Aptitude
Question 1 
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.
A  Statement 1 and Statement 3 
B  Statement 1 and Statement 2 
C  Statement 2 and Statement 4 
D  Statement 3 and Statement 4 
Statement 1: All students are inquisitive. Statement 3: No student is inquisitive
Question 2 
(i) Everybody in the class is prepared for the exam.
(ii) Babu invited Danish to his home because he enjoys playing chess.
Which of the following is the CORRECT observation about the above two sentences?
A  (i) is grammatically incorrect and (ii) is ambiguous 
B  (i) is grammatically correct and (ii) is ambiguous 
C  (i) is grammatically correct and (ii) is unambiguous 
D  (i) is grammatically incorrect and (ii) is unambiguous 
ii). Babu invited Danish to his home because he enjoys playing chess.
This statement is ambiguous as there is no guarantee that Danish knows playing chess.
Question 3 
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 
Gift cost = 10x
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
Method2: There were ten friends decided to buy a gift.
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.
Price of the gift= 6000.
Question 4 
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 
Question 5 
The search engine’s business model _____ around the fulcrum of trust.
A  bursts 
B  revolves 
C  sinks 
D  plays 
Question 6 
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 
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 7 
A court is to a judge as _____ is to a teacher.
A  a syllabus 
B  a student 
C  a punishment 
D  a school 
Question 8 
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 
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 9 
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 
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 10 
“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 
The court is judged that because of failure of the state to protect citizens through social security schemes beggars are created.
Question 11 
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 Southwest wing.
The shaded rooms are already occupied. WR is washroom.
A  
B  
C  
D 
Question 12 
In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. 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 
From the given diagram:
Total no. of people = 70 + 10 + 20 + 20 + 40 = 160
No. of Administrators = 50
% of Administrators = 50/160 = 31.25
Question 13 
“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 
Question 14 
“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 
Question 15 
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  πd^{2} 
C  (1/2)πd^{2} 
D  (1/2)πd 
Area of a square A = a^{2} (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 16 
What is the missing number in the following sequence?
2, 12, 60, 240, 720, 1440, _______, 0A  2880 
B  1440 
C  720 
D  0 
2 × 6 = 12
12 × 5 = 60
60 × 4 = 240
240 × 3 = 720
720 × 2 = 1440
1440 × 0 = 0
Question 17 
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 
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
MethodII:
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 18 
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 
→ p^{x} = 1/q ⟹ 1/p^{x} = 1/q
⟹ q = p^{x}
⟹ log q = log p^{x}
⟹ x log p = log q
⟹ x = log q/ log p
→ q^{y} = 1/r ⟹ 1/q^{y} = 1/r
⟹ q^{y} = r
⟹ y log q = log r
⟹ y = log r/ log q
→ r^{z} = 1/p ⟹ 1/r^{z} = 1/p
⟹ p = r^{z}
⟹ log r^{z} = 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 19 
In the figure below, ∠DEC + ∠BFC is equal to
A  ∠BCD – ∠BAD 
B  ∠BAD + ∠BCF

C  ∠BAD + ∠BCD 
D  ∠CBA + ADC 
→ ∠1 = ∠5 + ∠4 ………(i)
According to triangular property:
Angle of exterior = sum of interior angles
→ ∠4 = ∠3 + ∠2 ……….(ii)
By substituting (ii) in (i)
→ ∠1 = ∠5 + ∠3 + ∠2
→ ∠1 = ∠BCD
∠2 = ∠BAD
→ ∠BCD – ∠BAD = ∠1 – ∠2
= ∠5 + ∠3 + ∠2 – ∠2
= ∠ 5 + ∠3
= ∠DEC + ∠BFC
Question 20 
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 
→ 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 21 
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 
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 22 
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. 
→ 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 23 
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 
After Rajendrachola returned from his voyage to Indonesia, he wished to visit the temple in Tanjavur.
Question 24 
Research in the workplace reveals that people work for many reason __________.
A  money beside 
B  beside money 
C  money besides 
D  besides money 
Here we are using besides preposition “in addition to”.
Question 25 
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 
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 26 
Find the smallest number y such that y × 162 is a prefect cube.
A  24 
B  27 
C  32 
D  36 
⇒ 162 = 2×3×3×3×3 = 3^{3}×(2×3)
For (2×3) to be a perfect cube, it should be multiplied by (2^{2}×3^{2})
∴ Required number = y = 2^{2}×3^{2} = 36
Question 27 
The probability that a kdigit number does NOT contain the digits 0, 5 or 9 is
A  0.3^{k} 
B  0.6^{k} 
C  0.7^{k} 
D  0.9^{k} 
Total no.of possibilities = (10)^{k}
Required probability = (7)^{k} / (10)^{k} = 0.7^{k}
Question 28 
“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. 
That represents the history of nationalism.
Question 29 
Six people are seated around a circular table. There are atleast two men and two women. There are at least three righthanded persons. Every woman has a lefthanded person to her immediate right. None of the women are righthanded. The number of women at the table is
A  2 
B  3 
C  4 
D  Cannot be determined 
Atleast three right handed persons.
None of the women are righthanded.
⇒ All the righthanded persons are men. Every woman has a lefthanded person to her immediate right.
⇒ For this to happen, there must be three lefthandedpersons and one of them should be a male.
As three persons are righthanded and those being men.
The number of women at the table = 2
Question 30 
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 
CaseI: x > y
⇒ x – y = x – y
Expression ⇒ (x + y) – (x – y) / 2 = y
In this case value of expression is minimum of y.
CaseII: 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 31 
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 dislikes?
A  21 
B  18 
C  16 
D  14 
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
= ^{3}P_{3} + ^{3}P_{3} – ^{2}P_{2}
= 3! + 3! – 2!
= 10
∴ Required number of ways = 24 – 10 = 14
Question 32 
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 
∴ 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 33 
Choose the option with words that are not synonyms.
A  aversion, dislike 
B  luminous, radiant 
C  plunder, loot 
D  yielding, resistant 
Resistant means offering a resistance to something or someone.
Question 34 
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 
With adjectives and adverbs enough is comes after an adjectives and adverbs.
So, here we use bright enough to complete the sentence.
Question 35 
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 
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 36 
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 
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 37 
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 
The probability of selecting same colour is
⇒ ^{3}C_{2} / ^{10}C_{2} * ^{4}C_{2} / ^{10}C_{2} * ^{3}C_{2} / ^{10}C_{2}
⇒ 3/45 + 6/45 + 3/45
⇒ 12/45
= 4/15
Question 38 
“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’ 
(or)
As to give the impression of having a certain quality.
Question 39 
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 
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 40 
X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X^{3} will have
A  90 digits 
B  91 digits 
C  92 digits 
D  93 digits 
X = 4777……… (29 times (7))
X = 4.777…….. ×10^{29}
X = 5×10^{29} (4.777 rounded as 5)
X^{3} = 125×10^{87}
Total no. of digits = 3+87 [125=3 digit, 10^{87} = 87 digit]
= 90
Question 41 
The number of roots of e^{x} + 0.5x^{2} – 2 in the range [5, 5] is
A  0 
B  1 
C  2 
D  3 
e^{x} = 0.5x^{2} + 2
If we draw a graph for e^{x} and 0.5x^{2} + 2 in between [5, 5]
Question 42 
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 
Question 43 
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. 
Minister is a singular person, with a singular object, so verb ends with ‘s’. So option C is incorrect.
Option ‘D’ is correct.
Question 44 
A rewording of something written or spoken is a ______________.
A  paraphrase 
B  paradox 
C  paradigm 
D  paraffin 
Question 45 
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 
The use of the metaphorical words to explain about the thoughts instead of literal use of them.
Question 46 
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 
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 47 
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 
⇒ Side of cube = 4
Surface area of cube = 6s^{2} = 6 × 4^{2} = 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 48 
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 
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 49 
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. 
Which is inferred from the statement.
Option A, B, C are incorrect which are not properly inferred from the statement.
Question 50 
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) 
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.