MHTCET 20 Apr 2026 Shift 2 Paper

Concept:Implicit differentiation after simplifying the given radical equation.Explanation:Given:$$\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=6$$Rewrite the radicals as:$$\frac{\sqrt{x}}{\sqrt{y}}+\frac{\sqrt{y}}{\sqrt{x}}=6$$Taking LCM on the left-hand side:$$\frac{x+y}{\sqrt{xy}}=6$$So:$$x+y=6\sqrt{xy}$$Squaring both sides:$$(x+y)^2=36xy$$$$x^2+2xy+y^2=36xy$$$$x^2-34xy+y^2=0$$Now differentiate both sides with respect to $x$, using the product rule for $xy$:$$2x-34\left(y+x\frac{dy}{dx}\right)+2y\frac{dy}{dx}=0$$Expanding:$$2x-34y-34x\frac{dy}{dx}+2y\frac{dy}{dx}=0$$Group the terms containing $\frac{dy}{dx}$:$$(2y-34x)\frac{dy}{dx}=34y-2x$$Therefore:$$\frac{dy}{dx}=\frac{34y-2x}{2y-34x}$$Divide numerator and denominator by $2$:$$\frac{dy}{dx}=\frac{17y-x}{y-17x}$$Multiplying numerator and denominator by $-1$:$$\frac{dy}{dx}=\frac{x-17y}{17x-y}$$Thus, the correct option is Option B.Answer:$$\frac{x-17y}{17x-y}$$Option B.