Arrange the following compounds in the decreasing order of their reactivity towards $HBr$:
$(a)$ $(CH_3)_2C=CH_2$
$(b)$ $CH_3O-C(CH_3)=CH_2$
$(c)$ $CH_3OCH_2-C(CH_3)=CH_2$

Two blocks $A$ and $B$ of masses $1\,kg$ and $2\,kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of $K.E.s$ of both the blocks is

Pulses are obtained from which family?

$A$ tension of $20 ~N$ is applied to a copper wire of cross-sectional area $0.01 ~cm^2$. The Young's modulus of copper is $1.1 \times 10^{11} ~N/m^2$ and the Poisson's ratio is $0.32$. The decrease in the cross-sectional area of the wire is:

If $\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$, then $g(x)$ is equal to

The length of the transverse common tangent of the circles $x^2+y^2-2x+4y+4=0$ and $x^2+y^2+4x-2y+1=0$ is