### Mathematics - Cartesian Coordinate System

#### 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 $p$