Instrumentation (IN) 2013 GATE Paper (Set C) without solution GATE Notes | EduRev

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GATE : Instrumentation (IN) 2013 GATE Paper (Set C) without solution GATE Notes | EduRev

 Page 1


 
 
 
 
 
 
 
SESSION - 3 
 
 
 
 
 
 
 
 
Page 2


 
 
 
 
 
 
 
SESSION - 3 
 
 
 
 
 
 
 
 
2013                                                                                                                           Question Booklet Code                                                                           
 
IN-C 
 
1/20
IN : INSTRUMENTATION ENGINEERING 
   
Duration: Three Hours                   Maximum Marks: 100  
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully. If you find that either: 
a. The Question Booklet Code printed at the right hand top corner of this page does not match with 
the Question Booklet Code at the right hand top corner of the ORS or 
b. The Question Paper Code preceding the Registration number on the ORS is not IN,  
            then exchange the booklet immediately with a new sealed Question Booklet.  
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate 
bubble under each digit of your registration number and (ii) write your registration number, your 
name and name of the examination centre and put your signature at the specified location.  
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are 
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the 
bubbles in the ORS very carefully. 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE 
marks.  For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks 
questions, ? mark will be deducted for each wrong answer.  However, in the case of the linked 
answer question pair, there will be negative marks only for wrong answer to the first question and no 
negative marks for wrong answer to the second question.  
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the 
Question Booklet for rough work. 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ballpoint pen. 
Name 
 
 
Registration Number IN 
       
 
 
C 
Page 3


 
 
 
 
 
 
 
SESSION - 3 
 
 
 
 
 
 
 
 
2013                                                                                                                           Question Booklet Code                                                                           
 
IN-C 
 
1/20
IN : INSTRUMENTATION ENGINEERING 
   
Duration: Three Hours                   Maximum Marks: 100  
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully. If you find that either: 
a. The Question Booklet Code printed at the right hand top corner of this page does not match with 
the Question Booklet Code at the right hand top corner of the ORS or 
b. The Question Paper Code preceding the Registration number on the ORS is not IN,  
            then exchange the booklet immediately with a new sealed Question Booklet.  
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate 
bubble under each digit of your registration number and (ii) write your registration number, your 
name and name of the examination centre and put your signature at the specified location.  
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are 
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the 
bubbles in the ORS very carefully. 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE 
marks.  For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks 
questions, ? mark will be deducted for each wrong answer.  However, in the case of the linked 
answer question pair, there will be negative marks only for wrong answer to the first question and no 
negative marks for wrong answer to the second question.  
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the 
Question Booklet for rough work. 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ballpoint pen. 
Name 
 
 
Registration Number IN 
       
 
 
C 
2013                                                                                                                                         INSTRUMENTATION ENGG. - IN                                                                                                                       
 
IN-C 2/20
Q.1 to Q.25 carry one mark each. 
Q.1 
The transfer function 
) (
) (
1
2
s V
s V
 of the circuit shown below is 
 
 
 
(A) 
1
1 5 . 0
+
+
s
s
 (B) 
2
6 3
+
+
s
s
 (C) 
1
2
+
+
s
s
 (D) 
2
1
+
+
s
s
 
 
Q.2 
Assuming zero initial condition, the response ) (t y of the system given below to a unit step input 
) (t u is 
 
 
  
 
(A) ) (t u (B)  ) (t u t (C)  ) (
2
2
t u
t
 (D) ) (t u e
t - 
 
Q.3 The operational amplifier shown in the circuit below has a slew rate of . s / Volts 8 . 0 µ The input 
signal is . ) ( sin 25 . 0 t ? The maximum frequency of input  in kHz for which there is no distortion in 
the output is  
 
(A) 23.84  (B) 25.0  (C) 50.0 (D) 46.60  
 
Page 4


 
 
 
 
 
 
 
SESSION - 3 
 
 
 
 
 
 
 
 
2013                                                                                                                           Question Booklet Code                                                                           
 
IN-C 
 
1/20
IN : INSTRUMENTATION ENGINEERING 
   
Duration: Three Hours                   Maximum Marks: 100  
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully. If you find that either: 
a. The Question Booklet Code printed at the right hand top corner of this page does not match with 
the Question Booklet Code at the right hand top corner of the ORS or 
b. The Question Paper Code preceding the Registration number on the ORS is not IN,  
            then exchange the booklet immediately with a new sealed Question Booklet.  
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate 
bubble under each digit of your registration number and (ii) write your registration number, your 
name and name of the examination centre and put your signature at the specified location.  
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are 
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the 
bubbles in the ORS very carefully. 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE 
marks.  For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks 
questions, ? mark will be deducted for each wrong answer.  However, in the case of the linked 
answer question pair, there will be negative marks only for wrong answer to the first question and no 
negative marks for wrong answer to the second question.  
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the 
Question Booklet for rough work. 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ballpoint pen. 
Name 
 
 
Registration Number IN 
       
 
 
C 
2013                                                                                                                                         INSTRUMENTATION ENGG. - IN                                                                                                                       
 
IN-C 2/20
Q.1 to Q.25 carry one mark each. 
Q.1 
The transfer function 
) (
) (
1
2
s V
s V
 of the circuit shown below is 
 
 
 
(A) 
1
1 5 . 0
+
+
s
s
 (B) 
2
6 3
+
+
s
s
 (C) 
1
2
+
+
s
s
 (D) 
2
1
+
+
s
s
 
 
Q.2 
Assuming zero initial condition, the response ) (t y of the system given below to a unit step input 
) (t u is 
 
 
  
 
(A) ) (t u (B)  ) (t u t (C)  ) (
2
2
t u
t
 (D) ) (t u e
t - 
 
Q.3 The operational amplifier shown in the circuit below has a slew rate of . s / Volts 8 . 0 µ The input 
signal is . ) ( sin 25 . 0 t ? The maximum frequency of input  in kHz for which there is no distortion in 
the output is  
 
(A) 23.84  (B) 25.0  (C) 50.0 (D) 46.60  
 
2013                                                                                                                                         INSTRUMENTATION ENGG. - IN                                                                                                                       
 
IN-C 3/20
Q.4 Which one of the following statements is NOT TRUE for a continuous time causal and stable  
LTI system? 
(A) All the poles of the system must lie on the left side of the  j?
 
axis. 
(B) Zeros of the system can lie anywhere  in the s-plane. 
(C) All the poles must lie within 1 s = . 
(D) All the roots of the characteristic equation must be located on the left side of the
 
j? axis. 
 
Q.5 
A source ( ) cos100
s
v t V t p =
 
has an internal impedance of
 
4 + j3 ?. If a purely resistive load  
connected to this source has to extract the maximum power out of the source, its value in ?  should be 
(A) 3 (B) 4 (C) 5 (D) 7 
 
Q.6 In the transistor circuit as shown  below, the value of resistance R
E
 in k?  is approximately, 
  
+10 V
R
E
V
out
  
1.5 kO O O O
0.1µF
0.1µF
I
 C
 = 2.0 mA
V
CE 
=5.0 V
6kO O O O
15k O O O O
 
(A) 1.0  (B) 1.5  (C)  2.0  (D) 2.5  
 
Q.7 For a periodic signal ) 4 / 500 ( 6 300 10 100 30 ) ( p + + + = t sin t cos t sin t v , the fundamental frequency in 
rad/s is 
(A) 100 (B) 300 (C) 500 (D) 1500 
 
Q.8 For a vector E, which one of the following statements is NOT TRUE?  
(A) If 0, ? · = E  E is called solenoidal. 
(B) If 0, ? × = E E is called conservative.  
(C) If 0, ? × = E E is called irrotational. 
(D) If
 
0, ? · = E E is called irrotational. 
 
Q.9 The complex function tanh ( ) s is analytic over a region of the imaginary axis of the complex  
s-plane if the following is TRUE everywhere in the region for all integers n 
(A) ( ) 0 Re s = (B) ( ) Im s np ? 
(C) ( )
3
n
Im s
p
? (D) 
(2 1)
( )
2
n
Im s
p +
? 
Page 5


 
 
 
 
 
 
 
SESSION - 3 
 
 
 
 
 
 
 
 
2013                                                                                                                           Question Booklet Code                                                                           
 
IN-C 
 
1/20
IN : INSTRUMENTATION ENGINEERING 
   
Duration: Three Hours                   Maximum Marks: 100  
Read the following instructions carefully. 
 
1. Do not open the seal of the Question Booklet until you are asked to do so by the invigilator. 
2. Take out the Optical Response Sheet (ORS) from this Question Booklet without breaking the seal 
and read the instructions printed on the ORS carefully. If you find that either: 
a. The Question Booklet Code printed at the right hand top corner of this page does not match with 
the Question Booklet Code at the right hand top corner of the ORS or 
b. The Question Paper Code preceding the Registration number on the ORS is not IN,  
            then exchange the booklet immediately with a new sealed Question Booklet.  
3. On the right hand side of the ORS, using ONLY a black ink ballpoint pen, (i) darken the appropriate 
bubble under each digit of your registration number and (ii) write your registration number, your 
name and name of the examination centre and put your signature at the specified location.  
4. This Question Booklet contains 20 pages including blank pages for rough work. After you are 
permitted to open the seal, check all pages and report discrepancies, if any, to the invigilator. 
5. There are a total of 65 questions carrying 100 marks. All these questions are of objective type. Each 
question has only one correct answer. Questions must be answered on the left hand side of the ORS 
by darkening the appropriate bubble (marked A, B, C, D) using ONLY a black ink ballpoint pen 
against the question number. For each question darken the bubble of the correct answer. More 
than one answer bubbled against a question will be treated as an incorrect response. 
6. Since bubbles darkened by the black ink ballpoint pen cannot be erased, candidates should darken the 
bubbles in the ORS very carefully. 
7. Questions Q.1 – Q.25 carry 1 mark each. Questions Q.26 – Q.55 carry 2 marks each. The 2 marks 
questions include two pairs of common data questions and two pairs of linked answer questions. The 
answer to the second question of the linked answer questions depends on the answer to the first 
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted, 
then the answer to the second question in the pair will not be evaluated. 
8. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks. 
Questions Q.56 – Q.60 carry 1 mark each, and questions Q.61 – Q.65 carry 2 marks each. 
9. Questions not attempted will result in zero mark and wrong answers will result in NEGATIVE 
marks.  For all 1 mark questions, ? mark will be deducted for each wrong answer. For all 2 marks 
questions, ? mark will be deducted for each wrong answer.  However, in the case of the linked 
answer question pair, there will be negative marks only for wrong answer to the first question and no 
negative marks for wrong answer to the second question.  
10. Calculator is allowed whereas charts, graph sheets or tables are NOT allowed in the examination hall. 
11. Rough work can be done on the Question Booklet itself. Blank pages are provided at the end of the 
Question Booklet for rough work. 
12. Before the start of the examination, write your name and registration number in the space provided 
below using a black ink ballpoint pen. 
Name 
 
 
Registration Number IN 
       
 
 
C 
2013                                                                                                                                         INSTRUMENTATION ENGG. - IN                                                                                                                       
 
IN-C 2/20
Q.1 to Q.25 carry one mark each. 
Q.1 
The transfer function 
) (
) (
1
2
s V
s V
 of the circuit shown below is 
 
 
 
(A) 
1
1 5 . 0
+
+
s
s
 (B) 
2
6 3
+
+
s
s
 (C) 
1
2
+
+
s
s
 (D) 
2
1
+
+
s
s
 
 
Q.2 
Assuming zero initial condition, the response ) (t y of the system given below to a unit step input 
) (t u is 
 
 
  
 
(A) ) (t u (B)  ) (t u t (C)  ) (
2
2
t u
t
 (D) ) (t u e
t - 
 
Q.3 The operational amplifier shown in the circuit below has a slew rate of . s / Volts 8 . 0 µ The input 
signal is . ) ( sin 25 . 0 t ? The maximum frequency of input  in kHz for which there is no distortion in 
the output is  
 
(A) 23.84  (B) 25.0  (C) 50.0 (D) 46.60  
 
2013                                                                                                                                         INSTRUMENTATION ENGG. - IN                                                                                                                       
 
IN-C 3/20
Q.4 Which one of the following statements is NOT TRUE for a continuous time causal and stable  
LTI system? 
(A) All the poles of the system must lie on the left side of the  j?
 
axis. 
(B) Zeros of the system can lie anywhere  in the s-plane. 
(C) All the poles must lie within 1 s = . 
(D) All the roots of the characteristic equation must be located on the left side of the
 
j? axis. 
 
Q.5 
A source ( ) cos100
s
v t V t p =
 
has an internal impedance of
 
4 + j3 ?. If a purely resistive load  
connected to this source has to extract the maximum power out of the source, its value in ?  should be 
(A) 3 (B) 4 (C) 5 (D) 7 
 
Q.6 In the transistor circuit as shown  below, the value of resistance R
E
 in k?  is approximately, 
  
+10 V
R
E
V
out
  
1.5 kO O O O
0.1µF
0.1µF
I
 C
 = 2.0 mA
V
CE 
=5.0 V
6kO O O O
15k O O O O
 
(A) 1.0  (B) 1.5  (C)  2.0  (D) 2.5  
 
Q.7 For a periodic signal ) 4 / 500 ( 6 300 10 100 30 ) ( p + + + = t sin t cos t sin t v , the fundamental frequency in 
rad/s is 
(A) 100 (B) 300 (C) 500 (D) 1500 
 
Q.8 For a vector E, which one of the following statements is NOT TRUE?  
(A) If 0, ? · = E  E is called solenoidal. 
(B) If 0, ? × = E E is called conservative.  
(C) If 0, ? × = E E is called irrotational. 
(D) If
 
0, ? · = E E is called irrotational. 
 
Q.9 The complex function tanh ( ) s is analytic over a region of the imaginary axis of the complex  
s-plane if the following is TRUE everywhere in the region for all integers n 
(A) ( ) 0 Re s = (B) ( ) Im s np ? 
(C) ( )
3
n
Im s
p
? (D) 
(2 1)
( )
2
n
Im s
p +
? 
2013                                                                                                                                         INSTRUMENTATION ENGG. - IN                                                                                                                       
 
IN-C 4/20
Q.10 
Two systems with impulse responses 
1
( ) h t and 
2
( ) h t  are connected in cascade. Then the overall   
 impulse response of the cascaded system is given by 
(A) product of 
1
( ) h t and 
2
( ) h t (B) sum of  
1
( ) h t and
2
( ) h t 
(C) convolution of  
1
( ) h t and 
2
( ) h t (D) subtraction of 
2
( ) h t from 
1
( ) h t 
 
Q.11 If the A-matrix of the state space model of a SISO linear time invariant system is rank deficient, the 
transfer function of the system must have 
(A) a pole with a positive real part 
(B) a pole with a negative real part 
(C) a pole with a positive imaginary part 
(D) a pole at the origin 
 
Q.12 
The dimension of the  null space of the matrix 
0 1 1
1 1 0
1 0 1
- - - ? ?
? ?
? ?
? ?
 
 is  
(A) 0 (B) 1 (C)  2 (D)  3 
 
Q.13 
The Bode plot of a transfer function ) (s G is shown in the figure below.  
 
Gain (dB)
 
The gain (20 log ( ) ) G s is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is 
negative for all ?. Then ) (s G is 
(A) 
s
8 . 39
 (B) 
2
8 . 39
s
 (C)  
s
32
  (D)  
2
32
s
 
 
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