Processing math: 5%

CBSE Questions for Class 12 Commerce Maths Application Of Integrals Quiz 7 - MCQExams.com

If 10(4x3=f(x))f(x)dx=47, then the area of region bounded by y=f(x),x axis and the line x= and x=2 is
  • 112
  • 132
  • 152
  • 172
The are boundede by the curve y=x2,y=x and y2=4x3 is k, them the value of 9k is
  • 2
  • 3
  • 0
  • 4
If area bounded by to curves y2=4ax and y=mx is a23, then the value of m is 
  • 2
  • 1
  • 12
  • none of these
The area bounded by curves 3 x^2 + 5 y= 32 and y = |x-2| is
  • 25
  • 33/2
  • 17/2
  • 33
The area of the plane region bounded by the curves x+{ 2y }^{ 2 }=0 and x+{ 3y }^{ 2 }=1 is equal to 
  • \cfrac { 5 }{ 3 } sq.unit
  • \cfrac { 1 }{ 3 } sq.unit
  • \cfrac { 2 }{ 3 } sq.unit
  • \cfrac { 4 }{ 3 } sq.unit
The area of the figure formed by |x| + |y| = 2 is (in sq. units)
  • 2
  • 4
  • 6
  • 8
The area bounded by the curve y=\ln (x) and the lines y=\ln (3),y=0 and x=0 is equal 
  • 3
  • 3\ln (3)-2
  • 3\ln (3)+2
  • 2
The area (in sq.units) of the region described by \left\{(x,y):y^{2}\le 2x\ and\ y\ge 4x-1\right\} is 
  • \dfrac{15}{64}
  • \dfrac{9}{32}
  • \dfrac{7}{32}
  • \dfrac{5}{64}
The area bounded by the curves y = \log _ { e } x and y = \left( \log _ { e } x \right) ^ { 2 } is
  • 3 - e
  • e-3
  • \frac { 1 } { 2 } ( 3 - e )
  • \frac { 1 } { 2 } ( e - 3 )
The area common to the parabola y=2{ x }^{ 2 }\quad and \quad y={ x }^{ 2 }+4
  • \dfrac { 2 }{ 3 } sq.\quad units\quad
  • \dfrac { 3 }{ 2 } sq.\quad units\quad
  • \dfrac { 32 }{ 3 } sq.\quad units\quad
  • none of these.
The area bounded by a the curves y=x(1-/nX) and positive X-axis between X={ e }^{ -1 } amd X=e is:-
  • \left( \frac { { e }^{ 2 }-{ 4e }^{ -2 } }{ 5 } \right)
  • \left( \frac { { e }^{ 2 }-{ 5e }^{ -2 } }{ 4 } \right)
  • \left( \frac { { 4e }^{ 2 }-{ e }^{ -2 } }{ 5 } \right)
  • \left( \frac { { 5e }^{ 2 }-{ e }^{ -2 } }{ 4 } \right)
The area bounded by the curves y=x(x-3)^{2} and y=x is (in sq.units) is
  • 28
  • 32
  • 4
  • 8
The area bounded by the curve y={ x }^{ 2 }, X=axis and the ordinates z=1, z=3 is ____________.
  • \dfrac { 26 }{ 3 } sq.units
  • \dfrac { 28 }{ 3 } sq.unit
  • \dfrac { 1 }{ 3 } sq.units
  • 9\quad sq.units
The area bounded by the curves y=x(x-3)^{2} and y=x is (in sq.units) is
  • 28
  • 32
  • 4
  • 8
The area bounded by the curve y =  log x, X-axis and the ordinates x =1, x =2 is 
  • log 4 sq. units
  • log 2 sq units
  • (log 4 - 1) sq.units
  • (log 4 + 1)sq. units
The area enclosed by the curves xy^{2}=a^{2}(a-x) and (a-x)y^{2}=a^{2}x is
  • (\pi-2)a^{2}\ sq.units
  • (4-\pi)a^{2}\ sq.units
  • (\pi a^{2}/3\ sq.units
  • \dfrac{\pi+a^{2}}{4}\ sq.units
The area bounded by the curved { y }^{ 2 }=16x  and the line x=4 is  ___________________________.
  • \frac { 128 }{ 3 } sq-units
  • \frac { 64 }{ 3 } squnits
  • \frac { 32 }{ 3 } sq-units
  • \frac { 16 }{ 3 } sq-units
If A_{m} represents the area bounded by the curve y=\ln x^{m}., the x-axis and the lines x=1 and x=2, then A_{m}+m\ A_{m-1} is
  • m
  • m^{2}
  • m^{2}/2
  • m^{2}-1
The area of the region bounded by the curve y=x^{2}-3x with y \le 0 is
  • 3
  • \dfrac {9}{2}
  • \dfrac {5}{2}
  • none\ of\ these
If a curve y = a \sqrt { x } + bx passes through the point ( 1,2 ) and the area bounded by the curve, line x = 4 and x axis is 8 square units, then 
  • a = 3 , b = - 1
  • a = 3 , b = 1
  • a = - 3 , b = 1
  • a = - 3 , b = - 1
The area bounded by the circle x^{2}+y^{2}=8, the parabola x^{2}=2y and the line y=x in first quadrant is \dfrac{2}{3}+k\pi, where k=
  • \dfrac{5}{7}
  • 2
  • \dfrac{3}{5}
  • 3
The area enclosed between the curve y=\log_{e}\left(x+e\right) and the coordinate axes is
  • 1
  • 2
  • 3
  • 4
The area of the region formed by { x }^{ 2 }+{ y }^{ 2 }-6x-4y+12\le 0,y\le x\quad and\quad x\quad \le \quad \dfrac { 5 }{ 2 } is
  • \frac { \pi }{ 6 } -\frac { \sqrt { 3}+1  }{ 8 }
  • \frac { \pi }{ 6 } +\frac { \sqrt { 3}+1  }{ 8 }
  • \frac { \pi }{ 6 } -\frac { \sqrt { 3}-1  }{ 8 }
  • none of these
Area bounded by y=2x^{2} and y=\dfrac{4}{(1+x^{2})} will be (in sq units)
  • (2\pi+4/3)
  • (2\pi-4/3)
  • 4/3-2\tan^{-1}2+\pi/2
  • 4/3-8\tan^{-1}2+2\pi
Letf(x)={ sin }^{ -1 }(sin\quad x)+{ cos }^{ -1 }(\quad cos\quad x),\quad g(x)=mx\quad and\quad h(x)=x\quad are three functions. Now g(x) is divided area between f(x),x=\pi and y=0 into two equal parts.
The area bounded by the curve y=f(x), x=\pi and y=0 is:
  • \dfrac { { \pi }^{ 2 } }{ 4 } sq.\quad units
  • { \pi }^{ 2 }sq.units
  • \dfrac { { \pi }^{ 2 } }{ 8 } sq.\quad units
  • 2{ \pi }^{ 2 }sq.units
The area of the region bounded by the curves  1-y^{2}= \left | x \right | and \left | x \right |+\left | y \right |= 1   is 
  • \frac{1}{3}sq. unit
  • \frac{2}{3}sq. unit
  • \frac{4}{3}sq. unit
  • 1 sq.unit
Find the area of the region enclosed by the curves y=x\ \log x and y=2x-2x^{2}.
  • 1/12
  • 1/4
  • 2/12
  • 7/12
Area of the region bounded by x^{2}+y^{2}-6y\leq 0 and 3y\leq x^{2} is
  • \frac{9\pi }{2}-12
  • \frac{9\pi }{4}-6
  • 9\pi-24
  • \frac{9\pi }{2}+6
The area enclosed by the curves y = cosx - sin x and y = [socx - sin x] and between x = 0 and x =\dfrac{\pi}{2} is 
  • 2(\sqrt{2} + 1) sq. units
  • 2(\sqrt{2} - 1) sq. units
  • (\sqrt{2} - 1) sq. units
  • (\sqrt{2} + 1) sq. units
The area bounded by the parabola {{\text{y}}^{\text{2}}}{\text{ = 4}}\;{\text{ax}}\;{\text{and}}\;{{\text{x}}^{\text{2}}}\;{\text{ = }}\;{\text{4ay}}\; is
  • \dfrac{{8{a^2}}}{3}
  • \dfrac{{16{a^2}}}{3}
  • \dfrac{{32{a^2}}}{3}
  • \dfrac{{64{a^2}}}{3}
The area (in sq. units) bounded by the parabola y = x^{2} - 1, the tangent at the point (2, 3) to it and the y-axis is
  • \dfrac {14}{3}
  • \dfrac {56}{3}
  • \dfrac {8}{3}
  • \dfrac {32}{3}
The area ehclosed by the curves y = f(x) and  y =g(x), where f9x) = max {x , x^2} and g(x) = min {x, x^2} opver the interval [0,1] is 
  • \dfrac{1}{6}
  • \dfrac{1}{3}
  • \dfrac{1}{2}
  • 1
The region in the xy - plane is bounded by curve y=\sqrt {(25-x^2)} and the line y=0. If the point (a,a+1) lies in the interior of the region, then 
  • a \in \left( { - 4,3} \right)
  • a \in (- \infty, -1) \cup (3, \infty)
  • a \in (-1,3)
  • None of these
The area of the region bounded by the parabolas y^2= and x^2 = y, is
  • \dfrac{1}{3} q.units
  • \dfrac{8}{3} q.units
  • \dfrac{16}{3} q.units
  • \dfrac{4}{3} q.units
If the area of the region bounded by the curves, y=x^{2},y=\frac{1}{x} and the lines y=0 and x=t (t > 1) is 1 sq. unit, then t is equal to:
  • {\dfrac{10}{3}}
  • \dfrac{4}{3}
  • \dfrac{7}{3}
  • \dfrac{11}{3}
The area (in sq. units) in the  first quadrant bounded by the parabola, y = x^2 + 1, the tangent to it at the point (2, 5) and the coordinate axes is:-
  • \dfrac{14}{3}
  • \dfrac{187}{24}
  • \dfrac{37}{24}
  • \dfrac{8}{3}
The slope of the tangent to the curve y =f(x) at a point (x, Y) is 2x + 1 and the curve passes through (1, 2) The area of the region bounded by the curve, the x-axis and the line x= 1 is - 
  • 5/3 units
  • 5/6 units
  • 6/5 units
  • 6 units
The area (in sq. units) of the region  \{ { x },{ y }):{ y }^{ { 2 } }\geq 2{ x }  and  x ^ { 2 } + y ^ { 2 } \leq 4 x , x \geq 0 , y \geq 0 \}  is :
  • \pi - \dfrac { 4 \sqrt { 2 } } { 3 }
  • \dfrac { \pi } { 2 } - \dfrac { 2 \sqrt { 2 } } { 3 }
  • \pi - \dfrac { 4 } { 3 }
  • \pi - \dfrac { 8 } { 3 }
The area of the region
A=[(x,y):0\le y\le x|x|+1 and -1\le x\le 1] in sq . units is :
  • \dfrac{2}{3}
  • \dfrac{1}{3}
  • 2
  • \dfrac{4}{3}
The area (in sq. units) of the region bounded by the parabola,  y = x ^ { 2 } + 2  and the lines, y = x + 1 , x = 0  and  x = 3 ,  is :
  • \dfrac { 15 } { 4 }
  • \dfrac { 15 } { 2 }
  • \dfrac { 21 } { 2 }
  • \dfrac { 17 } { 4 }
If the area enclosed between the curves y=kx^2 and x=ky^2, (k > 0), is 1 square unit. Then k is?
  • \dfrac{1}{\sqrt{3}}
  • \dfrac{2}{\sqrt{3}}
  • \dfrac{\sqrt{3}}{2}
  • \sqrt{3}
The area of the region bounded by y=\left | x-1 \right | and \,\,y=1 is
  • 1
  • 2
  • 1/2
  • None of these
The area of the region  \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 1 \leq x + y \right\}  is
  • \dfrac { \pi ^ { 2 } } { 5 } \text { unit } ^ { 2 }
  • \dfrac { \pi ^ { 2 } } { 2 } \text { unit } ^ { 2 }
  • \dfrac { \pi ^ { 2 } } { 3 } \text { unit } ^ { 2 }
  • \left( \dfrac { \pi } { 4 } - \dfrac { 1 } { 2 } \right)\text { unit } ^ { 2 }
The area of the region bounded by the parabola y = x^2 3x with y 0 is
  • 3
  • \dfrac{3}{2}
  • \dfrac{9}{2}
  • {9}{}
The area of the quadrilateral formed by the tangents at the endpoints of the latus recta to the ellipse, \dfrac{x^{2}}{9}+\dfrac{y^{2}}{5}=1 is 
  • \dfrac{27}{4}
  • 18
  • \dfrac{27}{2}
  • 27
The area bounded by curve y=x^{2}-1 and tangents to it at (2,3) and y-axis is
  • 8/3
  • 2/3
  • 4/3
  • 1/3
The area bounded by the curves x+2|y|=1 and x=0 is?
  • \dfrac{1}{4}
  • \dfrac{1}{2}
  • 1
  • 2
Area included between  { y }=\dfrac { { x }^{ { 2 } } }{ 4{ a } }   and  y = \dfrac { 8 a ^ { 3 } } { x ^ { 2 } + 4 a ^ { 2 } }  is
  • \dfrac { a ^ { 2 } } { 3 } ( 6 \pi - 4 )
  • \dfrac { a ^ { 2 } } { 3 } ( 4 \pi + 3 )
  • \dfrac { a ^ { 2 } } { 3 } ( 8 \pi + 3 )
  • None of these
The area of the figure formed by a|x|+b|y|+c=0, is
  • \dfrac{c^{2}}{|ab|}
  • \dfrac{2c^{2}}{|ab|}
  • \dfrac{c^{2}}{2|ab|}
  • None\ of\ these
The area of the region bounded by the curves  y = \sin x  and  y = \cos x ,  and lying between the lines  x = \dfrac { \pi } { 4 }  and  x = \dfrac { 5 \pi } { 4 } ,  is
  • 2 + \sqrt { 2 }
  • 2
  • 2 \sqrt { 2 }
  • 2 - \sqrt { 2 }
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Maths Quiz Questions and Answers