3D Geometry · NDA previous year questions

2021 7 questions

1. Q612021 · 14 Nov 2021

   The locus of a point P(x, y, z) which moves in such a way that z = 7 is a

   1. A.line parallel to x - axis
   2. B.line parallel to y - axis
   3. C.line parallel to z - axis
   4. D.plane parallel to xy - plane
   Show answer

   Answer: D

2. Q622021 · 14 Nov 2021

   Consider the following statements: 1. A-line in space can have infinitely many direction ratios. 2. It is possible for certain lines that the sum of the squares of direction cosines can be equal to the sum of its direction cosines. 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
   Show answer

   Answer: C

3. Q632021 · 14 Nov 2021

   The xy-plane divides the line segment joining the points (-1, 3, 4) and (2, -5, 6)

   1. A.internally in the ratio 2 ∶ 3
   2. B.internally in the ratio 3 ∶ 2
   3. C.externally in the ratio 2 ∶ 3
   4. D.internally in the ratio 2 ∶ 1
   Show answer

   Answer: C

4. Q642021 · 14 Nov 2021

   The number of spheres of radius r touching the coordinate axes is

   1. A.4
   2. B.6
   3. C.8
   4. D.infinite
   Show answer

   Answer: C

5. Q1112021 · 18 Apr 2021

   What is the angle between the two lines having direction ratios (6, 3, 6) and (3, 3, 0)?

   1. A.$\frac{\pi }{6}$
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{\pi }{3}$
   4. D.$\frac{\pi }{2}$
   Show answer

   Answer: B

6. Q1122021 · 18 Apr 2021

   If $l,m,n$ are the direction cosines of the line $x-1=2(y+3)=1-z$, then what is $l^4+m^4+n^4$ equal to?

   1. A.1
   2. B.$\frac{11}{27}$
   3. C.$\frac{13}{27}$
   4. D.4
   Show answer

   Answer: B

7. Q1152021 · 18 Apr 2021

   The foot of the perpendicular drawn from the origin to the plane x + y + z = 3 is

   1. A.(0, 1, 2)
   2. B.(0, 0, 3)
   3. C.(1, 1, 1)
   4. D.(-1, 1, 3)
   Show answer

   Answer: C