Question 1 |

The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 \mu s, then the number of T-states needed for executing the instruction is

1 | |

6 | |

7 | |

8 |

Question 1 Explanation:

Given than,

f_{\mathrm{CLK}}=5 \mathrm{MHz}

Execution time =1.4 \mu \mathrm{s}

Execution time =n(T-\text { state })

n= number of T-states required to execute the instruction

T- state (or) T_{\mathrm{CLK}}=\frac{1}{f_{\mathrm{CLK}}}=0.2 \mu \mathrm{s}

So, \quad n=\frac{1.4 \mu \mathrm{s}}{T_{\mathrm{CLK}}}=\frac{1.4}{0.2}=7

f_{\mathrm{CLK}}=5 \mathrm{MHz}

Execution time =1.4 \mu \mathrm{s}

Execution time =n(T-\text { state })

n= number of T-states required to execute the instruction

T- state (or) T_{\mathrm{CLK}}=\frac{1}{f_{\mathrm{CLK}}}=0.2 \mu \mathrm{s}

So, \quad n=\frac{1.4 \mu \mathrm{s}}{T_{\mathrm{CLK}}}=\frac{1.4}{0.2}=7

Question 2 |

Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as

y[n]=\left\{\begin{matrix} n|x[n]| & for 0\leq n\leq 10\\ x[n]-x[n-1] & othrwise \end{matrix}\right.

Which one of the following statements is true about the system?

y[n]=\left\{\begin{matrix} n|x[n]| & for 0\leq n\leq 10\\ x[n]-x[n-1] & othrwise \end{matrix}\right.

Which one of the following statements is true about the system?

It is causal and stable | |

It is causal but not stable | |

It is not causal but stable | |

It is neither causal nor stable |

Question 2 Explanation:

Since present output does not depend upon future values of input, the system is causal and also every bounded input produces bounded output, so it is stable.

Question 3 |

Consider the following statement about the linear dependence of the real valued functions y_{1}=1, \; y_{2}=x \; and \; y_{3}=x^{2} , over the field of real numbers.

I. y_{1}, \; y_{2} \; and \; y_{3} are linearly independent on -1 \leq x \leq 0

II. y_{1}, \; y_{2} \; and \; y_{3} are linearly dependent on 0 \leq x \leq 1

III. y_{1}, \; y_{2} \; and \; y_{3} are linearly independent on 0 \leq x \leq 1

IV. y_{1}, \; y_{2} \; and \; y_{3} are linearly dependent on -1 \leq x \leq 0

Which one among the following is correct ?

I. y_{1}, \; y_{2} \; and \; y_{3} are linearly independent on -1 \leq x \leq 0

II. y_{1}, \; y_{2} \; and \; y_{3} are linearly dependent on 0 \leq x \leq 1

III. y_{1}, \; y_{2} \; and \; y_{3} are linearly independent on 0 \leq x \leq 1

IV. y_{1}, \; y_{2} \; and \; y_{3} are linearly dependent on -1 \leq x \leq 0

Which one among the following is correct ?

Both I and II are true | |

Both I and III are true | |

Both II and IV are true | |

Both III and IV are true |

Question 3 Explanation:

Any of the given three functions cannot be written
as the linear combination of other two functions.
Hence, the statements I and III are correct

Question 4 |

Consider the 5 x 5 matrix

A=\begin{bmatrix} 1 &2 &3 & 4 & 5\\ 5 & 1& 2& 3& 4\\ 4& 5&1 & 2&3 \\ 3 & 4 & 5 & 1 & 2\\ 2&3 & 4&5 & 1 \end{bmatrix}

It is given that A has only one real eigen value. Then the real eigen value of A is

A=\begin{bmatrix} 1 &2 &3 & 4 & 5\\ 5 & 1& 2& 3& 4\\ 4& 5&1 & 2&3 \\ 3 & 4 & 5 & 1 & 2\\ 2&3 & 4&5 & 1 \end{bmatrix}

It is given that A has only one real eigen value. Then the real eigen value of A is

-2.5 | |

0 | |

15 | |

25 |

Question 4 Explanation:

\begin{aligned} |A-\lambda I|&=0 \\ \begin{array}{|ccccc|} 1-\lambda & 2 & 3 & 4 & 5 \\ 5 & 1-\lambda & 2 & 3 & 4 \\ 4 & 5 & 1-\lambda & 2 & 3 \\ 3 & 4 & 5 & 1-\lambda & 2 \\ 2 & 3 & 4 & 5 & 1-\lambda \end{array}&=0\\ \end{aligned}

sum of all elements in every one row must be zero.

\begin{aligned} \text{i.e. }\quad 15-\lambda&=0\\ \lambda&=15 \end{aligned}

sum of all elements in every one row must be zero.

\begin{aligned} \text{i.e. }\quad 15-\lambda&=0\\ \lambda&=15 \end{aligned}

Question 5 |

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is V(\iota )=e^{-y \iota +j\omega t} volts, Where \iota is the distance along the length of the cable in meters. \gamma =(0.1+j40)m^{-1} is the complex propagation constant, and \omega = 2\pi \times 10^{9} rad/ s is the angular frequency. The absolute value of the attenuation in the cable in dB/meter is __________.

0.5 | |

0.86 | |

0.34 | |

0.94 |

Question 5 Explanation:

\begin{aligned} V(l) &=V_{O} e^{-\alpha l} e^{-j\beta l} e^{j\omega t} \\ \text { Attenuation } &=\frac{\mid \text { Input } \mid}{\mid \text { Output } \mid}=\frac{\left|V_{O}(0)\right|}{\left|V_{o}(l)\right|} \end{aligned}

Attenuation per meter =\frac{\left|V_{0}\right|}{\left|V_{0}(1 \mathrm{m})\right|}=e^{\alpha}

Attenuation in \mathrm{dB} / \mathrm{m}=\left(20 \log e^{\alpha}\right) \mathrm{dB} / \mathrm{m}

=20(0.1) \log e=0.868 \mathrm{dB} / \mathrm{m}

Attenuation per meter =\frac{\left|V_{0}\right|}{\left|V_{0}(1 \mathrm{m})\right|}=e^{\alpha}

Attenuation in \mathrm{dB} / \mathrm{m}=\left(20 \log e^{\alpha}\right) \mathrm{dB} / \mathrm{m}

=20(0.1) \log e=0.868 \mathrm{dB} / \mathrm{m}

There are 5 questions to complete.