GATE EC 2012 Question Paper (12-Feb-2012) (Shift 2)

The Fourier transform of a signal h(t) is H (jω) = (2 cosω ) (sin2ω) / ω . The value of h(0) is

State variable description of an LTI system is given by

≤ft[ {*20c {x_1}\\ {x_2}\\ {x_3} } ] = ≤ft[ {*20c 0&a_1&0\\ 0&0&a_2\\ a_3&0&0 } ]≤ft[ {*20c x_1\\ x_3\\ x_3 } ] + ≤ft[ {*20c 0\\ 0\\ 1 } ]U

Y = ≤ft[ {*20c 1&0&0 } ]≤ft[ {*20c x_1\\ x_2\\ x_3 } ]

Where Y is the output and u is input. System is controllable for

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

Consider the differential equation

$\frac{d^{2}y\left(t\right)}{d{t}^2}+2\frac{dy\left(t\right)}{dt}+y\left(t\right)=\delta \left(t\right)withy\left(t\right){|}_{t=0^{-}}=-2and\frac{dy}{dt}{|}_{t=0^{-}}=0$

The numerical value of $\frac{dy}{dt}{|}_{t=0^{+}}$ is

The direction of vector A is radially outward from the origin, with n |A| = krⁿ where r² = x² + y² + z² and k is a constant. The value of n for which ∇⋅A = 0 is