3D Geometry · NDA previous year questions

2023 9 questions

1. Q972023 · 3 Sept 2023

   Which one of the planes is parallel to the line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ ?

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

2. Q982023 · 3 Sept 2023

   What is the angle between the lines 2x = 3y = -z and 6x = -y = -4z?

   1. A.0°
   2. B.30°
   3. C.60°
   4. D.90°
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   Answer: D

3. Q992023 · 3 Sept 2023

   What is the equation of the sphere concentric with the sphere $x^2+y^2+z^2-2x-6y-8z-5=0$ and which passes through the origin?

   1. A.$x^2+y^2+z^2-2x-8z=0$
   2. B.$x^2+y^2+z^2-2x-6y=0$
   3. C.$x^2+y^2+z^2-6y-8z=0$
   4. D.$x^2+y^2+z^2-2x-6y-8z=0$
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   Answer: D

4. Q612023 · 16 Apr 2023

   Consider the following for the next two (02) items that follow : Let $A(1,-1,2)$ and $B(2,1,-1)$ be the end points of the diameter of the sphere $x^2+y^2+z^2+2ux+2vy+2wz-1=0$. What is $u+v+w$ equal to ?

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

5. Q622023 · 16 Apr 2023

   Consider the following for the next two (02) items that follow : Let A(1, -1, 2) and B(2, 1, -1) be the end points of the diameter of the sphere $x^2+y^2+z^2+2ux+2vy+2wz-1=0$. $P(x,y,z)$ is any point on the sphere, then what is $P{A}^2+P{B}^2$ equal to ?

   1. A.15
   2. B.14
   3. C.13
   4. D.6.5
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   Answer: B

6. Q632023 · 16 Apr 2023

   Consider the following for the next two (02) items that follow : Consider two lines whose direction ratios are (2, -1, 2) and (k, 3, 5). They are inclined at an angle $\frac{\pi }{4}$ What is the value of k?

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

7. Q642023 · 16 Apr 2023

   What are the direction ratios of a line which is perpendicular to both the lines ?

   1. A.(1, 2, 10)
   2. B.(-1, -2, 10)
   3. C.(11, 12, -10)
   4. D.(11, 2, -10)
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   Answer: D

8. Q652023 · 16 Apr 2023

   Consider the following for the next two (02) items that follow : Let $\vec{a}=3\hat{i}+3\hat{j}+3\hat{k}$ and $\vec{c}=\hat{j}-\hat{k}$. Let $\vec{b}$ be such that $\vec{a}\cdot \vec{b}=27$ and $\vec{a}\times \vec{b}=9\vec{c}$ What is $\vec{b}$ equal to ?

   1. A.$3\hat{i}+4\hat{j}+2\hat{k}$
   2. B.$5\hat{i}+2\hat{j}+2\hat{k}$
   3. C.$5\hat{i}-2\hat{j}+6\hat{k}$
   4. D.$3\hat{i}+3\hat{j}+4\hat{k}$
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   Answer: B

9. Q662023 · 16 Apr 2023
   
   1. A.$\frac{\pi }{2}$
   2. B.$\frac{\pi }{3}$
   3. C.$\frac{\pi }{4}$
   4. D.$\frac{\pi }{6}$
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   Answer: A