Chemical Engineering (CH) 2014 GATE Paper with solution Notes | Study GATE Past Year Papers for Practice (All Branches) - GATE

 Page 1


?CH-GATE-2014 PAPER| 
1 
Q.No-1-5 Carry One Mark Each 
1. A student is required to demonstrate a high level of comprehension of the subject, especially
in the social sciences.
The word closest in meaning to comprehension is
(A) understanding   (B) meaning   (C) concentration  (D) stability
Answer: (A) 
2. Choose the most appropriate word from the options given below to complete the following
sentence.
One of his biggest ______ was his ability to forgive.
(A) vice   (B) virtues   (C) choices   (D) strength
Answer: (B) 
3. Rajan was not happy that Sajan decided to do the project on his own. On observing his
unhappiness, Sajan explained to Rajan that he preferred to work independently.
Which one of the statements below is logically valid and can be inferred from the above
sentences?
(A) Rajan has decided to work only in a group.
(B) Rajan and Sajan were formed into a group against their wishes.
(C) Sajan had decided to give in to Rajan’s request to work with him.
(D) Rajan had believed that Sajan and he would be working together.
Answer: (D) 
4. If y = 5x
2
 + 3, then the tangent at x =  0, y = 3
(A) passes through x = 0, y = 0 (B) has a slope of +1 
(C) is parallel to the x-axis (D) has a slope of -1 
Answer: (C) 
Exp: 
2
x 0, y 3
dy
y 5x 3, 10x
dx
dy
Slope of tan gent 10 0 0
dx
= =
= + =
? ?
= = × =
? ?
? ?
Slope = 0 ? tangent is parallel to x-axis.
5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs
800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per
tonne for a daily production of 100 tonnes?
Answer: 1300 to 1300 
Exp: Fixed cost = Rs. 50,000 
Variable cost = Rs. 800Q 
Q = daily production in tones 
For 100 tonnes of production daily, total cost of production 
= 50,000+800×100 = 130,000 
So, cost of production per tonne of daily production
130,000
Rs.1300.
100
= = 
Page 2


?CH-GATE-2014 PAPER| 
1 
Q.No-1-5 Carry One Mark Each 
1. A student is required to demonstrate a high level of comprehension of the subject, especially
in the social sciences.
The word closest in meaning to comprehension is
(A) understanding   (B) meaning   (C) concentration  (D) stability
Answer: (A) 
2. Choose the most appropriate word from the options given below to complete the following
sentence.
One of his biggest ______ was his ability to forgive.
(A) vice   (B) virtues   (C) choices   (D) strength
Answer: (B) 
3. Rajan was not happy that Sajan decided to do the project on his own. On observing his
unhappiness, Sajan explained to Rajan that he preferred to work independently.
Which one of the statements below is logically valid and can be inferred from the above
sentences?
(A) Rajan has decided to work only in a group.
(B) Rajan and Sajan were formed into a group against their wishes.
(C) Sajan had decided to give in to Rajan’s request to work with him.
(D) Rajan had believed that Sajan and he would be working together.
Answer: (D) 
4. If y = 5x
2
 + 3, then the tangent at x =  0, y = 3
(A) passes through x = 0, y = 0 (B) has a slope of +1 
(C) is parallel to the x-axis (D) has a slope of -1 
Answer: (C) 
Exp: 
2
x 0, y 3
dy
y 5x 3, 10x
dx
dy
Slope of tan gent 10 0 0
dx
= =
= + =
? ?
= = × =
? ?
? ?
Slope = 0 ? tangent is parallel to x-axis.
5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs
800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per
tonne for a daily production of 100 tonnes?
Answer: 1300 to 1300 
Exp: Fixed cost = Rs. 50,000 
Variable cost = Rs. 800Q 
Q = daily production in tones 
For 100 tonnes of production daily, total cost of production 
= 50,000+800×100 = 130,000 
So, cost of production per tonne of daily production
130,000
Rs.1300.
100
= = 
?CH-GATE-2014 PAPER| 
2 
Q.No-6-10 Carry Two Marks Each 
6. Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK
(A) ALRVX    (B) EPVZB   (C) ITZDF (D) OYEIK 
Answer: (D) 
Exp: ALRVX?only one vowel 
EPVZB?only one vowel 
ITZDF?only one vowel 
OYEIK?three vowels 
7. Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed
building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an
even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live
on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does
not live on a floor immediately above or immediately below Bhola. Faisal lives three floors
above Dilip. Which of the following floor-person combinations is correct?
Anuj Bhola Chandan Dilip Eswar Faisal 
(A) 6 2 5 1 3 4 
(B) 2 6 5 1 3 4 
(C) 4 2 6 3 1 5 
(D) 2 4 6 1 3 5 
Answer: (B) 
Exp: (a) Anuj: Even numbered floor (2,4,6) 
(b) Bhola: Even numbered floor (2,4,6) 
(c) Chandan lives on the floor above that of Faisal. 
(d) Dilip: not on 2
nd
 floor. 
(e) Eswar: does not live immediately above or immediately below Bhola 
From the options its clear, that only option (B) satisfies condition (e). 
So, correct Ans is (B). 
8. The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.
The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is
twice its smallest angle. What is the sum, in degrees, of the second largest angle of the
triangle and the largest angle of the quadrilateral?
Answer: 180 to 180 
Exp: Let the angles of quadrilateral are 3x, 4x, 5x, 6x 
So, 3x+4x+5x+6x = 360 
x = 20 
Smallest angle of quadrilateral = 3×20 = 60° 
Smallest angle of triangle = 
2
60 40
3
× °= °
Largest angle of triangle = 2×40° = 60° 
Three angles of triangle are 40°, 60°, 80° 
Largest angle of quadrilateral is 120° 
Sum (2
nd
 largest angle of triangle + largest angle of quadrilateral) 
= 60°+120°=180°. 
Page 3


?CH-GATE-2014 PAPER| 
1 
Q.No-1-5 Carry One Mark Each 
1. A student is required to demonstrate a high level of comprehension of the subject, especially
in the social sciences.
The word closest in meaning to comprehension is
(A) understanding   (B) meaning   (C) concentration  (D) stability
Answer: (A) 
2. Choose the most appropriate word from the options given below to complete the following
sentence.
One of his biggest ______ was his ability to forgive.
(A) vice   (B) virtues   (C) choices   (D) strength
Answer: (B) 
3. Rajan was not happy that Sajan decided to do the project on his own. On observing his
unhappiness, Sajan explained to Rajan that he preferred to work independently.
Which one of the statements below is logically valid and can be inferred from the above
sentences?
(A) Rajan has decided to work only in a group.
(B) Rajan and Sajan were formed into a group against their wishes.
(C) Sajan had decided to give in to Rajan’s request to work with him.
(D) Rajan had believed that Sajan and he would be working together.
Answer: (D) 
4. If y = 5x
2
 + 3, then the tangent at x =  0, y = 3
(A) passes through x = 0, y = 0 (B) has a slope of +1 
(C) is parallel to the x-axis (D) has a slope of -1 
Answer: (C) 
Exp: 
2
x 0, y 3
dy
y 5x 3, 10x
dx
dy
Slope of tan gent 10 0 0
dx
= =
= + =
? ?
= = × =
? ?
? ?
Slope = 0 ? tangent is parallel to x-axis.
5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs
800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per
tonne for a daily production of 100 tonnes?
Answer: 1300 to 1300 
Exp: Fixed cost = Rs. 50,000 
Variable cost = Rs. 800Q 
Q = daily production in tones 
For 100 tonnes of production daily, total cost of production 
= 50,000+800×100 = 130,000 
So, cost of production per tonne of daily production
130,000
Rs.1300.
100
= = 
?CH-GATE-2014 PAPER| 
2 
Q.No-6-10 Carry Two Marks Each 
6. Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK
(A) ALRVX    (B) EPVZB   (C) ITZDF (D) OYEIK 
Answer: (D) 
Exp: ALRVX?only one vowel 
EPVZB?only one vowel 
ITZDF?only one vowel 
OYEIK?three vowels 
7. Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed
building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an
even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live
on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does
not live on a floor immediately above or immediately below Bhola. Faisal lives three floors
above Dilip. Which of the following floor-person combinations is correct?
Anuj Bhola Chandan Dilip Eswar Faisal 
(A) 6 2 5 1 3 4 
(B) 2 6 5 1 3 4 
(C) 4 2 6 3 1 5 
(D) 2 4 6 1 3 5 
Answer: (B) 
Exp: (a) Anuj: Even numbered floor (2,4,6) 
(b) Bhola: Even numbered floor (2,4,6) 
(c) Chandan lives on the floor above that of Faisal. 
(d) Dilip: not on 2
nd
 floor. 
(e) Eswar: does not live immediately above or immediately below Bhola 
From the options its clear, that only option (B) satisfies condition (e). 
So, correct Ans is (B). 
8. The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.
The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is
twice its smallest angle. What is the sum, in degrees, of the second largest angle of the
triangle and the largest angle of the quadrilateral?
Answer: 180 to 180 
Exp: Let the angles of quadrilateral are 3x, 4x, 5x, 6x 
So, 3x+4x+5x+6x = 360 
x = 20 
Smallest angle of quadrilateral = 3×20 = 60° 
Smallest angle of triangle = 
2
60 40
3
× °= °
Largest angle of triangle = 2×40° = 60° 
Three angles of triangle are 40°, 60°, 80° 
Largest angle of quadrilateral is 120° 
Sum (2
nd
 largest angle of triangle + largest angle of quadrilateral) 
= 60°+120°=180°. 
?CH-GATE-2014 PAPER| 
3 
9. One percent of the people of country X are taller than 6 ft. Two percent of the people of
country Y are taller than 6 ft. There are thrice as many people in country X as in country Y.
Taking both countries together, what is the percentage of people taller than 6 ft?
(A) 3.0    (B) 2.5     (C) 1.5    (D) 1.25
Answer: (D) 
Exp: Let number of people in country y = 100 
So, number of people in country x = 300 
Total number of people taller than 6ft in both the countries 
1 2
300 100 5
100 100
= × + × = 
% of people taller than 6ft in both the countries 
5
100 1.25%.
400
= × = 
10. The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following
figure. Which of the following are true? (k percentile is the value such that k percent of the
data fall below that value)
(i) On average, it rains more in July than in December  
(ii) Every year, the amount of rainfall in August is more than that in January  
(iii) July rainfall can be estimated with better confidence than February rainfall 
(iv) In August, there is at least 500 mm of rainfall 
 (A) (i) and (ii)   (B) (i) and (iii)   (C) (ii) and (iii) (D) (iii) and (iv) 
Answer: (B) 
Exp: In the question the monthly average rainfall chart for 50 years has been given. 
Let us check the options. 
(i) On average, it rains more in July than in December ? correct.
(ii) Every year, the amount of rainfall in August is more than that in January. 
? may not be correct because average rainfall is given in the question.
(iii) July rainfall can be estimated with better confidence than February rainfall. 
? From chart it is clear the gap between 5 percentile and 95 percentile from average is
higher in February than that in July ? correct.
(iv) In August at least 500 mm rainfall  
? May not be correct, because its 50 year average.
So correct option (B) (i) and (iii). 
800 
700 
600 
500 
400 
300 
200 
100 
0 
Jan Feb Mar Apr May 
Jun Jul Aug Sep Oct Nov Dec 
Average 
5 percentile 
95 percentile 
Page 4


?CH-GATE-2014 PAPER| 
1 
Q.No-1-5 Carry One Mark Each 
1. A student is required to demonstrate a high level of comprehension of the subject, especially
in the social sciences.
The word closest in meaning to comprehension is
(A) understanding   (B) meaning   (C) concentration  (D) stability
Answer: (A) 
2. Choose the most appropriate word from the options given below to complete the following
sentence.
One of his biggest ______ was his ability to forgive.
(A) vice   (B) virtues   (C) choices   (D) strength
Answer: (B) 
3. Rajan was not happy that Sajan decided to do the project on his own. On observing his
unhappiness, Sajan explained to Rajan that he preferred to work independently.
Which one of the statements below is logically valid and can be inferred from the above
sentences?
(A) Rajan has decided to work only in a group.
(B) Rajan and Sajan were formed into a group against their wishes.
(C) Sajan had decided to give in to Rajan’s request to work with him.
(D) Rajan had believed that Sajan and he would be working together.
Answer: (D) 
4. If y = 5x
2
 + 3, then the tangent at x =  0, y = 3
(A) passes through x = 0, y = 0 (B) has a slope of +1 
(C) is parallel to the x-axis (D) has a slope of -1 
Answer: (C) 
Exp: 
2
x 0, y 3
dy
y 5x 3, 10x
dx
dy
Slope of tan gent 10 0 0
dx
= =
= + =
? ?
= = × =
? ?
? ?
Slope = 0 ? tangent is parallel to x-axis.
5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs
800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per
tonne for a daily production of 100 tonnes?
Answer: 1300 to 1300 
Exp: Fixed cost = Rs. 50,000 
Variable cost = Rs. 800Q 
Q = daily production in tones 
For 100 tonnes of production daily, total cost of production 
= 50,000+800×100 = 130,000 
So, cost of production per tonne of daily production
130,000
Rs.1300.
100
= = 
?CH-GATE-2014 PAPER| 
2 
Q.No-6-10 Carry Two Marks Each 
6. Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK
(A) ALRVX    (B) EPVZB   (C) ITZDF (D) OYEIK 
Answer: (D) 
Exp: ALRVX?only one vowel 
EPVZB?only one vowel 
ITZDF?only one vowel 
OYEIK?three vowels 
7. Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed
building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an
even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live
on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does
not live on a floor immediately above or immediately below Bhola. Faisal lives three floors
above Dilip. Which of the following floor-person combinations is correct?
Anuj Bhola Chandan Dilip Eswar Faisal 
(A) 6 2 5 1 3 4 
(B) 2 6 5 1 3 4 
(C) 4 2 6 3 1 5 
(D) 2 4 6 1 3 5 
Answer: (B) 
Exp: (a) Anuj: Even numbered floor (2,4,6) 
(b) Bhola: Even numbered floor (2,4,6) 
(c) Chandan lives on the floor above that of Faisal. 
(d) Dilip: not on 2
nd
 floor. 
(e) Eswar: does not live immediately above or immediately below Bhola 
From the options its clear, that only option (B) satisfies condition (e). 
So, correct Ans is (B). 
8. The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.
The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is
twice its smallest angle. What is the sum, in degrees, of the second largest angle of the
triangle and the largest angle of the quadrilateral?
Answer: 180 to 180 
Exp: Let the angles of quadrilateral are 3x, 4x, 5x, 6x 
So, 3x+4x+5x+6x = 360 
x = 20 
Smallest angle of quadrilateral = 3×20 = 60° 
Smallest angle of triangle = 
2
60 40
3
× °= °
Largest angle of triangle = 2×40° = 60° 
Three angles of triangle are 40°, 60°, 80° 
Largest angle of quadrilateral is 120° 
Sum (2
nd
 largest angle of triangle + largest angle of quadrilateral) 
= 60°+120°=180°. 
?CH-GATE-2014 PAPER| 
3 
9. One percent of the people of country X are taller than 6 ft. Two percent of the people of
country Y are taller than 6 ft. There are thrice as many people in country X as in country Y.
Taking both countries together, what is the percentage of people taller than 6 ft?
(A) 3.0    (B) 2.5     (C) 1.5    (D) 1.25
Answer: (D) 
Exp: Let number of people in country y = 100 
So, number of people in country x = 300 
Total number of people taller than 6ft in both the countries 
1 2
300 100 5
100 100
= × + × = 
% of people taller than 6ft in both the countries 
5
100 1.25%.
400
= × = 
10. The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following
figure. Which of the following are true? (k percentile is the value such that k percent of the
data fall below that value)
(i) On average, it rains more in July than in December  
(ii) Every year, the amount of rainfall in August is more than that in January  
(iii) July rainfall can be estimated with better confidence than February rainfall 
(iv) In August, there is at least 500 mm of rainfall 
 (A) (i) and (ii)   (B) (i) and (iii)   (C) (ii) and (iii) (D) (iii) and (iv) 
Answer: (B) 
Exp: In the question the monthly average rainfall chart for 50 years has been given. 
Let us check the options. 
(i) On average, it rains more in July than in December ? correct.
(ii) Every year, the amount of rainfall in August is more than that in January. 
? may not be correct because average rainfall is given in the question.
(iii) July rainfall can be estimated with better confidence than February rainfall. 
? From chart it is clear the gap between 5 percentile and 95 percentile from average is
higher in February than that in July ? correct.
(iv) In August at least 500 mm rainfall  
? May not be correct, because its 50 year average.
So correct option (B) (i) and (iii). 
800 
700 
600 
500 
400 
300 
200 
100 
0 
Jan Feb Mar Apr May 
Jun Jul Aug Sep Oct Nov Dec 
Average 
5 percentile 
95 percentile 
?CH-GATE-2014 PAPER| 
4 
Q.No-1-25 Carry One Mark Each 
1. Gradient of a scalar variable is always
(A) a vector (B) a scalar (C) a dot product (D) zero 
Answer: (A) 
Exp. 




Gradient i j k
x y z
If f is a scalar point function
f f f
f grad f i j k is a vector.
x y z
? ? ?
?= + +
? ? ?
? ? ?
? = = + +
? ? ?

 


 

2. For the time domain function,  f(t) = t
2
 ,which ONE of the following is the Laplace transform
of  ( )
t
0
f t dt ?
?
( )
4
3
A
s
( )
2
1
B
4s
( )
3
2
C
s
( )
4
2
D
s
Answer: (D) 
Exp. We have  
( )
( )
( ) ( )
t
0
t
2 2
3 4 3
0
F s
L f t dt where F s L f t
s
2 2 2
L t dt 3 L t
s s s
? ?
= = ? ?
? ?
? ?
? ?
? ?
? ? ? ?
? ? ? = = =
? ? ? ? ? ?
? ?
? ? ? ?
? ?
?
?
?
3. If f*(x) is the complex conjugate of f(x) = cos(x) + i sin(x), then for real a and b,
( ) ( )
b
a
f * x f x dx is ALWAYS
?
( ) A positive ( ) B negative ( ) C real ( ) D imaginary
Answer: (C) 
Exp. ( ) ( ) ( ) f x cos x isin x = +
( ) ( ) ( )
( ) ( ) ( )( )
( )
b b
a a
b b
ix ix
a a
f * x cos x isin x
f * x .f x dx cos x isin x cos isin x dx
e .e dx 1.dx b a R a, b, R
Real for real a & b.
-
= -
= - +
= = = - ? ?
?
? ?
? ?
?
4. If f(x) is a real and continuous function of x, the Taylor series expansion of f(x) about
its minima will NEVER have a term containing
(A) first derivative     (B) second derivative
(C) third derivative     (D) any higher derivative
Answer: (A) 
Page 5


?CH-GATE-2014 PAPER| 
1 
Q.No-1-5 Carry One Mark Each 
1. A student is required to demonstrate a high level of comprehension of the subject, especially
in the social sciences.
The word closest in meaning to comprehension is
(A) understanding   (B) meaning   (C) concentration  (D) stability
Answer: (A) 
2. Choose the most appropriate word from the options given below to complete the following
sentence.
One of his biggest ______ was his ability to forgive.
(A) vice   (B) virtues   (C) choices   (D) strength
Answer: (B) 
3. Rajan was not happy that Sajan decided to do the project on his own. On observing his
unhappiness, Sajan explained to Rajan that he preferred to work independently.
Which one of the statements below is logically valid and can be inferred from the above
sentences?
(A) Rajan has decided to work only in a group.
(B) Rajan and Sajan were formed into a group against their wishes.
(C) Sajan had decided to give in to Rajan’s request to work with him.
(D) Rajan had believed that Sajan and he would be working together.
Answer: (D) 
4. If y = 5x
2
 + 3, then the tangent at x =  0, y = 3
(A) passes through x = 0, y = 0 (B) has a slope of +1 
(C) is parallel to the x-axis (D) has a slope of -1 
Answer: (C) 
Exp: 
2
x 0, y 3
dy
y 5x 3, 10x
dx
dy
Slope of tan gent 10 0 0
dx
= =
= + =
? ?
= = × =
? ?
? ?
Slope = 0 ? tangent is parallel to x-axis.
5. A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs
800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per
tonne for a daily production of 100 tonnes?
Answer: 1300 to 1300 
Exp: Fixed cost = Rs. 50,000 
Variable cost = Rs. 800Q 
Q = daily production in tones 
For 100 tonnes of production daily, total cost of production 
= 50,000+800×100 = 130,000 
So, cost of production per tonne of daily production
130,000
Rs.1300.
100
= = 
?CH-GATE-2014 PAPER| 
2 
Q.No-6-10 Carry Two Marks Each 
6. Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK
(A) ALRVX    (B) EPVZB   (C) ITZDF (D) OYEIK 
Answer: (D) 
Exp: ALRVX?only one vowel 
EPVZB?only one vowel 
ITZDF?only one vowel 
OYEIK?three vowels 
7. Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed
building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an
even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live
on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does
not live on a floor immediately above or immediately below Bhola. Faisal lives three floors
above Dilip. Which of the following floor-person combinations is correct?
Anuj Bhola Chandan Dilip Eswar Faisal 
(A) 6 2 5 1 3 4 
(B) 2 6 5 1 3 4 
(C) 4 2 6 3 1 5 
(D) 2 4 6 1 3 5 
Answer: (B) 
Exp: (a) Anuj: Even numbered floor (2,4,6) 
(b) Bhola: Even numbered floor (2,4,6) 
(c) Chandan lives on the floor above that of Faisal. 
(d) Dilip: not on 2
nd
 floor. 
(e) Eswar: does not live immediately above or immediately below Bhola 
From the options its clear, that only option (B) satisfies condition (e). 
So, correct Ans is (B). 
8. The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral.
The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is
twice its smallest angle. What is the sum, in degrees, of the second largest angle of the
triangle and the largest angle of the quadrilateral?
Answer: 180 to 180 
Exp: Let the angles of quadrilateral are 3x, 4x, 5x, 6x 
So, 3x+4x+5x+6x = 360 
x = 20 
Smallest angle of quadrilateral = 3×20 = 60° 
Smallest angle of triangle = 
2
60 40
3
× °= °
Largest angle of triangle = 2×40° = 60° 
Three angles of triangle are 40°, 60°, 80° 
Largest angle of quadrilateral is 120° 
Sum (2
nd
 largest angle of triangle + largest angle of quadrilateral) 
= 60°+120°=180°. 
?CH-GATE-2014 PAPER| 
3 
9. One percent of the people of country X are taller than 6 ft. Two percent of the people of
country Y are taller than 6 ft. There are thrice as many people in country X as in country Y.
Taking both countries together, what is the percentage of people taller than 6 ft?
(A) 3.0    (B) 2.5     (C) 1.5    (D) 1.25
Answer: (D) 
Exp: Let number of people in country y = 100 
So, number of people in country x = 300 
Total number of people taller than 6ft in both the countries 
1 2
300 100 5
100 100
= × + × = 
% of people taller than 6ft in both the countries 
5
100 1.25%.
400
= × = 
10. The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following
figure. Which of the following are true? (k percentile is the value such that k percent of the
data fall below that value)
(i) On average, it rains more in July than in December  
(ii) Every year, the amount of rainfall in August is more than that in January  
(iii) July rainfall can be estimated with better confidence than February rainfall 
(iv) In August, there is at least 500 mm of rainfall 
 (A) (i) and (ii)   (B) (i) and (iii)   (C) (ii) and (iii) (D) (iii) and (iv) 
Answer: (B) 
Exp: In the question the monthly average rainfall chart for 50 years has been given. 
Let us check the options. 
(i) On average, it rains more in July than in December ? correct.
(ii) Every year, the amount of rainfall in August is more than that in January. 
? may not be correct because average rainfall is given in the question.
(iii) July rainfall can be estimated with better confidence than February rainfall. 
? From chart it is clear the gap between 5 percentile and 95 percentile from average is
higher in February than that in July ? correct.
(iv) In August at least 500 mm rainfall  
? May not be correct, because its 50 year average.
So correct option (B) (i) and (iii). 
800 
700 
600 
500 
400 
300 
200 
100 
0 
Jan Feb Mar Apr May 
Jun Jul Aug Sep Oct Nov Dec 
Average 
5 percentile 
95 percentile 
?CH-GATE-2014 PAPER| 
4 
Q.No-1-25 Carry One Mark Each 
1. Gradient of a scalar variable is always
(A) a vector (B) a scalar (C) a dot product (D) zero 
Answer: (A) 
Exp. 




Gradient i j k
x y z
If f is a scalar point function
f f f
f grad f i j k is a vector.
x y z
? ? ?
?= + +
? ? ?
? ? ?
? = = + +
? ? ?

 


 

2. For the time domain function,  f(t) = t
2
 ,which ONE of the following is the Laplace transform
of  ( )
t
0
f t dt ?
?
( )
4
3
A
s
( )
2
1
B
4s
( )
3
2
C
s
( )
4
2
D
s
Answer: (D) 
Exp. We have  
( )
( )
( ) ( )
t
0
t
2 2
3 4 3
0
F s
L f t dt where F s L f t
s
2 2 2
L t dt 3 L t
s s s
? ?
= = ? ?
? ?
? ?
? ?
? ?
? ? ? ?
? ? ? = = =
? ? ? ? ? ?
? ?
? ? ? ?
? ?
?
?
?
3. If f*(x) is the complex conjugate of f(x) = cos(x) + i sin(x), then for real a and b,
( ) ( )
b
a
f * x f x dx is ALWAYS
?
( ) A positive ( ) B negative ( ) C real ( ) D imaginary
Answer: (C) 
Exp. ( ) ( ) ( ) f x cos x isin x = +
( ) ( ) ( )
( ) ( ) ( )( )
( )
b b
a a
b b
ix ix
a a
f * x cos x isin x
f * x .f x dx cos x isin x cos isin x dx
e .e dx 1.dx b a R a, b, R
Real for real a & b.
-
= -
= - +
= = = - ? ?
?
? ?
? ?
?
4. If f(x) is a real and continuous function of x, the Taylor series expansion of f(x) about
its minima will NEVER have a term containing
(A) first derivative     (B) second derivative
(C) third derivative     (D) any higher derivative
Answer: (A) 
?CH-GATE-2014 PAPER| 
5 
Exp. For a real valued function y = f(x) 
Taylor series expansion about ‘a’ 
( ) ( ) ( ) ( )
( )
( )
( )
2
x a
f x f a x a f ' a f '' a .....
2!
For min ima at x a, f ' a 0.
-
= + - + +
= =
So, Taylor series expansion of f(x) about ‘a’ will never contain first derivative term. 
5. From the following list, identify the properties which are equal in both vapour and
liquid phases at equilibrium
P. Density Temperature 
R. Chemical potential S.  Enthalpy 
(A) P and Q only (B) Q and R only 
(C) R and S only (D) P and S only 
Answer: (B) 
Exp. For phase equilibrium 
( )
g l
g l
g l
Temperature; T T
Pr essure; P P correct Ans is B .
Chemical potential;
? =
?
=
?
?
µ =µ
?
 
6. In a closed system, the isentropic expansion of an ideal gas with constant specific heats is
represented by
Answer: (D) 
Exp. For isentropic expansion, 
PV cons tan t
Taking log on both sides
ln P ln V 0
ln P
negative
ln V
?
=
+? =
=-?=
is positive slope of lnP vs ln V is negative. ? ?
( ) A
P
V
( ) B
P
V
( ) D
( ) ln P
( ) ln V
( ) C
( ) ln P
( ) ln V