Electrical Engineering (EE) 2016 GATE Paper (Set A) with solution | GATE Electrical Engineering (EE) Mock Test Series 2025 PDF Download

 Page 1


	: 	2 	: 	 			Electrical 	Engineering 	
Q. 1 – Q. 5 carry One mark each. 
01. The man who is now Municipal Commissioner worked as ___________
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Ans: (B) 
Sol: Option (A) and (D) cannot be the answers because of the word ‘the security’ 
02. Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with  (C) put down to  (D) put up against   
Ans:  (A) 
Sol: ‘cope with’ means put up with 
03. Find the odd one in the following group of words.
mock, deride , praise, jeer
(A) mock (B) deride  (C) praise  (D) jeer 
Ans: (C) 
Sol: ‘mock, deride and jeer’ are synonyms which means mockery. Therefore, the odd one is ‘praise’  
04. Pick the odd one from the following options.
(A) CADBE  (B) JHKIL (C) XVYWZ (D) ONPMQ  
Ans: (D) 
Sol: 
(A) (B)  (C) 
 (D) 
In options A, B and C, the letters skipped between consecutive pair of letters in the English 
alphabet is in increasing order (i,e) A and B, H and I and V and W but in option ‘D’ N and M are 
present instead of M and N so, option ‘D’ is odd one from the group. 
05. In a quadratic function, the value of the product of the roots ( ?, ?) is 4. Find the value of
n n
n n
? ?
? ? ?
? ? ?
 (A) n
4
 (B) 4
n
 (C) 2
2n –1
(D) 4
n–1
Ans: (B) 
Sol: 
n n
n n
n n
n n
n n
n n
n n
n n
1 1
? ? ? ?
? ? ?
? ? ?
? ? ?
?
?
?
?
? ? ?
?
? ? ?
? ? ?
? ?
  ?
n
 ? ?
n
 = ( ? ? ?)
n
 = (4)
n
 
A C D B E 
1 2 
J H K IL
9 8 
Z W Y V X
23 24
Q 
M P N O 
14 13 
Page 2


	: 	2 	: 	 			Electrical 	Engineering 	
Q. 1 – Q. 5 carry One mark each. 
01. The man who is now Municipal Commissioner worked as ___________
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Ans: (B) 
Sol: Option (A) and (D) cannot be the answers because of the word ‘the security’ 
02. Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with  (C) put down to  (D) put up against   
Ans:  (A) 
Sol: ‘cope with’ means put up with 
03. Find the odd one in the following group of words.
mock, deride , praise, jeer
(A) mock (B) deride  (C) praise  (D) jeer 
Ans: (C) 
Sol: ‘mock, deride and jeer’ are synonyms which means mockery. Therefore, the odd one is ‘praise’  
04. Pick the odd one from the following options.
(A) CADBE  (B) JHKIL (C) XVYWZ (D) ONPMQ  
Ans: (D) 
Sol: 
(A) (B)  (C) 
 (D) 
In options A, B and C, the letters skipped between consecutive pair of letters in the English 
alphabet is in increasing order (i,e) A and B, H and I and V and W but in option ‘D’ N and M are 
present instead of M and N so, option ‘D’ is odd one from the group. 
05. In a quadratic function, the value of the product of the roots ( ?, ?) is 4. Find the value of
n n
n n
? ?
? ? ?
? ? ?
 (A) n
4
 (B) 4
n
 (C) 2
2n –1
(D) 4
n–1
Ans: (B) 
Sol: 
n n
n n
n n
n n
n n
n n
n n
n n
1 1
? ? ? ?
? ? ?
? ? ?
? ? ?
?
?
?
?
? ? ?
?
? ? ?
? ? ?
? ?
  ?
n
 ? ?
n
 = ( ? ? ?)
n
 = (4)
n
 
A C D B E 
1 2 
J H K IL
9 8 
Z W Y V X
23 24
Q 
M P N O 
14 13 
	: 	3 	: 	 			GATE_2016_Afternoon 	Session 	
Q. 06 – Q. 10 carry two marks each. 
06. Among 150 faculty members in an institute, 55 are connected with each other through Facebook
??
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
 
or
WhatsApp
?
 accounts. The number of faculty members connected only through Facebook
?
accounts is _________
(A) 35   (B) 45    (C) 65   (D) 90
Ans: (A) 
Sol: Total faculty members = 150 
The faculty members having facebook account = FB = 55 
The faculty members having whatsapp = W = 85 
The faculty members do not have face book (or) Whats App accounts = 30 
The faculty members having any account = 150 ? 30 = 120 
The faculty members having both the accounts = (FB + W) ? 120 = (55 + 85) ? 120 = 20 
? The number of faculty members connected only through Facebook accounts = 55 ? 20 = 35
07. Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions.
(A) (i) only (B) (ii) only  (C) both  (i) and (ii)  (D) neither (i) nor (ii) 
Ans: (B) 
Sol: The first and second sentences tell us that computers are invented for computation and internet for 
intended invention. These sentences lead to option ii so option (B) is the right inference  
08. All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i)  Ooty in not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only  (B) (ii) only   (C) both (i) and (ii)  (D) neither (i) nor (ii)
35 20 65
150 
Facebook 
WhatsApp
Page 3


	: 	2 	: 	 			Electrical 	Engineering 	
Q. 1 – Q. 5 carry One mark each. 
01. The man who is now Municipal Commissioner worked as ___________
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Ans: (B) 
Sol: Option (A) and (D) cannot be the answers because of the word ‘the security’ 
02. Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with  (C) put down to  (D) put up against   
Ans:  (A) 
Sol: ‘cope with’ means put up with 
03. Find the odd one in the following group of words.
mock, deride , praise, jeer
(A) mock (B) deride  (C) praise  (D) jeer 
Ans: (C) 
Sol: ‘mock, deride and jeer’ are synonyms which means mockery. Therefore, the odd one is ‘praise’  
04. Pick the odd one from the following options.
(A) CADBE  (B) JHKIL (C) XVYWZ (D) ONPMQ  
Ans: (D) 
Sol: 
(A) (B)  (C) 
 (D) 
In options A, B and C, the letters skipped between consecutive pair of letters in the English 
alphabet is in increasing order (i,e) A and B, H and I and V and W but in option ‘D’ N and M are 
present instead of M and N so, option ‘D’ is odd one from the group. 
05. In a quadratic function, the value of the product of the roots ( ?, ?) is 4. Find the value of
n n
n n
? ?
? ? ?
? ? ?
 (A) n
4
 (B) 4
n
 (C) 2
2n –1
(D) 4
n–1
Ans: (B) 
Sol: 
n n
n n
n n
n n
n n
n n
n n
n n
1 1
? ? ? ?
? ? ?
? ? ?
? ? ?
?
?
?
?
? ? ?
?
? ? ?
? ? ?
? ?
  ?
n
 ? ?
n
 = ( ? ? ?)
n
 = (4)
n
 
A C D B E 
1 2 
J H K IL
9 8 
Z W Y V X
23 24
Q 
M P N O 
14 13 
	: 	3 	: 	 			GATE_2016_Afternoon 	Session 	
Q. 06 – Q. 10 carry two marks each. 
06. Among 150 faculty members in an institute, 55 are connected with each other through Facebook
??
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
 
or
WhatsApp
?
 accounts. The number of faculty members connected only through Facebook
?
accounts is _________
(A) 35   (B) 45    (C) 65   (D) 90
Ans: (A) 
Sol: Total faculty members = 150 
The faculty members having facebook account = FB = 55 
The faculty members having whatsapp = W = 85 
The faculty members do not have face book (or) Whats App accounts = 30 
The faculty members having any account = 150 ? 30 = 120 
The faculty members having both the accounts = (FB + W) ? 120 = (55 + 85) ? 120 = 20 
? The number of faculty members connected only through Facebook accounts = 55 ? 20 = 35
07. Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions.
(A) (i) only (B) (ii) only  (C) both  (i) and (ii)  (D) neither (i) nor (ii) 
Ans: (B) 
Sol: The first and second sentences tell us that computers are invented for computation and internet for 
intended invention. These sentences lead to option ii so option (B) is the right inference  
08. All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i)  Ooty in not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only  (B) (ii) only   (C) both (i) and (ii)  (D) neither (i) nor (ii)
35 20 65
150 
Facebook 
WhatsApp
	: 	4 	: 	 			Electrical 	Engineering 	
Ans: (D) 
Sol: Statement (i) is not true because Ooty is a hill station due Ooty has two lakes statement(ii) is also 
not true, because in given statements, for hill station one lake is compulsory but not mentioned 
about number of lakes. 
09. In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
 (A) 21   (B) 27    (C) 30 (D) 36 
Ans: (C) 
Sol: In given 2 ? 4 rectangle grid, the following type of rectangles are present. 
One figured rectangles = 8 
Two figured rectangles = 10 
Three figured rectangles = 4 
Four figured rectangles = 5 
Six figured rectangles = 2 
Eight figured rectangles = 1 
Total No. of rectangles = 30 
? The No. of rectangles observed in the given grid = 30. 
10. 
Choose the correct expression for f(x) given in the graph.  
 (A) f(x) = 1 – |x– 1|  (B) f(x) = 1 + |x –1|  
 (C) f(x) = 2 – |x –1| (D) f(x) = 2 + |x –1| 
Ans: (C) 
Sol: @ x = 3 from given graph f(x) must be equals to zero 
0 12 3 4 – 4 –3 –2 –1
–1
–1.5
–2
–2.5
–0.5
0 
0.5 
1 
1.5 
2 
2.5 
x
f(x) 
Page 4


	: 	2 	: 	 			Electrical 	Engineering 	
Q. 1 – Q. 5 carry One mark each. 
01. The man who is now Municipal Commissioner worked as ___________
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Ans: (B) 
Sol: Option (A) and (D) cannot be the answers because of the word ‘the security’ 
02. Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with  (C) put down to  (D) put up against   
Ans:  (A) 
Sol: ‘cope with’ means put up with 
03. Find the odd one in the following group of words.
mock, deride , praise, jeer
(A) mock (B) deride  (C) praise  (D) jeer 
Ans: (C) 
Sol: ‘mock, deride and jeer’ are synonyms which means mockery. Therefore, the odd one is ‘praise’  
04. Pick the odd one from the following options.
(A) CADBE  (B) JHKIL (C) XVYWZ (D) ONPMQ  
Ans: (D) 
Sol: 
(A) (B)  (C) 
 (D) 
In options A, B and C, the letters skipped between consecutive pair of letters in the English 
alphabet is in increasing order (i,e) A and B, H and I and V and W but in option ‘D’ N and M are 
present instead of M and N so, option ‘D’ is odd one from the group. 
05. In a quadratic function, the value of the product of the roots ( ?, ?) is 4. Find the value of
n n
n n
? ?
? ? ?
? ? ?
 (A) n
4
 (B) 4
n
 (C) 2
2n –1
(D) 4
n–1
Ans: (B) 
Sol: 
n n
n n
n n
n n
n n
n n
n n
n n
1 1
? ? ? ?
? ? ?
? ? ?
? ? ?
?
?
?
?
? ? ?
?
? ? ?
? ? ?
? ?
  ?
n
 ? ?
n
 = ( ? ? ?)
n
 = (4)
n
 
A C D B E 
1 2 
J H K IL
9 8 
Z W Y V X
23 24
Q 
M P N O 
14 13 
	: 	3 	: 	 			GATE_2016_Afternoon 	Session 	
Q. 06 – Q. 10 carry two marks each. 
06. Among 150 faculty members in an institute, 55 are connected with each other through Facebook
??
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
 
or
WhatsApp
?
 accounts. The number of faculty members connected only through Facebook
?
accounts is _________
(A) 35   (B) 45    (C) 65   (D) 90
Ans: (A) 
Sol: Total faculty members = 150 
The faculty members having facebook account = FB = 55 
The faculty members having whatsapp = W = 85 
The faculty members do not have face book (or) Whats App accounts = 30 
The faculty members having any account = 150 ? 30 = 120 
The faculty members having both the accounts = (FB + W) ? 120 = (55 + 85) ? 120 = 20 
? The number of faculty members connected only through Facebook accounts = 55 ? 20 = 35
07. Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions.
(A) (i) only (B) (ii) only  (C) both  (i) and (ii)  (D) neither (i) nor (ii) 
Ans: (B) 
Sol: The first and second sentences tell us that computers are invented for computation and internet for 
intended invention. These sentences lead to option ii so option (B) is the right inference  
08. All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i)  Ooty in not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only  (B) (ii) only   (C) both (i) and (ii)  (D) neither (i) nor (ii)
35 20 65
150 
Facebook 
WhatsApp
	: 	4 	: 	 			Electrical 	Engineering 	
Ans: (D) 
Sol: Statement (i) is not true because Ooty is a hill station due Ooty has two lakes statement(ii) is also 
not true, because in given statements, for hill station one lake is compulsory but not mentioned 
about number of lakes. 
09. In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
 (A) 21   (B) 27    (C) 30 (D) 36 
Ans: (C) 
Sol: In given 2 ? 4 rectangle grid, the following type of rectangles are present. 
One figured rectangles = 8 
Two figured rectangles = 10 
Three figured rectangles = 4 
Four figured rectangles = 5 
Six figured rectangles = 2 
Eight figured rectangles = 1 
Total No. of rectangles = 30 
? The No. of rectangles observed in the given grid = 30. 
10. 
Choose the correct expression for f(x) given in the graph.  
 (A) f(x) = 1 – |x– 1|  (B) f(x) = 1 + |x –1|  
 (C) f(x) = 2 – |x –1| (D) f(x) = 2 + |x –1| 
Ans: (C) 
Sol: @ x = 3 from given graph f(x) must be equals to zero 
0 12 3 4 – 4 –3 –2 –1
–1
–1.5
–2
–2.5
–0.5
0 
0.5 
1 
1.5 
2 
2.5 
x
f(x) 
	: 	5 	: 	 			GATE_2016_Afternoon 	Session 	
Option A 
 f(x) = 1 ? |x ? 1| 
@ x = 3 
f(x) = 1 ? |3 ? 1| 
 = 1 ? 2 = ? 1 
So, it is not 
Option B 
  f(x) = 1 + |x ? 1| 
@ x = 3 
f(x) = 1 + |3 ? 1| 
= 1 + 2 = 3 
So, it is not 
Option C 
  f(x) = 2 ? |x ? 1| 
@ x = 3 
f(x) = 2 ? |3 ? 1| 
 = 2 ? 2 = 0 
 So, it is true 
Option D 
  f(x) = 2 + |x ? 1| 
@ x = 3 
f(x) = 2 ? |3 ? 1| 
= 2 + 2 = 4 
So, it is not 
Page 5


	: 	2 	: 	 			Electrical 	Engineering 	
Q. 1 – Q. 5 carry One mark each. 
01. The man who is now Municipal Commissioner worked as ___________
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Ans: (B) 
Sol: Option (A) and (D) cannot be the answers because of the word ‘the security’ 
02. Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with  (C) put down to  (D) put up against   
Ans:  (A) 
Sol: ‘cope with’ means put up with 
03. Find the odd one in the following group of words.
mock, deride , praise, jeer
(A) mock (B) deride  (C) praise  (D) jeer 
Ans: (C) 
Sol: ‘mock, deride and jeer’ are synonyms which means mockery. Therefore, the odd one is ‘praise’  
04. Pick the odd one from the following options.
(A) CADBE  (B) JHKIL (C) XVYWZ (D) ONPMQ  
Ans: (D) 
Sol: 
(A) (B)  (C) 
 (D) 
In options A, B and C, the letters skipped between consecutive pair of letters in the English 
alphabet is in increasing order (i,e) A and B, H and I and V and W but in option ‘D’ N and M are 
present instead of M and N so, option ‘D’ is odd one from the group. 
05. In a quadratic function, the value of the product of the roots ( ?, ?) is 4. Find the value of
n n
n n
? ?
? ? ?
? ? ?
 (A) n
4
 (B) 4
n
 (C) 2
2n –1
(D) 4
n–1
Ans: (B) 
Sol: 
n n
n n
n n
n n
n n
n n
n n
n n
1 1
? ? ? ?
? ? ?
? ? ?
? ? ?
?
?
?
?
? ? ?
?
? ? ?
? ? ?
? ?
  ?
n
 ? ?
n
 = ( ? ? ?)
n
 = (4)
n
 
A C D B E 
1 2 
J H K IL
9 8 
Z W Y V X
23 24
Q 
M P N O 
14 13 
	: 	3 	: 	 			GATE_2016_Afternoon 	Session 	
Q. 06 – Q. 10 carry two marks each. 
06. Among 150 faculty members in an institute, 55 are connected with each other through Facebook
??
and 85 are connected through WhatsApp
?
. 30 faculty members do not have Facebook
?
 
or
WhatsApp
?
 accounts. The number of faculty members connected only through Facebook
?
accounts is _________
(A) 35   (B) 45    (C) 65   (D) 90
Ans: (A) 
Sol: Total faculty members = 150 
The faculty members having facebook account = FB = 55 
The faculty members having whatsapp = W = 85 
The faculty members do not have face book (or) Whats App accounts = 30 
The faculty members having any account = 150 ? 30 = 120 
The faculty members having both the accounts = (FB + W) ? 120 = (55 + 85) ? 120 = 20 
? The number of faculty members connected only through Facebook accounts = 55 ? 20 = 35
07. Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions.
(A) (i) only (B) (ii) only  (C) both  (i) and (ii)  (D) neither (i) nor (ii) 
Ans: (B) 
Sol: The first and second sentences tell us that computers are invented for computation and internet for 
intended invention. These sentences lead to option ii so option (B) is the right inference  
08. All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i)  Ooty in not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only  (B) (ii) only   (C) both (i) and (ii)  (D) neither (i) nor (ii)
35 20 65
150 
Facebook 
WhatsApp
	: 	4 	: 	 			Electrical 	Engineering 	
Ans: (D) 
Sol: Statement (i) is not true because Ooty is a hill station due Ooty has two lakes statement(ii) is also 
not true, because in given statements, for hill station one lake is compulsory but not mentioned 
about number of lakes. 
09. In a 2 ? 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
 (A) 21   (B) 27    (C) 30 (D) 36 
Ans: (C) 
Sol: In given 2 ? 4 rectangle grid, the following type of rectangles are present. 
One figured rectangles = 8 
Two figured rectangles = 10 
Three figured rectangles = 4 
Four figured rectangles = 5 
Six figured rectangles = 2 
Eight figured rectangles = 1 
Total No. of rectangles = 30 
? The No. of rectangles observed in the given grid = 30. 
10. 
Choose the correct expression for f(x) given in the graph.  
 (A) f(x) = 1 – |x– 1|  (B) f(x) = 1 + |x –1|  
 (C) f(x) = 2 – |x –1| (D) f(x) = 2 + |x –1| 
Ans: (C) 
Sol: @ x = 3 from given graph f(x) must be equals to zero 
0 12 3 4 – 4 –3 –2 –1
–1
–1.5
–2
–2.5
–0.5
0 
0.5 
1 
1.5 
2 
2.5 
x
f(x) 
	: 	5 	: 	 			GATE_2016_Afternoon 	Session 	
Option A 
 f(x) = 1 ? |x ? 1| 
@ x = 3 
f(x) = 1 ? |3 ? 1| 
 = 1 ? 2 = ? 1 
So, it is not 
Option B 
  f(x) = 1 + |x ? 1| 
@ x = 3 
f(x) = 1 + |3 ? 1| 
= 1 + 2 = 3 
So, it is not 
Option C 
  f(x) = 2 ? |x ? 1| 
@ x = 3 
f(x) = 2 ? |3 ? 1| 
 = 2 ? 2 = 0 
 So, it is true 
Option D 
  f(x) = 2 + |x ? 1| 
@ x = 3 
f(x) = 2 ? |3 ? 1| 
= 2 + 2 = 4 
So, it is not 
	: 	7 	: 	 			GATE_2016_Afternoon 	Session 	
Q. 1 – Q. 25 carry One mark each. 
01. The maximum value attained by the function f(x) = x(x –1) (x –2) in the interval [1, 2] is _______
Ans: 0 
Sol: f(x) = x(x ?1)(x ?2)  in   [1, 2] 
??
3
3 3
x 0 2 x 6 x 3 x f
2
?
? ? ? ? ? ? ?
?? 6 x 6 x f ? ? ? ? 
imum min 0 4 . 3
3
3 3
f ? ? ?
?
?
?
?
?
?
?
?
?
? ?
imum max 0 4 . 3
3
3 3
f ? ? ? ?
?
?
?
?
?
?
?
?
?
? ? 
f(1) = 0, f(2) = 0 
Max value = 0 
02. Consider 3 ?3 matrix with every element being equal to 1. Its only non-zero eigenvalue is
_________
Ans: 3 
Sol: 
?
?
?
?
?
?
?
?
?
?
?
1 1 1
1 1 1
1 1 1
A
Char equation is 0 I A ? ? ? ? ??
3
+3 ?
2
 = 0 
? ? = 3, 0, 0 
03. The Laplace Transform of f(t) = e
2t
 sin(5t) u(t) is
(A)
29 s 4 s
5
2
? ?
(B) 
5 s
5
2
?
(C) 
29 s 4 s
2 s
2
? ?
?
 (D) 
5 s
5
?
Ans: (A) 
Sol: 
2 2
LT
5 s
5
) t ( U t 5 sin
?
?
?? 25 2 s
5
) t ( tU 2 sin e
2
LT
t 2
? ?
?
( ? e
at
 f(t) 
?? a s F
LT
? ?
) 
?? 25 s 2 2 4 s
5
2
? ? ? ?
?
25 s 4 4 s
5
2
? ? ?
?
29 s 4 s
5
2
? ?
?