List of top Signals and Systems Questions on Laplace, Fourier and z-transforms

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $ 3\,\Omega $ resistor are as indicated.
The voltage (in Volts) at node $ X $ is _________.

Consider a continuous-time, real-valued signal $ f(t) $ whose Fourier transform \[ F(\omega) = \int_{-\infty}^{\infty} f(t) \exp(-j \omega t) \, dt { exists.} \] Which one of the following statements is always TRUE?

Let $X(j\omega)$ denote the Fourier transform of $x(t)$. If $X(j\omega) = 10 e^{-j\pi f} \left( \frac{\sin(\pi f)}{\pi f} \right)$, then $ \frac{1}{2\pi} \int_{-\infty}^{\infty} X(j\omega) d\omega = \underline{\hspace{1cm}}. $ (where $\omega = 2\pi f$)