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JEE Main 2012Offline
Exam
JEE Main
Year
2012
Mode
Offline
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2012 · Offline · Mathematics · Straight Lines

If the line 2 x+y=k passes through the point which divides the line...

If the line 2x+y=k2 x+y=k passes through the point which divides the line segment joining the points (1,1)(1,1) and (2,4)(2,4) in the ratio 3:23: 2, then kk equals

Options

  1. A295\frac{29}{5}
  2. B55
  3. C66
  4. D115\frac{11}{5}

Correct answer

C. 66

Step-by-step solution

Point p=(6+25,12+25)p=\left(\frac{6+2}{5}, \frac{12+2}{5}\right)\mathrm{p}=\left(\frac{8}{5}, \frac{14}{5}\right)p(85,145)p\left(\frac{8}{5}, \frac{14}{5}\right) lies on 2x+y=k⇒165+145=k⇒k=305=62 x+y=k \quad \Rightarrow \frac{16}{5}+\frac{14}{5}=k \quad \Rightarrow k=\frac{30}{5}=6
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