3D Geometry · NDA previous year questions

2018 7 questions

1. Q542018 · 9 Sept 2018

   What is the distance of the point $(2,3,4)$ from the plane $3x-6y+2z+11=0$?

   1. A.1 unit
   2. B.2 units
   3. C.3 units
   4. D.4 units
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   Answer: A

2. Q572018 · 9 Sept 2018

   Consider the following statements: 1. The angle between the planes $2x-y+z=1$ and $x+y+2z=3$ is $\frac{\pi }{3}$. 2. The distance between the planes $6x-3y+6z+2=0$ and $2x-y+2z+4=0$ is $\frac{10}{9}$. Which of the above statements is/are correct?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
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   Answer: C

3. Q212018 · 22 Apr 2018

   What is the number of triangles that can be formed by choosing the vertices from a set of 12 points in a plane, seven of which lie on the same straight line ?

   1. A.185
   2. B.175
   3. C.115
   4. D.105
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   Answer: A

4. Q222018 · 22 Apr 2018

   What is $C(n,r)+2C(n,r-1)+C(n,r-2)$ equal to ?

   1. A.$C(n+1,r)$
   2. B.$C(n-1,r+1)$
   3. C.$C(n,r+1)$
   4. D.$C(n+2,r)$
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   Answer: D

5. Q582018 · 22 Apr 2018

   What is the equation of the plane passing through the points $(-2,6,-6)$, $(-3,10,-9)$ and $(-5,0,-6)$?

   1. A.$2x-y-2z=2$
   2. B.$2x+y+3z=3$
   3. C.$x+y+z=6$
   4. D.$x-y-z=3$
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   Answer: A

6. Q592018 · 22 Apr 2018

   A sphere of constant radius $r$ through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the triangle ABC?

   1. A.$x^2+y^2+z^2=r^2$
   2. B.$x^2+y^2+z^2=4r^2$
   3. C.$9(x^2+y^2+z^2)=4r^2$
   4. D.$3(x^2+y^2+z^2)=2r^2$
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   Answer: C

7. Q1172018 · 22 Apr 2018

   What is the equation to the sphere whose centre is at $(-2,3,4)$ and radius is 6 units?

   1. A.$x^2+y^2+z^2+4x-6y-8z=7$
   2. B.$x^2+y^2+z^2+6x-4y-8z=7$
   3. C.$x^2+y^2+z^2+4x-6y-8z=4$
   4. D.$x^2+y^2+z^2+4x+6y+8z=4$
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   Answer: A