Maharashtra State BoardHSC Commerce 12th Board Exam
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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]

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12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 - Shaalaa.com
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Chapter 2: Application of Definite Integration

Q.1 (A)Q.1 (B)Q.1 (C)Q.2Q.3
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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
12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 - Shaalaa.com

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

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 chapter 2 (Application of Definite Integration) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. SCERT Maharashtra Question Bank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Application of Definite Integration exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in SCERT Maharashtra Question Bank Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exam.

Get the free view of chapter 2 Application of Definite Integration 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2021 and can use Shaalaa.com to keep it handy for your exam preparation

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