The temperature coefficient of a reaction is $2$. When the temperature is increased from $30^{\circ} C$ to $90^{\circ} C$,the rate of reaction is increased by: (in $\times$)

For the reaction $2NO + Cl_2 \rightarrow 2NOCl$,the rate is given by $Rate = K[NO]^2[Cl_2]$. How can the rate constant $(K)$ of the reaction be increased?

Consider the following statements related to the temperature dependence of rate constants. Identify the correct statements:
$A.$ The Arrhenius equation holds true only for an elementary homogeneous reaction.
$B.$ The unit of $A$ is the same as that of $k$ in the Arrhenius equation.
$C.$ At a given temperature,a low activation energy means a fast reaction.
$D.$ $A$ and $E_a$ as used in the Arrhenius equation depend on temperature.
$E.$ When $E_a > RT$,$A$ and $E_a$ become interdependent.
Choose the correct answer from the options given below:

Half life of a first order reaction is $900 \ \text{min}$ at $400 \ K$. Find its half life at $300 \ K$. Given: $\frac{E_a}{2.303 \ R} = 1.3056 \times 10^3 \ K$. (in $\text{min}$)

The rate constant is given by the equation $k = p Z e^{-E_a/RT}$. Which factor should register a decrease for the reaction to proceed more rapidly?

For a first order decomposition of a certain reaction,rate constant is given by the equation $\log k \left( s^{-1} \right) = 7.14 - \frac{1 \times 10^4 \ K}{T}$. The activation energy of the reaction (in $kJ \ mol^{-1}$) is $(R = 8.3 \ J \ K^{-1} \ mol^{-1})$ (in $.1$)