## Aptitude

 Question 1
Consider the following sentences:
(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
Question 1 Explanation:
i) Everybody in the class is prepared for the exam This is grammatically correct statement
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 2

 Items Cost (₹) Profit % Marked Price (₹) P 5,400 --- 5,860 Q --- 25 10,000
Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and  the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost Profit %=Selling price-CostCost100.

The discount on item Q, as a percentage of its marked price, is ______.
 A 25 B 5 C 10 D 12.5
Question 2 Explanation:
 Question 3
The ratio of boys to girls in a class is 7 to 3. Among the options below, an acceptable value for the total number of students in the class is:
 A 37 B 73 C 21 D 50
Question 3 Explanation:
The Ratio of boys to girls is 7:3
Number of boys = 7x
Number of girls = 3x
Total number of students = 10x
So the possible value should multiple by 10.
 Question 4
A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.
Which one of the following is NOT a convex polygon?
 A B C D
Question 4 Explanation:
 Question 5

A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like _______.
 A B C D
Question 5 Explanation:
 Question 6
We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm × 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is ______.
 A B C D
Question 6 Explanation:
 Question 7
______ is to surgery as writer is to ______
Which one of the following options maintains a similar logical relation in the above sentence?
 A Hospital, library B Medicine, grammar C Plan, outline D Doctor, book
Question 7 Explanation:
The given statement is to fill the relationship of the subject and the action done by the subject.
Doctor is to surgery as writer is to book.
 Question 8
There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two chocolates are identical is _____
 A 0.81225 B 0.4235 C 0.6976 D 0.3024
Question 8 Explanation:
Explanation :
There are 5 bags having identical sets of 10 distinct chocolates. one chocolate is drawn from each bag, probability to find at least 2 chocolate is identical
The total number of such selections possible = 10*10*10*10*10 = 10^5.
We need to select such that at least two of them are identical.
We can count the number of ways with no chocolate being repeated and subtract it from total possible ways to get the required probability.
The number of ways to select all different/distinct = 10*9*8*7*6
Required number of selections= 10^5-10*9*8*7*6 = 69760
Required probability = 69760/10^5 = 0.69760
 Question 9
Some people suggest anti-obesity measures (AOM) such as displaying calorie information in restaurant menus. Such measures sidestep addressing the core problems that cause obesity: poverty and income inequality.
Which one of the following statements summarizes the passage?
 A AOM are addressing the problem superficially. B The proposed AOM addresses the core problems that cause obesity. C AOM are addressing the core problems and are likely to succeed. D If obesity reduces, poverty will naturally reduce, since obesity causes poverty.
Question 9 Explanation:
The problems mentioned are poverty and income inequality. But AOMs are not addressing the main problems directly. But it is a kind of generic step taken to address obesity. So AOMs are only addressing the obesity problem superficially but not addressing the real problems.
 Question 10
Given below are two statements 1 and 2, and two conclusions I and II.
Statement I: All bacteria are microorganisms.
Statement II: All pathogens are microorganisms.
Conclusion I: Some pathogens are bacteria.
Conclusion II: All pathogens are not bacteria.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?
 A Only conclusion I is correct B Only conclusion II is correct C Neither conclusion I nor II is correct D Either conclusion I or II is correct
 Question 11

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°
Question 11 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 12

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
Question 12 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 13

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]
Question 13 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 14

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.
Question 14 Explanation:
GST is imposed at the point of usage of goods and services.
 Question 15

Select the word that fits the analogy:

` Cook : Cook :: Fly : _____  `
 A Flyer B Flying C Flew D Flighter
Question 15 Explanation:
Cook-cook - Noun-verb relation
Fly-Flyer
 Question 16

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.
Question 16 Explanation:
Billions of people are affected by melting glaciers.
 Question 17

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
Question 17 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 18

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
 Question 19

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

 A 80 B 110 C 40 D 90
Question 19 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 20

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

 A good B praiseworthy C extremely poor D desirable
Question 20 Explanation:
A Contrast is indicated in the above sentence.
 Question 21

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
Question 21 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 22

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
Question 22 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 23

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
Question 23 Explanation:
Mitigate = make (something bad) less severe, serious (or) painful
Synonyms = Diminish, alleviate, reduce etc.
 Question 24

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.
Question 24 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 25

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
Question 25 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 26

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
Question 26 Explanation:
Xenophobic which refers to having (or) showing a dislike of or prejudice against people from other countries.
 Question 27

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
Question 27 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 28

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
Question 28 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 29

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
Question 29 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 30

Given the sequence of terms: AD  CG  FK  JP, the next term is

 A OV B OW C PV D PW
Question 30 Explanation:

OV is the next term.
 Question 31

Out of a group of 21 persons, 9 eat vegetables, 10 eat fish and 7 eat eggs : 5 persons eat all three. How many persons eat at least two out the three dishes?

 A Theory Explanation.
 Question 32
Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music. Which one of the following statements is the CORRECT inference of the above passage?
 A Listening to music has no effect on learning and a positive effect on physical exercise. B Listening to music has a clear positive effect on physical exercise. Music has a positive effect on learning only in some students. C Listening to music has a clear positive effect both on physical exercise and on learning. D Listening to music has a clear positive effect on learning in all students. Music has a positive effect only in some students who exercise.
Question 32 Explanation:

From the first statement “Listening to music during exercise improves exercise performance and reduces discomfort. “ It is clear that listening to music has a positive effect on physical exercise.

From the statement “Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. “   it is clear that only on some students music has a positive effect.

 Question 33

A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like _______.
 A B C D
Question 33 Explanation:
Fold the sheet along the dotted line and join the shapes, we get option 2.
 Question 34
Gauri said that she can play the keyboard _______ her sister.
 A as worse as B as well as C as better as D as nicest as
Question 34 Explanation:
‘worse’, ‘better’ are comparative words which need the word ‘than’ for comparison. Out of the remaining two options ‘as well as’ is the correct answer.
 Question 35
Pen : Write :: Knife : _______ Which one of the following options maintains a similar logical relation in the above?
 A Vegetables B Sharp C Blunt D Cut
Question 35 Explanation:
A pen is used to write. Similarly, a knife is used to cut.
 Question 36
The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21. The total number of students in all the three classes in the beginning was:
 A 66 B 22 C 88 D 110
Question 36 Explanation:

Given Initial ratio : 3:13:6

Total number of students initially = 3x+13x+6x = 22x

From the given question, we can write 3x+18 = 15y -----I

13x+18 = 35y-----II

6x+18 = 21y------III

I - II => -10X = -20Y

X=2Y------IV

Put IV in III => 6(2y) + 18 = 21y

12y + 18 = 21y

9y = 18

y = 2 -----V

Substitute V in I => 3x + 18 = 30

3x = 12

x = 4

Number of initial students = 22x = 22(4) = 88

 Question 37

The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ₹ 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.
The ratio of the selling price in Year 2 to the selling price in Year 3 is ______.
 A 1:1 B 3:4 C 1:2 D 4:3
Question 37 Explanation:

According to the given data:

Year     Cost/unit   Number of units     Cost Price

1           ₹ 3                    100                     300

2           ₹ 2                     200                    400

3           ₹ 1                     300                    300

Cost Price = Cost/unit x Number of units

Net Profit = Selling Price - (Cost Price + (Tax%  x selling price )

Year 2:

296 = SP - (400 + (13/100) x SP)

=>296 = 0.87SP - 400

=> 0.87SP = 696

=> SP = ₹ 800

Year 3:

210 = SP - (300 + (15/100) x SP)

=> 210 = 0.85SP - 300

=>  0.85SP = 510

=> SP = ₹ 600

The ratio of selling price in Year 2 to the selling price in year 3 = 800:600

= 4:3

 Question 38

A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
 A B C D
Question 38 Explanation:
Rotate 90 degrees to the left and flip the piece in Option 2.
 Question 39
 A 2 B 4 C 8 D 6
Question 39 Explanation:

Expand the given equation:

x2+1/4 - x -x2 -9/4 +3x = x+2

=> -2 + 2x = x + 2

X = 4

 Question 40
If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos θ =
 A B C D
Question 40 Explanation:
 Question 41
Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.
Observation I: S is taller than R.
Observation II: Q is the shortest of all.
Observation III: U is taller than only one student.
Observation IV: T is taller than S but is not the tallest.
The number of students that are taller than R is the same as the number of students shorter than _______.
 A S B P C T D R
Question 41 Explanation:
The order will be PTSRUQ
Number of students taller than R = Number of students shorter than S = 3
 Question 42

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
Question 42 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 43

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
Question 43 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 44
The _________ is too high for it to be considered _________.
 A fair / fare B faer / fair C fare / fare D fare / fair
Question 44 Explanation:
Fare: The money paid for a journey. Fair: treating people equally without favouritism or discrimination (or) without cheating (or) trying to achieve unjust advantage The fare is too high for it to be considered fair.
 Question 45
A function y(x) is defined in the interval [0, 1] on the x-axis as

Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?
 A 5/6 B 6/5 C 13/6 D 6/13
Question 45 Explanation:

We know that area of a rectangle = length * breadth = L * B
Area of rectangle (1) = L*B = (1/3) * 2 = (2/3)
Area of rectangle (2) = L*B = (3/4 - 1/3 ) * 3 = (5/4 )
Area of rectangle (3) = L*B = (1 - 3/4) * 1 = 1/4
Therefore Total area = Area(1+2+3) = (2/3) + (5/4) + (1/4) = 26/12 = 13/6
 Question 46
Let r be a root of the equation x2 + 2x + 6 = 0. Then the value of the expression (r + 2)(r + 3)(r + 4)(r + 5) is
 A 51 B -51 C 126 D -126
Question 46 Explanation:
 Question 47
Given below are four statements.
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
Question 47 Explanation:
Explanation: Statement 1 & Statement 3 cannot be true simultaneously.
Statement 1: All students are inquisitive. Statement 3: No student is inquisitive
 Question 48
A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.

From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly once. The plates can be rotated in their plane.
 A B C D
Question 48 Explanation:
From the question we know that letters can rotate in the plane, now we will verify the options one by one. Option 1: A,D,D,D,J from these letters we can't form a palindrome.
Option 2: A,D,R,A,R from these we can form RADAR which is a palindrome.
Option 3: A,D,Z,E,D from these letters we can't form a palindrome.
Option 4: A,D,I,L,Y from these letters we can't form a palindrome.
 Question 49
Some people believe that “what gets measured, improves”.
Some others believe that “what gets measured, gets gamed”.
One possible reason for the difference in the beliefs is the work culture in organizations. In organizations with good work culture, metrics help improve outcomes.
However, the same metrics are counterproductive in organizations with poor work culture.
Which one of the following is the CORRECT logical inference based on the information in the above passage?
 A Metrics are useful in organizations with poor work culture B Metrics are useful in organizations with good work culture C Metrics are always counterproductive in organizations with good work culture D Metrics are never useful in organizations with good work culture
Question 49 Explanation:
From the given passage consider the sentence “In organizations with good work culture, metrics help improve outcomes” Option A: Metrics are useful in organizations with poor work culture. Which is incorrect based on the sentence.
Option B: Metrics are useful in organizations with good work culture. Which is correct and relevant to the considered sentence.
Option C: Metrics are always counterproductive in organizations with good work culture. Which is incorrect because we can't always guarantee good work culture.
Option D: Metrics are never useful in organizations with a good work culture. Incorrect metrics will help to make a good work culture.
 Question 50
In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of the qualified candidates. Which one of the following is the correct logical inference based on the information provided in the above passage?
 A Equal number of boys and girls qualified B Equal number of boys and girls appeared for the test C The number of boys who appeared for the test is less than the number of girls who appeared D The number of boys who qualified the test is less than the number of girls who Qualified
Question 50 Explanation:
The girls accounted for 60% of the qualified candidates.
60% can be written as ⅗. Which means among 5 qualified persons three of them are girls.
So, The number of boys qualified is less than the number of girls qualified.
There are 50 questions to complete.

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