Question # 1

If the focus lies on the x-axis with coordinates F(a, 0) and directrix of the parabola is = - a then the equation of parabola is:

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x² = 4ay

y²= 4ax

-x²= 4ay

-y²= 4ax

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Lagrange

Newtown

Leibniz

Cauchy

If (2, 1) is the mid point of the line segment joining the points (2, x) & (2, -5) then x =

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1

2

7

-7

The ordered pair _____ is a solution of the inequality x + 2y < 6.

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(3, 3)

(1, 1)

(4, 4)

(5, 5)

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x - axis

z - axis

y - axis

None of these

Two imaginary tangents can be drawn to a circle from any point P(x₁, y₁) _______ the circle:

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Inside

On

Outside

None of these

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

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Trapezium

Rectangle

Rhombus

None of these

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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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At

Not on

On

None of these

The distance between two points P₁ (x₁, y₁) and P₂ (x₂, y₂) on the co-ordinate plane is given by:

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the focal chord perpendicular to the axis of the parabola is called _____________ of the parabola:

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Directrix

Latus rectum

Focus

Focal chord

The directrix of the parabola x² = -4ay is:

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x = a

x = -a

y = a

y = -a

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

The conic is a parabola, if:

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e = 1

e > 1

0 < e < 1

e = 0

If 2 and 2 are x and y-components of a vector, then its angle with x-axis is:

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30°

45°

60°

90°

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

For a square of side x units, the rate of change of area with respect to the side is given by:

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x

x²

2x

2

If y = f(u) and u = F(x), then:

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x² + y² = 4 is:

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Function

Not a function

Ellipse

Line

If any two vectors of scalar triple product are equal, then its value is equal to:

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0

1

-1

2

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