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JEE Main 201212 MayOnline
Exam
JEE Main
Year
2012
Date
12 May
Mode
Online
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2012 · 12 May · Online · Mathematics · Straight Lines

If the point (1, a) lies between the straight lines x+y=1 and...

If the point (1,a)(1, a) lies between the straight lines x+y=1x+y=1 and 2(x+y)=32(x+y)=3 then a lies in intervalIf the point (1, a) lies between the straight lines x+y=1 and 2(x+y)=3 then a lies in intervalIf the point (1, a) lies between the straight lines x+y=1 and 2(x+y)=3 then a lies in interval

Options

  1. A(32,∞)\left(\frac{3}{2}, \infty\right)
  2. B(1,32)\left(1, \frac{3}{2}\right)
  3. C(−∞,0)(-\infty, 0)
  4. D(0,12)\left(0, \frac{1}{2}\right)

Correct answer

D. (0,12)\left(0, \frac{1}{2}\right)

Step-by-step solution

If the point (1, a) lies between the straight lines x+y=1 and 2(x+y)=3 then a lies in interval
Since, (1,a)(1, a) lies between x+y=1 and 2(x+y)=3∴2(x+y)=3\therefore Put x=1in2(x+y)=3x=1 in 2(x+y)=3. We get the range of yy. Thus, 2(1+y)=3 \Rightarrow y=32−\frac{3}{2}-1=12\frac{1}{2}Thus ' aa 'lies in (0,12)\left(0, \frac{1}{2}\right)
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