Instrumentation Engineering (IN) 2017

1

2017 · Unclassified

Instrumentation Engineering (IN) 2017

If \(\mathbf{v}\) is a non-zero vector of dimension \(3 \times 1\), then the matrix \(\mathbf{A} = \mathbf{v} \mathbf{v}^T\) has a rank = __________

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2

2017 · Unclassified

Instrumentation Engineering (IN) 2017

The figure shows a shape ABC and its mirror image A₁B₁C₁ across the horizontal axis (X-axis). The coordinate transformation matrix that maps ABC to A₁B₁C₁ is

A

\(\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\)

B

\(\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix}\)

C

\(\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}\)

D

\(\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}\)

3

2017 · Unclassified

Instrumentation Engineering (IN) 2017

Let \(z = x + jy\) where \(j = \sqrt{-1}\). Then \(\overline{\cos z} =\)

A

\(\cos z\)

B

\(\cos \bar{z}\)

C

\(\sin z\)

D

\(\sin \bar{z}\)

4

2017 · Unclassified

Instrumentation Engineering (IN) 2017

The eigenvalues of the matrix \(\mathbf{A} = \begin{bmatrix} 1 & -1 & 5 \\ 0 & 5 & 6 \\ 0 & -6 & 5 \end{bmatrix}\) are

A

\(-1, 5, 6\)

B

\(1, -5 \pm j6\)

C

\(1, 5 \pm j6\)

D

\(1, 5, 5\)

5

2017 · Unclassified

Instrumentation Engineering (IN) 2017

For a first order lowpass filter with unity d.c. gain and –3 dB corner frequency of \(2000\pi\) rad/s, the transfer function \(H(j\omega)\) is

A

\(\frac{1}{1000 + j\omega}\)

B

\(\frac{1}{1 + j1000\omega}\)

C

\(\frac{2000\pi}{2000\pi + j\omega}\)

D

\(\frac{1000\omega}{1 + j1000\omega}\)

6

2017 · Unclassified

Instrumentation Engineering (IN) 2017

A series R-L-C circuit is excited with a 50 V, 50 Hz sinusoidal source. The voltages across the resistance and the capacitance are shown in the figure. The voltage across the inductor (\(V_L\)) is __________ V.

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