CUET Mathematics 2025 21 May Shift 1 PYQs

Let $e^y(x+1) = 1$. Then which of the following are TRUE?

(A) $\frac{d^2y}{dx^2} = -\frac{1}{(x+1)^2}$

(B) $\frac{d^2y}{dx^2} = \left(\frac{dy}{dx}\right)^2$

(C) $\left.\frac{d^2y}{dx^2}\right|_{x=0} = -1$

(D) $\left.\frac{d^2y}{dx^2}\right|_{x=0} = 1$

(E) $\left.\frac{d^2y}{dx^2}\right|_{x=1} = \frac{1}{4}$

Choose the correct answer from the options given below:

If $x = e^t$ and $y = e^{2t}$ then $\frac{d^2y}{dx^2} =$

If $x = t^3$, $y = t^2$ then $\frac{d^2y}{d^2x}$ is equal to: