TS EAMCET · Maths · Permutation Combination
Let \(a, b, c \in \mathbb{N}\) and \(a+b+c=5\). Let \(\mathrm{L}, \mathrm{M}\) be the least and greatest values of \(2^a 3^b 5^c\) respectively. Then \(\mathrm{M}-\mathrm{L}=\)
- A \(2.3^2 .5 .7\)
- B \(2^2 .3 .5 .7\)
- C \(2.3^2 \cdot 5^2 \cdot 7^0\)
- D \(2^0 \cdot 3 \cdot 5^3 \cdot 7^0\)
Answer & Solution
Correct Answer
(A) \(2.3^2 .5 .7\)
Step-by-step Solution
Detailed explanation
Given expression is \(2^{\mathrm{a}} 3^{\mathrm{b}} 5^{\mathrm{c}}\) in which \(\mathrm{a}+\mathrm{b}+\mathrm{c}=5\) and \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) e. Total number of combinations of \(a, b, c\) to be a sum 5 . are \((1,1,3),(1,3,1),(3,1,1),(2,2,1),(1,2,2)\) and…
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