3D Geometry · JEE Main previous year questions

2018 6 questions

1. Q282018 · 16 Apr 2018 · Shift 1

   The sum of the intercepts on the coordinate axes of the plane passing through the point $(-2,-2,2)$ and containing the line joining the points $(1,-1,2)$ and $(1,1,1)$ is :

   1. A.4
   2. B.$-4$
   3. C.$-8$
   4. D.12
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   Answer: B

2. Q272018 · 15 Apr 2018 · Shift 1

   A variable plane passes through a fixed point (3,2,1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz -plane through A, a second plane is drawn parallel zx-plane through B and a third plane is drawn parallel to xy-plane through C. Then the locus of the point of intersection of these three planes, is :

   1. A.$\frac{x}{3}+\frac{y}{2}+\frac{z}{1}=1$
   2. B.$x+y+z=6$
   3. C.$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{11}{6}$
   4. D.$\frac{3}{x}+\frac{2}{y}+\frac{1}{z}=1$
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   Answer: D

3. Q282018 · 15 Apr 2018 · Shift 1

   An angle between the plane, $x+y+z=5$ and the line of intersection of the planes, $3x+4y+z-1=0$ and $5x+8y+2z+14=0$, is :

   1. A.${\sin }^{-1}\left(\sqrt{\frac{3}{17}}\right)$
   2. B.${\cos }^{-1}\left(\sqrt{\frac{3}{17}}\right)$
   3. C.${\cos }^{-1}(3/17)$
   4. D.${\sin }^{-1}(3/17)$
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   Answer: A

4. Q292018 · 15 Apr 2018 · Shift 1

   An aeroplane flying at a constant speed, parallel to the horizontal ground, $\sqrt{3}\text{km}$ above it, is observed at an elevation of $60^{\circ }$ from a point on the ground. If, after five seconds, its elevation from the same point, is $30^{\circ }$, then the speed (in km / hr) of the aeroplane, is :

   1. A.1500
   2. B.1440
   3. C.750
   4. D.720
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   Answer: B

5. Q262018 · 8 Apr 2018 · Shift 1

   If ${\mathrm{L}}_1$ is the line of intersection of the planes $2x-2y+3z-2=0$, $x-y+z+1=0$ and ${\mathrm{L}}_2$ is the line of intersection of the planes $x+2y-z-3=0$, $3x-y+2z-1=0$, then the distance of the origin from the plane, containing the lines ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$, is :

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

6. Q272018 · 8 Apr 2018 · Shift 1

   The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane, $x+y+z=7$ is :

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