GATE EC 2015 Question Paper (31-Jan-2015) (Shift 2)

For the voltage regulator circuit shown, the input voltage (Vᵢₙ) is 20 V ± 20% and the regulated output voltage (Vₒᵤₜ) is 10 V. Assume the opamp to be ideal. For a load R${}_L$ drawing 200 mA, the maximum power dissipation in Q₁ (in Watts) is _________.

In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical parameters with β ≫ 1 . The open circuit small signal voltage gain is approximately ________________________

Input $\mathrm{x}\left(\mathrm{t}\right)$ and output $\mathrm{y}\left(\mathrm{t}\right)$ of an LTI system are related by the differential equation $\mathrm{y}"\left(\mathrm{t}\right)-{\mathrm{y}}^{\prime }\left(\mathrm{t}\right)-6\mathrm{y}\left(\mathrm{t}\right)=\mathrm{x}\left(\mathrm{t}\right)$. If the system is neither causal nor stable, the impulse response h(t) of the system is

Consider two real sequences with time–origin marked by the bold value x₁[n] = {1, 2, 3, 0}, x₂[n] = {1, 3, 2, 1}. Let X₁(k) and X₂(k) be 4-point DFTs of x₁[n] and x₂[n] respectively. Another sequence x₃[n] is derived by taking 4-point inverse DFT of X₃(k) = X₁(k) X₂(k). The value of x₃[2] is _________.

Let $\mathrm{x}\left(\mathrm{t}\right)=\alpha \mathrm{s}\left(\mathrm{t}\right)+\mathrm{s}\left(-\mathrm{t}\right)$ with $\mathrm{s}\left(\mathrm{t}\right)=\beta {\mathrm{e}}^{-4\mathrm{t}}\mathrm{u}\left(\mathrm{t}\right)$, where u(t) is unit step function. If the bilateral Laplace transform of x(t) is $\mathrm{X}\left(\mathrm{s}\right)=\frac{16}{{\mathrm{s}}^2-16};-4<\mathrm{Re}\left\{\mathrm{s}\right\}<4$ .Then the value of β is __________.