Question # 1

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

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h² < ab

h²> ab

h²= ab

None of these

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Parallel lines

Non-parallel lines

Perpendicular lines

Coplanar lines

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

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3x + 2y - 8 = 0

3x - 2y + 8 = 0

3x - 2y - 8 = 0

3x + 2y + 8 = 0

x = 4 is a line:

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Parallel to x - axis

Parallel to y - axis

Perpendicular to y-axis

None of these

If in the case of translation of axes, O (-3, 2), (x, y) = (-6, 9) then (X, Y) =

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(-3, 9)

(-3, 7)

(-9, 11)

(3, 7)

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Parallel lines

Perpendicular lines

Non-parallel lines

None of these

X-co-ordinate of centroid of triangle ABC with A(-2, 3); B(-4, 1); C(3, 5) equals:

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-1

1

3

-3

The coordinate axes divide the plane into------------ equal parts:

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1

2

3

4

y = -2 is a line:

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Parallel to x-axis

Parallel to y-axis

Perpendicular to x-axis

None of these

The centroid of a triangle is a point that divides each median in the ratio:

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2 : 1

2 : 3

1 : 3

4 : 3

Joint equation of y + 2x = 0, y - 3x = 0 is:

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(y+2x)(y-3x) = 0

(y-2x)(y-3x) = 0

(y+2x)(y+3x) = 0

(y-2x)(y+3x) = 0

ax + by + c = 0, will represent equation of straight line parallel y-axis if:

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a = 0

b = 0

c = 0

a = 0, c = 0

A quadrilateral having two parallels and two non-parallel sides is called:

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Trapezium

Rectangle

Rhombus

None of these

Inclination of X-axis or of any line parallel to X-axis is:

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Zero

Undefined

The symbol | | is used for:

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Parallel lines

Perpendicular lines

Non-parallel lines

None of these

X-coordinate of any point on Y-axis:

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0

x

y

1

The point of intersection of internal bisectors of the angles of a triangle is called:

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Centroid

Ortho-centers

Circums-center

In-center

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

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a - b = 0

a + b = 0

a + b > 0

a - b < 0

General form of equation of line is:

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ax - by + c = 0

ax + by - c = 0

ax + by + c = 0

ax - by - c = 0

If the directed distances AP and PB have the opposite signs, i.e; p is beyond AB, then their ratio is negative and P is said to divide AB:

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Internally

May divide

Externally

None of these

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0

2

1

-1

Inclination of Y-axis or of any line parallel to Y-axis is:

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Zero

Undefined

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Line parallel to x-axis

Line parallel to y-axis

Line passing through the origin

Both (a) and (b)

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