Telangana TET Paper 2 Math and Science Model Paper 1

Concept:The given expression is a sum of 18 terms, each of the form $(1 + \frac{k}{19})$, where $k$ goes from 1 to 18. This forms an arithmetic progression (AP).Explanation:First, rewrite each term: $(1+\frac{1}{19}) = \frac{20}{19}$, $(1+\frac{2}{19}) = \frac{21}{19}$, ..., $(1+\frac{18}{19}) = \frac{37}{19}$.So the sum $S = \frac{20}{19} + \frac{21}{19} + \dots + \frac{37}{19}$.Factor out $\frac{1}{19}$: $S = \frac{1}{19}(20+21+\dots+37)$.Now find the sum of numbers from 20 to 37. There are 18 terms. First term $a=20$, common difference $d=1$, number of terms $n=18$.Sum of AP = $\frac{n}{2}[2a + (n-1)d] = \frac{18}{2}[2\times 20 + (18-1)\times 1] = 9[40+17] = 9 \times 57 = 513$.Thus $S = \frac{1}{19} \times 513 = 27$.Answer:27 (Option B)