SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 chapter 2 - Application of Definite Integration [Latest edition]

Chapters Chapter 2: Application of Definite Integration

Q.1 (A)Q.1 (B)Q.1 (C)Q.2Q.3
Q.1 (A)

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 Chapter 2 Application of Definite Integration Q.1 (A)

MCQ [1 Mark]

Q.1 (A) | Q 1

Choose the correct alternative:

Area of the region bounded by the curve y = x3, x = 1, x = 4 and the X-axis is ______

• 225/4 sq.units

• 256/4 sq.units

• 255/3 sq.units

• 256/3 sq.units

Q.1 (A) | Q 2

Choose the correct alternative:

Using the definite integration area of the circle x2 + y2 = 16 is ______

• 4π sq.units

• 4 sq.units

• 16 sq.units

• 16π sq.units

Q.1 (A) | Q 3

Choose the correct alternative:

Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______

• 26 sq.units

• 3 sq.units

• 3/26 sq.units

• 26/3 sq.units

Q.1 (A) | Q 4

Choose the correct alternative:

Area of the region bounded by the curve x2 = 8y, the positive Y-axis lying in the first quadrant and the lines y = 4 and y = 9 is ______

• (76sqrt(2))/3 sq.units

• (76sqrt(2))/2 sq.units

• (38sqrt(2))/3 sq.units

• 76sqrt(2) sq.units

Q.1 (A) | Q 5

Choose the correct alternative:

Area of the region bounded by y2 = 16x, x = 1 and x = 4 and the X axis, lying in the first quadrant is ______

• 56/3 sq.units

• 3/56 sq.units

• 56 sq.units

• 63 sq.units

Q.1 (A) | Q 6

Choose the correct alternative:

Area of the region bounded by x = y4, y = 1 and y = 5 and the Y-axis lying in the first quadrant is ______

• 3124/5 sq.units

• 3142/5 sq.units

• 3124/3 sq.units

• 3142/3 sq.units

Q.1 (A) | Q 7

Choose the correct alternative:

Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______

• (75sqrt(5))/2 sq.units

• (20sqrt(5))/3 sq.units

• (100sqrt(5))/3 sq.units

• (75sqrt(5))/3 sq.units

Q.1 (B)

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 Chapter 2 Application of Definite Integration Q.1 (B)

[1 Mark]

Q.1 (B) | Q 1

State whether the following statement is True or False:

y2 = 4ax is the standard form of parabola when curve lies on X-axis

• True

• False

Q.1 (B) | Q 2

State whether the following statement is True or False:

Standard form of parabola is x2 = – 4by, when curve lies in the positive Y-axis

• True

• False

Q.1 (B) | Q 3

State whether the following statement is True or False:

The area of portion lying below the X axis is negative

• True

• False

Q.1 (B) | Q 4

State whether the following statement is True or False:

The area bounded by the curve y = f(x) lies on the both sides of the X-axis is |int_"a"^"b" "f"(x)  "d"x| + |int_"b"^"c" "f"(x)  "d"x|

• True

• False

Q.1 (B) | Q 5

State whether the following statement is True or False:

The equation of the area of the circle is x^2/"a"^2 + y^2/"b"^2 = 1

• True

• False

Q.1 (B) | Q 6

State whether the following statement is True or False:

The equation of the area of the ellipse is x2 + y2 = a2

• True

• False

Q.1 (B) | Q 7

State whether the following statement is True or False:

The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is |int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x)  "d"x|

• True

• False

Q.1 (C)

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 Chapter 2 Application of Definite Integration Q.1 (C)

Fill in the following blanks [1 Mark]

Q.1 (C) | Q 1

The area bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant is ______

Q.1 (C) | Q 2

The area of the circle x2 + y2 = 16 is ______

Q.1 (C) | Q 3

The area of the region bounded by the curve y2 = 4x, the X axis and the lines x = 1 and x = 4 is ______

Q.1 (C) | Q 4

The area of the region lying in the first quadrant and bounded by the curve y = 4x2, and the lines y = 2 and y = 4 is ______

Q.1 (C) | Q 5

The area of the region bounded by the curve y2 = x and the Y axis in the first quadrant and lines y = 3 and y = 9 is ______

Q.1 (C) | Q 6

The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______

Q.1 (C) | Q 7

The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______

Q.2

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 Chapter 2 Application of Definite Integration Q.2

Attempt the following questions [3 Marks]

Q.2 | Q 1

Find the area of the region bounded by the parabola y2 = 25x and the line x = 5

Q.2 | Q 2

Find the area of the region bounded by the curve y = sqrt(9 - x^2), X-axis and lines x = 0 and x = 3

Q.2 | Q 3

Find the area of the region bounded by the curve y = sqrt(2x + 3), the X axis and the lines x = 0 and x = 2

Q.2 | Q 4

Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8

Q.2 | Q 5

Find the area of the region bounded by the curve y = (x2 + 2)2, the X-axis and the lines x = 1 and x = 3

Q.2 | Q 6

Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant

Q.2 | Q 7

Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2

Q.2 | Q 8

Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis

Q.2 | Q 9

Find area of the region bounded by the parabola x2 = 4y, the Y-axis lying in the first quadrant and the lines y = 3

Q.2 | Q 10

Find the area of the region bounded by the curve x = sqrt(25 - y^2), the Y-axis lying in the first quadrant and the lines y = 0 and y = 5

Q.2 | Q 11

Find the area of the region bounded by the curve y = sqrt(36 - x^2), the X-axis lying in the first quadrant and the lines x = 0 and x = 6

Q.3

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 Chapter 2 Application of Definite Integration Q.3

Attempt the following questions [4 Mark]

Q.3 | Q 1

Find area of the ellipse x^2/5^2 + y^2/4^2 = 1

Q.3 | Q 2

Find the area of the circle x2 + y2 = 62

Q.3 | Q 3

Find the area between the parabolas y2 = 5x and x2 = 5y

Q.3 | Q 4

Find the area of the circle x2 + y2 = 16

Q.3 | Q 5

Find area of the ellipse 4x2 + 9y2 = 36

Chapter 2: Application of Definite Integration

Q.1 (A)Q.1 (B)Q.1 (C)Q.2Q.3 SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 chapter 2 - Application of Definite Integration

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 chapter 2 Application of Definite Integration are Standard Forms of Parabola and Their Shapes, Standard Forms of Ellipse, Area Under Simple Curves.

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