GATE EE 2011 Question Paper (13-Feb-2011) (Shift 2)

The matrix $[A]=\left[\begin{array}{cc}2& 1\\ 4& -1\end{array}\right]$ is decomposed into a product of a lower triangular matrix [L] and an upper triangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are

The function f(x) = 2x – x ²+ 3 has

A lossy capacitor Cₓ, rated for operation of 5 kV, 50 Hz is represented by an equivalent circuit with an ideal capacitor Cp in parallel with a resistor Rp. Cp is 0.102 μF; and Rₚ = 1.25 MΩ. The power loss, and tan δ, of this lossy capacitor when operating at the rated voltage are, respectively

Let the Laplace transform of a function f(t) which exists for t>0 be F₁(s) and the Laplace transform of its delayed version f(t – τ) be F₂(s). Let F₁ * (s) be the complex conjugate of F₁(s) with the Laplace variable set s = σ + jω. If $G\left(s\right)=\frac{F_2\left(s\right)F_1\ast \left(s\right)}{{|F_1\left(s\right)|}^2}$, then the inverse Laplace transform of G(s) is

A zero mean random signal is uniformly distributed between limits – a and + a and its mean square value is equal to its variance. Then the r.m.s value of the signal is