}\] Thus  ?a' lies in \[\left( 0,\frac{1}{2} \right)\]