3D Geometry · NDA previous year questions

2013 14 questions

1. Q672013 · 11 Aug 2013

   What is the equation of the sphere with unit radius having centre at the origin?

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

2. Q682013 · 11 Aug 2013

   What is the sum of the squares of direction cosines of $x$-axis?

   1. A.0
   2. B.$\frac{1}{3}$
   3. C.1
   4. D.3
   Show answer

   Answer: C

3. Q452013 · 14 Apr 2013

   The shadow of a tower standing on a level plane is found to be 50 m longer when the Sun's elevation is $30^{\circ }$ than when it is $60^{\circ }$. The height of the tower is

   1. A.25 m
   2. B.$25\sqrt{3}\text{ m}$
   3. C.50 m
   4. D.None of the above
   Show answer

   Answer: B

4. Q462013 · 14 Apr 2013

   The angle of elevation of the top of a tower of height H from the foot of another tower in the same plane is $60^{\circ }$ and the angle of elevation of the top of the second tower from the foot of the first tower is $30^{\circ }$. If h is the height of the other tower, then which one of the following is correct?

   1. A.$H=2h$
   2. B.$H=\sqrt{3}h$
   3. C.$H=3h$
   4. D.None of the above
   Show answer

   Answer: C

5. Q472013 · 14 Apr 2013

   If $\csc \theta +\cot \theta =c$, then what is $\cos \theta$ equal to?

   1. A.$\frac{c}{c^2-1}$
   2. B.$\frac{c}{c^2+1}$
   3. C.$\frac{c^2-1}{c^2+1}$
   4. D.None of the above
   Show answer

   Answer: C

6. Q482013 · 14 Apr 2013

   If $\sin \theta +2\cos \theta =1$, then what is $2\sin \theta -\cos \theta$ equal to?

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

7. Q492013 · 14 Apr 2013

   If $A+B=90^{\circ }$, then what is $\sqrt{\sin A\sec B-\sin A\cos B}$ equal to?

   1. A.$\sin A$
   2. B.$\cos A$
   3. C.$\tan A$
   4. D.0
   Show answer

   Answer: B

8. Q502013 · 14 Apr 2013

   What is ${\tan }^{4}A-{\sec }^{4}A+{\tan }^{2}A+{\sec }^{2}A$ equal to?

   1. A.0
   2. B.1
   3. C.2
   4. D.$-1$
   Show answer

   Answer: A

9. Q592013 · 14 Apr 2013

   What is the angle between the planes $2x-y-2z+1=0$ and $3x-4y+5z-3=0$?

   1. A.$\frac{\pi }{6}$
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{\pi }{3}$
   4. D.$\frac{\pi }{2}$
   Show answer

   Answer: D

10. Q602013 · 14 Apr 2013

    If the straight line $\frac{x-x_0}{l}=\frac{y-y_0}{m}=\frac{z-z_0}{n}$ is parallel to the plane $ax+by+cz+d=0$, then which one of the following is correct?

    1. A.$l+m+n=0$
    2. B.$a+b+c=0$
    3. C.$\frac{a}{l}+\frac{b}{m}+\frac{c}{n}=0$
    4. D.$al+bm+cn=0$
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    Answer: D

11. Q612013 · 14 Apr 2013

    The sum of the direction cosines of z-axis is

    1. A.0
    2. B.1/3
    3. C.1
    4. D.3
    Show answer

    Answer: C

12. Q632013 · 14 Apr 2013

    What is the distance between the planes $x-2y+z-1=0$ and $-3x+6y-3z+2=0$?

    1. A.3 unit
    2. B.1 unit
    3. C.0
    4. D.None of the above
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    Answer: D

13. Q642013 · 14 Apr 2013

    If a line makes $30^{\circ }$ with the positive direction of x-axis, angle $\beta$ with the positive direction of y-axis and angle $\gamma$ with the positive direction of z-axis, then what is ${\cos }^2\beta +{\cos }^2\gamma$ equal to?

    1. A.1/4
    2. B.1/2
    3. C.3/4
    4. D.1
    Show answer

    Answer: A

14. Q652013 · 14 Apr 2013

    What should be the value of k for which the equation $3x^2+3y^2+(k+1)z^2+x-y+z=0$ represents the sphere?

    1. A.3
    2. B.2
    3. C.1
    4. D.$-1$
    Show answer

    Answer: B