ECAT Mathematics Chapter 20 Analytic Geometry Online Test

• 1 A
• 2 B
• -1 C
• 0 D

For all points (x,y) on y-axis

• x is positive A
• x = 0 B
• x is negative C
• y = 0 D

If origin is the mid point of (a,3) and (5,b) then

• a = -5 , b = -3 A
• a = 5 , b =3 B
• a = -5 , b = 3 C
• a = 5 , b = -3 D

If A(x₁, y₁) , B(x₂, y₂) and C(x₃, y₃) are the vertices of a triangle then its centroid is

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

The distance of the point (2,3) from y-axis is

• 2 A
• 3 B
• 5 C
• 
  D

The distance between the points (2, 2) and (3, 3) is

• 10 A
• 
  B
• 5 C
• 2 D

The measure of the acute angle between the lines represented by x2 -xy -6y2 =0 is

• 120° A
• 30° B
• 130° C
• 45° D

If line through (4,3) and (2,k) is perpendicular to y =2x +3, then k =_______

• -1 A
• 1 B
• -4 C
• 4 D

The distance of the point (2,-3) from y-axis is

• 2 A
• -3 B
• 1 C
• 5 D

• 0 A
• 1 B
• 
  C
• 
  D

The distance between the points (0,0) and (x,y) is

• x²+ y² A
• x B
• y C
• 
  D

The distance of the point (2, -3) from x-axis is

• -2 A
• -3 B
• 2 C
• 3 D

The distance between the points (0 , 0) and (2, 1) is

• 5 A
• 
  B
• 0 C
• 3 D

• 
  A
• 
  B
• 
  C
• 
  D

The centroid of a triangle divides each median in the ratio

• 2 : 1 A
• 3 : 1 B
• 3 : 2 C
• 1 : 1 D

• 
  A
• 
  B
• 
  C
• 
  D

The intercepts of the plane 2x - 3y + 4z = 12 on the co-ordinate axes are given by

• 2, -3, 4 A
• 6, -4, -3 B
• 6, -4, 3 C
• 3, -2, 1.5 D

The coordinates of the point that divides the join of A(-6,3) and B(5, -2) in the ratio 2:3 internally

• 
  A
• 
  B
• 
  C
• 
  D

If origin is the mid point of (a, -3) and (-5, b) then

• a = -5 , b = -3 A
• a = 5 , b =3 B
• a = -5 , b = 3 C
• a = 5 , b = -3 D

The point P (5,8) and the origin lie on the side of the line 3x+ 7y+ 15 =0

• Same side A
• P above and origin below B
• Opposite side C
• P below and origin above D

The distance of the point (-2 , -3) from y-axis is

• 2 A
• -2 B
• 3 C
• -3 D

The length of perpendicular from (3,1) to 4x +3y +20 =0 is

• 6 A
• 7 B
• 3 C
• 8 D

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

• -2 A
• 2 B
• 3 C
• -1 D

The point of concurrency of the right bisectors of the sides of a triangle is called

• incentre A
• circum center B
• e-center C
• centroid D

The mid point of the line segment joining the points (a,b) and (b,a) is

• 
  A
• 
  B
• 
  C
• 
  D

The mid point of the line segment joining the points (4,0) and (0,4) is

• (4,4) A
• (2,2) B
• (-4,-4) C
• (-2,-2) D

The distance of the plane 2x - 3y + 6z + 14 = 0 from the origin is

• 14 A
• 2 B
• -2 C
• 11 D

• 
  A
• 
  B
• 
  C
• none of these D

The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is

• x + y + z - 15 = 0 A
• x - y + z - 15 = 0 B
• x - y - z - 15 = 0 C
• x + y + z + 15 = 0 D