Test Preparation on GATE Electronics & Communication Engineering (Signals & Systems) Paper-1

A function is given by f(t) = sin²t +cos²t . Which of the following is true?

If the unit step response of a network is (1 - e^-αt), then its unit impulse response is

Two systems with impulse responses h₁(t) and h₂(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system. ẏ(t) + 5y(t) = u(t)
When y (0) = 1 and u(t) is a unit step function, y(t) is

Which of the following is true:

If u(t), r(t) denote unit the unit step and unit ramp functions respectively and
u(t) * r(t) their convolution, then the function u (t+1) * r(t-2) is given by