Question 1 :
Area bounded between the curve $x^2=y$ and the line $y=4x$ is

Question 2 :
Assertion: The area bounded by the curves $y={x}^{2}+2x-3$ and the line $y=\lambda x+1$ is least, if $\lambda=2$ Reason: The area bounded by the curve $y={x}^{2}+2x-3$ and $y=\lambda x+1$ is $=\dfrac{1}{6}{\left\{{\left(\lambda-2\right)}^{2}+16\right\}}^{\frac{3}{2}}$.sq.unit.

Question 3 :
The value of $a$ for which the area between the curves ${y^2} = 4ax$ and ${x^2} = 4ay$ is $1\,sq.\,unit$, is-

Question 4 :
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 5 :
Two vertices of a rectangle are on the positive x-axis. The other two vertices lie on the lines $y=4x$ and $y=-5x+6$. Then the maximum area of the rectangle is?

Question 6 :
What is the area of the region enclosed between the curve $y^2=2x$ and the straight line $y=x$ ?

Question 7 :
Points of inflexion of the curve<br>$y = x^4 - 6x^3 + 12x^2 + 5x + 7$ are

Question 8 :
The area of the region bounded by the curve $x={ y }^{ 2 }-2$ and $x=y$ is

Question 9 :
If area bounded by the curves $x=at^2$ and $y=ax^2$ is $1$, then a$=$ __________.

Question 11 :
The area of the region bounded by the parabola $(\mathrm{y}-2)^{2}=\mathrm{x}-1$, the tangent to the parabola at the point $(2,\ 3)$ and the $\mathrm{x}$-axis is<br><br>

Question 12 :
If the area enclosed by the parabolas$\displaystyle y=a-x^{2}$ and$\displaystyle y=x^{2}$is $\displaystyle 18\sqrt {2}$ sq. units Find the value of 'a'

Question 13 :
The area bounded by the curves ${y^2} = 4x$ and ${x^2} = 4y$ is :

Question 14 :
Find the area bounded by$\displaystyle y = \cos ^{-1}x,y=\sin ^{-1}x$ and $y-$axis

Question 15 :
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 17 :
The area bounded by $y=2-\left| 2-x \right|$ and $y=\frac { 3 }{ \left| x \right|&#160; }$ is :

Question 18 :
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 19 :
The area bounded by $ \displaystyle x=a\cos ^{3}\theta,y=a\sin ^{3}\theta $ is:<br/>

Question 20 :
The area of the triangle formed by the tan-gent and the normal at $(a,a)$ on the curve ${y^2} = \dfrac{{{x^3}}}{{2a - x}}$ and the line $x=2a$ is (in sq.units)