Maths Chapter 11 – Three-dimensional Geometry MCQ Question Answers for Various Entrance Exams

 

1. The plane x + y = 0
a.
b.
c.
d.

2. Question
a.
b.
c.
d.

3. If a line makes angles α, β, γ with the axis then cos 2α + cos 2β + cos 2γ =
a.
b.
c.
d.

4. Question
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b.
c.
d.

5. Question
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d.

6. The direction ratios of the line of intersection of the planes 3x + 2y – z = 5 and x – y + 2z = 3 are
a.
b.
c.
d.

7. Question
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b.
c.
d.

8. Question
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9. Question
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10. The direction cosines of the y-axis are:
a.
b.
c.
d.

11. Question
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b.
c.
d.

12. The equations of y-axis in space are
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b.
c.
d.

13. Question
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c.
d.

14. The equation of the plane through the point (0, -4, -6) and (-2, 9, 3) and perpendicular to the plane x – 4y – 2z = 8 is
a.
b.
c.
d.

15. Find the equation of the plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).
a.
b.
c.
d.

16. The acute angle between the planes 2x – y+z = 6 and x+y+2z = 3 is
a.
b.
c.
d.

17. The direction cosines of any normal to the xy plane are
a.
b.
c.
d.

18. Question
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b.
c.
d.

19. Question
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b.
c.
d.

20. Find the equation of plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).
a.
b.
c.
d.

21. The equation of the plane through the origin and parallel to the plane 3x – 4y + 5z + 6 = 0
a.
b.
c.
d.

22. Question
a.
b.
c.
d.

23. A line makes angle α, β, γ with x-axis, y-axis and z-axis respectively then cos 2α + cos 2β + cos 2γ is equal to
a.
b.
c.
d.

24. Question
a.
b.
c.
d.

25. Question
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b.
c.
d.

26. If 2x + 5y – 6z + 3 = 0 be the equation of the plane, then the equation of any plane parallel to the given plane is
a.
b.
c.
d.

27. The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2) is equal to
a.
b.
c.
d.

28. The equation xy = 0 in three dimensional space is represented by
a.
b.
c.
d.

29. The equation of the plane through point (1, 2, -3) which is parallel to the plane 3x- 5y + 2z = 11 is given by
a.
b.
c.
d.

30. Question
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b.
c.
d.

31. Question
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c.
d.

32. Question
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b.
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33. The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are:
a.
b.
c.
d.

34. Direction ratio of line joining (2, 3, 4) and (−1, −2, 1), are:
a.
b.
c.
d.

35. Question
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b.
c.
d.

36. Question
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37. The vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6) is:
a.
b.
c.
d.

38. Question
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c.
d.

39. Question
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d.

40. The coordinates of the midpoints of the line segment joining the points (2, 3, 4) and (8, -3, 8) are
a.
b.
c.
d.

41. The reflection of the point (a, β, γ) in the xy-plane is
a.
b.
c.
d.

42. Question
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43. Question
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44. Question
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b.
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45. The locus of xy + yz = 0 is
a.
b.
c.
d.

46.  How many lines through the origin make equal angles with the coordinate axis?
a.
b.
c.
d.

47. Question
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48. Question
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49. The line x = 1, y = 2 is
a.
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c.
d.

50. The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by:
a.
b.
c.
d.


 


 

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