Electronics and Communication Engineering (EC) 2016 GATE Paper (Set A) with solution Electronics and Communication Engineering (ECE) Notes | EduRev

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Electronics and Communication Engineering (ECE) : Electronics and Communication Engineering (EC) 2016 GATE Paper (Set A) with solution Electronics and Communication Engineering (ECE) Notes | EduRev

 Page 1


		: 	2 	: 	       Gate 2016 – ECE – Set 1 					
Q.1 – Q.5 Carry One Mark Each 
01. Which of the following is CORRECT with respect to grammar and usage?
Mount Everest is ______
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
01. Ans: (A)
Sol: Before superlative article ‘the’ has to be used. ‘one of ’ the expression should take plural noun and 
so option ‘C’ and ‘D’ can’t be the answer.
02. The policeman asked the victim of a theft, “What did you ______?”
(A) loose      (B) lose   (C) loss (D) louse 
02. Ans: (B)
Sol: ‘lose’ is verb. 
03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely
(A) effectiveness --- prescribed (B) availability ---- used 
(B) prescription ---- available (D) acceptable--- proscribed  
03. Ans: (A)
Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word 
‘medicine.’ 
04. In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits,
Of the unripe fruits, 45% are apples, Of the ripe ones, 66% are oranges. If the pile contains a total
of 5692000 fruits, how many of them are apples?
(A) 2029198    (B) 2467482   (C) 2789080  (D) 3577422
04. Ans: (A)
Sol: Total no. of fruits = 5692000 
 Unripe type of apples = 45% of 15% of 5692000 
5692000
100
15
100
45
? ? ?
         = 384210 
Ripe type of apples 5692000
100
85
100
34
? ? ? = 1644988 
?Total no. of apples = 384210 + 1644988 = 2029198 
05. Michael lives 10 km way from where I live. Ahmed lives 5km away and Susan lives 7 km away
from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From
the information provided here, what is one possible distance (in km) at which I live from Arun’s
place?
(A) 3.00      (B) 4.99   (C) 6.02  (D) 7.01
Page 2


		: 	2 	: 	       Gate 2016 – ECE – Set 1 					
Q.1 – Q.5 Carry One Mark Each 
01. Which of the following is CORRECT with respect to grammar and usage?
Mount Everest is ______
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
01. Ans: (A)
Sol: Before superlative article ‘the’ has to be used. ‘one of ’ the expression should take plural noun and 
so option ‘C’ and ‘D’ can’t be the answer.
02. The policeman asked the victim of a theft, “What did you ______?”
(A) loose      (B) lose   (C) loss (D) louse 
02. Ans: (B)
Sol: ‘lose’ is verb. 
03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely
(A) effectiveness --- prescribed (B) availability ---- used 
(B) prescription ---- available (D) acceptable--- proscribed  
03. Ans: (A)
Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word 
‘medicine.’ 
04. In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits,
Of the unripe fruits, 45% are apples, Of the ripe ones, 66% are oranges. If the pile contains a total
of 5692000 fruits, how many of them are apples?
(A) 2029198    (B) 2467482   (C) 2789080  (D) 3577422
04. Ans: (A)
Sol: Total no. of fruits = 5692000 
 Unripe type of apples = 45% of 15% of 5692000 
5692000
100
15
100
45
? ? ?
         = 384210 
Ripe type of apples 5692000
100
85
100
34
? ? ? = 1644988 
?Total no. of apples = 384210 + 1644988 = 2029198 
05. Michael lives 10 km way from where I live. Ahmed lives 5km away and Susan lives 7 km away
from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From
the information provided here, what is one possible distance (in km) at which I live from Arun’s
place?
(A) 3.00      (B) 4.99   (C) 6.02  (D) 7.01
		: 	3 	: 	 				Questions & Solutions 						
05. Ans: (c)
Sol: From given data, the following diagram is possible 
I = I live 
AH = Ahmed lives;  M = Michael lives 
   S = Susan lives;    A= Arun lives 
? Arun lives farthes away than Ahmed means more than 5 km but closer than Susan means less 
than 7 km, from given alternatives, option ‘C’ only possible. 
Q.6 – Q.10 Carry two marks each 
06. A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.
However, only 30% of infected people develop the disease. What percentage of people moving
through a tuberculosis prone zone remains infected but does not shows symptoms of disease?
(A) 15     (B) 33   (C) 35   (D) 37
06. Ans: (C)
Sol: 
  = 
100
50
100
70
? =
100
35
 = 35%
07. In a world filled with uncertainty, he was glad to have many good friends. He had always assisted
them in times of need and was confident that they would reciprocate. However, the events of the
last week proved him wrong.
Which of the following interference(s) is/are logically valid and can be inferred from the above
passage?
(i) His friends were always asking him to help them
(ii) He felt that when in need of help, his friends would let him down.
(iii) He was sure that his friends  would help him when in need.
(iv) His friends did not help him last week.
(A) (i) and (ii)      (B) (iii) and (iv)  (C) (iii) only  (D) (iv) only
07. Ans: (B)
Sol: The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to 
statements iii and iv as logically valid inferences. 
 I 
 AH
M 
A
 S
7 km
6.02 m
5 km 
10 km
Tuberculosic
Afected 
  50% 
Infected
  50% 
          Does not  
Develop the disease
70% of 50%
 Develop the disease
     30% of 50% 
Page 3


		: 	2 	: 	       Gate 2016 – ECE – Set 1 					
Q.1 – Q.5 Carry One Mark Each 
01. Which of the following is CORRECT with respect to grammar and usage?
Mount Everest is ______
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
01. Ans: (A)
Sol: Before superlative article ‘the’ has to be used. ‘one of ’ the expression should take plural noun and 
so option ‘C’ and ‘D’ can’t be the answer.
02. The policeman asked the victim of a theft, “What did you ______?”
(A) loose      (B) lose   (C) loss (D) louse 
02. Ans: (B)
Sol: ‘lose’ is verb. 
03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely
(A) effectiveness --- prescribed (B) availability ---- used 
(B) prescription ---- available (D) acceptable--- proscribed  
03. Ans: (A)
Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word 
‘medicine.’ 
04. In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits,
Of the unripe fruits, 45% are apples, Of the ripe ones, 66% are oranges. If the pile contains a total
of 5692000 fruits, how many of them are apples?
(A) 2029198    (B) 2467482   (C) 2789080  (D) 3577422
04. Ans: (A)
Sol: Total no. of fruits = 5692000 
 Unripe type of apples = 45% of 15% of 5692000 
5692000
100
15
100
45
? ? ?
         = 384210 
Ripe type of apples 5692000
100
85
100
34
? ? ? = 1644988 
?Total no. of apples = 384210 + 1644988 = 2029198 
05. Michael lives 10 km way from where I live. Ahmed lives 5km away and Susan lives 7 km away
from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From
the information provided here, what is one possible distance (in km) at which I live from Arun’s
place?
(A) 3.00      (B) 4.99   (C) 6.02  (D) 7.01
		: 	3 	: 	 				Questions & Solutions 						
05. Ans: (c)
Sol: From given data, the following diagram is possible 
I = I live 
AH = Ahmed lives;  M = Michael lives 
   S = Susan lives;    A= Arun lives 
? Arun lives farthes away than Ahmed means more than 5 km but closer than Susan means less 
than 7 km, from given alternatives, option ‘C’ only possible. 
Q.6 – Q.10 Carry two marks each 
06. A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.
However, only 30% of infected people develop the disease. What percentage of people moving
through a tuberculosis prone zone remains infected but does not shows symptoms of disease?
(A) 15     (B) 33   (C) 35   (D) 37
06. Ans: (C)
Sol: 
  = 
100
50
100
70
? =
100
35
 = 35%
07. In a world filled with uncertainty, he was glad to have many good friends. He had always assisted
them in times of need and was confident that they would reciprocate. However, the events of the
last week proved him wrong.
Which of the following interference(s) is/are logically valid and can be inferred from the above
passage?
(i) His friends were always asking him to help them
(ii) He felt that when in need of help, his friends would let him down.
(iii) He was sure that his friends  would help him when in need.
(iv) His friends did not help him last week.
(A) (i) and (ii)      (B) (iii) and (iv)  (C) (iii) only  (D) (iv) only
07. Ans: (B)
Sol: The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to 
statements iii and iv as logically valid inferences. 
 I 
 AH
M 
A
 S
7 km
6.02 m
5 km 
10 km
Tuberculosic
Afected 
  50% 
Infected
  50% 
          Does not  
Develop the disease
70% of 50%
 Develop the disease
     30% of 50% 
		: 	5 	: 	 				Questions & Solutions 						
 
08. Leela is older than her cousin Pavithra, pavithra’s brother Shiva is older than Leela. When Pavithra
and shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does.
Which one of the following statements must be TRUE based on the above?
(A) When Shiva plays chess with Leela and Pavithra. he often loses.
(B) Leela is the oldest of the three.
(C) Shiva is a better  chess palyer than Pavithra
(D) Pavithra is the young of the three
08. Ans: (D)
Sol: From given data, the following arrangement is possible 
Shiva
Leela
Pavithra
Among four alternatives, option D is TRUE.
09. If q
–a
 =
r
1
 and r
–b
 =
s
1
 and  S
–C
 =
q
1
, the value of abc is ____.
(A) (rqs)
–1
 (B) 0 (C) 1 (D) r+q+s 
09. Ans: (C)
Sol: 
r
1
q
a
?
?
  ?
r
1
q
1
a
? ? q
a
 
= r 
b
b
b
r s
s
1
r
1
s
1
r ? ? ? ? ?
?
q s
q
1
s
1
q
1
s
c
c
c
? ? ? ? ?
?
 
?? r s r s r q
ac
a
c a
? ? ? ? ?
  (s
ac
)
b
 
 = s 
   s
abc
 = s ? 
      ? abc = 1 
10. P,Q,R and S are working on a project. Q can finish the taks in 25 days, working alone for 12 hours
a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a
day but took sick leave in the beginning for two days. R worked  18 hours a day on all days. What
is the ratio of work done by Q and R after 7 days from the start of the project?
(A) 10:11  (B) 11:10   (C) 20:21  (D) 21:20
10. Ans: (C)
Sol: Q can finish the task = 25 days, 12 hrs/day 
= 300 hrs, 1 hr th
300
1
?
R can finish the task = 50 days, 12 hrs/day 
Page 4


		: 	2 	: 	       Gate 2016 – ECE – Set 1 					
Q.1 – Q.5 Carry One Mark Each 
01. Which of the following is CORRECT with respect to grammar and usage?
Mount Everest is ______
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
01. Ans: (A)
Sol: Before superlative article ‘the’ has to be used. ‘one of ’ the expression should take plural noun and 
so option ‘C’ and ‘D’ can’t be the answer.
02. The policeman asked the victim of a theft, “What did you ______?”
(A) loose      (B) lose   (C) loss (D) louse 
02. Ans: (B)
Sol: ‘lose’ is verb. 
03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely
(A) effectiveness --- prescribed (B) availability ---- used 
(B) prescription ---- available (D) acceptable--- proscribed  
03. Ans: (A)
Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word 
‘medicine.’ 
04. In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits,
Of the unripe fruits, 45% are apples, Of the ripe ones, 66% are oranges. If the pile contains a total
of 5692000 fruits, how many of them are apples?
(A) 2029198    (B) 2467482   (C) 2789080  (D) 3577422
04. Ans: (A)
Sol: Total no. of fruits = 5692000 
 Unripe type of apples = 45% of 15% of 5692000 
5692000
100
15
100
45
? ? ?
         = 384210 
Ripe type of apples 5692000
100
85
100
34
? ? ? = 1644988 
?Total no. of apples = 384210 + 1644988 = 2029198 
05. Michael lives 10 km way from where I live. Ahmed lives 5km away and Susan lives 7 km away
from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From
the information provided here, what is one possible distance (in km) at which I live from Arun’s
place?
(A) 3.00      (B) 4.99   (C) 6.02  (D) 7.01
		: 	3 	: 	 				Questions & Solutions 						
05. Ans: (c)
Sol: From given data, the following diagram is possible 
I = I live 
AH = Ahmed lives;  M = Michael lives 
   S = Susan lives;    A= Arun lives 
? Arun lives farthes away than Ahmed means more than 5 km but closer than Susan means less 
than 7 km, from given alternatives, option ‘C’ only possible. 
Q.6 – Q.10 Carry two marks each 
06. A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.
However, only 30% of infected people develop the disease. What percentage of people moving
through a tuberculosis prone zone remains infected but does not shows symptoms of disease?
(A) 15     (B) 33   (C) 35   (D) 37
06. Ans: (C)
Sol: 
  = 
100
50
100
70
? =
100
35
 = 35%
07. In a world filled with uncertainty, he was glad to have many good friends. He had always assisted
them in times of need and was confident that they would reciprocate. However, the events of the
last week proved him wrong.
Which of the following interference(s) is/are logically valid and can be inferred from the above
passage?
(i) His friends were always asking him to help them
(ii) He felt that when in need of help, his friends would let him down.
(iii) He was sure that his friends  would help him when in need.
(iv) His friends did not help him last week.
(A) (i) and (ii)      (B) (iii) and (iv)  (C) (iii) only  (D) (iv) only
07. Ans: (B)
Sol: The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to 
statements iii and iv as logically valid inferences. 
 I 
 AH
M 
A
 S
7 km
6.02 m
5 km 
10 km
Tuberculosic
Afected 
  50% 
Infected
  50% 
          Does not  
Develop the disease
70% of 50%
 Develop the disease
     30% of 50% 
		: 	5 	: 	 				Questions & Solutions 						
 
08. Leela is older than her cousin Pavithra, pavithra’s brother Shiva is older than Leela. When Pavithra
and shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does.
Which one of the following statements must be TRUE based on the above?
(A) When Shiva plays chess with Leela and Pavithra. he often loses.
(B) Leela is the oldest of the three.
(C) Shiva is a better  chess palyer than Pavithra
(D) Pavithra is the young of the three
08. Ans: (D)
Sol: From given data, the following arrangement is possible 
Shiva
Leela
Pavithra
Among four alternatives, option D is TRUE.
09. If q
–a
 =
r
1
 and r
–b
 =
s
1
 and  S
–C
 =
q
1
, the value of abc is ____.
(A) (rqs)
–1
 (B) 0 (C) 1 (D) r+q+s 
09. Ans: (C)
Sol: 
r
1
q
a
?
?
  ?
r
1
q
1
a
? ? q
a
 
= r 
b
b
b
r s
s
1
r
1
s
1
r ? ? ? ? ?
?
q s
q
1
s
1
q
1
s
c
c
c
? ? ? ? ?
?
 
?? r s r s r q
ac
a
c a
? ? ? ? ?
  (s
ac
)
b
 
 = s 
   s
abc
 = s ? 
      ? abc = 1 
10. P,Q,R and S are working on a project. Q can finish the taks in 25 days, working alone for 12 hours
a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a
day but took sick leave in the beginning for two days. R worked  18 hours a day on all days. What
is the ratio of work done by Q and R after 7 days from the start of the project?
(A) 10:11  (B) 11:10   (C) 20:21  (D) 21:20
10. Ans: (C)
Sol: Q can finish the task = 25 days, 12 hrs/day 
= 300 hrs, 1 hr th
300
1
?
R can finish the task = 50 days, 12 hrs/day 
		: 	6 	: 	       Gate 2016 – ECE – Set 1 					
       = 50 × 12  
       = 600 hrs, th
600
1
hr 1 ?
Q working hours ? (7 – 2) × 12 = 60 hrs 
R working hours ? 7 × 18 = 126 hrs 
After 7 days, the ratio of work done by Q and R 
    Q  :    R 
300
60
 :
600
126
     20   :    21 
Page 5


		: 	2 	: 	       Gate 2016 – ECE – Set 1 					
Q.1 – Q.5 Carry One Mark Each 
01. Which of the following is CORRECT with respect to grammar and usage?
Mount Everest is ______
(A) the highest peak in the world
(B) highest peak in the world
(C) one of highest peak in the world
(D) one of the highest peak in the world
01. Ans: (A)
Sol: Before superlative article ‘the’ has to be used. ‘one of ’ the expression should take plural noun and 
so option ‘C’ and ‘D’ can’t be the answer.
02. The policeman asked the victim of a theft, “What did you ______?”
(A) loose      (B) lose   (C) loss (D) louse 
02. Ans: (B)
Sol: ‘lose’ is verb. 
03. Despite the new medicine’s ___________ in treating diabetes, it is not ______ widely
(A) effectiveness --- prescribed (B) availability ---- used 
(B) prescription ---- available (D) acceptable--- proscribed  
03. Ans: (A)
Sol: ‘effectiveness’ is noun and ‘prescribed’ is verb. These words are apt and befitting with the word 
‘medicine.’ 
04. In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits,
Of the unripe fruits, 45% are apples, Of the ripe ones, 66% are oranges. If the pile contains a total
of 5692000 fruits, how many of them are apples?
(A) 2029198    (B) 2467482   (C) 2789080  (D) 3577422
04. Ans: (A)
Sol: Total no. of fruits = 5692000 
 Unripe type of apples = 45% of 15% of 5692000 
5692000
100
15
100
45
? ? ?
         = 384210 
Ripe type of apples 5692000
100
85
100
34
? ? ? = 1644988 
?Total no. of apples = 384210 + 1644988 = 2029198 
05. Michael lives 10 km way from where I live. Ahmed lives 5km away and Susan lives 7 km away
from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From
the information provided here, what is one possible distance (in km) at which I live from Arun’s
place?
(A) 3.00      (B) 4.99   (C) 6.02  (D) 7.01
		: 	3 	: 	 				Questions & Solutions 						
05. Ans: (c)
Sol: From given data, the following diagram is possible 
I = I live 
AH = Ahmed lives;  M = Michael lives 
   S = Susan lives;    A= Arun lives 
? Arun lives farthes away than Ahmed means more than 5 km but closer than Susan means less 
than 7 km, from given alternatives, option ‘C’ only possible. 
Q.6 – Q.10 Carry two marks each 
06. A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.
However, only 30% of infected people develop the disease. What percentage of people moving
through a tuberculosis prone zone remains infected but does not shows symptoms of disease?
(A) 15     (B) 33   (C) 35   (D) 37
06. Ans: (C)
Sol: 
  = 
100
50
100
70
? =
100
35
 = 35%
07. In a world filled with uncertainty, he was glad to have many good friends. He had always assisted
them in times of need and was confident that they would reciprocate. However, the events of the
last week proved him wrong.
Which of the following interference(s) is/are logically valid and can be inferred from the above
passage?
(i) His friends were always asking him to help them
(ii) He felt that when in need of help, his friends would let him down.
(iii) He was sure that his friends  would help him when in need.
(iv) His friends did not help him last week.
(A) (i) and (ii)      (B) (iii) and (iv)  (C) (iii) only  (D) (iv) only
07. Ans: (B)
Sol: The words ‘was confident that they would reciprocate’ and ‘last week proved him wrong’ lead to 
statements iii and iv as logically valid inferences. 
 I 
 AH
M 
A
 S
7 km
6.02 m
5 km 
10 km
Tuberculosic
Afected 
  50% 
Infected
  50% 
          Does not  
Develop the disease
70% of 50%
 Develop the disease
     30% of 50% 
		: 	5 	: 	 				Questions & Solutions 						
 
08. Leela is older than her cousin Pavithra, pavithra’s brother Shiva is older than Leela. When Pavithra
and shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does.
Which one of the following statements must be TRUE based on the above?
(A) When Shiva plays chess with Leela and Pavithra. he often loses.
(B) Leela is the oldest of the three.
(C) Shiva is a better  chess palyer than Pavithra
(D) Pavithra is the young of the three
08. Ans: (D)
Sol: From given data, the following arrangement is possible 
Shiva
Leela
Pavithra
Among four alternatives, option D is TRUE.
09. If q
–a
 =
r
1
 and r
–b
 =
s
1
 and  S
–C
 =
q
1
, the value of abc is ____.
(A) (rqs)
–1
 (B) 0 (C) 1 (D) r+q+s 
09. Ans: (C)
Sol: 
r
1
q
a
?
?
  ?
r
1
q
1
a
? ? q
a
 
= r 
b
b
b
r s
s
1
r
1
s
1
r ? ? ? ? ?
?
q s
q
1
s
1
q
1
s
c
c
c
? ? ? ? ?
?
 
?? r s r s r q
ac
a
c a
? ? ? ? ?
  (s
ac
)
b
 
 = s 
   s
abc
 = s ? 
      ? abc = 1 
10. P,Q,R and S are working on a project. Q can finish the taks in 25 days, working alone for 12 hours
a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a
day but took sick leave in the beginning for two days. R worked  18 hours a day on all days. What
is the ratio of work done by Q and R after 7 days from the start of the project?
(A) 10:11  (B) 11:10   (C) 20:21  (D) 21:20
10. Ans: (C)
Sol: Q can finish the task = 25 days, 12 hrs/day 
= 300 hrs, 1 hr th
300
1
?
R can finish the task = 50 days, 12 hrs/day 
		: 	6 	: 	       Gate 2016 – ECE – Set 1 					
       = 50 × 12  
       = 600 hrs, th
600
1
hr 1 ?
Q working hours ? (7 – 2) × 12 = 60 hrs 
R working hours ? 7 × 18 = 126 hrs 
After 7 days, the ratio of work done by Q and R 
    Q  :    R 
300
60
 :
600
126
     20   :    21 
		: 	7 	: 	 				Questions & Solutions 						
Q.1 – Q.25 Carry one mark each. 
01. Let M
4 
= I (where I denotes the identity matrix)and  M ? I,  M
2
 ? I and M
3
 ? I. Then, for any
natural number k,  M
–1
 equals:
(A) M
4k+1       
(B) M
4k+2
   (C) M
4k+3  
(D) M
4k 
01. Ans: (C)
Sol: M
4
 = I 
? M
8
 = M
4
 = I ? M
7
 = M
?1
 
? M
12
 = M
8
 = I ? M
11 
 = M
?1
 
? M
16
 = M
12
 = I ? M
15
 = M
?1
 
     ………………….. 
? M
?1
 = M
4K+ 3
, K is a natural number  
02. The second moment of a Poisson-distributed random variables is 2. The mean of the random
variable is _____.
02. Ans: ? = 1
Sol: E(x
2
) = 2 
V(X) = E (X
2
)- (E(X))
2
 
Let mean of the poission random variable be x 
x = 2 ? x
2
 
 x
2
 + x ? 2 = 0 
x = 1, ? 2 
? Mean is ? = 1 
03. Given the following statements about a function f: R ?R, select the right option:
P : If f(x) is continuous at x = x
0
, then it is also differentiable at x = x
0
Q : If f(x) is continuous at x = x
0
, then it may not be differentiable at x = x
0
R : If f(x) is continuous at x = x
0
, then it is also different at x = x
0
(A) P is true, Q is false, R is false (B) P is false, Q is true, R is true  
(C) P is false, Q is true, R is false (D) P is true, Q is false, R is true 
03. Ans: (B)
Sol: Since continuous function may not be differentiable. But differentiable function is always 
continuous. 
04. Which one of the following is a property of the solutions to the Laplace equation : ?
2
f  = 0?
(A) The solution have neither maxima nor minima anywhere except at the boundaries
(B) The solution are not separable in the coordinates
(C) The solution are not continuous
(D) The solution are not dependent on the boundary conditions
04. Ans: (A)
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