Mathematics - Cartesian Coordinate System

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Question - 1

The value of X for which the points (X, - 1), (2, 1) and (4, 5) are collinear, is

  • A 2
  • B - 1
  • C 1
  • D - 2

Question - 2

The two lines aX + bY = c and \({ a }^{ \prime }X+{ b }^{ \prime }Y={ c }^{ \prime }\) are perpendicular, if 

  • A \(a{ a }^{ \prime }+{ bb }^{ \prime }=0\)
  • B \(a{ b }^{ \prime }={ ba }^{ \prime }\)
  • C \(ab+{ a }^{ \prime }{ b }^{ \prime }=0\)
  • D \(a{ b }^{ \prime }+{ ba }^{ \prime }=0\)

Question - 3

The equation of the line passing through (1, 2) and perpendicular to X + Y+ 7 = 0 is

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

Question - 4

The equation of the line perpendicular to the line X - 7Y + 5 = 0 and having X-intercept 3, is

  • A 7x + y - 21 = 0
  • B 6x + y - 19 = 0
  • C 5x + 2y - 21 = 0
  • D 6x + 7y - 25 = 0

Question - 5

If k is a parameter, then the equation of the family of lines parallel to the line 3X + 4Y + 5 = 0 is

  • A 4x - 3y + k = 0
  • B 3x - 4y + k = 0
  • C 3x + 4y + k = 0
  • D 4x + 3y + k = 0

Question - 6

The base of a triangle lies along the line X = a and is of length a. The area of the triangle is a2 . If the vertex lies on the line parallel to the base of triangle, then that equation of line is

  • A x = 0
  • B x = a
  • C x = 3a
  • D x = - 3a

Question - 7

If lines aX + bY + c = 0, where 3a + 2b + 4c = 0 and \(a,b,c\varepsilon R\), then the given set of lines are concurrent at the point

  • A (3, 2)
  • B (2, 4)
  • C (3,  4)
  • D (3/4, 1/2)

Question - 8

The foot of the perpendicular from (2, 3) upon the line 4X - 5Y + 8 = 0 is

  • A (0, 0)
  • B (1, 1)
  • C \(\left( \frac { 41 }{ 78 } ,\frac { 128 }{ 75 } \right) \)
  • D \(\left( \frac { 78 }{ 41 } ,\frac { 128 }{ 41 } \right) \)

Question - 9

The distance between the lines 3X + 4Y = 9 and 6X + 8Y = 15 is

  • A \(\frac { 3 }{ 10 } \)
  • B \(\frac { 2 }{ 9 } \)
  • C \(\frac { 1 }{ 4} \)
  • D \(\frac { 1 }{ 3} \)

Question - 10

If p is the length of perpendicular from origin to the line whose intercept on the axes are a and b, then \(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } \) is equal to

  • A \(\frac { 1 }{ { p }^{ 3 } } \)
  • B \(\frac { 1 }{ { p }}\)
  • C \(\frac { 1 }{ { p }^{ 2 } } \)
  • D \(p\)
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