Question 1 :
The area bounded by the circles ${ x }^{ 2 }+{ y }^{ 2 }=1, { x }^{ 2 }+{ y }^{ 2 }=4$ in the first Quadrant is 

Question 2 :
If the line $y = \sqrt{2}x$ cuts the curve $x^2 + y^2 - 9 = 0$ at the points A, B then AB is

Question 3 :
The area bounded by curve $y=x^{2}-1$ and tangents to it at $(2,3)$ and $y-$axis is

Question 4 :
The area bounded by tangent, normal and x-axis at $\mathrm{P}(2,4)$ to the curve $y=x^{2}$<br/>

Question 5 :
Find the area of the region bounded by the curves ${y}^{2}=4ax$ and ${x}^{2}=4ay$.

Question 6 :
The area bounded by the loop of the curve $4{y}^{2}={x}^{2}(4-{x}^{2})$ is _____ S.U

Question 7 :
Area of the region bounded by rays $|x|+y=1$ and X-axis is ___________.

Question 8 :
The area bounded by the curve$y=\sqrt{x}$, the line $2y+3=x$ and the $x$-axis in the first quadrant is

Question 9 :
If the area enclosed between $y=m{x}^{2}$ and $x=n{y}^{2}$ is $\cfrac{1}{3}$ sq. units, then $m,n$ can be roots of (where $m,n$ are non zero real numbers)

Question 10 :
The common area between the curve $x^{2}+ y^{2}=8$ and $ y^{2}=2x$ is

Question 11 :
The parabolas $y^{2}=4x$ and $x^{2}=4y$ divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If $S_{1},S_{2},S_{3}$ are respectively the areas of these parts numbered from top to bottom(Example: $S_1$ is the area bounded by $y=4$ and $x^{2}=4y$ ); then $S_{1},S_{2},S_{3}$ is&#160;&#160;<br/>

Question 12 :
Area enclosed by the graph of the function $y=\ln ^{2}x-1$ lying in the $4th$ quadrant is

Question 13 :
Find the area enclosed the curves : $y=ex\log { x } $ and $\displaystyley=\frac { \log { x } }{ ex } $ where $\log { e } =1$

Question 14 :
If f(x) be an increasing function defined on [a, b] then<br/>max {f(t) such that $a\leq t\leq x$, $a\leq x\leq b$}=f(x)&#160; &amp; min {f(t), $a\leq t\leq x$, $a\leq x\leq b$}=f(a) and if f(x) be decreasing function defined on [a, b] then<br/>max {f(t), $a\leq t\leq x$, $a\leq x\leq b$}=f(a),<br/>min {f(t), $a\leq t\leq x$, $a\leq x\leq b$}=f(x).<br/>On the basis of above information answer the following questions.<br/>$\int_{0}^{\pi }max\left \{ \sin x, \cos x \right \}dx$ is equal to<br/>

Question 16 :
The ratio in which the area bounded by the curves$y^{2}=4x$ and $x^{2}=4y$ is divided by the line $x=1$ is

Question 17 :
$\sin x$ &amp; $\cos x$ meet each other at a number of points and develop symmetrical area.&#160;Area of one such region is

Question 18 :
The whole area of the curves $x=a\cos^3t, y=b\sin^3t$ is given by?

Question 19 :
For what value of 'a' is the area of the figure bounded by$\displaystyle y=\frac{1}{x}, y=\frac{1}{2x-1}$ $x = 2$ &amp; $x = a$ equal to$\displaystyle ln\frac{4}{\sqrt{5}}$?

Question 20 :
The area of the smaller region in which the curve $y=\left [ \frac{x^{3}}{100}+\frac{x}{50} \right ],$ where[.] denotes the greatest integer function, divides the circle $\left ( x-2 \right )^{2}+\left ( y+1 \right )^{2}=4,$ is equal to<br><br><br><br><br><br><br><br>