NCERT Solutions for Maths Class 12 Exercise 8.2
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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.
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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).