GATE EE 2014 Question Paper (02-Mar-2014) (Shift 2)

Two matrices A and B are given below:

A = ≤ft[ {*20c p&q\\ r&s } ] ; B = ≤ft[ {*20c p^2 + q^2&pr + qs\\ pr + qs&r^2 + s^2 } ]

If the rank of matrix A is N, then the rank of matrix B is

A particle, starting from origin at t = 0 s, is travelling along x-axis with velocity

$v=\frac{\pi }{2}\cos \left(\frac{\pi }{2}t\right)m/s$

At t = 3 s, the difference between the distance covered by the particle and the magnitude of displacement from the origin is _______

Let ∇⋅(fv) = x²y + y²z + z²x, where f and v are scalar and vector fields respectively. If v = yi + zj + xk, then v⋅∇f is

Lifetime of an electric bulb is a random variable with density f(x) = kx², where x is measured in years. If the minimum and maximum lifetimes of bulb are 1 and 2 years respectively, then the value of k is ______

A function f (t) is shown in the figure.



The Fourier transform F(ω) of f(t) is