If the rate of the reaction is equal to the rate constant,the order of the reaction is

$A$ vertical mass-spring system executes simple harmonic oscillations with a period of $2\,s$. $A$ quantity of this system which exhibits simple harmonic variation with a period of $1\,s$ is

$A$ person running horizontally observes that rain is falling on his head vertically with a speed of $10\,m/s$. When he stops,he observes that the rain is falling at an angle of $30^{\circ}$ with the vertical. Find the speed of the rain with respect to the ground.

$(\vec{a} \times \vec{b}) \times [(\vec{b} \times \vec{c}) \times (\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a})]$ is

The isothermal Bulk modulus of an ideal gas at pressure $P$ is

If $\left|\begin{array}{ccc}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0$ and $x \neq y \neq z$,then $1+x y z$ is equal to