The matrix $A=\left[\begin{array}{ccc}\frac{3}{2}& 0& \frac{1}{2}\\ 0& -1& 0\\ \frac{1}{2}& 0& \frac{3}{2}\end{array}\right]$ has three distinct eigenvalues and one of its eigenvectors is $\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right]$.
Which one of the following can be another eigenvector of A?
For a complex number z, $\begin{array}{c}\lim\\z\rightarrow i\end{array}\frac{z^2+1}{z^3+2z-i(z^2+2)}$ is
Let $ z(t)=x(t)\ast y(t), $ where $ "\ast" $ denotes convolution. Let $ c $ be a positive real-valued constant. Choose the correct expression for $ z(ct). $
A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will
Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are release but are constrained to move along the same straight line. Which of these will collide first?
The transfer function of a system is given by,
$ \frac{V_0(s)}{V_i(s)}=\frac{1-s}{1+s} $
Let the output of the system be ${v}_{o}\left(t\right)={V}_{m}\mathrm{sin}(\omega t+\phi )$ for the input, $ v_i(t)=V_m\;\sin\left(wt\right). $ Then the minimum and maximum values of $\varphi$ (in radius) are respectively
Consider the system with following input-output relation
$ y\lbrack n\rbrack=(1+(-1)^n)x\lbrack n\rbrack $
where, $ x\lbrack n\rbrack $ is the input and $ y\lbrack n\rbrack $ is the output. The system is
A 4 pole induction machine is working as an induction generator. The generator supply frequency is 60 Hz. The rotor current frequency is 5 Hz. The mechanical speed of the rotor in RPM is
A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $ V_{an}=220\;\sin\left(100\;\mathrm{πt}\right)\;V $ and $ i_a=10\;\sin\left(100\;\mathrm{πt}\right)\;A, $ respectively. Similarly for phase-b, the instantaneous voltage and current are $ V_{bn}=220\;\cos\left(100\;\mathrm{πt}\right)\;V $ and $ i_b=10\;\cos\left(100\;\mathrm{πt}\right)\;A, $, respectively.
The total instantaneous power flowing from the source to the load is
$ A\;3 $-bus power system is shown in the figure below, where the diagonal elements of $ Y $-bus matrix are: $ Y_{11}=-j12\;pu,\;Y_{22}=-j15\;pu $ and $ Y_{33}=-j7\;pu. $
The per unit values of the lines reactances $ p,q $ and $ r $ shown in the figure are
A closed loop system has the characteristic equation given by ${s}^{3}+K{s}^{3}+(K+2)s+3=0$. For this system to be stable, which one of the following conditions should be statisfied?
The slope and level detector circuit in a CRO has delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. In order to display correctly, a delay line of
The Boolean expression $AB+A\overline{)C}+BC$ simplifies to
For the circuit shown in the figure below, assume that diodes D_{1}, D_{2} and D_{3} are ideal.
The DC components of voltages v_{1} and v_{2}, respectively are
For the power semiconductor device IGBT, MOSFET, Diode and Thyristor, which one of the following statements is TRUE?
Consider $g(t)=\left\{\begin{array}{lc}t-\left\lfloor t\right\rfloor,&t\geq0\\t-\left\lceil t\right\rceil,&otherwise\end{array}\right.$, where $ t\in\mathbb{R}. $
Here, $\left\lfloor t\right\rfloor$ represent the largest integer less than or equal to t and $\left\lfloor t\right\rfloor$ denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic of the Fourier series represent g(t) is__________
Let $I=\;c\iint_R\;xy^2\;dxdy$, where R is the region shown in the figure and c = 6 × 10^{-4}. The value of I equals _________. (Give the answer up to two decimal places.)
The power supplied by the 25 V source in the figure shown below is _________ W.
The equivalent resistance between the terminal A and B is__________$ \Omega$.
A three-phase, 50 Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draw current at unity power factor (UPF). The synchronous reactance of the motor is 30 $\Omega$ per phase. The load angle is 30°. The power delivered to the motor in kW is________. (Give the answer up to two decimal phase).