MCQs For NCERT Class 12 Mathematics Chapter 8 Application of Integrals

Please refer to the MCQ Questions for Class 12 Mathematics Chapter 8 Application of Integrals with Answers. The following Application of Integrals Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

Application of Integrals Class 12 MCQ Questions with Answers

See below Application of Integrals Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. The area of the region bounded by the curve x² = 4 y and the straight line x = 4 y – 2 is

Question. The area bounded by the graph y =|[ x-3]|, the X-axis and the lines x = – 2 and x = 3 is ([·]× denotes the greatest integer function)
(a) 7 sq units
(b) 15 sq units
(c) 21 sq units
(d) 28 sq units

Question. The value of c for which the area of the figure bounded by the curve y=8x²-x⁵, the straight lines x = 1 and x c = and the x-axis is equal to 16/3 is
(a) 2
(b) √8- 17 
(c) 3
(d) -1

Question. Let f (x)= min{x+1 ,√(1-x)}, then area bounded by f (x) and X-axis is
(a) 1/6 sq unit
(b) 5/6 sq unit
(c) 7/6 sq units
(d) 11/6 sq units

Question. The area of the region bounded by the curve a⁴ y²= (2a-x)x⁵  is to that of the circle whose radius is a, is given by the ratio
(a) 4 : 5
(b) 5 : 8
(c) 2 : 3
(d) 3 : 2

Question. The area bounded by y=xe^|x|and lines|x| = 1, y=0 is
(a) 4 sq units
(b) 6 sq units
(c) 1 sq unit
(d) 2 sq units

Question. The slope of the tangent to a curve y f (x)at{ x,f (x)} is 2x +1. If the curve passes through the point (1,2), then the area of the region bounded by the curve, the X-axis and the line x = 1 is
(a) 5/6sq unit
(b) 6/5 sq units
(c) 1/6 sq unit
(d) 6 sq units

Question. The area bounded by the curve [x ]+ [y] = 4 in first quadrant is (where [· ] denotes the greatest integer function)
(a) 3 sq units
(b) 4 sq units
(c) 5 sq units
(d) 6 sq units

Question. The area enclosed by the curve 4 ≤ x²+ y² ≤ 2 
(| x|+|y|)  is
(a) 4 sq units
(b) 6 sq units
(c) 8 sq units
(d) 10 sq units

Question. The area enclosed by the curvess |y+x|≤1,|y- x|≤ 1 and 2×2+2y2=1 is
(a)(2+π/2) sq units
(b)(2-π/2) sq units
(c) (3+π/4) sq units
(d) (3-π/4) sq units

Question. Area of the region bounded by the curve y=25^x+1.6 and curve y=b.5^x+4  whose tangent at the point x = 1, makes an angle tan^-1 (40 log 5 ) with the X-axis is

Question. The area of the region bounded by the curves y= ex = log x and y= log x/ex is
(a) e²-5/4e
(b) e²+1/2e
(c) e²/2
(d) None of these

Question. The parabolas y²=4x and x²=4y divide the square region bounded the lines x= 4,y=4  and the coordinates axes. If S₁, S₂ and  S₃  are respectively the areas of these parts numbered from top to bottom, then
(a) S₃/s₂=1/2
(b) S₁/s₂=1
(c) S₁/s₂=1/2
(d) S₂/s₃=1

Question. The area of the region satisfying and max {| x|,| y|} ≤2 is
(a) (14+ 2log2) sq units
(b) 2log 3 sq units
(c) (1/4+ log3)sq unit
(d) None of these

Question. The area of the curve enclosed by the curve |x+y |+ |x-y |≤ 4,|x| ≤ 1, y ≥√ x²-2x+1 is
(a) 1 sq unit
(b) 4 sq units
(c) 2 sq units
(d) 6 sq units

Question. The area bounded by the curve

Question.

Question. The line y mx = bisects the area enclosed by the lines x =0,y=0 and x=3/2 and  the curve y = -x²+4x+1.
Then, the value m is equal to
(a) 13/6
(b) > 2
(c) < 1
(d) 2 (A,B)

Question. Area bounded by the line y = x, curve y f (x), f (x) >x,∀ x >1}and the lines x= 1,x=t is

Question. Area bounded by curves y=x²/4a and y=8ab/x²+4a² 

Question. The area bounded between the parabolas x²=y/4 and x²=9y  and the straight line y = 2 is 
(a) 20√2
(b) 10√2
(c) 20√2/3
(d) 10√

Question. The area (in square units) bounded by the curves y= √x, 2y-x+3=0, x- axis and lying in the first quadrant is
(a) 9
(b) 36
(c) 18
(d) 27/4

Question. The area bounded by the curves y^₂=4x and x²=4y is 
(a) 0
(b) 32/3
(c) 16/3
(d) 8/3

Question. The area of the region enclosed by the curves y =x, x=e, y=1/x and the positive X-axis is
(a) 1 sq unit
(b) 3/2sq unit
(c) 5/2 sq unit
(d) 1/2sq unit

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)16π sq units
(b) 4π sq units
(c) 32π sq units
(d) 24π sq units

Question. The area of the region bounded by the curve y = sin x between the ordinates x = 0, x = π/2 and the X-axis is
(a) 2 sq units
(b) 4 sq units
(c) 3 sq units
(d) 1 sq unit

Question. The area of the region bounded by the curve

(a) 8p sq units
(b) 20p sq units
(c)16p sq units
(d) 256p sq units

Question. The area of the region bounded by the Y-axis y = cos x and y = sin x, where 0 < x < π/2 is
(a) √2 sq units
(b) ( √2 + 1) sq units
(c) ( √2 -1) sq units
(d) (2 √2 -1) sq units

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

Question. The area of the region bounded by the curve x = 2y + 3 and the lines y = 1, y = -1 is
(a) 4 sq units
(b) (3/2) sq units
(c) 6 sq units
(d) 8 sq units

Question. The area of the region bounded by the ellipse

(a) 20π sq units
(b) 20 π² sq units
(c)16π² sq units
(d) 25π sq units

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

Question. The area of the region bounded by parabola y² = x and the straight line 2y = x is

Question. The area of the region bounded by the circle x² + y² = 1 is
(a) 2π sq units
(b) π sq units
(c) 3π sq units
(d) 4π sq units

Assertion and Reason
Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

Question. Statement I The area bounded by the curves y =x²-3 and y= kx = + 2 is least, if k = 0.
Statement II The area bounded by the curves y =x²-3 and y=kx+2 is √k²+20.

Question. Statement I The area of the ellipse 2x² + 3y² = 6     will be more than the area of the circle x²+ y²-2x+4y+4=0 
Statement II The length of the semi-major axis of ellipse 2x²+3y²=6 is more than the radius of the
circle x²+y²-2x+4y+4=0.

Question. Statement I Area enclosed by the curve| x |+ |y| =  2 is 8 units.
Statement II |x |+|y| = 2 represents a square of side length 8 units.

Question. Consider the curve f (x)= y= e^x3
Statement I Area enclosed by the curve f (x) between the lines x= a, x= b and x-axis 

Statement II f (x) is an increasing function.