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CBSE Questions for Class 12 Commerce Applied Mathematics Applications Of Integrals Quiz 6 - MCQExams.com

Let f(x)=x23x+2 be a function, for all xROn the basis of given information, answer the given question.
The area bounded by f(x), the xaxis and yaxis is,
  • 13.sq.unit
  • 23.sq.unit
  • 35.sq.unit
  • 56.sq.unit
Find the area of the region bounded by the curves y2=4ax and x2=4ay.
  • 163a2 sq.unit
  • 83a2 sq.unit
  • 63a2 sq.unit
  • None of these
The area (in sq. units) of the region {(x,y):y22xandx2+y24x,x0} is
  • π43
  • π83
  • π423
  • π2223
Let f and g be continuous function on axb and set p(x)=max{f(x),g(x)} and q(x)=min{f(x),g(x)}, the area bounded by the curves y=p(x),y=q(x) and the ordinates x=a and x=b is given by 
  • ba(f(x)g(x))dx
  • ba(p(x)q(x))dx
  • ba|p(x)q(x)|dx
  • ba|f(x)g(x)|dx
Area bounded by the curve y=lnx,y=0 and x=3 is 
  • (ln92).sq.unit
  • (ln272).sq.unit
  • ln(27e2).sq.unit
  • >3.sq.unit
The area bounded by the curve y=(x1)2, =(x+1)2 and the xaxis is
  • 13
  • 23
  • 43
  • 83
The area bounded by the curves y2=x3 and |y|=2x is 3 sq unit.
  • True
  • False
Area bounded by the lines y=x,x=1,x=2 and x-axis is- 
  • 52sq. units
  • 32sq units
  • 12sq units
  • None of these
Find the area of the region {(x,y):x2+y24,x+y2}.
  • π2
  • π1
  • 2π2
  • 4π2
Area of the region bounded by the curve y=25x+16 and curve y=b.5x+4 whose tangent at the point x=1, makes an angle tan1(40log5) with the xaxis is:
  • 2log5(e427)
  • 4log5(e427)
  • 3log5(e427)
  • None of these
A curve is such that the area of the region bounded by the coordinates axes, the curve and the ordinate of any point on it is equal to the cube of that ordinate the curve represent.
  • a pair of straight lines
  • a circle
  • a parabola
  • an ellipse
The area enclosed between the curves y=log(x+e);x=loge(1y) and x-axis is
  • 3
  • 1
  • -2
  • 0.222
The area of the region [(x,y):x2+y21x+y| is
  • π5
  • π4
  • π23
  • π412
The common area between the curve x2+y2=8 and y2=2x is
  • 43+2π
  • (22+π1)
  • (2+π1)
  • None of these
The area common to the circle x2+y2=16a2 and the parabola y2=6ax is
  • 4a2(8π3)
  • 4a2(4π+3)3
  • 8a2(4π3)5
  • none of these
The area bounded by the curve : max{|x|,|y|}=5 is
  • 10
  • 25
  • 100
  • 50
The area bounded by y=cosx,y=x+1,y=0 is 
  • 32
  • 23
  • 12
  • 52
The area enclosed between the curve y2=xandy=|x| is
  • 16
  • 13
  • 23
  • 1
The value of 11f(x)dx, is
  • 215(k+1)(2310k)
  • 215(k+1)(23+10k)
  • 215(k+1)(10k17)
  • 215(k+1)(10k+17)
Let P(x,y) be a moving point in the xy plane such that [x].[y]=2, where [.] denotes the greatest integer function, then area of the region containing the points P(x,y) is equal to:
  • 1 sq. units
  • 2 sq. units
  • 4 sq. units
  • None of these
The area bounded by the curve f(x) = x + sin x and its inverse function between the ordinates x=0andx=2π is
  • 4π
  • 8π
  • 4
  • 8
If θxπ; then the area bounded by the curve y=x and y=x+sinx is
  • 2
  • 4
  • 2π
  • 4π
The area of the region bounded by the x-axis and the curves
y=tanx(π3xπ3),andy=cotx(π6x3π2) is
  • log2
  • 2log2
  • log2
  • log(32)
Consider the functions f(x) and g(x), both defined from RR and are defined as f(x)=2xx2 and g(x)=xn where nN. If the area between f(x) and g(x) in first quadrant is 1/2 then n is not a divisor of :
  • 12
  • 15
  • 20
  • 30
The area bounded by the curves y=sinx,y=cosx and yaxes in first quadrant is:
  • 21
  • 2
  • 2+1
  • None of the above
The area bounded by y=x2,y=[x+1],x1 and the y-axis is, where [.] is greatest integer function
  • 13
  • 23
  • 1
  • 73
The area between the curves y = tanx, y = cotx and x - axis in the interval [0,π/2] is 
  • log2
  • log3
  • log2
  • None of these
The are included between the curves y2=4ax and x2=4ay is ____  sq units.
  • 16a23
  • 8a23
  • 4a23
  • 5a23
The area of the region enclosed by the curves y=x, x=e, y=\dfrac{1}{x} and the positive x-axis is . 
  • \dfrac{3}{2} square units
  • \dfrac{5}{2} square units
  • \dfrac{1}{2} square units
  • 1 square units
The area bounded by the curve y=cos ax in one are of the curve is where a=4n+1,n\in integer
  • 2a
  • 1/a
  • 2/a
  • 2{a^2}
Area enclosed between the curves \left| y \right| = 1 - {x^2} and {x^2} + {y^2} = 1 is 
  • \dfrac{{3\pi - 14}}{3} sq.units
  • \dfrac{{\pi - 8}}{3} sq.units
  • \dfrac{{2\pi - 8}}{3} sq.units
  • None of these
The area bounded by the curves y=xe, y=-xe and the line x=1 is-
  • \dfrac{e}{2}
  • e
  • \dfrac{1}{e}
  • \dfrac{3}{e}
The area of the region bounded by the curves y=ex\log x and y=\dfrac{\log x}{ex} is
  • \dfrac{e^{2}-5}{4e}
  • \dfrac{e^{2}+1}{2e}
  • \dfrac{e^{2}}{2}
  • None\ of\ these
The maximum area of the triangle whose sides a, b \, and \, c satisfy 0 \le a \le 1, \, 1 \le b \le 2 and 2 \le c \le 3
  • 1
  • \frac {1}{2}
  • 2
  • \frac {3}{2}
Area bounded by curve y = k \sin \,x between x = \pi and x = 2\pi, is
  • 2k sq. unit
  • 0
  • \dfrac{k^2}{2} sq. unit
  • None of these
Suppose that F(\alpha) denotes the area of the region bounded by x=0, x=2, y^2=4x and y=|\alpha x-1|+|\alpha x-2|+\alpha x, where \alpha \in \{0, 1\}. Then the value of F(\alpha)+\dfrac{8\sqrt{2}}{3}, when \alpha =0, is
  • 4
  • 5
  • 6
  • 9
The area bounded by the curve y=sin(x-[x]),y=sin1,\,x=1 and the x-axis is
  • sin1
  • 1-sin1
  • 1+sin1
  • 1-\cos1
The area of the region bounded by the curves y=x^2 and y = \dfrac {2}{1+x^2} is :
  • \pi - \dfrac {2}{3}
  • \pi + \dfrac {2}{3}
  • \dfrac {\pi}{3}
  • \dfrac { 2 \pi}{3}
The area of the region bounded by \left| arg\left( z+1 \right)  \right| \le \frac { \pi  }{ 3 } and \left|z+1   \right| \le \frac { \pi  }{ 4 } is given by
  • \dfrac{4\pi}{3}
  • \dfrac{16\pi}{3}
  • \dfrac{2\pi}{3}
  • \dfrac{20\pi}{3}
Area common to the curve y^2 = 16x and y = 2x, is : 
  • \dfrac{16}{3} sq. units
  • \dfrac{17}{3} sq. units
  • \dfrac{19}{3} sq. units
  • \dfrac{20}{3} sq. units
The curves y = x^{2} - 1, y = 8x - x^{2} - 9 at
  • Intersect at right angles at (2, 3)
  • Touch each other at (2, 3)
  • Do not intersect at (2, 3)
  • Intersect at an angle \dfrac {\pi}{3}
The area bounded by the curves y=f(x), the x-axis and the ordinates x=1 and x=\beta is (\beta -1)\sin(3\beta +4). Then f(x) is
  • (x-1)\cos(3x+4)
  • \sin(3x+4)
  • \sin(3x+4)+3(x-1)\cos(3x+4)
  • \sin(3x+4)+x
Two vertices of a rectangle are on the positive x-axis. The other two vertices lie on the lines y=4x and y=-5x+6. Then the maximum area of the rectangle is?
  • \dfrac{2}{3}
  • \dfrac{2}{4}
  • \dfrac{1}{3}
  • \dfrac{4}{3}
The area bounded by the curves x^2=4ay and y^2=4ax is,
  • 0
  • \dfrac {16a^2}{3}
  • \dfrac {8a^2}{3}
  • \dfrac {4a^2}{3}
The area of the region bounded by the curve {a^4}{y^2} = \left( {2a - x} \right){x^5} is to that curve whose radius is a, is given by the ration.
  • 5:4
  • 5 : 8
  • 2 : 3
  • 3 : 2
The area enclosed between the curves y=a{ x }^{ 2 } and x=a{ y }^{ 2 } \\ (a>0) is 1sq.unit. then a=
  • \dfrac { 1 }{ \sqrt { 3 } }
  • \dfrac { 2 }{ \sqrt { 3 } }
  • \dfrac { 4 }{ \sqrt { 3 } }
  • \sqrt { 3 }
If area bounded by f(x)=x^{\frac{1}{3}}(x-1) x-axis is A then find the value of 28A.
  • 5
  • 6
  • 7
  • 9
The area of the region bounded by the curves y=|x-2| and y=4-|x| is-   
  • 2
  • 4
  • 5
  • 6
The area enclosed between the curves y={ ax }^{ 2 } and x={ ay }^{ 2 } (a>0) is 1\ sq.unit. then a=
  • \dfrac { 1 }{ \sqrt { 3 } }
  • \dfrac { 2 }{ \sqrt { 3 } }
  • \dfrac { 4 }{ \sqrt { 3 } }
  • \sqrt { 3 }
The area of the region bounded by y=(x-4)^2, y=16-x^2 and the x axis,is
  • 16
  • 32
  • \dfrac{64}{3}
  • 64
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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers