3D Geometry · JEE Main previous year questions

2012 5 questions

1. Q292012 · 26 May 2012 · Shift 1

   Consider the following planes $P:x+y-2z+7=0$ $Q:x+y+2z+2=0$ $R:3x+3y-6z-11=0$

   1. A.$P$ and $R$ are perpendicular
   2. B.$Q$ and $R$ are perpendicular
   3. C.$P$ and $Q$ are parallel
   4. D.$P$ and $R$ are parallel
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   Answer: D

2. Q302012 · 26 May 2012 · Shift 1

   The equation of a plane containing the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$ and the point $(0,7,-7)$ is

   1. A.$x+y+z=0$
   2. B.$x+2y+z=21$
   3. C.$3x-2y+5z+35=0$
   4. D.$3x+2y+5z+21=0$
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   Answer: A

3. Q272012 · 7 May 2012 · Shift 1

   If two vertical poles $20\mathrm{m}$ and $80\mathrm{m}$ high stand apart on a horizontal plane, then the height (in $\mathrm{m}$) of the point of intersection of the lines joining the top of each pole to the foot of other is

   1. A.16
   2. B.18
   3. C.50
   4. D.15
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   Answer: A

4. Q292012 · 7 May 2012 · Shift 1

   The values of $a$ for which the two points $(1,a,1)$ and $(-3,0,a)$ lie on the opposite sides of the plane $3x+4y-12z+13=0$, satisfy

   1. A.$0<a<\frac{1}{3}$
   2. B.$-1<a<0$
   3. C.$a<-1\text{ or }a>\frac{1}{3}$
   4. D.$a=0$
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   Answer: C

5. Q302012 · 7 May 2012 · Shift 1

   A line with positive direction cosines passes through the point $P(2,-1,2)$ and makes equal angles with the coordinate axes. If the line meets the plane $2x+y+z=9$ at point $Q$, then the length $PQ$ equals

   1. A.$\sqrt{2}$
   2. B.2
   3. C.$\sqrt{3}$
   4. D.1
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   Answer: C