IN : INSTRUMENTATION ENGINEERING

Transcription

1 013 Quetion Booklet Code IN : INSTRUMENTATION ENGINEERING A Duration: Three Hour Maximum Mark: 100 Read the following intruction carefully. 1. Do not open the eal of the Quetion Booklet until you are aked to do o by the invigilator.. Take out the Optical Repone Sheet (ORS) from thi Quetion Booklet without breaking the eal and read the intruction printed on the ORS carefully. If you find that either: a. The Quetion Booklet Code printed at the right hand top corner of thi page doe not match with the Quetion Booklet Code at the right hand top corner of the ORS or b. The Quetion Paper Code preceding the Regitration number on the ORS i not IN, then exchange the booklet immediately with a new ealed Quetion Booklet. 3. On the right hand ide of the ORS, uing ONLY a black ink ballpoint pen, (i) darken the appropriate bubble under each digit of your regitration number and (ii) write your regitration number, your name and name of the examination centre and put your ignature at the pecified location. 4. Thi Quetion Booklet contain 0 page including blank page for rough work. After you are permitted to open the eal, check all page and report dicrepancie, if any, to the invigilator. 5. There are a total of 65 quetion carrying 100 mark. All thee quetion are of objective type. Each quetion ha only one correct anwer. Quetion mut be anwered on the left hand ide of the ORS by darkening the appropriate bubble (marked A, B, C, D) uing ONLY a black ink ballpoint pen againt the quetion number. For each quetion darken the bubble of the correct anwer. More than one anwer bubbled againt a quetion will be treated a an incorrect repone. 6. Since bubble darkened by the black ink ballpoint pen cannot be eraed, candidate hould darken the bubble in the ORS very carefully. 7. Quetion Q.1 Q.5 carry 1 mark each. Quetion Q.6 Q.55 carry mark each. The mark quetion include two pair of common data quetion and two pair of linked anwer quetion. The anwer to the econd quetion of the linked anwer quetion depend on the anwer to the firt quetion of the pair. If the firt quetion in the linked pair i wrongly anwered or i not attempted, then the anwer to the econd quetion in the pair will not be evaluated. 8. Quetion Q.56 Q.65 belong to General Aptitude (GA) ection and carry a total of 15 mark. Quetion Q.56 Q.60 carry 1 mark each, and quetion Q.61 Q.65 carry mark each. 9. Quetion not attempted will reult in zero mark and wrong anwer will reult in NEGATIVE mark. For all 1 mark quetion, ⅓ mark will be deducted for each wrong anwer. For all mark quetion, ⅔ mark will be deducted for each wrong anwer. However, in the cae of the linked anwer quetion pair, there will be negative mark only for wrong anwer to the firt quetion and no negative mark for wrong anwer to the econd quetion. 10. Calculator i allowed wherea chart, graph heet or table are NOT allowed in the examination hall. 11. Rough work can be done on the Quetion Booklet itelf. Blank page are provided at the end of the Quetion Booklet for rough work. 1. Before the tart of the examination, write your name and regitration number in the pace provided below uing a black ink ballpoint pen. Name Regitration Number IN IN-A 1/0

2 013 INSTRUMENTATION ENGG. - IN Q.1 to Q.5 carry one mark each. Q.1 The dimenion of the null pace of the matrix i (A) 0 (B) 1 (C) (D) 3 Q. If the A-matrix of the tate pace model of a SISO linear time invariant ytem i rank deficient, the tranfer function of the ytem mut have (A) a pole with a poitive real part (B) a pole with a negative real part (C) a pole with a poitive imaginary part (D) a pole at the origin Q.3 Two ytem with impule repone h ( t ) and 1 h ( ) t are connected in cacade. Then the overall impule repone of the cacaded ytem i given by (A) product of ( ) 1 (B) um of ( ) 1 (C) convolution of ( ) 1 (D) ubtraction of ( ) 1 Q.4 The complex function tanh ( ) i analytic over a region of the imaginary axi of the complex -plane if the following i TRUE everywhere in the region for all integer n (A) Re ( ) = 0 (B) Im ( ) nπ nπ (n 1) π (C) Im ( ) (D) Im ( ) 3 Q.5 For a vector E, which one of the following tatement i NOT TRUE? (A) If E = 0, E i called olenoidal. (B) If E = 0, E i called conervative. (C) If E = 0, E i called irrotational. (D) If E = 0, E i called irrotational. Q.6 For a periodic ignal v ( t) = 30 in100t 10co300t 6 in(500t π / 4), the fundamental frequency in rad/ i (A) 100 (B) 300 (C) 500 (D) 1500 IN-A /0

3 013 INSTRUMENTATION ENGG. - IN Q.7 In the tranitor circuit a hown below, the value of reitance R E in kω i approximately, 10 V 1.5 kω I C =.0 ma 15k Ω 0.1µF 6kΩ 0.1µF V CE =5.0 V V out R E (A) 1.0 (B) 1.5 (C).0 (D).5 Q.8 A ource v ( t) = V co100π t ha an internal impedance of 4 j3 Ω. If a purely reitive load connected to thi ource ha to extract the maximum power out of the ource, it value in Ω hould be (A) 3 (B) 4 (C) 5 (D) 7 Q.9 Which one of the following tatement i NOT TRUE for a continuou time caual and table LTI ytem? (A) All the pole of the ytem mut lie on the left ide of the jω axi. (B) Zero of the ytem can lie anywhere in the -plane. (C) All the pole mut lie within = 1. (D) All the root of the characteritic equation mut be located on the left ide of the jω axi. Q.10 The operational amplifier hown in the circuit below ha a lew rate of 0.8 Volt / µ. The input ignal i 0.5 in ( ω t). The maximum frequency of input in khz for which there i no ditortion in the output i (A) 3.84 (B) 5.0 (C) 50.0 (D) IN-A 3/0

4 013 INSTRUMENTATION ENGG. - IN Q.11 Auming zero initial condition, the repone y (t) of the ytem given below to a unit tep input u (t) i (A) u (t) (B) t u (t) (C) t u( t) (D) e t u (t ) Q.1 The tranfer function V ( ) V ( ) 1 of the circuit hown below i (A) (B) 3 6 (C) 1 (D) 1 Q.13 The type of the partial differential equation f t f = x i (A) Parabolic (B) Elliptic (C) Hyperbolic (D) Nonlinear Q.14 The dicrete-time tranfer function 1 z z 1 1 i (A) non-minimum phae and untable. (B) minimum phae and untable. (C) minimum phae and table. (D) non-minimum phae and table. Q.15 Match the following biomedical intrumentation technique with their application P : Otocopy Q : Ultraound Technique R : Spirometry S : Thermodilution Technique (A) P-U, Q-V, R-X, S-W (C) P-V, Q-W, R-U, S-X U : Repiratory volume meaurement V : Ear diagnotic W : Echo-cardiography X : Heart volume meaurement (B) P-V, Q-U, R-X, S-W (D) P-V, Q-W, R-X, S-U Q.16 A continuou random variable X ha a probability denity function f ( x) = e, 0 < x <. Then P { X > 1} i (A) (B) 0.5 (C) 0.63 (D) 1.0 IN-A 4/0 x

5 013 INSTRUMENTATION ENGG. - IN Q.17 A band-limited ignal with a maximum frequency of 5 khz i to be ampled. According to the ampling theorem, the ampling frequency in khz which i not valid i (A) 5 (B) 1 (C) 15 (D) 0 Q.18 The differential preure tranmitter of a flow meter uing a venturi tube read Pa for a flow rate of 0.5 m 3 /. The approximate flow rate in m 3 / for a differential preure Pa i (A) 0.30 (B) 0.18 (C) 0.83 (D) 0.60 Q.19 A bulb in a taircae ha two witche, one witch being at the ground floor and the other one at the firt floor. The bulb can be turned ON and alo can be turned OFF by any one of the witche irrepective of the tate of the other witch. The logic of witching of the bulb reemble (A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate Q.0 The impule repone of a ytem i h ( t) = t u( t). For an input u ( t 1), the output i (A) t u( t) (B) t ( t 1) u( t 1 ) ( t 1) (C) u( t 1) t 1 (D) u( t 1) Q.1 Conider a delta connection of reitor and it equivalent tar connection a hown. If all element of the delta connection are caled by a factor k, k> 0, the element of the correponding tar equivalent will be caled by a factor of R C R b R a R c R A R B (A) k (B) k (C) 1/k (D) k Q. An accelerometer ha input range of 0 to 10g, natural frequency 30 Hz and ma kg. The range of the econdary diplacement tranducer in mm required to cover the input range i (A) 0 to.76 (B) 0 to 9.81 (C) 0 to 11.0 (D) 0 to 5.10 Q.3 In the circuit hown below what i the output voltage ( V out ) in Volt if a ilicon tranitor Q and an ideal op-amp are ued? (A) 15 (B) 0.7 (C) 0.7 (D) 15 IN-A 5/0

6 013 INSTRUMENTATION ENGG. - IN Q.4 In the feedback network hown below, if the feedback factor k i increaed, then the v in v 1 A 0 v out v f = kv out k (A) input impedance increae and output impedance decreae (B) input impedance increae and output impedance alo increae (C) input impedance decreae and output impedance alo decreae (D) input impedance decreae and output impedance increae Q.5 The Bode plot of a tranfer function G () i hown in the figure below. Gain (db) The gain (0 log G( ) ) i 3 db and 8 db at 1 rad/ and 10 rad/ repectively. The phae i negative for all ω. Then G () i (A) 39.8 (B) 39.8 (C) 3 (D) 3 IN-A 6/0

7 013 INSTRUMENTATION ENGG. - IN Q.6 to Q.55 carry two mark each. Q.6 dy While numerically olving the differential equation xy 0, dx = y ( 0) = 1 uing Euler predictorcorrector (improved Euler-Cauchy) method with a tep ize of 0., the value of y after the firt tep i (A) 1.00 (B) 1.03 (C) 0.97 (D) Q.7 One pair of eigenvector correponding to the two eigenvalue of the matrix 1 0 i (A) 1 j, j 1 (B) 0 1, 1 0 (C) 1 0, j 1 (D) 1 j, j 1 Q.8 The digital circuit hown below ue two negative edge-triggered D-flip-flop. Auming initial condition of Q1 and Q0 a zero, the output Q1Q0 of thi circuit i D1 Q1 D0 Q0 D-Flip-flop Q1 D-Flip-flop Q0 clock (A) 00,01,10,11,00 (B) 00,01,11,10,00 (C) 00,11,10,01,00 (D) 00,01,11,11,00 Q.9 Conidering the tranformer to be ideal, the tranmiion parameter A of the -port network hown in the figure below i 1 Ω Ω 1: V 1 I 1 5Ω 5Ω I V 1 (A) 1.3 (B) 1.4 (C) 0.5 (D).0 IN-A 7/0

8 013 INSTRUMENTATION ENGG. - IN Q.30 The following arrangement conit of an ideal tranformer and an attenuator, which attenuate by a factor of 0.8. An ac voltagev WX 1 = 100V i applied acro WX to get an open circuit voltage V YZ1 acro YZ. Next, an ac voltagev YZ = 100V i applied acro YZ to get an open circuit voltagevwx acro WX. Then, VYZ 1 / V WX 1, VWX / V YZ are repectively, W 1:1.5 Y X Z (A) 15/100 and 80/100 (B) 100/100 and 80/100 (C) 100/100 and 100/100 (D) 80/100 and 80/100 Q.31 ω ( ) 10 The open-loop tranfer function of a dc motor i given a =. When connected in Va ( ) 1 10 feedback a hown below, the approximate value of K a that will reduce the time contant of the cloed loop ytem by one hundred time a compared to that of the open-loop ytem i (A) 1 (B) 5 (C) 10 (D) 100 Q.3 Two magnetically uncoupled inductive coil have Q factor q 1 and q at the choen operating frequency. Their repective reitance are R 1 and R. When connected in erie, the effective Q factor of the erie combination at the ame operating frequency i (A) q1 q (B) (1/ q1 ) (1/ q) (C) ( q1r1 qr ) / ( R1 R ) (D) ( q1r qr1 ) / ( R1 R ) IN-A 8/0

9 013 INSTRUMENTATION ENGG. - IN Q.33 For the circuit hown below, the knee current of the ideal Zener diode i 10 ma. To maintain 5 V acro R L, the minimum value of the load reitor R L in Ω and the minimum power rating of the Zener diode in mw, repectively, are 100 Ω 10 V I Load V Z = 5 V R L (A) 15 and 15 (B) 15 and 50 (C) 50 and 15 (D) 50 and 50 Q.34 The impule repone of a continuou time ytem i given by h( t) = δ ( t 1) δ ( t 3). The value of the tep repone at t = i (A) 0 (B) 1 (C) (D) 3 Q.35 Signal from fifteen thermocouple are multiplexed and each one i ampled once per econd with a 16-bit ADC. The digital ample are converted by a parallel to erial converter to generate a erial PCM ignal. Thi PCM ignal i frequency modulated with FSK modulator with 100 Hz a 1 and 960 Hz a 0. The minimum band allocation required for faithful reproduction of the ignal by the FSK receiver without conidering noie i (A) 840 Hz to 130 Hz (C) 1080 Hz to 130 Hz (B) 960 Hz to 100 Hz (D) 70 Hz to 1440 Hz Q.36 Three capacitor C 1, C and C 3 whoe value are 10µF, 5µF, and µf repectively, have breakdown voltage of 10V, 5V, and V repectively. For the interconnection hown below, the maximum afe voltage in Volt that can be applied acro the combination, and the correponding total charge in µc tored in the effective capacitance acro the terminal are, repectively, C C 3 (A).8 and 36 (B) 7 and 119 (C).8 and 3 (D) 7 and 80 Q.37 The maximum value of the olution y (t) of the differential equation y ( t) & y ( t) = 0 with initial condition y& ( 0) = 1 and y ( 0) = 1, for t 0 i (A) 1 (B) (C) π (D) IN-A 9/0 C 1

10 013 INSTRUMENTATION ENGG. - IN Q.38 The Laplace Tranform repreentation of the triangular pule hown below i 1 1 (A) [1 e ] (B) [1 e e ] 1 (C) [1 e e ] (D) 1 [1 e e ] Q.39 In the circuit hown below, if the ource voltage V S = Volt, then the Thevenin equivalent voltage in Volt a een by the load reitance R L i 3Ω j4 Ω j6 Ω 5Ω V L1 V S j40i 10V L1 R L =10 Ω I 1 I (A) (B) (C) (D) Q.40 A ignal V i ( t) = in100π t 10in 4000π t 10in100000π t i upplied to a filter circuit (hown below) made up of ideal op-amp. The leat attenuated frequency component in the output will be 0.1µ F kω 1µF 1kΩ 0.1µ F 750Ω 0.1µ F V i (t) V 0 (t) (A) 0 Hz (B) 50 Hz (C) khz (D) 50 khz IN-A 10/0

11 013 INSTRUMENTATION ENGG. - IN Q.41 The ignal flow graph for a ytem i given below. The tranfer function given a Y( ) U ( ) for thi ytem i (A) (B) 1 6 (C) 1 4 (D) Q.4 A voltage 1000 inωt Volt i applied acro YZ. Auming ideal diode, the voltage meaured acro WX in Volt, i W 1kΩ Y Z X 1kΩ _ (A) ωt (B) (inω t in ω t ) / (C) (inω t inω t )/ (D) 0 for all t Q.43 In the circuit hown below the op-amp are ideal. Then Vout in Volt i V 1 kω 1 kω 15 V 1 kω 15 V 15 V 15 V V out 1 V 1 kω 1 kω (A) 4 (B) 6 (C) 8 (D) 10 IN-A 11/0

12 013 INSTRUMENTATION ENGG. - IN Q.44 In the circuit hown below, Q 1 ha negligible collector-to-emitter aturation voltage and the diode drop negligible voltage acro it under forward bia. If V cc i 5 V, X and Y are digital ignal with 0 V a logic 0 and V cc a logic 1, then the Boolean expreion for Z i (A) X Y (B) X Y (C) X Y (D) XY Q.45 The circuit below incorporate a permanent magnet moving coil milli-ammeter of range 1 ma having a erie reitance of 10 kω. Auming contant diode forward reitance of 50 Ω, a forward diode drop of 0.7 V and infinite revere diode reitance for each diode, the reading of the meter in ma i _ ma 10k Ω 10k Ω 5V, 50Hz V o (A) 0.45 (B) 0.5 (C) 0.7 (D) 0.9 Q.46 Meaurement of optical aborption of a olution i diturbed by the additional tray light falling at the photo-detector. For etimation of the error caued by tray light the following data could be obtained from controlled experiment. Photo-detector output without olution and without tray light i 500 µw. Photo-detector output without olution and with tray light i 600 µw. Photo-detector output with olution and with tray light i 00 µw. The percent error in computing aborption coefficient due to tray light i (A) 1.50 (B) (C) (D) Q.47 Two ammeter A 1 and A meaure the ame current and provide reading I 1 and I, repectively. The ammeter error can be characterized a independent zero mean Gauian random variable of tandard deviation σ 1 and σ, repectively. The value of the current i computed a : I = µ I1 (1 µ ) I The value of µ which give the lowet tandard deviation of I i (A) σ σ 1 σ (B) σ σ1 1 σ σ (C) σ σ 1 σ1 (D) σ σ 1 IN-A 1/0

13 013 INSTRUMENTATION ENGG. - IN Common Data Quetion Common Data for Quetion 48 and 49: A tungten wire ued in a contant current hot wire anemometer ha the following parameter : Reitance at 0 C i 10Ω, Surface area i tungten wire i 4 10 m, Linear temperature coefficient of reitance of the / C, Convective heat tranfer coefficient i 5. W / 5 temperature i 30 C, wire current i 100 ma, ma-pecific heat product i.5 10 J / C m / C, flowing air Q.48 The thermal time contant of the hot wire under flowing air condition in m i (A) 4.5 (B) 1.5 (C) 6.15 (D) Q.49 At teady tate, the reitance of the wire in Ω i (A) (B) (C) 1.15 (D) Common Data for Quetion 50 and 51: A piezo-electric force enor, connected by a cable to a voltage amplifier, ha the following parameter : 9 5 Crytal propertie : Stiffne 10 N/m, Damping ratio 0.01, Natural frequency 10 rad/, Force-to-Charge 9 enitivity 10 9 C/N, Capacitance 10 F with it lo angle aumed negligible Cable propertie : Capacitance 9 10 F with it reitance aumed negligible Amplifier propertie : Input impedance 1 MΩ, Bandwidth 1MHz, Gain 3 Q.50 The maximum frequency of a force ignal in Hz below the natural frequency within it ueful midband range of meaurement, for which the gain amplitude i le than 1.05, approximately i, (A) 35 (B) 350 (C) 3500 (D) Q.51 The minimum frequency of a force ignal in Hz within it ueful mid-band range of meaurement, for which the gain amplitude i more than 0.95, approximately i, (A) 16 (B) 160 (C) 1600 (D) IN-A 13/0

14 013 INSTRUMENTATION ENGG. - IN Linked Anwer Quetion Statement for Linked Anwer Quetion 5 and 53: G = 1 1. Let Ku and T u be the ultimate gain and ultimate period correponding to the frequency repone baed cloed loop Ziegler-Nichol cycling method, repectively. The Ziegler-Nichol tuning rule for a P-controller i given a : K = 0.5 K u. Conider a plant with the tranfer function ( ) ( ) 3 Q.5 The value of Ku and T u, repectively, are (A) and π (B) 8 and π (C) 8 and π 3 (D) and π 3 Q.53 The gain of the tranfer function between the plant output and an additive load diturbance input of frequency π Tu in cloed loop with a P-controller deigned according to the Ziegler-Nichol tuning rule a given above i (A) 1.0 (B) 0.5 (C) 1.0 (D).0 Statement for Linked Anwer Quetion 54 and 55: A differential amplifier with ignal terminal X,Y,Z i connected a hown in Fig. (a) below for CMRR meaurement where the differential amplifier ha an additional contant offet voltage in the output. The obervation obtained are: when V = V, V0 = 3mV, and when V = 3 V, V0 = 4 mv. i i Fig. (a) Fig. (b) Q.54 Auming it differential gain to be 10 and the op-amp to be otherwie ideal, the CMRR i (A) 10 (B) 3 10 (C) 4 10 (D) Q.55 The differential amplifier i connected a hown in Fig. (b) above to a ingle train gage bridge. Let the train gage reitance vary around it no-load reitance R by ±1%. Aume the input impedance of the amplifier to be high compared to the equivalent ource reitance of the bridge, and the common mode characteritic to be a obtained above. The output voltage in mv varie approximately from (A) 18 to 18 (B) 18 to 1 (C) 1 to 1 (D) 99 to IN-A 14/0

15 013 INSTRUMENTATION ENGG. - IN General Aptitude (GA) Quetion Q.56 to Q.60 carry one mark each. Q.56 Statement: You can alway give me a ring whenever you need. Which one of the following i the bet inference from the above tatement? (A) Becaue I have a nice caller tune. (B) Becaue I have a better telephone facility. (C) Becaue a friend in need i a friend indeed. (D) Becaue you need not pay toward the telephone bill when you give me a ring. Q.57 Complete the entence: Dare mitake. (A) commit (B) to commit (C) committed (D) committing Q.58 Chooe the grammatically CORRECT entence: (A) Two and two add four. (B) Two and two become four. (C) Two and two are four. (D) Two and two make four. Q.59 They were requeted not to quarrel with other. Which one of the following option i the cloet in meaning to the word quarrel? (A) make out (B) call out (C) dig out (D) fall out Q.60 In the ummer of 01, in New Delhi, the mean temperature of Monday to Wedneday wa 41 C and of Tueday to Thurday wa 43 C. If the temperature on Thurday wa 15% higher than that of Monday, then the temperature in C on Thurday wa (A) 40 (B) 43 (C) 46 (D) 49 Q.61 to Q.65 carry two mark each. Q.61 Find the um to n term of the erie n n n n n 8 ( ) (A) 1 (B) ( ) 1 (C) ( ) n (D) ( ) Q.6 The et of value of p for which the root of the equation 3x xp(p 1) = 0 are of oppoite ign i (A) (, 0) (B) (0, 1) (C) (1, ) (D) (0, ) Q.63 A car travel 8 km in the firt quarter of an hour, 6 km in the econd quarter and 16 km in the third quarter. The average peed of the car in km per hour over the entire journey i (A) 30 (B) 36 (C) 40 (D) 4 IN-A 15/0

16 013 INSTRUMENTATION ENGG. - IN Q.64 What i the chance that a leap year, elected at random, will contain 53 Saturday? (A) /7 (B) 3/7 (C) 1/7 (D) 5/7 Q.65 Statement: There were different tream of freedom movement in colonial India carried out by the moderate, liberal, radical, ocialit, and o on. Which one of the following i the bet inference from the above tatement? (A) The emergence of nationalim in colonial India led to our Independence. (B) Nationalim in India emerged in the context of colonialim. (C) Nationalim in India i homogeneou. (D) Nationalim in India i heterogeneou. END OF THE QUESTION PAPER IN-A 16/0