Question

The value of
$\frac{(1111{)}^3+(2212{)}^3-(3.323{)}^3}{\left(1.111\right)\left(2212\right)(-3.323)}$
lies between?

• A. -0.5 and 0
• B. 0 and 0.5
• C. 0.5 and 1
• D. 2.5 and 3.5
• E. None of these

Answer 1

The correct option is D 2.5 and 3.5

Here, given expression is
$\frac{(1111{)}^3+(2212{)}^3-(3.323{)}^3}{\left(1.111\right)\left(2212\right)(-3.323)}$
Here, put a = 1.111, b = 2.112
and c = 3.323
So, given expression can also be written as
$\frac{a^3+b^3+(-c{)}^3}{-abc}Now,here,a+b+c=0$
$Hence,a^3+b^3+c^3=3abcSo,\frac{3abc}{abc}=3$
So, its value lies between 2.5 and 3.5