Home/ECAT/ECAT Mathematics Introduction to Analytic Geometry Online Test

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.
Test Helpful For:	ECAT Entry Test Mathematics Online Test Interview Questions about Mathematics All Universities Entrance Test Recruitments Tests

Please wait...

Page 1 of 3

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

(3, 2)

(-4, -1)

(-3, 1)

(9-3, -1)

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

Zero

-ve

+ve

None of these

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

m₁m₂ = 1

None of these

m₁ = m₂

m₁ + m₂

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

Collinear

Vertices of rectangle

All

Vertices of ∆

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

2x – y + 11 = 0

3x + 7y + 20 = 0

4y + 13x = 19

y + 2x + 7 = 0

8. The equation of the XOY plane is

y = 0

x = 0

z = 0

z = c, c ≠ 0

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

90°

None of these

0°

180°

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

None of these

6/4

- 4/5

4/5

11. 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)

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

x/p + y/q = 1

Y = mx + r

x cos a + y sin a = 1

None of these

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

(0, 0)

(1, 1)

(3, 3)

(2, 2)

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

In-center

Circumcentre

Orthocenter

Centroid

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

(3a – 2c/5, 3b – 2d/5)

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

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

3a – 2c, 3b – 2d

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

8x + 5y + 2 = 0

5x + 8y + 2 = 0

5x + 6y + 4 = 0

5x – 8y + 2 = 0

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

-2

-1

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

A circle

An ellipse

A straight

A parabola

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

<0, 1, 0>

<1, 0, 0>

<1, 1, 0>

<0, 0, 1>

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

Circum center

Artho center

In – center

Centroid

21. The other name of analytic geometry is

Trigonometry

None of these

Co – ordinate geometry

Geometry

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

2:5

3:5

1:2

2:3

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

59/3

13/2

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

3π/2

π/2

π/4

25. 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

d₁ = d₂

d₁ < d₂

√5

Page 2 of 3

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

-2

-1

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

√(x₂ – x₁)2 + (y₂ – y₁)2

√(x₁ – y₁)2 + (y₂ – y₂)2

√(x₂ – x₁) + (y₂ – y₁)

(x₂ – x₁)²+(y₂ – x₁)²

28. 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

29. Slope of a line 1 is negative if

None of these

0 < α < 90°

90° < α < 180°

0 < α < 180°

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

2:1

1:3

1:1

1:2

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

2√5 y + 16x – 13 = 0

5y + 3x – 26 = 0

9x + 2y + 17 = 0

5y + 3x = 0

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

√5

33. 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

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

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

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

None of these

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

√a – b

√a + b

√a² + b²

√a² – b²

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

-28

-8/5

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

37. The equation of XOY plane is

z = c, c ≠ 0

z = 0

y = 0

x = 0

38. 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 =

39. The slope of line with inclination 150° is

-√3

-1/√3

40. Which of the following is not homogeneous?

x² + 4y² + 2gy + 2fy = 0

3x² + 2y + 3xy = 0

x² + y² + 2gxy = 0

4x² + 5y² + 3xy = 0

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

√2

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

√41

√34

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

<1/√3,1/√3, 1/√3>

<1, 1, 1>

<1, 0, 0>

<0, 1, 0>

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

(a = -4, b = -3)

(a = 2, b = -5)

(a = 3, b = 1)

(a = 1, b = 1)

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

2|0A| < |0B|

|0A| = 2 |0B|

|0A| > |0B|

|0A| = |0B|

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

-2

-1

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

Trapezium

Square

Rhombus

Rectangular

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

(a–b/2, a–b/2)

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

(a + b, a + b)

(a/2, b/2)

49.

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

4a + b = 15

4a – b = 15

a + 4b = 15

a + 7b = c + 7d

Page 3 of 3

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

a = 2, b = 1

a = √3, b = 1

a = 2, b = 2√2, b

a = 1, b = 1

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

53.

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

(- 8/3, - 19/3)

(18, 26)

(19/3, 8/3)

(8/3, 19/3)

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

-1

-2

56.

57. 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

58. 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| = 2 |0B|

|0A| = |0B|

2|0A| < |0B|

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

a = 3, b = 1

b = 1

a = 1

a = -4 b = -3

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

√af + √bg + √ch = 0

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

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

None of these

You Can Learn and Gain more Knowledge through our Online Quiz and Testing system Just Search your desired Preparation subject at Gotest.

UET Peshawar Entry Test 2025 Registration Online ETEA Test D...
ECAT Statistics Test Set 17
ECAT Statistics Test Set 16
ECAT Statistics Test Set 15
ECAT Statistics Test Set 14
ECAT Statistics Test Set 13
ECAT Statistics Test Set 12
ECAT Statistics Test Set 11
ECAT Statistics Test Set 10
ECAT Statistics Test Set 9

Danial MalikLast Updated: April 18, 2025

Facebook Twitter Reddit WhatsApp Share via Email Print

ECAT Mathematics Introduction to Analytic Geometry Online Test

ECAT Math Introduction to Analytic Geometry

ECAT Math Introduction to Analytic Geometry Chapter Online Test

You Might Also Like

Danial Malik

Leave a Reply Cancel reply

ECAT Math Introduction to Analytic Geometry

ECAT Math Introduction to Analytic Geometry Chapter Online Test

You Might Also Like

Danial Malik

Your Related

NUST-Rawalpindi ECAT Physics Entry Test Preparation Online

ECAT Computer Science Computer Architecture Test Online

ECAT English Synonyms 4 Online Test

ECAT Physics Nuclear Physics Test Online

ECAT Mathematics Sets Functions and Groups Online Test

ECAT Physics Heat and Thermodynamics Online Test

Leave a Reply Cancel reply