ECAT Mathematics Chapter 20 MCQ Test With Answer for Mathematics chapter 20 (Analytic Geometry)

For all points (x,y) in third quadrant

• x > 0 , y < 0 A
• x > 0 , y > 0 B
• x < 0 , y < 0 C
• x < 0 , y > 0 D

The point which divides the line joining the points (2, 4, 5) and (3, 5, -4) in the ratio -2 : 3 lines on

• ZOX plane A
• XOY plane B
• YOZ plane C
• None of these D

Area bounded between the curve xy=2 and the lines x=1 and x=2

• ln2 square units A
• ln√2 square units B
• ln4 square units C
• Square units D

• 1 A
• 0 B
• 5 C
• 2 D

The square of the distance between two points P(x₁, y₁) and Q(x₂, y₂) is

• 
  A
• 
  B
• 
  C
• 
  D

The distance between the points A(3,1) and B(-2,-4) is

• 5 A
• 
  B
• 25 C
• 10 D

If k2x2 +2hxy- 4y2 =0 represents two perpendicular lines then

• k = 2 A
• k = ±2 B
• k = -2 C
• k ≠0 D

• 1 A
• 2 B
• -1 C
• 0 D

The angle between lines xy =0 is

• 45° A
• 60° B
• 90° C
• 180° D

The ratio in which the line y- x+ 2 =0 divides the line joining (3,-1) and (8,9) is

• 2:3 A
• -2:3 B
• 3:2 C
• -3:2 D

The obtuse angle between lines = -2 and y = x +2 is

• 120° A
• 135° B
• 150° C
• 140° D

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

• 2 A
• -3 B
• 3 C
• 5 D

If distance between (a,2) and (0,0) is 2 then a = _______

• 0 A
• 2 B
• 4 C
• 
  D

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

• 10 A
• 
  B
• 5 C
• 2 D

If l, m, n are the d.c.'s of a line, then

• l2+ m2+ n2= 0 A
• l2+ m2+ n2= 1 B
• l + m + n = 1 C
• l = m = n = 1 D

If distance of (a,b) from x-axis is 2 then

• a = 2 A
• b = 2 B
• a = b C
• b = 4 D

The slope of x-axis is

• 0 A
• undefined B
• 1 C
• 
  D

The distance of the point (2.3) from x-axis is

• 2 A
• 3 B
• 5 C
• 
  D

• x-axis A
• y-axis B
• z-axis C
• None of these D

For all points (x,y) in second quadrant

• x > 0 , y < 0 A
• x > 0 , y > 0 B
• x < 0 , y < 0 C
• x < 0 , y > 0 D

• 1 A
• 2 B
• 3 C
• 
  D

The points (5, -4, 2),(4, -3, 1),(7, -6, 4),(8, -7, 5) are vertices of a

• Square A
• Parallelogram B
• Rectangle C
• Rhombus D

The line through the intersection of the lines x+ 2y+ 3= 0 : 3x +4y +7 =0 and making equal intercepts on the axes is

• x+ y+ 1= 0 A
• x+ y- 2= 0 B
• x+ y+ 2= 0 C
• 2x +y +2 =0 D

The centroid of a triangle divides each median in the ratio

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

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

• 2 A
• -3 B
• 1 C
• 5 D

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

• 3 A
• 6 B
• 
  C
• 
  D

The equation of the sphere passing thro' (0, 0, 0), (a, 0, 0), (0, b, 0), (9, 0, c) is

• x²+ y²+ z²+ 2 ax +2 by + 2cz = 0 A
• x²+ y²+ z²- 2ax - 2 by - 2cz = 0 B
• x²+ y²+ z²- ax - by - cz = 0 C
• x²+ y²+ z²+ ax + by + cz = 0 D

The projections of a line segment on x, y, z axes are 12, 4, 3. The length and the direction cosines of the line segment are

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 1 B
• 
  C
• 
  D

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

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