NIMCET 2014 — Mathematics PYQ

1. Given Equations:

• $x^2+y\sqrt{xy}=336$

• $y^2+x\sqrt{xy}=112$

2. Simplifying the Equations:

Divide the first equation by $\sqrt{x}$:

Divide the second equation by $\sqrt{y}$:

3. Finding the Relationship between $x$ and $y$:

Since the left-hand sides of equations $(1)$ and $(2)$ are identical ($x\sqrt{x}+y\sqrt{y}$), we can equate the right-hand sides:

Squaring both sides:

4. Solving for $y$ and $x$:

Substitute the values from equations $(3)$ and $(4)$ into equation $(1)$:

Since $y$ must be a positive real number:

• $y=2$

• Using $x=9y$, we get $x=9(2)=18$

5. Final Calculation:

Correct Option: 3 ($20$)