For reaction $A \to B$,rate constant $K_1 = A_1 e^{-E_{a_1}/RT}$ and for the reaction $X \to Y$,rate constant $K_2 = A_2 e^{-E_{a_2}/RT}$. If $A_1 = 10^8, A_2 = 10^{10}$ and $E_{a_1} = 600 \ cal \ mol^{-1}$,$E_{a_2} = 1800 \ cal \ mol^{-1}$,then the temperature at which $K_1 = K_2$ is (given: $R = 2 \ cal \ K^{-1} \ mol^{-1}$):

In a reaction,for every $10\,^{\circ}C$ rise of temperature,the rate is doubled. If the temperature is increased from $10\,^{\circ}C$ to $100\,^{\circ}C,$ the rate of the reaction will become $.......$ times.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: $A$ reaction can have zero activation energy.
Reason $R$: The minimum extra amount of energy absorbed by reactant molecules so that their energy becomes equal to threshold value,is called activation energy.
In the light of the above statements,choose the correct answer from the options given below:

The rate constant for a reaction can be increased by $\underline{a}$ the stability of the reactant or by $\underline{b}$ the stability of the transition state. Select the correct choice for $a$ and $b$.

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 $times$)

$A$ catalyst: