CBSE Class 12 Mathematics Application of Integrals MCQs

Question. The area of the region bounded by the curve y = x + 1 and the lines x = 2 and x = 3, is
(a) 7/2 sq units
(b) 9/2 sq units
(c) 11/2 sq units
(d) 13/2 sq units
Answer : A

Question. The area of the region bounded by x² y = 4 , y = 2, y = 4 and the Y-axis in the first quadrant is
(a) 8/3 ( 4 + √2) sq units
(b) 8/3 ( 4 - √2) sq units
(c) 8( 4 + √2) sq units
(d) None of these
Answer : B

Question. Area of the region bounded by the curve y² = 4x , Y-axis and the line y = 3 is
(a) 2 sq units
(b) 9/4 sq units
(c) 9/3 sq units
(d) 9/2 sq units
Answer : B

Question. Area bounded by the curve y x e = log , x = 0, y ≤ 0 and X-axis is
(a) 1 sq unit
(b) 2 sq units
(c) 3 sq units
(d) 4 sq units
Answer : A

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. If we draw a rough sketch of the curve y = √x - 1 in the interval [1, 5], then the area under the curve and between the lines x = 1 and x = 5 is
(a) 16/9 sq units
(b) 8/3 sq units
(c) 16/3 sq units
(d) None of these
Answer : C

Question. A manufacturer’s marginal revenue function is given byMR = 300 - 3x + 4/3 x² . If the production is increased from 5 to 10 units, then increase in revenue is
(a) ₹ 1935
(b) ₹ 1776.38
(c) ₹ 1940
(d) ₹ 1825
Answer : B

Question. The demand function for a commodity is given by p = 30 + 5x - x². When market price is ₹ 5, then consumer’s surplus (CS) is
(a) 17.5
(b) 42.5
(c) 20.83
(d) 39
Answer : C

Question. Area bounded by the curve y = x³, the X-axis and the coordinates x = - 2 and x = 1 is
(a) - 9 sq unit
(b) -15/4 sq unit
(c) 15/4 sq units
(d) 17/4 sq units
Answer : D

Question. The area bounded by the curve y = x|x|, X-axis and the coordinates x = - 1 and x = 1 is given by
(a) 0
(b) 1/3 sq unit
(c) 2/3/sq unit
(d) 4/3 sq units
Answer : C

Case Based MCQs

Consider a square root curve y = √3x and the straight line 3x = 2y + 3.

On the basis of the above information, solve the following questions.

Question. The intersection point of curve and line is
(a) (- 3, 3)
(b) (3, 3)
(c) (3, - 3)
(d) ( - 3, - 3)
Answer : B

Question. The area between the curves is
(a) 1/3 sq unit
(b) 2 sq unit
(c) 3 sq unit
(d) 3/2 sq unit
Answer : C

Question. The area of region bounded by the curve y = x and the lines x =1 and x = √2 is
(a) 2(2√2 - 1) sq units 
(b) 1/3 (2√2 - 1) sq units
(c) 2/3 (2√2 - 1) sq units
(d) None of the above
Answer : C

Question. The area of region bounded by the lines
3x = 2y + 3, y =1 and y = 3 is
(a) 10/3 sq units
(b) 5/3 sq units
(c) 14/3 sq units
(d) 11/3 sq units
Answer : C

The marginal cost (MC) of producing x units of a commodity in a day is given asMC = 14x - 1720. The selling price is fixed at ₹ 11 per unit and the fixed cost ₹ 1900 per day.

On the basis of the above information, solve the following questions.

Question. Cost function (C) is
(a) 7x² - 1720 + 1900 
(b) 13x² - 1000 + 1800
(c) 13x² - 1000 + 1300
(d) 9x² - 1000 + 1700
Answer : A

Question. When x =1, then value of cost function is
(a) 311
(b) 187
(c) 410
(d) 176
Answer : B

Question. The revenue function (R) is
(a) 11x
(b) 9x
(c) 17x
(d) 20x
Answer : A

Question. The profit function (P) is
(a) - 5x² + 1731x - 1900 
(b) - 6x² + 1530x - 1300
(c) - 7x² + 1731x - 1900 
(d) - 5x² + 1530x + 1200
Answer : C

Question. When x = 2 , then profit is
(a) ₹ 1600
(b) ₹ 1534
(c) ₹ 1320
(d) ₹ 1420
Answer : B

Consumer surplus and producer surplus. 

The above graph showing the demand and supply curves of a tyre manufacturer company are linear. ‘ABC’ tyre manufacturer sold 25 units every month when the price of a tyre was ₹ 20000 per units and ‘ABC’ tyre manufacturer sold 125 units every month when the prize dropped to ₹ 15000 per unit. When the price was ₹ 25000 per unit, 180 tyres were, available per month for sale and when the price was
only ₹ 15000 per unit, 80 tyres remained.

On the basis of the above information, solve the following questions.

Question. The demand function D(x) is
(a) - 40x + 21000
(b) - 50x + 21250
(c) - 60x + 20000
(d) - 65x + 20000
Answer : B

Question. The supply function S(x) is
(a) 100x + 7000
(b) 110x + 6500
(c) 105x + 8000
(d) 90x + 6500
Answer : A

Question. The equilibrium point is
(a) (95, 16500)
(b) (92, 16000)
(c) (90, 17000)
(d) (97, 17200)
Answer : A

Question. The consumer surplus (CS) is
(a) ₹ 210720
(b) ₹ 227065
(c) ₹ 225625
(d) ₹ 2152729
Answer : C

Question. The producer surplus (PS) is
(a) ₹ 467230
(b) ₹ 451250
(c) ₹ 441623
(d) ₹ 468564
Answer : B

Consider the following equations of the parabola y² = 6x and the straight line y = 3x.

On the basis of the above information, solve the following questions.

Question. The point of intersection of given curves are
(a) (0, 0) and (- 1/3,  2/3)
(b) (0, 0) and (2, 1)
(c) (0, 0) and  (2/3, 2)
(d) (0, 0) and (3/2, - 2)
Answer : C

Question. The area of region bounded by the line between points O(0, 0), A (2/3, 2) and X-axis is
(a) 2/3 sq unit
(b) 3/2 sq unit
(c) 1/3 sq unit
(d) None of these
Answer : A

Question. The area of region bounded by the parabola between points O(0, 0), A(2/3, 2) and X-axis is
(a) 8/7 sq units
(b) 8/9 sq units
(c) 9/8 sq units
(d) None of these
Answer : B

Question. The area of region between parabola and the line is
(a) 9/8 sq unit
(b) 8/9 sq unit
(c) 8/7 sq unit
(d) 2/9 sq unit
Answer : D