3D Geometry · NDA previous year questions

2014 22 questions

1. Q402014 · 28 Sept 2014

   A lamp post stands on a horizontal plane. From a point situated at a distance 150 m from its foot, the angle of elevation of the top is $30^{\circ }$. What is the height of the lamp post ?

   1. A.50 m
   2. B.$50\sqrt{3}\text{ m}$
   3. C.$\frac{50}{\sqrt{3}}\text{ m}$
   4. D.100 m
   Show answer

   Answer: B

2. Q722014 · 28 Sept 2014

   Consider the function $f^{\prime \prime }(x)={\sec }^{4}x+4$ with $f(0)=0$ and $f^{\prime }(0)=0$. What is $f^{\prime }(x)$ equal to?

   1. A.$\tan x-\frac{{\tan }^{3}x}{3}+4x$
   2. B.$\tan x+\frac{{\tan }^{3}x}{3}+4x$
   3. C.$\tan x+\frac{{\sec }^{3}x}{3}+4x$
   4. D.$-\tan x-\frac{{\tan }^{3}x}{3}+4x$
   Show answer

   Answer: B

3. Q732014 · 28 Sept 2014

   Consider the function $f^{\prime \prime }(x)={\sec }^{4}x+4$ with $f(0)=0$ and $f^{\prime }(0)=0$. What is $f(x)$ equal to?

   1. A.$\frac{2\ln \sec x}{3}+\frac{{\tan }^{2}x}{6}+2x^2$
   2. B.$\frac{3\ln \sec x}{2}+\frac{{\cot }^{2}x}{6}+2x^2$
   3. C.$\frac{4\ln \sec x}{3}+\frac{{\sec }^{2}x}{6}+2x^2$
   4. D.$\ln \sec x+\frac{{\tan }^{4}x}{12}+2x^2$
   Show answer

   Answer: A

4. Q752014 · 28 Sept 2014

   Consider $\int x{\tan }^{-1}xdx=A(x^2+1){\tan }^{-1}x+Bx+C$, where C is the constant of integration. What is the value of B?

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

   Answer: C

5. Q762014 · 28 Sept 2014

   What is ${\int }_0^{\pi /2}\frac{dx}{a^2{\cos }^{2}x+b^2{\sin }^{2}x}$ equal to?

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

   Answer: C

6. Q772014 · 28 Sept 2014

   For the next three (03) items that follow: Consider $I={\int }_0^{\pi }\frac{xdx}{1+\sin x}$ What is $I$ equal to?

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

   Answer: C

7. Q782014 · 28 Sept 2014

   For the next three (03) items that follow: Consider $I={\int }_0^{\pi }\frac{xdx}{1+\sin x}$ What is ${\int }_0^{\pi }\frac{(\pi -x)dx}{1+\sin x}$ equal to?

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

   Answer: A

8. Q792014 · 28 Sept 2014

   For the next three (03) items that follow: Consider $I={\int }_0^{\pi }\frac{xdx}{1+\sin x}$ What is ${\int }_0^{\pi }\frac{dx}{1+\sin x}$ equal to?

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

   Answer: B

9. Q1142014 · 28 Sept 2014

   For the next three (03) items that follow : Consider a sphere passing through the origin and the points $(2,1,-1),(1,5,-4),(-2,4,-6)$. What is the radius of the sphere?

   1. A.$\sqrt{12}$
   2. B.$\sqrt{14}$
   3. C.12
   4. D.14
   Show answer

   Answer: B

10. Q1152014 · 28 Sept 2014

    For the next three (03) items that follow : Consider a sphere passing through the origin and the points $(2,1,-1),(1,5,-4),(-2,4,-6)$. What is the centre of the sphere?

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

    Answer: A

11. Q1162014 · 28 Sept 2014

    For the next three (03) items that follow : Consider a sphere passing through the origin and the points $(2,1,-1),(1,5,-4),(-2,4,-6)$. Consider the following statements : 1. The sphere passes through the point $(0,4,0)$. 2. The point $(1,1,1)$ is at a distance of 5 unit from the centre of the sphere. Which of the above statements is/are correct?

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
    Show answer

    Answer: A

12. Q1172014 · 28 Sept 2014

    For the next two (02) items that follow : The line joining the points $(2,1,3)$ and $(4,-2,5)$ cuts the plane $2x+y-z=3$. Where does the line cut the plane?

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

    Answer: D

13. Q1182014 · 28 Sept 2014

    For the next two (02) items that follow : The line joining the points $(2,1,3)$ and $(4,-2,5)$ cuts the plane $2x+y-z=3$. What is the ratio in which the plane divides the line?

    1. A.$1:1$
    2. B.$2:3$
    3. C.$3:4$
    4. D.None of the above
    Show answer

    Answer: D

14. Q1192014 · 28 Sept 2014

    For the next two (02) items that follow : Consider the plane passing through the points $A(2,2,1),B(3,4,2)$ and $C(7,0,6)$. Which one of the following points lies on the plane?

    1. A.$(1,0,0)$
    2. B.$(1,0,1)$
    3. C.$(0,0,1)$
    4. D.None of the above
    Show answer

    Answer: A

15. Q1202014 · 28 Sept 2014

    For the next two (02) items that follow : Consider the plane passing through the points $A(2,2,1),B(3,4,2)$ and $C(7,0,6)$. What are the direction ratios of the normal to the plane?

    1. A.$<1,0,1>$
    2. B.$<0,1,0>$
    3. C.$<1,0,-1>$
    4. D.None of the above
    Show answer

    Answer: C

16. Q432014 · 20 Apr 2014

    From an aeroplane above a straight road the angles of depression of two positions at a distance 20 m apart on the road are observed to be $30^{\circ }$ and $45^{\circ }$. The height of the aeroplane above the ground is:

    1. A.$10\sqrt{3}\mathrm{m}$
    2. B.$10(\sqrt{3}-1)\mathrm{m}$
    3. C.$10(\sqrt{3}+1)\mathrm{m}$
    4. D.$20\mathrm{m}$
    Show answer

    Answer: C

17. Q1102014 · 20 Apr 2014

    For the next three (03) items that follow: A straight line passes through $(1,-2,3)$ and perpendicular to the plane $2x+3y-z=7$. What are the direction ratios of normal to plane?

    1. A.$<2,3,-1>$
    2. B.$<2,3,1>$
    3. C.$<-1,2,3>$
    4. D.None of the above
    Show answer

    Answer: A

18. Q1112014 · 20 Apr 2014

    For the next three (03) items that follow: A straight line passes through $(1,-2,3)$ and perpendicular to the plane $2x+3y-z=7$. Where does the line meet the plane?

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

    Answer: D

19. Q1122014 · 20 Apr 2014

    For the next three (03) items that follow: A straight line passes through $(1,-2,3)$ and perpendicular to the plane $2x+3y-z=7$. What is the image of the point $(1,-2,3)$ in the plane?

    1. A.$(2,-1,5)$
    2. B.$(-1,2,-3)$
    3. C.$(5,4,1)$
    4. D.None of the above
    Show answer

    Answer: C

20. Q1132014 · 20 Apr 2014

    For the next two (02) items that follow: Consider the spheres $x^2+y^2+z^2-4y+3=0$ and $x^2+y^2+z^2+2x+4z-4=0$. What is the distance between the centres of the two spheres?

    1. A.5 unit
    2. B.4 unit
    3. C.3 unit
    4. D.2 unit
    Show answer

    Answer: C

21. Q1142014 · 20 Apr 2014

    For the next two (02) items that follow: Consider the spheres $x^2+y^2+z^2-4y+3=0$ and $x^2+y^2+z^2+2x+4z-4=0$. Consider the following statements: 1. The two spheres intersect each other. 2. The radius of first sphere is less than that of second sphere. Which of the above statements is/are correct?

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
    Show answer

    Answer: C

22. Q1202014 · 20 Apr 2014

    A line passes through the points $(6,-7,-1)$ and $(2,-3,1)$. What are the direction ratios of the line?

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

    Answer: C