Mathematics Introduction to Analytic Geometry Online Test

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Question 1

1. 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

Question 2

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

Answer

<1/√3,1/√3, 1/√3>

Question 3

3. The slope of line with inclination 150° is

Question 4

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

Answer

a = 2, b = 2√2, b

Answer

a = √3, b = 1

Answer

a = 1, b = 1

Answer

a = 2, b = 1

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Answer

None of these

Question 9

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

Question 10

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

Answer

(8/3, 19/3)

Answer

(- 8/3, - 19/3)

Answer

(19/3, 8/3)

Question 11

11. 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

Answer

11, < 12/11, 4/11, 3/11 >

Answer

13, < 12/13, 4/13, 3/13 >

Answer

None of these

Answer

19, < 12/19, 4/19, 3/19 >

Question 12

12. The equation of the XOY plane is

Answer

z = c, c ≠ 0

Question 13

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

Answer

|0A| = 2 |0B|

Answer

|0A| = |0B|

Answer

2|0A| < |0B|

Answer

|0A| > |0B|

Question 14

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

Answer

None of these

Question 15

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

Answer

3a – 2c, 3b – 2d

Answer

(3a + 2c/5, 3b + 2d/5)

Answer

(3a + 2c/5, 3c + 2d/5)

Answer

(3a – 2c/5, 3b – 2d/5)

Question 16

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

Answer

√a – b

Answer

√a² – b²

Answer

√a² + b²

Question 17

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

Question 18

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

Answer

y + 2x + 7 = 0

Answer

2x – y + 11 = 0

Answer

4y + 13x = 19

Answer

3x + 7y + 20 = 0

Question 19

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

Answer

2|0A| < |0B|

Answer

|0A| = |0B|

Answer

|0A| > |0B|

Answer

|0A| = 2 |0B|

Question 20

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

Answer

a/f + b/g + c/h = 0

Answer

√af + √bg + √ch = 0

Answer

f/a + g/b + h/c = 0

Answer

None of these

Question 21

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

Answer

(a+b/2, a+b/2)

Answer

(a/2, b/2)

Answer

(a + b, a + b)

Answer

(a–b/2, a–b/2)

Question 22

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

Question 23

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

Answer

2√5 y + 16x – 13 = 0

Answer

5y + 3x – 26 = 0

Answer

5y + 3x = 0

Answer

9x + 2y + 17 = 0

Question 24

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

Question 25

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

Question 26

26. Which of the following is not homogeneous?

Answer

x² + y² + 2gxy = 0

Answer

4x² + 5y² + 3xy = 0

Answer

x² + 4y² + 2gy + 2fy = 0

Answer

3x² + 2y + 3xy = 0

Question 27

27.

Question 28

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

Answer

Rectangular

Question 29

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

Question 30

30.

Question 31

31. The other name of analytic geometry is

Answer

Trigonometry

Answer

None of these

Answer

Co – ordinate geometry

Question 32

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

Answer

5x – 8y + 2 = 0

Answer

5x + 6y + 4 = 0

Answer

5x + 8y + 2 = 0

Answer

8x + 5y + 2 = 0

Question 33

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

Answer

a + 4b = 15

Answer

4a + b = 15

Answer

4a – b = 15

Answer

a + 7b = c + 7d

Question 34

34. The equation of XOY plane is

Answer

z = c, c ≠ 0

Question 35

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

Question 36

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

Answer

None of these

Question 37

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

Question 38

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

Question 39

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

Question 40

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

Answer

(2, -1, 3)

Answer

(-1, -2, -3)

Answer

(3, -2, 1)

Answer

(3, 1, -2)

Question 41

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

Answer

None of these

Answer

x/p + y/q = 1

Answer

x cos a + y sin a = 1

Answer

Y = mx + r

Question 42

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

Answer

m₁m₂ = 1

Answer

None of these

Answer

m₁ + m₂

Answer

m₁ = m₂

Question 43

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

Answer

d₁ = d₂

Answer

d₁ > d₂

Answer

d₁ < d₂

Question 44

44. 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 =

Question 45

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

Answer

A parabola

Answer

A straight

Answer

An ellipse

Question 46

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

Answer

(a = 2, b = -5)

Answer

(a = -4, b = -3)

Answer

(a = 3, b = 1)

Answer

(a = 1, b = 1)

Question 47

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

Question 48

48. Slope of a line 1 is negative if

Answer

0 < α < 90°

Answer

90° < α < 180°

Answer

0 < α < 180°

Answer

None of these

Question 49

49.

Question 50

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

Answer

l² + m² + n² = 1

Answer

l = m = n = 1

Answer

l + m + n = 1

Answer

l² + m² + n² = 0

Question 51

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

Question 52

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

Question 53

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

Question 54

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

Answer

Artho center

Answer

In – center

Answer

Circum center

Question 55

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

Answer

√(x₂ – x₁) + (y₂ – y₁)

Answer

√(x₁ – y₁)2 + (y₂ – y₂)2

Answer

(x₂ – x₁)²+(y₂ – x₁)²

Answer

√(x₂ – x₁)2 + (y₂ – y₁)2

Question 56

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

Answer

a = 3, b = 1

Answer

a = -4 b = -3

Question 57

57.

Question 58

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

Answer

Vertices of ∆

Answer

Vertices of rectangle

Question 59

59.

Question 60

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

Answer

Orthocenter

Answer

Circumcentre

Question 61

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Total Questions:	60
Time Allowed:	25 Minutes
Total Marks:	60
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Important Math Introduction to Analytic Geometry Question and Answer

Math Introduction to Analytic Geometry Practice Test Online With Explanation

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Key Preparation Tips:

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