1) If $2+\frac{1}{x +\frac{1}{y+\frac{1}{z}}}=\frac{37}{13}$ where x, y, z are natural numbers, then x,y,z are: A) 1,2,5 B) 1,5,2 C) 5,2,11 D) 11,2,5 Answer: Option BExplanation:$2+\frac{1}{x +\frac{1}{y+\frac{1}{z}}}=\frac{37}{13}$$=2 \frac{11}{13}=2+\frac{11}{13}$$\Rightarrow\frac{1}{x +\frac{1}{y+\frac{1}{z}}}=\frac{11}{13}$$\Rightarrow x+\frac{1}{y+\frac{1}{z}}=\frac{13}{11}$$\Rightarrow x+\frac{1}{y+\frac{1}{z}}=1 +\frac{2}{11}$$\Rightarrow x =1 $, $y+\frac{1}{z}=\frac{11}{2}$$=5\frac{1}{2}=5+\frac{1}{2}$$\Rightarrow$ x =1, y = 5, z = 2
