GATE IN 2013 Question Paper (10-Feb-2013) (Shift 2)

While numerically solving the differential equation $\frac{dy}{dx}+2x{y}^2=0,$ y(0) = 1 using Euler’s predictor corrector (improved Euler-Cauchy) method with a step size of 0.2, the value of y after the first step is

One pair of eigenvectors corresponding to the two eigenvalues of the matrix $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ is

The digital circuit shown below uses two negative edge-triggered D-flip-flops. Assuming initial condition of Q₁ and Q₀ as zero, the output Q₁Q₀ of this circuit is

Considering the transformer to be ideal, the transmission parameter ‘A’ of the 2-port network shown in the figure below is

The following arrangement consists of an ideal transformer and an attenuator, which attenuates by a factor of 0.8. An ac voltage V${}_{WX1}$ = 100V is applied across WX to get an open circuit voltage V${}_{YZ1}$ across YZ. Next, an ac voltage V${}_{YZ2}$ = 100V is applied across YZ to get an open circuit voltage V${}_{WX2}$ across WX. Then, VYZ1 / VWX1 , VWX2 / VYZ2 are respectively