Aptitude

Question 1
   
A
∠BCD-∠BAD
B
∠BAD+∠BCF
C
∠BAD+∠BCD
D
∠CBA+ADC
       Aptitude       Numerical       Gate 2018
Question 1 Explanation: 

→ ∠1 = ∠5 + ∠4 ………(i)
According to triangular property:
Angle of exterior = sum of interior angles
→ ∠4 = ∠3 + ∠2 ……….(ii)
By substituting (ii) in (i)
→ ∠1 = ∠5 + ∠3 + ∠2
→ ∠1 = ∠BCD
∠2 = ∠BAD
→ ∠BCD - ∠BAD = ∠1 - ∠2
= ∠5 + ∠3 + ∠2 - ∠2
= ∠ 5 + ∠3
= ∠DEC + ∠BFC
Question 2
In a party, 60% of the invited guests are male and 40% are female. If 80% of the invited guests attended the party and if all the invited female guests attended, what would be the ratio of males to females among the attendees in the party?
A
2:3
B
1:1
C
3:2
D
2:1
       Aptitude       Numerical       Gate 2018
Question 2 Explanation: 
Let us consider total no. of guests = 100
→ 60% invited guests are males i.e., 60 males
→ 40% invited guests are females i.e., 40 females
→ 80% invited guests are attended i.e., total guests attended to a party = 80
→ All the invited females are attended then remaining people are males = 80 – 40 = 40 males
40 males : 40 females
1 : 1
Question 3
In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs 750 to each male senior citizen in the town and Rs 1000 to each female senior citizen. Altogether, there were 300 senior citizens eligible for this gift. However, only 8/9th of the eligible men and 2/3rd of the eligible women claimed the gift. How much money (in Rupees) did the philanthropist give away in total?
A
1,50,000
B
2,00,000
C
1,75,000
D
1,51,000
       Aptitude       Numerical       Gate 2018
Question 3 Explanation: 
Male senior citizen’s gift = Rs.750
Female senior citizen’s gift = Rs. 1000
No. of males = a say
No. of females = b say
Altogether no. of persons eligible for gift = 300
i.e., a+b = 300
Total amount be given = (8x/9 × 750) + (2y/3 × 1000)
= (2000x/3) + (2000y/3)
= 2000/3 (x+y)
= 2000/3 (300)
= 2,00,000
Question 4
A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment?
A
Three green faces and four red faces.
B
Four green faces and three red faces.
C
Five green faces and two red faces.
D
Six green faces and one red face.
       Aptitude       Numerical       Gate 2018
Question 4 Explanation: 
→ Each side of a unbiased die can have equal probability i.e., = 1/6
→ If we roll a die for six time then we get 4 green faces and 2 red faces.
→ And if we roll for seventh time green face can have more probability to become a outcome.
→ Then most likely outcome is five green faces and two red faces.
Question 5
“From where are they bringing their books? __________ bringing __________ books from __________.” The words that best fill the blanks in the above sentence are
A
Their, they’re, there
B
They’re, their, there
C
There, their, they’re
D
They’re, there, there
       Aptitude       Verbal       Gate 2018
Question 5 Explanation: 
Question 6

"A _______ investigation can sometimes yield new facts, but typically organized ones are more successful."

The word that best fills the blank in the above sentence is

 

A
meandering
B
timely
C
consistent
D
systematic
       Aptitude       Verbal       Gate 2018
Question 6 Explanation: 
Meandering means "Proceeding in a convoluted way (or) undirected fashion".
Question 7
The area of a square is d.  What is the area of the circle which has the diagonal of the square as its diameter?
A
πd
B
πd2
C
(1/2)πd2
D
(1/2)πd
       Aptitude       Numerical       Gate 2018
Question 7 Explanation: 
In general,
Area of a square A = a2 (where a is side)
In the question,
Area of a square = d
The side of a square = √d
Diagonal of a square = Diameter of circle

From Pythagoras theorem,
Question 8
What is the missing number in the following sequence? 2, 12, 60, 240, 720, 1440, _______, 0  
A
2880
B
1440
C
720
D
0
       Aptitude       Numerical       Gate 2018
Question 8 Explanation: 

2×6=12
12×5=60
60×4=240
240×3=720
720×2=1440

1440×0=0
Question 9

What would be the smallest natural number which when divided either by 20 or by 42 or by 76 leaves a remainder of '7' in each case?

A
3047
B
6047
C
7987
D
63847
       Aptitude       Numerical       Gate 2018
Question 9 Explanation: 
Method-I:
Take the LCM of 20,42,76 i.e., 7980.
⟹ Remainder = 7
⟹ Smallest number divisible by 20 (or) 42 (or) 72 which leaves remainder 7 is = 7980+7 = 7987
Method- II:
Option I:
3047 – 7 = 3040
3040 not divisible by 42
Option II:
6040 not divisible by 42
Option III:
7980 divisible by 20, 42, 76
Option IV:
63840 divisible by 20, 42, 76
→ Smallest (7980, 63840) = 7980
→ 7980 + remainder 7 = 7987
Question 10
If pqr≠0and p -x=1/q, q -y=1/r, r -z=1/p, what is the value of the product xyz?
A
-1
B
1/pqr
C
1
D
pqr
       Aptitude       Numerical       Gate 2018
Question 10 Explanation: 
pqr≠0
→ p-x = 1/q ⟹ 1/px = 1/q
⟹ q = px
⟹ log q = log px
⟹ x log p = log q ⟹ x = log q/ log p → q-y = 1/r ⟹ 1/qy = 1/r
⟹ qy = r
⟹ y log q = log r
⟹ y = log r/ log q
→ r-z = 1/p ⟹ 1/rz = 1/p
⟹ p = rz
⟹ log rz = log p
⟹ z log r = log p
⟹ z = log p/ log r
XYZ = log q/ log p * log r/ log q * log p/ log r =1
Question 11
After RajendraChola returned from his voyage to Indonesia, he _________ to visit the temple in Thanjavur.
A
was wishing
B
is wishing
C
wished
D
had wished
       Aptitude       Verbal       Gate 2017 set-01
Question 11 Explanation: 
When the main clause is in the past or past perfect tense, the subordinate clause must be in the past or past perfect tense.
After Rajendrachola returned from his voyage to Indonesia, he wished to visit the temple in Tanjavur.
Question 12
Research in the workplace reveals that people work for many reason __________.
A
money beside
B
beside money
C
money besides
D
besides money
       Aptitude       Verbal       Gate 2017 set-01
Question 12 Explanation: 
Besides is an adverb (or) preposition and it is a preposition it means in addition to apart from as an adverb it means furthermore (or) as well.
Here we are using besides preposition "in addition to".
Question 13
Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali,Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other?
A
Rahul and Murali
B
Srinivas and Arul
C
Srinivas and Murali
D
Srinivas and Rahul
       Aptitude       Numerical       Gate 2017 set-01
Question 13 Explanation: 
Assuming, they face the center of the table

Srinivas and Murali and Arul and Rahul are opposite to each other.
They face away from the center of table

Even in this case,
Srinivas and Murali and Arul and Rahul are opposite to each other.
Question 14
Find the smallest number y such that y×162 is a prefect cube.
A
24
B
27
C
32
D
36
       Aptitude       Numerical       Gate 2017 set-01
Question 14 Explanation: 
Prime factorize: 162
⇒162 =2×3×3×3×3 = 33×(2×3)
For (2×3) to be a perfect cube, it should be multiplied by (22×32)
∴ Required number = y = 22×32 = 36
Question 15
The probability that a k-digit number does NOT contain the digits 0, 5 or 9 is
A
0.3k
B
0.6k
C
0.7k
D
0.9k
       Aptitude       Numerical       Gate 2017 set-01
Question 15 Explanation: 
Possibilities of doesn't contain 0,5,9 = (7)k
Total no.of possibilities = (10)k
Required probability = (7)k / (10)k = 0.7k
Question 16
“The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history.” Which of the following statements best reflects the author’s opinion?
A
Nationalists are highly imaginative.
B
History is viewed through the filter of nationalism.
C
Our colonial past never happened.
D
Nationalism has to be both adequately and properly imagined.
       Aptitude       Verbal       Gate 2017 set-01
Question 16 Explanation: 
The author is explaining about the colonial past. That represents the history of nationalism.
Question 17
Six people are seated around a circular table. There are atleast two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is
A
2
B
3
C
4
D
Cannot be determined
       Aptitude       Numerical       Gate 2017 set-01
Question 17 Explanation: 
There are atleast two men and two women.
Atleast three right- handed persons.
None of the women are right-handed.
⇒ All the right-handed persons are men. Every woman has a left-handed person to her immediate right.
⇒ For this to happen, there must be three left-handed-persons and one of them should be a male.
As three persons are right-handed and those being men.
The number of women at the table = 2
Question 18
The expression (x+y)-|x-y|/2 is equal to
A
the maximum of x and y
B
the minimum of x and y
C
1
D
none of the above
       Aptitude       Numerical       Gate 2017 set-01
Question 18 Explanation: 
As the given expression has modulus, let us consider:
Case-I: x>y
⇒ |x-y| = x-y
Expression ⇒ (x+y)-(x-y)/ 2 = y
In this case value of expression is minimum of y.
Case-II: x ⇒ |x-y| = -(x-y)
Expression ⇒ (x+y) - (x-y) / 2
⇒ (x+y) - [-(x-y)]/2 ⇒ x
In this case value of expression is minimum of x.
Finally, the value of expression is minimum of x & y.
Question 19
Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she likes?
A
21
B
18
C
16
D
14
       Aptitude       Numerical       Gate 2017 set-01
Question 19 Explanation: 
Total number of ways that each select one shirt without any condition = 4P4 = 4! = 24
Number of ways Arun chooses red or Shweta chooses white
= Number of ways Arun chooses red + Number of ways Shweta chooses white - Number of ways Arun chooses red and Shweta chooses white
= 3P3 + 3P3 - 22P2
= 3! + 3! - 2!
= 10
∴ Required number of ways = 24 - 10 = 14
Question 20
 
A
P,Q
B
P,Q,T
C
R,S,T
D
Q,R,S
       Aptitude       Numerical       Gate 2017 set-01
Question 20 Explanation: 
The contour lines are shown at 25m interval in this plot.
∴ From the plot,
P=575m
Q=525m
R=475m
S=425m
T=500m
For a village to be submerged, the water level should rise to level greater than the village.
If water level rises to 525m, villages which are at heights below 525m, get submerged.
Here, R, S, T get submerged.
Question 21
Choose the option with words that are not synonyms.
A
aversion, dislike
B
luminous, radiant
C
plunder, loot
D
yielding, resistant
       Aptitude       Verbal       GATE 2017(set-02)
Question 21 Explanation: 
Yeilding means produce (or) provide (a natural, agricultural or industrial product)
Resistant means offering a resistance to something or someone.
Question 22
Saturn is __________ to be seen on a clear night with the naked eye.
A
enough bright
B
bright enough
C
as enough bright
D
bright as enough
       Aptitude       Verbal       GATE 2017(set-02)
Question 22 Explanation: 
In this question enough is used with bright, where bright is an adjective.
With adjectives and adverbs enough is comes after an adjectives and adverbs.
So, here we use bright enough to complete the sentence.
Question 23
There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W, Z is to the East of X and the West of V, W is to the West of Y. Which is the building in the middle?
A
V
B
W
C
X
D
Y
       Aptitude       Numerical       GATE 2017(set-02)
Question 23 Explanation: 
V is to west of W = VW .........(i)
Z is to East of X and west of V = XZV ........(ii)
W is to west of Y = WY .........(iii)
From (i) and (ii) ⇒ VWY .........(iv)
From (ii) and (iv) ⇒ XZVWY
→While building V is in the middle.
Question 24
A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have?
A
12
B
15
C
18
D
19
       Aptitude       Numerical       GATE 2017(set-02)
Question 24 Explanation: 
No. of 3 marks questions = X say
No. of 4 marks questions = Y say
No. of questions X+Y = 20
Total no. of marks = 100
⇒ 3X+11Y = 100
Option I: If X=12; Y=8 ⇒ 3(12)+11(8) ⇒ 36+88 ≠ 100
Option II: If X=15; Y=5 ⇒ 3(15)+11(5) ⇒ 100 = 100
Option III: If X=18; Y=2 ⇒ 3(18)+11(2) ≠ 100
Option IV: If X=19; Y=1 ⇒ 3(19)+11(1) ≠ 100
Question 25
There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is
A
1⁄5
B
7⁄30
C
1⁄4
D
4⁄15
       Aptitude       Numerical       GATE 2017(set-02)
Question 25 Explanation: 
Totally there are 3 red socks, 4 green socks, 3 blue socks. In those we need to select 2 socks
The probability of selecting same colour is
3C2 / 10C2 * 4C2 / 10C2 * 3C2 / 10C2
⇒ 3/45 + 6/45 + 3/45
⇒ 12/45
= 4/15
Question 26
“We lived in a culture that denied any merit to literary works, considering them important only when they are handmaidens to something seemingly more urgent – namely ideology. This was a country where all gestures, even the most private, were interpreted in political terms.” The author’s belief that ideology is not as important as literature is revealed by the word:
A
‘culture’
B
‘seemingly’
C
‘urgent’
D
‘political’
       Aptitude       Verbal       GATE 2017(set-02)
Question 26 Explanation: 
Seemingly means that "according to the facts as one knows them" as far as one knows.
(or)
As to give the impression of having a certain quality.
Question 27
There are three boxes. One contains apples, another contains oranges and the last one contains both apple and oranges. All three are known to be incorrectly labeled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?
A
The box labeled ‘Apples’
B
The box labeled ‘Apples and Oranges’
C
The box labeled ‘Oranges’
D
Cannot be determined
       Aptitude       Numerical       GATE 2017(set-02)
Question 27 Explanation: 
Correct Answer is option B i.e., the box labeled Apples an Oranges.
If we open a box labeled as apples and oranges that contains either apples (or) oranges:
Case I: If it contains apples, then the box labeled oranges can contain apples and oranges and box labeled apples can contain oranges.
Case II: If it contains oranges, then box labeled apples can contains apples and oranges and box labeled oranges can contains apples.
Question 28
X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X3 will have
A
90 digits
B
91 digits
C
92 digits
D
93 digits
       Aptitude       Numerical       GATE 2017(set-02)
Question 28 Explanation: 
X is a 30 digit number starting with digit 4 and followed by the digit 7
X = 4777......... (29 times (7))
X = 4.777........ ×1029
X = 5×1029 (4.777 rounded as 5)
X3 = 125×1087
Total no. of digits = 3+87 [125=3 digit, 1087 = 87 digit]
= 90
Question 29
The number of roots of ex + 0.5x2 – 2 in the range [-5, 5] is
A
0
B
1
C
2
D
3
       Aptitude       Numerical       GATE 2017(set-02)
Question 29 Explanation: 
ex+0.5x2-2=0
ex=-0.5x2+2
If we draw a graph for ex and -0.5x2+2 in between [-5, 5]
Question 30
A
P
B
Q
C
R
D
S
       Aptitude       Numerical       GATE 2017(set-02)
Question 30 Explanation: 
Region R can have more air pressure as compared to other regions because it has maximum number of lines crossing the area.
Question 31
Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.
A
I will not leave the place until the minister does not meet me.
B
I will not leave the place until the minister doesn’t meet me.
C
I will not leave the place until the minister meet me.
D
I will not leave the place until the minister meets me.
       Aptitude       Verbal       2016 set-01
Question 31 Explanation: 
In option A and B, 'not' is already embedded until so both are incorrect.
Minister is a singular person, with a singular object, so verb ends with 's'. So option C is incorrect.
Option 'D' is correct.
Question 32
A rewording of something written or spoken is a ______________.
A
paraphrase
B
paradox
C
paradigm
D
paraffin
       Aptitude       verbal       2016 set-01
Question 32 Explanation: 
Paraphase means that "express the meaning of (something written or spoken) using different words.
Question 33
 
A
figurative
B
collateral
C
literal
D
figurine
       Aptitude       verbal       2016 set-01
Question 33 Explanation: 
Figurative means that "departing from a literal use of words"; Metaphorical.
The use of the metaphorical words to explain about the thoughts instead of literal use of them.
Question 34
If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’?
A
zentaga
B
tagafer
C
tagazen
D
relffer
       Aptitude       verbal       2016 set-01
Question 34 Explanation: 
relftaga - carefree → (1)
otaga - careful → (2)
fertaga - careless → (3)
From (1) & (2),
taga = care (and it is in the first half of the word)
From (3),
fer = less
Aftercare - tagazen
Care is in the second half of the word ⇒ taga should be in the first half.
Question 35
A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is __________.
A
56
B
64
C
72
D
96
       Aptitude       Numerical       2016 set-01
Question 35 Explanation: 
64 cubic blocks are used to make the cube
⇒ Side of cube = 4
Surface area of cube = 6s2 = 6 × 42 = 96
Each corner block is associated with three faces of cube. When they are removed, three new faces are exposed, thus there appears no net change in the exposed surface area.
Hence, Surface area = 96
Question 36
 
A
Elegance
B
Executive
C
Smooth
D
Soft
       Aptitude       Numerical       2016 set-01
Question 36 Explanation: 
Revenue from Elegance = (27300+25222+28976+21012)×48 = Rs. 4920480
Revenue from Smooth = (20009+19392+22429+18229)×63 = Rs. 5043717
Revenue from Soft = (17602+18445+19544+16595)×78 = Rs.5630508
Revenue from Executive = (9999+8942+10234+10109)×173 = Rs. 6796132
Clearly, Executive contributes the greatest fraction to the revenue of the company as the revenue from it is the highest.
Question 37
In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.
A
40.00
B
46.02
C
60.01
D
92.02
       Aptitude       numerical       2016 set-01
Question 37 Explanation: 
In a process, the number of cycles to failure decrease exponentially with an increase in load.
General exponential function = a⋅e-bx
i.e., No. of cycles to failure = a⋅e-bx
load = x
At a load of 80 units, it takes 100 cycles to failure.
So, no. of cycles to failure = 100
load = 80
i.e., 100 = a⋅e-b(80) --------(1)
When the load is halved, it takes 10000 cycles to failure.
No. of cycles to failure = 10,000
load = 40
i.e., 10,000 = a⋅e-b(40) ---------(2)

No. of cycles to failure = 5,000
load = x?
i.e., 5000 = a⋅e-bx
Multiply with 2 on both sides,
10,000 = 2⋅a⋅e-bx ------- (4)
Question 38
Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of the nation’s diversity, nothing else is. Which of the following can be logically inferred from the above sentences?  
A
India is a country of exactly seventeen languages.
B
Linguistic pluralism is the only indicator of a nation’s diversity.
C
Indian currency notes have sufficient space for all the Indian languages.
D
Linguistic pluralism is strong evidence of India’s diversity.
       Aptitude       verbal       2016 set-01
Question 38 Explanation: 
Option D is Correct Answer.
Which is inferred from the statement.
Option A, B, C are incorrect which are not properly inferred from the statement.
Question 39
 
A
(i) only
B
(ii) only
C
(i) and (ii)
D
neither (i) nor (ii)
       Aptitude       numerical       2016 set-01
Question 39 Explanation: 
From statements I, II & IV, we can say that
All three can beat S.
But from statement III,
S loses to P only sometimes.
(ii) Cannot be inferred.
And in poker, the transitive law does not apply. This can be seen from statement III.
As S loses to P only sometimes which states that wins against P most of the time.
So, (i) cannot be logically inferred.
Question 40
If f(x) = 2x7 + 3x - 5, which of the following is a factor of f(x)?
A
(x 3 +8)
B
(x-1)
C
(2x-5)
D
(x+1)
       Aptitude       Numerical       2016 set-01
Question 40 Explanation: 
f(x)=2x7+3x - 5
For (x - a) to be a factor of f(x)
f(a) = 0
From options,
Only a=1, satisfies the above equation
∴ (x - 1) is a factor of f(x).
Question 41
The man who is now Municipal Commissioner worked as ____________________.
A
the security guard at a university
B
a security guard at the university
C
a security guard at university
D
the security guard at the university
       Aptitude       Verbal       GATE 2016 set-2
Question 41 Explanation: 
Security guard is a general post, so we use the artical 'a' before the security.
And coming to university it is an organization. So we use are 'the' before university.
Question 42
A
put up with
B
put in with
C
put down to
D
put up against
       Aptitude       Verbal       GATE 2016 set-2
Question 42 Explanation: 
"Put up with" is means that "tolerate" which is the closest meaning of "cope with".
→ Cope with is doesn't means that put someone into competition with some other.
Question 43
A
mock
B
deride
C
praise
D
jeer
       Aptitude       Verbal       GATE 2016 set-2
Question 43 Explanation: 
Mock = Tease or laugh
Deride = express contempts for; ridicule
Jeer = Make rude and mocking remarks
→ These three are negative things
Praise = express warm approval
Question 44
Pick the odd one from the following options.
A
CADBE
B
JHKIL
C
XVYWZ
D
ONPMQ
       Aptitude       Numerical       GATE 2016 set-2
Question 44 Explanation: 
In all the given options except D, the 1st, 3rd, 5th alphabets are consecutive (increasing order) and 2nd and 4th are consecutive (increasing order).
But in D, 2nd and 4th are in decreasing order.
Question 45
 
A
n4
B
4n
C
22n-1
D
4n-1
       Aptitude       Numerical       GATE 2016 set-2
Question 45 Explanation: 
Given,
Product of roots (α, β) = 4
⇒ αβ = 4

(αβ)n = 4n
Question 46
Among 150 faculty members in an institute, 55 are connected with each other through Facebook® and 85 are connected through WhatsApp®. 30 faculty members do not have Facebook® or WhatsApp® accounts. The number of faculty members connected only through Facebook® accounts is ______________.
A
35
B
45
C
65
D
90
       Aptitude       Numerical       GATE 2016 set-2
Question 46 Explanation: 
Total number of faculty = 150
Number of faculty members connected through Facebook = 55
Number of faculty members connected through Whatsapp = 85
Number of faculty members with Facebook (or) Whatsapp accounts = 30
Number of faculty members with either Facebook (or) Whatsapp accounts = 150 - 30 = 120
Number of faculty members with both Facebook and Whatsapp accounts = 85 + 55 - 120 = 20
Number of faculty members with only Facebook accounts = 55 - 20 = 35
Question 47
 
A
(i) only
B
(ii) only
C
both (i) and (ii)
D
neither (i) nor (ii)
       Aptitude       Verbal       GATE 2016 set-2
Question 47 Explanation: 
The author, has no where said that the computers are bad, authoring is talking about the way computers are being used today and the author questioned this way. So, statement I does not follow.
→ "Many believes that the internet itself is unintended consequence of the original invention.
So, statement II does not follow, so Answer is Option D.
Question 48
 
A
(i) only
B
(ii) only
C
both (i) and (ii)
D
neither (i) nor (ii)
       Aptitude       Verbal       GATE 2016 set-2
Question 48 Explanation: 
Given,
All hill-stations have a lake → (1)
Ooty has two lakes → (2)
From (1), it cannot be inferred that every place having a lake is a hill station.
⇒ (i) cannot be logically intended.
From (1), it cannot be inferred how many lakes will be there in a hill station.
⇒ (ii) cannot be logically inferred.
Question 49
   
A
21
B
27
C
30
D
36
       Aptitude       Numerical       GATE 2016 set-2
Question 49 Explanation: 
Number of rectangles in a grid with 'm' horizontal and 'n' vertical lines = 5C2 × 3C2 = 10 × 3 = 30
Question 50
 
A
f(x)=1-|x-1|
B
f(x)=1+|x-1|
C
f(x)=2-|x-1|
D
f(x)=2+|x-1|
       Aptitude       Numerical       GATE 2016 set-2
Question 50 Explanation: 
From the graph,
x = -1 ⇒ f(x) = 0
x = 0 ⇒ f(x) = 1
We have check, which option satisfies both the conditions.
Only option (C) satisfies both of them.
Question 51
Didn’t you buy _________ when you went shopping?
A
any paper
B
much paper
C
no paper
D
a few paper
       Aptitude       Verbal       GATE 2015 (Set-01)
Question 51 Explanation: 
In negative sentence we can use "any" with plural countable nouns.
Question 52
Which of the following combinations is incorrect?
A
Acquiescence – Submission
B
Wheedle – Roundabout
C
Flippancy – Lightness
D
Profligate – Extravagant
       Aptitude       Verbal       GATE 2015 (Set-01)
Question 52 Explanation: 
Acceptance = The reluctant acceptance of something without protest
Wheedle = Use endearments (or) flattery to persuade some to do something
Flippancy = Lack of respect (or) seriousness
Profligate = Recklessly extravagant
Question 53
Given set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is probability that the sum of the two numbers equals 16?
A
0.20
B
0.25
C
0.30
D
0.33
       Aptitude       Numerical       GATE 2015 (Set-01)
Question 53 Explanation: 
Favourable outcomes = {2,14}, {3,13}, {4,12}, {5,11} = 4
Total outcomes = 4C1 × 5C1 = 20
Probability = Favourable outcomes/ Total outcomes = 4/20 = 0.20
Question 54
A
She had a terrible time at the party.
B
She had a horrible time at the party.
C
She had a terrific time at the party
D
She had a terrifying time at the party
       Aptitude       Verbal       GATE 2015 (Set-01)
Question 54 Explanation: 
The options A, B and D means that she didn't enjoy the party.
→ Horrible and terrible means fearful.
→ Terrific = Wonderful
→ So, C is the Answer.
Question 55
       
A
Statement I alone is sufficient, but statement II alone is not sufficient.
B
Statement II alone is sufficient, but statement I alone is not sufficient.
C
Both statements together are sufficient, but neither statement alone is sufficient.
D
Statement I and II together are not sufficient.
       Aptitude       Numerical       GATE 2015 (Set-01)
Question 55 Explanation: 
When you climbing, only height matters not the width.
Statement I:
Each step is 3/4 foot high.
No. of steps = 9/(3/4) = 12 steps
Statement I alone is sufficient.
Statement II:
Each step is 1 foot wide.
Statement II alone is not sufficient.
Question 56

     
A
32
B
33
C
34
D
35
       Aptitude       Numerical       GATE 2015 (Set-01)
Question 56 Explanation: 
Male to female students in each department = 5 : 4
There are 40 males in Electrical Engineering.
⇒ Number of females in Electrical Engineering = 4/5 × 40 = 32
Total number of students in Electrical Engineering = 40+32 = 72
This constitutes 20% of the strength of college.
Number of students in Civil department = 30/100 × 72 = 108
Number of female students in Civil department = 4/(4+5) × 108 = 48
Number of students in Mechanical department = 10/20 × 72 = 36
Number of female students in Mechanical department = 4/(4+5) × 36 = 16
Required Difference = 48 - 16 = 32
Question 57
Select the alternative meaning of the underlined part of the sentence. The chain snatchers took to their heels when the police party arrived.
A
took shelter in a thick jungle
B
open indiscriminate fire
C
took to flight
D
unconditionally surrendered
       Aptitude       Verbal       GATE 2015 (Set-01)
Question 57 Explanation: 
The words took to their heels and took to flight means that runaway.
Question 58
     
A
Only relation I is true
B
Only relation II is true
C
Relations II and III are true.
D
Relations I and III are true.
       Aptitude       Numerical       GATE 2015 (Set-01)
Question 58 Explanation: 
75% of students have a chance of passing atleast one subject = 1 - (1 - m) (1 - p) (1 - c) = 0.75 ----(i)
50% of students have a chance pass in atleast two
(1 - m)pc + (1 - p)mc + (1 - c) mp + mpc = 0.5 ----(ii)
40% of students have a chance of passing exactly two
(1 - m)pc + (1 - p)mc + (1 - c)mp = 0.4 ----(iii)
From equation (ii) and (iii) we can get
mpc = 0.1
⇒ m*p*c = 1/10
Statement (III) is correct.
→ Simplify eq (i), we get ⇒ p+c+m - (mp+mc+pc) + mpc = 0.75
⇒ p+c+m - (mp+mc+pc) = 0.65 ----(iv) → Simplify equation (iii), we get
⇒ pc + mc + mp - 3mpc = 0.4
From (iv) and (v)
p + c +m - 0.7 = 0.65
⇒ p + c + m = 1.35 = 27/20
Statement (I) is correct.
Question 59
A
Statements I and II follow
B
Statements I and III follow
C
Statements II and III follow
D
All statements follow
       Aptitude       Verbal       GATE 2015 (Set-01)
Question 59 Explanation: 
The statement III is not correct, banning of water in lower areas is not the solution of the problem.
Question 60
A
2.290
B
2.970
C
6.795
D
8.795
       Aptitude       Numerical       GATE 2015 (Set-01)
Question 60 Explanation: 
Total number of students = 44 (Answered- correctly+Answered-wrongly+Not-attempted)
Total marks obtained = 21×2+15×3+11×1+23×2+31×5=299
Average marks = 299/44 = 6.795
Question 61
   
A
Statement I alone is not sufficient
B
Statement II alone is not sufficient
C
Either I or II alone is sufficient
D
Both statements I and II together are not sufficient.
       Aptitude       Numerical       GATE 2015 -(Set-2)
Question 61 Explanation: 
Statement-I:
One fourth of the weight of a pole is 5Kg. ⇒ Weight of pole is 4×5=20Kg
Weight of 10 poles each of same weight = 10×20 = 200 Kg
∴Statement I alone is sufficient.
Statement-II:
Let, Weight of each pole = W Kg
Given,
10W = 2W + 160
⇒ 8W = 160
W = 20Kg
∴ Weight of each pole = 20 Kg
∴ Weight of 10 poles = 10×20 Kg = 200 Kg
∴ Statement II alone is sufficient.
Option (C) is the answer.
Either I or II alone is sufficient.
Question 62
Consider a function f(x= 1 - |x| on -1 ≤ x ≤ 1. The value of x at which the function attains a maximum and the maximum value of the function are
A
0, -1
B
-1, 0
C
0, 1
D
-1, 2
       Aptitude       Numerical       GATE 2015 -(Set-2)
Question 62 Explanation: 
f(x) = 1 - |x| on -1 ≤ x ≤ 1
In the given function, it is given as
-|x| ⇒ To obtain the maximum of this function we have to minimize the value -|x| and the minimum value is 0.
∴ Maximum value of f(x) is at f(0) and i.e., f(x) = 1
Maximum value is 1 at x=0.
Question 63
A generic term that include various items of clothing such as a skirt, a pair of trousers and a shirt is
A
fabric
B
textile
C
fibre
D
apparel
       Aptitude       Verbal       GATE 2015 -(Set-2)
Question 63 Explanation: 
apparel- clothing, especially outerwear; garments; attire; raiment
Question 64
Choose the statement where underlined word is used correctly.
A
The industrialist load a personnel jet.
B
I write my experience in my personnel diary.
C
All personnel are being given the day off.
D
Being religious is a personnel aspect.
       Aptitude       Verbal       GATE 2015 -(Set-2)
Question 64 Explanation: 
personnel- people employed in an organization or engaged in an organized undertaking such as military service.
Question 65
We __________________ our friend’s birthday and we ______________ how to make it up to him.
A
Completely forgot - - - don’t just know
B
Forgot completely - - - don’t just know
C
Completely forgot - - - just don’t know
D
Forgot completely - - - just don’t know
       Aptitude       Verbal       GATE 2015 -(Set-2)
Question 65 Explanation: 
We compltetely forgot our friend's birthday and we just don't know how to make it up to him.
Question 66
   
A
B
C
D
       Aptitude       Numerical       GATE 2015 -(Set-2)
Question 66 Explanation: 
Question 67
Out of the following four sentences, select the most suitable sentence with respect to grammar and usage.
A
Since the report lacked needed information, it was of no use to them.
B
The report was useless to them because there were no needed information in it.
C
Since the report did not contain the needed information, it was not real useful to them
D
Since the report lacked needed information, it would not have been useful to them.
       Aptitude       Verbal       GATE 2015 -(Set-2)
Question 67 Explanation: 
(B) there was no needed information
(C) not really useful
(D) would not have been
Question 68
A
I only
B
I and II
C
II and III
D
I and III
       Aptitude       Numerical       GATE 2015 -(Set-2)
Question 68 Explanation: 
If any set of numbers are in a arithmetic sequence and if a common number if added (or) subtracted from each of these numbers, the new set will also be in arithmetic sequence.
Hence, II is an arithmetic sequence.
If the set of numbers is multiplied by the common number, even then the new set will also be in arithmetic sequence.
Hence, I is an arithmetic sequence.
Question 69
 
A
8
B
9
C
7
D
6
       Aptitude       Numerical       GATE 2015 -(Set-2)
Question 69 Explanation: 
h(2,5,7,3) = remainder of (7×3)/(2×5)
= remainder of 21/10
=1
fg(1,4,6,8) = f(1,4,6,8)×g(1,4,6,8)
= max(1,4,6,8) × min(1,4,6,8)
= 8×1
= 8
Question 70
Four branches of a company are located at M, N, O and P. M is north of N at a distance of 4km; P is south of O at a distance of 2 km; N is southeast of O by 1 km. What is the distance between M and P in km?
A
5.34
B
6.74
C
28.5
D
45.49
       Aptitude       Numerical       GATE 2015 -(Set-2)
Question 70 Explanation: 
Question 71
An unordered list contains n distinct elements. The number of comparisons to find an element in this list that is neither maximum nor minimum is
A
Θ(nlog n)
B
Θ(n)
C
Θ(log n)
D
Θ(1)
       Aptitude       Numerical       GATE 2015 -(Set-2)
Question 71 Explanation: 
Consider first three element of the list, atleast one of them will be neither minimum nor maximum. ∴ Θ(1)
Question 72
Extreme focus on syllabus and studying for tests has become such a dominant concern of Indian students that they close their minds to anything _____ to the requirements of the exam
A
related
B
extraneous
C
outside
D
useful
       Aptitude       Verbal       GATE 2015(Set-03)
Question 72 Explanation: 
extraneous -irrelevant or unrelated to the subject being dealt with.
Question 73
A function f(x) is linear and has a value of 29 at x = -2 and 39 at x = 3. Find its value at x = 5.
A
59
B
45
C
43
D
35
       Aptitude       Numerical       GATE 2015(Set-03)
Question 73 Explanation: 
f(x)=2x+33
Question 74
The Tamil version of ________ John Abraham-starrer Madras café ________ cleared by the Censor Board with no cuts last week but the film’s distributors _________ no takers among the exhibitors for a release in Tamil Nadu _________ this Friday.
A
Mr., was, found, on
B
a, was, found, at
C
the, was, found, on
D
a, being, find at
       Aptitude       Verbal       GATE 2015(Set-03)
Question 74 Explanation: 
John-Abraham starrer Madras Café talks about the movie not the person, so Mr. is ruled out. ‘Find no takers’ is not the correct phrase. At this Friday is incorrect. So, option C is correct.
Question 75
If ROAD is written as URDG, then SWAN should be written as:
A
VXDQ
B
VZDQ
C
VZDP
D
UXDQ
       Aptitude       Numerical       GATE 2015(Set-03)
Question 75 Explanation: 
R+3=U, O+3=R, A+3=D, D+3=G;
S+3=V, W+3=Z, A+3=D, N+3=Q.
Question 76
Select the pair that best expresses a relationship similar to that expressed in the pair: Children: Pediatrician
A
Adult: Orthopedist
B
Females: Gynecologist
C
Kidney: Nephrologist
D
Skin: Dermatologist
       Aptitude       verble       GATE 2015(Set-03)
Question 76 Explanation: 
Community of people: Doctor
Question 77
A
2006
B
2007
C
2008
D
2009
       Aptitude       Numerical       GATE 2015(Set-03)
Question 77 Explanation: 
Increase in exports in 2006 = 100 - 70/70 = 42.8%
Increase in imports in 2006 = 120 - 90/90 = 33.3% which is more than any other year.
Question 78
A
P-Home, Q-Power, R-Defense, S-Telecom, T-Finance
B
R-Home, S-Power, P-Defense, Q-Telecom, T-Finance
C
P-Home, Q-Power, T-Defense, S-Telecom, U-Finance
D
Q-Home, U-Power, T-Defense, R-Telecom, P-Finance
       Aptitude       Numerical       GATE 2015(Set-03)
Question 78 Explanation: 
Since U does not want any portfolio, (C) and (D) are ruled out. R wants Home, or Finance or No portfolio, (A) is not valid. Hence option (B) is correct
Question 79
A
x=y-|y|
B
x=-(y-|y|)
C
x=y+|y|
D
x=-(y+|y|)
       Aptitude       Numerical       GATE 2015(Set-03)
Question 79 Explanation: 
Verify which of the options satisfies the x=2 when y=-1.
Then the Answer is x = - (y - |y|)
Question 80
A
(iii) and (iv)
B
(ii) and (iii)
C
(i), (ii) and (iii)
D
(ii) only
       Aptitude       Verbal       GATE 2015(Set-03)
Question 80 Explanation: 
Statement (ii) and (iii) are True.
→ He is unlikely due to lack of requisite temperament ------- (ii) is True
→ He was guilty of throwing away his wicket severral times ------- (iii) is True
Question 81
Alexander turned his attention towards India, since he had conquered Persia. Which one of the statements below is logically valid and can inferred from the above sentence?
A
Alexander would not have turned his attention towards India had he not conquered Persia.
B
Alexander was not ready to rest on his laurels, and wanted to march to India
C
Alexander was completely in control of his army and could command it to move towards India
D
Since Alexander’s kingdom extended to Indian borders after the conquest of Persia, he was keen to move further
       Aptitude       Verbal       GATE 2015(Set-03)
Question 81 Explanation: 
Let X be "Alexander turned his attention towards India"
Y be " he had conquered Persia"
Like that
∼X be "Alexander would not have turned his attention towards India"
then
∼Y be "he had not conquered Persis"
Answer is option A.
Question 82
 
A
adopt to
B
adapt to
C
adept in
D
accept with
       Aptitude       Verbal       GATE 2014(Set-01)
Question 82 Explanation: 
Cope: Deal effectively with something difficult.
(1) Adopt ⇒ Legally take and bring it up as one's own.
(2) Adapt ⇒ Make suitable for a new use or purpose.
(3) Adept ⇒ Very skilled (or) proficienct at something.
(4) Accept ⇒ Believe (or) come to recognize as valid (or) correct.
Option B is correct.
Question 83
A
superb
B
medium
C
mediocre
D
exhilarating
       Aptitude       Verbal       GATE 2014(Set-01)
Question 83 Explanation: 
Mediocre ⇒ Average quality (or) Not very good.
Question 84
In a press meet on the recent scam, the minister said, "The buck stops here". What did the minister convey by the statement?
A
He wants all the money
B
He will return the money
C
He will assume final responsibility
D
He will resist all enquiries
       Aptitude       Verbal       GATE 2014(Set-01)
Question 84 Explanation: 
"The buck stops here" means "The responsibility for something cannot (or) should not passed to someone else.
⇒ It represents that this is the final stage of responsibility.
Question 85
If (z + 1/z)= 98, compute (z2+ 1/z2).
A
96
B
97
C
98
D
99
       Aptitude       Numerical       GATE 2014(Set-01)
Question 85 Explanation: 
z2+1/z2+2∙z∙ 1/z=98⇒z2 + 1/z2=96
Question 86
The roots of ax2+ bx + c = 0 are real and positive. a, b and c are real. Then ax+ b|x|+ c = 0 has
A
no roots
B
2 real roots
C
3 real roots
D
4 real roots
       Aptitude       Numerical       GATE 2014(Set-01)
Question 86 Explanation: 
ax2+bx+c=0
For roots to be real & positive b2-4ac>0
This will have 2 real positive roots.
ax2+b|x|+c=0
Discriminant =b2-4ac>0
ax2+bx+c
(-b)2-4ac
⇒b2-4ac
Is also > 0. This will have real roots.
⇒ This will have 4 real roots.
Question 87
A
The Palghat gap is caused by high rainfall and high temperatures in southern Tamil Nadu and Kerala
B
The regions in Tamil Nadu and Kerala that are near the Palghat Gap are low-lying
C
The low terrain of the Palghat Gap has a significant impact on weather patterns in neighbouring parts of Tamil Nadu and Kerala
D
Higher summer temperatures result in higher rainfall near the Palghat Gap area
       Aptitude       Verbal       GATE 2014(Set-01)
Question 87 Explanation: 
The given passage says that "it results neighbouring regions of Tamilnadu getting more rainfall from the south west monsoon and neighbouring regions of Kerela having higher summer temperatures".
⇒ Option C is suitable option.
Question 88
A
Strategies are now available for eliminating psychiatric illnesses
B
Certain psychiatric illnesses have a genetic basis
C
All human diseases can be traced back to genes and how they are expressed
D
In the future, genetics will become the only relevant field for identifying psychiatric illnesses
       Aptitude       Verbal       GATE 2014(Set-01)
Question 88 Explanation: 
The first sentence can represents the two specific illness depression and schizophernia. ⇒ Option B is the only option that contain illness.
Question 89
Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare.  In addition, groups of 4 or more get a discount of 5% on the total fare.  If the one way single person fare is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs _________.
A
850
B
851
C
852
D
853
       Aptitude       Numerical       GATE 2014(Set-01)
Question 89 Explanation: 
One way fare for a single person = Rs.100
Round trip, there is a discount of 10% of total fare.
Group of 4 or more, Discount of 5% of total fare.
∴ 5 tourists ⇒ Total fare = 5 × 200 = 1000
Total discount = 10% of 1000 + 5% of 1000
= 100 + 50
= ₹150
∴ Fare charged = 1000 - 150 = ₹850
Question 90
 
A
48
B
49
C
50
D
51
       Aptitude       Numerical       GATE 2014(Set-01)
Question 90 Explanation: 
Total respondents = 300
[No. of respondents who do not own a scooter] = [No. of respondents who own's only a car + No. of respondents who do not own any vehicle]
= 40 + 34 + 70
= 144
Percentage = 144/300 × 100 = 48%
Question 91
When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? _____________
A
6
B
7
C
8
D
9
       Aptitude       Numerical       GATE 2014(Set-01)
Question 91 Explanation: 
Tetrahedron is a pyramid like structure with 4 corner points (vertical).
→ If you take a point inside a tetrahedron, then you have 5 points.
→ An internal plane is formed by joining any of the three points.
→ No. of planes = 5 C 3 = 10
But 4 of them will be faces of tetrahedron.
∴ New planes = 10 - 4 = 6
Question 92
A
∀x:glitters(x) ⇒¬gold(x)
B
∀x:gold(x) ⇒glitters()
C
∃x: gold(x)∧¬glitters(x)
D
∃x:glitters(x)∧¬gold(x)
       Aptitude       Numerical       GATE 2014(Set-01)
Question 92 Explanation: 
Method 1:
Not all that glitters is gold.
Option A:
∀x:glitters(x) ⇒¬gold(x)
which means that every item (x), which glitters is not gold.
Option B:
∀x:gold(x) ⇒glitters()
Every item (x) which is gold is a glitter.
(or)
Every golden item glitters.
Option C:
∃x: gold(x)∧¬glitters(x)
There are some gold items which does not glitters.
Option D:
∃x:glitters(x)∧¬gold(x)
There exists some glitters which are not gold.
(or)
Not all glitters are gold.

The answer is Option (D).
Method 2:

⇒ (∼∀x) (∼ (glitters(x) ⇒ gold(x))
⇒ ∃x (∼ (∼glitters(x) ∨ gold(x))
⇒ ∃x (glitters ∧ gold(x))
Question 93
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
A
0.25
B
0.26
C
0.27
D
0.28
       Aptitude       Numerical       GATE 2014(Set-01)
Question 93 Explanation: 
We break a unit length rod into two pieces at a uniformly chosen point.

If we break at point x, length of the one piece x and the other piece is 1 – x.
Length of the shorter stick is between 0 to 0.5. If it is more than 0.5 then it will be longer stick.
The random variable (l) follows a uniform distribution. The probability function of l is
1/(b-a)=1/(0.5-0)=2 (length is between 0 to 0.5)
Expected value of length
(where P(l) is the probability density function)
Question 94
A
1
B
2
C
3
D
4
       Aptitude       Numerical       GATE 2014(Set-01)
Question 94 Explanation: 
Given:
3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x – 2y + 7z = 0
This is a non-homogeneous equation system.
The Augmented matrix for above set of equations is

For matrix (A):
R4→ R4+R1

R4→ R4-R2

Rank = 3
For matrix (AB):

R4→(R4+R1 )-R2

Rank = 3
Rank of (A) = Rank (AB), so Unique solution
rank = 3 = no. of variables
Working Rule for Non-homogeneous equation:
(1) rank (A) < rank (AB), Inconsistent solution
(2) is rank (A) = rank (AB) = r then
if r = n, Unique solution
r < n, Infinite solution
Question 95
A
It was a former British colony
B
Indian Information Technology professionals have colonized the world
C
India does not follow any colonial practices
D
India has helped other countries gain freedom
       Aptitude       Verbal       Gate 2014 Set -02
Question 95 Explanation: 
India is a post-colonial (or) existing after the end of cononial rule.
India is a post-colonial country because "It was a former British colony" that means if a country is called post colonial then it came into existence after the colonies rules and it can become a independent.
Question 96
Who ___________ was coming to see us this evening?
A
you said
B
did you say
C
did you say that
D
had you said
       Aptitude       Verbal       Gate 2014 Set -02
Question 96 Explanation: 
From the given options, option B is make the sentence to be fullfilled.
Question 97
A
1 : S, 2 : P, 3 : Q, 4 : R
B
1 : P, 2 : Q, 3 : R, 4 : S
C
1 : Q, 2 : R, 3 : S, 4 : P
D
1 : S, 2 : P, 3 : R, 4 : Q
       Aptitude       Verbal       Gate 2014 Set -02
Question 97 Explanation: 
Eradicate = destroy utterly
Distort = misrepresent
Saturate = Soak completely
Utilize = use
Question 98
What is the average of all multiples of 10 from 2 to 198?
A
90
B
100
C
110
D
120
       Aptitude       Numerical       Gate 2014 Set -02
Question 98 Explanation: 
Average of 10, 20, 30, ..., 180, 190
Average = 10+20+30+...+180+190 / 19 = (19/2 [10+190]) / 19 = 100
Question 99
 
A
3.464
B
3.932
C
4.000
D
4.444
       Aptitude       Numerical       Gate 2014 Set -02
Question 99 Explanation: 
Let,

Squaring on both sides,
x2 = 12+x
x2 - x - 12 = 0
(x-4) (x+3) = 0
∴ x = 4 (x ≠ -3)
Question 100

The old city of Koenigsberg, which had a German majority population before World War 2, is now called Kaliningrad.  After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the Baltic Sea on the north and the countries of Poland to the south and west and Lithuania to the east respectively.  Which of the statements below can be inferred from this passage?

A
Kaliningrad was historically Russian in its ethnic make up
B
Kaliningrad is a part of Russia despite it not being contiguous with the rest of Russia
C
Koenigsberg was renamed Kaliningrad, as that was its original Russian name
D
Poland and Lithuania are on the route from Kaliningrad to the rest of Russia
       Aptitude       Verbal       Gate 2014 Set -02
Question 100 Explanation: 
Kaliningrad is a part of Russia despite it not being contiguous with rest of Russia because it is surrounded by countries of Poland in the south and west, Lithuania in the east and Baltic sea on north, and it has a predominantly Russian population.
Question 101
A
A high proportion of the affected population has returned from neighbouring countries where dengue is prevalent
B
More cases of dengue are now reported because of an increase in the Municipal Office’s administrative efficiency
C
Many more cases of dengue are being diagnosed this year since the introduction of a new and effective diagnostic test
D
The number of people with malarial fever (also contracted from mosquito bites) has increased this year
       Aptitude       Verbal       Gate 2014 Set -02
Question 101 Explanation: 
Malarial fever and dengue fever both are contracted from mosquito bites. So as the mosquito population has increased then the number of people suffering from dengue and malarial fever also increased.
Question 102
If x is real and |x2 - 2x + 3| = 11, then possible values of |- x3 + x2 - x| include
A
2, 4
B
2, 14
C
4, 52
D
14, 52
       Aptitude       Numerical       Gate 2014 Set -02
Question 102 Explanation: 
Given,
|x2 - 2x + 3| = 11, x is real
x2-2x+3 = 11
x2-2x+8 = 0
(x-4)(x+2) = 0
x = 4, -2
x2-2x+3 = -11
x2-2x+14 = 0
x is not real in this case.
|-x3+x2-x|
when x=-2
⇒ |-(-2)3+(-2)2-(-2)|
= |(-(8) + (4) + 2| = 14
x=4
⇒ |-(4)3+(4)2-(4)|
= |-64 + 16 -4|
= 52
Possible values of |-x3+x2-x| include 14, 52.
Question 103
   
A
140
B
141
C
142
D
143
       Aptitude       Numerical       Gate 2014 Set -02
Question 103 Explanation: 
Number of male in 2008 = x
Number of female in 2008 = y
Number of female in 2009 = 2y
Given,
x/y = 2.5 ⇒ y = 2x/5
Let, number of male in 2009 = M
Given, M/2y = 3
M/2(2x/5) = 3 ⇒ M = 12x/5
Percentage increase = M-x/x × 100
= 12x/5-x/ x × 100
= 7/5 × 100
= 140%
Question 104
At what time between 6 a.m. and 7 a.m. will the minute hand and hour hand of a clock make an angle closest to 60°?
A
6:22 am
B
6:27 am
C
6:38 am
D
6:45 am
       Aptitude       Numerical       Gate 2014 Set -02
Question 104 Explanation: 
At 6 a.m., the angle between minute hand and hour hand is 180°.
And for every minute, the angle between them decreases by 6° - (1/2)° = 5 (1/2)°
∴ For the angle to be closest to 60°, the angle must be reduced by atmost 120°.
1 min - 5(1/2)°
x min - 120°
x = 2/11 × 120 = 240/11 = 21.81 m ≈ 22 min
i.e. 6.22 a.m. the angle between minute hand and hour hand will be closest to 60°.
Question 105
A
I
B
II
C
III
D
IV
       Aptitude       Verbal       Gate 2014 Set -03
Question 105 Explanation: 
Losing consiousness represents that it is a continuous process of losing the consiousness. It is not appropriate, he just lost the consiousness.
Question 106
If she _____________ how to calibrate the instrument, she ______________ done the experiment.
A
knows, will have
B
knew, had
C
had known, could have
D
should have known, would have
       Aptitude       Verbal       Gate 2014 Set -03
Question 106 Explanation: 

Rule: If + past perfect then result to be perfect conditional (or) perfect continuous condition.
Then answer is Option C.
Question 107
Choose the word that is opposite in meaning to the word “coherent”.
A
sticky
B
well-connected
C
rambling
D
friendly
       Aptitude       Verbal       Gate 2014 Set -03
Question 107 Explanation: 
Coherent = logical and consistent
Rambling = lengthy and confused (or) inconsequential
Question 108
A
17
B
37
C
64
D
26
       Aptitude       Numerical       Gate 2014 Set -03
Question 108 Explanation: 
2,5, 10, 17, 26, 37, 50, 64
2 = 12+1
5 = 22+1
10 = 32+1
17 = 42+1
26 = 52+1
37 = 62+1
50 = 72+1
64 = 82+0
64 does not belong to the series.
Question 109
A
1.34
B
1.74
C
3.02
D
3.91
       Aptitude       Numerical       Gate 2014 Set -03
Question 109 Explanation: 
Number of students = 21+17+6 (or) 15+27+2 (or) 23+18+3 = 44
Total marks obtained = (21×2)+(15×3)+(23×2) = 133
Average marks = 133/44 = 3.02
Question 110
A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is  
A
Students should come at 9.00 a.m. and parents should come at 10.00 a.m.
B
Participating students should come at 9.00 a.m. accompanied by a parent, and other parents
and students should come by 10.00 a.m.
C
Students who are not participating should come by 10.00 a.m. and they should not bring their
parents. Participating students should come at 9.00 a.m.
D
Participating students should come before 9.00 a.m. Parents who accompany them should
come at 9.00 a.m. All others should come at 10.00 a.m.
       Aptitude       Numerical       Gate 2014 Set -03
Question 110 Explanation: 
Students who are particularly in the program and they need to come an hour earlier i.e., 09.00 am because the program is start of 10.00 am.
→ All other students and parents should come in time for the programme i.e. 10.00 am.
→ Option B is correct answer.
→ In option D, they gave, all other should come at 10.00 am that includes student's parents, staff and all ohers. So this is not correct option.
Question 111
A
(i), (ii) and (iv)
B
(iii) only
C
(i) and (iv)
D
(iv) only
       Aptitude       Verbal       Gate 2014 Set -03
Question 111 Explanation: 
Paradign shift means a fundamental change in approach to something. This change, as per the question, was verified with the experimental measurements of the position of a star that was behind the sun.
(i) is incorrect as it generalizes the experimental evidence of the star and assumes it to be always true, which may not be the case every time.
(ii) and (iii) is anyway wrong.
Hence, answer is option (D).
Question 112
The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate.  During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/ USD to Rs. 60/ USD. India’s GDP in USD during the period 2012-2013
A
increased by 5%
B
decreased by 13%
C
decreased by 20%
D
decreased by 11%
       Aptitude       Numerical       Gate 2014 Set -03
Question 112 Explanation: 
Let,
GDP in rupees = x
GDP in dollars = x/50
Increase in GDP in rupees = 7%
∴ New GDP in rupees = 1.07x
New GDP in dollars = 1.07x/60
Change = ((1.07x/60) - (x/50))/(x/50) = -6.5/60 = -10.83%
As it is negative, the value has decreased.
GDP in VSD has decreased by 11%.
Question 113
 
A
1:1
B
2:1
C
1.5:1
D
2.5:1
       Aptitude       Numerical       Gate 2014 Set -03
Question 113 Explanation: 
Given,
Male to female students ratio in 2011 = 1 : 1
Male to female students ratio in 2012 = 1.5 : 1 = 3 : 2

⇒ M1/F1 = 1:1
M1 = F1 ------- (1)
⇒ M2/F2 = 1:1
2M2 = 3F2 ------- (2)
Given,
F1 = F2 ------- (3) From (1) & (2)
M1/M2 = F1/(3F2/2) = 2F1/3F2
But from (3)
M1/M2 = 2/3
We need to find
M2 : M1 = 3 : 2 = 1.5 : 1
Question 114
Consider the equation: (7526)8 - (Y)= (4364)8, where (X)N stands for X to the base N. Find Y.
A
1634
B
1737
C
3142
D
3162
       Aptitude       Numerical       Gate 2014 Set -03
Question 114 Explanation: 
(7526)8 - (Y)8 = (4364)8
⇒ 1/8 = (7526)8 - (4364)8
Base 8 ⇒ 0 to 7 digits

When you are borrowing you will add the value of the base, hence 2 becomes (2+8) = 10
Y = 3142
Question 115
A
Highest
B
Lowest
C
Medium
D
Integration
       Aptitude       Verbal       Gate 2013
Question 115 Explanation: 
Nadir = The lowest (or) most unsuccessful point in a situation.
Question 116
A
specificity
B
neutrality
C
generality
D
adaptation
       Aptitude       Verbal       Gate 2013
Question 116 Explanation: 
Universalism = The belief that all human kind will eventually be saved.
Particularism = Exclusive attachment to one's own group, party (or) Nation.
Diffuseness = The spatial property of being spread out over a wide area (or) through a large volume.
Specificity = The quality of belonging (or) relating uniquely to a particular subject.
Question 117
What will be the maximum sum of 44, 42, 40, ...... ?
A
502
B
504
C
506
D
500
       Aptitude       Numerical       Gate 2013
Question 117 Explanation: 
44, 42, 40, ......
44, 42, 40, ...... 0
2(22 + 21 + 20 + …. 1)
Sum(n)=(n(n+1))/2=(22×23)/2=253
⇒2(253)
=506
Question 118
Were you a bird, you ______________ in the sky.
A
would fly
B
shall fly
C
should fly
D
shall have flown
       Aptitude       Verbal       Gate 2013
Question 118 Explanation: 
Were you a bird, you would fly in the sky.
Question 119
Choose the grammatically INCORRECT sentence:
A
He is of Asian origin.
B
They belonged to Africa.
C
She is an European.
D
They migrated from India to Australia.
       Aptitude       Verbal       Gate 2013
Question 119 Explanation: 
"She is an European"
→ We can't use "an" infront of European. It can be pronounced as European. Here E is silent.
→ So, option C is the answer
Question 120
A
7
B
8
C
9
D
10
       Aptitude       Numerical       Gate 2013
Question 120 Explanation: 

Multiply on numerator & denominator

=-1+9
=8
Question 121
Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?
A
13/90
B
12/90
C
78/90
D
77/90
       Aptitude       Numerical       Gate 2013
Question 121 Explanation: 
⇨ Total number of 2 digit numbers from 1 to 100 = 90
⇨ Find which can be divisible by 7 upto 100
14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98
Total = 13
Probability of divisible by 7 is = 13/90
Which can’t be divisible by 7 is
⇒ 1 – (probability of divisible by 7)
⇒ 1 – (13/90)
⇒ 77/90
Question 122
A
Failure is the pillar of success.
B
Honesty is the best policy.
C
Life begins and ends with adventures.
D
No adversity justifies giving up hope.
       Aptitude       Verbal       Gate 2013
Question 122 Explanation: 
Option A, B, C are not able to given correct sense about the information.
Option D is related to the given information.
Question 123
A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is
A
36
B
30
C
24
D
18
       Aptitude       Numerical       Gate 2013
Question 123 Explanation: 

Let ‘x’ be the total distance,
Speed = distance/ time
Total speed = (total distance)/(total time); Time =distance/speed
Time taken for train journey = (x⁄2)/60kmph=x/120
Time taken for bus journey = (x⁄4)/30kmph=x/120
Time taken for cycle journey = (x⁄4)/10kmph=x/40
Total time = x/120+x/120+x/40=5x/120
Total speed = (total distance)/(total time)=x/(5x⁄120)=(120×x)/5x=24kmph
Question 124
The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs. is
A
16,500
B
15,180
C
11,000
D
10,120
       Aptitude       Numerical       Gate 2013
Question 124 Explanation: 
Current wages is increased by (1/5) ⇒ 1+1/5 ⇒ 6/5
Working hours decreased by (1/24) ⇒ 1-1/24 ⇒ 23/24
The new cost of erection = 13,200 × 6/5 × 23/24 =15,180
Question 125
The cost function for a product in a firm is given by 5q2, where q is the amount of production. The firm can sell the product at a market price of ₹50 per unit. The number of units to be produced by the firm such that the profit is maximized is
A
5
B
10
C
15
D
25
       Aptitude       Numerical       Gate 2012
Question 125 Explanation: 
Total selling price =50q
Profit = 50q - 5q2
This is maximum at q = 5.
Question 126
A
attempts
B
setbacks
C
meetings
D
delegations
       Aptitude       Verbal       Gate 2012
Question 126 Explanation: 
Setback = a reversal (or) setback in a progress (or) something that happens that delays
Despite several setbacks the mission succeeded in its attempt to resolve the conflict.
Question 127
A
Diminish
B
Divulge
C
Dedicate
D
Denote
       Aptitude       Verbal       Gate 2012
Question 127 Explanation: 
Mitigate = make (something bad) less severe, serious (or) painful
Synonyms = Diminish, alleviate, reduce etc.
Question 128
Choose the grammatically INCORRECT sentence:
A
They gave us the money back less the service charges of Three Hundred rupees.
B
This country’s expenditure is not less than that of Bangladesh.
C
The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser sum.
D
This country’s expenditure on educational reforms is very less.
       Aptitude       Verbal       Gate 2012
Question 128 Explanation: 
The country's expenditure on educational reforms is very less.
In the sentence "very less" is incorrect instead of this we use "much less" or else "very little".
Question 129
A
that
B
which
C
who
D
whom
       Aptitude       Verbal       Gate 2012
Question 129 Explanation: 
Suresh's dog is the one that was hurt in the stampede.
that can refer groups of things.
who can refer to people.
which can introduces a non-essential clause.
whom can refer to object of a verb (or) preposition.
Question 130
 
A
Gender-discriminatory
B
Xenophobic
C
Not designed to make the post attractive
D
Not gender-discriminatory
       Aptitude       Verbal       Gate 2012
Question 130 Explanation: 
Xenephobic which refers to having (or) showing a dislike of or prejudice against people from other countries.
Question 131
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x - 0.1x2 where y is the height of the arch in meters. The maximum possible height of the arch is
A
8 meters
B
10 meters
C
12 meters
D
14 meters
       Aptitude       Numerical       Gate 2012
Question 131 Explanation: 
Given,
y = 2x - 0.1x2
Differentiating both sides,
dy/dx = 2 - 0.2x
For maximum, dy/dx = 0
2 - 0.2x = 0
0.2x = 2
x = 10
Question 132
 
A
0.288
B
0.334
C
0.667
D
0.720
       Aptitude       Numerical       Gate 2012
Question 132 Explanation: 
Probability that a shock absorber from X is reliable = 0.6×0.96 = 0.576
Probability that a shock absorber from Y is reliable = 0.4×0.72 = 0.288
Probability that a randomly selected reliable absorber is from Y is = 0.288/(0.576+0.288) = 0.334
Question 133
   
A
P, Q
B
Q, R
C
P, R
D
R, S
       Aptitude       Numerical       Gate 2012
Question 133 Explanation: 
If a value of 'x' is addered (or) multiplied to everagery element in the list, the average also changes by same value.
⇒ P, R are correct
Question 134
Given the sequence of terms: AD  CG  FK  JP, the next term is
A
OV
B
OW
C
PV
D
PW
       Aptitude       Numerical       Gate 2012
Question 134 Explanation: 

OV is the next term.
Question 135
If Log (P) = (1/2) Log (Q) = (1/3) Log (R), then which of the following options is TRUE?  
A
P2 = Q3R2
B
Q2 = PR
C
Q2 = R3P
D
R = P2Q2
       Aptitude       Numerical       Gate 2011
Question 135 Explanation: 
logP = 1/2 logQ = 1/3 log (R) = k
∴ P = bk, Q = b2k, R = b3k
Now, Q2 = b4k = b3k bk = PR
Question 136
 
A
to visit
B
having to visit
C
visiting
D
for a visit
       Aptitude       Verbal       Gate 2011
Question 136 Explanation: 
Contemplate is a transitive verb and hence is followed by a gerund Hence the correct usage of contemplate is verb + ing form.
Question 137
 
A
hyperbolic
B
restrained
C
argumentative
D
indifferent
       Aptitude       Verbal       Gate 2011
Question 137 Explanation: 
the tone of the sentence clearly indicates a word that is similar to understated is needed for the blank. Alternatively, the word should be antonym of strong (fail to make strong impression). Therefore, the best choice is restrained which means controlled/reserved/timid.
Question 138
 
A
merge
B
split
C
collect
D
separate
       Aptitude       Verbal       Gate 2011
Question 138 Explanation: 
Amalgamate means combine or unite to form one organization of structure. So the best option here is spilt. Separate on the other hand, although a close synonym, it is too general to be the best antonym in the given question while Merge is the synonym; Collect is not related.
Question 139
 
A
Incomprehensible
B
Indelible
C
Inextricable
D
Infallible
       Aptitude       Verbal       Gate 2011
Question 139 Explanation: 
Inexplicable means not explicable; that cannot be explained, understood, or accounted for. So the best synonym here is incomprehensible.
Question 140
 
A
P
B
Q
C
R
D
S
       Aptitude       Numerical       Gate 2011
Question 140 Explanation: 
By observation of the table, we can say S
Question 141
The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?  
A
5
B
4
C
7
D
6
       Aptitude       Numerical       Gate 2011
Question 141 Explanation: 
Checking with all options in formula: (4q+100/q) i.e. (V+F). Option A gives the minimum cost.
Question 142
A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?
A
4
B
5
C
6
D
7
       Aptitude       Numerical       Gate 2011
Question 142 Explanation: 
Let each truck carry 100 units.
2800 = 4n + e; n = normal
300 = 10n + 2; e = excess/pending
n = 100/3, e = 8000/3
5 days: 500 ×(5⋅100/3)+ 8000/3
Minimum possible = 6
Question 143
A container originally contains 10 litres of pure spirit. Form this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?
A
7.58 litres
B
7.84 litres
C
7 litres
D
7.29 litres
       Aptitude       Numerical       Gate 2011
Question 143 Explanation: 
10(729/1000×1=7.29 litres)
Question 144
 
A
how to write a letter of condolence
B
what emotional stages are passed through in the healing process
C
what the leading causes of death are
D
how to give support to a grieving friend
       Aptitude       Verbal       Gate 2011
Question 144 Explanation: 
The given passage clearly deals with how to deal with bereavement and grief and so after the tragedy occurs and not about precautions. Therefore, irrespective of the causes of death, a school student, rarely gets into details of causes–which is beyond the scope of the context. Rest all the important in dealing with grief.
Question 145
A
masked
B
belied
C
betrayed
D
suppressed
       Aptitude       Verbal       2010
Question 145 Explanation: 
Masked - opposite to given
Belied - Not appropriate to given
Betrayed - Most appropriate to given (Reveal intentionally)
Suppressed - Irrevalent to given
Answer is option C.
Question 146
Which of the following options is closest in meaning to the word Circuitous.
A
cyclic
B
indirect
C
confusing
D
crooked
       Aptitude       Verbal       2010
Question 146 Explanation: 
Synonyms for Circuitous are indirect, oblique, winding, meandering etc.
Question 147
A
uphold
B
restrain
C
cherish
D
conserve
       Aptitude       Verbal       2010
Question 147 Explanation: 
Uphold - cause to remain
Restrain - keep under control
Cherish - befond of
Conserve - protect from harm i.e., keeping safety, loss of destruction
Answer is option d.
Question 148
25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:
A
2
B
17
C
13
D
3
       Aptitude       Numerical       2010
Question 148 Explanation: 

Total number of persons = a+b+c = 25 → (1)
Number of persons who play hockey = a+b = 15 → (2)
Number of persons who play football = b+c = 17 → (3)
Number of persons who play hockey and football = b = 10 → (4)
From (2) ⇒ a=5
From (3) ⇒ c=7
From (1) ⇒ d = 3
Number of persons who play neither hockey nor football = d = 3
Question 149
 
A
fallow: land
B
unaware: sleeper
C
wit: jester
D
renovated: house
       Aptitude       Verbal       2010
Question 149 Explanation: 
→ A worker who is working is called unemployed.
→ Same as a land which is not used called fallow.
Question 150
If 137+276 = 435 how much is 731+672?
A
534
B
1403
C
1623
D
1513
       Aptitude       Numerical       2010
Question 150 Explanation: 
Let, base = x
(137)x + (276)x = (435)x
x2 + 3x + 7 + 2x2 + 7x + 6 = 4x2 + 3x + 5
x2 - 7x - 8 = 0
x = 8 (or) -1
∴ x = 8 (-1 cannot be a base)
(731)x + (672)x = (731)8 +( 672)8
= 7 × 82 + 3× 8 + 1×1 + 6 × 82 + 7 × 8 + 2 × 1
= 915
From the options, 915 can be written as 1623 in base 8.
Question 151
   
A
HSIG
B
SGHI
C
IGSH
D
IHSG
       Aptitude       Numerical       2010
Question 151 Explanation: 
Let us solve using option elimination approach .
Option A: HSIG
from (ii) , we can say that Gita and Saira are successive siblings.
Hence, option A is not true.
Option C: IGSH

In any of the above 4 cases, (i) is not true.
Hence, option C is not true.
Option D: IHSG

In any of the above 4 cases, (i) is not true.
Hence, option D is not true.
Option B: SGHI

In last two cases, all the facts are true.
∴ The order is SGHI.
Question 152
 
A
Modern warfare has resulted in civil strife.
B
Chemical agents are useful in modern warfare.
C
Use of chemical agents in warfare would be undesirable.
D
People in military establishments like to use chemical agents in war.
       Aptitude       Verbal       2010
Question 152 Explanation: 
→ People in military establishments like to use chemical agents in war.
Question 153
5 skilled workers can build a wall in 20 days: 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?
A
20
B
10
C
16
D
15
       Aptitude       Numerical       2010
Question 153 Explanation: 
5 skilled workers can build the wall in 20 days ⇒ 1 skilled worker can build the wall in 100 days
Capacity = 1/100
8 semi-skilled workers can build the wall in 25 days
⇒ 1 semi-skilled worker can build the wall in 200 days
Capacity = 1/200
10 un-skilled workers can build the wall in 30 days
⇒ 1 un-skilled worker can build the wall in 300 days
Capacity = 1/300
1 day work (2 skilled + 6 semi-skilled + 5 unskilled) = 2(1/100) + 6(1/200) + 5(1/300) = 1/15
∴ They can complete the work in 15 days.
Question 154
Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?
A
50
B
51
C
52
D
54
       Aptitude       Numerical       2010
Question 154 Explanation: 
Greater than 3000
⇒ First digit: 3 or 4
(i) First digit - 3:
We have to choose 3 digits from (2, 2, 3, 3, 4, 4, 4, 4).
Any place can have either 2 or 3 or 4, but (222, 333) is not possible as we have only two 2's and two 3's.
Total = 3 × 3 × 3 - 2 = 25
(ii) First digit - 4:
We have to choose 4 digits from (2, 2, 3, 3, 4, 4, 4, 4).
Any place can have either 2 or 3 or 4, but (222) is not possible we have only two 2's.
Total = 3 × 3 × 3 - 1 = 26
∴ Total number possible = 25 + 26 = 51
Question 155

In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?

A
B
C
D
       Aptitude       Numerical       Gate 2004-IT
Question 155 Explanation: 
Let us consider total no. of families = 100
In that 50% of families having 3 childrens
i.e., 50×3 = 150 (No. of children)
→ Likes that 30% have 2 childrens = 30×2 = 60
→ 20% have 1 children = 20×1 = 20
Probability of choosing a children the family have two children
= 60/(150+60+20) = 60/230 = 6/23
Question 156

In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 students have taken Computer Organization course; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Data Structures and Computer Organization; 30 students have taken both Data Structures and Computer Organization, 15 students have taken all the three courses.How many students have not taken any of the three courses?

A
15
B
20
C
25
D
35
       Aptitude       Numerical       Gate 2004-IT
Question 156 Explanation: 
n = 200
PL = 125
DS = 85
CO = 65
PL & DS = 50
DS & CO = 35
CO & PL = 30
PL & DS & CO = 15

⇒ Not taken any course = 200 - (60 +15+15+35+15+15+20)
= 200 - 175
= 25
There are 156 questions to complete.