ECAT Mathematics Introduction to Analytic Geometry Online Test

1. If the distance of the point (5, b) from x – axis is 3, then b =

2. Which is intercept form of the equation px + qy + r = 0

3. The equation of line through (2, 4) and (7, 1) is

4. If a rod of length/slides down against a wall group, the locus of midpoint of the rod is

5. A line makes angles α, β, γ, δ with the four diagonals of a cube, then cos² α + cos² β + cos² γ + cos² δ has the value

6. Slope of line 4x + 5y + 6 = 0 is

7. Equation of straight line through (-2, 10) and (6, -4) is

8. If a > b, and 0 (0,0)A(a cos θ, a sin θ), B(b cos θ, b sin θ) then

9. In the figure, the values of a and b are

10. Which of the following is not homogeneous?

12. The distance between two points A (x₁, y₁) and (x₂, y₂) is

13. The distance of the point (a, b) from origin is

14. The distance of the point (1,2) from y – axis is

15. The distance of the point 2 cos θ from origin is

16. The equation of the XOY plane is

18. The distance b/w parallel lines 4x + 3y – 2 = 0 and 4x + 3y + 8 = 0 is

19. If the slope of line through Pts (2, a)(b, 7) is 4 then

21. The points (5, -2)(1, 2)(-2, 5) are

22. The equation of XOY plane is

23. The distance between the point (0, 0), (1, 2) is

24. The ratio is which x –axis divides the line joining points (2, -3) and (-5, 6) is

25. If d₁ is the distance between point (0,0),(1.2) and d₂ is the distance between points (1,2)(2,1), then d₁² – d₁² =

26. For O(0,0), A(3cosθ, 3 sin θ), B(7 cos θ, 7 sin θ), then

27. Slope of a line 1 is negative if

28. The point which divides segment joining points (4, -2) and (8, 6) in the ratio 7:5 internally is

29. The distance of the point (-1, 2) from y – axis is

30. Which point is above the line 4/3 x + y = 1?

31. If d₁ is distance between the points (0,0),(1,2) and d₂ is the distance between points (1, 2), (2, 1), then

32. If the distance between points (a, 5) and (1, 3) is √2a + 1, then a =

33. The direction cosines of a line equally inclined with co-ordinate axes are

34. The linc x+3/3 = y – 2/-2 = z+1/1 and the plane 4x + 5y + 3z – 5 = 0 intersect at a point

35. If P (x, y) divides A (-6, 3) and B (5, -2) in ratio 2:3 internally then x =

36. The distance of the point (3, 4, 5) from y-axis is

37. The point which divides segment joining points (a, b) and (c, d) in the ration 2:3 internally is

38. Midpoint of the line segment joining the points (a, b) and (b, a) is

40. If origin is the midpoint of (a, 3) and (4, b), then

41. A quadrilateral having two parallel line and two non-parallel line is called

42. The point of concurrency of the medians of a triangle is called its

43. Midpoint of the line segment joining the points (3, -1) and (-3, 1) is

44. Inclination of any line, parallel to y – axis is

45. The projections of a line segment on x, y, z axes are 12, 4, 3. The length and the direction cosines of the lines segment are

46. If m₁ & m₂ are slopes of two straight lines L₁ and L₂ respectively, then L₁ II L₂ if

48. If I, m, n are the d.c.’s of a line, then

49. The angle b/w lines represented by 9x² + 24xy + 16y² = 0 is

50. Centroid of triangle is a point that divides each median in the ratio

51. The other name of analytic geometry is

52. The lines l₁ and l₂ intersect, the shortest distance b/w is

53. If (3, 5) is mid – points of (5, a) and (b, 7) then

54. The direction cosines of any normal to the xy-plane are

55. The slope of line with inclination 150° is

56. The st. lines whose direction cosines satisfy al + bm + cn = 0, fmn + gnl + hlm = 0 are perpendicular if

57. The equation of line through (-3, 50 and “Ʇ ar ” to line x + 2y + 3 = 0) is

58. The points (5,2,4)(6, -1,2) and (8, -7, k) are collinear if k is equal to

59. The distance of the point (-1,-2) from x – axis is

60. The point of concurrency of the medians of a triangle is called its