Question 1 :
The area bounded by the curve $y = f\left( x \right)$, above the $x$-axis, between $x = a$ and $x = b$ is:
Question 3 :
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
Question 4 :
Area bounded by curve $x\left( { x }^{ 2 }+p \right) =y-1$ with $y=1$ $p<0$is -
Question 5 :
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
Question 6 :
The area of the region bounded by the curve $x={ y }^{ 2 }-2$ and $x=y$ is
Question 7 :
If the area bounded by the x-axis, curve $y=f(x)$ and the lines $x=1$, $x=b$ is equal to $\sqrt{b^2+1}-\sqrt{2}$ for all $b > 1$, then $f(x)$ is
Question 8 :
Find the area of the closed figure bounded by the following curves $y = 2$ $\cos^2 x (1 \, + \,  \sin^2 x)$ on the interval $[0, 2\pi]$ and the abscissa axis.
Question 9 :
Points of inflexion of the curve<br>$y = x^4 - 6x^3 + 12x^2 + 5x + 7$ are
Question 10 :
The value of $a$ for which the area between the curves ${y^2} = 4ax$ and ${x^2} = 4ay$ is $1\,sq.\,unit$, is-
Question 12 :
The area included between the parabolas<br>$y=\dfrac { { x }^{ 2 } }{ 4a }$ and $y=\dfrac { 8{ a }^{ 3 } }{ { x }^{ 2 }+4{ a }^{ 2 } }$ is<br>
Question 13 :
Find the area of the closed figure bounded by the following curves y = cos x (0 $\leqslant  x \leqslant  \pi/2)$, y = 0, x = 0, and a straight. line which is a tangent to the curve y = cos x at the point x = $\pi/4$.
Question 14 :
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?
Question 15 :
The area of the figure bounded by $f\left(x\right)=\sin{x}, g\left(x\right)=\cos{x}$ in the first quadrant is:
Question 16 :
The area bounded by the curve $|x| = \cos^{-1} y $ and the line $|x| = 1$ and the $x$ - axis is 
Question 17 :
The area bounded by the curves $y=(x-3)^2$ and $y=x$ (in sq. units to nearest integer):
Question 18 :
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 $k=$
Question 19 :
The area enclosed by the circle $x^{2} + y^{2} = 2$ is equal to
Question 20 :
Consider the functions $f(x)$ and $g(x)$, both defined from $R \rightarrow R$ and are defined as $f(x)=2x-x^{2}$ and $g(x)=x^{n}$ where $n \in N$. If the area between $f(x)$ and $g(x)$ in first quadrant is $1/2$ then $n$ is not a divisor of :
Question 21 :
A polynomial $P$ is positive for $x>0$ and the area of the region bounded by $P\left(x\right),$ the $x-$axis and the vertical lines $x=0$ and $x=\lambda$ is $\dfrac{{\lambda}^{2}\left(\lambda+3\right)}{3}$ sq.unit. Then polynomial $P\left(x\right)$ is:
Question 22 :
The area bounded by the circles ${ x }^{ 2 }+{ y }^{ 2 }=1, { x }^{ 2 }+{ y }^{ 2 }=4$ in the first Quadrant is 
Question 23 :
The area bounded by the curves $y=\sqrt{-x}$ and $x=-\sqrt{-y}$, where $x,y\le0$, is equal to
Question 24 :
$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.<br/>The area bounded by the curve y=f(x), x=$\pi $ and y=0 is:
Question 25 :
The area bounded by the line $\mathrm{x}=1$ and the curve $\sqrt{\dfrac{y}{x}}+\sqrt{\dfrac{x}{y}}=4$ is<br>
Question 26 :
The common area between the curve $x^{2}+ y^{2}=8$ and $ y^{2}=2x$ is
Question 27 :
Area of the region bounded by the curve $y={25}^{x}+16$ and curve $y=b.{5}^{x}+4$ whose tangent at the point $x=1,$ makes an angle ${\tan}^{-1}\left(40\log{5}\right)$ with the $x-$axis is:
Question 28 :
Area bounded by the curves $y = e^x, y = e^{-x}$ and the straight line $x = 1$ is (in sq units)
Question 29 :
The area bound by circled $ x^{2} + y^{2} = r^{2}, r=1,2 $ and rays given by $2x^{2}-3xy-2y^{2} = 0,  $ is 
Question 30 :
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 31 :
The area bounded by $y^{2}=4ax$ and $y=mx$ is $\displaystyle \frac{a^{2}}{3}$ sq. units then $\mathrm{m}$<span><br/></span>
Question 32 :
The area enclosed by the curves $y^{2} = x$ and $y = |x|$ is
Question 33 :
Find the area of the region bounded by the curves ${y}^{2}=4ax$ and ${x}^{2}=4ay$.
Question 34 :
The area inside the parabola $5x^2-y=0$ but outside the parabola $2x^2-y+9=0$, is
Question 35 :
The area bounded by curve $y=x^{2}-1$ and tangents to it at $(2,3)$ and $y-$axis is
Question 36 :
The area of the region described by $ \begin{Bmatrix} (x,,y)/x^2 +y^2 \leq 1 and\   y^2\leq1-x\end{Bmatrix}$ is
Question 37 :
The area bounded by the curve $y={ e }^{ x }$ and the lines y = |x - 1|, x = 2 is given by :
Question 38 :
The value of the parameter $a$ such that the area bounded by $y=a^{2}x^{2}+ax+1,$ coordinate axes and the line $x=1$ attains its least value, is equal to
Question 40 :
The area common to the circle ${x}^{2}+{y}^{2}=16{a}^{2}$ and the parabola ${y}^{2}=6ax$ is
Question 41 :
The area enclosed between the curves $y = a x ^ { 2 }$ and $x = a y ^ { 2 } ( a > 0 )$ is $1$ sq. unit, then the value of $a$ is
Question 42 :
Area enclosed by the graph of the function $y=\ln ^{2}x-1$ lying in the $4th$ quadrant is
Question 43 :
The area bounded by $ \displaystyle y=\frac{3x^{2}}{4} $ and the line $ \displaystyle 3x-2y+12=0 $ is:<br/>
Question 44 :
Find the equation of the line passing through the origin and dividing the curvilinear triangle with vertex at the origin, bounded by the curves $y=2x-x^2, y=0$ and $x=1$ into two parts of equal area.
Question 45 :
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>
Question 46 : <div>Let function $f_n$ 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 $n=3$, ${f_3} = 3,since, 3 = 3, 3 = 2 + 1$ and $ 3 = 1+1+1$. Then${f_5} =$</div>
Question 47 :
The whole area of the curves $x=a\cos^3t, y=b\sin^3t$ is given by?
Question 48 :
Let $g(x) = \cos x^{2}, f(x) = \sqrt {x}$, and $\alpha, \beta (\alpha < \beta)$ be the roots of the quadratic equation $18x^{2} - 9\pi x + \pi^{2} = 0$. Then the area (in $sq.\ units$) bounded by the curve $y = (gof)(x)$ and the lines $x = \alpha, x = \beta$ and $y = 0$, is
Question 49 :
The area bounded by the curves ${y^2} = 4x$ and ${x^2} = 4y$ is :
Question 50 :
The triangle formed by the tangent to the parabola $y^2=4x$ at the point whose abscissa lies in the interval $\left[a^2, 4a^2\right]$, the ordinate and the x-axis, has the greatest area equal to?
Question 51 :
$R=((x,y):|x|\le |y|\quad and\quad { x }^{ 2 }+{ y }^{ 2 }\le 1)is$
Question 52 :
Area bounded by the curves $y=\log _{ e }{ x } \quad$ and  $y={ \left( \log _{ e }{ x }  \right)  }^{ 2 }$ is ?<br/>
Question 53 : On the real line R, we define two functions f and g as follows:<br/>$f(x) = min [x - [x], 1 - x + [x]]$,<br/>$g(x) = max [x - [x], 1 - x + [x]]$,<br/>where [x] denotes the largest integer not exceeding x. <div>The positive integer n for which $\displaystyle \int_{0}^{n}{(g(x) - f(x) ) dx = 100}$ is?</div>
Question 54 :
The area bounded by $y=2-\left| 2-x \right|$ and $y=\frac { 3 }{ \left| x \right|  }$ is :
Question 55 :
Area bounded by the curves $y = \sin x ,$ tangent drawn to it at $x = 0$ and the line $x = \frac { \pi } { 2 }$ is equal to
Question 56 :
The area bounded by the curve $ y = \dfrac { \sin { x }  }{ { x } } , x-$ axis and the ordinates $ x=0,x=\dfrac { \pi }{ { 4 } }$ is:
Question 57 :
For what value of 'a' is the area of the figure bounded by $\displaystyle y=\frac{1}{x}, y=\frac{1}{2x-1}$ $x = 2$ & $x = a$ equal to $\displaystyle ln\frac{4}{\sqrt{5}}$?
Question 58 :
The smaller area enclosed by $y=f(x)$, where $f(x)$ is polynomial of least degree satisfying $\displaystyle{ \left[ \lim _{ x\rightarrow 0 }{ 1+\frac { f\left( x \right)  }{ { x }^{ 3 } }  }  \right]  }^{ \tfrac { 1 }{ x }  }=e$ and the circle $x^2+y^2=2$ above the $x-$axis is
Question 59 :
Area of the region bounded by curves y=x log x and $y={ 2x-x }^{ 2 }$ is
Question 60 :
The area (in square units) bounded by the curves $x\, =\, -2y^2$ and $x\, =\, 1-3y^2$ is
Question 61 :
The area bounded by the curve $f(x) = \mid \mid tanx + cotx \mid - \mid tanx - cotx \mid \mid$ between the lines $x=0, \ x= \dfrac{\pi}{2}$ and the $X-$axis is
Question 62 :
the volume of a solid obtained by revolving about y-axis enclosed between the ellipse ${x}^{2}+9{y}^{2}=9$ and the straight line $x+3y=3$ in the first quadrant is
Question 63 : Match the following:<br/><table class="wysiwyg-table"><tbody><tr><td>List-I</td><td>List-II</td></tr><tr><td>1. Area of region bounded by $y=2x-x^{2}$ and $x-$axis</td><td>a. $\dfrac13$</td></tr><tr><td>2. Area of the region $\{(x, y):x^{2}\leq y\leq|x|\}$</td><td>b. $\dfrac12$</td></tr><tr><td>3. Area bounded by $y=x$ and $y=x^{3}$</td><td>c. $\dfrac23$</td></tr><tr><td>4. Area bounded by $y=x|x|$, ${x}$-axis and ${x}=-1,\ {x}=1$</td><td>d. $\dfrac43$</td></tr></tbody></table>The correct match for $1\ 2\ 3\ 4$ is
Question 64 :
Area bounded by the curves $\displaystyle y = \left[ \frac{x^2}{64} + 2 \right]$ ([.] denotes the greatest integer function) $y = x - 1$ and $x = 0$ above the x-axis is
Question 65 :
Find the area bounded by $\displaystyle y = \cos ^{-1}x,y=\sin ^{-1}x$ and $y-$axis
