3D Geometry · NDA previous year questions

2009 12 questions

1. Q562009 · 30 Aug 2009
   
   1. A.$1\mathrm{s}$
   2. B.$(\ln 10)\mathrm{s}$
   3. C.$2(\ln 10)\mathrm{s}$
   4. D.$10\mathrm{s}$
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   Answer: B

2. Q572009 · 30 Aug 2009

   What is the product of the perpendiculars from the two points $(\pm \sqrt{b^2-a^2},0)$ to the line $ax\cos \varphi +by\sin \varphi =ab$ ?

   1. A.$a^2$
   2. B.$b^2$
   3. C.$ab$
   4. D.$a/b$
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   Answer: A

3. Q592009 · 30 Aug 2009

   The direction cosines of a line are proportional to $(2,1,2)$ and the line intersects a plane perpendicularly at the point $(1,-2,4)$. What is the distance of the plane from the point $(3,2,3)$ ?

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

4. Q602009 · 30 Aug 2009

   The foot of the perpendicular drawn from the origin to a plane is the point $(1,-3,1)$. What is the intercept cut on the $x$-axis by the plane ?

   1. A.1
   2. B.3
   3. C.$\sqrt{11}$
   4. D.11
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   Answer: D

5. Q612009 · 30 Aug 2009

   A line makes the same angle $\alpha$ with each of the $x$ and $y$-axes. If the angle $\theta$, which it makes with the $z$-axis, is such that ${\sin }^2\theta =2{\sin }^2\alpha$, then what is the value of $\alpha$ ?

   1. A.$\pi /4$
   2. B.$\pi /6$
   3. C.$\pi /3$
   4. D.$\pi /2$
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   Answer: A

6. Q632009 · 30 Aug 2009

   What is the equation of the sphere which has its centre at $(6,-1,2)$ and touches the plane $2x-y+2z-2=0$ ?

   1. A.$x^2+y^2+z^2+12x-2y+4z+16=0$
   2. B.$x^2+y^2+z^2+12x-2y+4z-16=0$
   3. C.$x^2+y^2+z^2-12x+2y-4z+16=0$
   4. D.$x^2+y^2+z^2-12x+2y-4z+25=0$
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   Answer: C

7. Q642009 · 30 Aug 2009

   What are the direction ratios of the line determined by the planes $x-y+2z=1$ and $x+y-z=3$ ?

   1. A.$(-1,3,2)$
   2. B.$(-1,-3,2)$
   3. C.$(2,1,3)$
   4. D.$(2,3,2)$
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   Answer: A

8. Q892009 · 19 Apr 2009

   What is the angle between the planes $2x-y+z=6$ and $x+y+2z=3$?

   1. A.$\pi /2$
   2. B.$\pi /3$
   3. C.$\pi /4$
   4. D.$\pi /6$
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   Answer: B

9. Q902009 · 19 Apr 2009

   What is the equation of a plane through the $x$-axis and passing through the point $(1,2,3)$?

   1. A.$x+y+z=6$
   2. B.$x=1$
   3. C.$y+z=5$
   4. D.$z+y=1$
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   Answer: Dropped in the final answer key (full marks to everyone)

10. Q922009 · 19 Apr 2009

    What is the number of planes passing through three non-collinear points?

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

11. Q932009 · 19 Apr 2009

    What is the angle between the lines $x+z=0,y=0$ and $20x=15y=12z$?

    1. A.${\cos }^{-1}(1/5)$
    2. B.${\cos }^{-1}(1/7)$
    3. C.${\sin }^{-1}(1/5)$
    4. D.${\sin }^{-1}(1/7)$
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    Answer: A

12. Q952009 · 19 Apr 2009

    Under what condition does the equation $x^2+y^2+z^2+2ux+2vy+2wz+d=0$ represent a real sphere?

    1. A.$u^2+v^2+w^2=d^2$
    2. B.$u^2+v^2+w^2>d$
    3. C.$u^2+v^2+w^2<d$
    4. D.$u^2+v^2+w^2<d^2$
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    Answer: B