Please refer to MCQ Questions Chapter 8 Application of Integrals Class 12 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 12 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 12 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 7 Application of Integrals in Class 12 Mathematics provided below to get more marks in exams.

**Chapter 8 Application of Integrals MCQ Questions**

**Question. The area included between the parabolas y ^{2} = 4a (x + a) and y^{2} = 4b(x – a), b > a > 0, is**

**Answer**

B

**Question. The area bounded by the y-axis, y = cos x and y = sin x when 0 ≤ x ≤ π/2 is **

(a) 2(√2-1)

(b) √2 – 1

(c) √2 + 1

(d) √2

**Answer**

B

**Question. The ratio in which the area bounded by the curves y ^{2} = 12x and x^{2} = 12y is divided by the line x = 3 is **

(a) 15 : 49

(b) 13 : 37

(c) 15 : 23

(d) 17 : 50

**Answer**

B

**Question. The area bounded by the curve y = sin x from 0 to π and x-axis is ______ sq. units. **

(a) 2

(b) 4

(c) 6

(d) 8

**Answer**

A

**Question. The area bounded by the line y = x, x-axis and lines x = – 1 to x = 2, is **

(a) 0 sq. unit

(b) 1/2 sq. units

(c) 3/2 sq. units

(d) 5/2 sq. units

**Answer**

D

**Question.** Area lying in the first quadrant and bounded by circle x^{2} + y^{2 }= 4 and the lines x = 0 and x = 2 is

(A) p

(B) π/2

(C) π/3

(D) π/4

**Answer**

A

**Question.****Area of the region bounded by the curve y ^{2} =4x, y-axis and the line y = 3 is**

(A) 2

(B) 9/4

(C) 9/3

(D) 9/2

**Answer**

B

**Question.** Smaller area enclosed by the circle x^{2 }+ y^{2} = 4 and the line x + y = 2

(A) 2(π − 2)

(B) π − 2

(C) 2π − 1

(D) 2(π + 2)

**Answer**

B

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

(a) 2/21

(b) 21

(c) 21/2

(d) 9/2

**Answer**

C

**Question. Area bounded by the lines y = |x| – 2 and y = 1 – |x – 1| is equal to **

(a) 4 sq. units

(b) 6 sq. units

(c) 2 sq. units

(d) 8 sq. units

**Answer**

A

**Question. Area enclosed between the curves y = sin ^{2}x, y = cos^{2}x and y = 0 in the interval [0, π/2] is **

(a) 1/3(2π – 1) sq. units

(b) 1/2 (π – 3) sq. units

(c) 1/4(π – 2) sq. units

(d) (2π + 3) sq. units

**Answer**

C

**Question. The area under the curve y = x2 and the line x = 3 and x axis is ______ sq. units. **

(a) 0

(b) 1

(c) 3

(d) 9

**Answer**

D

**Question. Area of triangle whose two vertices formed from the x-axis and line y = 3 – |x| is **

(a) 9 sq. units

(b) 9/4 sq. units

(c) 3 sq. units

(d) None of these

**Answer**

D

**Question.** The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ p/2 is

(A) 2 sq. units

(B) ( 2 + 1) sq. units

(C) ( 2 − 1) sq. units

(D) (2 2 − 1) sq. units

**Answer**

C

**Question. Using the method of integration the area of the triangle ABC, coordinates of whose vertices are A (2, 0), B (4, 5) and C (6, 3) is **

(a) 2

(b) 4

(c) 7

(d) 8

**Answer**

C

**Question. The area lying above x-axis and included between the circle x ^{2} + y^{2} = 8x and inside of parabola y^{2} = 4x is **

(a) 1/3(2+3π) sq. units

(b) 2/3 (4+3π) sq. units

(c) 6 + 3π sq. units

(d) 4/3 (8+3π) sq. units

**Answer**

D

**Question. AOB is a positive quadrant of the ellipse x ^{2}/a^{2} + y^{2}/b^{2} = 1 , where OA = a, OB = b. The area between the arc AB and chord AB of the ellipse is **

(a) π ab sq. units

(b) (π – 2)ab sq. units

(c) ab(π+2)/2 sq. units

(d) abab(π-2)/2 sq. units

**Answer**

D

**Question.** The area of the region bounded by the curve x^{2} = 4y and the straight-line x = 4y – 2 is

**Answer**

D

**Question.** Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 = 32 is

(A) 16p sq. units

(B) 4p sq. units

(C) 32p sq. units

(D) 24p sq. units

**Answer**

B

**Question.****Area of the region bounded by the curve y = cos x** **between x = 0 and x = p is**

(A) 2 sq. units

(B) 4 sq. units

(C) 3 sq. units

(D) 1 sq. unit

**Answer**

A

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

**Answer**

A

**Question.****The area of the region bounded by the curve x = 2y + 3 and the y 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. Area lying between the curve y^{2} = 4x and y = 2x**(a) 2/3

(B) 1/3

(C) 1/4

(D) 3/4

**Answer**

B

**Question.****Area bounded by the curve y = x ^{3}, the x-axis and the ordinates x = −2 and x = 1 is**

(A) −9

(B) − 15/4

(C) 15/4

(D) 17/4

**Answer**

C

**Question.** The area of the circle x^{2} + y^{2} = 16 exterior to the**parabola y ^{2} = 6x is**

**Answer**

C

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

**Answer**

A

**Question.** The area of the region bounded by the ellipse

(A) 20p sq. units

(B) 20p^{2} sq. units

(C) 16p^{2} sq. units

(D) 25p sq. units

**Answer**

A

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

(A) 2p sq. units

(B) p sq. units

(C) 3p sq. units

(D) 4p sq. units

**Answer**

B

**Case-based MCQs**

**Read the following text and answer the following questions on the basis of the same:**

The bridge connects two hills 100 feet apart. The arch on the bridge is in a parabolic form. The highest point on the bridge is 10 feet above the road at the middle of the bridge as shown in the figure.

**Question.** The equation of the parabola designed on the**bridge is**

(A) x^{2} = 250y

(B) x^{2} =−250y

(C) y^{2} = 250x

(D) y^{2} = 250y

**Answer**

A

**Question.** The value of the integral

(A) 1000/3

(B) 250/3

(C) 1200

(D) 0

**Answer**

A

**Question.****The integrand of the integral**

**function.**(A) Even

(B) Odd

(C) Neither odd nor even

(D) None of these

**Answer**

A

**Question.****The area formed by the curve x ^{2} = 250y, x-axis,**

**y = 0 and y = 10 is**

(A) 1000 √2/3

(B) 4/3

(C) 1000/3

(D) 0

**Answer**

C

**Question.****The area formed between x ^{2} = 250y, y-axis, y = 2 and y = 4 is**

(A) 1000/3

(B) 0

(C) 1000 √2/3

(D) None of these

**Answer**

D

**Read the following text and answer the following questions on the basis of the same:**

In the figure O(0, 0) is the centre of the circle. The line y = x meets the circle in the first quadrant at the point B.

** Question. The equation of the circle is _______.**(A) x

^{2}+ y

^{2}= 4 √2

(B) x

^{2}+ y

^{2}= 16

(C) x

^{2}+ y

^{2}= 32

(D) (x – 4 √2 )2 + 0

**Answer**

C

** Question. The co-ordinates of B are _______.**(A) (1, 1)

(B) (2, 2)

(C) (4 √2, 4 √2)

(D) (4, 4)

**Answer**

D

**Question.****Area of DOBM is _______ sq. units**

(A) 8

(B) 16

(C) 32

(D) 32 p

**Answer**

A

**Question.****Ar (BAMB) = _______ sq. units**

(A) 32 π

(B) 4π

(C) 8

(D) 4π – 8

**Answer**

D

**Question.** Area of the shaded region is _______ sq. units.

(A) 32 π

(B) 4π

(C) 8

(D) 4π – 8

**Answer**

B

**Read the following text and answer the following questions on the basis of the same:**

A farmer has a square plot of land. Three of its boundaries are x = 0, y = 0 and y = 4. He wants to divide this land among his three sons A, B and C as shown in figure.

** Question. Equation of PQ is _.**(A) x = 0

(B) x = 2

(C) x = 4

(d) y = 4

**Answer**

C

**Question.** The co-ordinates of Q are _______.

(A) (2, 2)

(B) (4, 4)

(C) (1, 1)

(D) (5, 5)

**Answer**

B

**Question.** Area received by son B is _______ sq. units.

(A) 4

(B) 16

(C) 16/3

(D) 8/3

**Answer**

C

** Question. Area received by son A is _______ sq. units.**(A) 4

(B) 16

(C) 16/3

(D) 8/3

**Answer**

C

** Question. Total area of the square field is _______ sq. units.**(A) 4

(B) 16

(C) 16/3

(D) 8/3

Ans. Option (B) is correct.

**Answer**

**Assertion – Reason Type Questions :**

**(a) Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.****(b) Assertion is correct, Reason is correct; Reason is not a correct explanation for Assertion****(c) Assertion is correct, Reason is incorrect****(d) Assertion is incorrect, Reason is correct.**

**Question. Assertion : The area bounded by the circle y = sin x and y = –sin x from 0 to π is 3 sq. unit. ****Reason :The area bounded by the curves is symmetric about x-axis.**

**Answer**

D

**Question. Assertion : The area bounded by the curves y ^{2} = 4a^{2}(x – 1) and lines x = 1 and y = 4a is 16 a/3 sq. units. **

**Reason : The area enclosed between the parabola y**

^{2}= x^{2}– x + 2 and the line y = x + 2 is 8/3 sq. units.**Answer**

C

**Question. Assertion : The area bounded by the curve y = cos x in I quadrant with the coordinate axes is 1 sq. unit. ****Reason : **

**Answer**

A

**Question. Assertion : The area bounded by the circle x ^{2} + y^{2} = a^{2} in the first quadrant is given by **

**Reason :The same area can also be found by **

**Answer**

B

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