Question 1 |
The inverse Laplace transform of
H(s)=\frac{s+3}{s^2+2s+1} \; for \; t\geq 0 is
H(s)=\frac{s+3}{s^2+2s+1} \; for \; t\geq 0 is
3te^{-t}+e^{-t} | |
3e^{-t} | |
2te^{-t}+e^{-t} | |
4te^{-t}+e^{-t} |
Question 1 Explanation:
\begin{aligned} L^{-1}\left ( \frac{s+3}{s^2+2s+1} \right )&=L^{-1}\left ( \frac{s+1+2}{(s+1)^2} \right )\\ &=L^{-1}\left ( \frac{1}{s+1}+\frac{2}{(s+1)^2} \right )\\ &=e^{-t}+2te^{-t} \end{aligned}
Question 2 |
M is a 2x2 matrix with eigenvalues 4 and 9. The eigenvalues of M^2 are
4 and 9 | |
2 and 3 | |
-2 and -3 | |
16 and 81 |
Question 2 Explanation:
M is 2 x 2 matrix with eigen values 4 and 9. The eigen values of M^2 are 16 and 81.
Question 3 |
The partial differential equation
\frac{\partial^2 u}{\partial t^2}-c^2\left ( \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2} \right )=0; where c\neq 0
is known as
\frac{\partial^2 u}{\partial t^2}-c^2\left ( \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2} \right )=0; where c\neq 0
is known as
heat equation | |
wave equation | |
Poisson's equation | |
Laplace equation |
Question 4 |
Which one of the following functions is analytic in the region |z|\leq 1?
\frac{z^2-1}{z} | |
\frac{z^2-1}{z+2} | |
\frac{z^2-1}{z-0.5} | |
\frac{z^2-1}{z+j0.5} |
Question 4 Explanation:
By Cauchy integral theorem,
\int \frac{z^2-1}{z+2}dz=0
Therefore, \frac{z^2-1}{z+2} is analytic in the region |z|\leq 1.
Question 5 |
The mean-square of a zero-mean random process is \frac{kT}{C}, where k is Boltzmann's constant, T is the absolute temperature, and C is a capacitance. The standard deviation of the random process is
\frac{kT}{C} | |
\sqrt{\frac{kT}{C}} | |
\frac{C}{kT} | |
\frac{\sqrt{kT}}{C} |
Question 5 Explanation:
Given that,
\begin{aligned} E(x^2)&=\frac{kT}{C}\\ E(x)&=0\\ &=E(x^2)-(E(x))^2\\ Var(x)&=\frac{kT}{C}-0=\frac{kT}{C} \end{aligned}
Standard deviation =\sqrt{\frac{kT}{C}}
\begin{aligned} E(x^2)&=\frac{kT}{C}\\ E(x)&=0\\ &=E(x^2)-(E(x))^2\\ Var(x)&=\frac{kT}{C}-0=\frac{kT}{C} \end{aligned}
Standard deviation =\sqrt{\frac{kT}{C}}
Question 6 |
A system transfer function is H(s)=\frac{a_1s^2+b_1s+c_1}{a_2s^2+b_2s+c_2}. If a_1=b_1=0, and all other coefficients are positive, the transfer function represents a
low pass filter | |
high pass filter | |
band pass filter | |
notch filter |
Question 6 Explanation:
\begin{aligned} H(s)&=\frac{c_1}{a_2s^2+b_2s+c_2}\\ & as \;\; a_1=b_1=0\\ &=\frac{c_1}{(1+s\tau _1)(1+s\tau _2)}\\ \text{Put }s&=0,\; H(0)=\frac{c_1}{c_2}\\ \text{Put }s&=\infty ,\; H(\infty )=0 \end{aligned}
which represents second order low pass filter.
which represents second order low pass filter.
Question 7 |
The symbols, a and T, represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?
e^{+at}u(t) | |
e^{-a(t+T)}u(t) | |
1+e^{-at}u(t) | |
e^{-a(t-T)}u(t) |
Question 7 Explanation:
a and T represents positive quantities.
u(t) is unit step function.
h(t)=1+e^{-at}u(t), is non-causal
Here '1' is a constant and two sided so the system will be non-causal, because for causal system,
h(t)=0,\;\;\; t \lt 0
h(t) \neq 0,\;\;\; t \gt 0
u(t) is unit step function.
h(t)=1+e^{-at}u(t), is non-causal
Here '1' is a constant and two sided so the system will be non-causal, because for causal system,
h(t)=0,\;\;\; t \lt 0
h(t) \neq 0,\;\;\; t \gt 0
Question 8 |
A 5 kVA, 50 V/100 V, single-phase transformer has a secondary terminal voltage of 95 V when loaded. The regulation of the transformer is
4.50% | |
9% | |
5% | |
1% |
Question 8 Explanation:
\begin{aligned} \text{Voltage regulation } &=\frac{V_{NL}-V_{FL}}{V_{NL}} \times 100 \\ &= \frac{100-95}{100} \times 100=5\% \end{aligned}
Question 9 |
A six-pulse thyristor bridge rectifier is connected to a balanced three-phase, 50Hz AC source. Assuming that the DC output current of the rectifier is constant, the lowest harmonic component in the AC input current is
100Hz | |
150Hz | |
250Hz | |
300Hz |
Question 9 Explanation:
For 6 pulse converter harmonics present in AC current are 6k\pm 1
Lowest order harmonic =5
Lowest harmonic frequency = 5 x 50 =250Hz
Lowest order harmonic =5
Lowest harmonic frequency = 5 x 50 =250Hz
Question 10 |
The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is
rotor resistance | |
rotor leakage reactance | |
magnetizing reactance | |
stator resistance |
There are 10 questions to complete.