3D Geometry · JEE Main previous year questions

2009 3 questions

1. Q62009 · 27 Apr 2009 · Shift 1

   The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is :

   1. A.$\frac{2\sqrt{3}}{8}$
   2. B.$\frac{3\sqrt{2}}{5}$
   3. C.$\frac{\sqrt{3}}{4}$
   4. D.$\frac{3\sqrt{2}}{8}$
   Show answer

   Answer: D

2. Q82009 · 27 Apr 2009 · Shift 1

   Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance of any one of them from the point $(1,0)$ to the distance from the point $(-1,0)$ is equal to $\frac{1}{3}$. Then the circumcentre of the triangle ABC is at the point :

   1. A.$(\frac{5}{4},0)$
   2. B.$(\frac{5}{2},0)$
   3. C.$(\frac{5}{3},0)$
   4. D.$(0,0)$
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   Answer: A

3. Q282009 · 27 Apr 2009 · Shift 1

   Let the line $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$ lie in the plane $x+3y-\alpha z+\beta =0$. Then $(\alpha ,\beta )$ equals

   1. A.$(-6,7)$
   2. B.$(5,-15)$
   3. C.$(-5,5)$
   4. D.$(6,-17)$
   Show answer

   Answer: A