Answer: The correct option is (B) less than 2.
Step-by-step explanation: Given that Y varies directly with X and has a constant rate of change of 6.
We are to find the possible value of X when the value of Y is 11.
Since Y varies directly with X, so we can write
[tex]Y\propto X\\\\\Rightarrow Y=kx~~~~~~~~~~~~~~~(i),~~~~~~~~~\textup{[where 'k' is the constant of variation]}[/tex]
Since the rate of change is constant and is equal to 6, so we must have
[tex]k=6.[/tex]
So, from equation (i), we have
[tex]Y=kX\\\\\Rightarrow Y=6X~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Now, when Y = 11, then from equation (ii), we get
[tex]Y=6X\\\\\Rightarrow 11=6X\\\\\Rightarrow X=\dfrac{11}{6}<\dfrac{12}{6}=2\\\\\\\Rightarrow X<2.[/tex]
Thus, the value of X is less than 2 when Y = 11.
Option (B) is CORRECT.