CTET Paper II (Mathematics and Science) 24 Dec 2021 Solved Paper

Concept:Simplify the numerator and denominator separately using fraction operations, then find the reciprocal of the final value.Explanation:First, simplify the numerator: $-\frac{3}{4} \times \left(\frac{2}{3} + \frac{-5}{6}\right)$. Inside the bracket, $\frac{2}{3} - \frac{5}{6} = \frac{4-5}{6} = \frac{-1}{6}$. So numerator becomes $-\frac{3}{4} \times \frac{-1}{6} = \frac{3}{24} = \frac{1}{8}$.Now simplify the denominator: $-\frac{2}{3} \times \frac{3}{5} + \frac{5}{2} - \frac{3}{5} \times \frac{1}{6}$. The first term is $-\frac{2}{5}$, the third term is $-\frac{3}{30} = -\frac{1}{10}$. Combine: $-\frac{2}{5} + \frac{5}{2} - \frac{1}{10} = \frac{-4+25-1}{10} = \frac{20}{10} = 2$. So denominator is $2$.Thus $p = \frac{\frac{1}{8}}{2} = \frac{1}{8} \times \frac{1}{2} = \frac{1}{16}$.The reciprocal of $\frac{1}{16}$ is $16$.Answer:Option D: 16