GATE EE 2016 Question Paper (07-Feb-2016) (Shift 2)

The Boolean expression $\overline{\left(a+\bar{b}+c+\bar{d}\right)+\left(b+\bar{c}\right)}$ simplifies to

For the circuit shown below, taking the Op-amp as ideal, the output voltage $V_{out}$ in terms of the input voltages $V_1,V_{2}and{V}_3$ is

Let $x_1\left(t\right)\leftrightarrow X_1\left(\omega \right)$ and $x_2\left(t\right)\leftrightarrow X_2\left(\omega \right)$ be two signals whose Fourier Transforms are as shown in the figure below. In the figure, $h\left(t\right)=e^{-2|t|}$ denotes the impulse response.



For the system shown above, the minimum sampling rate required to sample y(t), so that y(t) can be uniquely reconstructed from its samples, is

The value of the integral $2\underset{-\infty }{\overset{\infty }{\int }}\left(\frac{sin2\pi t}{\pi t}\right)dt$ is equal to

Let $y\left(x\right)$ be the solution of the differential equation $\frac{d^{2}y}{d{x}^2}-4\frac{dy}{dx}+4y=0$ with initial conditions $y\left(0\right)=0$ and ${\frac{dy}{dx}|}_{x=0}=1$. Then the value of $y\left(1\right)$ is________.