GATE EC 2014 Question Paper (16-Feb-2014) (Shift 2)

With initial values y(0) = 𝑦′(0) = 1, the solution of the differential equation$\frac{d^{2}y}{d{x}^2}+4\frac{dy}{dx}+4y=0$ at x =1 is _______

Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has a probability $\frac{1}{5}$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office is_________.

The unilateral Laplace transform of f(t) is$\frac{1}{s^2+s+1}$ . Which one of the following is the unilateral Laplace transform of g(t) = t⋅f(t)?

For a right-angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have a maximum area of the triangle, the angle between the hypotenuse and the side is

The steady state output of the circuit shown in the figure is given by y(t)=A(ω)sin(ωt+φ). If the amplitude |A(ω)|= 0.25, then the frequency ω is