The input voltage to the \( R C \) circuit is given as \( \boldsymbol{x}(t)=t e^{-t / R C} u(t) \) and impulse response of the circuit is given by \( \mathbf{h}(\mathbf{t})=\frac{\mathbf{1}}{\mathbf{R C}} e^{-t / R C} \mathbf{u}(t) \) Find the output \( y(t) \).

(ix) The equation \( \frac{1}{r r} \frac{\partial}{r}\left(r \frac{\partial u}{r r}\right)=\frac{1}{c^{2}} \frac{\partial^{2} u}{\partial t^{2}} \) is one dimensional wave equation in: (a) Cylindrical coordinate (b) Polar coordinate (c) Spherical coordinate (d) None of these

Corruption has been a persistent issue in West Africa's governance. What is one reason public officials engage in corruption? a. Widespread support for autocratic governance models b. International organizations encourage the privatization of public services c. Strict enforcement of anti-corruption laws by civil society d. Low salaries, poverty, and greed create incentives for bribery

Cocoa farming in Ghana is supported by specific agricultural practices. What method is most commonly used for drying cocoa beans after fermentation? a. Sun drying combined with artificial heating b. Employing large-scale solar drying panels c. Using mechanized dryers for rapid drying d. Spreading beans in the open air for six days

A developing nation introduces measures to increase economic productivity per capita. Which theory does this align with? a. Optimum population theory b. Malthusian theory c. Population bomb theory d. Demographic transition model

Regions with projected low support ratios by 2050 will primarily face challenges in: a. Increasing agricultural productivity. b. Attracting international migration. c. Reducing fertility rates. d. Sustaining elderly care systems.