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CBSE Questions for Class 12 Commerce Applied Mathematics Applications Of Integrals Quiz 11 - MCQExams.com

The area bounded by the curves y=logx, y=log|x|, y=|logx| and y=|log|x||
  • 4 sq. units
  • 6 sq. units
  • 10 sq. units
  • None of these
Find the area bounded by y=x and y=x.
  • 18sq.units
  • 14sq.units
  • 112sq.units
  • 16sq.units
The area of the figure bounded by y2=2x+1 and xy1=0 is:
  • 2/3
  • 4/3
  • 8/3
  • 11/3
The parabolas y2=4x and x2=4y divide the square region bounded by the lines x=4,y=4 and the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to bottom; S1:S2:S3 is
  • 1:2:3
  • 1:2:1
  • 1:1:1
  • 2:1:2
Find the area of the region bounded by the curves x=12,x=2,y=logx and y=2x
  • 42log252log2+32sq.units
  • 4+2log232log2+52sq.units
  • 42log232log2+52sq.units
  • 4+2log252log2+32sq.units
The curve f(x)=Ax2+Bx+C passes through the point (1, 3) and line 4x+y=8 is tangent to it at the point (2, 0). The area enclosed by y=f(x), the tangent line and the y-axis is
  • 43
  • 83
  • 163
  • 323
For which of the following values of m is the area of the region bounded by the curve y=xx2 and the line y=mx equals to 9/2 ?
  • - 4
  • - 2
  • 2
  • 4
The area bounded between the curve y=tanxtangent drawn to it at x=π4 and y0 is
  • 14(loge41)
  • 12(loge41)
  • 12(loge4+1)
  • 14(loge4+1)
The  area bounded by y2+8x=16 and y224x=48 is a6c, then a+c=
  • 30
  • 32
  • 35
  • None
Suppose g(x)=2x+1 and h(x)=4x2+4x+5 and h(x)=(fog)(x) The area enclosed by the graph of the function y=f(x) and the pair of tangents drawn to it from the origin is
  • 8/3
  • 16/3
  • 32/3
  • none
Consider two curves C1:y=1x and C2 : y=lnx on the xy plane Let D1 denotes the region surrounded by C1C2 and the line x=1 and D2 denotes the region surrounded by C1C2 and the line x=a If D1=D2 then the value of 'a':
  • e2
  • e
  • e1
  • 2(e1)
Suppose y=f(x) and y=g(x) are two functions whose graphs intersect at three points (0,4),(2,2) and (4,0) with f(x)>g(x) for 0<x<2 and f(x)<g(x) for 2<x<4. if 40(f(x)g(x))dx=10 and 42(g(x)f(x))dx=5, the area between two curves for 0<x<2, is:
  • 5
  • 10
  • 15
  • 20
The area bounded by the curves y=x and x=y were x,y0 
  • Can not be determined
  • is 1/3
  • is 2/3
  • is same as that of the figure by the curves y=x;x0 and x=y;y0
The area of the figure bounded by y2=2x+1 and xy1=0 is
  • 163
  • 83
  • 43
  • None of these
Area of the region enclosed between the curves x=y21 and x=|y|1y2 is
  • 1
  • 4/3
  • 2/3
  • 2
The smaller area enclosed by y=f(x), where f(x) is polynomial of least degree satisfying [limx01+f(x)x3]1x=e and the circle x2+y2=2 above the xaxis is
  • π2+35
  • π235
  • π265
  • None of these
The line 3x+2y=13 divides the area enclosed by the curve 9x2+4y218x16y11=0 in two parts Find the ratio of the larger area to the smaller area
  • 3π+2π2
  • 3π2π+2
  • π+2π2
  • π2π+2
If the area enclosed by the parabolas y=ax2 and y=x2 is 182 sq. units Find the value of 'a'
  • a=9
  • a=6
  • a=9
  • a=6
The area enclosed between the curves y=x3 and y=x is (in square units)
  • 53
  • 54
  • 512
  • 125
Find the area bounded by y=cos1x,y=sin1x and yaxis
  • (22) sq. units
  • (22) sq. units
  • 22 sq. units
  • 2 sq. units
Find the area enclosed between the curves y=loge(x+e),x=loge(1/y) & the x-axis
  • 1 sq. units
  • 2 sq. units
  • 3 sq. units
  • 4 sq. units
Find the value(s) of the parameter 'a' (a > 0) for each of which the area of the figure bounded by the straight line y=a2ax1+a4 & the parabola y=x2+2ax+3a21+a4 is the greatest
  • a=21/4
  • a=51/4
  • a=71/4
  • a=31/4
Find the positive value of 'a' for the which the parabola y=x2+1 bisects the area of the rectangle with vertices (0,0),(a,0),(0,a2+1) and (a,a2+1)
  • 2
  • 3
  • 5
  • 7
A figure is bounded by the curves y=|2sinπx4| y=0,x=2 & x=4. At what angles to the positive x-axis straight lines must be drawn through (4,0), so that these lines divide the figure into three parts of the same size
  • πtan1223π,π+tan1423π
  • πtan1222π,πtan1422π
  • πtan1223π,πtan1423π
  • π+tan1222π,πtan1422π
In what ratio does the x-axis divide the area of the region bounded by the parabolas y=4xx2 and y=x2x?
  • 4 : 121
  • 4 : 144
  • 4 : 169
  • 4 : 100
For what value of 'a' is the area of the figure bounded by y=1x,y=12x1 x=2 & x=a equal to ln45?
  • a=4
  • a=8
  • a=4or25(621)
  • none of these
A polynomial function f(x) satisfies the condition f(x+1)=f(x)+2x+1 Find f(x) if f(0)=1 Find also the equations of the pair of tangents from the origin on the curve y=f(x) and compute the area enclosed by the curve and the pair of tangents
  • f(x)=x2+1;y=±x;A=23sq.units
  • f(x)=x2+1;y=±x;A=43sq.units
  • f(x)=x2+1;y=±2x;A=23sq.units
  • f(x)=x2+1;y=±2x;A=43sq.units
Area enclosed between the curves { y }^{ 2 }=x and { x }^{ 2 }=y is equal to
  • \displaystyle 2\int _{ 0 }^{ 1 }{ \left( x-{ x }^{ 2 } \right) dx }
  • \displaystyle \frac { 1 }{ 3 }
  • area of region \left\{ \left( x,y \right) :{ x }^{ 2 }\le y\le \left| x \right|  \right\}
  • \displaystyle \frac { 2 }{ 3 }
Let f(x) be a continuous function given by \displaystyle f\left ( x \right )=2x for \displaystyle \left | x \right |\leq 1 for \displaystyle f\left ( x \right )=x^{2}+ax+b for \displaystyle \left | x \right |> 1. Find the area of the region in the third quadrant bounded by the curves \displaystyle x=-2y^{2} and y = f(x) lying on the left of the line 8x + 1 = 0
  • \dfrac{235}{192} ; a = 2 ; b = - 1
  • \dfrac{235}{192} ; a = -1 ; b = 2
  • \dfrac{257}{192} ; a = -1 ; b = 2
  • \dfrac{257}{192} ; a = 2 ; b = - 1
Let \displaystyle C_{1}\displaystyle C_{2} be two curves passing through the origin as shown in the figure A  curve C is said to "bisect the area" the region between \displaystyle C_{1}\displaystyle C_{1} if for each point P of C the two shaded regions A & B shown in the figure have equal areas Determine the upper curve \displaystyle C_{2} given that the bisecting curve C has the equation \displaystyle y=x^{2} & that the lower curve \displaystyle C_{1} has the equation \displaystyle y=x^{2}/2 
261710_21f627180e0e4e76a665804f347bc987.png
  • \displaystyle \left ( 16/9 \right )x^{2}
  • \displaystyle \left ( 25/9 \right )x^{2}
  • \displaystyle \left ( 25/16 \right )x^{2}
  • \displaystyle \left ( 9/25 \right )x^{2}
Find the area bounded by y = x + sinx and its inverse between x = 0 and x = \displaystyle 2\pi
  • 2
  • 4
  • 6
  • 8
The area of the region bounded by the parabola y={x}^{2}-4x+5 and the straight line y=x+1 is
  • \cfrac{1}{2}
  • 2
  • 3
  • \cfrac{9}{2}
Area bounded by \displaystyle y=1-\ell { n }^{ 2 }x,x-axis which is common with \displaystyle x\ge 1, is -
  • \displaystyle e-\frac { 5 }{ e }
  • \displaystyle e-2
  • \displaystyle 3
  • \displaystyle 1
 Area bounded by \displaystyle y=2x-{ x }^{ 2 } & \displaystyle (x-1{ ) }^{ 2 }+{ y }^{ 2 }=1 in first quadrant, is: 
  • \displaystyle \frac { \pi }{ 2 } -\frac { 4 }{ 3 }
  • \displaystyle \frac { \pi }{ 2 } -\frac { 2 }{ 3 }
  • \displaystyle \frac { \pi }{ 2 } +\frac { 4 }{ 3 }
  • \displaystyle \frac { \pi }{ 2 } +\frac { 2 }{ 3 }
The area of the region bounded by the curves x^{2} + y^{2} = 8 and y^{2} = 2x is
  • 2\pi + \dfrac {1}{3}
  • \pi + \dfrac {1}{3}
  • 2\pi + \dfrac {4}{3}
  • \pi + \dfrac {4}{3}
Area common to the curves 5x^2  = 0 and 2x^2  + 9 = 0 is equal to
  • 12 \sqrt 3
  • 6 \sqrt3
  • 36
  • 18
The area of the region, bounded by the curves y = \sin^{-1} x + x (1 - x) and y = \sin^{-1} x - x (1 - x) in the first quadrant, is
  • 1
  • \dfrac {1}{2}
  • \dfrac {1}{3}
  • \dfrac {1}{4}
The area of the region enclosed between by the {x^2} + {y^2} = 16  and the parabola  {y^2} = 6x.
  • \dfrac{2}{3} (\sqrt 3 + 4\pi) sq. units
  • \dfrac{4}{3} (\sqrt 3 + 4\pi) sq. units
  • \dfrac{2}{3} (\sqrt 3 + 8\pi) sq. units
  • \dfrac{4}{3} (\sqrt 3 + 8\pi) sq. units
The area of the region enclosed between parabola {y}^{2}=x and the line y=mx is \cfrac{1}{48}. Then, the value of m is
  • -2
  • -1
  • 1
  • 2
The area of the region bounded by the curves, y^{2} = 8x and y = x is
  • \dfrac {64}{3}
  • \dfrac {32}{3}
  • \dfrac {16}{3}
  • \dfrac {8}{3}
The area of the region described by \left \{(x, y)/ x^{2} + y^{2} \leq 1\ and\ y^{2} \leq 1 - x\right \} is
  • \dfrac {\pi}{2} - \dfrac {2}{3}
  • \dfrac {\pi}{2} + \dfrac {2}{3}
  • \dfrac {\pi}{2} + \dfrac {4}{3}
  • \dfrac {\pi}{2} - \dfrac {4}{3}
The area (in square units) of the region bounded by the curves x=y^2 and x=3-2y^2 is
  • \dfrac{3}{2}
  • 2
  • 3
  • 4
The area (in square units) bounded by the curves x\, =\, -2y^2 and x\, =\, 1-3y^2 is
  • \displaystyle \frac{2}{3}
  • 1
  • \displaystyle \frac{4}{3}
  • \displaystyle \frac{5}{3}
The area (in square units) of the region bounded by x=-1, x=2, y=x^2+1 and y=2x-2 is 
  • 10
  • 7
  • 8
  • 9
Area of region \displaystyle \left\{ \left( x,y \right) \in { R }^{ 2 }:y\ge \sqrt { \left| x+3 \right|  } ,5y\le x+9\le 15 \right\}  is equal to
  • \displaystyle \frac { 1 }{ 6 }
  • \displaystyle \frac { 4 }{ 3 }
  • \displaystyle \frac { 3 }{ 2 }
  • \displaystyle \frac { 5 }{ 3 }
Area bounded by curve y=x^2 and y=2-x^2 is ?
  • \dfrac{8}{3} sq units
  • \dfrac{3}{8} sq units
  • \dfrac{3}{2} sq units
  • None of these
If the area bounded by the curves y=a{ x }^{ 2 } and x=a{ y }^{ 2 }, (a>0) is 1 sq.units, then the value of a is
  • \cfrac { 2 }{ 3 }
  • \cfrac { 1 }{ \sqrt 3 }
  • 1
  • 4
The ratio of the areas of two regions of the curve C_1 : 4x^2 + \pi^2y^2 = 4\pi^2 divided by the curve C_2 : y = -sgn \left(x - \dfrac{\pi}{2}\right) \cos x (where sgn(x) denotes signum function) is - 
  • \dfrac{\pi^2 +4}{\pi^2-2\sqrt{2}}
  • \dfrac{\pi^2-2}{\pi^2+2}
  • \dfrac{\pi^2+6}{\pi^2+3\sqrt{3}}
  • \dfrac{\pi^2+1}{\pi^2-\sqrt{2}}
If z is not purely real then area bounded by curves lm\left(z+\dfrac{1}{z}\right) = 0 and |z-1| = 2 is (in square units)-
  • 4\pi
  • 3\pi
  • 2\pi
  • \pi
The graphs of f(x)=x^{2} and g(x)=cx^{3}(c>0) intersect at the points (0, 0) and (\dfrac{1}{c}, \dfrac{1}{c^{2}}). If the region which lies between these graphs and over the interval [0, \dfrac{1}{c}] has the area equal to (\dfrac{2}{3})sq.\ units, then the value of c is :
  • \dfrac{1}{3}
  • \dfrac{1}{2}
  • 1
  • 2
0:0:1


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