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

If the line x=α divides the area of region R={(x,y)R2:x3yx,0x1} into two equal parts, then
  • 2α44α2+1=0
  • α4+4α21=0
  • 0<α12
  • 12<α<1
The area bounded by the parabolas y2=4a(x+a) and y2=4a(xa)  is
  • 163a2 sq units
  • 83 sq units
  • 43a2 sq units
  • None of these
The area of the region bounded by the curves y=2x,y=2xx2 and x=2 is
  • 3log243
  • 3log249
  • 32log29
  • None of these
The area of the portion of the circle x2+y2=64 which is exterior to the parabola y2=12x, is
  • (8π3) sq units
  • 163(83) sq units
  • 163(8π3) sq units
  • None of the above
The area bounded byu the curve y = cos x, the line joining  (π/4,cos(π/4)) and (0, 2) and the line joining  (π/4,cos(π/4)) and (0, 2) is :
  • 4+28π2
  • 4+28π+2
  • 4+24π2
  • 4+24π+2
Area common to the curves y2=ax and x2+y2=4ax is equal to
  • (93+4π)a23
  • (93+4π)a2
  • (934π)a23
  • None of these
Let function fn be the number of way in which a positive integer n can be written as an ordered sum of several positive integers. For example, for n=3, f3=3,since,3=3,3=2+1 and 3=1+1+1. Thenf5=
  • 4
  • 5
  • 6
  • 7
Area bounded by the curves y= [x264+2],y=x1 and x=0 above x-axis is where [.] denotes greatest x.
  • 2 sq. unit
  • 3 sq. unit
  • 4 sq. unit
  • none of these
The area bounded by circles x2+y2=r2, r=1,2 and rays given by 2x23xy2y2=0(y>0) is?
  • π
  • 3π4
  • π2
  • π4
On the real line R, we define two functions f and g as follows:
f(x)=min[x[x],1x+[x]],
g(x)=max[x[x],1x+[x]],
where [x] denotes the largest integer not exceeding x. 
The positive integer n for which n0(g(x)f(x))dx=100 is?
  • 100
  • 193
  • 200
  • 202
The parabola y2=4x+1 divides the disc x2+y21 into two regions with areas A1 and A2. Then |A1A2| equals.
  • 13
  • 23
  • π4
  • π3
The area bounded by the curves y=sinx,y=cosx and x-axis from x=0 to x=π/2 is
  • 2+2
  • 2
  • 2
  • 22
The area bounded by min (|x|, |y|) = 2 and max (|x|, |y|) = 4 is
  • 8 sq unit
  • 16 sq unit
  • 24 sq unit
  • 32 sq unit
Area bounded by the curves y=[x264+2] ([.] denotes the greatest integer function) y=x1 and x=0 above the x-axis is
  • 2
  • 3
  • 4
  • none of these
The area bounded by the curves y=14|4x2| and y=7|x| is
  • 18
  • 32
  • 36
  • 64
Consider two curves C1:(y3)2=4(x2) and C2:x2+y2=(6+22)x+23y6(1+2) then
  • C1andC2 touch each other only at one point.
  • C1andC2 touch each other exactly at two points.
  • C1andC2 intersect (but do not touch) at exactly two points.
  • C1andC2 neither intersect nor touch each other.
The area bounded by x2+y22x=0 & y=sinπx2 in the upper half of the circle is?
  • π24π
  • π42π
  • π8π
  • None
Consider two curves C1:y=1xandC2:y=nx  on the xy plane. Let D1 denotes the region surrounded by C1,C2 and the lines x=1  and D2 denotes the region the region surrounded by C1,D2 and the line x=a. If a D1=D2 then the value of a -
  • e2
  • e
  • 1
  • 2(e1)
What is the area of the region bounded by the parabola y2=6(x1) and y2=3x
  • 63
  • 263
  • 463
  • 563
Area common to the circle x2+y2=64 and the parabola y2=4x is
  • 163(4π+3)
  • 163(8π+3)
  • 163(4π3)
  • none of these
The area bounded by the curves x=acos3t,y=asin3t is 
  • 3πa28
  • 3πa216
  • 3πa232
  • None of the above
Letf(x)=2|x1|andg(x)=(x1)2,then
  • area bounded by f(x) and g(x) is 76
  • area bounded by f(x) and g(x) is 73
  • area bounded by f(x)g(x) and x axis is 53
  • area bounded by f(x)g(x) and x axis is 56
In the square ABCD, the "shaded" region is the intersection of two circular regions centered at B and D respectively. If AB= 10, then what is the area of the shaded region?
1035047_d234b612381142cbb1a35321b59c1619.png
  • 25(π2)
  • 50(π2)
  • 25π
  • 50π
  • 40π(52)
The area bounded by the curves y=(x1)2,y=(x+1)2 and y=14 is 
  • 13sq unit
  • 23sq unit
  • 14sq unit
  • 15sq unit
Find area curved by three circles 
  • (5π33)units2
  • (5π+43)units2
  • (5π+33)units2
  • (5π+32)units2
If f(x)=max{sinx,cosx,12}, then the area of the region bounded by the curves y=f(x),xaxis yaxis and x=2π is
  • (5π12+3).sq.unit
  • (5π12+2).sq.unit
  • (5π12+3).sq.unit
  • (5π12+2+3).sq.unit
The parabola y=x22 divides the circle x2+y2=8 into two parts. Find the area of both parts.
  • 6π+432π43
  • 6π432π+43
  • 6π+232π23
  • 6π232π+23
The area enclosed by the curve y=(4x2),y2sin(xπ22) and x-axis is divided by y-axis in the ratio.
  • π28π2+8
  • π24π2+4
  • π4π+4
  • 2π2π2+2π8
If k=2 then f(x) attains point of inflection at
  • 0
  • 2
  • 2
  • None of these
Area bounded by |x1|2 and x2y2=1, is
  • 62+12 In |3+22|
  • 62+12 In |322|
  • 62 In |3+22|
  • none of these
Consider the two curves 
C1:y2=4x
C2:x2+y26x+1=0
Then, the area of region between these curves?
  • 2032π
  • 1032π
  • 203π
  • 103π
The area enclosed between the curve y=x3 and y=x is 
  • 53
  • 54
  • 512
  • None of these
The area between the curves y=tan x, cot x and axis in the interval [0,π/2]is ?
  • log 2
  • log 3
  • log 5
  • none of these
The area bounded by the curves y=sin(x[x]),y=sin1 and the x-axis is
  • sin1
  • 1sin1
  • 1+sin1
  • None of these
The area (in square units) bounded by the curves y=cos1|cosx| and y=(cos1|cosx|)2,x[0,π] is
  • 43+π24(π31)
  • 43+π24(π3+1)
  • 23+π24(π31)
  • 23+π24(π3+1)
The area bounded by the curves y=sin1|sinx| and y=(sin1|sinx|)2,0x2π is
  • (π33+43) sq. unit
  • (π36π22+43) sq. unit
  • (π2243) sq. unit
  • (π26π4+43) sq. unit
The area bounded by the curves y2=4x and x2=4y is : 
  • 323
  • 163
  • 83
  • 0
The area bounded by y=2|2x| and y=3|x| is :
  • 4+3n32
  • 43n32
  • 32+n3
  • 12+n3
Area of the region defined by 1 |x|+|y| and x22x+11y2 is kπ then k=.....sq units 
  • 34
  • 76
  • 1285
  • 103
Area bounded by the curves y=logex and  y=(logex)2 is ?
  • e2
  • 3e
  • e
  • e1
The maximum area bounded by the curves y2=4ax,y=axa and y=xa,1a2  is 
  • 44sq.units
  • 74sq.units
  • 84sq.units
  • 114sq.units
The area bounded by the curves y=xex,y=xex and the line x=1, is
  • 2e
  • 12e
  • 1e
  • 11e
The area (in sq.units) of the region {(x,y):y22x and x2+y24x,x0,y0 is 
  • π83
  • π423
  • π2223
  • π43
The area bounded by the curves x+y=1 and x+y=1 is ?
  • 13
  • 16
  • 12
  • 56
  • 14
In a system of three curves C1,C2 and C3,C1 is a circle whose equation is x2+y2=4. C2 is the locus of orthogonal tangents drawn on C1.C3 is the intersection of perpendicular tangents drawn on C2. Area enclosed between the curve C2 and C3 is-
  • 8π sq. units
  • 16π sq. units
  • 32π sq. units
  • None of these
Area bounded between the curves y=4x2 and y2=3|x| is/are?
  • π13
  • 2π133
  • 2π33
  • 2π333
Area bounded by the curves y=cos1(sinx) and y=sin1(sinx) in the interval [0,π] is 
  • π216
  • π232
  • π24
  • π28
Area bounded between asymptomes of curves f(x) and f1(x) is 
  • 4
  • 9
  • 16
  • 25
The area of the region bounded by the X-axis and the curves defined by y=tanx(π3xπ3)andy=cotx(π6x3π2)
  • log32
  • log32
  • 2log32
  • log(32)
The area bounded by the curves is |x|+|y|=a and x2+y2=a2 (where a>0) is 
  • (π23)a2 sq units
  • (π+23)a2 sq units
  • (π+23)a3 sq units
  • (π23)a3 sq units
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