The area (in sq. units) bounded by the curves $y=\sqrt{x}$,$2y-x+3=0$,$X$-axis and lying in the first quadrant is

An electric fan has blades of length $30 \, cm$ as measured from the axis of rotation. If the fan is rotating at $1200 \, r.p.m.$,the acceleration of a point on the tip of the blade is approximately ........ $m/s^2$.

The rate of steady volume flow of water through a capillary tube of length $l$ and radius $r$, under a pressure difference of $p$ is $V$. This tube is connected with another tube of the same length but half the radius, in series. Then, the rate of steady volume flow through them is (The pressure difference across the combination is $p$.)

Suppose that the points $(h, k)$,$(1, 2)$,and $(-3, 4)$ lie on the line $L_1$. If a line $L_2$ passing through the points $(h, k)$ and $(4, 3)$ is perpendicular to $L_1$,then $\frac{k}{h}$ equals

$A$ wall has two layers $A$ and $B$, each made of a different material. Both the layers have the same thickness. The thermal conductivity of the material of $A$ is twice that of $B$. Under thermal equilibrium, the temperature difference across the wall is $36^{\circ}C$. The temperature difference across the layer $A$ is ......... $^{\circ}C$

The mean of the numbers obtained on throwing a die having $1$ on three faces,$2$ on two faces,and $5$ on one face is