Question : If $x=\frac{3}{2}$, then the value of $27x^{3}-54x^{2}+36x-11$ is:
Option 1: $11\frac{3}{8}$
Option 2: $11\frac{5}{8}$
Option 3: $12\frac{3}{8}$
Option 4: $12\frac{5}{8}$
Correct Answer: $12\frac{5}{8}$
Solution :
Given: $27x^{3}–54x^{2}+36x–11$
Putting the value of $x=\frac{3}{2}$ in the above equation
$27×(\frac{3}{2})^{3}–54×(\frac{3}{2})^{2}+36×\frac{3}{2}–11$
= $27×(\frac{27}{8})–54×(\frac{9}{4})+36×\frac{3}{2}–11$
= $\frac{729}{8}–\frac{486}{4}+\frac{108}{2}–11$
= $\frac{729–972+432–88}{8}$
= $\frac{101}{8}$
= $12\frac{5}{8}$
Hence, the correct answer is $12\frac{5}{8}$.
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