For the adsorption of hydrogen on platinum, the activation energy is $$30 ~\mathrm{k} ~\mathrm{J} \mathrm{mol}^{-1}$$ and for the adsorption of hydrogen on nickel, the activation energy is $$41.4 ~\mathrm{k} ~\mathrm{J} \mathrm{mol}^{-1}$$. The logarithm of the ratio of the rates of chemisorption on equal areas of the metals at $$300 \mathrm{~K}$$ is __________ (Nearest integer)
Given: $$\ln 10=2.3$$
$$\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$
Let $$A = \{ x \in R:[x + 3] + [x + 4] \le 3\} ,$$
$$B = \left\{ {x \in R:{3^x}{{\left( {\sum\limits_{r = 1}^\infty {{3 \over {{{10}^r}}}} } \right)}^{x - 3}} < {3^{ - 3x}}} \right\},$$ where [t] denotes greatest integer function. Then,
The sum of the first $$20$$ terms of the series $$5+11+19+29+41+\ldots$$ is :
A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is $$\frac{k}{3^{11}}$$, then $$k$$ is equal to :