Let S be the set of all ordered pairs (x, y) | vedclass

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

Question

(B) Given $	ext{HCF}(x, y) = 16$ and $	ext{LCM}(x, y) = 48000$. Let $x = 16a$ and $y = 16b$,where $	ext{HCF}(a, b) = 1$. We know that $	ext{LCM}(x

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) Given $	ext{HCF}(x, y) = 16$ and $	ext{LCM}(x, y) = 48000$. Let $x = 16a$ and $y = 16b$,where $	ext{HCF}(a, b) = 1$. We know that $	ext{LCM}(x, y) = 	ext{HCF}(x, y) 	imes a 	imes b$. $48000 = 16 	imes a 	imes b \implies ab = \frac{48000}{16} = 3000$. Prime factorization of $3000 = 3 	imes 1000 = 3^1 	imes 2^3 	imes 5^3$. Since $	ext{HCF}(a, b) = 1$,the prime factors $2^3, 3^1, 5^3$ must be distributed between $a$ and $b$ such that no prime factor is common to both. For each prime factor $p^k$,we have two choices: either it is a factor of $a$ or it is a factor of $b$. There are $3$ distinct prime factors $(2, 3, 5)$. For each prime factor,there are $2$ choices. Total number of pairs $(a, b) = 2^3 = 8$. Since each pair $(a, b)$ corresponds to a unique pair $(x, y)$,the number of elements in $S$ is $8$.

Let $S$ be the set of all ordered pairs $(x, y)$ of positive integers,with $\text{HCF}(x, y) = 16$ and $\text{LCM}(x, y) = 48000$. The number of elements in $S$ is

Similar Questions

Let $A$ denote the set of all real numbers $x$ such that $x^3-[x]^3=(x-[x])^3$,where $[x]$ is the greatest integer less than or equal to $x$. Then,

The number of polynomials $p(x)$ with integer coefficients such that the curve $y=p(x)$ passes through $(2,2)$ and $(4,5)$ is

Let $A = \{\theta \in R \mid \cos^2(\sin \theta) + \sin^2(\cos \theta) = 1\}$ and $B = \{\theta \in R \mid \cos(\sin \theta) \sin(\cos \theta) = 0\}$. Then,$A \cap B$ is:

If $A, B,$ and $C$ are three sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$,then

Let $S = \{ x \in \mathbb{R} : x \ge 0 \text{ and } 2|\sqrt{x} - 3| + \sqrt{x}(\sqrt{x} - 6) + 6 = 0 \}$. Then $S$:

Vedclass Test Series

Exam Paper Generator

Online Exam Module