| | GATE-2015-PAPER-01 IN www.gateforum.com General Aptitude Q. No. 1 – 5 Carry One Mark Each 1. An apple costs Rs. 10. An onion costs Rs. 8. Select the most suitable sentence with respect to grammar and usage. (A) The price of an apple is greater than an onion. (B) The price of an apple is more than onion. (C) The price of an apple is greater than that of an onion. (D) Apples are more costlier than onions. Key: (C) 2. The Buddha said, “Holding on to anger is like grasping a hot coal with the intent of throwing it at someone else; you are the one who gets burnt.” Select the word below which is closest in meaning to the word underlined above. (A) burning (B) igniting (C) clutching (D) flinging Key: (C) 3. M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-law of M. How is P related to M? (A) P is the son-in-law of M. (B) P is the grandchild of M. (C) P is the daughter-in law of M. (D) P is the grandfather of M. Key: (B) 4. The number that least fits this set: (324, 441, 97 and 64) is ________. (A) 324 (B) 441 (C) 97 (D) 64 Key: (C) Exp: 324182;441212;6482 but 97x2 for any positive integer i.e. 97 is odd man out 5. It takes 10 s and 15 s, respectively, for two trains travelling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of the second train is 150 m. The magnitude of the difference in the speeds of the two trains (in m/s) is ____________. (A) 2.0 (B) 10.0 (C) 12.0 (D) 22.0 Key: (A) length Exp: Speed  lengthspeedtime time 12010s s 12 1 1 15015s s 10 2 2 s s 2 1 2  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 1 | | GATE-2015-PAPER-01 IN www.gateforum.com Q. No. 6 – 10 Carry Two Marks Each 6. The velocity V of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the 7 seconds, how much will the odometer reading increase by (in m)? (A) 0 (B) 3 (C) 4 (D) 5 Key: (D) 7. The overwhelming number of people infected with rabies in India has been flagged by the World Health Organization as a source of concern. It is estimated that inoculating 70% of pets and stray dogs against rabies can lead to a significant reduction in the number of people infected with rabies. Which of the following can be logically inferred from the above sentences? (A) The number of people in India infected with rabies is high. (B) The number of people in other parts of the world who are infected with rabies is low. (C) Rabies can be eradicated in India by vaccinating 70% of stray dogs (D) Stray dogs are the main sources of rabies worldwide. Key: (A) 8. A flat is shared by four first year undergraduate students. They agreed to allow the oldest of them to enjoy some extra space in the flat. Manu is two months older than Sravan, who is three months younger than Trideep. Pavan is one month older than Sravan. Who should occupy the extra space in the flat? (A) Manu (B) Sravan (C) Trideep (D) Pavan Key: (C) 9. Find the area bounded by the lines 3x+2y=14, 2x-3y=5 in the first quadrant. (A) 14.95 (B) 15.25 (C) 15.70 (D) 20.35 Key: (B)  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 2 | | GATE-2015-PAPER-01 IN www.gateforum.com y 14  Exp A  ,0  3  B B0,7 3x2y14 5  C ,0 2   5 D0,  E 2x3y5  3  R E 4,1 x Required area is area of O C A OAB– area of CEA 114 113   7  115.25sq.units 2 3  2 6  D 10. A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0.1 and has a slope of −0.02. What is the value of y at x = 5 from the fit? (A) −0.030 (B) −0.014 (C) 0.014 (D) 0.030 Key: (A) a Exp: yabx, wherex l x and 0.1, b0.02 n b a0.02x a 0.002 0.0020.02x atx 5,y0.0020.021.6090.03018 0.030 Instrumentation Engineering Q. No. 1 – 25 Carry One Mark Each 1. A straight line of the form y = mx + c passes through the origin and the point (x, y) = (2, 6). The value of m is ____________. Key: 3 Exp: y=mx+c passing through (0,0)00cc0 y=mx+c passing through(2,6)62mm3   2. lim n2 n  n2 1 is ____________. n Key: 0.5   n2 n  n2 1 Exp: im n2 n  n2 1  n n2 n  n2 1  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 3 | | GATE-2015-PAPER-01 IN www.gateforum.com n2 nn2 1 1 1n 1  im  t  n n2 n  n2 1 n 1 1 2 1  1 n n2 3. A voltage V1 is measured 100 times and its average and standard deviation are 100 V and 1.5 V respectively. A second voltage V2, which is independent of V1, is measured 200 times and its average and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2. Then the standard deviation of V3 in volt is _____________. Key: 2.5 Exp: VarV VarV V VarV VarV 2.2546.25 3 1 2 1 2 Standard deviation of V =  Var(V )  6.25 2.5 3 3 4. The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is . (A) (i –2j + k) (B) (–i + 2j –k) (C) (0i + 0j + 0k) (D) (4i +3 j + 5k) Key: (D)     Exp: We know that if a.b0 then aand b are perpendicular Verify options (a) , (b), (c) are perpendicular Option (d) is not perpendicular 5. In the neighborhood of z = 1, the function f(z) has a power series expansion of the form f(z) = 1+(1-z)+(1- z)2+ ………… Then f(z) is 1 1 z1 1 (A) (B) (C) (D) z z2 z1 2z1 Key: (A) Exp: 11z1z3 put w1z, then thegiven series becomes 1ww2 w3 1 1 1    1w 1(1z) z 6. Three currents i1, i2 and i3 meet at a node as shown in the figure below. If i 3cost ampere, 1 i 4sint ampere and i I cost ampere, the value of I3 in ampere is . 2 3 3 Key: 5  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 4 | | GATE-2015-PAPER-01 IN www.gateforum.com Exp: By KCL i (t)i (t)i (t) 1 2 3 i (t)i (t)i (t) 3 1 2 By phasor I  I  I 3 1 2 30490o553.13   i (t)5cos(t53.13) 3 So by comparison I 5. 3 7. An air cored coil has a Q of 5 at a frequency of 100 kHz. The Q of the coil at 20 kHz (neglecting skin effect) will be ________ . Key: 1 L Exp: Q R L 2100103L L at100kHz, 5   7.9577106 R R R L at 20kHz, Q 2201037.9577106 1 R 8. A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial charge. The voltage across the capacitor for t > 2 s in volt is Key: 8 1 1 Exp: V   idt  8u(t1)u(t2)dt8r(t1)r(t2) c C 1 8 1 2 V(t2)8V c  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 5 | | GATE-2015-PAPER-01 IN www.gateforum.com 9. The signal x[n] shown in the figure below is convolved with itself to get y[n]. The value of y[-1] is __________. Key: 2 1 1 1 Exp: xn1,1,11n1 1 1 1 1  1 1 1 1 ynxn*xn1,2,1,2,1 1 1 1 1 y12 10. In the circuit shown below   1sin210000t1sin230000tV. The RMS value of 1 2   the current through the resistor R will be minimum if the value of the capacitor C in microfarad is _________. Key: 0.28 to 0.283 s2 11. If X(s), the Laplace transform of signal x(t) is given by Xs , then the value of x(t) as s1s3 t  is ______. Key: 0 s2 Exp: t ft t s 0 t s0 s1s2 s1 12. The number of times the Nyquist plot of Gs will encircle the origin clockwise is ______. s1 Key: 1 s1 Exp: G(s) s1 1 G(s)  1 1  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 6 | | GATE-2015-PAPER-01 IN www.gateforum.com G(s)1802tan1() G(s)1180o 2tan1() G(0)1180o G()10o G(1)190o Using G(0), G(1), GG() information, the plot will look like  Hence it encircle the origin only 1 time in clockwise direction 3 2 13. The value of a0 which will ensur e that the polynomial s + 3s + 2s + a0 has roots on the left half of the s-plane is (A) 11 (B) 9 (C) 7 (D) 5 Key: (D) Exp: S3 1 2 S2 3 a 0 6a S1 0 3 S0 a 0 6a For Stability 0 0 a 6 3 0 8 14. The input it2sin3t is applied to a system whose transfer function Gs . s102 The amplitude of the output of the system is . Key: 0.1467 8 8 8 Exp: Gs   s102 s2 20s100 1002 j20 8 60 8 Gs tan1  33.4o 10022 3600 91 109 yt2 8 sin3t33.4o0.1467sin3t146.6o  109 So amplitude is 0.1467.  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 7 | | GATE-2015-PAPER-01 IN www.gateforum.com 15. The diode D used in the circuit below is ideal. The voltage drop Vab across the 1k resistor in volt is ____________. Key: 0 Exp: 1k 5k 1k 5k 3V 5V 3V 5V Since V V diode is open circuit and no current flow through 1k, So V 0V. P N 1k 16. In the circuit given below, the op-amp is ideal. The output voltage VO in volt is _______- . Key: -1 V 2 V V  1 1 1  2 Exp: x  x  x 0V     V 1122 20 20 10 x20 20 10 20 x 1 V  x 2 R 201 V  f V  1V   0 R x 102  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 8 | | GATE-2015-PAPER-01 IN www.gateforum.com 17. In the circuit given below, the diodes D1 and D2 have a forward voltage drop of 0.6 V. The op-amp used is ideal. The magnitude of the negative peak value of the output VO in volt is ______. Key: 1.6 18. The Boolean expression XYX'Y'Z is equivalent to (A) XYZ'X'Y'Z (B) X'Y'Z'XYZ (C) (X+Z) (Y+Z) (D) X'YY'Z Key: (C) Exp: FXYXZYZ The min term of F are X Y  X  Z  Y Z  1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 1 Fm(1,3,5,6,7) If we go for option B F(xz)(yz)zxy  Its minterms are   Z X Y  0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 Fm(1,3,5,6,7) Since minterms are same these two functions are equal  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 9 | | GATE-2015-PAPER-01 IN www.gateforum.com 19. In the digital circuit given below, F is (A) XYYZ (B) XYYZ (C) XYYZ (D) XZY Key: (B) Exp: From the circuit FXY.YZXYYZ 20. A 3 ½ digit DMM has an accuracy specification of 1% of full scale (accuracy class 1). A reading of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in milliampere is  ____________. Key: 2 Exp: Since all information are given n in mA unit assume the scale in mA unit.  Since it is given that error is 1% of full scale 1 0 0 0 mA So, error 1%of 200mA2mA.   So if it measures 100mA then the reading will 200mArange be in the range 1002mA decimalpoint  the worst source error is 2mA. 21. A dc potentiometer, shown in figure below, is made by connecting fifteen 10 resistors and a 10 slide wire of length 1000 mm in series. The potentiometer is standardized with the current Ip = 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11 (11 numbers of the fixed 10 resistor are included) and the slide wire is on the 234th mm position. The unknown voltage (up to four decimal places) in volt is ______. Key: 1.1234  ICP–Intensive Classroom Program  eGATE-Live Internet Based Classes DLP  TarGATE-All India Test Series Leaders in GATE Preparations  65+ Centers across India   © All rights reserved by Gateforum Educational Services Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. 10