## Aptitude

 Question 1

Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs 150 more. The cost of the gift was Rs. _____.

 A 12000 B 666 C 3000 D 6000
Aptitude       Verbal       GATE 2019
Question 1 Explanation:
Total no. of friends = 10
When two people are not going to contribute then remaining friends have to pay Rs 150 more.
Two friends contribution = 150 × 8 = 1200
One friend contribution = 600
Ten friends contribution = 6000
Cost of the Gift = 6000

Out of ten members two members are not able to pay their share.
So, two members amount was paid by remaining eight members.
Then the eight members has to pay 150 more, which is 150*8= 1200( two persons share).
One person share= 1200/2=600.
Ten members share= 600*10= 6000.
 Question 2

The expenditure on the project _____ as follows; equipment Rs.20 lakhs, salaries Rs.12 lakhs, and contingency Rs.3 lakhs.

 A break down B break C breaks down D breaks
Aptitude       Verbal       GATE 2019
Question 2 Explanation:
Breaks down means separated (or) classify the thing into smaller parts.
 Question 3

The search engine's business model _____ around the fulcrum of trust.

 A bursts B revolves C sinks D plays
Aptitude       Verbal       GATE 2019
Question 3 Explanation:
Revolves: Treat as the most important element.
 Question 4

Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 Km/h and the speed of the second car is 60 Km/h. The number of hours it takes for the distance between the two cars to be 20 Km is _____.

 A 2 B 3 C 1 D 6
Aptitude       Numerical       GATE 2019
Question 4 Explanation:
Speed of the first car = 50 km/h
Speed of the second car = 60 km/h
Let no. of hours = x say
⇒ From the question we can write
(60)x - (50)x = 20
10x = 20
∴ x = 2 hrs
 Question 5

A court is to a judge as _____ is to a teacher.

 A a syllabus B a student C a punishment D a school
Aptitude       Verbal       GATE 2019
Question 5 Explanation:
A court is to a judge as a school is to a teacher.
 Question 6

In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only in the Maths club, 40 students are in both Drama and Dance clubs, 12 students are in both Dance and Maths clubs, 7 students are in both Drama and Maths club, and 2 students are in all the clubs. If 75% of the students in the college are not in any of these clubs, then the total number of students in the college is _____.

 A 900 B 975 C 225 D 1000
Aptitude       Numerical       GATE 2019
Question 6 Explanation: No. of students present in three student clubs
= 60 + 80 + 30 + 38 + 2 + 10 + 5
= 225 [i.e., 25% of the students in the college]
Total no. of students in the college = 225 × 4 = 900
 Question 7

The police arrested four criminals - P, Q, R and S. The criminals knew each other. They made the following statements:

P says "Q committed the crime."
Q says "S committed the crime."
R says "I did not do it."
S says "What Q said about me is false."

Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?

 A P B Q C R D S
Aptitude       Verbal       GATE 2019
Question 7 Explanation:
⇒ I true: 'Q' is Criminal
II, III, IV are false.
II is false: 'S' is not criminal.
IV is also false: 'S' committed crime.
There is conflict among I, IV now as P, S both should be criminals.
⇒ II true: 'S' is criminal.
I, III, IV are false.
IV is false. So, 'S' is not criminal.
III is false. So. 'R' is criminal.
There is conflict among II, III as S, R both should be criminal.
III is true: Criminal ≠ R.
I, II, IV are false.
I is false. So, 'Q' is also not criminal.
II is false. So, 'S' is not criminal.
IV is false. So, 'S' is not criminal.
Q, R, S are not criminals. So, 'P' is criminal.
IV is true: I, II, III are false.
II is false. So, 'S' is not criminal.
IV is true. So, 'S' is criminal.
I is false. So, 'Q' is not criminal.
III is false. So, 'R' is criminal.
There is conflict, as R, S both should be criminals.
 Question 8

"A recent High Court judgement has sought to dispel the idea of begging as a disease — which leads to its stigmatization and criminalization — and to regard it as a symptom. The underlying disease is the failure of the state to protect citizens who fall through the social security net."

Which of the following statements can be inferred from the given passage?

 A Beggars are created because of the lack of social welfare schemes B Beggars are lazy people who beg because they are unwilling to work C Begging is an offence that has to be dealt with firmly D Begging has to be banned because it adversely affects the welfare of the state
Aptitude       Verbal       GATE 2019
Question 8 Explanation:
Beggars are created because of the lack of social welfare scheme.
The court is judged that because of failure of the state to protect citizens through social security schemes beggars are created.
 Question 9

Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests.

Request by X: Due to pollen allergy, I want to avoid a wing next to the garden.
Request by Y: I want to live as far from the washrooms as possible, since I am very sensitive to smell.
Request by Z: I believe in Vaastu and so want to stay in the South-west wing.

 A B C D Aptitude       Numerical       GATE 2019
Question 9 Explanation:
Consider Option D, which satisfies all the given three statements.
 Question 10

In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectngle. Out of the total number of the people, the percentage of administrators shall be in the range of _____. A 16 to 30 B 0 to 15 C 46 to 60 D 31 to 45
Aptitude       Numerical       GATE 2019
Question 10 Explanation: From the given diagram: Total no. of people = 70 + 10 + 20 + 20 + 40 = 160
% of Administrators = 50/160 = 31.25
 Question 11

“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 11 Explanation: Question 12

"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 12 Explanation:
Meandering means "Proceeding in a convoluted way (or) undirected fashion".
 Question 13

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 13 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 14

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 14 Explanation: 2 × 6 = 12
12 × 5 = 60
60 × 4 = 240
240 × 3 = 720
720 × 2 = 1440 1440 × 0 = 0
 Question 15

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 15 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 16

If pqr ≠ 0 and 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 16 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 17

In the figure below, ∠DEC + ∠BFC is equal to Aptitude       Numerical       GATE 2018
Question 17 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
→ ∠BCD - ∠BAD = ∠1 - ∠2
= ∠5 + ∠3 + ∠2 - ∠2
= ∠ 5 + ∠3
= ∠DEC + ∠BFC
 Question 18

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 18 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 19

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 19 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 20

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 20 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 21

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-1]
Question 21 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 22

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-1]
Question 22 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 23

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-1]
Question 23 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 24

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-1]
Question 24 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 25

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-1]
Question 25 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 26

“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-1]
Question 26 Explanation:
The author is explaining about the colonial past.
That represents the history of nationalism.
 Question 27

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-1]
Question 27 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 28

The expression 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-1]
Question 28 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 < y
⇒ |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 29

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-1]
Question 29 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 - 2P2
= 3! + 3! - 2!
= 10
∴ Required number of ways = 24 - 10 = 14
 Question 30

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot. If in a flood, the water level rises to 525 m, which of the villages P, Q, R, S, T get submerged? A P, Q B P, Q, T C R, S, T D Q, R, S
Aptitude       Numerical       GATE 2017 [Set-1]
Question 30 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 31

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-2]
Question 31 Explanation:
Yielding means produce (or) provide (a natural, agricultural or industrial product).
Resistant means offering a resistance to something or someone.
 Question 32

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-2]
Question 32 Explanation:
In this question enough is used with bright, where bright is an adjective.
So, here we use bright enough to complete the sentence.
 Question 33

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-2]
Question 33 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 34

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-2]
Question 34 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 35

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-2]
Question 35 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 36

“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-2]
Question 36 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 37

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-2]
Question 37 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 38

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-2]
Question 38 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 39

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-2]
Question 39 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 40

An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot. If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?

 A P B Q C R D S
Aptitude       Numerical       GATE 2017 [Set-2]
Question 40 Explanation:
Region R can have more air pressure as compared to other regions because it has maximum number of lines crossing the area.
 Question 41

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       GATE 2016 [Set-1]
Question 41 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 42

A rewording of something written or spoken is a ______________.

Aptitude       verbal       GATE 2016 [Set-1]
Question 42 Explanation:
Paraphrase means that "express the meaning of (something written or spoken) using different words.
 Question 43

Archimedes said, “Give me a lever long enough and a fulcrum on which to place it, and I will move the world.”

The sentence above is an example of a ___________ statement.

 A figurative B collateral C literal D figurine
Aptitude       verbal       GATE 2016 [Set-1]
Question 43 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 44

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       GATE 2016 [Set-1]
Question 44 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 45

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       GATE 2016 [Set-1]
Question 45 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 46

A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The table below shows the numbers of each razor sold in each quarter of a year. Which product contributes the greatest fraction to the revenue of the company in that year?

 A Elegance B Executive C Smooth D Soft
Aptitude       Numerical       GATE 2016 [Set-1]
Question 46 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 47

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 Linguistic pluralism is the only indicator of a nation’s diversity. D Linguistic pluralism is strong evidence of India’s diversity.
Aptitude       verbal       GATE 2016 [Set-1]
Question 47 Explanation:
Which is inferred from the statement.
Option A, B, C are incorrect which are not properly inferred from the statement.
 Question 48

Consider the following statements relating to the level of poker play of four players P, Q, R and S.

I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q

Which of the following can be logically inferred from the above statements?

(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set
 A (i) only B (ii) only C (i) and (ii) D neither (i) nor (ii)
Aptitude       numerical       GATE 2016 [Set-1]
Question 48 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 49

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       GATE 2016 [Set-1]
Question 49 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 50

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 B 46.02 C 60.01 D 92.02
Aptitude       numerical       GATE 2016 [Set-1]
Question 50 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
At a load of 80 units, it takes 100 cycles to failure.
So, no. of cycles to failure = 100
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
i.e., 10,000 = a⋅e - b(40) ---------(2) No. of cycles to failure = 5,000
i.e., 5000 = a⋅e - bx
Multiply with 2 on both sides,
10,000 = 2⋅a⋅e - bx ------- (4) Question 51

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 51 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 52

Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia.

Choose the option which is closest in meaning to the underlined phrase in the above sentence.

 A put up with B put in with C put down to D put up against
Aptitude       Verbal       GATE 2016 [Set-2]
Question 52 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 53

Find the odd one in the following group of words.

mock,   deride,   praise,   jeer
 A mock B deride C praise D jeer
Aptitude       Verbal       GATE 2016 [Set-2]
Question 53 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 54

Pick the odd one from the following options.

 A CADBE B JHKIL C XVYWZ D ONPMQ
Aptitude       Numerical       GATE 2016 [Set-2]
Question 54 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 55

In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of A n4 B 4n C 22n-1 D 4n-1
Aptitude       Numerical       GATE 2016 [Set-2]
Question 55 Explanation:
Given,
Product of roots (α, β) = 4
⇒ αβ = 4 (αβ)n = 4n
 Question 56

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 56 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 57

Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required.

Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph?

(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions.
 A (i) only B (ii) only C both (i) and (ii) D neither (i) nor (ii)
Aptitude       Verbal       GATE 2016 [Set-2]
Question 57 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 58

All hill-stations have a lake. Ooty has two lakes.

Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?

(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
 A (i) only B (ii) only C both (i) and (ii) D neither (i) nor (ii)
Aptitude       Verbal       GATE 2016 [Set-2]
Question 58 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 59

In a 2 × 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid? A 21 B 27 C 30 D 36
Aptitude       Numerical       GATE 2016 [Set-2]
Question 59 Explanation:
Number of rectangles in a grid with 'm' horizontal and 'n' vertical lines = 5C2 × 3C2 = 10 × 3 = 30
 Question 60 Choose the correct expression for f(x) given in the graph.

 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 60 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 61

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-1]
Question 61 Explanation:
In negative sentence we can use "any" with plural countable nouns.
 Question 62

Which of the following combinations is incorrect?

 A Acquiescence – Submission B Wheedle – Roundabout C Flippancy – Lightness D Profligate – Extravagant
Aptitude       Verbal       GATE 2015 [Set-1]
Question 62 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 63

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 0.2 B 0.25 C 0.3 D 0.33
Aptitude       Numerical       GATE 2015 [Set-1]
Question 63 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 64

Which of the following options is the closest in meaning to the sentence below?

She enjoyed herself immensely at the party.

 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-1]
Question 64 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 65

Based on the given statements, select the most appropriate option to solve the given question.

If two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building?

Statements:
(I) Each step is 3/4 foot high.
(II) Each step is 1 foot wide.
 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-1]
Question 65 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 66

The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012. The proportion of male to female students in each department is 5:4. There are 40 males in Electrical Engineering. What is the difference between numbers of female students in the Civil department and the female students in the Mechanical department? A 32 B 33 C 34 D 35
Aptitude       Numerical       GATE 2015 [Set-1]
Question 66 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 67

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-1]
Question 67 Explanation:
The words took to their heels and took to flight means that runaway.
 Question 68

The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in m, p, c:

(I) p + m + c = 27/20
(II) p + m + c = 13/20
(III) (p) × (m) × (c) = 1/10
 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-1]
Question 68 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 69

The given statement is followed by some courses of action. Assuming the statement to be true, decide the correct option.

Statement:

There has been a significant drop in the water level in the lakes supplying water to the city.

Course of action:

(I) The water supply authority should impose a partial cut in supply to tackle the situation.
(II) The government should appeal to all the residents through mass media for minimal use of water.
(III)The government should ban the water supply in lower areas.
 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-1]
Question 69 Explanation:
The statement III is not correct.
Banning of water in lower areas is not the solution of the problem.
 Question 70

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking. What is the average of the marks obtained by the class in the examination?

 A 2.29 B 2.97 C 6.795 D 8.795
Aptitude       Numerical       GATE 2015 [Set-1]
Question 70 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 71

Based on the given statements, select the most appropriate option to solve the given question, What will be the total weight of 10 poles each of same weight?

Statements:
(I) One fourth of the weight of a pole is 5 kg
(II) The total weight of these poles is 160 kg more than the total weight of two poles.
 A Statement I alone is not sufficient B Statement II alone is not sufficient C Statement II alone is not sufficient D Both statements I and II together are not sufficient.
Aptitude       Numerical       GATE 2015 [Set-2]
Question 71 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.
Either I or II alone is sufficient.
 Question 72

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 72 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 73

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 73 Explanation:
Apparel- clothing, especially outerwear; garments; attire; raiment
 Question 74

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 74 Explanation:
personnel- people employed in an organization or engaged in an organized undertaking such as military service.
 Question 75

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 75 Explanation:
We completely forgot our friend's birthday and we just don't know how to make it up to him.
 Question 76

In a triangle PQR, PS is the angle bisector of ∠QPR and ∠QPS = 60º. What is the length of PS? A (q+r)/qr B qr/(q+r) C √(q2 + r2) D (q+r)2 /qr
Aptitude       Numerical       GATE 2015 [Set-2]
Question 76 Explanation:
Given, ∠QPS = 60º
and PS is angle bisector of ∠QPR
⇒ ∠QPS = ∠SPR = 60º
and ∠QPR = 120º
Let, PS = s
Area of ΔPQR = Area of ΔPQS + Area of ΔSPR
1/2 qr Sin∠QPR = 1/2 rs Sin∠QPS + 1/2 sq∠SPR
1/2 qr Sin 120º = 1/2 rs Sin 60º + 1/2 sq 60º
1/2 qr Sin × √3/2 = 1/2 rs × √3/2 + 1/2 × √3/2
qr = rs + sq
∴ s = qr/q+r
PS = qr/q+r
 Question 77

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 77 Explanation:
(B) there was no needed information
(C) not really useful
(D) would not have been
 Question 78

If the list of letters, P, R, S, T, U is an arithmetic sequence, which of the following are also in arithmetic sequence?

I. 2P, 2R, 2S, 2T, 2U
II. P-3, R-3, S-3, T-3, U-3
III. P2, R2, S2, T2, U2
 A I only B I and II C II and III D I and III
Aptitude       Numerical       GATE 2015 [Set-2]
Question 78 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 79

If p, q, r, s are distinct integers such that:

f(p,q,r,s) = max(p,q,r,s)
g(p,q,r,s) = min(p,q,r,s)
h(p,q,r,s) = remainder of (p×q)(r×s) if (p×q)>(r×s) OR remainder of (r×s)(p×q) if (r×s)>(p×q)

Also a function fgh(p,q,r,s) = f(p,q,r,s) × g(p,q,r,s) ×h(p,q,r,s)

Also the same operations are valid with two variable functions of the form f(p,q).

What is the value of fg(h(2,5,7,3),(4,6,8)?

 A 8 B 9 C 7 D 6
Aptitude       Numerical       GATE 2015 [Set-2]
Question 79 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 80

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 80 Explanation: Question 81

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 81 Explanation:
Consider first three element of the list, atleast one of them will be neither minimum nor maximum. ∴ Θ(1)
 Question 82

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-3]
Question 82 Explanation:
Extraneous - irrelevant or unrelated to the subject being dealt with.
 Question 83

Choose the most appropriate phrase from the options given below to complete the following sentence.

India is a post-colonial country because

 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-2]
Question 83 Explanation:
India is a post-colonial (or) existing after the end of colonial 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 84

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-3]
Question 84 Explanation:
f(x) = 2x + 33
 Question 85

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-3]
Question 85 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 86

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-3]
Question 86 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 87

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-3]
Question 87 Explanation:
Community of people: Doctor
 Question 88

The exports and imports (in crores of Rs.) of a country from the year 2000 to 2007 are given in the following bar chart. In which year is the combined percentage increase in imports and exports the highest? A 2006 B 2007 C 2008 D 2009
Aptitude       Numerical       GATE 2015 [Set-3]
Question 88 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 89

The head of a newly formed government desires to appoint five of the six selected members P, Q, R, S, T and U to portfolios of Home, Power, Defense, Telecom, and Finance. U does not want any portfolio if S gets one of the five. R wants either Home or Finance or no portfolio. Q says that if S gets either Power of telecom, then she must get the other one. T insists on a portfolio if P gets one Which is the valid distribution of portfolios?

 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-3]
Question 89 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 90

Choose the most appropriate equation for the function drawn as a thick line, in the plot below A x = y - |y| B x = -(y - |y|) C x = y + |y| D x = -(y + |y|)
Aptitude       umerical       GATE 2015 [Set-3]
Question 90 Explanation:
Verify which of the options satisfies the x=2 when y=-1.
Then the Answer is x = - (y - |y|)
 Question 91

Most experts feel that in spite of possessing all the technical skills required to be a batsman of the highest order, he is unlikely to be so due to lack of requisite temperament. He was guilty of throwing away his wicket several times after working hard to lay a strong foundation. His critics pointed out that until he addressed this problem, success at the highest level will continue to elude him. Which of the statements(s) below is/are logically valid and can be inferred from the above passage?

(i) He was already a successful batsman at the highest level.
(ii) He has to improve his temperament in order to become a great batsman.
(iii) He failed to make many of his good starts count.
(iv) Improving his technical skills will guarantee success.
 A (iii) and (iv) B (ii) and (iii) C (i), (ii) and (iii) D (ii) only
Aptitude       Verbal       GATE 2015 [Set-3]
Question 91 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 several times ------- (iii) is True
 Question 92

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-3]
Question 92 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"
 Question 93

Which of the following options is the closest in meaning to the phrase underlined in the sentence below? It is fascinating to see life forms cope with varied environmental conditions.

Aptitude       Verbal       GATE 2014 [Set-1]
Question 93 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 94

Choose the most appropriate word from the options given below to complete the following sentence. He could not understand the judges awarding her the first prize, because he thought that her performance was quite __________.

 A superb B medium C mediocre D exhilarating
Aptitude       Verbal       GATE 2014 [Set-1]
Question 94 Explanation:
Mediocre ⇒ Average quality (or) Not very good.
 Question 95

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-1]
Question 95 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 96

If (z + 1/z) = 98, compute (z2+ 1/z2).

 A 96 B 97 C 98 D 99
Aptitude       Numerical       GATE 2014 [Set-1]
Question 96 Explanation:
z2 + 1/z2 + 2∙z∙ 1/z
= 98
⇒ z2 + 1/z2
= 96
 Question 97

The roots of ax2 + bx + c = 0 are real and positive. a, b and c are real. Then ax2 + 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-1]
Question 97 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 98

The Palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures. What can be inferred from this passage?

 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-1]
Question 98 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 99

Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy. On which of the following assumptions does the statement above rely?

 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-1]
Question 99 Explanation:
The first sentence can represents the two specific illness depression and schizophrenia.
⇒ Option B is the only option that contain illness.
 Question 100

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-1]
Question 100 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 101

In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. The irresponses are tabulated below. What percent of respondents do not own a scooter? A 48 B 49 C 50 D 51
Aptitude       Numerical       GATE 2014 [Set-1]
Question 101 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 102

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-1]
Question 102 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 103

Consider the statement

`    “Not all that glitters is gold”  `

Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?

 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-1]
Question 103 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. Method 2: ⇒ (∼∀x) (∼ (glitters(x) ⇒ gold(x))
⇒ ∃x (∼ (∼glitters(x) ∨ gold(x))
⇒ ∃x (glitters ∧ gold(x))
 Question 104

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-1]
Question 104 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 105

Consider the following system of equations:

3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x – 2y + 7z = 0

The number of solutions for this system is _______.

 A 1 B 2 C 3 D 4
Aptitude       Numerical       GATE 2014 [Set-1]
Question 105 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 106

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-2]
Question 106 Explanation:
From the given options, option B is make the sentence to be fulfilled.
 Question 107

Match the columns.

```   Column 1          Column 2
2) distort         Q) soak completely
3) saturate        R) use
4) utilize         S) destroy utterly```
 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-2]
Question 107 Explanation:
Distort = misrepresent
Saturate = Soak completely
Utilize = use
 Question 108

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-2]
Question 108 Explanation:
Average of 10, 20, 30, ..., 180, 190
Average = 10+20+30+...+180+190 / 19 = (19/2 [10+190]) / 19 = 100
 Question 109

The value of is

 A 3.464 B 3.932 C 4 D 4.444
Aptitude       Numerical       GATE 2014 [Set-2]
Question 109 Explanation:
Let, Squaring on both sides,
x2 = 12+x
x2 - x - 12 = 0
(x-4) (x+3) = 0
∴ x = 4 (x ≠ -3)
 Question 110

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-2]
Question 110 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 111

The number of people diagnosed with dengue fever (contracted from the bite of a mosquito) in north India is twice the number diagnosed last year. Municipal authorities have concluded that measures to control the mosquito population have failed in this region.

Which one of the following statements, if true, does not contradict this conclusion?

 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-2]
Question 111 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 112

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in 2009, by what percent did the number of male students increase in 2009? A 140 B 141 C 142 D 143
Aptitude       Numerical       GATE 2014 [Set-2]
Question 112 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 113

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-2]
Question 113 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 114

While trying to collect(I) an envelope from under the table(II), Mr. X fell down (III) and was losing consciousness (IV) Which one of the above underlined parts of the sentence is NOT appropriate?

 A I B II C III D IV
Aptitude       Verbal       GATE 2014 [Set-3]
Question 114 Explanation:
Losing consiousness represents that it is a continuous process of losing the consiousness. It is not appropriate, he just lost the consiousness.
 Question 115

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-3]
Question 115 Explanation: Rule: If + past perfect then result to be perfect conditional (or) perfect continuous condition.
 Question 116

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-3]
Question 116 Explanation:
Coherent = logical and consistent
Rambling = lengthy and confused (or) inconsequential
 Question 117

Which number does not belong in the series below?

`2, 5, 10, 17, 26, 37, 50, 64`
 A 17 B 37 C 64 D 26
Aptitude       Numerical       GATE 2014 [Set-3]
Question 117 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 118

The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. What is the average of the marks obtained by the class in the examination?

 A 1.34 B 1.74 C 3.02 D 3.91
Aptitude       Numerical       GATE 2014 [Set-3]
Question 118 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 119

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-3]
Question 119 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 others. So this is not correct option.
 Question 120

By the beginning of the 20th century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun.

Which of the following inference(s) may be drawn from the above passage?

(i) Our understanding of the universe changes based on the positions of stars
(ii) Paradigm shifts usually occur at the beginning of centuries
(iii) Stars are important objects in the universe
(iv) Experimental evidence was important in confirming this paradigm shift
 A (i), (ii) and (iv) B (iii) only C (i) and (iv) D (iv) only
Aptitude       Verbal       GATE 2014 [Set-3]
Question 120 Explanation:
Paradigm 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.
 Question 121

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-3]
Question 121 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 122

The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011? A 1:1 B 2:1 C 1.5:1 D 2.5:1
Aptitude       Numerical       GATE 2014 [Set-3]
Question 122 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 123

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-3]
Question 123 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 124

Which one of the following options is the closest in meaning to the word given below?

` Nadir `
 A Highest B Lowest C Medium D Integration
Aptitude       Verbal       GATE 2013
Question 124 Explanation:
Nadir = The lowest (or) most unsuccessful point in a situation.
 Question 125

Complete the sentence: Universalism is to particularism as diffuseness is to _________________

 A specificity B neutrality C generality D adaptation
Aptitude       Verbal       GATE 2013
Question 125 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 126

What will be the maximum sum of 44, 42, 40, ...... ?

 A 502 B 504 C 506 D 500
Aptitude       Numerical       GATE 2013
Question 126 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 127

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 127 Explanation:
Were you a bird, you would fly in the sky.
 Question 128

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 128 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 129

Find the sum of the expression A 7 B 8 C 9 D 10
Aptitude       Numerical       GATE 2013
Question 129 Explanation: Multiply on numerator & denominator = -1+9
= 8
 Question 130

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 130 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 131

After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history. Which one of the following assertions is best supported by the above information?

 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 131 Explanation:
Option A, B, C are not able to given correct sense about the information.
Option D is related to the given information.
 Question 132

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 132 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 133

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 133 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 134

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 134 Explanation:
Total selling price = 50q
Profit = 50q - 5q2
For Profit to be maximum,
d(Profit)/dq = 0
d(50q - 5q2) /dq = 0
50 - 10q = 0
50 = 10q
q = 5
 Question 135

Choose the most appropriate alternative from the options given below to complete the following sentence:

Despite several ––––––––– the mission succeeded in its attempt to resolve the conflict.

 A attempts B setbacks C meetings D delegations
Aptitude       Verbal       GATE 2012
Question 135 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 136

Which one of the following options is the closest in meaning to the word given below?

Mitigate
 A Diminish B Divulge C Dedicate D Denote
Aptitude       Verbal       GATE 2012
Question 136 Explanation:
Mitigate = make (something bad) less severe, serious (or) painful
Synonyms = Diminish, alleviate, reduce etc.
 Question 137

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 137 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 138

Choose the most appropriate alternative from the options given below to complete the following sentence:

Suresh’s dog is the one ––––––––– was hurt in the stampede.

 A that B which C who D whom
Aptitude       Verbal       GATE 2012
Question 138 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 139

Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal interviews to collect and collate economic data. Requirements: High School-pass, must be available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.

Which one of the following is the best inference from the above advertisement?

 A Gender-discriminatory B Xenophobic C Not designed to make the post attractive D Not gender-discriminatory
Aptitude       Verbal       GATE 2012
Question 139 Explanation:
Xenophobic which refers to having (or) showing a dislike of or prejudice against people from other countries.
 Question 140

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 140 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 141

An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

 A 0.288 B 0.334 C 0.667 D 0.72
Aptitude       Numerical       GATE 2012
Question 141 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 142

Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged
 A P, Q B Q, R C P, R D R, S
Aptitude       Numerical       GATE 2012
Question 142 Explanation:
If a value of 'x' is added (or) multiplied to every element in the list, the average also changes by same value.
⇒ P, R are correct
 Question 143

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 143 Explanation: OV is the next term.
 Question 144

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 144 Explanation:
logP = 1/2 logQ = 1/3 log (R) = k
∴ P = bk, Q = b2k, R = b3k
Now, Q2 = b4k = b3k bk = PR
 Question 145

Choose the most appropriate word(s) from the options given below to complete the following sentence.

I contemplated ______________Singapore for my vacation but decided against it.

 A to visit B having to visit C visiting D for a visit
Aptitude       Verbal       GATE 2011
Question 145 Explanation:
Contemplate is a transitive verb and hence is followed by a gerund Hence the correct usage of contemplate is verb + ing form.
 Question 146

Choose the most appropriate word from the options given below to complete the following sentence.

If you are trying to make a strong impression on your audience, you cannot do so by being understated, tentative or __________.

 A hyperbolic B restrained C argumentative D indifferent
Aptitude       Verbal       GATE 2011
Question 146 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 147

Choose the word from the options given below that is most nearly opposite in meaning to the given word:

Amalgamate
 A merge B split C collect D separate
Aptitude       Verbal       GATE 2011
Question 147 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 148

Which of the following options is the closest in the meaning to the word below:

Inexplicable
 A Incomprehensible B Indelible C Inextricable D Infallible
Aptitude       Verbal       GATE 2011
Question 148 Explanation:
Inexplicable means not explicable; that cannot be explained, understood, or accounted for. So the best synonym here is incomprehensible.
 Question 149

P,Q,R and S are four types of dangerous microbes recently found in a human habit. The area of each circle with it diameter printed in brackets represents the growth of a single microbe surviving human immunity system with in 24 hours of entering the body. The danger to human begin varies proportionality with the toxicity, potency and growth attributed to a microbe show in the figure below A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should be the  company target in its first attempt?

 A P B Q C R D S
Aptitude       Numerical       GATE 2011
Question 149 Explanation:
By observation of the table, we can say S Question 150

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 150 Explanation:
Checking with all options in formula: (4q+100/q) i.e. (V+F). Option A gives the minimum cost.
 Question 151

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 151 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 152

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 152 Explanation:
10(729/1000×1 = 7.29 litres)
 Question 153

Few school curricula include a unit on how to deal with bereavement and grief, and ye all students at some point in their lives suffer from losses through death and parting.

Based on the above passage which topic would not be included in a unit on bereavement?

 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 153 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 154

Choose the most appropriate word from the options given below to the complete the following sentence:

His rather casual remarks on politics ___________ his lack of seriousness about the subject.

 A masked B belied C betrayed D suppressed
Aptitude       Verbal       GATE 2010
Question 154 Explanation:
Belied - Not appropriate to given
Betrayed - Most appropriate to given (Reveal intentionally)
Suppressed - Irrelevant to given
 Question 155

Which of the following options is closest in meaning to the word below:

Circuitous
 A cyclic B indirect C confusing D crooked
Aptitude       Verbal       GATE 2010
Question 155 Explanation:
Synonyms for Circuitous are indirect, oblique, winding, meandering etc.
 Question 156

Choose the most appropriate word from the options given below to complete the following sentence:

If we manage to ____________ our natural resources, we would leave a better planet for our children.

 A uphold B restrain C cherish D conserve
Aptitude       Verbal       GATE 2010
Question 156 Explanation:
Uphold - cause to remain
Restrain - keep under control
Cherish - be fond of
Conserve - protect from harm i.e., keeping safety, loss of destruction
 Question 157

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       GATE 2010
Question 157 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 158

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.

Unemployed: Worker
 A fallow: land B unaware: sleeper C wit: jester D renovated: house
Aptitude       Verbal       GATE 2010
Question 158 Explanation:
→ A worker who is working is called unemployed.
→ Same as a land which is not used called fallow.
 Question 159

If 137+276 = 435 how much is 731+672?

 A 534 B 1403 C 1623 D 1513
Aptitude       Numerical       GATE 2010
Question 159 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 160

Hari(H), Gita(G), Irfan(I) and Saira(S) are siblings (i.e., brothers and sisters). All were born on 1st January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:

i. Hari's age + Gita's age > Irfan's age + Saira's age.
ii. The age difference between Gita and Saira is 1 year. However Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.

In what order were they born (oldest first)?

 A HSIG B SGHI C IGSH D IHSG
Aptitude       Numerical       GATE 2010
Question 160 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 161

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.

Which of the following statements best sums up the meaning of the above passage:

 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       GATE 2010
Question 161 Explanation:
→ People in military establishments like to use chemical agents in war.
 Question 162

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       GATE 2010
Question 162 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 163

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       GATE 2010
Question 163 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 164

Two straight lines are drawn perpendicular to each other in X-Y plane. If α and β are the acute angles the straight lines make with the X-axis, then α+β is ______.

 A 60° B 120° C 180° D 90°
Aptitude       Numerical       GATE 2020
Question 164 Explanation:
Two st. line perpendicular to each other in X-Y, if α & β are acute angles then α + β = ____ We know a + α + β = 180
α + β = 180 - 90
α + β = 90
 Question 165

The total revenue of a company during 2014-2018 is shown in the bar graph. If the total expenditure of the company in each year is 500 million rupees, then the aggregate profit or loss (in percentage) on the total expenditure of the company during 2014-2018 is ______. A 20% profit B 20% loss C 16.67% loss D 16.67% profit
Aptitude       Numerical       GATE 2020
Question 165 Explanation:
Bar-graph:
2014-2018
Total expenditure = 500 million/year = 500 × 5 = 2500 million
Revenue total (from the graph)
= 400 + 500 + 600 + 700 + 800
= 3000 million
Profit = 3000 - 2500 = 500
⟹ 500/2500 = 20% profit
 Question 166

The figure below shows an annular ring with outer and inner radii as b and a, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is ______. A π[(b2 - a2) + π/4(b - a)2] B π[(b2 - a2) - π/4(b - a)2] C π[(b2 - a2) - n(b - a)2] D π[(b2 - a2) + n(b - a)2]
Aptitude       Numerical       GATE 2020
Question 166 Explanation: Area of non-painted between 2 circles area of part 1 = πb2 - πa2 = π(b2 - a2)
Radius of painted circles = b-a/2
Area of painted circle = π(b-a/2)2
For n circles = nπ(b-a/2)2
Non-painted area = π[b2 - a2- n/4(b - a)2]
 Question 167

Goods and Services Tax (GST) is an indirect tax introduced in India in 2017 that is imposed on the supply of goods and services, and it subsumes all indirect taxes except few. It is a destination-based tax imposed on goods and services used, and it is not imposed at the point of origin from where goods come. GST also has a few components specific to state governments, central government and Union Territories (UTs).

Which one of the following statements can be inferred from the given passage?

 A GST includes all indirect taxes. B GST is imposed at the point of usage of goods and services. C GST does not have a component specific to UT. D GST is imposed on the production of goods and services.
Aptitude       Verbal       GATE 2020
Question 167 Explanation:
GST is imposed at the point of usage of goods and services.
 Question 168

Select the word that fits the analogy:

` Cook : Cook :: Fly : _____  `
 A Flyer B Flying C Flew D Flighter
Aptitude       Verbal       GATE 2020
Question 168 Explanation:
Cook-cook - Noun-verb relation
Fly-Flyer
 Question 169

The drawn of the 21st century witnessed the melting glaciers oscillating between giving too much and too little to billions of people who depend on them for fresh water. The UN climate report estimates that without deep cuts to man-made emissions, at least 30% of the northern hemisphere’s surface permafrost could melt by the end of the century. Given this situation of imminent global exodus of billions of people displaced by rising seas, nation-states need to rethink their carbon footprint for political concerns, if not for environmental ones.

Which one of the following statements can be inferred from the given passage?

 A Nation-states are responsible for providing fresh water to billions of people. B Billions of people are affected by melting glaciers. C Nation-states do not have environmental concerns. D Billions of people are responsible for man-made emissions.
Aptitude       Verbal       GATE 2020
Question 169 Explanation:
Billions of people are affected by melting glaciers.
 Question 170

There are multiple routes to reach from node 1 to node 2, as shown in the network. The cost of travel on an edge between two nodes is given in rupees. Nodes ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, and ‘f’ are toll booths. The toll price at toll booths marked ‘a’ and ‘e’ is Rs.200, and is Rs.100 for the other toll booths. Which is the cheapest route from node 1 to node 2?

 A 1-f-e-2 B 1-f-b-2 C 1-b-2 D 1-a-c-2
Aptitude       Numerical       GATE 2020
Question 170 Explanation: 1 - f - e - 2 ─ 100 + 100 + 200 = 400
1 - f - b - 2 ─ 100 + 0 + 200 = 300 ⇾ shortest [Answer]
1 - b - 2 ─ 300 + 200 = 500
1 - a - c ─ 2 - 200 + 100 + 100 = 400
 Question 171

Raman is confident of speaking English _____ six months as he has been practicing regularly_____the last three weeks.

 A for, in B during, for C for, since D within, for
Aptitude       Verbal       GATE 2020
 Question 172

If P = 3, R = 27, T = 243, then Q+S = ______.

 A 80 B 110 C 40 D 90
Aptitude       Numerical       GATE 2020
Question 172 Explanation:
P=3, R=27, T=243, Q+5=?
P=31, Q=32, R=33, S=34, T=35
Q+S = 32 + 34 = 9+81 = 90
 Question 173

His knowledge of the subject was excellent but his classroom performance was ______.

 A good B praiseworthy C extremely poor D desirable
Aptitude       Verbal       GATE 2020
Question 173 Explanation:
A Contrast is indicated in the above sentence.
 Question 174

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 3/23 B 6/23 C 3/10 D 3/5
Aptitude       Numerical       GATE 2004-IT
Question 174 Explanation:
Let us consider total no. of families = 100
In that 50% of families having 3 children
i.e., 50×3 = 150 (No. of children)
→ Likes that 30% have 2 children = 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 175

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 175 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
 Question 176
The arithmetic mean of attendance of 49 students of class A is 40% and that of 53 students of class B is 35%. Then the percentage of arithmetic mean of attendance of class A and B is
 A 27.2% B 50.25% C 51.13% D 37.4%
Aptitude       Aptitude       ISRO CS 2011
Question 176 Explanation:
The number of class A students are 49
The arithmetic mean of attendance of Class A is 40%
Arithmetic mean of 49 students attendance of Class A is 49x40
The number of class B students are 53
The arithmetic mean of attendance of Class A is 35%
Arithmetic mean of 53 students attendance of Class A is 53x35
The percentage of arithmetic mean of attendance of class A and B is
= (40x49 + 35x53 )/ (49 + 53)=3815/102
= 37.40
 Question 177
How many diagonals can be drawn by joining the angular points of an octagon?How many diagonals can be drawn by joining the angular points of an octagon?
 A 14 B 20 C 21 D 28
Aptitude       Geometry       ISRO CS 2013
Question 177 Explanation:
→A polygon's diagonals are line segments from one corner to another (but not the edges).
→The number of diagonals of an n-sided polygon is: n(n − 3) / 2.
→Examples: Question 178
The distance from your home to your office is 4 kilometres and your normal walking speed is 4 km/hr. On the first day, you walk at your normal walking speed and take time T1 to reach office.
On the second day, you walk at a speed of 3 km/hr for 2 kilometres, and at a speed of 5 km/hr for the remaining 2 kilometres and you take time T2 to reach office.
On the third day, you walk at a speed of 3 km/hr for 30 minutes, and at 5 km/hr for the remaining time and take time T3 to reach office.
What can you say about the ordering of T1, T2 and T3?
 A T1 > T2 and T1 < T3. B T1 = T2 = T3 C T1 < T2 and T1 < T3 D T1 = T2 and T1 < T3 E T1 < T2 and T1 = T3
Aptitude       Numerical       TIFR PHD CS & SS 2018
 Question 179
In boolean algebra 1+1+1+1...800 times ones=___
 A 1 B 0 C 11 D 800
Aptitude       Nielit STA 17-12-2017
Question 179 Explanation:
In Boolean Algebra, the operator + represents OR operation.
I.1+ X = 1. So 1+(1+1…+1)= 1+(X)= 1
II.0+ X = X
 Question 180
A can is filled with 5 paise coins. Another can is filled with 10 paise coins. Another can is filled with 25 paise coins. All the cans are given wrong labels. If the can labeled 25 paise is not having the 10 paise coins, what will the can, labeled 10 paise have?
 A 25 paise B 5 paise C 10 paise D cannot be determined
Aptitude       Numerical       Nielit Scientific Assistance CS 15-10-2017
Question 180 Explanation:
A diagram will make it easy to comprehend. It is easy to find that the can labeled 25 Paise must have 5 paise coins in it. So, the can labeled 10 Paise, must have 25 Paise coins in it.
 Question 181
Choose the most appropriate option. One-sixth of a certain number is four more than one-twelfth the number. Find the number.
 A 6 B 18 C 36 D 48
Aptitude       Ratios       NIELIT Technical Assistant_2016_march
 Question 182
Choose the most appropriate option. Six less than (1/9)​th​ of 45 is
 A -1 B -2 C 1 D 3
Aptitude       Numerical       NIELIT Technical Assistant_2016_march
 Question 183
Choose the most appropriate option. Twelve times one-half of a number is thirty six. What is the number?
 A 3 B 6 C 8 D 18
Aptitude       Numerical       NIELIT Technical Assistant_2016_march
 Question 184
A suitcase weighs one kilogram plus half of its weight. How much does the suitcase weigh?
 A 1.333... kilograms B 1.5 kilograms C 1.666... kilograms D 2 kilograms E cannot be determined from the given data
Aptitude       Numerical       TIFR PHD CS & SS 2017
 Question 185
A pilgrim covers half of his journey by bus at 60 km/h, two thirds of the remainder by auto at 20 km/h and the rest by walk at 4 km/h. The average speed of the tourist in km/h during his entire journey is
 A 12 B 15 C 20 D 25 E 24
Aptitude       Numerical       HCU PHD CS 2018 December
Question 185 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 186
Two motorists set out at the same time from A to B, a distance of 100 miles. They both followed the same route and travelled at different though uniform speeds of integral number of miles /hour. The difference in their speeds was a prime number of miles/hour. After they had been driving for 2 hrs, the distance of the slower car from A was five times that of the faster car from B. How fast did the motorists drive?
 A 30 and 37 miles/hour B 40 and 42 miles/hour C 47 and 49 miles/hour D None of the above
Aptitude       Numerical       HCU PHD CS MAY 2017
Question 186 Explanation:
The two motorists:
Let d=the distance the faster car has traveled. Then it still has 100-d miles to go, and the slow car has, therefore, gone 500-5d miles. Let A and B be the rates of the fast and slow cars in mph. Then d/A = (500-5d)/B = 2
We get B=250-5B
Then A-B=6f-250
=(3A-125).
But since A-B is prime 3A-125=1
hence A=42mph and B=40 mph
 Question 187

The age of a father is twice that of the elder son. After ten years the age of the father will be three times that of younger son. If the difference of ages of the two sons is 15 years then what will be the age of the father?

 A 50 B 54 C 56 D 58
Aptitude       Numerical       APPSC-2012-DL CA
Question 187 Explanation:
Let the age of elder son = E
The age of father = 2E
Let the age of younger son = Y
Then according to question,
2E + 1 = 3(Y + 10) --- (I)
and
E - Y = 15
Y = E - 15 ---(II)
Putting (II) in (I),
2E + 10 = 3(E - 15 + 10)
2E + 10 = 3(E - 5)
2E + 10 = 3E - 15
25 = E
∴ Age of father = 2E = 2 × 25 = 50
 Question 188
In a class of 45 students, a boy is ranked 20th. When two boys joined, his rank was dropped by one. What is his new rank from the end ?
 A 25th B 26th C 27th D 28th
Aptitude       Numerical       TNPSC-2017-Polytechnic-CS
Question 188 Explanation:
Initially the no. of students in the class is 45, and the rank of boy was 20.
Now two boys joined, so now the total no. of students in the class is 47. Also the rank of boy now is 21.
So the new rank of boy from the end is,
47 - 21 + 1 = 26 + 1 = 27
 Question 189
Let A and B be two containers. Container A contains 50 litres of liquid X and container B contains 100 litres of liquid Y . Liquids X and Y are soluble in each other. We now take 30ml of liquid X from container A and put it into container B. The mixture in container B is then thoroughly mixed and 20ml of the resulting mixture is put back into container A. At the end of this process let VAY be the volume of liquid Y in container A and VBX be the volume of liquid X in container B. Which of the following must be TRUE?
 A VAY < VBX B VAY > VBX C VAY = VBX D VAY + VBX = 30 E VAY + VBX = 20
Aptitude       Numerical       TIFR PHD CS & SS 2019
 Question 190
Avni and Badal alternately choose numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} without replacement (starting with Avni). The first person to choose numbers of which any 3 sum to 15 wins the game (for example, Avni wins if she chooses the numbers 8, 3, 5, 2, since 8 + 5 + 2 = 15). A player is said to have a winning strategy if the player can always win the game, no matter what the other player does. Which of the following statements is TRUE?
As a hint, there are exactly 8 ways in which 3 numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} can sum up to 15, shown as the three rows, the three columns, and the two diagonals in the following square:
8 1 6
3 5 7
4 9 2
 A Avni has a winning strategy B Badal has a winning strategy C Both of them have a winning strategy D Neither of them has a winning strategy E The player that picks 9 has a winning strategy
Aptitude       Numerical       TIFR PHD CS & SS 2019
 Question 191
Suppose there are n guests at a party (and no hosts). As the night progresses, the guests meet each other and shake hands. The same pair of guests might shake hands multiple times, for some parties stretch late into the night, and it is hard to keep track. Still, they don’t shake hands with themselves. Let Odd be the set of guests who have shaken an odd number of hands, and let Even be the set of guests who have shaken an even number of hands. Which of the following stays invariant throughout the night?
 A |Odd| mod 2 B |Even| C |Even| • |Odd| D 2|Even| − |Odd| E 2|Odd| − |Even|
Aptitude       Numerical       TIFR PHD CS & SS 2019
 Question 192
On planet TIFR, the acceleration of an object due to gravity is half that on planet earth. An object on planet earth dropped from a height h takes time t to reach the ground. On planet TIFR, how much time would an object dropped from height h take to reach the ground?
 A t/√2 B √2t C 2t D h/t E h/2t
Aptitude       Numerical       TIFR PHD CS & SS 2017
 Question 193
In a tutorial on geometrical constructions, the teacher asks a student to construct a right-angled triangle ABC where the hypotenuse BC is 8 inches and the length of the perpendicular dropped from A onto the hypotenuse is h inches, and oﬀers various choices for the value of h. For which value of h can such a triangle NOT exist?
 A 3.90 inches B 2√2 inches C 2√3 inches D 4.1 inches E none of the above
Aptitude       Numerical       TIFR PHD CS & SS 2017
 Question 194
Consider the following game with two players, Aditi and Bharat. There are n tokens in a bag. The players know n, and take turns removing tokens from the bag. In each turn, a player can either remove one token or two tokens. The player that removes the last token from the bag loses. Assume that Aditi always goes ﬁrst. Further, we say that a player has a winning strategy if she or he can win the game, no matter what the other player does. Which of the following statements is TRUE?
 A For n = 3, Bharat has a winning strategy. For n = 4, Aditi has a winning strategy B For n = 7, Bharat has a winning strategy. For n = 8, Aditi has a winning strategy C For both n = 3 and n = 4, Aditi has a winning strategy D For both n = 7 and n = 8, Bharat has a winning strategy E Bharat never has a winning strategy
Aptitude       Numerical       TIFR PHD CS & SS 2017
 Question 195
A 1 X 1 chessboard has one (1) square, a 2 X 2 chessboards has five (5) squares. Continuing along this fashion, what is the number of squares on the (regular) 8 X 8 chessboard?
 A 64 B 65 C 204 D 144 E 256
Aptitude       Numerical       TIFR PHD CS & SS 2015
 Question 196
Consider a square of side length 2. We throw five points into the square. Consider the following statements:
(i) There will always be three points that lie on a straight line.
(ii) There will always be a line connecting a pair of points such that two points lie on one side of the line and one point on the other.
(iii) There will always be a pair of points which are at distance at most √2 from each other.
Which of the above is true:
 A (i) only B (ii) only C (iii) only D (ii) and (iii) E None of the above
Aptitude       Numerical       TIFR PHD CS & SS 2015
 Question 197
All that glitters is gold. No gold is silver.
Claims:
1. No silver glitters.
2. Some gold glitters.
Then, which of the following is TRUE?
 A Only claim 1 follows B Only claim 2 follows C Either claim 1 or claim 2 follows but not both D Neither claim 1 nor claim 2 follows E Both claim 1 and claim 2 follow
Aptitude       Numerical       TIFR PHD CS & SS 2014
 Question 198
Let m and n be any two positive integers. Then, which of the following is FALSE?
 A m + 1 divides m2n − 1 B For any prime p, mp ≡ m (modp) C If one of m, n is prime, then there are integers x, y such that mx + ny = 1 D If m E If 2n − 1 is prime, then n is prime.
Aptitude       Numerical       TIFR PHD CS & SS 2014
 Question 199
A person went out between 4pm and 5pm to chat with her friend and returned between 5pm and 6pm. On her return, she found that the hour-hand and the minute-hand of her (well-functioning) clock had just exchanged their positions with respect to their earlier positions at the time of her leaving. The person must have gone out to chat at
 A Twenty five minutes past 4pm B Twenty six and 122/143 minutes past 4pm C Twenty seven and 1/3 minutes past 4pm. D Twenty eight minutes past 4pm E None of the above
Aptitude       Numerical       TIFR PHD CS & SS 2014
 Question 200
A large community practices birth control in the following peculiar fashion. Each set of parents continues having children until a son is born; then they stop. What is the ratio of boys to girls in the community if, in the absence of birth control, 51% of the babies are born male?
 A 51:49 B 1:1 C 49:51 D 51:98 E 98:51
Aptitude       Numerical       TIFR PHD CS & SS 2014
 Question 201
If the word FORGET is encoded as DPPHCU, then THINK is encoded as
 A VGKMM B RIILI C RIGOI D RIGOR
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 201 Explanation: Question 202
Consider the following game. There is a list of distinct numbers. At any round, a player arbitrarily chooses two numbers a, b from the list and generates a new number c by subtracting the smaller number from the larger one. The numbers a and b are put back in the list. If the number c is non-zero and is not yet in the list, c is added to the list. The player is allowed to play as many rounds as the player wants. The score of a player at the end is the size of the final list.
Suppose at the beginning of the game the list contains the following numbers: 48, 99, 120, 165 and 273. What is the score of the best player for this game?
 A 40 B 16 C 33 D 91 E 123
Aptitude       Numerical       TIFR PHD CS & SS 2014
 Question 203

Here is a puzzle: find a number x such that x leaves a remainder of 9 when divided by 10, a remainder of 8 when divided by 9, a remainder of 7 when divided by 8, ... , a remainder of 2 when divided by 3 and a remainder of 1 when divided by 2.

How many such numbers are there?
 A 0 B Exactly 1 C 2``` D Infinite
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 203 Explanation:
The lowest number divisible by all the numbers 1 to 10. So, for minimum value of N,
===>N+1=2520 (LCM of 1,2,3,....10)
or,N=2519
This property is satisfied by the number N=2520∗K−1, where K is a positive integer.
 Question 204
Car A goes 200 Kms at an average speed of 40 Kmph in one direction and returns to the starting point covering the distance of 200 Kms at an average speed of 50 Kmph. Another Car B goes 200 Kms at an average speed of 45 Kmph and does the return journey of 200 Kms also at an average speed of 45 Kmph. Which statement is TRUE about the two cars A and B?
 A Car A takes less time than Car B B Car B takes less time than Car A C Both Cars A and B take the same time D Cannot be determined from the data given
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 204 Explanation:
Time taken by car A for complete journey = t1 + t2
= 200/40 + 200/50
= 5 + 4
= 9 hr
Time taken by car B for complete journey = t 1 + t2
= 200/45 + 200/45
= 8.88 hr
Car B takes less time than car A.
 Question 205 Which of the following is correctly represented by the Venn diagram above?
 A Elephants, Wolves, Animals B Dogs, Cats, Pets C Pigeons, Dogs, Birds D Tables, Chairs, Furniture
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 205 Explanation:
Let’s check option wise,
A) Can’t be the answer because all Elephants and Wolves are animals hence the diagram would be, B) Yes, True. Because there are some dogs which are pets and there are some cats which are pets. Not all of them are pets. So in the given diagram naming will be, C)Can’t be the answer because Dogs are not selected to be pigeons and birds.
D)Can’t be the answer because all Tables and chairs are furniture. Hence diagram will be same like (A).
 Question 206

When looking back on any kind of movement or revolution, one always likes to point to a beginning: "It began right there - it all started with so-and-so's famous speech ... " If structured

programming can be thought of as a revolution, then surely Dijkstra's land-mark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. Virtually

the entire gospel of structured programming is contained in a few short pages: the arguments

against goto statements, the notion of top-down design, the emphasis on program correctness

and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves.

In addition to these fundamental concepts, there are some rather classic phrases that first appeared in this paper, and that have popped-up in dozens of subsequent articles and books. For

example, when discussing the "divide and conquer" approach characterizing top-down design,

Dijkstra admits, "I have only a very small head, ,and must live with it." What seems obvious to us today was a rather novel idea in 1965: the idea that while computers were - and still are

- getting faster and more powerful, human beings weren't.

This theme is repeated again and again, and is essentially the entire subject matter of Dijkstra's

1972 speech, "The Humble Programmer." ... Once you do read it, you can see why Dijkstra has

the reputation he does. His writing is succinct and yet convincing. Reading Dijkstra, someone

said, has been compared to eating marzipan - it's best to take very small bites, chew slowly,

and digest the mouthful before moving on to the next bite.

What is said to have begun with Dijkstra's landmark paper, "Programming Considered as a Human Activity" in 1965?
 A Structured programming B Programs which modify themselves that eventually led to viruses C High salaries to programmers D Computer revolution
Aptitude       Verbal       HCU PHD CS MAY 2019
Question 206 Explanation:
From the line
“ If structured programming can be thought of as a revolution, then surely Dijkstra's land-mark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. ” , clearly the answer is (A) .
 Question 207

When looking back on any kind of movement or revolution, one always likes to point to a beginning: "It began right there - it all started with so-and-so's famous speech ... " If structured

programming can be thought of as a revolution, then surely Dijkstra's land-mark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. Virtually

the entire gospel of structured programming is contained in a few short pages: the arguments

against goto statements, the notion of top-down design, the emphasis on program correctness

and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves.

In addition to these fundamental concepts, there are some rather classic phrases that first appeared in this paper, and that have popped-up in dozens of subsequent articles and books. For

example, when discussing the "divide and conquer" approach characterizing top-down design,

Dijkstra admits, "I have only a very small head, ,and must live with it." What seems obvious to us today was a rather novel idea in 1965: the idea that while computers were - and still are

- getting faster and more powerful, human beings weren't.

This theme is repeated again and again, and is essentially the entire subject matter of Dijkstra's

1972 speech, "The Humble Programmer." ... Once you do read it, you can see why Dijkstra has

the reputation he does. His writing is succinct and yet convincing. Reading Dijkstra, someone

said, has been compared to eating marzipan - it's best to take very small bites, chew slowly,

and digest the mouthful before moving on to the next bite.

Which of the following is NOT a part of structured programming?
 A Elimination of goto statements B Top-down design C Self-modifying code D Emphasis on elegance
Aptitude       Verbal       HCU PHD CS MAY 2019
Question 207 Explanation:
From the line
“Virtually the entire gospel of structured programming is contained in a few short pages: the arguments against goto statements, the notion of top-down design, the emphasis on program correctness and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves. ”
Option (C) is wrong, because we can see that it is saying that argument against programs that modify themselves, means not favouring the self modifying code.Hence option C is wrong.
 Question 208

When looking back on any kind of movement or revolution, one always likes to point to a beginning: "It began right there - it all started with so-and-so's famous speech ... " If structured

programming can be thought of as a revolution, then surely Dijkstra's land-mark paper, "Programming Considered as a Human Activity," published in 1965, marks its beginning. Virtually

the entire gospel of structured programming is contained in a few short pages: the arguments

against goto statements, the notion of top-down design, the emphasis on program correctness

and quality (or "elegance," as Dijkstra prefers to call it), and the strong argument against programs that modify themselves.

In addition to these fundamental concepts, there are some rather classic phrases that first appeared in this paper, and that have popped-up in dozens of subsequent articles and books. For

example, when discussing the "divide and conquer" approach characterizing top-down design,

Dijkstra admits, "I have only a very small head, ,and must live with it." What seems obvious to us today was a rather novel idea in 1965: the idea that while computers were - and still are

- getting faster and more powerful, human beings weren't.

This theme is repeated again and again, and is essentially the entire subject matter of Dijkstra's

1972 speech, "The Humble Programmer." ... Once you do read it, you can see why Dijkstra has

the reputation he does. His writing is succinct and yet convincing. Reading Dijkstra, someone

said, has been compared to eating marzipan - it's best to take very small bites, chew slowly,

and digest the mouthful before moving on to the next bite.

Reading Dijkstra should be like eating marzipan - what does this mean?
 A His prose is very difficult to read like marzipan which should be eaten slowly to appreciate its taste B His prose is so good that it should be read slowly to enjoy and understand it just like marzipan which should be eaten slowly to really enjoy its taste C His prose is difficult and we cannot read it quickly just like eating marzipan whose taste is so nasty that we can only eat small pieces D His prose is so good that it should be read all at once like swallowing something tasty
Aptitude       Verbal       HCU PHD CS MAY 2019
 Question 209
The ratio of the number of boys and girls in a class is 4:3. If 100% of the boys and 20% of the girls are scholarship holders, what is the percentage of students who do not get scholarships?
 A 76 B 75*(5/7) C 85*(5/7) D 86
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 209 Explanation:
Since the ratio of boys and girls = 4/3
So, let the no. of boys = 4x
No. of girls = 3x
So, total no. of students = 7x
Now no. of boys who got scholarship = 0.1 × 4x = 0.4x
No. of girls who got scholarship = 0.2 × 3x = 0.6x
So no. of students who got scholarship = 0.4x + 0.6x = x
∴ No. of students who do not got scholarship = 7x - x = 6x
Hence the required percentage is,
6/7 × 100 = 85 (5/7)%
 Question 210

How many squares are there in the following figure? A 14 B 15 C 17 D 18
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 210 Explanation:
For straight squares,
No. of 1 box square = 10
No. of 4 box square = 3
For cross squares,
No. of 1 box square = 4
No. of 4 box square = 1
Hence, total no. of squares = 10 + 3 + 4 + 1 = 18
 Question 211
Two candidates were contesting for the post of the chairperson of a committee, 3/4th of the members voted for A and 3/5th for B, 30 members voted in favour of both the candidates and 9 members did not cast their vote. Find the total number of members who cast their votes.
 A 60 B 80 C 57 D 51
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 211 Explanation:
Let the total no. of members be x.
Now,
No. of members who casted votes + no. of members who not casted votes = x
(3x/4 + 3x/5 - 30) + 9 = x
27x/20 - 21 = x
7x/20 = 21
X = 60
Hence total no. of members who casted their votes
= 3x/4 + 3x/5 - 30
= 3/4 × 60 + 3/5 × 60 - 30
= 45 + 36 - 30
= 51
 Question 212

Answer Questions 24 - 26 based on the following information.

A, 'B, C, D, E and Fare 6 relatives. Their relationships are:

(a) B is the son of C, but C is not the mother of B

(b) D is the daughter of A

(c) F is the brother of B

(d) A and C are a married couple

(e) E is the brother of C

Who is the mother of B?
 A F B E C D D A
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 212 Explanation:
Let’s connect given information,
B is the son of C, but C is not the mother of B, means C is the father of B.
A and C are married couples, so since C is father of B, then definitely A is mother of B.
D is daughter of A, means B is brother of D or D is sister of B.
F is brother of B. So in total there are three children of A and C.
E is the brother of C. Means E is uncle of B, D and F.
Clearly, A is the mother of B.
 Question 213

Answer Questions 24 - 26 based on the following information.

A, 'B, C, D, E and Fare 6 relatives. Their relationships are:

(a) B is the son of C, but C is not the mother of B

(b) D is the daughter of A

(c) F is the brother of B

(d) A and C are a married couple

(e) E is the brother of C

How many children does A have?
 A 1 B 2 C 3 D 4
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 213 Explanation:
Let’s connect given information,
B is the son of C, but C is not the mother of B, means C is the father of B.
A and C are married couples, so since C is father of B, then definitely A is mother of B.
D is daughter of A, means B is brother of D or D is sister of B.
F is brother of B. So in total there are three children of A and C.
E is the brother of C. Means E is uncle of B, D and F.
A have total three children,
D, B, F
 Question 214

Answer Questions 24 - 26 based on the following information.

A, 'B, C, D, E and Fare 6 relatives. Their relationships are:

(a) B is the son of C, but C is not the mother of B

(b) D is the daughter of A

(c) F is the brother of B

(d) A and C are a married couple

(e) E is the brother of C

Which of the following statements is/are TRUE?
 A E is D's uncle B E is D's daughter C F is E's son D D and F are sisters
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 214 Explanation:
Let’s connect given information,
B is the son of C, but C is not the mother of B, means C is the father of B.
A and C are married couples, so since C is father of B, then definitely A is mother of B.
D is daughter of A, means B is brother of D or D is sister of B.
F is brother of B. So in total there are three children of A and C.
E is the brother of C. Means E is uncle of B, D and F.
P∩F = {2,3,5}
Hence cardinality of P∩F = 3.
 Question 215

Words are sorted according to the following two rules applied in order: (a) nouns come before verbs, verbs come before adjectives, adjectives come before adverb; (b) a letter with less number of straight line segments comes before one with more straight lines, e.g., V (2 straight lines) comes before E (4 straight lines).

Given the words, ACADEMY, NEST, SUPERB. SUNDAY, NOTING, the correct ascending order is
 A NEST, SUNDAY, SUPERB, ACADEMY, NOTING B SUNDAY, ACADEMY, NEST, NOTING, SUPERB C SUNDAY, SUPERB, ACADEMY, NEST, NOTING D ACADEMY, NEST, NOTING, SUNDAY, SUPERB
Aptitude       Numerical       HCU PHD CS MAY 2019
Question 215 Explanation:
According to the rules given in the question ,The correct answer is SUNDAY, ACADEMY, NEST, NOTING, SUPERB
 Question 216
A shelf has between 75 and 100 books. 1/6th of them are novels and 12.5% of them are biographies_ .Find the number of books.
 A 76 B 88 C 96 D None of the Above
Aptitude       Numerical       HCU PHD CS MAY 2019
 Question 217
What is the first letter of a meaningful English word formed from the 1st, 4th, 7th and 11th letters of "SUPERFLUOUS"?
 A E B L C R D S
Aptitude       Verbal       HCU PHD CS MAY 2019
Question 217 Explanation:
The 1st ,4th ,7th, and 11th letters are S,E,L,S and the meaningful words formed from these letters are ELSE. And the first letter of this word is E.
 Question 218

The following figure shows a ring containing 105 teeth inside which is a wheel with 80 teeth. The black dots - one on the wheel and one on the ring are initially aligned as shown. The wheel is now rotated anti-clockwise along the ring with no slippage.After how many revolutions of the wheel will it return to the initial alignment? A 5 B 15 C 21 D 26
Aptitude       Numerical       HCU PHD CS MAY 2019
 Question 219
You are allotted a rectangular room of a fixed height. You have decided to paint the three walls and put wallpaper on the fourth one. Walls can be painted at a cost of Rs. 10 per meter and the wall paper can be put at the rate of Rs 20 per meter for that specified height. What is the minimum cost at which you can achieve this covering for a 200 square meter room?
 A 400 × √3 B 400 C 400 × √2 D 200 × √3 E 500
Aptitude       Numerical       TIFR PHD CS & SS 2014
 Question 220
Long ago, in a planet far far away, there lived three races of intelligent inhabitants: the Blues (who always tell the truth), the Whites (who always lie), and the Pinks (who, when asked a series of questions, start with a lie and then tell the truth and lie alternately). To three creatures, chosen from the planet and seated facing each other at A, B and C (see figure), the following three questions are put:
(i) What race is your left-hand neighbour?
(ii) What race is your right-hand neighbour?
(iii) What race are you? A: (i) White (ii) Pink (iii) Blue
B: (i) Pink (ii) Pink (iii) Blue
C: (i) White (ii) Blue (iii) Blue
What is the actual race of each of the three creatures?
 A A is Pink, B is White, C is Blue B A is Blue, B is Pink, C is White C A is Pink, B is Blue, C is Pink D A is White, B is pink, C is blue E Cannot be determined from the above data
Aptitude       Numerical       TIFR PHD CS & SS 2012
 Question 221
Let ABC be a triangle with n distinct points inside. A triangulation of ABC with respect to the n points is obtained by connecting as many points as possible such that no more line segment can be added without intersecting other line segments. In other words, ABC has been partitioned into triangles with end points at the n points or at the vertices A, B, C. For example, the following figure gives one possible triangulation of ABC with two points inside it. Although there are many different ways to triangulate ABC with the n points inside, the number of triangles depends only on n. In the above figure it is five. How many triangles are there in a triangulation of ABC with n points inside it?
 A 3n − 1 B n2 + 1 C n + 3 D 2n + 1 E 4n − 3
Aptitude       Numerical       TIFR PHD CS & SS 2012
 Question 222
A certain pair of used shoes can be repaired for Rs. 1250 and will last for 1 year. A pair of the same kind of shoes can be purchased new for Rs. 2800 and will last for 2 years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?
 A 5% B 12% C 15% D 3% E 24%
Aptitude       Numerical       TIFR PHD CS & SS 2012
 Question 223
Walking at 4/5 is normal speed a man is 10 minute too late. Find his usual time in minutes
 A 81 B 64 C 52 D 40 E It is not possible to determine the usual time from given data
Aptitude       Numerical       TIFR PHD CS & SS 2012
 Question 224
A large community practices birth control in the following peculiar fashion. Each set of parents continues having children until a son is born; then they stop. What is the ratio of boys to girls in the community if, in the absence of birth control, 51% of the babies are born male?
 A 51:49 B 1:1 C 49:51 D 51:98 E 98:51
Aptitude       Numerical       TIFR PHD CS & SS 2012
 Question 225
A contiguous part, i.e., a set of adjacent sheets, is missing from Tharoor’s GRE preparation book. The number on the first missing page is 183, and it is known that the number on the last missing page has the same three digits, but in a different order. Note that every sheet has two pages, one at the front and one at the back. How many pages are missing from Tharoor’s book?
 A 45 B 135 C 136 D 198 E 450
Aptitude       Numerical       TIFR PHD CS & SS 2020
 Question 226
In a certain year there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the 20th of January fall that year (recall that January has 31 days)?
 A Sunday B Monday C Wednesday D Friday E None of the others
Aptitude       Numerical       TIFR PHD CS & SS 2020
 Question 227
The hour needle of a clock is malfunctioning and travels in the anti-clockwise direction, i.e., opposite to the usual direction, at the same speed it would have if it was working correctly. The minute needle is working correctly. Suppose the the two needles show the correct time at 12 noon, thus both needles are together at the 12 mark. After how much time do the two needles meet again?
 A 10/11 hour B 11/12 hour C 12/13 hour D 19/22 hour E One hour
Aptitude       Numerical       TIFR PHD CS & SS 2020
 Question 228
What is the area of the largest rectangle that can be inscribed in a circle of radius R?
 A R2/2 B π X R2/2 C R2 D 2R2 E None of the above
Aptitude       Numerical       TIFR PHD CS & SS 2020
 Question 229
A ball is thrown directly upwards from the ground at a speed of 10 ms−1, on a planet where the gravitational acceleration is 10 ms−2. Consider the following statements:
1. The ball reaches the ground exactly 2 seconds after it is thrown up
2. The ball travels a total distance of 10 metres before it reaches the ground
3. The velocity of the ball when it hits the ground is 10 ms−1
What can you say now?
 A Only Statement 1 is correct B Only Statement 2 is correct C Only Statement 3 is correct D None of the Statements 1, 2 or 3 is correct E All of the Statements 1, 2 and 3 are correct
Aptitude       Numerical       TIFR PHD CS & SS 2020
 Question 230
The sequence s0, s1, . . . , s9 is defined as follows: what is s0
 A 81 B 95 C 100 D 121 E 190
Aptitude       Numerical       TIFR PHD CS & SS 2020
There are 230 questions to complete.