61 questions from the UPSC 2021 examination.
61 questions
Consider the four variables logic function defined as follows : F(A, B, C, D) = AC + AD + BC + BD + ABC bar(D) Assuming input variables as A, B, C and D, propose a logic circuit using only three logic gates to implement the function.
Consider the signal X(t) shown in Figure 2(b)(ii) below. Represent the signal X(t) in terms of rectangular pulse signal V(t) shown in the same figure.
The two top rows of a Routh table of a characteristic polynomial is given in the table. Determine the roots of the characteristic equation which lie in the left half s-plane. Complete the remaining rows of the table.
Determine the closed loop gain of the inverting amplifier shown in Figure 4(c) below. Explain the result if R1 -> 0 or R3 -> 0.
Consider a signal detector with an input r = \pm A + n where +A and -A occur with equal probability and the noise variable n is characterized by the Laplacian pdf shown. (i) Determine the probability of error as a function of the parameters A and \sigma. (ii) Determine the SNR required to achieve an error probability of 10^{-6}.
In Figure 1(a) shown below, the two-port network is characterized in terms of y-parameters with y11 = 3.3 x 10^-3 S, y22 = 5 x 10^-3 S and y12 = y21 = 0. Find the voltage across 200 ohm load.
A system is described by the following state equations : \dot{x}_1 = x_1 + x_2 + 3x_3 \dot{x}_2 = 2x_1 + 3x_2 + u_1 \dot{x}_3 = 2x_2 + x_3 + u_2 Check the controllability of the system.
The magnetic field intensity of a linearly polarized uniform plane wave propagating in the +Y-direction in sea water (epsilon_r = 80, mu_r = 1, sigma = 4 S/m) is H = 0.1 sin (10^10 pi t - pi/3) a_x A/m. At Y = 0, determine the following : (i) The attenuation constant, intrinsic impedance, the wavelength and skin depth. (ii) The location at which the amplitude of H is 0.01 A/m. (iii) The expression for E(y, t) and H(y, t) at Y = 0.5 (m) as functions of t.
A discrete memoryless source (DMS) has five symbols x_1, x_2, x_3, x_4 and x_5 with P(x_1) = 0.4, P(x_2) = 0.19, P(x_3) = 0.16, P(x_4) = 0.15 and P(x_5) = 0.1. (i) Construct a Shannon Fano code for the source and calculate the efficiency of the code. (ii) Repeat for Huffman code. Compare the results of (i) and (ii).
For a 3-bus power system, assume Voltage at bus - 1 : V_1 = (1.05 + j 0) pu, Voltage at bus - 2 : V_2 = (0.9812 - j 0.0522) pu and Voltage at bus - 3 : V_3 = (0.999 - j 0.0468) pu. The line impedances are shown below : Bus code / Impedances (in p.u.) 1 - 2 / (0.02 + j 0.04) 1 - 3 / (0.01 + j 0.03) 2 - 3 / (0.0125 + j 0.025) Compute Real and Reactive power loss in all the lines and also compute total system loss.
A convolutional code is described by g_1 = [1\ 1\ 0], g_2 = [1\ 0\ 1], g_3 = [1\ 1\ 1]. Find the transfer function and the free distance for this code. Also verify whether or not this code is catastrophic.
For the network shown in figure, draw a block diagram representing each circuit element by a block. Use block diagram reduction technique to obtain the transfer function of the network. The voltage V_i(t) is the applied input and the voltage across the capacitor V_o(t) is the output.
Show that the minimum Hamming distance of a linear block code is equal to the minimum number of columns of its parity check matrix that are linearly dependent. From this conclude that the minimum Hamming distance of a Hamming code is always equal to 3.
400 KV, त्रिकला शक्ति तन्त्र में प्रयोग होने वाले केबल का अति मितव्ययी विधुत रोधन सहित सम्पूर्ण व्यास का निर्धारण करें । केबल का सीमान्त अधिकतम रोधक प्रतिबल 100 KV/cm है । [Note: English translation not explicitly printed separately for this sub-part number label other than the Hindi text above, but context implies the same meaning as the Hindi.] Calculate the most economical overall diameter of insulation of a cable to be operated at 400 KV, 3 phase power system if maximum stress is limited to 100 KV/cm.
Write advantages, disadvantages and application of spectrum analyzer.
Explain the following related to computer programming : (i) Machine Language (ii) Assembly Language (iii) Compiler (iv) Interpreter (v) ASCII
A step down dc chopper is feeding a load of R = 10 ohm and L = 20 mH. The dc supply voltage is 100 V. The chopper is switching at a frequency of 2 kHz with a duty cycle of 50%. Determine the load current and the peak-to-peak ripple current as an absolute value and as percentage of dc value.
Explain what happens when a circuit shown in Figure 3(a)(i) below is constructed using logarithmic amplifier.
Consider a connected graph G = (N, A) with N nodes and A arcs, and a weight w_{ij} for each arc (i, j) \in A. (i) Define minimum weight spanning tree (MST). (ii) If all arcs weights of G are distinct, prove that there exists a unique MST.
In a certain material with sigma = 0, epsilon = epsilon0 epsilon_r and mu = mu0 mu_r, the magnetic field intensity component is given by H = 10 sin (10^8 t - 2x) a_z A/m. Find the following : (i) Displacement current density (ii) Electric field intensity
Derive the conditions of balance of an Anderson's bridge and also draw the phasor diagram of the bridge under balanced condition. Determine the unknown quantities in terms of known parameters and comment on easy convergence of balance of the bridge.
A mixer (analog multiplier) is used as a process in some analog communication systems. Two signals X1(t) and X2(t) are mixed to produce the output y(t) = X1(t) X2(t). If X1(t) = 10 sin c(10t) and X2(t) = 2 cos (1000 pi t), then calculate and plot the magnitude of the Fourier transform of output signal. Further, specify and prove the property of Fourier transform used in calculations.
A 220 V, 1500 rpm, 10 A separately excited dc motor has an armature resistance of 1 ohm. It is fed from a single phase fully-controlled bridge rectifier with an ac source voltage of 230 V, 50 Hz. Assuming continuous load current, determine the following : (i) Motor speed at the firing angle of 30 degrees and torque of 5 Nm (ii) Developed torque at the firing angle of 45 degrees and speed of 1000 rpm
A transmitter with a 10 kW carrier transmits 11.2 kW when modulated with a single sine wave. Calculate the modulation index. If the carrier is simultaneously modulated with two other sine waves also at 50% modulation, calculate the total power transmitted.
Compute the convolution X[n] * h[n], where X[n] = (1/2)^(-n) u[-n - 2] h[n] = u[n - 2].
A lossless transmission line has characteristic impedance Z0 = 50 ohm. Its length is 30 m and operates at 5 MHz. The line is terminated with a load ZL = 60 + j50 ohm. If the phase velocity u = 0.6c on the line, find the following : (i) The reflection coefficient Gamma (ii) The standing wave ratio S (iii) The input impedance Z_in
Use an 8 to 1 multiplexer and logic gates to implement the following function : F(A, B, C, D, E) = sum m(0, 1, 2, 4, 5, 6, 7, 13, 14, 20, 21, ..., 28, 29, 30, 31)
Discuss the percentage differential Relay with harmonic restraint with the help of diagram and also draw the conceptual representation of it.
Draw the sequence networks and calculate the load sequence impedances of a load circuit as shown in figure. The load circuit is connected to a balanced three phase supply. The value of z_1, z_2 and z_n are (4 + j6) \Omega, -j45 \Omega and j4 \Omega.
For the circuit shown in Figure 5(e), vC(0+) = 2 V and i(0+) = 2/3 A. Calculate the value of vC(t) for t > 0.
For an FM communication system with beta = 2 and white channel noise with PSD S_n(omega) = 10^-10, the output SNR is found to be 28 dB. The base band signal m(t) is Gaussian, band-limited to 15 kHz, and 3sigma loading is used. Determine the following : (i) The received signal power S (ii) The output signal power S_o (iii) The output noise power N_o
Prove that the minimum distance of any linear (n, k) block code satisfies d_{min} \le 1 + n - k.
A current of (0.5 + 0.3 \sin \omega t - 0.2 \sin 2\omega t) amps is passed through the circuit shown in figure. Determine the reading of each instrument if \omega = 10^6 rad/sec.
List the functional classification of 8085 instruction set. Give one example for each class.
The following test data are obtained for a three-phase, 195 MVA, 15 kV, 50 Hz star connected synchronous machine. Open circuit test : If (A): 150, 300, 450, 600, 750, 900, 1200 VLL (kV): 3.75, 7.5, 11.2, 13.6, 15, 15.8, 16.5 Short circuit test : If = 750 A, Ia = 7000 A The armature resistance is small. (i) Draw the open circuit characteristic, the short circuit characteristic, the airgap line and the modified airgap line. (ii) Determine the unsaturated and saturated values of the synchronous reactance in pu. (iii) Find the field current required, if the synchronous machine is to deliver 100 MVA at rated voltage, at 0.8 leading power factor.
Consider a discrete time system with transfer function given by H(z) = Y(z)/R(z) = 1 / [(1 - z^-1) (1 - 1/2 z^-1 + 2/9 z^-2)] Calculate the following : (i) The impulse response of the system (ii) The step response of the system with zero initial conditions (iii) The step response of the system with initial conditions y[-1] = 1 and y[-2] = 2
A single phase, single line diagram of a power system is shown in figure. Find the sending end voltage and the value of load resistance in p.u. referred to sending end if the voltage across load resistance is 9.8 KV.
For the circuit shown in Figure 3(b), calculate the voltage V0(t) as function of time, where V(t) = 10 sin (6t + 60 degrees) V and I(t) = 5 cos (4t + 30 degrees) A.
A sinusoidal voltage of 10 V amplitude at 100 Hz is applied to a lead network shown in figure. The phase difference between the input voltage V_i(t) and output voltage V_o(t) is 44.43^{\circ}. If C = 0.1 \mu F and R_1 = 100 k\Omega, determine the value of R_2 and the magnitude of steady state output voltage.
State Nyquist stability criterion. Is the feedback system shown in figure in open loop stable? Determine the closed loop stability of the system using Nyquist stability criterion. Show all the required plots clearly.
A three-phase, 4-pole, 50 Hz induction motor has a rotor resistance of 4.5 ohm/phase and a standstill reactance of 8.5 ohm/phase with no external resistance in the rotor circuit. The starting torque of the motor is 85 Nm. Neglecting stator voltage drop, determine the following : (i) The rotor voltage at standstill (ii) The starting torque, if a 3 ohm resistance were added in each rotor phase (iii) The rotor induced voltage and the torque at a slip of 0.03
The approximate magnitude plot, obtained experimentally, of a nonminimum phase system is shown in figure. Calculate the phase in degrees at \omega = 3 rad/sec.
For the transistor circuit shown in Figure 1(d), determine the value of reverse saturation current, Is, that would give a collector current of 1 mA, if beta = 80, VA = infinity and VT = 26 mV at T = 300 K.
Find the Thevenin's equivalent of the circuit shown in Figure 2(a) below as seen from the load impedance ZL. Also find the value of ZL for maximum power transfer.
A 220 V dc shunt motor has armature resistance Ra = 0.13 ohm, field resistance Rf = 250 ohm and rotational loss 230 W. On full-load, the line current is 9.5 A with the motor running at 1440 rpm. Determine the following : (i) The mechanical power developed (ii) The power output (iii) The load torque (iv) The full-load efficiency
A coil of 300 V moving iron voltmeter has a resistance of 500 ohms and an inductance of 0.8 H. The instrument reads correctly at 50 Hz AC supply and takes 100 mA at full scale deflection. What is the percentage error in the instrument reading, when it is connected to 200 V DC supply.
Explain the ratio error and phase angle error of current transformer.
A three-phase, full-wave thyristor bridge converter is operated from a three-phase, Y-connected 220 V, 50 Hz supply and the load resistance is 20 ohm. It is required to obtain an average output voltage of 50% of the maximum possible output voltage. Determine the following : (i) The delay angle alpha (ii) The rms and average output currents (iii) The rms and average thyristor currents (iv) The rectification efficiency (v) The input PF
A synchronous machine is connected to an infinite bus through a transformer and a double circuit line as shown in figure. The infinite bus voltage is V = 1.0 \angle 0^{\circ} p.u. The direct axis transient reactance of the machine is 0.20 p.u., the transformer reactance is 0.10 p.u. and the reactance of each of the transmission lines is 0.4 p.u. all the values are to a base of the rating of the synchronous machine. Initially, the machine is delivering 0.8 p.u. power with a terminal voltage |V| = 1.05 p.u. The inertia constant H = 5 MJ/MVA. All resistances are neglected. Determine the equation of motion of the machine rotor.
A DPCM system uses a linear predictor with a single tap. The normalized autocorrelation function of the input signal for a lag of one sampling interval is 0.75. The predictor is designed to minimize the prediction error variance. Determine the processing gain attained by the use of this predictor.
A pulse is applied to a piezo-electric transducer for a time T. Prove that in order to keep the undershoot of the response to a value within 5%, the value of time constant should be approximately 20T.
Consider the circuit shown in Figure 2(c) below. Let inputs A, B and C be all initially LOW. Output Y is supposed to go HIGH only when A, B and C go HIGH in a certain sequence. Determine the sequence that will make Y go HIGH. Modify this circuit to use D-Flip-flops.
The configuration of a 400 KV 3 phase line is shown in figure. The radius of each sub-conductor is 2 cm. Calculate the charging mega volt-amperes if line is operating at 50 Hz and has a length of 300 km.
Let the measurement error of a physical quantity be defined by a random variable X and its density function as follows : f(x) = { K(3 - x^2), -1 <= x <= 1; 0, elsewhere } Determine the value of 'K' and find the probability that a random error in measurement is less than 1/2.
For the signal shown in Figure 1(b), calculate the total energy of the signal X(t). Also sketch y(t) = X(10t - 5).
Verify by determining the logic equation for the output and by constructing the truth table for the logic circuit shown in Figure 4(b).
Explain what happens if the topology is modified as shown in Figure 3(a)(ii) below.
A solidly earthed 400 KV, 3 phase busbar system is connected with two incoming and four outgoing lines (feeders). A differential protection is provided with switchgear of 4000 MVA capacity having the following parameters : CT secondary resistance = 0.8 \Omega Lead wire resistance = 1.2 \Omega Relay load = 1.0 \Omega CT magnetization current = 0.3 mA/V Max. full load current in one feeder = 100 A Voltage setting of over current relay = 100 V If the O.C. relay in the spill path is set at 1.0 A, find the following : (a) The maximum 'through fault' current up to which the protection scheme remains stable. (b) Whether the switchgear is capable to handle maximum through fault current. (c) The value of minimum internal fault current that can be detected by protection scheme. (d) The pick-up setting for detecting minimum internal fault current of 90 Amp.
A Scott connected transformer shown in Figure 5(c) is supplied from 11 kV, 3-phase, 50 Hz mains. Secondaries are series connected and supply 1100 A at a voltage of 100 root 2 V to a resistive load. The phase sequence of the 3-phase supply is ABC. (i) Calculate the turns ratio of the teaser transformer. (ii) Calculate the line current IB and its phase angle with respect to the voltage of phase A to neutral on the 3-phase side.
A three-phase bridge inverter shown in Figure 6(b) is used to feed a Y-connected resistive load with R = 10 ohm per phase. The dc input to the inverter VS = 400 V and the output frequency is 50 Hz. If the inverter is operating with 180 degrees conduction mode, (i) compute the rms value of the load current, (ii) compute the rms value of the current in each switching device, (iii) calculate the output power, and (iv) draw the waveforms of phase and line voltages.
A commercial interface unit uses different names for the handshake lines associated with the transfer of data from the I/O device into the interface unit. The interface input handshake line is labelled STB (strobe), and the interface output handshake line is labelled IBF (input buffer full). A low-level signal on STB loads data from the I/O bus into the interface data register. A high-level signal on IBF indicates that the data item has been accepted by the interface. IBF goes low after an I/O read signal from the CPU when it reads the content of the data register. (i) Draw the block diagram showing the CPU, the interface, and the I/O device together with the pertinent interconnections among the three units. (ii) Draw a timing diagram for the handshaking transfer. (iii) Obtain a sequence of events flowchart for the transfer from the device to the interface and from the interface to the CPU.