Question 1 : <div><span>Conclude from the following:</span><br/></div>$n^2 > 10$, and n is a positive integer.<div>A: $n^3$</div><div>B: $50$</div>
Question 2 :
If $x+y \leq 2, x\leq 0, y\leq 0$ the point at which maximum value of $3x+2y$ attained will be.<br/>
Question 3 :
Find the output of the program given below if$ x = 48$<br/>and $y = 60$<br/>10  $ READ x, y$<br/>20  $Let x = x/3$<br/>30  $ Let y = x + y + 8$<br/>40  $ z = \dfrac y4$<br/>50  $PRINT z$<br/>60  $End$
Question 4 :
The value of $a$ for which the area between the curves ${y^2} = 4ax$ and ${x^2} = 4ay$ is $1\,sq.\,unit$, is-
Question 5 :
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 7 :
If area bounded by the curves $x=at^2$ and $y=ax^2$ is $1$, then a$=$ __________.
Question 9 :
The area of the region bounded by the curve $x={ y }^{ 2 }-2$ and $x=y$ is
Question 10 :
Area bounded by curve $x\left( { x }^{ 2 }+p \right) =y-1$ with $y=1$ $p<0$is -
Question 11 :
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 12 :
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 13 :
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 14 :
The area bounded by the curve $y = f\left( x \right)$, above the $x$-axis, between $x = a$ and $x = b$ is:
Question 15 :
What is the area of the region enclosed between the curve $y^2=2x$ and the straight line $y=x$ ?
Question 16 :
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 17 :
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 18 :
Points of inflexion of the curve<br>$y = x^4 - 6x^3 + 12x^2 + 5x + 7$ are
Question 19 :
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 20 :
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 21 :
The area bounded by the line $y=x$, x-axis and ordinates $x=-1$ and $x=2$ is?
Question 22 :
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 23 :
The area enclosed between the curve $\displaystyle y=1+{ x }^{ 2 }$, the y-axis and the straight line $\displaystyle y=5$ is given by
Question 24 :
Find the area of the closed figure bounded by the following curves <span>y =$0.5x^2$ - 2x + 2 and the tangents to it: y = -x + 1.5 at the point (1, 1/2), and y = 2x - 6 at the point (4, 2).</span>
Question 25 :
It the area bounded between $x-$ axis and the graph of $y= 6-3x^2$ between the ordiantes $x=1$ and $x=a $ is $19$ square units then $a$ can take the values :
Question 26 :
The area bounded by the curve $y={ e }^{ x }$ and the lines y = |x - 1|, x = 2 is given by :
Question 27 :
The area (in square units) bounded by the curves $y^{2} = 4x$ and $x^{2} = 4y$ is
Question 28 :
Area bounded by the line $y=x,$ curve $y=f\left(x\right),\left(f\left(x\right)>x,x>1\right)$ and the lines $x=1,x=t$ is $\left(t+\sqrt{\left(1+{t}^{2}\right)}\right)-\left(1+\sqrt{2}\right)$ for all $t>1$. Then $f\left(x\right)=$
Question 29 :
The area enclosed between the parabolas $y^{2} = 16x$ and $x^{2} = 16y$ is
Question 30 :
The are included between the curves $y^2 = 4ax \,$ and $\, x^2 = 4 ay$ is ____  sq units.
Question 31 :
The area bounded by the circles ${ x }^{ 2 }+{ y }^{ 2 }=1, { x }^{ 2 }+{ y }^{ 2 }=4$ in the first Quadrant is 
Question 32 :
What is the area of the region bounded by X-axis, the curve $y=f(x)$ and the two ordinates $x = \dfrac{1}{2}$ and $x=1$?
Question 33 :
The area bounded by the curve $y^2 = 4x$ and the line $2x - 3y + 4 = 0$ is
Question 34 :
What is the area of the rectangle , whose length is $5\sqrt 3\ cm$ and breadth is $5\ cm$.
Question 35 :
The area bounded by the parabolas $y=4x^2,\,y=\dfrac{x^2}{9}$ and line $y=2$ is
Question 36 :
Tangents are drawn from a point $P$ to a parabola $y^{2}=4ax$. The area enclosed by the tangents and the corresponding chord of contact is $4a^{2}$. Then point $P$ satisfies
Question 38 :
The area bounded by $\displaystyle y={ xe }^{ |X| }$ and $\displaystyle |x|=1$ is -
Question 39 :
The area bounded by the curve $y=\sqrt{x}$, the line $2y+3=x$ and the $x$-axis in the first quadrant is
Question 40 :
Consider the function $f\left( x \right) = \left| {x - 1} \right| + {x^2},\,\,where\,\,x \in R$<br/>What is the area of the region bounded by X-axis, the  curve $y = f\left( x \right)$ and the two ordinates $x = \frac{1}{2}\,\,\,and\,\,\,x = 1$.
Question 42 :
The area of the figure bounded by the curves $y=\left|x-1\right|$ and $y=3-\left|x\right|$ is
Question 44 :
The area bounded by the curve $y=cos ax$ in one are of the curve is where $a=4n+1,n\in integer$
Question 45 :
Area bounded between the curve $x^2=y$ and the line $y=4x$ is
Question 46 :
The area bounded by the curve $|x| = \cos^{-1} y $ and the line $|x| = 1$ and the $x$ - axis is 
Question 47 :
The area bounded by the line $\mathrm{x}=1$ and the curve $\sqrt{\dfrac{y}{x}}+\sqrt{\dfrac{x}{y}}=4$ is<br>
Question 48 :
Tangents are drawn to the ellipse $\dfrac {x^{2}}{9} + \dfrac {y^{2}}{5} = 1$ at the ends of both latus rectum. The area of the quadrilateral so formed is
Question 49 :
The area common to the circle ${x}^{2}+{y}^{2}=16{a}^{2}$ and the parabola ${y}^{2}=6ax$ is
Question 50 :
The area of the region bounded by $y=(x-4)^2, y=16-x^2$ and the x axis,is
Question 51 :
Find the area bounded on the right by the line x+2=y, on the left by the parabola $y=x^{2}$ and above the x-axis
Question 52 :
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
Question 53 : <p>The area bounded by $y = f\left( x \right),x - axis$ and the line $y = 1$, where $f\left( x \right) = 1 + \dfrac{1}{x}\int\limits_1^x {f\left( t \right)dt} $  is</p>
Question 54 : <div>Find the area lying in first quadrant and included between the circle ${ x }^{ 2 }+{ y }^{ 2 }=8$ and $x$ axis.</div>
Question 55 :
The area enclosed between the curve $x^2 - 3x - y = 0$ and the line $y = x$, is 
Question 56 :
The area of the region bounded by the curves $y={ xe }^{ x },y={ xe }^{ -x }$ and the line $x=1$ is
Question 57 :
Let $f(x)={ x }^{ 2 }-3x+2$ then area bounded by the curve $f\left( \left| x \right| \right) $ (in square units) and x-axis is
Question 58 :
Compute the area of the figure bounded by straight lines $x = 0$, $x = 2$ and the curves $y = 2^{x}$ and $y = 2x - x^{2}$.
Question 59 :
The area bounded by the graph $y=\left|\left[x-3\right]\right|$, the $x-$axis and the lines $x=-2$ and $x=3$ is ($\left[.\right]$ denotes the greatest Integer function):
Question 60 :
Find the area cut off from the parabola $4y={3x}^{2}$ by the straight line $2y=3x+12$.
Question 61 :
The area of the region bounded by the curve $y=2x-x^2$ and the line $y=x$ is ________ square units.
Question 62 :
The area of the region bounded by the curve $y=\phi(x),y=0$ and $x=10$ is
Question 64 :
Let $A$ be the area bounded by the curve $y={(\tan{x})}^{n}$ for $n> 2$ and the lines $x=0$ and $y=0$ and $x=\cfrac{\pi}{4}$ then the range of ${A}_{10}$ is
Question 65 :
The area bounded by the curves $y = \log _ { e } x$ and $y = \left( \log _ { e } x \right) ^ { 2 }$ is
Question 66 :
The area inside the parabola $5x^2-y=0$ but outside the parabola $2x^2-y+9=0$, is
Question 67 :
$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 68 :
The area bounded by the curves $y=\sqrt{-x}$ and $x=-\sqrt{-y}$, where $x,y\le0$, is equal to
Question 69 :
If $f\left(x+y\right)=f\left(x\right)+f\left(y\right)-xy$ for all $x,y\in R$ and $\lim _{ h\rightarrow 0 }{ \frac { f(h) }{ h }  } =3$, then the area bounded by the curves $y=f\left(x\right)$ and $y={x}^{2}$ is:
Question 70 :
The area bounded by the curves $y = -x^2 + 3$ and $y = 0$
