Consider the following for the next three (03) items that follow :

Let f(x) = Pe^x + Qe^2x + Re^3x where P, Q, R are real numbers. Further f(0) = 6, f'(ln 3) = 282 and $\int_0^{\ln 2} f(x) d x=11$

What is f'(0) equal to ?  

Consider the following for the next two (02) items that follow :

Suppose E is the differential equation representing family of curves y² = 2cx + 2c√c where c is a positive parameter.  

What is the order of the differential equation ?

Consider the following for the next two (02) items that follow :

Suppose E is the differential equation representing family of curves y² = 2cx + 2c√c where c is a positive parameter.  

What is the degree of the differential equation ? 

Consider the following for the next three (03) items that follow :

Let f(x) = $\left|\begin{array}{ccc} \cos x & x & 1 \\ 2 \sin x & x^2 & 2 x \\ \tan x & x & 1 \end{array}\right|$

What is f(0) equal to ?