Electronics and Communication Engineering (EC) 2016 GATE Paper (Set C) with solution - GATE Past Year Papers for Practice (All Branches)

 Page 1


			: 	2 	: 	 	Gate 2016 – ECE 	– 	Set	3 	
Q.1 – Q.5 Carry one mark each 
01. 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
01. Ans: (C)
Sol: Based on the given sentences option ‘C’ is the correct sentence which is in the comparative degree. 
Option ‘A’ and ‘B’ convey the wrong comparison and ‘D’ has double comparative and so they are
wrong.
02. 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 work underlined above.
(A) Burning   (B) igniting     (C) clutching   (D) flinging
02. Ans: (C)
Sol: The underlined word ‘grasping’ means clutching or holding something tightly. 
03. 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
03. Ans: (B)
Sol: Q and R are the son and Daughter of M, E is the mother of  P and daughter-in-law of M means Q 
and E are married couples in the family
? P is the grandchild of M
04. The number that least fits this set: (324, 441, 97 and 64) is ____________.
(A) 324     (B) 441   (C) 97 (D) 64 
04. Ans: (C)
Sol:  In the given set of numbers, all are perfect squares but 97 is not  
324 is square of 18 ? (18)
2
 = 324 
441 is square of 21 ? (21)
2
 = 441 
64 is square of 8 ? (8)
2
 = 64 
97 is not the square of any number  
? The number that least fits in given set is 97. 
Page 2


			: 	2 	: 	 	Gate 2016 – ECE 	– 	Set	3 	
Q.1 – Q.5 Carry one mark each 
01. 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
01. Ans: (C)
Sol: Based on the given sentences option ‘C’ is the correct sentence which is in the comparative degree. 
Option ‘A’ and ‘B’ convey the wrong comparison and ‘D’ has double comparative and so they are
wrong.
02. 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 work underlined above.
(A) Burning   (B) igniting     (C) clutching   (D) flinging
02. Ans: (C)
Sol: The underlined word ‘grasping’ means clutching or holding something tightly. 
03. 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
03. Ans: (B)
Sol: Q and R are the son and Daughter of M, E is the mother of  P and daughter-in-law of M means Q 
and E are married couples in the family
? P is the grandchild of M
04. The number that least fits this set: (324, 441, 97 and 64) is ____________.
(A) 324     (B) 441   (C) 97 (D) 64 
04. Ans: (C)
Sol:  In the given set of numbers, all are perfect squares but 97 is not  
324 is square of 18 ? (18)
2
 = 324 
441 is square of 21 ? (21)
2
 = 441 
64 is square of 8 ? (8)
2
 = 64 
97 is not the square of any number  
? The number that least fits in given set is 97. 
		: 	3 	: 	     Questions & Solutions 	
05. It takes 10s and 15s, respectively, for two trains traveling 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
is150 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 
05. Ans: (A)
Sol: 
) T ( Time
) D ( ce tan Dis ) LT ( train the of length
) ST ( train the of speed
?
?
T
D LT
) ST (
?
?
D = Distance (or) length of the plat form = 0 
? Speed of the first train (ST
1
) 
10
120
? = 12 m/s
Speed of the second train (ST
2
 
15
150
? = 10 m/s
? The magnitude of the difference in the speeds of the two trains (m/s) = 12 ? 10 = 2 
Page 3


			: 	2 	: 	 	Gate 2016 – ECE 	– 	Set	3 	
Q.1 – Q.5 Carry one mark each 
01. 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
01. Ans: (C)
Sol: Based on the given sentences option ‘C’ is the correct sentence which is in the comparative degree. 
Option ‘A’ and ‘B’ convey the wrong comparison and ‘D’ has double comparative and so they are
wrong.
02. 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 work underlined above.
(A) Burning   (B) igniting     (C) clutching   (D) flinging
02. Ans: (C)
Sol: The underlined word ‘grasping’ means clutching or holding something tightly. 
03. 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
03. Ans: (B)
Sol: Q and R are the son and Daughter of M, E is the mother of  P and daughter-in-law of M means Q 
and E are married couples in the family
? P is the grandchild of M
04. The number that least fits this set: (324, 441, 97 and 64) is ____________.
(A) 324     (B) 441   (C) 97 (D) 64 
04. Ans: (C)
Sol:  In the given set of numbers, all are perfect squares but 97 is not  
324 is square of 18 ? (18)
2
 = 324 
441 is square of 21 ? (21)
2
 = 441 
64 is square of 8 ? (8)
2
 = 64 
97 is not the square of any number  
? The number that least fits in given set is 97. 
		: 	3 	: 	     Questions & Solutions 	
05. It takes 10s and 15s, respectively, for two trains traveling 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
is150 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 
05. Ans: (A)
Sol: 
) T ( Time
) D ( ce tan Dis ) LT ( train the of length
) ST ( train the of speed
?
?
T
D LT
) ST (
?
?
D = Distance (or) length of the plat form = 0 
? Speed of the first train (ST
1
) 
10
120
? = 12 m/s
Speed of the second train (ST
2
 
15
150
? = 10 m/s
? The magnitude of the difference in the speeds of the two trains (m/s) = 12 ? 10 = 2 
			: 	4 	: 	 	Gate 2016 – ECE 	– 	Set	3 	
Q.6 – Q.10 carry Two marks each 
06. 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 
06. Ans: (D)
Sol: The odometer reading increases from starting point to end point 
Area of the given diagram = Odometer reading 
Area of the velocity and time graph per second 
 1
st
 sec ? triangle = 
2
1
1 1
2
1
? ? ?
 2
nd
 sec ? square = 1 ? 1 = 1 
 3
rd
 sec ? square + triangle = 1 ? 1 + 
2
1
? 1 ? 1 =
2
1
1
 4
th
 sec ? triangle = 1 2 1
2
1
? ? ? 
 5
th
 sec ? straight line = 0 
 6
th
 sec ? triangle = 
2
1
1 1
2
1
? ? ?
 7
th
 sec ? triangle = 
2
1
1 1
2
1
? ? ?
Total Odometer reading at 7 seconds 
  = 5
2
1
2
1
0 1
2
1
1 1
2
1
? ? ? ? ? ? ? 
–1
1 
2 
1 2 3 4 5 6 7 Time (s) 
V (m/s) 
Page 4


			: 	2 	: 	 	Gate 2016 – ECE 	– 	Set	3 	
Q.1 – Q.5 Carry one mark each 
01. 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
01. Ans: (C)
Sol: Based on the given sentences option ‘C’ is the correct sentence which is in the comparative degree. 
Option ‘A’ and ‘B’ convey the wrong comparison and ‘D’ has double comparative and so they are
wrong.
02. 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 work underlined above.
(A) Burning   (B) igniting     (C) clutching   (D) flinging
02. Ans: (C)
Sol: The underlined word ‘grasping’ means clutching or holding something tightly. 
03. 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
03. Ans: (B)
Sol: Q and R are the son and Daughter of M, E is the mother of  P and daughter-in-law of M means Q 
and E are married couples in the family
? P is the grandchild of M
04. The number that least fits this set: (324, 441, 97 and 64) is ____________.
(A) 324     (B) 441   (C) 97 (D) 64 
04. Ans: (C)
Sol:  In the given set of numbers, all are perfect squares but 97 is not  
324 is square of 18 ? (18)
2
 = 324 
441 is square of 21 ? (21)
2
 = 441 
64 is square of 8 ? (8)
2
 = 64 
97 is not the square of any number  
? The number that least fits in given set is 97. 
		: 	3 	: 	     Questions & Solutions 	
05. It takes 10s and 15s, respectively, for two trains traveling 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
is150 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 
05. Ans: (A)
Sol: 
) T ( Time
) D ( ce tan Dis ) LT ( train the of length
) ST ( train the of speed
?
?
T
D LT
) ST (
?
?
D = Distance (or) length of the plat form = 0 
? Speed of the first train (ST
1
) 
10
120
? = 12 m/s
Speed of the second train (ST
2
 
15
150
? = 10 m/s
? The magnitude of the difference in the speeds of the two trains (m/s) = 12 ? 10 = 2 
			: 	4 	: 	 	Gate 2016 – ECE 	– 	Set	3 	
Q.6 – Q.10 carry Two marks each 
06. 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 
06. Ans: (D)
Sol: The odometer reading increases from starting point to end point 
Area of the given diagram = Odometer reading 
Area of the velocity and time graph per second 
 1
st
 sec ? triangle = 
2
1
1 1
2
1
? ? ?
 2
nd
 sec ? square = 1 ? 1 = 1 
 3
rd
 sec ? square + triangle = 1 ? 1 + 
2
1
? 1 ? 1 =
2
1
1
 4
th
 sec ? triangle = 1 2 1
2
1
? ? ? 
 5
th
 sec ? straight line = 0 
 6
th
 sec ? triangle = 
2
1
1 1
2
1
? ? ?
 7
th
 sec ? triangle = 
2
1
1 1
2
1
? ? ?
Total Odometer reading at 7 seconds 
  = 5
2
1
2
1
0 1
2
1
1 1
2
1
? ? ? ? ? ? ? 
–1
1 
2 
1 2 3 4 5 6 7 Time (s) 
V (m/s) 
		: 	5 	: 	     Questions & Solutions 	
07. The overshelming 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 f 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 source of rabies worldwide.
07. Ans: (A)
Sol: Only option ‘A’ can be logically inferred from the information provided in the argument. 
08. 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 falt?
(A) Manu     (B) Sravan    (C) Trideep    (D) Pavan
08. Ans: (C)
Sol: Manu age = sravan age + 2 months 
Manu age = Trideep age ? 3 months
Pavan age = Sravan’s age + 1 month
From this Trideep age > Man> Pavan > Sravan
? Trideep can occupy the extra spane in the flat
09. 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) 20.23 
09. Ans: (B)
Sol: 
??
?
?
?
?
?
? ?
?
?
?
?
?
?
?
? ?
?
?
?
?
?
?
?
3
5
, 0 D 0 ,
2
5
C , 7 , 0 B 0 ,
3
14
A E = [4,1], F = [0, 1] 
Required area = Area of ?le OAB – Area of ?le CEA 
?
?
?
?
?
?
?
?
?
?
?
?
?
? ? ?
?
?
?
?
?
?
? ? ? 1
2
5
3
14
2
1
7
3
14
2
1
 = 15.25 sq.units 
F 
O 
D 
C A 
X
E 2x ? 3y = 5
3x+2y = 4 
y 
B 
Page 5


			: 	2 	: 	 	Gate 2016 – ECE 	– 	Set	3 	
Q.1 – Q.5 Carry one mark each 
01. 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
01. Ans: (C)
Sol: Based on the given sentences option ‘C’ is the correct sentence which is in the comparative degree. 
Option ‘A’ and ‘B’ convey the wrong comparison and ‘D’ has double comparative and so they are
wrong.
02. 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 work underlined above.
(A) Burning   (B) igniting     (C) clutching   (D) flinging
02. Ans: (C)
Sol: The underlined word ‘grasping’ means clutching or holding something tightly. 
03. 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
03. Ans: (B)
Sol: Q and R are the son and Daughter of M, E is the mother of  P and daughter-in-law of M means Q 
and E are married couples in the family
? P is the grandchild of M
04. The number that least fits this set: (324, 441, 97 and 64) is ____________.
(A) 324     (B) 441   (C) 97 (D) 64 
04. Ans: (C)
Sol:  In the given set of numbers, all are perfect squares but 97 is not  
324 is square of 18 ? (18)
2
 = 324 
441 is square of 21 ? (21)
2
 = 441 
64 is square of 8 ? (8)
2
 = 64 
97 is not the square of any number  
? The number that least fits in given set is 97. 
		: 	3 	: 	     Questions & Solutions 	
05. It takes 10s and 15s, respectively, for two trains traveling 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
is150 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 
05. Ans: (A)
Sol: 
) T ( Time
) D ( ce tan Dis ) LT ( train the of length
) ST ( train the of speed
?
?
T
D LT
) ST (
?
?
D = Distance (or) length of the plat form = 0 
? Speed of the first train (ST
1
) 
10
120
? = 12 m/s
Speed of the second train (ST
2
 
15
150
? = 10 m/s
? The magnitude of the difference in the speeds of the two trains (m/s) = 12 ? 10 = 2 
			: 	4 	: 	 	Gate 2016 – ECE 	– 	Set	3 	
Q.6 – Q.10 carry Two marks each 
06. 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 
06. Ans: (D)
Sol: The odometer reading increases from starting point to end point 
Area of the given diagram = Odometer reading 
Area of the velocity and time graph per second 
 1
st
 sec ? triangle = 
2
1
1 1
2
1
? ? ?
 2
nd
 sec ? square = 1 ? 1 = 1 
 3
rd
 sec ? square + triangle = 1 ? 1 + 
2
1
? 1 ? 1 =
2
1
1
 4
th
 sec ? triangle = 1 2 1
2
1
? ? ? 
 5
th
 sec ? straight line = 0 
 6
th
 sec ? triangle = 
2
1
1 1
2
1
? ? ?
 7
th
 sec ? triangle = 
2
1
1 1
2
1
? ? ?
Total Odometer reading at 7 seconds 
  = 5
2
1
2
1
0 1
2
1
1 1
2
1
? ? ? ? ? ? ? 
–1
1 
2 
1 2 3 4 5 6 7 Time (s) 
V (m/s) 
		: 	5 	: 	     Questions & Solutions 	
07. The overshelming 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 f 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 source of rabies worldwide.
07. Ans: (A)
Sol: Only option ‘A’ can be logically inferred from the information provided in the argument. 
08. 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 falt?
(A) Manu     (B) Sravan    (C) Trideep    (D) Pavan
08. Ans: (C)
Sol: Manu age = sravan age + 2 months 
Manu age = Trideep age ? 3 months
Pavan age = Sravan’s age + 1 month
From this Trideep age > Man> Pavan > Sravan
? Trideep can occupy the extra spane in the flat
09. 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) 20.23 
09. Ans: (B)
Sol: 
??
?
?
?
?
?
? ?
?
?
?
?
?
?
?
? ?
?
?
?
?
?
?
?
3
5
, 0 D 0 ,
2
5
C , 7 , 0 B 0 ,
3
14
A E = [4,1], F = [0, 1] 
Required area = Area of ?le OAB – Area of ?le CEA 
?
?
?
?
?
?
?
?
?
?
?
?
?
? ? ?
?
?
?
?
?
?
? ? ? 1
2
5
3
14
2
1
7
3
14
2
1
 = 15.25 sq.units 
F 
O 
D 
C A 
X
E 2x ? 3y = 5
3x+2y = 4 
y 
B 
			: 	6 	: 	 	Gate 2016 – ECE 	– 	Set	3 	
Another method: 
Required area = Area of ?
le
 BFE + Area of FEOC 
 1 ) 5 . 2 4 (
2
1
6 4
2
1
? ? ? ? ? ? ? = 12 + 3.25 = 15.25 sq.units 
10. A straight line is fit to a data set (In x, y). This line intercepts the abscissa at In 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
10. Ans: (A)
Sol:  Straight line equation y = mx + c 
 m = slope = ?0.02 
 set (log x, y) 
  If log x = X, then set  
y = mX + C 
o= ? 0.02 ? 0.1 + C
  ? C = 0.002 
y = mX + C 
   y = ? 0.02 ? logx + C 
@ x = 5 
   y = ? 0.02 ? log 5 + 0.002 
   = ? 0.030 
0.1 0 
(x, y)