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

Rhombus

Trapezium

Rectangular

Square

2. 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

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

None of these

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

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

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

59/3

13/2

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

90°

180°

None of these

0°

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

-1

-2

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

√2

7. 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 =

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

√(x₂ – x₁)2 + (y₂ – y₁)2

(x₂ – x₁)²+(y₂ – x₁)²

√(x₂ – x₁) + (y₂ – y₁)

√(x₁ – y₁)2 + (y₂ – y₂)2

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

1:2

2:3

2:5

3:5

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

Artho center

In – center

Centroid

Circum center

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

(- 8/3, - 19/3)

(8/3, 19/3)

(18, 26)

(19/3, 8/3)

12. 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

4/3

5/3

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

a = 2, b = 1

a = √3, b = 1

a = 1, b = 1

a = 2, b = 2√2, b

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

a = -4 b = -3

b = 1

a = 3, b = 1

a = 1

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

A parabola

An ellipse

A circle

A straight

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

√5

d₁ = d₂

d₁ < d₂

d₁ > d₂

17. The equation of the XOY plane is

z = c, c ≠ 0

y = 0

x = 0

z = 0

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

None of these

4/5

6/4

- 4/5

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

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

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

(3a – 2c/5, 3b – 2d/5)

3a – 2c, 3b – 2d

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

(3, 3)

(1, 1)

(0, 0)

(2, 2)

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

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

2√5 y + 16x – 13 = 0

5y + 3x = 0

5y + 3x – 26 = 0

9x + 2y + 17 = 0

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

√34

√41

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

4a + b = 15

a + 4b = 15

4a – b = 15

a + 7b = c + 7d

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

None of these

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

√af + √bg + √ch = 0

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

Page 2 of 3

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

None of these

+ve

Zero

-ve

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

(3, 2)

(-4, -1)

(9-3, -1)

(-3, 1)

28.

29.

30. Slope of a line 1 is negative if

0 < α < 180°

90° < α < 180°

None of these

0 < α < 90°

31. Which of the following is not homogeneous?

3x² + 2y + 3xy = 0

x² + y² + 2gxy = 0

x² + 4y² + 2gy + 2fy = 0

4x² + 5y² + 3xy = 0

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

<1, 0, 0>

<1, 1, 1>

<1/√3,1/√3, 1/√3>

<0, 1, 0>

33. The slope of line with inclination 150° is

-1/√3

-√3

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

Circumcentre

Orthocenter

Centroid

In-center

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

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

<0, 1, 0>

<1, 1, 0>

<1, 0, 0>

<0, 0, 1>

37.

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

2:1

1:2

1:3

1:1

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

m₁m₂ = 1

m₁ + m₂

None of these

m₁ = m₂

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

|0A| = |0B|

|0A| > |0B|

|0A| = 2 |0B|

2|0A| < |0B|

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

5x – 8y + 2 = 0

8x + 5y + 2 = 0

5x + 6y + 4 = 0

5x + 8y + 2 = 0

42.

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

√5

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

l = m = n = 1

l + m + n = 1

l² + m² + n² = 1

l² + m² + n² = 0

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

(a = 3, b = 1)

(a = 2, b = -5)

(a = -4, b = -3)

(a = 1, b = 1)

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

-1

-2

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

3π/2

π/4

π/2

48. The other name of analytic geometry is

Co – ordinate geometry

Geometry

Trigonometry

None of these

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

2|0A| < |0B|

|0A| = |0B|

|0A| > |0B|

|0A| = 2 |0B|

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

(3, 1, -2)

(3, -2, 1)

(-1, -2, -3)

(2, -1, 3)

Page 3 of 3

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

3x + 7y + 20 = 0

2x – y + 11 = 0

y + 2x + 7 = 0

4y + 13x = 19

52. 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/2, b/2)

(a + b, a + b)

53.

54. The equation of XOY plane is

z = 0

x = 0

y = 0

z = c, c ≠ 0

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

All

Collinear

Vertices of rectangle

Vertices of ∆

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

-2

-1

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

-28

-8/5

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

Y = mx + r

None of these

x/p + y/q = 1

x cos a + y sin a = 1

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

√a² + b²

√a² – b²

√a – b

√a + b

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

-1

-2

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

ECAT Introduction to Computers Online Test
ECAT Physics Optical Instruments 1 Test Online
ECAT Computer File Handling in “C” Test Online
ECAT Computer Functions in “C” Test Online
ECAT Computer Loop Constructs Test Online
ECAT Computer Decision Constructs Test Online
ECAT Computer Input Output Test Online
ECAT Computer Elements of “C” Test Online
ECAT Computer Getting Started with “C” Test Online
ECAT Computer Science Microsoft Access-Forms and Reports Tes...

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

ECAT English Antonyms Online Test

ECAT English Spotting Errors Test 11 Online

ECAT Physics Of Solids Online Test

ECAT Mathematics Fundamentals of Trigonometry Online Test

NUST-Rawalpindi ECAT English Entry Test Preparation Online

ECAT English Direct and Indirect Narration Test 2 Online

Leave a Reply Cancel reply