Page 1
?MEGATE2014 PAPER03
1
Q. No. 1 – 5 Carry One Mark Each
1. “India is a country of rich heritage and cultural diversity.” Which one of the following facts
best supports the claim made in the above sentence?
(A) India is a union of 28 states and 7 union territories.
(B) India has a population of over 1.1 billion.
(C) India is home to 22 official languages and thousands of dialects.
(D) The Indian cricket team draws players from over ten states.
Answer: C
Exp: Diversity is shown in terms of difference language
2. The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian
Rupee has ____________.
(A) Depressed (B) Depreciated (C) Appreciated (D) Stabilized
Answer: B
3. 'Advice' is ________________.
(A) a verb (B) a noun
(C) an adjective (D) both a verb and a noun
Answer: B
4. The next term in the series 81, 54, 36, 24 … is ________
Answer: 16
Exp:
2
81 54 27;27 18
3
 = × =
2
54 36 18;18 12
3
2
36 24 12;12 8
3
24 8 16
 = × =
 = × =
?  =
5. In which of the following options will the expression P < M be definitely true?
(A) M < R > P > S (B) M > S < P < F
(C) Q < M < F = P (D) P = A < R < M
Answer: D
Q. No. 6 – 10 Carry Two Marks Each
6. Find the next term in the sequence: 7G, 11K, 13M, ___
(A) 15Q (B) 17Q (C) 15P (D) 17P
Answer: B
Page 2
?MEGATE2014 PAPER03
1
Q. No. 1 – 5 Carry One Mark Each
1. “India is a country of rich heritage and cultural diversity.” Which one of the following facts
best supports the claim made in the above sentence?
(A) India is a union of 28 states and 7 union territories.
(B) India has a population of over 1.1 billion.
(C) India is home to 22 official languages and thousands of dialects.
(D) The Indian cricket team draws players from over ten states.
Answer: C
Exp: Diversity is shown in terms of difference language
2. The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian
Rupee has ____________.
(A) Depressed (B) Depreciated (C) Appreciated (D) Stabilized
Answer: B
3. 'Advice' is ________________.
(A) a verb (B) a noun
(C) an adjective (D) both a verb and a noun
Answer: B
4. The next term in the series 81, 54, 36, 24 … is ________
Answer: 16
Exp:
2
81 54 27;27 18
3
 = × =
2
54 36 18;18 12
3
2
36 24 12;12 8
3
24 8 16
 = × =
 = × =
?  =
5. In which of the following options will the expression P < M be definitely true?
(A) M < R > P > S (B) M > S < P < F
(C) Q < M < F = P (D) P = A < R < M
Answer: D
Q. No. 6 – 10 Carry Two Marks Each
6. Find the next term in the sequence: 7G, 11K, 13M, ___
(A) 15Q (B) 17Q (C) 15P (D) 17P
Answer: B
?MEGATE2014 PAPER03
2
7. The multilevel hierarchical pie chart shows the population of animals in a reserve forest. The
correct conclusions from this information are:
(i) Butterflies are birds
(ii) There are more tigers in this forest than red ants
(iii) All reptiles in this forest are either snakes or crocodiles
(iv) Elephants are the largest mammals in this forest
(A) (i) and (ii) only (B) (i), (ii), (iii) and (iv)
(C) (i), (iii) and (iv) only (D) (i), (ii) and (iii) only
Answer: D
Exp: It is not mentioned that elephant is the largest animal
8. A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream,
as to row downstream, then find the stream velocity in km per hour.
Answer: 4
Exp: Speed of man=8; Left distance =d
Time taken=
d
8
Upstream:
Speed of stream=s
speed upstream S' (8 s)
d
t'
8 s
? = = 
? ?
=
? ?

? ?
Downstream:
Given
d
speed downstream t ''
8 s
= =
+
3d d
3t ' t ''
8 s 8 s
3d d
s 4km / hr
8 s 8 s
? = ? =
 +
? = ? =
 +
Red ant 
Beetle Tiger
Elephant
Mammal
In sec t
Honey
bee 
Moth
Hawk
Bird
Re ptile
Leopard
Snake
Crocadile
Butterfly
Drongo
Bulbul
Page 3
?MEGATE2014 PAPER03
1
Q. No. 1 – 5 Carry One Mark Each
1. “India is a country of rich heritage and cultural diversity.” Which one of the following facts
best supports the claim made in the above sentence?
(A) India is a union of 28 states and 7 union territories.
(B) India has a population of over 1.1 billion.
(C) India is home to 22 official languages and thousands of dialects.
(D) The Indian cricket team draws players from over ten states.
Answer: C
Exp: Diversity is shown in terms of difference language
2. The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian
Rupee has ____________.
(A) Depressed (B) Depreciated (C) Appreciated (D) Stabilized
Answer: B
3. 'Advice' is ________________.
(A) a verb (B) a noun
(C) an adjective (D) both a verb and a noun
Answer: B
4. The next term in the series 81, 54, 36, 24 … is ________
Answer: 16
Exp:
2
81 54 27;27 18
3
 = × =
2
54 36 18;18 12
3
2
36 24 12;12 8
3
24 8 16
 = × =
 = × =
?  =
5. In which of the following options will the expression P < M be definitely true?
(A) M < R > P > S (B) M > S < P < F
(C) Q < M < F = P (D) P = A < R < M
Answer: D
Q. No. 6 – 10 Carry Two Marks Each
6. Find the next term in the sequence: 7G, 11K, 13M, ___
(A) 15Q (B) 17Q (C) 15P (D) 17P
Answer: B
?MEGATE2014 PAPER03
2
7. The multilevel hierarchical pie chart shows the population of animals in a reserve forest. The
correct conclusions from this information are:
(i) Butterflies are birds
(ii) There are more tigers in this forest than red ants
(iii) All reptiles in this forest are either snakes or crocodiles
(iv) Elephants are the largest mammals in this forest
(A) (i) and (ii) only (B) (i), (ii), (iii) and (iv)
(C) (i), (iii) and (iv) only (D) (i), (ii) and (iii) only
Answer: D
Exp: It is not mentioned that elephant is the largest animal
8. A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream,
as to row downstream, then find the stream velocity in km per hour.
Answer: 4
Exp: Speed of man=8; Left distance =d
Time taken=
d
8
Upstream:
Speed of stream=s
speed upstream S' (8 s)
d
t'
8 s
? = = 
? ?
=
? ?

? ?
Downstream:
Given
d
speed downstream t ''
8 s
= =
+
3d d
3t ' t ''
8 s 8 s
3d d
s 4km / hr
8 s 8 s
? = ? =
 +
? = ? =
 +
Red ant 
Beetle Tiger
Elephant
Mammal
In sec t
Honey
bee 
Moth
Hawk
Bird
Re ptile
Leopard
Snake
Crocadile
Butterfly
Drongo
Bulbul
?MEGATE2014 PAPER03
3
9. A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the
share of raw material, labour, energy, plant & machinery, and transportation costs in the total
manufacturing cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In
2013, the raw material expenses increased by 30% and all other expenses increased by 20%.
If the company registered a profit of Rs. 10 lakhs in 2012, at what price (in Rs.) was each air
purifier sold?
Answer: 20,000
Exp: Total expenditure=
15
x 4,50,000
100
= =
x=3×10
6
Profit=10 lakhs
So, total selling price =40,00,000 … (1)
Total purifies=200 … (2)
S.P of each purifier=(1)/(2)=20,000
10. A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch
is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.
The probability that the current batch is accepted is _________
Answer: 0.8145
Exp: Probability for one bulb to be non defective is
95
100
? Probabilities that none of the bulbs is defectives
4
95
100
? ?
? ?
? ?
= 0.8145
Trans
portat
ion
10%
Labour
15%
Plant and
machinery
30%
Energy
25%
Raw Material
20%
Page 4
?MEGATE2014 PAPER03
1
Q. No. 1 – 5 Carry One Mark Each
1. “India is a country of rich heritage and cultural diversity.” Which one of the following facts
best supports the claim made in the above sentence?
(A) India is a union of 28 states and 7 union territories.
(B) India has a population of over 1.1 billion.
(C) India is home to 22 official languages and thousands of dialects.
(D) The Indian cricket team draws players from over ten states.
Answer: C
Exp: Diversity is shown in terms of difference language
2. The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian
Rupee has ____________.
(A) Depressed (B) Depreciated (C) Appreciated (D) Stabilized
Answer: B
3. 'Advice' is ________________.
(A) a verb (B) a noun
(C) an adjective (D) both a verb and a noun
Answer: B
4. The next term in the series 81, 54, 36, 24 … is ________
Answer: 16
Exp:
2
81 54 27;27 18
3
 = × =
2
54 36 18;18 12
3
2
36 24 12;12 8
3
24 8 16
 = × =
 = × =
?  =
5. In which of the following options will the expression P < M be definitely true?
(A) M < R > P > S (B) M > S < P < F
(C) Q < M < F = P (D) P = A < R < M
Answer: D
Q. No. 6 – 10 Carry Two Marks Each
6. Find the next term in the sequence: 7G, 11K, 13M, ___
(A) 15Q (B) 17Q (C) 15P (D) 17P
Answer: B
?MEGATE2014 PAPER03
2
7. The multilevel hierarchical pie chart shows the population of animals in a reserve forest. The
correct conclusions from this information are:
(i) Butterflies are birds
(ii) There are more tigers in this forest than red ants
(iii) All reptiles in this forest are either snakes or crocodiles
(iv) Elephants are the largest mammals in this forest
(A) (i) and (ii) only (B) (i), (ii), (iii) and (iv)
(C) (i), (iii) and (iv) only (D) (i), (ii) and (iii) only
Answer: D
Exp: It is not mentioned that elephant is the largest animal
8. A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream,
as to row downstream, then find the stream velocity in km per hour.
Answer: 4
Exp: Speed of man=8; Left distance =d
Time taken=
d
8
Upstream:
Speed of stream=s
speed upstream S' (8 s)
d
t'
8 s
? = = 
? ?
=
? ?

? ?
Downstream:
Given
d
speed downstream t ''
8 s
= =
+
3d d
3t ' t ''
8 s 8 s
3d d
s 4km / hr
8 s 8 s
? = ? =
 +
? = ? =
 +
Red ant 
Beetle Tiger
Elephant
Mammal
In sec t
Honey
bee 
Moth
Hawk
Bird
Re ptile
Leopard
Snake
Crocadile
Butterfly
Drongo
Bulbul
?MEGATE2014 PAPER03
3
9. A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the
share of raw material, labour, energy, plant & machinery, and transportation costs in the total
manufacturing cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In
2013, the raw material expenses increased by 30% and all other expenses increased by 20%.
If the company registered a profit of Rs. 10 lakhs in 2012, at what price (in Rs.) was each air
purifier sold?
Answer: 20,000
Exp: Total expenditure=
15
x 4,50,000
100
= =
x=3×10
6
Profit=10 lakhs
So, total selling price =40,00,000 … (1)
Total purifies=200 … (2)
S.P of each purifier=(1)/(2)=20,000
10. A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch
is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.
The probability that the current batch is accepted is _________
Answer: 0.8145
Exp: Probability for one bulb to be non defective is
95
100
? Probabilities that none of the bulbs is defectives
4
95
100
? ?
? ?
? ?
= 0.8145
Trans
portat
ion
10%
Labour
15%
Plant and
machinery
30%
Energy
25%
Raw Material
20%
?MEGATE2014 PAPER03
4
Q. No. 1 – 25 Carry One Mark Each
1. Consider a 3 × 3 real symmetric matrix S such that two of its eigen values are a 0 ? , b 0 ?
with respective eigenvectors
1 1
2 2
3 3
x y
x , y
x y
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
. If a b ? then x
1
y
1
+ x
2
y
2
+ x
2
y
2
equals
(A) a (B) b (C) ab (D) 0
Answer: (D)
Exp: We know that the Eigen vectors corresponding to distinct Eigen values of real symmetric
matrix are orthogonal.
1 1
2 2 1 1 2 2 3 3
3 3
x y
x y x y x y x y 0
x y
? ? ? ?
? ? ? ?
= + + =
? ? ? ?
? ? ? ?
? ? ? ?
2. If a function is continuous at a point,
(A) The limit of the function may not exist at the point
(B) The function must be derivable at the point
(C) The limit of the function at the point tends to infinity
(D) The limit must exist at the point and the value of limit should be same as the value of the
function at that point
Answer: (D)
Exp: We know that ( ) f x is continuous at x=a, if ( )
x a
lim f x
?
exists and equal to ( ) f a
3. Divergence of the vector field
2 2
ˆ ˆ ˆ
x zi xyj yz k +  at (1, 1, 1) is
(A) 0 (B) 3 (C) 5 (D) 6
Answer: (C)
Exp:
( ) ( ) ( )
( )
2 2
2 2
Given F x ai xy j yz k
div F .F
x z xy yz
x y z
2xz x 2yz
div F at 1, 1,1 2 1 2 5
= + 
= ?
? ? ?
= + + 
? ? ?
= + 
 = + + =
4. A group consists of equal number of men and women. Of this group 20% of the men and
50% of the women are unemployed. If a person is selected at random from this group, the
probability of the selected person being employed is _______
Answer: 0.64 to 0.66
Page 5
?MEGATE2014 PAPER03
1
Q. No. 1 – 5 Carry One Mark Each
1. “India is a country of rich heritage and cultural diversity.” Which one of the following facts
best supports the claim made in the above sentence?
(A) India is a union of 28 states and 7 union territories.
(B) India has a population of over 1.1 billion.
(C) India is home to 22 official languages and thousands of dialects.
(D) The Indian cricket team draws players from over ten states.
Answer: C
Exp: Diversity is shown in terms of difference language
2. The value of one U.S. dollar is 65 Indian Rupees today, compared to 60 last year. The Indian
Rupee has ____________.
(A) Depressed (B) Depreciated (C) Appreciated (D) Stabilized
Answer: B
3. 'Advice' is ________________.
(A) a verb (B) a noun
(C) an adjective (D) both a verb and a noun
Answer: B
4. The next term in the series 81, 54, 36, 24 … is ________
Answer: 16
Exp:
2
81 54 27;27 18
3
 = × =
2
54 36 18;18 12
3
2
36 24 12;12 8
3
24 8 16
 = × =
 = × =
?  =
5. In which of the following options will the expression P < M be definitely true?
(A) M < R > P > S (B) M > S < P < F
(C) Q < M < F = P (D) P = A < R < M
Answer: D
Q. No. 6 – 10 Carry Two Marks Each
6. Find the next term in the sequence: 7G, 11K, 13M, ___
(A) 15Q (B) 17Q (C) 15P (D) 17P
Answer: B
?MEGATE2014 PAPER03
2
7. The multilevel hierarchical pie chart shows the population of animals in a reserve forest. The
correct conclusions from this information are:
(i) Butterflies are birds
(ii) There are more tigers in this forest than red ants
(iii) All reptiles in this forest are either snakes or crocodiles
(iv) Elephants are the largest mammals in this forest
(A) (i) and (ii) only (B) (i), (ii), (iii) and (iv)
(C) (i), (iii) and (iv) only (D) (i), (ii) and (iii) only
Answer: D
Exp: It is not mentioned that elephant is the largest animal
8. A man can row at 8 km per hour in still water. If it takes him thrice as long to row upstream,
as to row downstream, then find the stream velocity in km per hour.
Answer: 4
Exp: Speed of man=8; Left distance =d
Time taken=
d
8
Upstream:
Speed of stream=s
speed upstream S' (8 s)
d
t'
8 s
? = = 
? ?
=
? ?

? ?
Downstream:
Given
d
speed downstream t ''
8 s
= =
+
3d d
3t ' t ''
8 s 8 s
3d d
s 4km / hr
8 s 8 s
? = ? =
 +
? = ? =
 +
Red ant 
Beetle Tiger
Elephant
Mammal
In sec t
Honey
bee 
Moth
Hawk
Bird
Re ptile
Leopard
Snake
Crocadile
Butterfly
Drongo
Bulbul
?MEGATE2014 PAPER03
3
9. A firm producing air purifiers sold 200 units in 2012. The following pie chart presents the
share of raw material, labour, energy, plant & machinery, and transportation costs in the total
manufacturing cost of the firm in 2012. The expenditure on labour in 2012 is Rs. 4,50,000. In
2013, the raw material expenses increased by 30% and all other expenses increased by 20%.
If the company registered a profit of Rs. 10 lakhs in 2012, at what price (in Rs.) was each air
purifier sold?
Answer: 20,000
Exp: Total expenditure=
15
x 4,50,000
100
= =
x=3×10
6
Profit=10 lakhs
So, total selling price =40,00,000 … (1)
Total purifies=200 … (2)
S.P of each purifier=(1)/(2)=20,000
10. A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch
is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs.
The probability that the current batch is accepted is _________
Answer: 0.8145
Exp: Probability for one bulb to be non defective is
95
100
? Probabilities that none of the bulbs is defectives
4
95
100
? ?
? ?
? ?
= 0.8145
Trans
portat
ion
10%
Labour
15%
Plant and
machinery
30%
Energy
25%
Raw Material
20%
?MEGATE2014 PAPER03
4
Q. No. 1 – 25 Carry One Mark Each
1. Consider a 3 × 3 real symmetric matrix S such that two of its eigen values are a 0 ? , b 0 ?
with respective eigenvectors
1 1
2 2
3 3
x y
x , y
x y
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
? ? ? ?
. If a b ? then x
1
y
1
+ x
2
y
2
+ x
2
y
2
equals
(A) a (B) b (C) ab (D) 0
Answer: (D)
Exp: We know that the Eigen vectors corresponding to distinct Eigen values of real symmetric
matrix are orthogonal.
1 1
2 2 1 1 2 2 3 3
3 3
x y
x y x y x y x y 0
x y
? ? ? ?
? ? ? ?
= + + =
? ? ? ?
? ? ? ?
? ? ? ?
2. If a function is continuous at a point,
(A) The limit of the function may not exist at the point
(B) The function must be derivable at the point
(C) The limit of the function at the point tends to infinity
(D) The limit must exist at the point and the value of limit should be same as the value of the
function at that point
Answer: (D)
Exp: We know that ( ) f x is continuous at x=a, if ( )
x a
lim f x
?
exists and equal to ( ) f a
3. Divergence of the vector field
2 2
ˆ ˆ ˆ
x zi xyj yz k +  at (1, 1, 1) is
(A) 0 (B) 3 (C) 5 (D) 6
Answer: (C)
Exp:
( ) ( ) ( )
( )
2 2
2 2
Given F x ai xy j yz k
div F .F
x z xy yz
x y z
2xz x 2yz
div F at 1, 1,1 2 1 2 5
= + 
= ?
? ? ?
= + + 
? ? ?
= + 
 = + + =
4. A group consists of equal number of men and women. Of this group 20% of the men and
50% of the women are unemployed. If a person is selected at random from this group, the
probability of the selected person being employed is _______
Answer: 0.64 to 0.66
?MEGATE2014 PAPER03
5
Exp: Let M men
W women
E employed
U unemployed
?
?
?
?
Given ( )
( )
( )
( )
P M 0.5
P W 0.5
U
P 0.20
M
U
P 0.50
W
=
=
=
=
By Total probability,
( ) ( )
( )
( )
( )
U U
P U P M P P W P
M M
0.5 0.20 0.5 0.50 0.35
= +
= × + × =
Required probability = ( ) ( ) P E 1 P U 1 0.35 0.65 =  =  =
5. The definite integral
3
1
1
dx
x
?
is evaluated using Trapezoidal rule with a step size of 1. The
correct answer is ________
Answer: 1.1 to 1.2
Exp: Given,
3
1
1
dx
x
h stepsize 1
31
n no.of.sub intervals = 2
1
= =
= =
?
Let
1
y
x
x 1 2 3
1 1 1
y 1
x 2 3
=
=
By trapezoidal rule
( ) ( ) ( )
n
0
x
0 n 1 n 1
x
3
1
h
f x dx y y 2 y .......... y
2
1 1 1 1 1 4 1 7
dx 1 2 1 1.1667
x 2 3 2 2 3 2 3

= ? + + + + ?
? ?
? ? ? ? ? ? ? ?
= + + = + = × =
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
?
?
6. A rotating steel shaft is supported at the ends. It is subjected to a point load at the centre. The
maximum bending stress developed is 100 MPa. If the yield, ultimate and corrected
endurance strength of the shaft material is 300 MPa, 500 MPa and 200 MPa, respectively,
then the factor of safety for the shaft is _______
Answer: 1.9 to 2.1
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