UPSC CAPF Archives

21. The least integer when multiplied by 2940 becomes a perfect square is

The least integer when multiplied by 2940 becomes a perfect square is

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The correct answer is B) 15.

To find the least integer by which 2940 must be multiplied to make it a perfect square, we need to find the prime factorization of 2940.
2940 = 294 * 10
294 = 2 * 147 = 2 * 3 * 49 = 2 * 3 * 7^2
10 = 2 * 5
So, 2940 = (2 * 3 * 7^2) * (2 * 5) = 2^2 * 3^1 * 5^1 * 7^2.
For a number to be a perfect square, the exponents of all prime factors in its prime factorization must be even.
In the prime factorization of 2940 (2^2 * 3^1 * 5^1 * 7^2), the exponents of the prime factors are 2 (for 2), 1 (for 3), 1 (for 5), and 2 (for 7).
The exponents of 3 and 5 are odd. To make them even, we need to multiply 2940 by 3^1 and 5^1.
The least integer needed to multiply is 3 * 5 = 15.
When multiplied by 15, the number becomes 2^2 * 3^1 * 5^1 * 7^2 * (3 * 5) = 2^2 * 3^2 * 5^2 * 7^2 = (2 * 3 * 5 * 7)^2. This is a perfect square.

A number is a perfect square if and only if all the exponents in its prime factorization are even. To find the least multiplier to make a number a perfect square, identify the prime factors with odd exponents and multiply the number by the product of these prime factors raised to the power needed to make their exponents even (which will always be 1 for each such prime factor).

22. The next term of the series BCYX, EFVU, HISR, KLPO, ………. is

The next term of the series BCYX, EFVU, HISR, KLPO, ………. is

NOML

NOLM

ONML

ONLM

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The correct answer is A) NOML.

Let’s analyze the pattern of the letters in each group based on their position in the English alphabet (A=1, B=2, … Z=26).
BCYX: (2, 3, 25, 24)
EFVU: (5, 6, 22, 21)
HISR: (8, 9, 19, 18)
KLPO: (11, 12, 16, 15)

Let’s look at the sequence of positions for each position in the four-letter group:
1st letter: 2, 5, 8, 11. This is an arithmetic progression with a common difference of +3. The next term is 11 + 3 = 14 (N).
2nd letter: 3, 6, 9, 12. This is an arithmetic progression with a common difference of +3. The next term is 12 + 3 = 15 (O).
3rd letter: 25, 22, 19, 16. This is an arithmetic progression with a common difference of -3. The next term is 16 – 3 = 13 (M).
4th letter: 24, 21, 18, 15. This is an arithmetic progression with a common difference of -3. The next term is 15 – 3 = 12 (L).

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Combining the next letters based on the pattern: N O M L.
Thus, the next term in the series is NOML.

Series problems often involve sequences based on alphabetical order, arithmetic progressions, skipping letters, reversing sequences, or combinations thereof. Analyzing the positions of letters is a common method to identify the underlying pattern.

23. By selling an article for ₹ 2700, a man loses 10%. If he sells it for

By selling an article for ₹ 2700, a man loses 10%. If he sells it for ₹ 3600, his gain per cent is

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The correct answer is C) 20.

Let the Cost Price (CP) of the article be ₹ x.
When sold for ₹ 2700, there is a loss of 10%.
Selling Price (SP) = CP * (1 – Loss Percentage / 100)
2700 = x * (1 – 10/100)
2700 = x * (1 – 0.10)
2700 = x * 0.90
x = 2700 / 0.90 = 27000 / 9 = ₹ 3000.
So, the Cost Price of the article is ₹ 3000.
Now, if the article is sold for ₹ 3600, the Selling Price is ₹ 3600.
The gain is SP – CP = 3600 – 3000 = ₹ 600.
The gain percentage is (Gain / CP) * 100.
Gain percentage = (600 / 3000) * 100 = (6 / 30) * 100 = (1 / 5) * 100 = 20%.

The formula for SP with loss is SP = CP * (100 – Loss%) / 100.
The formula for SP with gain is SP = CP * (100 + Gain%) / 100.
Gain percentage is (Gain / CP) * 100.

24. In a test consisting of 150 questions, Neha answered 40% of the first

In a test consisting of 150 questions, Neha answered 40% of the first 90 questions correctly. What per cent of the 60 questions does she need to answer correctly for her score in the entire test to be 60% ?

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The correct answer is D) 90.

The total number of questions in the test is 150. Neha wants to score 60% in the entire test, which means she needs to answer 60% of 150 questions correctly.
Total correct answers required = 0.60 * 150 = 90.
In the first 90 questions, she answered 40% correctly.
Number of correct answers in the first 90 questions = 0.40 * 90 = 36.
The number of remaining questions is 150 – 90 = 60.
To achieve a total of 90 correct answers, she needs an additional 90 – 36 = 54 correct answers from the remaining 60 questions.
The percentage of correct answers needed from the remaining 60 questions is (Number of correct answers needed / Total remaining questions) * 100.
Percentage = (54 / 60) * 100 = (9 / 10) * 100 = 90%.

This is a basic percentage calculation problem involving weighted averages implicitly. The overall percentage is a weighted average of percentages in segments of the test.

25. INSPIRE is an ongoing initiative of Government of India for

INSPIRE is an ongoing initiative of Government of India for

attraction of talent for science and research

research advancement through nurturing

promoting research among various S & T stakeholders

augmenting quality manpower in niche areas of research

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The correct answer is A) attraction of talent for science and research.

The INSPIRE (Innovation in Science Pursuit for Inspired Research) program is a flagship initiative of the Department of Science & Technology (DST), Government of India. Its core objective is to attract bright young students to study science and pursue research careers. The program includes components like scholarships, fellowships, and research grants aimed at different age groups, from school children to researchers.

INSPIRE has various components like INSPIRE Award-MANAK (Million Minds Augmenting National Aspirations and Knowledge) for school students, SHE (Scholarship for Higher Education) for undergraduates, AORC (Assured Opportunity for Research Careers) which includes INSPIRE Fellowship and INSPIRE Faculty Scheme for post-graduate and post-doctoral researchers respectively.

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26. Which one of the following is NOT a palaeoclimatic geological indicato

Which one of the following is NOT a palaeoclimatic geological indicator ?

Lacustrine deposits

Ice sheets and ice cores

Evaporite deposits

Sedimentary deposits

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The correct answer is D) Sedimentary deposits. While many types of sedimentary deposits are excellent palaeoclimatic indicators (such as lacustrine deposits, evaporites, tills, coal seams, etc.), the term “Sedimentary deposits” itself is too general. Not all sedimentary deposits provide clear palaeoclimate information, and it is the specific characteristics or type of sedimentary deposit that makes it an indicator, unlike the other options which represent specific types of deposits known to be valuable palaeoclimate proxies.

– Palaeoclimatic geological indicators are geological features, structures, or deposits that contain evidence about past climate conditions.
– Lacustrine deposits (lake sediments) often preserve pollen, microfossils, and sediment layers that reflect changes in precipitation, temperature, and vegetation.
– Ice sheets and ice cores contain trapped gases, isotopes, and impurities that provide high-resolution records of past atmospheric composition and temperature.
– Evaporite deposits (e.g., salt, gypsum) form in environments with high evaporation rates, indicating arid or semi-arid conditions.
– Sedimentary deposits encompass a vast range of rocks and unconsolidated sediments formed by deposition. While climate influences many sedimentary processes and products, some sedimentary deposits are formed primarily by tectonic or erosional processes without a strong, direct, or easily interpretable climate signal. The term is too broad to be a specific indicator type in the same way as the others listed.

Specific types of sedimentary rocks like glacial till (indicating past glaciation), coal (indicating warm, humid, swampy conditions), loess (wind-blown silt indicating arid/semi-arid conditions), and certain marine sediments are indeed used as palaeoclimate indicators. However, “Sedimentary deposits” as a general category is not a specific indicator type itself.

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27. The gently sloping accumulation of coarse alluvium deposits by a braid

The gently sloping accumulation of coarse alluvium deposits by a braided stream is known as

sand bar

alluvial fan

bajada

diaras

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The correct answer is B) alluvial fan. A gently sloping accumulation of coarse alluvium deposited by a stream, especially where it exits a confined area (like a mountain valley) onto a flatter plain, is known as an alluvial fan. Braided streams, due to their high sediment load and variable discharge, are commonly associated with the formation of alluvial fans, particularly in arid or semi-arid environments or areas with high sediment supply.

– Alluvial fans are triangular or cone-shaped depositional landforms created by streams.
– They form where a stream undergoes a decrease in gradient and/or velocity, leading to the deposition of its sediment load.
– Braided streams are often the type of channel found on the surface of alluvial fans, as they are effective transporters and depositors of coarse sediment.
– The deposits typically consist of sand, gravel, and larger clasts (coarse alluvium).

While a braided stream can deposit material in other forms (like sandbars within channels or extensive alluvial plains), the description “gently sloping accumulation” points towards a large, widespread landform, and among the given options, ‘alluvial fan’ best fits the description of a significant depositional feature composed of coarse alluvium deposited by a stream, often braided, losing energy.

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28. Doldrum are 1. equatorial calms 2. calm and light winds 3. roaring

Doldrum are

1. equatorial calms
2. calm and light winds
3. roaring forties
4. variable both in position and in extent

Select the correct answer using the code given below :

1, 2 and 4

2 and 3 only

1 and 3

2, 3 and 4

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The correct answer is A) 1, 2 and 4. Doldrums are characterized by being equatorial calms, having calm and light winds, and being variable in position and extent. Statement 3, “roaring forties,” refers to completely different latitudes and wind patterns.

– The doldrums are a belt of low atmospheric pressure around the equator (typically between 5°N and 5°S latitude).
– This zone is characterized by calm or very light and variable winds due to the convergence of trade winds and rising air.
– The location and width of the doldrums (Intertropical Convergence Zone – ITCZ) are not fixed but shift seasonally with the overhead sun.
– The “Roaring Forties” are strong westerlies found between latitudes 40°S and 50°S, known for strong winds and large waves.

Historically, the doldrums were problematic for sailing ships that relied on wind power, as they could get stuck for days or weeks. Modern ships are less affected, but the zone is still associated with significant convective weather and squalls.

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29. Which one of the following does NOT fall in the areas of tropical deci

Which one of the following does NOT fall in the areas of tropical deciduous forest biomes ?

The Neotropics mainly West Indies

Indo-Malaysian zone mainly in south and south-east Asia except equatorial evergreen rainforest areas

Eastern Africa and northern Australia

North America mainly South-west America

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The correct answer is D) North America mainly South-west America. Tropical deciduous forests are found in regions with a tropical climate characterized by a distinct dry season. Southwest America (USA/Mexico border region) is predominantly an arid and semi-arid desert biome, not a tropical deciduous forest biome.

– Tropical deciduous forests (or tropical dry forests) are found in parts of the tropics with significant seasonal variation in rainfall, leading trees to shed their leaves during the dry season.
– Examples of regions with tropical deciduous forests include parts of India, Southeast Asia, Northern Australia, Eastern Africa, Mexico, Central America, and parts of the Caribbean.
– The Southwest region of the United States, however, is characterized by arid and semi-arid climates supporting desert vegetation, chaparral, and grasslands, not tropical deciduous forests.

The distribution of biomes is determined by climate patterns, primarily temperature and precipitation. Tropical deciduous forests require both high temperatures and a significant amount of rainfall, concentrated in a specific wet season, which is not characteristic of the Southwest American climate.

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30. Which one of the following is the correct arrangement of the countries

Which one of the following is the correct arrangement of the countries in descending order according to Human Development Index (HDI) value ?

Ireland, Norway, Australia, Switzerland

Norway, Switzerland, Australia, Ireland

Norway, Australia, Ireland, Switzerland

Switzerland, Ireland, Norway, Australia

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The correct answer is D) Switzerland, Ireland, Norway, Australia. Based on the Human Development Index (HDI) 2023/2024 report (which uses 2022 data), Switzerland ranks 1st, Ireland 4th, Norway 5th, and Australia 10th among the given options. Arranging them in descending order of HDI value gives Switzerland > Ireland > Norway > Australia.

– The Human Development Index (HDI) is a composite statistic of life expectancy, education, and per capita income indicators, used to rank countries into four tiers of human development.
– HDI values are published annually by the United Nations Development Programme (UNDP).
– The relative rankings of countries can change slightly from year to year based on updated data. To answer this question accurately, one needs to refer to a recent HDI report.

The HDI is a standard means of measuring well-being. While the top countries often remain high, their exact ranking can fluctuate. As of the 2023/2024 report, European countries like Switzerland, Norway, and Ireland consistently rank among the very high human development group, along with Australia.

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