Let a, b, c in mathbb{N} and a+b+c=5. Let L a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given $a, b, c \in \mathbb{N}$ (positive integers) such that $a+b+c=5$. The possible triplets $(a, b, c)$ are $(1, 1, 3), (1, 3, 1), (3, 1, 1), (2

Vedclass · Accepted Answer

$2 \cdot 3^2 \cdot 5 \cdot 7$

Vedclass · Answer

(A) Given $a, b, c \in \mathbb{N}$ (positive integers) such that $a+b+c=5$. The possible triplets $(a, b, c)$ are $(1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1), (1, 2, 2), (2, 1, 2)$.Calculating the values of $2^a 3^b 5^c$ for each triplet:$(1, 1, 3) \implies 2^1 \cdot 3^1 \cdot 5^3 = 6 \cdot 125 = 750$$(1, 3, 1) \implies 2^1 \cdot 3^3 \cdot 5^1 = 2 \cdot 27 \cdot 5 = 270$$(3, 1, 1) \implies 2^3 \cdot 3^1 \cdot 5^1 = 8 \cdot 3 \cdot 5 = 120$$(2, 2, 1) \implies 2^2 \cdot 3^2 \cdot 5^1 = 4 \cdot 9 \cdot 5 = 180$$(1, 2, 2) \implies 2^1 \cdot 3^2 \cdot 5^2 = 2 \cdot 9 \cdot 25 = 450$$(2, 1, 2) \implies 2^2 \cdot 3^1 \cdot 5^2 = 4 \cdot 3 \cdot 25 = 300$The greatest value $M = 750$ and the least value $L = 120$.Then $M - L = 750 - 120 = 630$.Prime factorization of $630 = 2 \cdot 3^2 \cdot 5 \cdot 7$.Thus,option $A$ is correct.

Let $a, b, c \in \mathbb{N}$ and $a+b+c=5$. Let $L$ and $M$ be the least and greatest values of $2^a 3^b 5^c$ respectively. Then $M-L=$

Similar Questions

The number of ways of selecting $8$ letters from $24$ letters,of which $8$ are $a$,$8$ are $b$,and the remaining $8$ are distinct,is given by:

If $^n{P_4} = 30 \times {^n}{C_5}$,then $n = $

The number of permutations of the letters $a_1, a_2, a_3, a_4, a_5$ in which the first letter $a_1$ does not occupy the first position and the second letter $a_2$ does not occupy the second position is:

If all the letters of the word $'GANGARAM'$ are arranged,then the number of words in which exactly two vowels are together but no two $'G'$ occur together is-

If $^{n}P_{4} = 24 \times ^{n}C_{5}$,then the value of $n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module