For which of the following values of m , is the area of the region bounded by the curve y = x - and the line y = mx equal to ?

**A. ** -2

**B. ** none of these

**C. ** 2

**D. ** -4

**Answer : ****Option A**

**Explaination / Solution: **

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The area bounded by the curve y =x, the x – axis and the ordinates x = 1 and x = -1 is given by

**A. ** 1/2

**B. ** 2/3

**C. ** None of these

**D. ** 0

**Answer : ****Option B**

**Explaination / Solution: **

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The area bounded by the curve y = x (x – 1 ) ( x – 2 ) and the x – axis is equal to

**A. ** none of these.

**B. ** 1/4

**C. ** 1

**D. ** 1/2 sq.units

**Answer : ****Option D**

**Explaination / Solution: **

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The area bounded by the curve y = 2x - and the line x + y = 0 is

**A. ** none of these.

**B. ** 35/6 sq. units

**C. ** 19/6 sq. units

**D. ** 9\2 sq. units

**Answer : ****Option D**

**Explaination / Solution: **

The equation y = i.e.represents a downward parabola with vertex at ( 1, 1 ) which meets x – axis where y = 0 .i .e . where x = 0 , 2. Also , the line y = - x meets this parabola where – x = i.e. where x = 0 , 3.

Therefore , required area is :

The equation y = i.e.represents a downward parabola with vertex at ( 1, 1 ) which meets x – axis where y = 0 .i .e . where x = 0 , 2. Also , the line y = - x meets this parabola where – x = i.e. where x = 0 , 3.

Therefore , required area is :

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The area bounded by the curves and the x- axis in the first quadrant is

To find area the curves y = and x = 2y + 3 and x – axis in the first quadrant., We have ;

,( y – 3 ) ( y + 1) = 0 . y = 3 , - 1 . In first quadrant , y = 3 and x = 9.

Therefore , required area is ;

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The area bounded by the curves and is equal to

Eliminating y, we get:

Required area:

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The area bounded by the parabolas y= is equal to
**A. ** 1/3

**B. ** 1/6

**C. ** 4

**D. ** 4/3

**Answer : ****Option A**

**Explaination / Solution: **

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The area bounded by the parabolas y =
**A. ** 4√3 sq.units

**B. ** 6√2 sq.units

**C. ** 12√2 sq.units

**D. ** 12√3 sq.units

**Answer : ****Option D**

**Explaination / Solution: **

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The tangents are

since .

It passes through ( -2 , 0 ).

The tangents are :

Required area :

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The area bounded by the angle bisectors of the lines

The angle bisectors of the line given by are x = 0 , y = 1. Required area : =

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