| Directions: In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer. |
| I. \[\frac{{{2}^{5}}+{{(11)}^{3}}}{6}={{x}^{3}}\] |
| II. \[4{{y}^{3}}=-\ (589\div 4)+5{{y}^{3}}\] |
A) If \[x>y\]
B) If \[x\ge y\]
C) If \[x<y\]
D) If \[x\le y\]
E) If \[x=y\] or the relationship cannot be established
Correct Answer: A
Solution :
| I. \[\frac{{{2}^{5}}+{{(11)}^{3}}}{6}={{x}^{3}}\]\[\Rightarrow \]\[\frac{32+1331}{6}={{x}^{3}}\] |
| \[\Rightarrow \]\[\frac{1363}{6}={{x}^{3}}\]\[\Rightarrow \]\[x=\sqrt[3]{227.17}\] |
| II. \[4{{y}^{3}}=-\frac{(589)}{4}+5{{y}^{3}}\] |
| \[\Rightarrow \]\[-\,\,{{y}^{3}}=\frac{-\,\,589}{4}\]\[\Rightarrow \]\[y=\sqrt[3]{147.25}\] |
| \[\therefore \]\[x>y\] |
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