GATE EC 2024 Question Paper (11-Feb-2024) (Shift 1)

A causal and stable LTI system with impulse response $h(t)$ produces an output $y(t)$ for an input signal $x(t)$. A signal $x(0.5t)$ is applied to another causal and stable LTI system with impulse response $h(0.5t)$. The resulting output is

For non-degenerately doped n-type silicon, which one of the following plots represents the temperature $(T)$ dependence of free electron concentration $(n)$?

In the circuit shown, the $n:1$ step-down transformer and the diodes are ideal. The diodes have no voltage drop in forward biased condition. If the input voltage (in Volts) is $V_s(t)=10\sin \omega t$ and the average value of load voltage $V_L(t)$ (in Volts) is $2.5/\pi$, the value of $n$ is ________

For a causal discrete-time LTI system with transfer function
$H(z)=\frac{2z^2+3}{(z+\frac{1}{3})(z-\frac{1}{3})}$,
which of the following statements is/are true?

Let $\rho (x,y,z,t)$ and $u(x,y,z,t)$ represent density and velocity, respectively, at a point $(x,y,z)$ and time $t$. Assume $\frac{\partial \rho }{\partial t}$ is continuous. Let $V$ be an arbitrary volume in space enclosed by the closed surface $S$ and $\hat{n}$ be the outward unit normal of $S$ Which of the following equations is/are equivalent to $\frac{\partial \rho }{\partial t}+\nabla \cdot (\rho u)=0$?