Instrumentation (IN) 2016 GATE Paper with solution - GATE Past Year Papers for Practice (All Branches)

 Page 1


		: 	2 	: 	 		Gate 2016 - IN 	
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 word 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 is the son and Daughter’s 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 - IN 	
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 word 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 is the son and Daughter’s 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 10 s and 15 s, 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
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 
05. Ans: (A)
Sol: Speed of the train ??
? ? ? ?
?? T Time
D e c tan Dis LT train the of length
ST
?
?
??
T
D LT
ST
?
?
D = Distance (or) length of the plat form = 0 
? Speed of the first train ?? s / m 12
10
120
ST
1
? ? 
Speed of the second train ?? s / m 10
15
150
ST
2
? ? 
? The magnitude of the difference in the speeds of the two trains (m/s) = 12 – 10 = 2  
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
? ? ? ?
V(m/s) 
2 
1 
–1
1 2 3 4
5
6
7
Time (s)
Page 3


		: 	2 	: 	 		Gate 2016 - IN 	
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 word 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 is the son and Daughter’s 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 10 s and 15 s, 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
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 
05. Ans: (A)
Sol: Speed of the train ??
? ? ? ?
?? T Time
D e c tan Dis LT train the of length
ST
?
?
??
T
D LT
ST
?
?
D = Distance (or) length of the plat form = 0 
? Speed of the first train ?? s / m 12
10
120
ST
1
? ? 
Speed of the second train ?? s / m 10
15
150
ST
2
? ? 
? The magnitude of the difference in the speeds of the two trains (m/s) = 12 – 10 = 2  
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
? ? ? ?
V(m/s) 
2 
1 
–1
1 2 3 4
5
6
7
Time (s)
		: 	4 	: 	 		Gate 2016 - IN 	
 2
nd
 sec ? square = 1 ? 1 = 1 
 3
rd
 sec ? square + triangle 
2
1
1 1 1
2
1
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
? ? ? ? ? ? ? ? 
07. 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 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 flat?
(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 > Manu > Pavan > Sravan  
? Trideep can occupy the extra space 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) 20.35 
Page 4


		: 	2 	: 	 		Gate 2016 - IN 	
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 word 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 is the son and Daughter’s 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 10 s and 15 s, 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
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 
05. Ans: (A)
Sol: Speed of the train ??
? ? ? ?
?? T Time
D e c tan Dis LT train the of length
ST
?
?
??
T
D LT
ST
?
?
D = Distance (or) length of the plat form = 0 
? Speed of the first train ?? s / m 12
10
120
ST
1
? ? 
Speed of the second train ?? s / m 10
15
150
ST
2
? ? 
? The magnitude of the difference in the speeds of the two trains (m/s) = 12 – 10 = 2  
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
? ? ? ?
V(m/s) 
2 
1 
–1
1 2 3 4
5
6
7
Time (s)
		: 	4 	: 	 		Gate 2016 - IN 	
 2
nd
 sec ? square = 1 ? 1 = 1 
 3
rd
 sec ? square + triangle 
2
1
1 1 1
2
1
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
? ? ? ? ? ? ? ? 
07. 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 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 flat?
(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 > Manu > Pavan > Sravan  
? Trideep can occupy the extra space 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) 20.35 
		: 	5 	: 	 	Questions & Solutions 								
09. Ans: (B)
Sol: ??, 7 , 0 B , 0 ,
3
14
A ?
?
?
?
?
?
?
? 
,
3
5
, 0 D , 0 ,
2
5
C
?
?
?
?
?
? ?
?
?
?
?
?
?
?
?
?? ? ? 1 , 0 F , 1 , 4 E ? ?
Required area = Area of ? OAB – Area of ? CEA 
?
?
?
?
?
?
?
?
?
?
?
?
?
? ? ?
?
?
?
?
?
?
? ? ? 1
2
5
3
14
2
1
7
3
14
2
1
= 15.25 sq. units 
Another method:  
Required area = Area of ? 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 (ln 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
e
 x,y) 
)
0
y ,
1 . 0
x ( set  x then  x log if
?
?
?
y = mX + C 
0 = –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 
F 
O 
D 
C A
X
E 2x ? 3y = 5
3x+2y =14
y
B 
Page 5


		: 	2 	: 	 		Gate 2016 - IN 	
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 word 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 is the son and Daughter’s 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 10 s and 15 s, 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
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 
05. Ans: (A)
Sol: Speed of the train ??
? ? ? ?
?? T Time
D e c tan Dis LT train the of length
ST
?
?
??
T
D LT
ST
?
?
D = Distance (or) length of the plat form = 0 
? Speed of the first train ?? s / m 12
10
120
ST
1
? ? 
Speed of the second train ?? s / m 10
15
150
ST
2
? ? 
? The magnitude of the difference in the speeds of the two trains (m/s) = 12 – 10 = 2  
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
? ? ? ?
V(m/s) 
2 
1 
–1
1 2 3 4
5
6
7
Time (s)
		: 	4 	: 	 		Gate 2016 - IN 	
 2
nd
 sec ? square = 1 ? 1 = 1 
 3
rd
 sec ? square + triangle 
2
1
1 1 1
2
1
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
? ? ? ? ? ? ? ? 
07. 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 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 flat?
(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 > Manu > Pavan > Sravan  
? Trideep can occupy the extra space 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) 20.35 
		: 	5 	: 	 	Questions & Solutions 								
09. Ans: (B)
Sol: ??, 7 , 0 B , 0 ,
3
14
A ?
?
?
?
?
?
?
? 
,
3
5
, 0 D , 0 ,
2
5
C
?
?
?
?
?
? ?
?
?
?
?
?
?
?
?
?? ? ? 1 , 0 F , 1 , 4 E ? ?
Required area = Area of ? OAB – Area of ? CEA 
?
?
?
?
?
?
?
?
?
?
?
?
?
? ? ?
?
?
?
?
?
?
? ? ? 1
2
5
3
14
2
1
7
3
14
2
1
= 15.25 sq. units 
Another method:  
Required area = Area of ? 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 (ln 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
e
 x,y) 
)
0
y ,
1 . 0
x ( set  x then  x log if
?
?
?
y = mX + C 
0 = –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 
F 
O 
D 
C A
X
E 2x ? 3y = 5
3x+2y =14
y
B 
		: 	7 	: 	 	Questions & Solutions 								
Q.1 – Q.25 Carry One Mark Each 
01. 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 __________.
01. Ans:  3
y = mx + c ------- (1)
Equation (1) passes through (0,0) we get C = 0
Equation (1) passes through (2,6), we get 6 = 2 m
m = 3
02. ? ? 1 n n n lim
2 2
n
? ? ?
? ?
 is ________. 
02. Ans:  0.5 
? ? 1 n n n lt
2 2
n
? ? ?
? ?
  
??? ?
? ? 1 n n n
1 n n n
lt
2 2
2 2
n
? ? ?
? ? ?
?
? ?
  
??
?
?
?
?
?
?
?
?
? ? ?
?
?
? ?
2
n
n
1
1
n
1
1 n
1 n
lt
2
1
?
           = 0.5 
03. A voltage V
1
 is measured 100 times and its average and standard deviation are 100 V and 1.5 V
respectively. A second voltage V
2
, which is independent of V
1
, is measured 200 times and its
average and standard deviation are 150 V and 2 V respectively. V
3
 is computed as: V
3
 = V
1
 + V
2
.
Then the standard deviation of V
3
 in volt is ___________.
03. Ans: 2.5
Sol:  Given V
1
 = 100 V 
?
1
  = 1.5 V 
 V
2
 = 150 V 
?
2
 = 2V 
 V
3
 = V
1
 + V
2
 
?? ? ?
2 2
3
5 . 1 2 ? ? ?
     = 2.5 Volt 
04. 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 + 3j + 5k) 
04. Ans: (D)