2nd Year Mathematics Chapter 4 Online MCQ Test for 12th Class Mathematics Unit 4 (Introduction to Analytic Geometry)

The pair of lines of homogeneous second-degree equation ax² + 2hxy + by² = 0 are real and coincident, if:

• h² < ab A
• h²> ab B
• h²= ab C
• None of these D

y = mx + c is the equation of straight line in:

• Slope-intercept form A
• Two points from B
• Point slope form C
• Intercepts form D

Point of intersection of lines x - 2y + 1 = 0 and 2x - y + 2 = 0 equals:

• (1, 0) A
• (0, 1) B
• (-1, 0) C
• (0, -1) D

A pair of lines of homogeneous second degree equation ax² + 2hxy + by² = 0 are othogonal, if:

• a - b = 0 A
• a + b = 0 B
• a + b > 0 C
• a - b < 0 D

The distance between the points (1, 2), (2, 1).

• 1 A
• 
  B
• 
  C
• 2 D

y - ordinate of the centroid of triangle with vertices A(-2, 3) B(-4, 1), C(3, 2) is:

• 3 A
• 1 B
• 2 C
• 0 D

The point of intersection of the altitudes of a triangle is called:

• Centroid A
• Ortho-center B
• Circums-center C
• In-center D

• Line parallel to x-axis A
• Line parallel to y-axis B
• Line passing through the origin C
• Both (a) and (b) D

• Line parallel to x - axis A
• Line parallel to y - axis B
• Inclined C
• Both (a) and (b) D

For any point (x, y) and y - axis:

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

x = c is a line:

• Perpendicular to x-axis A
• Parallel to x-axis B
• Perpendicular to y-axis C
• None of these D

The ratio in which the line segments joining (2, 3) and (4, 1) is divided by the line joining (1, 3) and (4, 3) is:

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

If (x, y) are the coordinate of a point ordered pair is called:

• Abscissa A
• Ordinate B
• Coordinate C
• Ordered pair D

The line y = a is below the x-axis, if:

• a > 0 A
• a < 0 B
• a = 0 C
• 
  D

The equation of a straight line which parallel to the line 3x - 2y + 5 = 0 and passes through (2, -1) is:

• 3x + 2y - 8 = 0 A
• 3x - 2y + 8 = 0 B
• 3x - 2y - 8 = 0 C
• 3x + 2y + 8 = 0 D

ax + by + c = 0 has matrix from as:

• 
  A
• |ax + by| = |-c| B
• [ax + by ] = [c] C
• [ax - by] = [-c] D

x = 4 is a line:

• Parallel to x - axis A
• Parallel to y - axis B
• Perpendicular to y-axis C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

In the translation of axes which formula is true:

• x = X + h A
• X = x + h B
• x + X = h C
• None D

• 
  A
• 
  B
• 
  C
• 2 D