UPSC CAPF Archives

1. Assume that the Earth is a spherical ball of radius x km with a smooth

Assume that the Earth is a spherical ball of radius x km with a smooth surface so that one can travel along any direction. If you have travelled from point P on the Earth’s surface along the East direction a distance of πx km, which direction do you have to travel to return to P so that the distance required to travel is minimum ?

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East only

West only

East or West but not any other direction

Any fixed direction

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UPSC CAPF – 2023

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The most plausible intended option, considering typical geography/math puzzles and the specific options provided, is C) East or West but not any other direction.

The Earth is a sphere of radius x km. A great circle on this sphere has a circumference of 2πx km. Travelling a distance of πx km is travelling exactly half the circumference of a great circle.
The question states you travel “along the East direction a distance of πx km”. Travelling purely East means moving along a circle of latitude. A circle of latitude is a great circle only if it is the Equator (latitude 0).
If P is on the Equator, travelling East a distance πx along the Equator will take you to the point antipodal (exactly opposite) to P. Let this point be Q.
From Q (the antipodal point), the shortest distance back to P is along a great circle, and this distance is πx km. You can travel along the Equator back to P, either East or West. Both directions along the Equator lead to P in a distance of πx.
Other great circle paths from Q to P also exist, for instance, travelling North along a meridian to the North Pole (distance πx/2) and then South along a meridian from the North Pole to P (distance πx/2), totaling πx. Similarly, going via the South Pole takes πx. The initial directions from Q along these meridian paths are North and South respectively.
However, option C specifically limits the directions to “East or West but not any other direction”. This makes sense only in the simplified scenario where P is on the Equator, Q is antipodal, and the considered return paths are limited to East or West along the Equator. In this specific (likely intended) case, starting East or West from Q along the equator constitutes a minimum distance path back to P.

If P is not on the Equator, travelling East a distance πx along a latitude circle (which is not a great circle) does not necessarily take you to the antipodal point, and the shortest path back to P is a great circle whose initial direction from Q would generally be some combination of North/South and West, not purely East or West. The specific distance πx being half a great circle circumference strongly points towards the Equator/antipodal case as the intended scenario. While theoretically, North and South also yield minimum distance paths from an antipodal point, option C suggests a specific constraint or focus on the East-West movement along the original path line (the equator).

2. Suppose A, B and C are three taps fixed to the bottom of a tank with d

Suppose A, B and C are three taps fixed to the bottom of a tank with draining capacity 1 : 2 : 3. When all three of them are on, it takes 1 hour to drain out the full tank. If A and C are on but B is off, then how much time, in minutes, will it take to empty out a full tank of water ?

105

120

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UPSC CAPF – 2023

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The correct option is B) 90.

Let the volume of the tank be V.
Let the draining capacities (rates) of taps A, B, and C be R_A, R_B, and R_C respectively.
The ratio of capacities is 1:2:3, so we can write R_A = k, R_B = 2k, and R_C = 3k for some constant k.

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When all three taps are on, the total draining rate is R_A + R_B + R_C = k + 2k + 3k = 6k.
It takes 1 hour (60 minutes) to drain the full tank.
So, V = (Total Rate) * Time = (6k) * 60 = 360k.

When taps A and C are on, and B is off, the total draining rate is R_A + R_C = k + 3k = 4k.
Let T be the time in minutes it takes to empty the full tank with A and C on.
The volume drained is V.
V = (Rate A+C) * T = (4k) * T.

We know V = 360k.
So, 360k = 4k * T.
Divide both sides by 4k (assuming k > 0):
T = 360k / 4k = 360 / 4 = 90 minutes.

This problem assumes the rates are constant and additive. The unit of rate (k) cancels out in the calculation of time. The key is setting up the relationship between volume, rate, and time (Volume = Rate × Time) and using the given information about the ratio of rates and the time taken when all taps are open.

3. Car A takes 1 hour more than car B, which travels at a speed of 60 km

Car A takes 1 hour more than car B, which travels at a speed of 60 km per hour, to cover some fixed distance. If car A had doubled its speed, it could cover the distance in 1 hour less time than car B travelling at 60 km per hour. What is the original speed of car A in km per hour ?

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UPSC CAPF – 2023

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The correct option is C) 45.

Let the distance be D km, the original speed of car A be S_A km/hr, and the speed of car B be S_B = 60 km/hr.
Time taken by car B = T_B = D/60 hours.
Time taken by car A originally = T_A = D/S_A hours.
According to the first condition: T_A = T_B + 1 => D/S_A = D/60 + 1 (Equation 1)

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If car A doubles its speed (2*S_A), the new time taken is T_A’ = D/(2*S_A).
According to the second condition: T_A’ = T_B – 1 => D/(2*S_A) = D/60 – 1 (Equation 2)

Multiply Equation 2 by 2:
2 * [D/(2*S_A)] = 2 * [D/60 – 1]
D/S_A = D/30 – 2

Now we have two expressions for D/S_A:
From Eq 1: D/S_A = D/60 + 1
From the modified Eq 2: D/S_A = D/30 – 2

Equating the two expressions:
D/60 + 1 = D/30 – 2
Rearrange the terms to solve for D:
1 + 2 = D/30 – D/60
3 = (2D – D) / 60
3 = D/60
D = 180 km.

Now substitute the value of D back into Equation 1 to find S_A:
180/S_A = 180/60 + 1
180/S_A = 3 + 1
180/S_A = 4
S_A = 180 / 4
S_A = 45 km/hr.

To verify the answer, check the conditions with D=180 and S_A=45:
Car B time: 180/60 = 3 hours.
Original Car A time: 180/45 = 4 hours. 4 hours is 1 hour more than 3 hours. Condition 1 holds.
Car A doubled speed: 2 * 45 = 90 km/hr.
Car A new time: 180/90 = 2 hours. 2 hours is 1 hour less than 3 hours. Condition 2 holds.
The original speed of car A is 45 km/hr.

4. Using the code given below identify the type of farming on the basis o

Using the code given below identify the type of farming on the basis of given characteristics :

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1. The produce is consumed entirely or mainly by the family who work the land or tend the livestock.
2. If a small surplus is produced, it may be sold or bartered.
3. It is generally small scale and labour intensive with little or no technological input.

Code :

Extensive farming

Intensive farming

Subsistence farming

Commercial farming

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UPSC CAPF – 2023

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The correct option is C) Subsistence farming.

The provided characteristics describe farming primarily aimed at meeting the needs of the farming family. Producing mainly for self-consumption, selling or bartering only a small surplus, using small-scale, labour-intensive methods with little technology are all hallmarks of subsistence farming.

– Extensive farming is characterized by large land areas and relatively low inputs of labour or capital per unit area. Output per unit area is low, but total output can be high.
– Intensive farming is characterized by high inputs of labour or capital per unit area on relatively small plots to maximize yield per unit area.
– Commercial farming is undertaken with the primary objective of selling the produce in the market for profit, rather than for self-consumption. It often involves larger scale, higher technology input, and specialization.

5. Which one of the following is the busiest sea route and links two indu

Which one of the following is the busiest sea route and links two industrially developed regions of the world ?

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Mediterranean – Indian Ocean sea route

The Northern Atlantic sea route

Cape of Good Hope sea route

The North Pacific sea route

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UPSC CAPF – 2023

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The correct option is B) The Northern Atlantic sea route.

The Northern Atlantic sea route is the busiest sea route in the world. It connects two major industrially developed regions: Western Europe and Eastern North America. The high volume of trade between these highly industrialized areas contributes to its status as the busiest route.

Other important sea routes:
– Mediterranean – Indian Ocean sea route connects Europe/North Africa/Middle East to Asia/Australia via the Suez Canal. It is extremely important and busy, but generally considered less busy than the North Atlantic in terms of total freight volume.
– Cape of Good Hope sea route goes around the southern tip of Africa. Historically vital before the Suez Canal, it is still used, particularly by very large vessels or when the Suez Canal is closed or congested, but it is not the busiest.
– The North Pacific sea route connects East Asia and North America. It is a major route for trade between these significant economies but carries less volume than the North Atlantic route.

6. Which one among the following statements about ‘Drumlin’ is correct ?

Which one among the following statements about ‘Drumlin’ is correct ?

It is a streamlined hill moulded in glacial drift on the till plains.

It is a city located in central Europe.

It is a river.

It is a narrow road in Tibet.

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UPSC CAPF – 2023

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The correct answer is A. A drumlin is a glacial landform, specifically a streamlined hill composed of glacial till, molded by ice flow.

– Drumlins are typically elongated features, with their long axis oriented parallel to the direction of glacial movement.
– They are formed beneath glacial ice sheets or glaciers.
– They are composed of unconsolidated glacial drift or till (sediment deposited directly by the glacier).
– Drumlins often occur in fields or swarms, giving a characteristic landscape appearance.

The shape of a drumlin is thought to be a result of the ice molding the underlying sediment as it flows over it. They typically have a blunt, steeper “stoss” end facing up-ice and a tapering, gentler “lee” end pointing down-ice. The term “drumlin” comes from the Irish word “droimnín”, meaning “little ridge”.

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7. The greatest diversity of animal and plant species is found in :

The greatest diversity of animal and plant species is found in :

Temperate forests

Deserts and Savannas

Arctic and Alpine systems

Tropical moist forests

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UPSC CAPF – 2023

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The correct answer is D. Tropical moist forests, also known as rainforests, are characterized by warm temperatures, high rainfall, and high primary productivity, leading to the greatest diversity of animal and plant species on Earth.

– Biodiversity tends to be highest in regions with stable, favourable climates (warm and wet), high energy input (sunlight), and complex habitats.
– Tropical moist forests provide these conditions, supporting a vast array of ecological niches and complex food webs.
– Diversity generally decreases as one moves towards the poles or into drier/harsher environments.

Temperate forests have significant diversity but less than tropical forests. Deserts, Savannas, Arctic, and Alpine systems experience more extreme or seasonal conditions, which limit the number of species that can survive there compared to tropical rainforests. Factors like stable climate, high productivity, complex structure (multiple layers of vegetation), and evolutionary history contribute to the high biodiversity in tropical moist forests.

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8. Which one of the following is the deepest, inland and protected port o

Which one of the following is the deepest, inland and protected port on the east coast of India ?

Chennai

Paradip

Tuticorin

Visakhapatnam

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UPSC CAPF – 2023

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The correct answer is D. Visakhapatnam Port, located on the east coast of India in Andhra Pradesh, is known for being a natural harbour and one of the deepest and most protected (landlocked within a bay) ports in India.

– Visakhapatnam Port is situated within a sheltered bay protected by the Dolphin’s Nose hill, providing a naturally safe and protected harbour.
– It is a major port on the east coast and is known for its depth, which facilitates the handling of large vessels.
– While other ports like Chennai, Paradip, and Tuticorin are also important east coast ports, Visakhapatnam fits the description of being naturally deep, inland (relative to the open sea due to the bay), and protected most accurately among the options.

Chennai is an artificial port. Paradip is a major deepwater port at the confluence of the Mahanadi river and the Bay of Bengal, but perhaps not as “inland” or naturally protected as Visakhapatnam. Tuticorin is another artificial deepwater port. Visakhapatnam’s unique geographical setting makes it a premier natural harbour on the east coast.

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9. Which one of the following is a permeable rock that allows water to pa

Which one of the following is a permeable rock that allows water to pass through it ?

Granite

Limestone

Quartzite

Sill

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UPSC CAPF – 2023

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The correct answer is B. Permeability is the measure of the ability of a material to transmit fluids. Among the given options, limestone is generally considered permeable, especially when fractured or dissolved to form karst features.

– Permeable rocks contain interconnected pores or fractures that allow water (or other fluids) to flow through them.
– Limestone is a sedimentary rock primarily composed of calcium carbonate. While the rock matrix itself can have some porosity, its permeability is often significantly enhanced by dissolution of the carbonate material by acidic groundwater, creating channels, caves, and fractures. This forms karst topography and makes limestone important aquifers.
– Granite, Quartzite, and Sill (intrusive igneous) are typically dense, crystalline rocks with low primary porosity and permeability unless they are significantly fractured.

Permeability is distinct from porosity, which is the percentage of void space in a material. A material can be porous but not permeable if the pores are not connected. For example, clay can be highly porous but has very low permeability. Limestone can exhibit both porosity and, importantly, high permeability, particularly secondary permeability developed through dissolution and fracturing.

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10. Which one of the following conservation laws is a consequence of the N

Which one of the following conservation laws is a consequence of the Newton’s third law of motion ?

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Conservation of energy

Conservation of momentum

Conservation of charge

Conservation of mass

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UPSC CAPF – 2023

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The correct answer is B. The law of conservation of momentum is a direct consequence of Newton’s third law of motion when applied to a system of particles.

– Newton’s third law states that for every action, there is an equal and opposite reaction. If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
– When considering a system of two interacting objects, the forces they exert on each other are internal forces. According to the third law, these internal forces cancel out as a pair ($\vec{F}_{\text{AB}} = -\vec{F}_{\text{BA}}$).
– Applying Newton’s second law ($\vec{F} = m\vec{a} = d\vec{p}/dt$) to the system, the total internal force is zero. Thus, the rate of change of total momentum of the system due to internal forces is zero.
– In the absence of external forces, the total momentum of the system remains constant. This is the principle of conservation of momentum.

Newton’s laws of motion are fundamental to classical mechanics. While conservation of energy, charge, and mass are also fundamental physical laws, the conservation of momentum is the one most directly and explicitly derived from Newton’s third law in the context of interactions between particles.