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ECAT Mathematics Introduction to Analytic Geometry Online Test

Danial MalikLast Updated: April 18, 2025

ECAT Math Introduction to Analytic Geometry

ECAT Math Introduction to Analytic Geometry Chapter Online Test

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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Page 1 of 3

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

A straight

A parabola

An ellipse

A circle

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

<1, 0, 0>

<0, 0, 1>

<0, 1, 0>

<1, 1, 0>

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

(3, 2)

(-3, 1)

(-4, -1)

(9-3, -1)

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

5y + 3x – 26 = 0

5y + 3x = 0

2√5 y + 16x – 13 = 0

9x + 2y + 17 = 0

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

8x + 5y + 2 = 0

5x – 8y + 2 = 0

5x + 8y + 2 = 0

5x + 6y + 4 = 0

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

m₁ + m₂

None of these

m₁m₂ = 1

m₁ = m₂

7. The equation of XOY plane is

z = 0

y = 0

x = 0

z = c, c ≠ 0

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

y + 2x + 7 = 0

4y + 13x = 19

3x + 7y + 20 = 0

2x – y + 11 = 0

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

(18, 26)

(19/3, 8/3)

(8/3, 19/3)

(- 8/3, - 19/3)

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

-2

-1

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

|0A| > |0B|

|0A| = |0B|

2|0A| < |0B|

|0A| = 2 |0B|

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

3:5

2:5

1:2

2:3

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

d₁ = d₂

√5

d₁ > d₂

d₁ < d₂

14. The equation of the XOY plane is

z = c, c ≠ 0

x = 0

z = 0

y = 0

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

Rhombus

Trapezium

Square

Rectangular

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

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

4a – b = 15

4a + b = 15

a + 7b = c + 7d

a + 4b = 15

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

√(x₂ – x₁)2 + (y₂ – y₁)2

(x₂ – x₁)²+(y₂ – x₁)²

√(x₁ – y₁)2 + (y₂ – y₂)2

√(x₂ – x₁) + (y₂ – y₁)

19. Which of the following is not homogeneous?

4x² + 5y² + 3xy = 0

x² + 4y² + 2gy + 2fy = 0

x² + y² + 2gxy = 0

3x² + 2y + 3xy = 0

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

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

None of these

√af + √bg + √ch = 0

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

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

√2

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

(0, 0)

(2, 2)

(3, 3)

(1, 1)

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

Circum center

Artho center

In – center

Centroid

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

(a = 1, b = 1)

(a = -4, b = -3)

(a = 3, b = 1)

(a = 2, b = -5)

25. 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

5/3

4/3

Page 2 of 3

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

In-center

Centroid

Circumcentre

Orthocenter

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

l + m + n = 1

l² + m² + n² = 1

l² + m² + n² = 0

l = m = n = 1

28. 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

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

None of these

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

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

29. The other name of analytic geometry is

None of these

Co – ordinate geometry

Geometry

Trigonometry

30. 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 =

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

<1, 1, 1>

<1/√3,1/√3, 1/√3>

<0, 1, 0>

<1, 0, 0>

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

√5

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

a = 3, b = 1

a = 1

b = 1

a = -4 b = -3

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

√41

√34

35.

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

-2

-1

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

Vertices of ∆

All

Collinear

Vertices of rectangle

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

13/2

59/3

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

90°

0°

180°

None of these

40.

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

√a² + b²

√a – b

√a + b

√a² – b²

42. The slope of line with inclination 150° is

-√3

-1/√3

43. Slope of a line 1 is negative if

0 < α < 90°

None of these

90° < α < 180°

0 < α < 180°

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

-1

-2

45.

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

-28

-8/5

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

2:1

1:2

1:1

1:3

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

a = √3, b = 1

a = 2, b = 2√2, b

a = 1, b = 1

a = 2, b = 1

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

-2

-1

50.

Page 3 of 3

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

|0A| > |0B|

2|0A| < |0B|

|0A| = 2 |0B|

|0A| = |0B|

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

(-1, -2, -3)

(3, 1, -2)

(2, -1, 3)

(3, -2, 1)

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

+ve

None of these

-ve

Zero

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

π/2

3π/2

π/4

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

(a/2, b/2)

(a + b, a + b)

(a–b/2, a–b/2)

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

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

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

3a – 2c, 3b – 2d

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

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

(3a – 2c/5, 3b – 2d/5)

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

4/5

- 4/5

6/4

None of these

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

None of these

Y = mx + r

x/p + y/q = 1

x cos a + y sin a = 1

60.

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Danial MalikLast Updated: April 18, 2025

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ECAT Mathematics Introduction to Analytic Geometry Online Test

ECAT Math Introduction to Analytic Geometry

ECAT Math Introduction to Analytic Geometry Chapter Online Test

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