The area of the region bounded by the lines $y=mx$,$x=1$,$x=2$,and the $x$-axis is $6$ sq. units. Then,the value of $m$ is:

The area of the region bounded by the curve $y=x$,the lines $x=1$ and $x=10$ using integration is . . . . . . sq. units.

The area bounded by the curve $x(x^2 + p) = y - 1$ and the line $y = 1$ is:

The area of the region bounded by the curve $5y = 5 - x$,the $X$-axis,and the lines $x = 1$ and $x = 4$ is . . . . . . sq. units.

$AOB$ is the positive quadrant of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ in which $OA=5, OB=3$. The area between the arc $AB$ and the chord $AB$ of the ellipse in sq. units is

If the straight line $x=b$ divides the area enclosed by $y=(1-x)^2$,$y=0$,and $x=0$ into two parts $R_1 (0 \leq x \leq b)$ and $R_2 (b \leq x \leq 1)$ such that $R_1 - R_2 = \frac{1}{4}$,then $b$ equals: