3D Geometry · NDA previous year questions

2026 8 questions

1. Q172026 · 12 Apr 2026

   A plane is observed to be approaching the airport. It is at a distance of 10 km from the point of observation and makes an angle of elevation of $67\cdot 5^{\circ }$. What is the height of the plane above the ground ?

   1. A.$10\sqrt{2+\sqrt{2}}\mathrm{km}$
   2. B.$10\sqrt{2-\sqrt{2}}\mathrm{km}$
   3. C.$5\sqrt{2+\sqrt{2}}\mathrm{km}$
   4. D.$5\sqrt{2-\sqrt{2}}\mathrm{km}$
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   Answer: C

2. Q182026 · 12 Apr 2026
   
   1. A.-1
   2. B.0
   3. C.1
   4. D.4
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   Answer: D

3. Q192026 · 12 Apr 2026
   
   1. A.$\frac{\gamma }{\alpha }$
   2. B.$\frac{\gamma }{\beta }$
   3. C.$\frac{2\gamma }{\alpha }$
   4. D.$\frac{2\gamma }{\beta }$
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   Answer: B

4. Q1052026 · 12 Apr 2026

   Passage: The equation of the sphere $S$ is $x^2+y^2+z^2-4x-6y-12z+k=0$. Question: If the radius of the sphere $S$ is 8 units, what is the value of $k$ ?

   1. A.$-15$
   2. B.7
   3. C.10
   4. D.15
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   Answer: A

5. Q1072026 · 12 Apr 2026

   Passage: A line $L$ passing through the point $(-1,2,-3)$ is perpendicular to the plane $P$ given by $2x+3y+z+5=0$. Question: What are the direction ratios of a line $M$ parallel to the plane $P$ ?

   1. A.$⟨-3,2,1⟩$
   2. B.$⟨3,2,-6⟩$
   3. C.$⟨1,3,2⟩$
   4. D.$⟨2,2,-10⟩$
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   Answer: D

6. Q1082026 · 12 Apr 2026

   Passage: A line $L$ passing through the point $(-1,2,-3)$ is perpendicular to the plane $P$ given by $2x+3y+z+5=0$. Question: What is the equation of the line $L$ ?

   1. A.$1-x=y+2=3-z$
   2. B.$-(x+1)=y-2=z+3$
   3. C.$3x+3=2y-4=6z+18$
   4. D.$3x-3=2y+4=6z-18$
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   Answer: C

7. Q1092026 · 12 Apr 2026

   Passage: $P(-2,-3,5),Q(4,-1,5),R(6,-4,8)$ and $S(2,-6,10)$ are four points. Question: What is $(P{Q}^2+2Q{S}^2-2P{R}^2)$ equal to ?

   1. A.$-1$
   2. B.0
   3. C.1
   4. D.2
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   Answer: B

8. Q1102026 · 12 Apr 2026

   Passage: $P(-2,-3,5),Q(4,-1,5),R(6,-4,8)$ and $S(2,-6,10)$ are four points. Question: Consider the following statements : I. $PQ$ is parallel to $RS$. II. $PR$ is perpendicular to $QS$. Which of the statements given above is/are correct ?

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