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# RD Sharma Solution CLass 12 Mathematics Chapter 21 Areas of Bounded Regions

## Chapter 21 – Areas of bounded regions Exercise Ex. 21.1

Question 1
Solution 1

Question 2

Solution 2

Question 3
Solution 3

Question 4
Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Thus, Required area = square units

Question 8

Solution 8

Question 9

Solution 9

Question 10

and evaluate the area of the region under the curve and above the x-axis.

Solution 10

Question 11

Sketch
the region {(x, y):9x2 + 4y2 = 36} and find the area
enclosed by it, using integration.

Solution 11

9x2 + 4y2 =
36

Area of Sector OABCO =

Area of the whole figure = 4 × Ar. D
OABCO

= 6p
sq. units

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

What dose this integral represent on the graph?.

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Find the area of the minor segment of the circle x2 + y2 = a2 cut off by the line x =

Solution 27

Question 28

Find the area of the region bounded by the curve x = at2, y = 2at between the ordinates corresponding t = 1 and t = 2.

Solution 28

Question 29

Find the area enclosed by the curve x = 3 cost,

y = 2 sin t.

Solution 29

## Chapter 21 – Areas of Bounded Regions Exercise Ex. 21.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Find
the area of the region bounded by x2 = 4ay and its latusrectum.

Solution 3

Question 4

Find
the area of the region bounded by x2 + 16y = 0 and its latusrectum.

Solution 4

Question 5

Find the area of the region bounded by the curve ay2 = x3, the y-axis and the lines y = a and y = 2a.

Solution 5

## Chapter 21 – Areas of Bounded Regions Exercise Ex. 21.3

Question 1

Calculate the area of the region bounded by the parabolas y2 = 6x and x2 = 6y.

Solution 1

Question 2

Find
the area of the region common to the parabolas 4y2 = 9x and 3x2
= 16y.

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Find the area of the region between the circles x2 + y2 = 4 and (x – 2)2 + y2 = 4.

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Find the area of the region bounded by y =, x = 2y + 3 in the first quadrant and x-axis.

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Using
Integration, find the area of the region bounded by the triangle whose
vertices are ( 1, 2), (1, 5) and (3,
4).

Solution 23

Equation of side AB,

Equation of side BC,

Equation of side AC,

Area of required region

= Area of EABFE + Area of BFGCB –
Area of AEGCA

Question 24

Find the area of the bounded by y =and y = x.

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Find the area enclosed by the curve y = -x2 and the straight line x + y + 2 = 0.

Solution 28

Question 29

Solution 29

Question 30

Using the method of integration, find the area of the region bounded by the following lines: 3x – y – 3 = 0,

2x + y – 12 = 0, x – 2y – 1 = 0.

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Find the area of the region enclosed by the parabola

x2 = y and the line y = x + 2.

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Solution 46

Question 47

Solution 47

Question 48

Solution 48

Question 49

Solution 49

Question 50

Solution 50

Question 51

Solution 51

## Chapter 21 – Areas of Bounded Regions Exercise Ex. 21.4

Question 1

Find the area of the region between the parabola x = 4y – y2 and the line x = 2y – 3.

Solution 1

Question 2

Find the area bounded by the parabola x = 8 + 2y – y2; the y-axis and the lines y = -1 and y = 3.

Solution 2

Question 3

Find the area bounded by the parabola y2 = 4x and the line

y = 2x – 4.

i. By using horizontal strips

ii. By using vertical strips

Solution 3

Question 4

Find the area of the region bounded the parabola y2 = 2x and straight line x – y = 4.

Solution 4

## Chapter 21 – Areas of Bounded Regions Exercise MCQ

Question 1

a. 1/ 2

b. 1

c. -1

d. 2

Solution 1

Correct option: (b)

Question 2

The area included between the parabolas y2=4x and x2 = 4y is (in square units)

a. 4/3

b. 1/3

c. 16/3

d. 8/3

Solution 2

Correct option: (c)

Question 3

The area bounded by the curve y= loge x and x-axis and the straight line x =e is

1. e. sq. units
2. 1 sq. units
Solution 3

Correct option: (b)

Question 4

The area bounded by y=2-x2 and x + y =0 is

Solution 4

Correct option: (b)

Question 5

The area bounded by the parabola x =4 -y2 and y-axis, in square units, is

Solution 5

Correct option: (b)

Question 6

If An be the area bounded by the curve y = (tan x)n and the lines x = 0, y =0 and x =π /4, then for x > 2

Solution 6

Correct option: (a)

Question 7

The area of the region formed by x2+y2-6x-4y+12 x and x 5/2 is

Solution 7

Correct option: (c)

Question 8

a. 2

b. 1

c. 4

d. None of these

Solution 8

Correct option: (a)

Question 9

The area of the region bounded by the parabola (y-2)2 =x-1 , the tangent to it at the point with the ordinate 3 and the x-axis is

1. 3
2. 6
3. 7
4. None of these
Solution 9

Correct option: (d)

NOTE: Answer not matching with back answer.

Question 10

The area bounded by the parabola y2 = 4ax and x2 = 4 ay is

Solution 10

Correct option: (b)

Question 11

The area bounded by the curves y = sin x between the ordinates x =0 , x =π and the x-axis is

1. 2 sq. units
2. 4 sq. units
3. 3 sq. units
4. 1 sq. units
Solution 11

Correct option: (a)

Question 12

The area bounded by the curve y=x4-2x3+x2+3 with x-axis and ordinates corresponding to the minima of y is

Solution 12

Correct option: (b)

Question 13

The area bounded by the parabola y2=4ax, latus rectum and x-axis is

Solution 13

Correct option: (b)

Question 14

Solution 14

Correct option: (c)

NOTE: Answer not matching with back answer.

Question 15

The area common to the parabola y = 2x2 and y=x2+4 is

Solution 15

Correct option: (c)

Question 16

The area of the region bounded by the parabola y=x2+1 and the straight line x + y =3 is give by

Solution 16

Correct option: (d)

Question 17

The ratio of the areas between the curves y= cos x and y = cos 2x and x-axis from x =0 to x = π/3 is

1. 1:2
2. 2:1
3. None of these

Solution 17

Correct options: (d)

NOTE: Answer not matching with back answer.

Question 18

The area between x-axis and curve y = cos x when 0 x 2 π is

1. 0
2. 2
3. 3
4. 4
Solution 18

Correct option: (d)

Question 19

Area bounded by parabola y2=x and staright line 2y = x is

1. 4/3
2. 1
3. 2/3
4. 1/3

Solution 19

Correct option: (a)

NOTE: Options are modified.

Question 20

The area bounded by the curve y = 4x-x2 and x-axis is

Solution 20

Correct option: (c)

Question 21

Area enclosed between the curve y2(2a-x)=x3 and the line x =2a above x-axis is

Solution 21

Correct option: (b)

Question 22

The area of the region (in square units)bounded by the curve x2=4y, line x =2 and x-axis is

1. 1
2. 2/3
3. 4/3
4. 8/3
Solution 22

Correct option: (b)

Question 23

The area bounded by the curve y=f (x), x-axis, and the ordinates x =1 and x=b is (b-1) sin (3b+4). Then, f (x) is

1. (x-1) cos (3x+4)
2. Sin (3x+4)
3. Sin (3x+4)+3(x-1)cos (3x+4)
4. None of these

Solution 23

Correct option: (c)

Question 24

The area bounded by the curve y2 =8x and x2=8y is

Solution 24

NOTE: Answer is not matching with back answer.

Question 25

The area bounded by the parabola y2=8x, the x-axis, and the latus rectum is

Solution 25

Correct option: (a)

NOTE: Answer is not matching with back answer.

Question 26

Area bounded by the curve y=x3, the x-axis and the ordinates x =-2 and x =1 is

Solution 26

Correct option: (d)

Question 27

The area bounded by the curve y = x |x| and the ordinates x =-1 and x = 1 is given by

Solution 27

Correct option: (c)

Question 28

Solution 28

Correct option:(b)

Question 29

The area of the circle x2 +y2=16 interior to the parabola y2=6x is

Solution 29

Correct option: (c)

Question 30

Smaller area enclosed by the circle x2+y2=4 and the line x + y =2 is

1. 2(π-2)
2. π-2
3. 2π-1
4. 2(π+2)
Solution 30

Correct option: (b)

Question 31

Area lying between the curves y2=4x and y = 2x is

Solution 31

Correct option: (b)

Question 32

Area lying in first quadrant and bounded by the circle x2+y2=4 and the lines x =0 and x =2, is

Solution 32

Correct option: (a)

Question 33

Area of the region bounded by the curve y2=4x ,y-axis and the line y =3, is

Solution 33

Correct option: (b)

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