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

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

Equation of a line parallel to x-axis:

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x = 0

x = y

y = a

x = a

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

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Zero

Undefined

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

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Line parallel to x-axis

Line parallel to y-axis

Line passing through the origin

Both (a) and (b)

Infinite number of lines can pass through:

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One point

Two points

Three points

Four points

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4

2

1

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

In the translation of axes which formula is true:

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x = X + h

X = x + h

x + X = h

None

Distance of the point (-3, 7) from x-axis is:

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3

-3

7

10

If a pair of opposite sides of a quadrilateral are equal and parallel then it is:

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Rectangle

Rhombus

Parallelogram

None of these

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

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Centroid

Ortho-center

Circums-center

In-center

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)

If (1, x) is the mid point of the line segment joining the points (1, 2) & (1, 6) then x =

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1

2

3

4

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Line parallel to x-axis

Line parallel to y-axis

Line passing through the origin

Both (a) and (b)

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

If the directed distances AP and PB have same signs, then their ratio is positive and P is said to divide AB:

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Internally

May be divide

Externally

None of these

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Parallel lines

Perpendicular lines

Non-parallel lines

None of these

The equation to the straight line which passes through the point (2, 9) and makes an angle of 45° with x-axis is:

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x + y + 7 = 0

x - y + 7 = 0

y - x + 7 = 0

None of these

The perpendicular distance of the line 3x + 4y + 10 = 0 from the origin is:

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0

1

2

3

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