GATE EE 2015 Question Paper (07-Feb-2015) (Shift 2)

Given $f\left(z\right)=g\left(z\right)+h\left(z\right)$, where f, g, h are complex valued functions of a complex variable z. which one of the following statements is TRUE?

We have a set of 3 linear equations in 3 unknowns. ‘X ≡ Y’ means X and Y are equivalent statements and ‘X ≢ Y’ means X and Y are not equivalent statements.

P: There is a unique solution.

Q: The equations are linearly independent.

R: All eigenvalues of the coefficient matrix are nonzero.

S: The determinant of the coefficient matrix is nonzero.

Which one of the following is TRUE?

Match the following

The Laplace transform of $f\left(t\right)=2\sqrt{\frac{t}{\pi }}$ is $s^{-\frac{3}{2}}$. The Laplace transform of $g\left(t\right)=\sqrt{\frac{1}{\pi t}}$ is

Match the following:

Instrument type

P) Permanent magnet moving coil

Q) Moving iron connected through current transformer

R) Rectifier

S) Electrodynamometer

Used for

1. DC only

2. AC only

3. DC and AC