NCERT Solutions for Maths Class 12 Exercise 8.2

# NCERT Solutions for Maths Class 12 Exercise 8.2

## NCERT Solutions for Maths Class 12 Exercise 8.2

Hello Students. Welcome to maths-formula.com. In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 8.2.

You can download the PDF of NCERT Books Maths Chapter 9 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 8.2.

Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

NCERT Solutions for Maths Class 12 Exercise 8.2 helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.

NCERT Solutions for Maths Class 12 Exercise 8.2 are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

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NCERT Solutions for Maths Class 12 Exercise 8.1

## NCERT Solutions for Maths Class 12 Exercise 8.2

Maths Class 12 Ex 8.2 Question 1.

Find the area of the circle 4x² + 4y² = 9 which is interior to the parabola x² = 4y.

Solution:

The required area is bounded by the circle 4x² + 4y² = 9 and interior of the parabola x² = 4y.
Putting x² = 4y in x² + y² = 9/4
We get 4y + y² = 9/4

Maths Class 12 Ex 8.2 Question 2.

Find the area bounded by curves (x – 1)² + y² = 1 and x² + y² = 1.

Solution:

The given circles are x² + y² = 1           … (i)
and (x – 1)² + y² = 1                … (ii)
The centre of the circle (i) is O(0, 0) and the radius is 1.

Maths Class 12 Ex 8.2 Question 3.

Find the area of the region bounded by the curves y = x² + 2, y = x, x = 0 and x = 3.

Solution:

The equation of the parabola is y = x² + 2 or x² = y – 2
Its vertex is (0, 2) and the axis is y-axis.
Boundary lines are y = x, x = 0 and x = 3.
Graphs of the curve and lines have been shown in the following figure.
Area of the region PQRO = Area of the region OAQR – Area of region OAP

Maths Class 12 Ex 8.2 Question 4.

Using integration, find the area of region bounded by the triangle whose vertices are (–1, 0), (1, 3) and (3, 2).

Solution:

The points A(–1, 0), B(1, 3) and C(3, 2) are plotted and joined.
Area of ∆ABC = Area of ∆ ABL + Area of trapezium BLMC – Area of ∆ACM      … (i)
The equation of the line joining the points

Maths Class 12 Ex 8.2 Question 5.

Using integration, find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4.

Solution:

The given lines are y = 2x + 1             … (i)
y = 3x + 1                                               … (ii)
and x = 4                                                … (iii)
Subtracting equation (i) from equation (ii), we get x = 0.

Putting x = 0 in equation (i), we get y = 1
Lines (ii) and (i) intersect at A(0, 1)

Putting x = 4 in equation (ii), we get y = 12 + 1 = 13
Lines (ii) and (iii) intersect at B(4, 13)

Putting x = 4 in equation (i), we get y = 8 + 1 = 9
Lines (i) and (iii) intersect at C(4, 9)

Choose the correct answer in the following exercises 6 and 7.

Maths Class 12 Ex 8.2 Question 6.

Smaller area bounded by the circle x² + y² = 4 and the line x + y = 2 is
(A) 2(Ï€ – 2)
(B) Ï€ – 2
(C) 2Ï€ – 1
(D) 2(Ï€ + 2)

Solution:

(B) A circle of radius 2 and centre at O is drawn. The line AB: x + y = 2 is passed through (2, 0) and (0, 2).

Area of the region ACB = Area of quadrant OAB – Area of ∆OAB         … (i)

Hence, the correct answer is option (B).

Maths Class 12 Ex 8.2 Question 7.

Area lying between the curves y² = 4x and y = 2x is
(A) 2/3
(B) 1/3
(C) 1/4
(D) 3/4

Solution:

(B) The curve is y² = 4x         … (i)
and the line is y = 2x             … (ii)

Hence, the correct answer is option (B).

NCERT Solutions for Maths Class 12 Exercise 8.1