CTET Paper II (Mathematics and Science) 22 Dec 2021 Solved Paper

Concept:Ascending order means arranging numbers from the smallest to the largest. Negative numbers are always smaller than positive numbers. Compare the two negative numbers first, then compare the three positive numbers.Explanation:Convert the mixed fractions to improper fractions: $-1\frac{3}{5} = -\frac{8}{5}$ and $-2\frac{1}{3} = -\frac{7}{3}$.To compare them, get a common denominator: $-\frac{8}{5} = -\frac{24}{15}$, $-\frac{7}{3} = -\frac{35}{15}$.Since $-\frac{35}{15} < -\frac{24}{15}$, we have $-2\frac{1}{3} < -1\frac{3}{5}$.Now compare the three positive numbers: $\frac{1}{2} = 0.5$, $\frac{2}{5} = 0.4$, and $(\frac{2}{5})^{100} = (0.4)^{100}$.Since $0.4$ is less than $1$, raising it to a large power makes it smaller: $(0.4)^{100} < 0.4$.Thus, $(0.4)^{100} < 0.4 < 0.5$, i.e., $(\frac{2}{5})^{100} < \frac{2}{5} < \frac{1}{2}$.Combining all: $-2\frac{1}{3} < -1\frac{3}{5} < (\frac{2}{5})^{100} < \frac{2}{5} < \frac{1}{2}$.Answer:Option C: $-2\frac{1}{3}, -1\frac{3}{5}, (\frac{2}{5})^{100}, \frac{2}{5}, \frac{1}{2}$.