IPMAT 2024 Question Paper May 23 is available for download here. IIM Indore conducted IPMAT 2024 on May 23 from 2 PM to 4 PM. IPMAT 2024 Question Paper consists of three sections: Quantitative ability, Logical reasoning, and Verbal ability carrying 4 mark each and -1 for incorrect answers to be attempted in the duration of 2 hours.
IPMAT 2024 Question Paper with Answer Key PDF May 23
| IPMAT 2024 May 23 Question Paper with Answer Key | Check Solution |
The number of factors of 1800 that are multiple of 6 is _________.
The number of real solutions of the equation \( (x^2 - 15x + 55)^{x^2 - 5x + 6} = 1 \) is __________.
The highest possible age of an employee of company A is _________.
In a group of 150 students, 52 like tea, 48 like juice, and 62 like coffee. If each student in the group likes at least one among tea, juice, and coffee, then the maximum number of students that like more than one drink is ________.
Let \( ABC \) be a triangle right-angled at \( B \) with \( AB = BC = 18 \). The area of the largest rectangle that can be inscribed in this triangle and has \( B \) as one of the vertices is ________.
A fruit seller has oranges, apples, and bananas in the ratio 3:6:7. If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is _________.
The number of pairs \( (x, y) \) of integers satisfying the inequality \( |x - 5| + |y - 5| \leq 6 \) is ________.
The price of a chocolate is increased by \( x% \) and then reduced by \( x% \). The new price is 96.76% of the original price. Then \( x \) is:
Let \( f \) and \( g \) be two functions defined by \( f(x) = |x + |x|| \) and \( g(x) = \frac{1}{x} \) for \( x \neq 0 \). If \( f(a) + g(f(a)) = 13/6 \) for some real \( a \), then the maximum possible value of \( f(g(a)) \) is:
The following table shows the number of employees
and their median age in eight companies located in a
district.

It is known that the age of all employees are integeRs.
It is known that the age of every employee in A is
strictly less than the age of every employee in B, the
age of every employee in B is strictly less than the age
of every employee in C the age of every employee in G is strictly less than the age of every employee in H.
The median age of an employee across the eight companies is ________.
The following table shows the number of employees
and their median age in eight companies located in a
district.

It is known that the age of all employees are integeRs.
It is known that the age of every employee in A is
strictly less than the age of every employee in B, the
age of every employee in B is strictly less than the age
of every employee in C the age of every employee in G is strictly less than the age of every employee in H.
In company F, the lowest possible sum of the ages of all employees is _________.
If \(4 \log_2 x - 4 \log_3 x - 16 x + 68 = 0\), then \(x - 2\) equals _________.
Person A borrows Rs. 4000 from another person B for a duration of 4 yeaRs. He borrows a portion of it at 3% simple interest per annum, while the rest at 4% simple interest per annum. If B gets Rs. 520 as total interest, then the amount A borrowed at 3% per annum in Rs. is ________.
The number of triangles with integer sides and with perimeter 15 is _______.

The angle of elevation of the top of a pole from a point A on the ground is 30°. The angle of elevation changes to 45°, after moving 20 metres towards the base of the pole. Then the height of the pole, in metres, is:
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If \(|\square + 1| + (\square + 2)^2 = 0\) and \(\square\square - 3\square\square = 1\), then the value of \(\square\) is:
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If \(\log_4 x = a\) and \(\log_{25} x = b\), then \(\log_x 10\) is:
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Let ABC be an equilateral triangle, with each side of length \(k\). If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is:
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Let ABC be a triangle with AB = AC and D be a point on BC such that \( \angle BAD = 30^\circ \). If E is a point on AC such that AD = AE, then \( \angle CDE \) equals:
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If 5 boys and 3 girls randomly sit around a circular table, the probability that there will be at least one boy sitting between any two girls, is:
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The side AB of a triangle ABC is c. The median BD is of length k. If \( \angle BDA = \theta < 90^\circ \), then the area of triangle ABC is:
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Let \( a = \frac{(\log 4) (\log 5 - \log 2)}{(\log 25)(\log 8 - \log 4)} \). Then the value of \( 5^a \) is:
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For some non-zero real values of \( a, b, \) and \( c \), it is given that \( |a| = 4 \), \( |b| = 1 \), and \( \frac{a}{c} = -\frac{3}{4} \). If \( ac > 0 \), then \( (a + c) \) equals:
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The difference between the maximum real root and the minimum real root of the equation \( (x^2 - 5)^4 + (x^2 - 7)^4 = 16 \) is:
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If \( \theta \) is the angle between the pair of tangents drawn from the point \( A(0, 2) \) to the circle \( x^2 + y^2 - 4x + 16y + 88 = 0 \), then \( \tan \theta \) equals:
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The numbers \(2^{2024}\) and \(5^{2024}\) are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is:
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A boat goes 96 km upstream in 8 hours and covers the same distance moving downstream in 6 hours. On the next day, the boat starts from point A, goes downstream for 1 hour, then upstream for 1 hour and repeats this four more times, that is, 5 upstream and 5 downstream journeys. Then the boat would be:
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If the shortest distance of a given point to a given circle is 4 cm and the longest distance is 9 cm, then the radius of the circle is:
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In a survey of 500 people, it was found that 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither a 4-wheeler nor a 2-wheeler. Then the number of people who owned both is:
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The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of \(n\) for which the sum of its first \(n\) terms is closest to 100, is:
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Let \( n \) be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then:
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The greatest number among \( 2^{3000} \), \( 3^{2000} \), \( 4^{1000} \), \( 2^{1000} \times 3^{1000} \) is:
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Given that \({^{17 - x}C_{3x + 1}}\) is defined, find the number of integer values of \(x\).
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The number of integer solutions of the equation \(x_1 + x_2 + x_3 + x_4 = 50\), where \(x_1 \ge 1\), \(x_2 \ge 2\), \(x_3 \ge 0\), and \(x_4 \ge 0\), is:
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Sagarika divides her savings of 10000 rupees to invest across two schemes A and B. Scheme A offers an interest rate of 10% per annum, compounded half-yearly, while scheme B offers a simple interest rate of 12% per annum. If at the end of the first year, the value of her investment in scheme B exceeds the value of her investment in scheme A by 2310 rupees, then the total interest, in rupees, earned by Sagarika during the first year of investment is:
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A fruit seller had a certain number of apples, bananas, and oranges at the start of the day. The number of bananas was 10 more than the number of apples, and the total number of bananas and apples was a multiple of 11. She was able to sell 70% of apples, 60% of bananas, and 50% of oranges during the day. If she was able to sell 55% of the fruits she had at the start of the day, then the minimum number of oranges she had at the start of the day was:
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The terms of a geometric progression are real and positive. If the \( p \)-th term of the progression is \( q \) and the \( q \)-th term is \( p \), then the logarithm of the first term is:
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The number of real solutions of the equation \(x^2 - 10 |x| - 56 = 0\) is:
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The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is:
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The constituency in which B got lower number of votes compared to A and C is:
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The number of votes obtained by B in S2 is:
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Assume that A and C had formed an alliance and any voter who voted for either A or C would have voted for this alliance. Then the number of seats this alliance would have won is:
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The number of votes obtained by A in S5 is:
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Comparing the number of votes obtained by A across different constituencies, the lowest number of votes were in constituency:
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Question 46:
Recently, India was in the news again as a world leader – but this time for the wrong
reason. According to the Swiss firm IQAir’s assessment of the air quality of world cities
2023, New Delhi is back to being the world’s most polluted capital. New Delhi’s annual
air quality rating is 19 times the World Health Organization’s annual limit
recommended in 2021 for its pollutant level. The picture is no better as far as the larger
Union Territory of Delhi is considered – its annual record of pollutant levels makes it
the third most polluted region globally.
Read more
Delhi may have hogged the headlines on air pollution, but the problem is far fromunique to metropolises. IQAir’s findings reveal that even lower-tier cities and towns in
India are choking because of very poor air quality. Indeed, Begusarai in Bihar is the
world’s most polluted city. Partly industrialized, housing among others an oil refinery,
Begusarai is primarily agrarian. And Begusarai is not an outlier: Mullanpur in
Punjab, which is transitioning to an urban settlement, and Siwan in Bihar are among
the 42 Indian cities/towns that are among the 50 most polluted globally.
Many judicial pronouncements have upheld “the right to clean air” as a corollary to
the fundamental right to life and pushed governments to act. But Delhi’s bad air is
despite the introduction of CNG in public transport and the building of a metro
network in the early years of this decade, and in spite of the presence of a Graded
Response Action Plan (GRAP) that kicks in when the air quality turns bad and
becomes more stringent as the air quality worsens.
Improving air quality across Indian cities requires three fundamental changes. One,
governments must turn to science to understand, measure, and monitor the problem.
Two, they have to understand that the response will have to include behavioural
changes and use a combination of incentives and penalties to achieve this. And three,
clean air has to be seen as a common public good. To be sure, it is not just the
responsibility of the Centre or a battle for courts to wage, but a fight that states and
municipal governments have to be a part of. This is the battle for our future.
Based on the information in the passage, who has endorsed the right to clean air?
In the last sentence of the passage, “This is the battle for our future,” the writer is:
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Based on the information in the passage, which one of the following statements is correct?
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The first sentence in the passage mentions that India was in the news again as a world leader. What is the writer’s intention in pointing this out?
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Which of the following points is not made by the writer?
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Question 51:
Anxiety: A Normal but Subjective Emotion
Anxiety is an emotion that all people experience from time to time, and we do that for good
reasons. It has been built into us; we have inherited it from our evolutionary past, because, in
general, anxiety has a survival function. It kicks in whenever we sense danger – we freeze,
we devote all of our attention to the danger, and our bodies react with a big release of
adrenalin, an increase in blood flow to the muscles, getting us ready to run as fast as we can
or fight as fiercely as we might.
Anxiety also helps us to focus on things when we have deadlines and, if someone is driving
too fast when we cross the road, it helps us to jump out of the way quickly. So, there is
nothing wrong with anxiety in general, and in fact, we would have difficulties if we did not
experience it to some extent. However, it can get problematic if the danger is imagined rather
than real, or is something that is exaggerated. In those cases, particularly if the perceived
danger is out of proportion to the real danger, and it is persistent and disabling, then there is a
danger of an anxiety disorder.
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Scientists are looking at what role genes play in the development of these disorders and arealso investigating the effects of environmental factors such as pollution, physical and
psychological stress, and diet. Several parts of the brain are key actors in the production of
fear and anxiety. Using brain imaging technology and neurochemical techniques, scientists
have discovered that the amygdala plays a significant role in most anxiety disorders. By
learning more about how the brain creates fear and anxiety, scientists may be able to devise
better treatments for these disorders.
The first psychotherapy treatment that was shown to be effective was ‘exposure therapy’,
which essentially encourages people in a graded way to go into their feared situations and
stay in them for as long as they can and build their confidence that way. Another is ‘group
cognitive behaviour therapy’, a talking therapy that helps people to understand the link
between negative thoughts and mood and how altering their behaviour can enable them to
manage anxiety and feel in control. There are, of course, drugs that can help people with
anxiety, but medication will not cure an anxiety disorder, it can only help to keep it under
control while the person receives psychotherapy.
There is plenty of evidence that exercise can help with anxiety problems. When stress affects
the brain, with its many nerve connections, the rest of the body feels the impact as well.
Exercise and other physical activity produce endorphins, which are chemicals in the brain
that act as natural painkillers. Additionally, getting physically tired can help people fall
asleep faster and have deeper, more relaxing sleep. As many people suffering from anxiety
often have problems with insomnia, just the ability to get a good night’s rest can change their
perspectives.
Anxiety is a normal but highly subjective human emotion. While normal anxiety serves a
beneficial and adaptive purpose, it can also become the cause of tremendous suffering for
millions of people. It is important that people recognise excessive anxiety in themselves at
the earliest, as treatment can be very successful. Leaving it untreated can be a misery
Which of the following best indicates the relationship between anxiety and survival?
Question 52:
In what way might the relationship between exercise or physical activity and anxiety relief suggest a potential solution for individuals with anxiety disorders?
In the passage, the information about anxiety treatments is organized in which of the following ways?
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Based on the information in the passage, which of the following statements best describes the potential danger associated with anxiety disorder?
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The passage is chiefly concerned with:
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Based on the information in the passage, which one of the following statements is correct?
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My supervisor seemed to be in a bad mood because he when I asked if I could leave an hour early.
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In a circus where performers share dressing rooms, training spaces and work in a fast-paced environment, the success of a show fostering team-work and collaboration.
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Anil could not go to his friend’s party, as he had fever and was .
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In his address to the candidates contesting the student council elections, the Principal said, “If you want others to take you seriously then you must ______ on issues like gender bias and inclusivity.”
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The students’ picnic plans when it started raining heavily in the morning.
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All the employees agreed that the new regulations had positive changes in the workplace.
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Sheila keeps interrupting Manohar when he is playing with his friends, but he because she is his younger sister.
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He is very careless and has loosed his keys all the time.
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I had been having a headache, so I will not attend the meeting.
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The negotiations are unsuccessful, and the Boards’ hopes to continuing talks on a future deal seems to be increasingly improbable.
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In my opinion, the psychological thrillers of Alfred Hitchcock, who is a master of suspense and horror, have more lasting impact than any other filmmaker in history.
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While the bustling city streets were filled with the cacophony of honking horns and chatter of pedestrians, the serene countryside, where time seemed to move at a slower pace, provide a welcome retreat for their seeking solace amidst the chaos of urban living.
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Most artificial intelligence (AI) applications in the fields of healthcare, industry, finance, transportation, and writing, rely heavily on deep learning and natural language processing. However, while AI systems can mimic existing styles and patterns, there is an ongoing debate about whether AI can truly possess creativity in the same sense as humans. ..............
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In an era where privacy and individualism are often prized above all else, Japanese architect Riken Yamamoto blurs the boundary between public and private. ............... His work is a testament to the power of architecture to break down barriers and to foster a sense of community. Through his innovative designs, he challenges traditional notions of public and private spaces, seamlessly blending the two realms.
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The pursuit of a career in sports offers individuals opportunities for personal fulfilment and professional success. ........... Athletes must therefore undergo rigorous training regimens to maintain peak physical condition and hone their skills. Additionally, competition in the sports industry is fierce, requiring dedication, perseverance, and mental resilience to succeed. Despite the challenges, successful athletes can enjoy lucrative contracts, endorsements, and global recognition for their achievements.
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This happened after a lorry laden with tomatoes worth 21 lakh rupees went missing. One of the three traders who had sent his tomatoes on the lorry said that they had lost contact with the driver in Nashik and that his GPS had been switched off. The traders were not sure if the truck had been hijacked or if the driver had stolen the tomatoes. This is the third time tomatoes have been stolen following the rise of tomato prices to Rs.150 per kg.
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An .......... found that one of the marathon runners had .......... slowed down in the last two kilometres and after ......... to the one behind him had let him cross the finish line just one second before he did.
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The outbreak of COVID-19 resulted in a health crisis and a drop in economic activity that were without ________ in history. While containing and ________ the spread of the virus was the first priority of public authorities, reducing the ________ of the disease and limiting the pressure on healthcare systems were also considered equally important.
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In today's fast-paced world, individuals are inundated with information, necessitating the cultivation of critical thinking skills in order to navigate the influx of data .......... . Additionally, the prevalence of fake news and misinformation presents a .......... challenge, undermining people’s trust in media and institutions. Promoting media literacy and cultivating a culture of scepticism are vital for ............ informed citizenship and democratic values.
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Conspiracy theorists suggest that if climate change is slowly turning the planet into an oven, then this must have been the outcome of our enemies’ intentional _____\. If there are no coincidences in the world, then everything, including events, can be controlled. It is only a matter of power and ______.
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It is widely argued that social media can benefit aspiring ______. Populists in particular latch on to social media today as a way to connect directly with people, _____\ restraints on their behaviour that political parties would have provided in the pre-internet age. They can also profit from echo chambers, which reinforce the sense that a whole ______ people supports a populist leader.
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In an era of globalization, cultural diversity is celebrated and valued across societies. However, the rise of xenophobia and intolerance poses a challenge to social cohesion and harmony. Building inclusive communities and promoting intercultural dialogue are essential for mutual understanding and respect among diverse populations. Additionally, educating individuals about the benefits of cultural diversity and challenging ______ are crucial steps toward creating inclusive societies and encouraging peaceful coexistence.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.
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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. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 53412 is valid, and responses such as 53412. or 53 41 2 are invalid.
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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. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 3412 is valid, and responses such as 3412. or 3 41 2 are invalid.
% Sentences
1. Farmers, however, especially during the peak farming season, ignore the warnings of the weather forecast.
2. People from some states of India have demanded that families of those who have been killed by lightning strikes should receive compensation.
3. The Minister for Disaster Management announced that over 2800 people have died after being struck by a lightning last year.
4. The Minister responded that pamphlets on the dangers of lightning and precautions to be taken are being distributed in villages.
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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. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 53412 is valid, and responses such as 53412. or 53 41 2 are invalid.
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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. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 3412 is valid, and responses such as 3412. or 3 41 2 are invalid.
% Sentences
1. In this microgravity environment, your blood also tends to move towards the heart and head.
2. Both effects are only short-lived and, after a brief period of readjustment on arriving back home, the heart and spine return to normal.
3. The heart interprets this as an increase in the amount of blood in the body and that it needs to pump less, so it shrinks.
4. In space with less gravitational force than on Earth, there’s less pressure on your spine and so it’ll get a bit longer, effectively making you as much as two inches taller.
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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. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 3412 is valid, and responses such as 3412. or 3 41 2 are invalid.
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