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

A 220V 15KW 1000rpm shunt motor with armature resistance of 0.25 has a rated line current of 68 A and a rated field current of 2.2A. The change in field flux required to obtain a speed of 1600 rpm while drawing a line current of 52.8 A and a field current of 1.8A is

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, 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

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

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