Check the below NCERT MCQ Class 12 Mathematics Chapter 8 Application of Integrals with Answers available with PDF free download. MCQ Questions for Class 12 Mathematics with Answers were prepared based on the latest syllabus and examination pattern issued by CBSE, NCERT and KVS. Our teachers have provided below Application of Integrals Mathematics Class 12 Mathematics MCQs Questions with answers which will help students to revise and get more marks in exams

## Application of Integrals Class 12 Mathematics MCQ Questions with Answers

Refer below for MCQ Class 12 Mathematics Chapter 8 Application of Integrals with solutions. Solve questions and compare with the answers provided below

**Question. The area of the region enclosed by the parabola x ^{2} = y, the line y = x + 2 and the x-axis, is **

(a) 2/9

(b) 9/2

(c) 9

(d) 2

**Answer**

B

**Question. The area (in sq. units) bounded by the curves y = √x , 2y – x + 3 = 0 and x-axis lying in the first quadrant is **

(a) 9

(b) 36

(c) 18

(d) 27/4

**Answer**

A

**Question. The area (sq. units) bounded by the parabola y2 = 4ax and the line x = a and x = 4a is : **

(a) 35 a^{2}/3

(b) 4a^{2}/3

(c) 7a^{2}/3

(d) 56 a^{2}/3

**Answer**

D

**Question. The area bounded by the curve y = 3/2 √x , the line x = 1 and x-axis is ______ sq. units. **

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

B

**Question. Area bounded by the parabola y = x ^{2} – 2x + 3 and tangents drawn to it from the point P(1, 0) is equal to **

(a) 4√2 sq. units

(b) 4√2/3 sq. units

(c) 8√2/3 sq. units

(d) 16/3 √2 sq. units

**Answer**

C

**Question. The area of the region bounded by the ellipse x ^{2/}16 + y^{2}/9 = 1 is **

(a) 12 π

(b) 3 π

(c) 24 π

(d) π

**Answer**

A

**Question. The area bounded by the curve y2 = 16x and line y = mx is 2/3 , then m is equal to **

(a) 3

(b) 4

(c) 1

(d) 2

**Answer**

B

**Question. Area bounded by the circle x ^{2} + y^{2} = 1 and the curve | x | + | y | = 1 is **

(a) 2π

(b) π– 2

(c) π

(d) π+ 3

**Answer**

B

**Question. The area of the region bounded by the curve x = 2y + 3 and lines y = 1 and y = –1 is **

(a) 4 sq. units

(b) 3/2 sq. units

(c) 6 sq. units

(d) 8 sq. units

**Answer**

C

**Question. The area bounded by the parabola y ^{2} = 36x, the line x = 1 and x-axis is ______ sq. units. **

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

B

**Question. Area between the curves y = x and y = x ^{3} is **

(a) √3/2

(b) 1/2

(c) 2 √2

(d) 1/4

**Answer**

B

**Question. The area bounded by the line y = 2x – 2, y = – x and x-axis is given by **

(a) 9/2 sq. units

(b) 43/6 sq. units

(c) 35/6 sq. units

(d) None of these

**Answer**

D

**Question. Area of the region between the curves x ^{2} + y^{2} = π^{2}, y = sin x and y-axis in first quadrant is **

(a) π

^{3}– 8/4 sq. units

(b) π

^{3}– 4/8 sq. units

(c) π

^{2}– 8/4 sq. units

(d) π

^{2}– 4/8 sq. units

**Answer**

A

**Question. Area between the parabolas y ^{2} = 4ax and x^{2} = 4ay is **

(a) 2/3 a

^{2}– 5

(b) 15/4 a

^{2}+ 5

(c) 16/3 a

^{2}+ 2

(d) 16/3 a

^{2}

**Answer**

D

**Question. The area of the region bounded by y = | x – 1 | and y = 1 is **

(a) 2

(b) 1

(c) 1/2

(d) 1/4

**Answer**

B

**Question. For the area bounded by the curve y = ax, the line x = 2 and x-axis to be 2 sq. units, the value of a must be equal to **

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

B

**Question. The area of the plane region bounded by the curves x + 2y ^{2} = 0 and x + 3y^{2} = 1is equal to **

(a) 5/3

(b) 1/3

(c) 2/3

(d) 4/3

**Answer**

D

**Question. The area of the region enclosed by the lines y = x, x = e and curve y = 1/x and the positive x-axis is **

(a) 1 sq. unit

(b) 3/2 sq. units

(c) 5/2 sq. units

(d) 1/2 sq. units

**Answer**

B

**Question. The area of the region bounded by the parabola y = x ^{2} and y = |x| is **

(a) 3

(b) 1/2

(c) 1/3

(d) 2

**Answer**

C

**Question. The area bounded by y –1 = |x|, y = 0 and |x| = 1/2 will be : **

(a) 3/4

(b) 3/2

(c) 5/4

(d) None of these

**Answer**

C

**Question. Area of the region bounded by y = |x – 1| and y = 1 is **

(a) 2 sq. units

(b) 1 sq. unit

(c) 1/2 sq. units

(d) None of these

**Answer**

B

**Question. The area of the smaller region bounded by the ellipse x ^{2}/9 + y^{2}/4 = 1 and the line x/3 + y/2 = 1 is **

(a) 3 (π – 2)

(b) 3/2 π

(c) 3/2(π – 2)

(d) 2/3 (π – 2)

**Answer**

C

**Question. Area between the parabola x ^{2} = 4y and line x = 4y –2 is **

(a) 8/9

(b) 9/7

(c) 7/9

(d) 9/8

**Answer**

D

**Question. The area of the ellipse x ^{2}/9 + y^{2}/4 = 1 in first quadrant is 6π sq. units. **

**The ellipse is rotated about its centre in anti-clockwise direction till its major axis coincides with y-axis. Now the area of the ellipse in first quadrant is π sq. units.**

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

B

**Question. Area bounded by the curve y = log x and the coordinate axes is **

(a) 2

(b) 1

(c) 5

(d) 2 √2

**Answer**

B

**Question. The line y = mx bisects the area enclosed by lines x =0, y = 0 and x = 3/2 and the curve y = 1 + 4x – x ^{2}. Then the value of m is **

(a) 13/6

(b) 13/2

(c) 13/5

(d) 13/7

**Answer**

A

**Question. What is the area of the triangle bounded by the lines y = 0, x + y = 0 and x = 4 ? **

(a) 4 units

(b) 8 units

(c) 12 units

(d) 16 units

**Answer**

B

**Question. The area common to the ellipse x ^{2}/a^{2} + y^{2}/b^{2} = 1 and x^{2}/b^{2} + y^{2}/a^{2} = 1 , 0 < b < a is **

(a) (a + b)

^{2}tan

^{-1}b/a

(b) (a + b)

^{2}tan

^{-1}a/b

(c) 4ab tan

^{-1}b/a

(d) 4ab tan-1 a/b

**Answer**

C

**Question. The area of the triangle formed by the tangent and normal at the point (1, √3) on the circle x ^{2} + y^{2} = 4 and the x-axis is **

(a) 3 sq. units

(b) 2 √3 sq. units

(c) 3 √2 sq. units

(d) 4 sq. units

**Answer**

B

**Question. Area bounded by the curve y = cos x between x = 0 and x = 3π/2 is **

(a) 1 sq. unit

(b) 2 sq. units

(c) 3 sq. units

(d) 4 sq. units

**Answer**

C

**Question. Area of the region bounded by the curve y = |x + 1| + 1, x = –3, x = 3 and y = 0 is **

(a) 8 sq units

(b) 16 sq units

(c) 32 sq units

(d) None of these

**Answer**

B

**Question. The area bounded by the curves y = sin x, y = cos x and x = 0 is **

(a) ( √2 -1) sq. units

(b) 1 sq. unit

(c) √2 sq. units

(d) (1+ √2 ) sq. units

**Answer**

A

**Question. The area enclosed between the graph of y = x ^{3} and the lines x = 0, y = 1, y = 8 is **

(a) 45/4

(b) 14

(c) 7

(d) None of these

**Answer**

A

**Question. The area bounded by curves (x – 1) ^{2} + y^{2} = 1 and x^{2} + y^{2} = 1 is **

(a) (2π/3 – √3/2)

(b) 2π/3

(c) √3/2

(d) 2π/3 + √3/2

**Answer**

A

**Question. Consider the following statements ****Statement I :** The area bounded by the curve y =sin x between x = 0 and x = 2p is 2 sq. units.**Statement II :** The area bounded by the curve y = 2 cos x and the x-axis from x = 0 to x = 2p is 8 sq. units.

(a) Statement I is true

(b) Statement II is true

(c) Both statements are true

(d) Both statements are false

**Answer**

B

**Question. The area of the region bounded by the curves y =| x – 2 |, x = 1, x = 3 and the x-axis is **

(a) 4

(b) 2

(c) 3

(d) 1

**Answer**

D

**Question. The area bounded by f (x) = x ^{2}, 0 • x • 1, g(x)= – x + 2,1≤ x≤ 2 and x – axis is **

(a) 3/2

(b) 4/3

(c) 8/3

(d) None of these

**Answer**

D

**Question. The area bounded by the curves x + 2y ^{2} = 0 and x + 3y^{2} = 1 is **

(a) 1 sq. unit

(b) 1/3 sq. units

(c) 2/3 sq. units

(d) 4/3 sq. units

**Answer**

D

**Question. The area of the region {(x, y) : y2 ≤ 4x, 4×2 + 4y2 ≤ 9} is **

(a) √2/6 + 9π/8 – 9/4 sin-1(1/5)

(b) √2/6 – 9π/8

(c) 9π/8 – 9/4 sin-1(1/3)

(d) None of these

**Answer**

A

**Question. Area between the curve y = cos ^{2} x, x-axis and ordinates x = 0 and x = p in the interval (0, p) is **

(a) 2π/3

(b) 2π

(c) π

(d) π/2

**Answer**

D