3D Geometry · NDA previous year questions

2025 8 questions

1. Q352025 · 14 Sept 2025

   For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear. How many triangles can be formed by joining these points?

   1. A.56
   2. B.54
   3. C.53
   4. D.52
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   Answer: D

2. Q362025 · 14 Sept 2025

   How many quadrilaterals can be formed by joining these points?

   1. A.70
   2. B.69
   3. C.53
   4. D.None of the above
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   Answer: C

3. Q512025 · 14 Sept 2025

   For the following two (02) items: A plane P is parallel to the line having direction ratios $⟨1,3,2⟩$ and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y + 3z = 0 Which of the following are the direction ratios of the line of intersection of the given planes?

   1. A.$⟨2,23,16⟩$
   2. B.$⟨2,-23,-16⟩$
   3. C.$⟨2,3,2⟩$
   4. D.$⟨-1,3,-2⟩$
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   Answer: B

4. Q522025 · 14 Sept 2025

   For the following two (02) items: A plane P is parallel to the line having direction ratios $⟨1,3,2⟩$ and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y + 3z = 0 What is the equation of the plane P?

   1. A.2x - 20y + 29z + 2 = 0
   2. B.2x + 3y + 2z - 4 = 0
   3. C.2x - 20y + 29z - 2 = 0
   4. D.x - 3y + 2z + 5 = 0
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   Answer: A

5. Q532025 · 14 Sept 2025
   Passage

   For the following two (02) items: Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0) B(0, 1, 0) and C(0, 0, 1)

   What is the radius of S?

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

6. Q542025 · 14 Sept 2025
   Passage

   For the following two (02) items: Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0) B(0, 1, 0) and C(0, 0, 1)

   On which one of the following planes does the centre of S lie?

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

7. Q652025 · 13 Apr 2025

   What is the equation of the plane passing through the point (1,1,1) and perpendicular to the line whose direction ratios are (3,2,1)?

   1. A.x+2y+3z=6
   2. B.3x+2y+z=6
   3. C.x+y+z=3
   4. D.3x+2y+z=0
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   Answer: B

8. Q662025 · 13 Apr 2025

   A line makes angles $\alpha$, $\beta$ and $\gamma$ with the positive directions of the coordinate axes. If $\vec{a}=({\sin }^2\alpha )\hat{i}+({\sin }^2\beta )\hat{j}+({\sin }^2\gamma )\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}+\hat{k}$ , then what is $\vec{a}.\vec{b}$ equal to?

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