Coordinate Geometry · NDA previous year questions

2025 29 questions

1. Q602025 · 13 Apr 2025

   If any point on an ellipse is $(3\sin \alpha ,5\cos \alpha )$, then what is the eccentricity of the ellipse?

   1. A.4/3
   2. B.4/5
   3. C.3/4
   4. D.1/2
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   Answer: B

2. Q622025 · 13 Apr 2025

   A(1,2,−1), B(2,5,−2) and C(4,4,−3) are three vertices of a rectangle. What is the area of the rectangle?

   1. A.8 square units
   2. B.9 square units
   3. C.$\sqrt{66}$ square units
   4. D.$\sqrt{68}$ square units
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   Answer: C

3. Q632025 · 13 Apr 2025

   ABC is a triangle right-angled at B. If A(k,1,−1), B(2k,0,2) and C(2+2k,k,1) are the vertices of the triangle, then what is the value of k?

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

4. Q642025 · 13 Apr 2025

   If a line $\frac{x+1}{p}=\frac{y-1}{q}=\frac{z-2}{r}$ where p=2q=3r, makes an angle $\theta$ with the positive direction of y-axis, then what is $\cos 2\theta$ equal to?

   1. A.-31/49
   2. B.-37/49
   3. C.31/49
   4. D.37/49
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   Answer: A