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CBSE Questions for Class 12 Commerce Applied Mathematics Applications Of Integrals Quiz 10 - MCQExams.com

Area bounded by the curves satisfying the conditions x225+y2361x5+y6 is given by
  • 15(π2+1) sq.units
  • 154(π21) sq.units
  • 30(π1) sq.unit
  • 152(π2) sq.unit
If A1 and A2 respectively represents the area bounded by the curves f(x,y) 4x2y3x and g (x,y)4x2y|3x| then A1 : A2 equals:
  • 2:1
  • 3:1
  • 1:2
  • 1:3
sinx & cosx meet each other at a number of points and develop symmetrical area. Area of one such region is
  • 42
  • 32
  • 22
  • 2
Area bounded by the curves yx=logx and y2=x2+x equals:
  • 7/12
  • 12/7
  • 7/6
  • 6/7
The area of the plane region bounded by the curves x+2y2=0 and x+3y2=1 is
  • 13
  • 23
  • 43
  • 53
The area enclosed between the curves, x2=y and y2=x is equal to:
  • 13 sq. unit
  • 210(xx2)dx
  • Area enclosed by the region {(x,y):x2yx}
  • Area enclosed by the region {(x,y):x2yx}
The function f(x)=max {x2,(1x)2,2x(1x)0x1} then area of the region bounded by the curve y=f(x) , x-axis and x=0, x= 1 is equals
  • 2717
  • 1727
  • 1817
  • 1917

The ratio in which the area bounded by the curves y2=12x and x2=12y is divided by the line x = 3 is

  • 15 : 16
  • 15 : 49
  • 1 : 2
  • None of these
The area bounded by the tangent and normal to the curve y(6x)=x2 at (3,3) and the x-axis is
  • 5
  • 6
  • 15
  • 3
If |z(4+4i)|4, then area of the region bounded by the locii of z,iz,z and iz is:
  • 4(4π)
  • 16(4π)
  • 16(π1)
  • 4(π1)
The area of the region bounded by the curve y =16x24 and y=sec1[sin2x], where [.] stands for the greatest integer function is:
  • (4π)3/2
  • 83(4π)3/2
  • 43(4π)3/2
  • 83(4π)
The parabola 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 the areas of these parts numbered from top to bottom respectively, then
  • S1:S21:1
  • S2:S31:2
  • S1:S31:1
  • S1:(S1+S2)1:2
The area of the smaller region in which the curve y=[x3100+x50], where[.] denotes the greatest integer function, divides the circle (x2)2+(y+1)2=4, is equal to







  • 2π333sq.units
  • 33π3sq.units
  • 4π333sq.units
  • 5π333sq.units
  • 4π336sq.units
Area of the region bounded by the curve y=x2 and y=sec1[sin2x] (where [ . ] denotes the greatest integer function) is
  • π3π
  • 2ππ3
  • 4ππ3
  • 6ππ3
  • 3ππ2
If A1 is the area bounded by y=cosx,y=sinxx=0  and A2 the area bounded by y=cosx,y=sinx,y=0 in (0,π2) then A1A2 equals to :
  • 12
  • 12
  • 1
  • None of these
The area bounded by the curves y=sin1|sinx| and y=(sin1|sinx|)2, where 0x2π, is:
  • 13+π24 sq. units
  • 16+π38 sq. units
  • 2 sq. units
  • 43+π2π36sq.units
Area lying in the first quadrant and bounded by the circle x2+y2=4 and the line x=y3 is:
  • π
  • π2
  • π3
  • None of these
Area bounded by the region R{(x,y):y2x|y|} is
  • 43
  • 34
  • 13
  • 14
Area bounded by curves y2=x and y=|x| is given by
  • 16
  • 23
  • 16
  • 13
If the area bounded by the curve |y|=sin1|x| and  x=1 is a(π+b), then the value ab is:
  • 1
  • 2
  • 3
  • 4
The area bounded by y=3|3x| and y=6|x+1| is:
  • 1526 ln 2 sq. units
  • 1323 ln 2 sq. units
  • 1326 ln 2 sq. units
  • None of these
The area bounded by y=sec1x,y=cosec1x and the line x1=0 is:
  • ln(3+22)π2
  • π2+ln(3+22)
  • πln3
  • π+ln3
The area of the smaller part bounded by the semi-circle y=4x2,y=x3 and x-axis is
  • π3
  • 2π3
  • 4π3
  • none of these
The area enclosed by x2+y2=4,y=x2+x+1,  y=[sin2x4+cosx4] and x-axis (where [.] denotes the greatest integer function) is:
  • 2π3+316
  • 2π3+2316
  • 2313
  • π3+3
The area bounded by the function f(x)=x2:R+R+ and its inverse function is:
  • 12sq.units
  • 13sq.units
  • 23sq.units
  • 16sq.units
Find the area of the region bounded by the curves y=logex, y=sin4πx, x=0
  •  118sq.units
  •  98sq.units
  •  138sq.units
  •  158sq.units
State the following statement is True or False
The area bounded by the circle x2+y2=1,x2+y2=4 and the pair of lines 3(x2+y2)=4xy, is equal to π2. The statement is true or false.
  • True
  • False
Find the area bounded by the curves  y=1x2 and  y=x3x. Also find the ratio in which the y-axis divide this area
  •  π2 ,  π1π+1
  •  π4 ,  π1π+1
  •  π2 ,  π+1π1
  • None of these
Area bounded by the curve y=sin1(sinx),y=x2πx is
  • π24+π3
  • π24+π32
  • π36
  • π24+π36
Find the area enclosed the curves : y=exlogx and y=logxex where loge=1
  • e254e
  • e2+54e
  • e232e
  • e2+32e
Sketch the region bounded by the curves y=x2 &  y=2/(1+x2). Find the area:
  •  π23
  •  π13
  •  π53
  •  π73
The ratio in which the area bounded by the curves y2=4x and x2=4y is divided by the line x=1 is
  • 64:49
  • 15:34
  • 15:49
  • none of these
Find the equation of the line passing through the origin and dividing the curvilinear triangle with vertex at the origin, bounded by the curves y=2xx2,y=0 and x=1 into two parts of equal area.
  • y=2x/3
  • y=x/3
  • y=2x/5
  • y=5x/3
For the curve f(x)=11+x2, let two points on it be A(α,f(α)),B(1α,f(1α))(α>0). Find the minimum area bounded by the line segments OA, OB and f(x), where 'O' is the origin.
  • (π1)2
  • π2
  • (π2)2
  • Maximum area is always infinite
Find the area of the region enclosed between the two circles  x2+y2=1 & (x1)2+y2=1
  •  π632 sq.units
  •  π332 sq.units
  •  π634 sq.units
  •  π334 sq.units
The area bounded by the region by the curves |x|=1y2 and |x|+|y|=1 is
  • 13
  • 1
  • 12
  • 23
Compute the area of the curvilinear triangle bounded by the y-axis & the curve,  y=tanx &  y=(2/3)cosx
  •  13+ln[32]sq.units
  •  13ln[32]sq.units
  •  23+ln[32]sq.units
  •  13+ln[12]sq.units
The area lying in the first quadrant inside the circle x2+y2=12 and bounded by the parabolas y2=4x,x2=4y is:
  • 2(23+32sin113)
  • 4(23+32sin113)
  • (23+32sin113)
  • 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=±2x; , A=23 sq.units
  • f(x)=x21;, y=±2x; , A=23 sq.units
  • f(x)=x2+1;, y=±2x; , A=32 sq.units
  • f(x)=x21;, y=±2x; , A=32 sq.units
If f(x) be an increasing function defined on [a, b] then
max {f(t) such that atx, axb}=f(x)  & min {f(t), atx, axb}=f(a) and if f(x) be decreasing function defined on [a, b] then
max {f(t), atx, axb}=f(a),
min {f(t), atx, axb}=f(x).
On the basis of above information answer the following questions.
Let f(x)=min{1,1cosx,2sinx} then π0f(x)dx is
  • π3+13
  • 2π31+3
  • 5π6+13
  • π6+13
The area included between the curve x2+y2=a2 and |x|+|y|=a(a>0) is:
  • (π+23)a2
  • (π23)a2
  • 23a2
  • 2π3a2
Let y=f(x) be the given curve and x=a, x=b be two ordinates then area bounded by the curve y=f(x), the axis of x between the ordinates x=a & x=b, is given by definite integral
baydx or baf(x)dx and the area bounded by the curve x=f(y), the axis of y & two abscissae y=c & y=d is given by dcxdy or dcf(x)dy. Again if we consider two curves y=f(x), y=g(x) where f(x)g(x) in the interval [a, b] where x=a & x=b are the points of intersection of these two curves Shown by the graph given
Then area bounded by these two curves is given by
ba[f(x)g(x)]dx
On the basis of above information answer the following questions.

The area bounded by parabolas y=x2+2x+1 & y=x22x+1 and the line y=14 is equal to

161838_6c80fc7958864f1f961bdcd5221bb036.png
  • 23 square unit
  • 13 square unit
  • 32 square unit
  • 12 square unit
Let f(x)=min{x+1,1x} then area bounded by y=f(x) and x-axis is:
  • 76
  • 56
  • 16
  • 116
If f(x) be an increasing function defined on [a, b] then
max {f(t) such that atx, axb}=f(x)  & min {f(t), atx, axb}=f(a) and if f(x) be decreasing function defined on [a, b] then
max {f(t), atx, axb}=f(a),
min {f(t), atx, axb}=f(x).
On the basis of above information answer the following questions.
π/20min{sinx,cosx}dx equals
  • 2(31)
  • 2(21)
  • (31)
  • 2(2+1)
If f(x) be an increasing function defined on [a, b] then
max {f(t) such that atx, axb}=f(x)  & min {f(t), atx, axb}=f(a) and if f(x) be decreasing function defined on [a, b] then
max {f(t), atx, axb}=f(a),
min {f(t), atx, axb}=f(x).
On the basis of above information answer the following questions.
π0max{sinx,cosx}dx is equal to
  • 21
  • 112
  • 1+12
  • None of these
The ratio of the area's bounded by the curves y2=12x and x2=12y is divided by the line x=3 is
  • 15 : 49
  • 9 : 15
  • 7 : 15
  • 7 : 5
The function f(x)=max{x2,(1x)2,2x(1x)0x1} then area of the region bounded by the curve y=f(x), x-axis and x=0,x=1 is equals,
  • 2717
  • 917
  • 1817
  • None of these
The area bounded by x=acos3θ,y=asin3θ is:
  • 3πa216
  • 3πa28
  • 3πa232
  • 3πa2
The area bounded by y=3x24 and the line 3x2y+12=0 is:
  • 9
  • 18
  • 27
  • None of these
Find the area bounded by the curves x=y2 and x=32y2
  • 2 sq. units
  • 4 sq. units
  • 6 sq. units
  • 8 sq. units
0:0:2


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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers