If $\frac{1}{4}, \mathrm{a}, \mathrm{b}, \frac{1}{19}$ form a H.P. then the values of a and $\mathrm{b}$ are…

If $\frac{1}{4}, \mathrm{a}, \mathrm{b}, \frac{1}{19}$ form a H.P. then the values of a and $\mathrm{b}$ are respectively
  1. $\frac{1}{12}, \frac{1}{15}$
  2. $\frac{1}{5}, \frac{1}{7}$
  3. $\frac{1}{9}, \frac{1}{14}$
  4. $\frac{1}{11}, \frac{1}{17}$

Solution

$\frac{1}{4}, a, b, \frac{1}{19} \longrightarrow$ H.P. $4, \frac{1}{a}, \frac{1}{b}, 19 \rightarrow$ AP $a=\frac{1}{9}, b=\frac{1}{14}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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