Match List - I with list- II

List-I , Differential equation	List - II , Degree
A. $\left(\frac{dy}{dx}\right)^3 + yx = 0$	2
B. $e^{\frac{dy}{dx}} + y^2 + y'' = 0$	1
C. $Xyy'' + x(y')^2 - yy' = 0$	Not defined
D. $(Y'')^2 + y = 0$	3

Choose the correct option below :

If $x = 6t^2$, $y = \frac{6}{t^2}$, then $\frac{d^2 y}{dx^2}$ is equal to :

Match List - I with List - II.

Choose the correct answer from the options given below :

If $x = \log t$ and $y = \frac{1}{t^2}$, then $\frac{d^2 y}{d x^2}$ is equal to

The interval in which where the function $f(x) = x^3 - 3x^2 + 4x + 1, x \in R$ is increasing in, is :

If $R(x)$ is the total revenue received and $C(x)$ is the total cost incurred in the production of x units of a commodity, then the profit function $P(x)$

If $y = \log_e \left(\frac{x^3}{e^3}\right)$, then $\frac{d^2 y}{d x^2}$ is equal to