# MCQs for Mathematics Class 12 with Answers Chapter 8 Application of Integrals

Students of class 12 Mathematics should refer to MCQ Questions Class 12 Mathematics Application of Integrals with answers provided here which is an important chapter in Class 12 Mathematics NCERT textbook. These MCQ for Class 12 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 12 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 12 Mathematics examination

**Chapter 8 Application of Integrals MCQ with Answers Class 12 Mathematics**

MCQ Questions Class 12 Mathematics Application of Integrals provided below have been prepared by expert teachers of grade 12. These objective questions with solutions are expected to come in the upcoming Standard 12 examinations. Learn the below provided MCQ questions to get better marks in examinations.

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

(a) √2 sq units

(b) (√2 + 1) sq units

(c) (√2 – 1) sq unit

(d) (2√2 – 1) sq units

## Answer

C

**Question.** **The area between x =y ^{2} and x = 4 is divided into two equal parts by the line x a = , the value of a is**

(a) (2 )

^{2/3}

(b) √2

(c) (4)

^{4/3}

(d) (4 )

^{2/3}

## Answer

D

**Question. The area of the region bounded by the curve y ^{2}=4x and the line x = 3 is**

(a) 2 √3 sq units

(b) 8 √3 sq units

(c) 4 √3 sq units

(d) 3 √3 sq units

## Answer

B

**Question.** **The area of the region bounded by y ^{2}=9x, x=2,x=4 and the X-axis in the first quadrant is **(a) 16 sq units

(b) 4 √2 sq units

(c) 4 (4- √2 sq units

(d) 4 (4+ √2) + sq units

## Answer

C

**Question.** **Sketch the graph of y = + |x+3 |and the value of**

(a) 9 sq units

(b) 9/2 sq units

(c) 3 sq units

(d) 11 sq units

## Answer

A

**Question.** **The area bounded by the curve y = x| x|, -axis and the coordinates x = -1 and x = 1 is given by**

(a) 0

(b) 1/3

(c) 2/3

(d) 4/3

## Answer

C

**Question.** **Area lying in the first quadrant and bounded by the circle x2 +y ^{2}=4 and the lines x = 0 and x = 2 is**

(a) π units

(b) π/2 units

(c) π/3 units

(d) π/4 units

## Answer

A

**Question.** ** Draw a rough sketch of the curve y= √x-1 in the interval[1,5]. The area under the curve and between the lines x = 1 and x = 5 is **

(a) 4/3 sq units

(b) 8/3 sq units

(c) 16/3 sq units

(d) None of these

## Answer

C

**Question.** **The area of the region bounded by the curve ay ^{2} =x^{3},the Y-axis and the lines y = a and y= 2a is**

## Answer

A

**Question.** **Using integration, the area of the region bounded by the line 2y= 5x+ 7, x axis and the lines x = 2 and x = 8 is**

(a) 96 sq units

(b) 72 sq units

(c) 84 sq units

(d) None of these

## Answer

A

**Question.** **The area of the region bounded by the curve xy- 3x- 2y -10=0, X-axis and the lines x=3,x=4 **

(a) 3 sq units

(b) 3 + 16 log 2 sq units

(c) 16 log 2 sq units

(d) None of these

## Answer

B

**Question.** **The area bounded by the curve x=2- y-y ^{2} and Y-axis is**

(a) 3/2 sq units

(b) 5/2 sq units

(c) 9/2 sq units

(d) None of these

## Answer

C

**Question.** **The area bounded by the curve |x| +y = 1 and axis of x is**

(a) 1 sq unit

(b) 2 sq units

(c) 8 sq units

(d) None of these

## Answer

A

**Question.** **The area bounded by the curves f (x)= ce ^{x}(c>0), the X-axis and the two ordinates x= p = and x= q = , is proportional t**o

(a) f (p) f(q)

(b) |f (p)- f(q)|

(c) f (p) +f(q)

(d) √f(p f(q)

## Answer

B

**Question.** **The area bounded by x=1, x=2, xy =1 and X-axis is**

(a) (log )2 sq unit

(b) 2 sq units

(c) 1 sq unit

(d) None of these

## Answer

A

**Question.** **The area included between the curves y=1/x2+1 and X-axis is**

(a)π/2 sq units

(b) π sq units

(c) 2π sq units

(d) None of these

## Answer

B

**Question. The area between the curve y=4+3x-x2 and X-axis is**

(a) 125/6 sq units

(b) 125/3 sq units

(c) 125/2 sq units

(d) None of these

## Answer

A

**Question.** **If the area above X-axis, bounded by the curves y=2 ^{kx} and x = 0 and x = 2 is 3/log2, then the value of k is**

(a) 1/2

(b) 1

(c) -1

(d) 2

## Answer

B

**Question.** **The area bounded by y =tan-1 x, x=1 and X- axis is**

## Answer

B

**Question.** **Area enclosed between the curve y ^{2}(2a-x)= x^{3} and line x= 2a above X-axis is**

(a)πa

^{2}sq units

(b) 3πa

^{2}/2 sq units

(c) p πa

^{2}sq units

(d) 32a

^{2}sq units

## Answer

B

**Question.** **The area bounded by the curve y = sin2 x and lines x= π/2,x= π and X-axis is**

(a) π/2 sq unit

(b) π/4 sq unit

(c) π/8 sq unit

(d) None of these

## Answer

B

**Question.** **The area bounded by the curve y x y = = sec ^{2} x, y=0 0 and |x| =p/3 is**

(a) √3 sq units

(b) √2 sq units

(c) 2 √3 sq units

(d) None of these

## Answer

C

**Question.** **The area bounded by y= sin ^{-1} x, x=1/√2 and X-axis is**

## Answer

D

**Question.** **The area bounded by y= e ^{-x}, X- axis and x≥ 0 is**

(a) 1

(b) 2

(c) 1/e

(d) e

## Answer

A

**Question. The area bounded by the curve y = f(x)log _{e} x, the X-axis and the straight line x = e is**

(a)1- 1/e sq unit

(b) 1 sq unit

(c) 1-1/e sq unit

(d) 1+1/e sq unit

## Answer

B

**Question.** **The area of the smaller part of the circle x ^{2} +y^{2}=a^{2} cut-off by the line x=a/√2 is**

## Answer

B

**Question.** **The area bounded by y =x ^{3}-4x and X-axis is**

(a) 5

(b) 9

(c) 8

(d) 12

## Answer

C

**Question. Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle** **x ^{2} + y^{2} = 32 is**

(a) 16π sq units

(b) 4π sq units

(c) 32π sq units

(d) 24 sq units

## Answer

B

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

(a) 4/3 sq units

(b) 7/2 sq units

(c) 17/2 sq units

(d) 16/3 sq units

## Answer

C

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

(a) 2 sq units

(b) 4 sq units

(c) 3 sq units

(d) 1 sq unit

## Answer

A

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

(a) 4/3 (4π – √3h sq. units

(b) 4/3 (4π + √3h sq. units

(c) 4/3 (8π – √3h sq. units

(d) 4/3 (8π + √3h sq. units

## Answer

C

**Question. The area of the region bounded by the curve x = 2y + 3 and the 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 of the region bounded by the parabola y ^{2} = x and the straight line 2y = x is**

(a) 4/3 sq. units

(b) 1 sq. unit

(c) 2/3 sq. unit

(d) 1/3 sq. unit

## Answer

A

**Question. The area of the curve y = sin x between 0 and π is**

(a) 2 sq units

(b) 4 sq units

(c) 12 sq units

(d) 14 sq units

## Answer

A

**Question. The area enclosed by the circle x ^{2} + y^{2} = 2 is equal to **

(a) 4π sq units

(b) 2 2r sq units

(c) 4π2 sq units

(d) 2π sq units

## Answer

D

**Question. The area of the region bounded by the curve ay ^{2} = x^{3}, the y-axis and the lines y = a and y = 2a is**

(a) 3 sq units

(b) 3/5 a2 |2X2

^{2/3}–1 | sq units

(c) 3/5 a |2

^{2/3}–1 | sq units

(d) 1 sq unit

## Answer

B

**Question. The area bounded by the curve y = |sin x|, x-axis and ordinates x = p and x = 10p is equal to**

(a) 8 sq. units

(b) 10 sq. units

(c) 18 sq. units

(d) 20 sq. units

## Answer

C

**Question. The area enclosed by the curve x = 3 cos t, y = 2 sin t is**

(a) 4π sq units

(b) 6π sq units

(c) 14π sq units

(d) 7π sq units

## Answer

B

**Question. The area bounded by the curve y = x |x|, x-axis and the ordinates x = – 1 and x = 1 is given by**

(a) 0 sq. units

(b) 1/3 sq. unit

(c) 2/3 sq. unit

(d) 4/3 sq. units

## Answer

C

**Question. The area enclosed by the ellipse x2/a2 + y2/b2 =1+ = is equal to **

(a) π2 ab sq units

(b) π ab sq units

(c) πa2 b sq units

(d) π ab2 sq units

## Answer

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

(a) r sq. units

(b) π/2 sq. units

(c) π/3 sq. units

(d) π/4 sq. units

## Answer

A

**Question. The area of the region bounded by the curve y = x ^{2} and the line y = 16 is**

(a) 37/3sq units

(b) 256/3 sq units

(c) 64/3sq units

(d) 128/3sq units

## Answer

B

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

(a) 3/8 sq unit

(b) 5/8 sq unit

(c) 7/8 sq unit

(d) 9/8 sq units

## Answer

D

**Question. The area of the region bounded by the curves x = at2 and y = 2at between the ordinate corresponding to t = 1 and t = 2 is**

(a) 56/3 a2 sq units

(b) 40/3 a2 sq units

(c) 5π sq units

(d) None of these

## Answer

A

**Question. The area of a minor segment of the circle x2 + y2 = a2 cut off by the line x = a/2 is**

(a) a2/12(4π -3√3) sq units

(b) a2/4(4π -3√3) sq units

(c) a2/12(3π -4) sq units

(d) None of these

## Answer

A

**Question. The area of the region bounded by the curve y = x ^{3} and y = x + 6 and x = 0 is**

(a) 7 sq units

(b) 6 sq units

(c) 10 sq units

(d) 14 sq units

## Answer

C

**Question. The area under the curve y = 2√x included between the lines x = 0 and x = 1 is**

(a) 4 sq units

(b) 3 sq units

(c) 4/3 sq units

(d) None of these

## Answer

C

**Question. The area under the curve y = √(a2 – x ^{2}) included between the lines x = 0 and x = a is**

(a) πa2/4 sq units

(b) a2/4 sq units

(c) πa2 sq units

(d) 4π sq units

## Answer

A

**Question. The area of the region bounded by the curve y = √(16 – x ^{2}) and x-axis is**

(a) 8 p sq units

(b) 20π sq units

(c) 16π sq units

(d) 256π sq units

## Answer

A

**Question. The area of the region bounded by the triangle whose vertices are (–1, 1), (0, 5) and (3, 2) is**

(a) 15/2 sq units

(b) 15 sq units

(c) 4 sq units

(d) 10 sq units

## Answer

A

**Question. The area of the region bounded by the curve y2 = 9x, y = 3x is**

(a) 1 sq unit

(b) 1/2sq unit

(c) 4 sq units

(d) 14 sq units

## Answer

B

**Question. The area of the region bounded by the curve x = y2, y-axis and the line y = 3 and y = 4 is ___________. **

## Answer

**37/3 sq. units**

**Question. The area bounded by the curve y = sin x, x-axis and the ordinates x = 0 and x = p is ___________. **

## Answer

**2 sq. units**

**Question. The area of the region bounded by the curve y = x – x2 between x = 0 and x = 1 is ___________. 1/6 sq. unit**

## Answer

**Question. The area of the region bounded by the ellipse x2/25 + y2/16 =1 is ___________. 20p sq. units**

## Answer

We hope the above multiple choice questions for Class 12 Mathematics for Chapter 8 Application of Integrals provided above with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Application of Integrals is an important chapter in Class 12 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 12 students. Please go through these and let us know if you have any feedback in the comments section.