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CBSE Questions for Class 12 Commerce Maths Application Of Integrals Quiz 9 - MCQExams.com

The area of the region in 1st quadrant bounded by the yaxis,y=x4,y=1+xandy=2x
  • 23sq.units
  • 83sq.units
  • 113sq.units
  • 136sq.units
The area of the region bounded by x2+y22x3=0 and y=|x|+1 is
  • π21sq.units
  • 2πsq.units
  • 4πsq.units
  • π2sq.units
The value of the parameter a such that the area bounded by y=a2x2+ax+1, coordinate axes and the line x=1 attains its least value, is equal to 
  • 14
  • 12
  • 34
  • 1
Which of the following have the same bounded area
  • f(x)= sinx,g(x)= sin2x, where 0x10π
  • f(x)= sinx,g(x)=| sinx|, where 0x20π
  • f(x)=| sinx|,g(x)= sin3x, where 0x10π
  • f(x)= sinx,g(x)= sin4x, where 0x10π
The area bounded by y=sec1xy=cosec1x and line x1=0 is
  • log(3+22)π2sq.units
  • π2log(3+22)sq.units
  • πloge3sq.units
  • None of these
Let A(k) be the are bounded by the curves y=x23 and y=kx+2.
  • The range of A(k) is [1053,)
  • The range of A(k) is [2053,)
  • If function kA(k) is defined by for k[2,), then A(k) is many-one function.
  • The value of k for which area is minium is 1.
If the curve y=ax12+bx passes through the point (1,2) and lies above the xaxis for 0x9 and the area enclosed by the curve, the xaxis and the line x=4 is 8 sq.units. Then
  • a=1
  • b=1
  • a=3
  • b=1
The area of the closed figure bounded by x=1,x=2 and y=x2+2,x1 and y=2x1,x>1 and the abscissa axis is 
  • 163sq.units
  • 103sq.units
  • 133sq.units
  • 73sq.units
The area of the region whose boundaries are defined by the curves y=2 cosx,y=3 tanx and the yaxis is 
  • 1+3ln(23)sq.units
  • 1+32ln33ln2sq.units
  • 1+32ln3ln2sq.units
  • ln3ln2sq.units
A tangent having slope of 43 to the ellipse x218+y232=1 intersects the major and minor axes at points A and B respectively. If C is the center of the ellipse , then area of the triangle ABC is
  • 12 sq. units
  • 24 sq. units
  • 36 sq. units
  • 48 sq. units
The area bounded by the circles x2+y2=1,x2+y2=4 and the pair of lines 3(x2+y2)=4xy, is equal to
  • π2
  • 5π2
  • 3π
  • π4
The area enclosed by the curves xy2=a2(ax) and (ax)y2=a2x is
  • (π2)a2 sq. units
  • (4π)a2 sq. units
  • πa23 sq. units
  • None of these
The sequence S0,S1,S2.... forms a G.P with common ratio
  • eπ2
  • eπ
  • eπ
  • eπ2
The area of the loop of the curve, ay2=x2(ax) is 
  • 4a2 sq. units
  • 8a215 sq. units
  • 16a29 sq. units
  • none of these
The area enclosed by the circle x2+y2=2 is equal to
  • 4π sq units
  • 22π sq\ units$$
  • 4π2sq units
  • 2πsq units
The area of the region bounded by the circle x2+y2=1 is
  • 2πsq units
  • πsq units
  • 3πsq units
  • 4πsq units
The area of the region bounded by the curve y=sinx between the ordinates x=0,x=π2 and the x-axis is
  • 2 sq units
  • 4 sq units
  • 3 sq units
  • 1 sq units
The area of the region bounded by the curve x=2y+3 and the y lines. y=1 and y=1 is
  • 4 sq units
  • 32 sq units
  • 6 sq units
  • 8 sq units
The area of the region bounded by the curve x2=4y and the straight line x=4y2 is
  • 38sq units
  • 58sq units
  • 78sq units
  • 98sq units
The area of the region bounded by parabola y2=x and the straight line 2y=x is
  • 43sq units
  • 1sq units
  • 23sq units
  • 13sq units
The area of the region bounded by the curve y=x+1 and the lines x=2 and x=3 is
  • 72sq units
  • 92sq units
  • 112sq units
  • 132sq units
The area of the region bounded by the curve y=16x2 and x-axis is
  • 8π sq.units
  • 20π sq.units
  • 16π sq.units
  • 256π sq.units
The area of the region bounded by the ellipse x225+y216=1 is
  • 20πsq units
  • 20π2sq units
  • 16π2sq units
  • 25πsq units
Area of the region in the first quadrant enclosed by the x-axis, the line y=x and the circle x2+y2=32 is
  • 16π squnits
  • 4π squnits
  • 32π squnits
  • 24π squnits
Area lying in the first quadrant and bounded by the circle x2+y2=4 and the lines x=0 and x=2 is
  • π
  • π2
  • π3
  • π4
Area of the region bounded by the curve y2=4x,y axis and the line y=3 is 
  • 2
  • 94
  • 93
  • 92
I: The area bounded by the curves y=sinx, y=cosx and Y-axis is 21 sq. units.
II: The area bounded by y=cosx, y=x+1, y=0 is 3/2 sq. units.

Which of the above statement is correct?
  • Only I
  • Only II
  • Both I and II
  • Neither I nor II.
Arrangement of the following areas between the curves is descending order:
A:y2=4x, x2=4y
B. y=x, y=x3
C. y2=8x,y=2x
D. y=x, y=x2
  • A,B,C,D
  • A,C,B,D
  • D,B,C,A
  • D,C,B,A
Match the following:
List-IList-II
Area of the region bounded by y=|5sinx| from x=0 to x=4π and x-axisa. 3/2
The area bounded by y= cosx in [0,2π] and the X-axisb. 21
The area bounded by y=sinx,y=cosx and the y-axisc. 4
The area bounded by y=cosx,y=x+1,y=0d. 40
The correct match is
  • a,b,c,d
  • d,b,a,c
  • d,c,b,a
  • d,a,b,c
The area bounded by the y=|sinx|, x-axis and the lines |x|=π is
  • 2 square units
  • 1 square units
  • 4 square units
  • None of these
The area of the region bounded by the curves y=exlogx and y=logxex is:
  • e254e
  • e54
  • e45
  • e414e
The area (in square units) bounded by the curves y=x, 2yx+3=0, Xaxis, and lying in the first quadrant is:
  • 36
  • 18
  • 274
  • 9
Match the following:
List-IList-II
Area of region bounded by y=2xx2 and xaxisa. 13
2. Area of the region {(x,y):x2y|x|}b. 12
3. Area bounded by y=x and y=x3c. 23
4. Area bounded by y=x|x|, x-axis and x=1, x=1d. 43
The correct match for 1 2 3 4 is
  • 1b,2c.3d,4a
  • 1c,2d,3a,4b
  • 1d,2a,3b,4c
  • 1a,2b,3c,4d
The area enclosed by the curves y=sinx+cosx and y=|cosxsinx |over the interval [0,π2]is

  • 4 (21)
  • 22(21)
  • 2 (2+1)
  • 22(2+1)
Area of the figure bounded by the lines y=x,x[0,1], y=x2, x[1,2] and y=x2+2x+4,x0,2] is:
  • 107
  • 35
  • 43
  • 193

The area bounded by the parabolas y2=5x+6 and x2=y
  • 195
  • 215
  • 235
  • 275
The ratio of the areas into which the circle x2+y2=64 is divided by the parabola y2=12x is:
  • 4π38π+3
  • 4π+38π3
  • 4π38π3
  • 4π+38π+3
The area bounded by the parabola y2=4a(x+a) and y2=4a(xa) is
  • 163a2
  • 83a2
  • 43a2
  • 23a2
sinx & cosx meet each other at a number of points and develop symmetrical area. Area of one such region is
  • 42
  • 32
  • 22
  • 2
Let f(x)=min, then the area bounded by \mathrm{y}={f}({x}) and {x}-axis is:
  • \dfrac76
  • \dfrac56
  • \dfrac16
  • \dfrac{11}{6}
Area bounded by the curves \displaystyle \frac{y}{x}=\log x and \displaystyle \frac{y}{2}=-x^{2}+x equals:
  • 7/12
  • 12/7
  • 7/6
  • 6/7
The area bounded by the curves \mathrm{y}=2^{\mathrm{x}},\mathrm{y}=2\mathrm{x}-\mathrm{x}^{2} between the lines \mathrm{x}=0,\ \mathrm{x}=2 is
  • \displaystyle \frac{3}{\log 2}-\frac{4}{3} sq. units
  • \displaystyle \frac{3}{\log 2}+\frac{4}{3} sq.units
  • 3-4\log 2 sq. units
  • \displaystyle \frac{4}{3}-\frac{3}{\log 2} sq.units
The area bounded by two branches of the curve (y-x)^{2}=x^{3} \& x=1 equals
  • 3/5
  • 5/4
  • 6/5
  • 4/5
Area bounded by x^{2}=4ay and y=\displaystyle \frac{8a^{3}}{x^{2}+4a^{2}} is:
  • \displaystyle \frac{a^{2}}{3}(6\pi-4)
  • \displaystyle \frac{\pi a^{2}}{3}
  • \displaystyle \frac{a^{2}}{3}(6\pi+4)
  • 0
Area bounded by the curves satisfying the conditions \displaystyle \frac{x^{2}}{25}+\frac{y^{2}}{36}\leq 1\leq\frac{x}{5}+\frac{y}{6} is given by
  • 15(\displaystyle \dfrac{\pi}{2}+1) sq.units
  • \dfrac{15}{4}(\dfrac{\pi}{2}-1) sq.units
  • 30(\pi-1) sq.unit
  • \displaystyle \dfrac{15}{2}(\pi-2) sq.unit
The area of the region bounded by the curve y \displaystyle =\frac{16-x^{2}}{4} and \displaystyle y=sec^{-1}[-sin^{2}x], where [.] stands for the greatest integer function is:
  • (4-\pi )^{3/2}
  • \dfrac{8}{3}(4-\pi )^{3/2}
  • \dfrac{4}{3}(4-\pi )^{3/2}
  • \dfrac{8}{3}(4-\pi )
The area enclosed between the curves, x^{2}=y and y^{2}=x is equal to:
  • \dfrac{1}{3} sq. unit
  • 2\displaystyle \int_{0}^{1}(x-x^{2})dx
  • Area enclosed by the region \{(x,y):x^{2}\leq y\leq\sqrt x\}
  • Area enclosed by the region \{(x, y):x^{2}\leq y\leq x\}
The area of the smaller region in which the curve y=\left [ \frac{x^{3}}{100}+\frac{x}{50} \right ], where[.] denotes the greatest integer function, divides the circle \left ( x-2 \right )^{2}+\left ( y+1 \right )^{2}=4, is equal to







  • \frac{2\pi-3\sqrt{3}}{3}sq. units
  • \frac{3\sqrt{3}-\pi}{3}sq. units
  • \frac{4\pi-3\sqrt{3}}{3}sq. units
  • \frac{5\pi-3\sqrt{3}}{3}sq. units
  • \frac{4\pi-3\sqrt{3}}{6}sq. units
The function \displaystyle \mathrm{f}(\mathrm{x})=\max \{x^{2},(1-x)^{2},2x(1-x) \forall 0\leq x \leq 1\} then area of the region bounded by the curve \mathrm{y}=\mathrm{f}(\mathrm{x}) , \mathrm{x}-axis and \mathrm{x}= 0,\ \mathrm{x} = 1 is equals
  • \dfrac{27}{17}
  • \dfrac{17}{27}
  • \dfrac{18}{17}
  • \dfrac{19}{17}

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

  • 15 : 16
  • 15 : 49
  • 1 : 2
  • None of these
0:0:1


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