Q. 4 There are 5 parallel lines on the plane. On
the same plane, there are n other lines which
are perpendicular to the 5 parallel lines. If the
number of distinct rectangles formed by these
lines is 360, what is the value of n?
Q. 5 There are two taps, T1 and T2, at the bottom
of a water tank, either or both of which may
be opened to empty the water tank, each at
a constant rate. If T1 is opened keeping T2
closed, the water tank (initially full) becomes
empty in half an hour. If both T1 and T2 are
kept open, the water tank (initially full)
becomes empty in 20 minutes. Then, the time
(in minutes) it takes for the water tank (initially
full) to become empty if T2 is opened while
T1 is closed is ______
Q. 6 A class consists of 30 students. Each of
them has registered for 5 courses. Each
course instructor conducts an exam out of
200 marks. The average percentage marks
of all 30 students across all courses they have
registered for, is 80%. Two of them apply for
revaluation in a course. If none of their marks
reduce, and the average of all 30 students
across all courses becomes 80.02%, the
maximum possible increase in marks for
either of the 2 students is
Q. 7 What is the minimum number of weights
which enable us to weigh any integer number
of grams of gold from 1 to 100 on a standard
balance with two pans? (Weights can be
placed only on the left pan.)
Q. 8 If one of the lines given by the equation
2x2 + axy + 3y2 = 0 coincides with one of
those given by 2x2 + bxy – 3y2 = 0, and the
other lines represented by them are
perpendicular then a2 + b2 is ______.
Q. 10 In a class, 60% and 68% of students passed
their Physics and Mathematics examinations
respectively. Then at least ______ percentage
of students passed both their Physics and
Mathematics examinations.
Q. 11 Suppose that a real-valued function f (x) of
real numbers satisfies f(x + xy) = f(x) + f(xy)
for all real x, y, and that f(2020) = 1. Compute
f(2021).
Q. 18 ABCD is a quadrilateral whose diagonals AC
and BD intersect at O. If triangles AOB and
COD have areas 4 and 9 respectively, then
the minimum area that ABCD can have is
Q. 20 Consider the polynomials f(x) = ax2 + bx + c,
where a > 0, b, c are real, and g(x) = –2x. If
f(x) cuts x-axis at (– 2, 0) and g(x) passes
through (a, b), then the minimum value of f(x)
+ 9a + 1 is ____
Q. 21 In a city, 50% of the population can speak in
exactly one language among Hindi, English
and Tamil, while 40% of the population can
speak in at least two of these three languages.
Moreover, the number of people who cannot
speak in any of these three languages is twice
the number of people who can speak in all
these three languages. If 52% of the
population can speak in Hindi and 25% of the
population can speak exactly in one language
among English and Tamil, then the percentage
of the population who can speak in Hindi and
in exactly one more language among English
and Tamil is _____
Q. 22 A train left point A at 12 noon. Two hours later,
another train started from point A in the same
direction. It overtook the first train at 8 PM. It
is known that the sum of the speeds of the
two trains is 140 km/hr. Then, at what time
would the second train overtake the first train,
if instead the second train had started from
point A in the same direction 5 hours after the
first train? Assume that both the trains travel
at constant speeds.
Q. 24 There are 10 points in the plane, of which 5
points are collinear and no three among the
remaining are collinear. Then the number of
distinct straight lines that can be formed out
of these 10 points is
Q. 25 The x-intercept of the line that passes through
the intersection of the lines x + 2y = 4 and
2x + 3y = 6, and is perpendicular to the line
3x – y = 2 is
Directions for questions 26 to 30: In a football
tournament six teams A, B, C, D, E and F
participated. Every pair of teams had exactly one
match among them. For any team, a win fetches 2
points, a draw fetches 1 point, and a loss fetches no
points. Both the teams E and F ended with less
than 5 points. At the end of the tournament points
table is as follows (some of the entries are not shown):
It is known that: (1) Team B defeated Team
C, and (2) Team C defeated Team D.
Directions for questions 31 to 36: Read the
following passage and choose the answer that is
closest for each of the questions that arc based on
the passage.
From ancient Rome up to the Victorian era, a training
in logic and rhetoric was meant to help privileged
young men recognise spurious arguments and facts.
Times have changed, but contemporary Italy is
determined that its youth are prepared, as their
ancient counterparts were, to engage meaningfully
with the present-day version of the Forum – social
media. At the end of October, 8,000 Italian schools
will teach their students how to spot fake news
through a programme developed with the help of
journalists as well as tech giants Google and
Facebook. In Israel, the University of Haifa is
launching a course titled "Fake News".
The purpose of these courses is to ensure that public
debate, particularly during election campaigns, is
not hijacked by vested interests. Since the US
presidential election in 2016, the spectre of Russia
and its use of on line propaganda has loomed large
over public discourse in the West. In other parts of
the world too, doctored images and blatant lies have
been published by "news" websites. Given the speed
with which information is shared online, the damage
is already done by the time a fake story is exposed.
The voters of tomorrow certainly need to be armed
with the ability to sift bare facts from motivated fiction.
The effects of social media on the formation of
opinion, however, go far beyond fake news.
Traditional or legacy media is ordered by a need for
balance. A newspaper, for example, has sections
that deal with politics, crime, sports, the arts et al.
There is, at least in principle, an attempt to tell both
sides of a story in each report. On social media, the
only editor is the user herself. Algorithms ensure
that people see more of what they "like", that biases
are reinforced rather than countered. Fake news is
certainly a crucial aspect of online propaganda. But
for young citizens to form opinions based on multiple
viewpoints, they need to consciously seek out more
than they are comfortable with.
The writer suggests that the purpose of education
remains the same. Refer to the first and second
paragraphs of the passage where such an
observation has been made.
Q. 32 The passage points out that an important
difference between traditional media and
social media is that
Option (a) is correct in the light of the 3rd paragraph.
Refer tothe sentences, “On social media, the only
editor is the user herself. Algorithms ensure that
people see more of what they “like”, that biases are
reinforced rather than countered.” Option (b) is
exactly the opposite of what the passage says.
Refer to the first paragraph where the activities of
the forum are discussed. There was nothing political
about the forums. Therefore, options (a) and (c) are
out.
Directions for questions 37 to 42: Complete the
following sentences by choosing the appropriate
word/phrase from the options given below
Q. 37 The impatient and intolerant mother made
every effort to
‘Domineer’ means ‘to bully’. Option (a) is the only
grammatically correct option. In option (d), the word
‘dominion’ is used. ‘Dominion is a noun. Hence,
incorrect. The remaining two options do not convey
any sense.
Q. 38 To avoid the ecological issues, scientists and
government agencies consider how
sustainable development
The correct expression here is ‘cut corners’ which
means doing something perfunctorily so as to save
time or money. The phrase ‘poor quality materials’ is
the key here.
Q. 42 Our team has won every single match that
they have played since January. They seem
to be
On a roll is the correct expression. On a roll means
on a streak of success. Hence other options are
incorrect.
Directions for questions 43 to 45: Choose the
alternative so that the underlined part of the sentence
is rendered correct.
Q. 43 Other politicians may have claims to seniority
over their peers, based upon their
accomplishments and their ability to lead
campaigns, but Alexandria Ocasio-Cortex,
who is often described as merely being a
junior member of the House f Representatives,
has an unparalleled seniority over all of them
by virtue of her prowess in social media
management.
Here ‘as merely being’ is incorrect. Option (d) is the
correct option. It should be ‘ as a mere junior member’.
Q. 44 Although the coastal city of Kundapur was
once home to a flourishing maritime trade,
their economy has been dependent in more
recent years on the cotton textile and sugar
industries.
In (a), it’s means ‘it is’ which is incorrect. Kundapur is
singular so ‘their’ is also incorrect. It should be ‘its’.
Q. 45 Due to the progress in the field of modern
medicine and advances in nutrition and
hygiene, less people die every year from
infectious diseases then ever before.
‘less’ cannot be used with people which is
quantifiable. Also, ‘then’ should be replaced with ‘than’.
This makes only option (c) correct. ‘than have ever
before’ makes (d) incorrect.
Directions for questions 46 and 47: Each of the
paragraphs given below has a sentence missing
which is indicated by a blank. From the choices
given below each paragraph, choose the sentence
that seems most logically appropriate to complete
the paragraph.
Q. 46 Captive breeding has helped revive wildlife
such as the Eurasian beaver; the cheetah and
the Arabian Onyx. Several species have been
reintroduced into locations in order that the
ecological balance is restored. When
herbivorous bandicoots were set free in the
wild, they dug the ground and redistributed
dry leaves and branches, reducing the chance
of bush fires. But some predators may
overhunt or threaten other vulnerable species.
It is clear from the given paragraph that it is the eating
habit of the reintroduced species that is the main
concern here. (a) is incorrect as it does not promote
herbivores over carnivorous animals. The word
‘complex’ makes option (b) incorrect. (d) is a
farfetched statement that cannot be verified.
Q. 47 Postponed from last year, the Tokyo Olympics
are set to begin this year. The locals are wary,
the athletes are anxious, training sessions
are truncated, and restrictions are extensive.
_________________ Yet Japan, in many
ways is seen as a safe choice, because of
its past experience of hosting big events. It
has an impeccable reputation for discipline
and the ability to deliver the goods.
The word ‘yet’ is the clue. This means anything
preceding yet should follow the same tone which is
there at the beginning, that is, Japan is worried about
hosting the Olympics. This makes options(a) and (c)
incorrect. Option (b) is also incorrect as the Olympic
was postponed due to a pandemic. Now it is
happening, so the shadow is not there anymore.
Hence, (d) is the only logical option.
Directions for questions 48 to 52: The sentences
below have words that are missing. Choose the best
option from those given below to complete the
sentence.
Q. 48 When we think about listening, we tend to
assume that it is basically the same as
hearing; this is a ________ because it leads
us to believe that effective listening is
________. As a result, we make little effort to
learn, or develop listening skills and thereby
________ a vital communication function.
(b) is incorrect because of the term ‘impulsive’ - it
should be instinctive. It is instinctive for us to consider
that both listening and hearing are the same thing.
Also, ‘misconception’ is a better option than ‘fallacy’.
Q. 49 As vaccination rates rise and governments
relax their pandemic ________ the recovery
of the event ecosystem is happening faster
than expected. Event management ______
see the number of events and event
attendance reaching and potentially _______
pre-pandemic levels in 2019.
Regulations is the correct fit for the first blank.
Regulations are often proposed by the government.
It should be event management professionals and
not masters or experts. For the 3rd blank surpassing
is the correct word.
Q. 50 This ______, ______ man was actually the
______ manager the company ever had.
The three blanks here should complement each other.
Being well-groomed and the assertive nature of the
man have made him compassionate as a manager.
Hence (c) is the only logical option.
Q. 51 The best strategy to give an ______ is to deliver
it orally as well as in ______· It is also
important to ______ the employee's
achievements in the same manner.
The sentence is talking about the appraisal process.
The most prominent hint is for the second blank that
says ‘orally as well as…...’. Now, the correct contrast
word is ‘in writing’, making option c the correct
answer.
Q. 52 The Aravalli range is the oldest ______
geological feature anywhere in the world.
These were once tall mountains, possibly as
high as the Himalayas. Over hundreds of
millions of years these tall mountains have
been ______ to low hills and ridges. Yet, these
diminutive hills have been ______ to many
important events in Indian history.
Both ‘existing’ and ‘surviving’ can work in the first
blank. However, mountains are usually eroded and
one bears witness to events. Thus, option c has the
correct choice of words.
Q. 53 Directions for questions 53 to 57: One of the
statements below contains a word used incorrectly.
Choose the option which has the incorrect or
inappropriate usage of the word.
The use of ‘climactic’ in the fourth sentence is
incorrect. Climactic refers to (of an action, event, or
scene) exciting or thrilling and acting as a climax to a
series of events. The given sentence needs the word
‘climatic’.
Q. 54 Directions for questions 53 to 57: One of the
statements below contains a word used incorrectly.
Choose the option which has the incorrect or
inappropriate usage of the word.
Luxuriant means (of vegetation) rich and profuse in
growth; lush. It also refers to thick and healthy hair.
Hence, its usage in the second sentence is incorrect.
Q. 55 Directions for questions 53 to 57: One of the
statements below contains a word used incorrectly.
Choose the option which has the incorrect or
inappropriate usage of the word.
The difference between “intensive” and “intense” is
subtle but important. Intensive means involving a lot
of work or activity done in a short time while
intense means very strong and extreme. Hence, the
use of intensive in the first sentence is incorrect.
Q. 56 Directions for questions 53 to 57: One of the
statements below contains a word used incorrectly.
Choose the option which has the incorrect or
inappropriate usage of the word.
Apprise means to inform or tell someone about
something. Hence, the last sentence needs ‘apprise’
and not ‘appraise’.
Q. 57 Directions for questions 53 to 57: One of the
statements below contains a word used incorrectly.
Choose the option which has the incorrect or
inappropriate usage of the word.
Skin lightening is the practice of using chemical
substances in an attempt to lighten the skin or provide
an even skin color by reducing the melanin
concentration in the skin.
Q. 58 Directions for questions 58 to 60: The sentences
given below, when properly sequenced, form a
coherent paragraph. Each sentence is labelled with
a number. Decide on the most logical order and enter
the sequence of numbers in the space provided, for
e.g., 1234.
(1) In the past, companies with international
aspirations simply familiarised themselves
with any differences in the legal system
or in the procedures used in the day-today
business of import and export.
(2) Modern trade, however, demands more
from companies.
(3) Today, the company seeking international
success must also understand the people
who live and work in countries they deal
with, how they think, behave and do
business.
(4) To succeed in today's global market place,
it is essential to learn as much as
possible about the conditions in overseas
markets.
4123
To succeed in today’s global market place, it is
essential to learn as much as possible about the
conditions in overseas markets.In the past, companies
with international aspirations simply familiarised
themselves with any differences in the legal system
or in the procedures used in the day-today business
of import and export. Modern trade, however,
demands more from companies. Today, the company
seeking international success must also understand the people who live and work in countries they deal
with, how they think, behave and do business.
Q. 59 Directions for questions 58 to 60: The sentences
given below, when properly sequenced, form a
coherent paragraph. Each sentence is labelled with
a number. Decide on the most logical order and enter
the sequence of numbers in the space provided, for
e.g., 1234.
(1) It mentions a video on TikTok that
questioned an influencer's possible views
on the Israel-Palestine crisis.
(2) Social media has given us the expectation
that every video, every tweet needs to be
irreproachable and encompass the lived
experiences of the audience.
(3) Should celebs always have a take, asks
an article in a magazine.
(4) "Do you guys even care about the issue
or do you care about influencers caring
about the issue?"
2314
Social media has given us the expectation that every
video, every tweet needs to be irreproachable and
encompass the lived experiences of the audience.
Should celebs always have a take, asks an article in
a magazine. It mentions a video on TikTok that
questioned an influencer’s possible views on the
Israel-Palestine crisis. “Do you guys even care about
the issue or do you care about influencers caring
about the issue?”
Q. 60 Directions for questions 58 to 60: The sentences
given below, when properly sequenced, form a
coherent paragraph. Each sentence is labelled with
a number. Decide on the most logical order and enter
the sequence of numbers in the space provided, for
e.g., 1234.
(1) In a recent incident, villagers in a tea
estate were shocked to find a leopard cub
in a trench.
(2) The cub was then taken to the area where
she was discovered and reunited with her
mother.
(3) The 12,500 leopards in India stray into
villages due to their shrinking habitat.
(4) The wildlife vet examined and declared it
to be uninjured but dehydrated.
3142
The 12,500 leopards in India stray into villages due to
their shrinking habitat. In a recent incident, villagers
in a tea estate were shocked to find a leopard cub in
a trench. The wildlife vet examined and declared it to
be uninjured but dehydrated. The cub was then taken
to the area where she was discovered and reunited
with her mother.
