Question

If $x\propto y,y\propto z\text{and}x\propto z$, then which of the following is the product of three non-zero variation constant.

• A. 2
• B. 3
• C. 0
• D. 1

Answer 1

The correct option is D 1

$x\propto y\Rightarrow x=k_{1}y(k_1$ = non-zero varitaion constant )

$\Rightarrow k_1=\frac{x}{y}$...........................(1)

$y\propto z\Rightarrow y=k_{2}z(k_2$ = non-zero varitaion constant )

$\Rightarrow k_2=\frac{y}{z}$...........................(2)

$z\propto x\Rightarrow z=k_{3}x(k_3$ = non-zero varitaion constant )

$\Rightarrow k_3=\frac{z}{x}$...........................(3)

Now, multiplying (1),(2) and (3) we get, $k_1.k_2.k_3=\frac{x}{y}\times \frac{y}{z}\times \frac{z}{x}$

or, $k_1,k_2,k_3=1$.

Hence the product of non-zero varitaion constant is $1$.