Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 119

HARD

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IMPORTANT

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A point equidistant from the lines $4 x + 3 y + 10 = 0, 5 x - 12 y + 26 = 0$ and $7 x + 24 y - 50 = 0$ is

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Important Questions on Straight Line

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 120

The midpoint of the sides of a triangle are

A (5, 0), B (5, 12)

and

C (0, 12)

. The orthocentre of this triangle is

HARD

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 121

The equation of a line passing through the point of intersection of the lines

4 x - 3 y - 1 = 0

and

5 x - 2 y - 3 = 0

and parallel to the line

2 y - 3 x + 2 = 0

is

EASY

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 122

If

a, b

and

c

are in

A . P .

then

a x + b y + c = 0

will always pass through a fixed point whose co-ordinates are

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 123

The equation of the line parallel to the line

2 x - 3 y = 1

and passing through the middle point of the line segment joining the points

(1, 3)

and

(1, - 7),

is

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 124

In

∆ A B C

, if

A \equiv (1, 2)

and equations of the medians through

B

and

C

are

x + y = 5

and

x = 4

, then point

B

must be

HARD

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 125

Two sides of a rhombus are along the lines,

x - y + 1 = 0

and

7 x - y - 5 = 0

. If its diagonals intersect at

(- 1, - 2),

then which one of the following is a vertex of this rhombus?

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 126

If

α, β

and

γ

are the roots of the equation

x^{3} - 3 p x^{2} + 3 q x - 1 = 0

, then the centroid of the triangle, whose vertices are

A (α, \frac{1}{α}), B (β, \frac{1}{β})

and

C (γ, \frac{1}{γ}),

is

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IMPORTANT

Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 127

If the points

(- 2, 0), (- 1, \frac{1}{\sqrt{3}})

and

(\cos θ, \sin θ)

are collinear, then the number of values of

θ \in [0, 2 π]

is