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CBSE Questions for Class 12 Commerce Maths Application Of Integrals Quiz 1 - MCQExams.com

The area of the region bounded by the parabola (y2)2=x1, the tangent to the parabola at the point (2, 3) and the x-axis is 

  • 3
  • 6
  • 9
  • 12
The area (in square units) of the region bounded by the curves y+2x2=0 and y+3x2=1, is equal to 
  • 13
  • 43
  • 35
  • 34
The area (in sq. units) of the region {(x,y):x0,x+y3,x24y and y1+x} is.
  • 5912
  • 32
  • 73
  • 52
The area of the region described by A=(x,y):x2+y21 and y21x is:
  • π2+43
  • π243
  • π223
  • π2+23
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(Example: S1 is the area bounded by y=4 and x2=4y ); then S1,S2,S3 is  
  • 1:2:1
  • 1:2:3
  • 2:1:2
  • 1:1:1
The area of the region bounded by the curves x+2y2=0 and x+3y2=1 is equal to 
  • 23
  • 43
  • 53
  • 13
 The area bounded by the curves y= cosx and y= sinx between the ordinates x=0 and x=3π2:
  • 42+2
  • 421
  • 42+1
  • 422
The area(in sq. units) of the smaller portion enclosed between the curves, x2+y2=4 and y2=3x, is.
  • 13+4π3
  • 123+π3
  • 123+2π3
  • 13+2π3
The area bounded between the parabolas 4x2=y and x2=9y, and the straight line y=2 is:
  • 202
  • 1023
  • 2023
  • 102
The area enclosed between the curves y=ax2 and x=ay2(a>0) is 1 sq. unit, then the value of a is
  • 1/3
  • 1/2
  • 1
  • 1/3

The area of the region between the curves y=1+sinxcosx and y=1sinxcosx bounded by the lines x=0 and x=π4 is
  • 210t(1+t2)1t2dt
  • 2104t(1+t2)1t2dt
  • 2+104t(1+t2)1t2dt
  • 2+10t(1+t2)1t2dt
Area of the region bounded by the curve y=ex and lines x=0 and y=e is:
  • e1
  • e1ln(e+1y)dy
  • e10exdx
  • e1lnydy
Area enclosed between the curves y=8x2 and y=x2, is:
  • 32/3
  • 64/3
  • 30/4
  • 9
If area bounded by the curves x=at2 and y=ax2 is 1, then a= __________.
  • 12
  • 13
  • 13
  • 3
Calculate the area of the shaded region in the figure, where ABCD is a square with side 8 cm each. (π=3.14)

181715_76bd65b085eb4bcbb726ff6c949c5b0b.png
  • 36.48cm2
  • 25.40cm2
  • 15cm2
  • 65cm2
The area included between the parabolas
y=x24a and y=8a3x2+4a2 is
  • a2(2π+23)
  • a2(2π83)
  • a2(π+43)
  • a2(π43)
The area in the first quadrant enclosed by the x - axis, the line  x=y3 and the circle x2+y2=4 is
  • π
  • π2
  • π4
  • π3
Find the area of the region bounded by the curve y2=4x and the line x=3.
  • 43
  • 83
  • 6
  • 23
The area enclosed between the y2=x and y=|x| is
  • 13
  • 23
  • 1
  • 16
The value of a for which the area between the curves y2=4ax and x2=4ay is 1sq.unit, is-
  • 3
  • 4
  • 43
  • 34
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  • Assertion is correct but Reason is incorrect
  • Assertion is false and Reason are correct
The area bounded by curves 3x^2 + 5y = 32 and y = \left|x-2\right| is 
  • 25
  • 17/2
  • 33/2
  • 33
The area bounded by the x-axis, the curve y=f\left(x\right) and the lines x=1 and x=b is equal to \left(\sqrt{{b}^{2}+1}-\sqrt{2}\right) for all b>1, then f\left(x\right) is
  • \sqrt{x-1}
  • \sqrt{x+1}
  • \sqrt{{x}^{2}+1}
  • \dfrac{x}{\sqrt{{x}^{2}+1}}
The area of the figure bounded by f\left(x\right)=\sin{x}, g\left(x\right)=\cos{x} in the first quadrant is:
  • 2\left(\sqrt{2}-1\right) sq.unit
  • \sqrt{3}+1 sq.unit
  • 2\left(\sqrt{3}-1\right).sq.unit
  • none of these.
Points of inflexion of the curve
y = x^4 - 6x^3 + 12x^2 + 5x + 7 are
  • (1, 19); (1, 12)
  • (1, 19); (2, 33)
  • (1, 2); (2, 1)
  • (1, 7); (2, 6)
The area under the curve y=2x^3+4x^2 between x=2,x=4 is 
  • 192.6
  • 198.6
  • 88.3
  • 172.3
If the curves y=x^3+ax and y=bx^2+c pass through the point (-1, 0) and have common tangent line at this point, then the value of a+b is?
  • 0
  • -2
  • -3
  • -1
The area (in sq. units) of the region \{ x \in R:x \ge ,y \ge 0,y \ge x - 2\   and  y \le \sqrt x \} , is
  • \dfrac{{13}}{3}
  • \dfrac{{8}}{3}
  • \dfrac{{16}}{3}
  • \dfrac{{5}}{3}
The area of the plane region bounded by the curves  x + 2 y ^ { 2 }= 0 \text { and } x + 3 y ^ { 2 } = 1
  • \dfrac { 4 } { 3 }
  • \dfrac { 5 } { 3 }
  • \dfrac { 2 } { 3 }
  • \dfrac { 1 } { 3 }
What is the area of the region enclosed between the curve y^2=2x and the straight line y=x ?
  • \dfrac{2}{3} square units
  • \dfrac{4}{3} square units
  • \dfrac{1}{3} square units
  • 1 square unit

The area bounded by the parabola y=x^{2} and the straight line \mathrm{y}=2\mathrm{x} is
  • \displaystyle \frac{4}{3} sq. units
  • \displaystyle \frac{3}{4} sq. units
  • \displaystyle \frac{2}{3} sq. units
  • \displaystyle \frac{1}{3} sq. units
The area bounded by the two parabolas y^{2}=8x and x^{2}=8y is
  • 64 sq. units
  • \displaystyle \frac{64}{3} sq, units
  • \displaystyle \frac{32}{3} sq. units
  • \displaystyle \frac{1}{3} sq. units
The area of the region bounded by the curve y=x^{2}+1 and y=2x-2 between {x}=-1 and {x}=2 is:
  • 9sq. units
  • 12sq. units
  • 15sq. units
  • 14sq. units
The area between the curve y^{2}=9x and the line y=3x is
  • \displaystyle \frac{1}{3} sq. units
  • \displaystyle \frac{8}{3} sq. units
  • \displaystyle \frac{1}{2} sq, units
  • \displaystyle \frac{1}{5} sq. units
The area of the region bounded by 3x\pm 4y\pm 6=0 in sq. units is
  • 3
  • 1.5
  • 4.5
  • 6
The area of the smaller part of the circle { x }^{ 2 }+{ y }^{ 2 }={ a }^{ 2 }, cut off by the line \displaystyle x=\frac { a }{ \sqrt { 2 }  } , is given by:
  • \displaystyle \frac { { a }^{ 2 } }{ 2 } \left( \frac { \pi }{ 2 } +1 \right)
  • \displaystyle \frac { { a }^{ 2 } }{ 2 } \left( \frac { \pi }{ 2 } -1 \right)
  • \displaystyle { a }^{ 2 }\left( \frac { \pi }{ 2 } -1 \right)
  • None of these
The area bounded by the parabola y^{2}=4x and its latusrectum is:
  • \displaystyle \frac{8}{3} sq. units
  • \displaystyle \frac{3}{8} sq. units
  • 12 sq. units
  • \displaystyle \frac{1}{3} sq. units
The area of the curve x=a\cos^{3}t,y=b\sin^{3}t in sq. units is :
  • \displaystyle \frac{3\pi ab}{4}
  • \displaystyle \frac{3\pi ab}{8}
  • \displaystyle \frac{\pi ab}{4}
  • \displaystyle \frac{\pi ab}{8}
Area of the region R=\{[(x,y)/x^{2}\leq y\leq x]\} is
  • 1/6
  • 2/3
  • 4/3
  • 2
Area of the region bounded by x=|y+4| and \mathrm{y} axis is sq. units
  • 4
  • 8
  • 16
  • 32
The area of the region between the curves y=x^{2} and y=x^{3} is
  • \displaystyle \frac{1}{12} sq. units
  • \displaystyle \frac{1}{3} sq. units
  • \displaystyle \frac{1}{4} sq. units
  • \displaystyle \frac{1}{2} sq. units
AOB is the positive quadrant of the ellipse \displaystyle \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 where \mathrm{O}\mathrm{A}={a},\ {O}\mathrm{B}={b}. Then area between the arc \mathrm{A}\mathrm{B} and chord \mathrm{A}\mathrm{B} of the ellipse is
  • \pi\ ab
  • (\pi-2)ab
  • \displaystyle \frac{ab(\pi+2)}{2}
  • \displaystyle \frac{ab(\pi-2)}{4}

The area enclosed between y=\sin 2x,y=\sqrt{3}\sin x between x=0 and x=\displaystyle \frac{\pi}{6} is
  • \displaystyle \frac{7}{4}-\sqrt{3} sq. units
  • \displaystyle \frac{7}{4}+\sqrt{3} sq. units
  • \displaystyle \frac{7\sqrt{3}}{4} sq, units
  • 7-\displaystyle \frac{\sqrt{3}}{4} sq. units
Area of the region \{(x,y)/x^{2}+y^{2}\leq 1\leq x+y\} is:
  • \displaystyle \frac{\pi}{4}+\frac{1}{2}
  • \displaystyle \frac{\pi}{4}-\frac{1}{2}
  • \displaystyle \frac{\pi}{4}+\frac{3}{4}
  • \pi+1
The area bounded by the curves y=\cos x,y=\cos 2x between the ordinates x=0,x=\displaystyle \frac{\pi}{3} are in the ratio
  • 2\sqrt{3}:4-\sqrt{3}
  • 2: 1
  • 2\sqrt{3}:4+\sqrt{3}
  • 1: 3
The area bounded by y=3x and y=x^{2} is (in square units)
  • 10
  • 5
  • 4.5
  • 9
The area bounded by the two curves y=\sin x,\ y=\cos x and the \mathrm{X}-axis in the first quadrant \left[0,\displaystyle \frac{\pi}{2}\right] is
  • 2-\sqrt{2} sq. units
  • 2+\sqrt{2} sq,. units
  • 2(\sqrt{2}-1) sq. units
  • 4 sq. units
The area bounded by y^{2}=4ax and y=mx is \displaystyle \frac{a^{2}}{3} sq. units then \mathrm{m}
  • 1
  • 2
  • 3
  • 4
Area of the segment cut off from the parabola x^{2}=8y by the line x-2y+8=0 is:
  • 12
  • 24
  • 48
  • 36
Area bounded by y=\sqrt{a^{2}-x^{2}},\ x+y=0 and \mathrm{y}-axis in sq. units is:
  • a^{2}(\displaystyle \frac{\pi}{2})
  • a^{2}(\displaystyle \frac{\pi}{4})
  • a^{2}(\displaystyle \frac{\pi}{8})
  • a^{2}\pi
0:0:1


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