Instrumentation Engineering Q. No. 1 to 25 Carry One Mark Each (C)

Transcription

1 IN GATE-07-PAPER Instrumentation Engineering Q. No. to 5 Carry One Mark Each. A system is described by the following differential equation: dy t dt dx t yt xt,x0 y0 0 dt Where x(t) and y(t) are the input and output variables respectively. The transfer function of the inverse system is (A) s s (B) (B) s s We know for inverse system h t *h t t I s s XS HSHIt HIS HS YS Y S XS So the transfer function of inverse system is It is given that dy t dx t zyt x t dt dt SY S Y S SX S X S Y S X S S XS S Y S S H I S XS YS (D) s s. If v is a non-zero vector of dimension 3, then the matrix A=vv T has a rank = to V is non zero T T V.V and V.V V Rank of the matrix T A V.V is 3. A periodic signal x(t) is shown in the figure. The fundamental frequency of the signal x (t) in Hz is ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India

2 IN GATE-07-PAPER to 0 T0 Fince fundamental time period T 0 = so the fundamental frequency f 0 =/T 0 =Hz 4. The silicon diode, shown in the figure, has a barrier potential of 0.7 V. There will be no forward current flow through the diode, if V dc, in volt, is greater than (A) 0.7 (B).3.8 (D).6 (D) Vdc ID V I dc d.c when I 0 D V.6V D 5. For a first order low pass filter with unity d.c. gain and -3 db corner frequency of 000 rad/s, the transfer function H( j) is (A) 000 j (B) j j A first order LPF that satisfy unity D.C. Gain should of forms a HS s a s a And the 3 db cut off frequency should be a so that i H D.C.gain j a H0 j0 j a 000 Only option is of form s a 000 s (D) 000 j000 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India

3 IN GATE-07-PAPER 6. A and B are the logical inputs and X is the logical output shown in the figure. The output X is related to A and B by (A) X AB BA (B) X AB BA X AB AB (D) X AB BA A A A.B B B AB A B AB 7. The most suitable pressure gauge to measure pressure in the range of 0 to0 4 3 (A) Bellows (B) Barometer Strain gauge (D) Pirani gauge (D) Pirani Gauge is best suitable for the above range 0 to0 Vacuum Pressure 4 3 torr is torr Application is to measure 8. The standard for long distance analog signal transmission in process control industry is (A) 4-0 mv (B) 0-0mA 4-0mA (D) 0-5V In process industries, the control signal used is Current 4-0 ma Pressure 3-5 psi 9. If a continuous-time signal xt cos t sequence x(n) at n = 5 is is sampled at 4 Hz, the value of the discrete-time (A) (B) - 0 (D) xt cos t If the sampling interval is T s then the sampled signal x nts cos nts cos n ; sin ce fs 4Hz fs n 5 xnts xncos n cos x5 cos 0 4 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 3

4 IN GATE-07-PAPER 0. The term hysteresis is associated with (A) ON-OFF control (B) P-I control Feed-forward control (D) Ratio control (A) Hyeres s is need to be introduce in on off control to reduce the oscillation.. A current waveform, i(t), shown in the figure, is passed through a Permanent Magnet Moving coil (PMMC) type ammeter. The reading of the ammeter up to two decimal places is (A) -0.5 A (B) -0.A 0.37 A (D) 0.5 A (A) Consider the PMMC as zero centered meter Average value of the above signal is tdt dt T 0 t 0 t 0.5 Amps.. The connection of two -port networks is shown in the figure. The ABCD parameters of N and N networks are given as A B 5 A B 0 and C D 0 C D 0. N N A The ABCD parameters of the combined -port network are (A) 5 0. T T T (B) (D) ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 4

5 IN GATE-07-PAPER 3. The figure shows a shape ABC and its mirror image A B C across the horizontal axis X axis. The coordinate transformation matrix that maps ABC to A B C is 0 0 (A) 0 (B) 0 (D) Mirror image across 0 0 (D) 0 0 A, Ax y A x y x y 0 B x y x y C x y x y 0 0 x y y x x, y 3 y,x 3 x, y x y y x x y 0 4. The differential amplifier, shown in the figure, has a differential gain of Ad 00 and common mode gain of Ac 0.. If V 5.0V and V 5.00V, then V,in 0 volt (up to one decimal place) is..4 to.6 Given Ac 0.; V 5.0V; V 5.00V; Ad 00 V A V A V o d d c c V V V V d V V Vc 5.005V V V.5V 0 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 5

6 IN GATE-07-PAPER 5. A circuit consisting of dependent and independent sources is shown in the figure. If the voltage at Node- is V, then the voltage at Node- is V. to I A V 0.5 V 0.5 V V R V 4V V 4 V R 0.5 A A V R I V V RI 3 V I 6. The eigen values of the matrix 5 A are (A),5,6 (B), 5 j6, 5 j6 (D), 5, 5 Characteristic equation is ; j 5 j6 7. The figure shows a phase locked loop. The output frequency is locked at f0 5kHz. The value of f i in khz is. to f0 nfi 5 fi khz 5 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 6

7 IN GATE-07-PAPER 8. Identify the instrument that does not exist: (A) Dynamometer-type ammeter Moving-iron voltmeter (D) To Measure power we require to coils (C.C & P.C) (B) Dynamometer-type wattmeter (D) Moving-iron wattmeter Dynamo meter will consist two coils. So it can measure power. Dynamo meter can also measure current and voltage, if we connect C.C & P.C in series. Moving Iron meter will have only one coil, so it can measure current and voltage But not power. Note: Moving Iron wattmeter doesn t exist. 9. The output V o shown in the figure, in volt, is close to (A) 0 (B) 5 5 (D) 0 (B) R V0 Vi 0 0V R V V 0 sat so V V 5V 0 sat 0. An 8-bit microcontroller with 6 address lines has 3 fixed interrupts i.e., Int, Int and Int3 with corresponding interrupt vector addresses as 0008H. 000H and 008H. To execute a 3- byte long Interrupt Service Subroutine for Int starting at the address ISSI, The location 0008H onwards should ideally contain (A) a CALL to ISSI a conditional JUMP to ISSI (A) or (B) (B) an unconditional JUMP to ISSI (D) only ISSI. A series R-L-C circuit is excited with a 50V, 50 Hz sinusoidal source. The voltage across the resistance and the capacitance are shown in the figure. The voltage across the inductor (V L ) is V 50 to 50 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 7

8 IN GATE-07-PAPER bc3 V V50VThe circuit is at resonance R at resonance V V V 50V L C L:. The condition for oscillation in a feedback oscillator circuit is that at the frequency of oscillation, initially the loop gain is greater than unity while the total phase shift around the loop in degree is (A) 0 (B) (D) 70 A 3. Let z x jy where j. Then cosz (A) cos z (B) cos z sin z (D) sin z (B) cos z cos z 4. The region of Convergence (ROC) of the Z-transform of a causal unit step discrete-time sequence is (A) z (B) z z (D) z The Z-transform of unit step sequence is xz un z z ; z z z n 0 n z a only when a 0 a z z 5. The pressure drop across an orifice plate for a particular flow rate is 5 kg/m. If the flow rate is doubled (within the operating range of the orifice), the corresponding pressure drop in kg/m 3 is (A).5 (B) (D) 5.0 In case of an orifice plate Q P Q 5 Q P 5 or P P 5 4 0kg / m Q. No. 6 to 55 Carry Two Marks Each 6. The two-input voltage multiplier, shown in the figure, has a scaling factor of and produces voltage output. If V 5V and V 3V, the value of V 0 in volt is. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 8

9 IN GATE-07-PAPER -5 to -5 Given V 5V; V 3V U sin g nodal analysis 0 V 0 V V R R V V V ; 0 V V0 V 5 V0 5V For the circuit, shown in the figure, the total real power delivered by the source to the loads is kw.75 to.96 I I I Re al power VI cos cos5.86kw 8. The magnetic flux density of an electromagnetic flow meter is 00 mwb/m. The electrodes are wall-mounted inside the pipe having a diameter of 0.5m. A voltage of V is generated when a conducting fluid is passed through the flow meter. The volumetric flow rate of the fluid in m 3 /s is..9 to ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 9

10 IN GATE-07-PAPER 9. In the circuit, shown in the figure, the MOSFET is operating in the saturation zone. The characteristics of the MOSFET is given by I D VGS ma, where V GS is in V. If Vs 5V, then the value of R S in k is. 9.9 to 0. Given V s 5V; ID VGS ma 5 7 VG 7V; 5 V V V 7 5 V GS G S I D 0.5mA V 5 R 0k S S ID The hot junction of a bare thermocouple, initially at room temperature (30 o C), is suddenly dipped in molten metal at t = 0s. The cold junction is kept at room temperature. The thermocouple can be modeled as a first-order instrument with a time constant of.0s and a o static sensitivity of 0 V C. If the voltage, measured across the thermocouple indicates 0.0 mv at t =.0s, then the temperature of the molten metal in o C is. 605 to A series R-L-C circuit is excited with an a.c. voltage source. The quality factor (Q) of the circuit is given as Q 30. The amplitude of current in ampere at upper half-power frequency will be. 6 to 7 L Q R C 3 R L 00 5 Q C at upper half power frequency z V 5 I A Z 5 5 R 3 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 0

11 IN GATE-07-PAPER 3. An angle modulated signal with carrier frequency m c 6 c 0 rad s is given by t cos t 5sin 000t 0sin 000 t. The maximum deviation of the frequency in the angle modulated signal from that of the carrier is khz. to 3 mt cos ct 5sin 000 t 0sin 000 t Instantaneous phase i d t ct 5sin 000 t 0sin 000 t i t t 5000cos000t a t i i Instantaneous frequency c 0 000cos 000t f t f 500cos 000t 0000cos 000t c Maximum deviation in maximum value is 500cos 000t 0000cos 000t kHz 33. Three DFT coefficients, out of five DFT coefficients of a five-point real sequence are given as X 0 4,X j X 3 j. The zero-th value of the sequence x(n), x(0), is as: and (A) (B) 3 (D) 4 (B) We know for N point DFT (for real sequence) * * x K x N K, here N 5 so x K x 5 K...() The standard IDFT N j Kn N xn x Ke, Substituting n 0 N K0 N x0 xk if N 5 then N K0 K0 4 x 0 x x x 3 x 4 x0 xk It is given that x 0 4 x j x 3 j usin g equation () x x * 5 x *(3) j * j x 4 x * 5 4 x * j * j usin g equation () 4 j j j j x ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India

12 IN GATE-07-PAPER A closed-loop system is shown in the figure. The system parameter is not known. The condition for asymptotic stability of the closed loop system is (A) 0.5 (B) (D) 0.5 (D) The characteristic equation of the unity feedback system is + G(S)=0 S S S S 3 S S S S S S S 0 3 By R-H criterian if the equation is of form is bc > ad, Using this as bs cs d 0 then the condition for stability 35. The power delivered to a single phase inductive load is measured with a dynamometer type wattmeter using a potential transformer (PT) of turns ratio 00: and the current transformer (CT) of turns ratio :5. Assume both the transformers to be ideal. The power factor of the load is 0.8. If the wattmeter reading is 00W, then the apparent power of the load in kva is. 50 to 50 I N I N I I N V V N I I 5 N N V V 00 I through C.C I V / g cross P.C V 00 : Power measured by w/m will be 00 V.I cos V I I VI 0 50kVA C.T 5 I P.T V V ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India

13 IN GATE-07-PAPER The overall closed loop transfer function C s, R s represented in the figure, will be 3 G s G sh s 3 G s G s G3 s (A) G s G s H s G s G s G s H s G s (A) Gs G3s (B) G s H s G s G3 s G sg sh s (D) G (s)h (s) G (s)g (s) 3 The Parallel connection of G,G can be replaced by G + G. G G (G +G ) forms a feedback loop with H, it can be replaced by G G H Final considering G 3 and the unity feedback G G G3 G G H G S G SG3 S 3 C S G G G H R S G G G H G S G S H S G S 37. When the voltage across a battery is measured using a d.c. potentiometer, the reading shows.08v. But when the same voltage is measured using a Permanent Magnet Moving Coil (PMMC) voltmeter, the voltmeter reading shows 0.99V. If the resistance of the voltmeter is 00, the internal resistance of the battery, in, is. 00 to 00 We use potentiometer to measure unknown voltages (very low) it is a Null type instrument R r Slidewire G Un known v g Battery ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 3

14 IN GATE-07-PAPER The Galvanometer reads zero when the voltage drop across slide wire and unknown Battery voltages are equal. Given that potentiometer reading as.08v i.e., The Battery voltage will be.08 volts. R i v.08v V m R m R 00 V PMMC reads, R se v m 0.99V. ByKVL V V 0.09 Volts. V 0.99 m 4 Im 9 0 AMPS. R V 00 V 0.09 R 00. i 4 Im The probability that a communication system will have high fidelity is 0.8. The probability that the system will have both high fidelity and high selectivity is 0.8. The probability that a given system with high fidelity will have high selectivity is (A) 0.8 (B) (D) 0.86 Let A, B be the events respectively that the communication system will have high fidelity, high selectivity then P A 0.8and P A B 0.8 P A B 0.8 required probabilityis P B A 0. P A The current response of a series R-L circuit to a unit step voltage is given in the table. The value of L is H. t in s t(t) in A to We know i(t) = R t e L ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 4

15 IN GATE-07-PAPER V t at t, it 0.5 R R 0.5 at t 0.5 R 0.5 R R L e L H L 40. A resistance temperature detector (RTD) is connected to a circuit, as shown in the figure, Assume the op-amp to be ideal. If V.0V, then the value of x is. 0.9 to 0. At the inverting terminal of the op-amp i.e., at V By virtual ground V V t 0 0 V 0 0 o R x R R 0 0 x x. 0. R x R R x 0 o 4. The circuit of a Schmitt trigger is shown in the figure. The zener-diode combination maintains the output between 7V. The width of the hysteresis band is V. 0.6 to 0.7 When zener diode combination maintains output of 7V VUTP 0.333V VLTP 0.333V 0.5 Width of hysteresis band V V V UTP LTP ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 5

16 IN GATE-07-PAPER 4. The loop transfer function of a closed-loop system is given by breakaway point of the root-loci will be. K s 6 G s H s. s s The. to -.0 To obtain the Break point first of all we have to arrange K intevms of GH, then the roots of dk 0 ds gives break point K S 6 S S GH K S S S 6 d K S 6 ds S 6 S 6 S 5 S 5 S 6 S 5 dk ds ds 0 S 6 S S 5 S S S S 5 0 S S 0 S., 0.83 To decide which among the two root is Breakaway draw the pole zero plot & mark real axis branch. d 6 So break away point be in 0 to - so break away point is The unbalanced voltage of the Wheatstone bridge, shown in the figure, is measured using digital voltmeter having infinite input impedance and a resolution of 0.mV. If R 000, then the minimum value of R in to create a detectable unbalanced voltage is. 0.7 to 0.3 k R Vx By Voltagedivision Rule. k R V.000volts By KVL x.000 k R k R. Bysolving aboveequation, weget 0. R ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 6

17 IN GATE-07-PAPER In the circuit diagram, shown in the figure, S was closed and S was open for a very long time. At t = 0, S is opened and S is closed. The voltage across the capacitor, in volt, at t = 5 s is..43 to.63 at t 0 c V 0 V at t VC 3 V R eq Ceq 0 0 s 3 3 V t V V 0 V e C C C C e t t 3V VC 0 V VC 0 C V 5s e.57v 45. The block diagram of a closed-loop control system is shown in the figure. The values of k and k p are such that the system has a damping ratio of 0.8 and an undamped natural frequency n of 4 rad/s respectively. The value of k p will be. 0.3 to 0.4 +GH=0 represent the characteristic equation of the close loop ve feed back system K K S S S P 0 S S K KPS 0 S S K KK S 0 S KK S K 0 P Comparing with standard nd order equation S S 0 K 4 K K 6 n n n Using K=6, the characteristic equation becomes P ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 7

18 IN GATE-07-PAPER S 6KP S 6 0 n 6K P n KP 46. Assuming the op-amp shown in the figure to be ideal, the frequency at which the magnitude of V o will be 95% of the magnitude of V in is khz..9 to 3 V V i i x RCS S V V i i x j0 4 f j f 0 i V V R Vi Vi V0 Vx 4 4 R j6.80 f j6.80 f when V 0.95V 0.95V i V f 6.80 f f f f kHz 4 i ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 8

19 IN GATE-07-PAPER The following table lists an n th n n order polynomial f x a x a x a x a and the n n 0 forward differences evaluated at equally spaced values of x. The order of the polynomial is x f(x) f f 3 f (A) (B) 3 (D) 4 (D) 4 Clearly the entries in the fourth forward difference The order of the polynomial is 4. i.e. f areallsamewhichis Consider two discrete-time signals: and x n, x n,, for n 0.. The Z-transform of the convoluted sequence xn x n * x n is (A) z 3z (B) 3z z (D) z 3z z 3z z In the a.c. bridge, shown in the figure, R 0 and C 0 F. If the bridge is balanced at a frequency, the value of 0 0 in rad/s is to 0000 According to bridge balancing condition ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 9

20 IN GATE-07-PAPER R jc R R R jc R j C R R R R jc jcr R jc R R jc jcr R jc R jcr R jc 3 jc R R jc jcr R R jc 3 jc jcr R R R R C R 3 R R RC C RC The junction semiconductor temperature sensor shown in the figure is used to measure the temperature of hot air. The output voltage V o is.v. The current output of the sensor is given by I T A where T is the temperature in K. Assuming the opamp to be ideal, the temperature of the hot air in o C is approximately. 76 to 78 Voltage at point V A, is 5V VA Vo. 0.7V 3 By virtual ground V V 0.7 V V 0.7V I B V k 000 B As given I I A 350 A I V B k Temperature Sensor V A k k V o o o T 350K C 77 C ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 0

21 IN GATE-07-PAPER 5. In a sinusoidal amplitude modulation scheme (with carrier) the modulated signal is given by Am t 00cos ct 50cos mt cos ct, where c is the carrier frequency and m is the modulation frequency. The power carried by the sidebands in % of total power is % to. Given amplitude modulated signal A t 00cos t 50cos t cos t m c m c 00cos t 5cos t 5cos c c m c m Carrier Side Branch PC PSB Total power = Power carried by the side bands in % of total power.% The angle between two vectors x 6 4 T and x 8 6 T. in radian is 0.65 to 0.8 cos 0.7 radians Quantum efficiency of a photodiode (ratio between the number of liberated electrons and the 34 number of incident photons) is 0.75 at 830 nm. Given Plank s constant h J, the 9 charge of an electron e.6 0 C and the velocity of light in the photodiode 8 Cm 0 m s. For an incident optical power of 00 W at 830 nm, the photocurrent in A is to Responsivity R e IP Now R P o IP R Po A 75.8A ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India

22 IN GATE-07-PAPER The two inputs A and B are connected to an R-S latch via two AND gates as shown in the figure. If A = and B = 0, the output QQ is (A) 00 (B) 0 0 (D) (B) It is similar to JKFF A = J, B = K J K Q 0 0 Q Q n n n A B Previous State J K Next State [Q n ] A. Q B. Q Qn Qn (Previous output) The Laplace transform of a causal signal t = 0. s is unit. -.4 to -.0 S S 6 4 S YS S 6 S 6 S 6 S 6 S 6 Taking inverse Laplace 6t y t t e u t y e u e 4e.9 s y t is Y s. The value of the signal y(t) at s 6 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India

23 IN GATE-07-PAPER General Aptitude Q. No. - 5 Carry One Mark Each. The event would have been successful if you able to come. (A) are (B) had been have been (D) would have been B. Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are, 3, red and blue. Proposition: If a card has an even value on one side, then its opposite face is red. The cards which MUST be turned over to verify the above proposition are (A), red (B), 3, red, blue (D), red, blue C To check even red, we must confirm that back of is red and back of blue is an odd number. x x What is the value of x when 8 44? 5 5 (A) (B) - - (D) cannot be determined B x x x4 x 4 x x There was no doubt that their work was thorough. Which of the words below is closest in meaning to the underlined word above? (A) Pretty (B) complete sloppy (D) haphazard B 5. Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is B (A) /9 (B) /9 /3 (D) 4/9 Required probability= ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 3

24 IN GATE-07-PAPER Q. No. 6-0 Carry Two Marks Each 6. Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer. From this, what can one conclude? (A) The centre operates on a first-come-first-served basis, but with variable service times, depending on specific customer needs. (B) Customers were served in an arbitrary order, since they took varying amounts of time of service completion in the centre. Since some people came out within a few minutes of entering the centre, the system is likely to operate on a last-come-first-served basis. (D) Entering the centre early ensured that one would have shorter service times and most people attempted to do this. (A) People coming out in the same order in which they enter indicates that the centre operates on a first-come-first-serve basis. 7. The points in the graph below represent the halts of a lift for durations of minute, over a period of hour. Which of the following statements are correct? (i) The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period (ii) The elevator stays on the fourth floor for the longest duration over the one hour period (A) Only i (B) Only ii Both i and ii (D) Neither i nor ii (D) (i) is incorrect as it moves directly (ii) is incorrect as it stayed for maximum duration on ground floor. 8. A map show the elevations of Darjeeling, Gangtok, Kalimpong, Pelling, and Siliguri, Kalimpong is at a lowest elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation than Siliguri. Darjeeling is at a higher elevation than Gangtok. Which of the following statements can be inferred from the paragraph above? (i) Pelling is at a higher elevation than Kalimpong (ii) Kalimpong is at a lower elevation than Darjeeling (iii) Kalimpong is at a higher elevation than Siliguri (iv) Siliguri is at a lower elevation than Gangtok (A) Only ii (B) Only ii and iii Only ii and iv (D) Only iii and iv ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 4

25 IN GATE-07-PAPER The given information is K<G, P<G, S<P and G<D From these it can be inferred S<P<G<D and also K<G So K<D as well but no comparison between K and S (or) K and P is given. 9. P, Q, R, S, T and U are seated around a circular table. R is seated two places to the right of Q. P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats, which of the following must necessarily be true? (A) P is immediately to the right of R (B) T is immediately to the left of P T is immediately to the left of P or P is immediately to the right of Q (D) U is immediately to the right of R or P is immediately to the left of T Following two possibilities can be drawn U T R S T R P S P U Q Q Given in question P and U interchange then new diagram can be drawn. T T P R S R U S U P Q now only option verifies. Q 0. Budhan covers a distance of 9 km in hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 6 km in hours. The speed in km/h at which Budhan walks is (A) (B) 4 5 (D) 6 (D) Let cycling speed = c and walking speed = w Given 3 c w 9 (i) c w 6 (ii) On solving eq(i) and (ii), we get w 6km / hr ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 5