CBSE Questions for Class 12 Commerce Applied Mathematics Applications Of Integrals Quiz 2 - MCQExams.com

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:
  • $$9$$sq. units
  • $$12$$sq. units
  • $$15$$sq. units
  • $$14$$sq. 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:
  • $$a^{2}(\displaystyle \frac{\pi}{2})$$
  • $$a^{2}(\displaystyle \frac{\pi}{4})$$
  • $$a^{2}(\displaystyle \frac{\pi}{8})$$
  • $$ a^{2}\pi$$

Area ofthe region bounded by $$y=|x|$$ and $$\mathrm{y}=2$$ is 
  • $$4$$ sq units
  • $$2$$ sq. units
  • $$1$$ sq. units
  • $$\displaystyle \frac{1}{2}$$ sq. units
The area of a region bounded by $$\mathrm{X}$$-axis and the curves defined by $$y=\tan x ,  0\displaystyle \leq x\leq\frac{\pi}{4}$$ and $$y=\displaystyle \cot x,\frac{\pi}{4}\leq x\leq\frac{\pi}{2}$$ is:
  • $$log3$$ sq. unlts
  • $$log5$$ sq. unlts
  • $$log 1$$ sq. unit
  • $$log 2$$ sq. units

The area bounded by $$y=\cos x,\ y=x+1$$ and $$y=0$$ in the second quadrant is
  • $$\displaystyle \frac{3}{2}$$ sq. units
  • 2 sq. units
  • 1 sq. unit
  • $$\displaystyle \frac{1}{2}$$ sq,. units
The area bounded by tangent, normal and x-axis at $$\mathrm{P}(2,4)$$ to the curve $$y=x^{2}$$
  • $$34$$
  • $$32$$
  • $$36$$
  • $$24$$
Area of the region bounded by $$y=|x|$$ and $$y=1-|x|$$ is
  • $$\displaystyle \frac{1}{3}$$ sq. units
  • 1 sq. units
  • $$\displaystyle \frac{1}{2}$$ sq. unit
  • 2 sq. units
The area in square units bounded by the curves $$y=x^{3},\ y=x^{2}$$ and the ordinates $${x}=1, {x}=2$$ is
  • $$\displaystyle \frac{17}{12}$$
  • $$\displaystyle \frac{12}{13}$$
  • $$\displaystyle \frac{2}{7}$$
  • $$\displaystyle \frac{7}{2}$$
The area, in square units of the region bounded by the parabolas $$y^{2}=4x$$ and $$x^{2}=4y$$ is
  • $$\dfrac{16}{3}$$
  • $$\dfrac{32}{3}$$
  • $$\dfrac{8}{3}$$
  • $$\dfrac{4}{3}$$
The area bounded by the two curves $$y=\sqrt{x}$$ and  $$x=\sqrt{y}$$ is:
  • $$\displaystyle \frac{1}{3}$$ sq, units
  • $$\displaystyle \frac{2}{3}$$ sq. units
  • $$\displaystyle \frac{1}{5}$$ sq. units
  • $$\displaystyle \frac{1}{7}$$ sq. units
The area of the region bounded by $$x^{2}=8y,\ x=4$$ and the $$\mathrm{x}$$-axis is
  • $$\displaystyle \frac{2}{3}$$
  • $$\displaystyle \frac{4}{3}$$
  • $$\displaystyle \frac{8}{3}$$
  • $$\displaystyle \frac{10}{3}$$
The area bounded by the parabola $$x^{2}=4ay,\ \mathrm{x}$$-axis and the straight line $$\mathrm{y}=2\mathrm{a}$$ is:
  • $$16\sqrt{2}a^{2}$$ sq. units
  • $$\displaystyle \frac{16\sqrt{2}}{3}a^{2}$$ sq. units
  • $$\displaystyle \frac{32\sqrt{2}}{3}a^{2}$$ sq. units
  • $$\displaystyle \frac{32\sqrt{2}}{5}a^{2}$$ sq. units

Area of the figure bounded by Y-axis, $$y=Sin^{-1}x,\ y=Cos^{-1}x$$ and the first point of intersection from the origin is
  • $$2\sqrt{2}$$
  • $$2\sqrt{2}+1$$
  • $$\sqrt{2}-1$$
  • $$\sqrt{2}+1$$

The area bounded by the parabola $$x=y^{2}$$ and the line $$y=x-6$$ is
  • $$\displaystyle \frac{125}{3}$$ sq. units
  • $$\displaystyle \frac{125}{6}$$ sq. units
  • $$\displaystyle \frac{125}{4}$$ sq. units
  • $$\displaystyle \frac{115}{3}$$ sq. units
The area of the region bounded by $$y=x,\ y=x^{3}$$ is:
  • $$\displaystyle \frac{1}{4}$$ sq. units
  • $$\displaystyle \frac{1}{12}$$ sq. units
  • $$\displaystyle \frac{1}{3}$$ sq. units
  • $$\displaystyle \frac{1}{2}$$ sq. units
The area bounded by the curve $$y^{2}=x$$ and the line $$\mathrm{x}=4$$ is:
  • $$\displaystyle \frac{32}{3}$$ sq. units
  • $$\displaystyle \frac{16}{3}$$ sq. units
  • $$\displaystyle \frac{8}{3}$$ sq. units
  • $$\displaystyle \frac{4}{3}$$ sq. units
The area between the curve $$y=x^{2}$$ and $$y=x+2$$ is:
  • $$\displaystyle \frac{9}{2}$$ sq. units
  • $$\displaystyle \frac{3}{2}$$ sq. units
  • 9 sq. units
  • 6 sq. units
The area of the region between the curve $$y=4x^{2}$$ and the line $$y=6x-2$$ is:
  • $$\displaystyle \frac{1}{9}$$ sq. units
  • $$\displaystyle \frac{1}{12}$$ sq. units
  • $$\displaystyle \frac{3}{2}$$ sq. units
  • $$\displaystyle \frac{1}{5}$$ sq. units
The area bounded by the parabola $$y^{2}=4x$$ and the line $$y=2x-4$$:
  • 9 sq. units
  • 5 sq. units
  • 4 sq. units
  • 2 sq. units
The area bounded by the line $$\mathrm{x}=1$$ and the curve $$\sqrt{\dfrac{y}{x}}+\sqrt{\dfrac{x}{y}}=4$$ is
  • $$2\sqrt{3}$$
  • $$\sqrt{3}$$
  • $$3\sqrt{2}$$
  • $$4\sqrt{3}$$
Area of the region enclosed by $$y^{2}=8x$$ and $${y}=2{x}$$ is
  • $$\dfrac{4}{3}$$
  • $$\dfrac{3}{4}$$
  • $$\dfrac{1}{4}$$
  • $$\dfrac{1}{2}$$
The area between the curves $$y=\sqrt{x}$$ and $$y=x^{3}$$ is
  • $$\displaystyle \frac{1}{12}$$ sq. units
  • $$\displaystyle \frac{5}{12}$$ sq. units
  • $$\displaystyle \frac{3}{5}$$ sq. units
  • $$\displaystyle \frac{4}{5}$$ sq. units
The area bounded by the curves $$y=\sin x,y=$$ cosx and the $$\mathrm{y}$$-axis and the first point of intersection is:
  • $$\sqrt{2}$$ sq,.units
  • $$\sqrt{2}-1$$ sq. units
  • $$2+\sqrt{2}$$ sq. units
  • 0 sq, units
Assertion(A): The area bounded by $$y^{2}=4x$$ and $$x^{2}=4y$$ is $$\displaystyle \frac{16}{3}$$ sq. units.

Reason(R): The area bounded by $$y^{2}=4ax$$ and $$x^{2}=4ay$$ is $$\displaystyle \frac{16a^2}{3}$$ sq. units
  • Both A and R are true and R is the correct explanation of A.
  • Both A and R are true but R is not the correct explanation of A.
  • A is true but R is false.
  • A is false but R is true.
I : The area bounded by $$ x=2\cos\theta,\  y=3\sin\theta$$ is $$ 36\pi$$ sq. units.
II: The area bounded by $$ x=2\cos\theta,\  y=2\sin\theta$$ is $$ 4\pi$$ sq.units.
Which of the above statement is correct?
  • Only I
  • Only II
  • Both I and II
  • Neither I nor II.
The area of the triangle formed by the positive X-axis and the normal and tangent to the circle $$x^{2}+y^{2}=4$$ at $$(1,\sqrt{3})$$ in sq. units is:
  • $$\sqrt{3}$$
  • $$\displaystyle \frac{1}{\sqrt{3}}$$
  • $$2\sqrt{3}$$
  • $$3\sqrt{3}$$

The area between the curves $$y=\tan x$$,$$y=\cot x$$ and $$\mathrm{x}$$-axis $$(0\displaystyle \leq x\leq\frac{\pi}{2})$$ is
  • $$\log 2$$
  • $$2 \log 2$$
  • $$\displaystyle \frac{1}{2}$$ $$\log2$$
  • $$1$$
I: The area bounded by the line $$\mathrm{y}=\mathrm{x}$$ and the curve $$y=x^{3}$$ is $$1/_{2}$$ sq. units.
II: The area bounded by the curves $$y=x^{3}$$ and $$ y=x^{2}$$and the ordinates $$x=1$$, $$x=2$$ is $$\frac{7}{12}$$ sq. units.
Which of the above statement is correct?
  • Only I
  • Only II
  • Both I and II
  • Neither I nor II.
Assertion(A): The area bounded by $$y^{2}=4x$$ and $$y=x$$ is $$\displaystyle \frac{8}{3}$$ sq. units.

Reason(R): The area bounded by $$y^{2}=4ax$$ and $$y=mx$$ is $$\displaystyle \frac{8a^{2}}{3m^{3}}$$ sq. units.
  • Both A and R are true and R is the correct explanation of A.
  • Both A and R are true but R is not the correct explanation of A.
  • A is true but R is false.
  • A is false but R is true.

The area of the region bounded by $$y=\tan x$$ and tangent at $$x=\displaystyle \frac{\pi}{4}$$ and the $$\mathrm{x}$$-axis is
  • $$\displaystyle \log\sqrt{2}-\frac{\pi}{4}+\dfrac{{\pi}^2}{16}$$ sq. units
  • $$\displaystyle \log\sqrt{2}+\frac{1}{4}$$ sq. units
  • $$\log\sqrt{2}$$
  • log 2
Area bounded by $$\displaystyle \mathrm{f}(\mathrm{x})=\max.(\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{x},\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{x})$$ $$\displaystyle \forall 0\leq x\leq\frac{\pi}{2}$$ and the co-ordinate axis is equal to:
  • $$\displaystyle \frac{1}{\sqrt{2}}$$ sq.units
  • $$\sqrt{2}$$ sq.units
  • $$2$$ sq.units
  • $$1 $$ sq. unit
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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers