A linear transformation maps a point (𝑥, 𝑦) in the plane to the point (𝑥̂, 𝑦̂) according to the rule

𝑥̂ = 3𝑦, 𝑦̂ = 2𝑥.

Then, the disc 𝑥² + 𝑦² ≤ 1 gets transformed to a region with an area equal to _________ . (Rounded off to two decimals)

Use π = 3.14. 

The value of k that makes the complex-valued function

𝑓(𝑧) = 𝑒−𝑘𝑥 (cos 2𝑦 − 𝑖 sin 2𝑦)

analytic, where 𝑧 = 𝑥 + 𝑖𝑦, is _________.

(Answer in integer)

Which one of the options given is the inverse Laplace transform of $\rm \frac{1}{s^3-s}$? 𝑢(𝑡) denotes the unit-step function.

The smallest perimeter that a rectangle with area of 4 square units can have is ______ units.

(Answer in integer)