UPSC CDS-2 Archives

11. Which one of the following statements is correct regarding the travel

Which one of the following statements is correct regarding the travel of a light beam from a rare to a dense medium?

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A light beam travelling from a rare medium to a dense medium slows down and bends towards the normal.

A light beam travelling from a rare medium to a dense medium speeds up and bends towards the normal.

A light beam travelling from a rare medium to a dense medium slows down and bends away from the normal.

A light beam travelling from a rare medium to a dense medium speeds up and bends away from the normal.

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UPSC CDS-2 – 2023

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When a light beam travels from a rarer medium (lower refractive index, e.g., air) to a denser medium (higher refractive index, e.g., glass or water), its speed decreases. This change in speed causes the light ray to bend unless it is incident normally to the surface.

According to Snell’s Law of refraction (n₁ sin θ₁ = n₂ sin θ₂), where n₁ and n₂ are the refractive indices of the first and second media, and θ₁ and θ₂ are the angles of incidence and refraction respectively (measured from the normal). If light goes from a rarer medium (n₁) to a denser medium (n₂), then n₂ > n₁. For the equation to hold, sin θ₂ must be less than sin θ₁, which means θ₂ < θ₁ (for angles in the first quadrant). A smaller angle of refraction (θ₂) compared to the angle of incidence (θ₁) means the light ray bends towards the normal.

Conversely, when light travels from a denser medium to a rarer medium, its speed increases, and it bends away from the normal. Refractive index is defined as the ratio of the speed of light in vacuum to the speed of light in the medium (n = c/v). A denser medium has a higher refractive index and thus a lower speed of light.

12. Which one of the following is the correct relation between Celsius and

Which one of the following is the correct relation between Celsius and Fahrenheit temperature scales? (Symbols carry their usual meanings)

TF = (5/9)TC + 32

TF = (9/5)TC + 36

TF = (5/9)TC + 36

TF = (9/5)TC + 32

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The Celsius and Fahrenheit scales are two common temperature scales. The relationship between them is linear. On the Celsius scale, water freezes at 0°C and boils at 100°C. On the Fahrenheit scale, water freezes at 32°F and boils at 212°F.

The interval between the freezing and boiling points of water is 100 degrees on the Celsius scale and 180 degrees (212 – 32) on the Fahrenheit scale. Thus, 100°C corresponds to 180°F. This means a 1°C change is equivalent to a 1.8°F (180/100 = 9/5) change. Starting from the freezing point (0°C = 32°F), the formula to convert Celsius (T_C) to Fahrenheit (T_F) is T_F = (9/5)T_C + 32.

To convert Fahrenheit (T_F) to Celsius (T_C), the formula is T_C = (5/9)(T_F – 32). The two scales intersect at -40 degrees, where -40°C = -40°F.

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13. A charged particle moves through a magnetic field B with a velocity v.

A charged particle moves through a magnetic field B with a velocity v. Which one of the following statements is true for the force (F) experienced by the particle?

F is maximum when v and B are parallel to each other.

F is maximum when v and B are anti-parallel to each other.

F is maximum when v and B are perpendicular to each other.

The force F is independent of the angle between v and B.

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UPSC CDS-2 – 2023

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The force experienced by a charged particle moving through a magnetic field is given by the Lorentz force formula, F = q(v × B), where q is the charge of the particle, v is its velocity, and B is the magnetic field vector. The magnitude of this force is |F| = |q| |v| |B| sin(θ), where θ is the angle between the velocity vector (v) and the magnetic field vector (B). The force is maximum when sin(θ) is maximum.

The sine function has a maximum value of 1, which occurs when the angle θ is 90 degrees (or π/2 radians). This means the magnetic force is maximum when the velocity of the charged particle is perpendicular to the magnetic field.

When v and B are parallel (θ = 0) or anti-parallel (θ = 180 degrees), sin(θ) = 0, and the magnetic force F is zero. The magnetic force is always perpendicular to both the velocity vector and the magnetic field vector.

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14. In which of the following media is the speed of sound the maximum?

In which of the following media is the speed of sound the maximum?

Glass

Stainless steel

Water

Oxygen

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UPSC CDS-2 – 2023

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The speed of sound is generally highest in solids, lower in liquids, and lowest in gases. Within solids, the speed of sound depends on the material’s density and elasticity (stiffness). Among the given options, Stainless steel is a solid with high density and stiffness, allowing sound waves to travel fastest through it compared to glass (another solid), water (liquid), and oxygen (gas).

The speed of sound is determined by the medium’s properties, specifically its bulk modulus (a measure of stiffness) and density. The formula for the speed of sound is approximately $v = \sqrt{B/\rho}$ for liquids and solids, where B is the bulk modulus and $\rho$ is the density. Solids generally have much higher bulk moduli than liquids and gases, leading to higher sound speeds, even though they might also have higher densities. Among solids, stiffer materials tend to have higher sound speeds.

Approximate speeds of sound at room temperature:
– Oxygen (Gas): ~316 m/s
– Water (Liquid): ~1480 m/s
– Glass (Solid): ~4500 – 6000 m/s (varies with type)
– Stainless Steel (Solid): ~5790 m/s (in bulk)
Comparing these values, stainless steel has the highest speed of sound among the given options.

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15. The following diagram shows a pendulum at different positions. Which o

The following diagram shows a pendulum at different positions. Which one of the following statement is true ?
[Image of a pendulum at positions P, Q, R, S, T]

The pendulum has minimum potential energy at positions P and T.

The pendulum has minimum potential energy at positions Q and S.

The pendulum has minimum potential energy at position R.

The pendulum has same potential energy at all positions.

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UPSC CDS-2 – 2023

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In a simple pendulum, potential energy is related to its height above a reference point. The lowest point in the swing represents the minimum height, and therefore, the minimum potential energy. In the diagram, position R is the lowest point of the pendulum’s swing.

Potential energy is given by PE = mgh, where m is mass, g is acceleration due to gravity, and h is height. As the pendulum swings, its height above the equilibrium position (lowest point) changes. Potential energy is maximum at the extreme positions (P and T), where the pendulum is momentarily at its highest point and stops before changing direction. Potential energy is minimum at the mean position (R), where the pendulum is at its lowest point and moving with maximum speed.

At the extreme positions (P and T), the kinetic energy is minimum (zero) because the velocity is zero. At the mean position (R), the kinetic energy is maximum because the velocity is maximum. In the absence of air resistance and friction, the total mechanical energy (sum of potential and kinetic energy) of the pendulum remains conserved throughout its swing.

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16. Which one of the following taxes is not subsumed under the Goods and

Which one of the following taxes is not subsumed under the Goods and Services Tax in India ?

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Customs Duties

Central Excise Duties

Service Tax

Taxes on Petroleum and Petroleum Products

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UPSC CDS-2 – 2023

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While many Central and State indirect taxes were subsumed under the Goods and Services Tax (GST) in India, taxes on petroleum and petroleum products are currently not subsumed and continue to be levied under the old tax regime (Central Excise Duty and State VAT/Sales Tax).

Central taxes subsumed include Central Excise Duty, Duties of Excise (Medicinal and Toilet Preparations), Additional Duties of Excise (Goods of Special Importance), Additional Duties of Excise (Textiles and Textile Products), Additional Duties of Customs (commonly known as CVD and SAD), Service Tax, and Cesses and surcharges insofar as they relate to supply of goods or services. State taxes subsumed include State VAT, Central Sales Tax, Luxury Tax, Entry Tax (all forms), Entertainment and Amusement Tax (except when levied by local bodies), Taxes on advertisements, Purchase Tax, Taxes on lotteries, betting and gambling, and State cesses and surcharges. Basic Customs Duty is also not subsumed under GST.

The taxes not subsumed under GST in India include Basic Customs Duty (BCD), Export Duty, Toll Tax, Stamp Duty, Property Tax, Electricity Duty, Taxes on Motor Vehicles, Taxes on passengers and goods, and Taxes on specific commodities like petroleum crude, high-speed diesel, motor spirit (petrol), natural gas, aviation turbine fuel, and alcohol for human consumption. While Basic Customs Duty is also not subsumed, the continued exclusion of taxes on petroleum products from the general GST framework is a key aspect of the current GST system.

17. Which of the following is/are the effects of devaluation or depreciati

Which of the following is/are the effects of devaluation or depreciation of currency ?

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1. It leads to increase in imports and decrease in exports.
2. It leads to increase in exports and decrease in imports.
3. It leads to increase in domestic inflation.
4. It leads to decrease in domestic inflation.

Select the correct answer using the code given below :

1 and 3 only

1 and 4 only

2 and 3 only

3 only

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UPSC CDS-2 – 2023

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Devaluation or depreciation of a currency makes a country’s goods cheaper for foreign buyers (increasing exports) and foreign goods more expensive for domestic buyers (decreasing imports). It also tends to increase domestic inflation due to the higher cost of imports and potential demand-pull effects from increased exports.

1. **It leads to increase in imports and decrease in exports:** Incorrect. Depreciation makes imports more expensive, thus decreasing them. It makes exports cheaper, thus increasing them.
2. **It leads to increase in exports and decrease in imports:** Correct. This is the primary intended effect of depreciation/devaluation, improving the trade balance.
3. **It leads to increase in domestic inflation:** Correct. Imports become more expensive, increasing the cost of imported raw materials and finished goods, leading to cost-push inflation. Increased foreign demand for domestic goods can also lead to higher prices if supply cannot keep up (demand-pull inflation).
4. **It leads to decrease in domestic inflation:** Incorrect.

The effects of devaluation/depreciation on trade balance are described by the Marshall-Lerner condition, which states that a currency devaluation will only improve the balance of trade if the sum of the price elasticities of demand for imports and exports is greater than one. Inflationary effects are a common side effect, especially in economies reliant on imports.

18. Which of the following are included in the definition of Narrow Money

Which of the following are included in the definition of Narrow Money ?

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1. Currency with the public
2. Demand deposits
3. ‘Other’ deposits with Reserve Bank of India
4. Banker’s deposits with Reserve Bank of India

Select the correct answer using the code given below :

1, 2 and 4

1 and 2 only

1, 2 and 3

3 and 4 only

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UPSC CDS-2 – 2023

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In India, Narrow Money (M1) is defined by the Reserve Bank of India as the sum of Currency with the Public, Demand Deposits with the Banking System, and ‘Other’ Deposits with the Reserve Bank of India. The components listed in options 1, 2, and 3 align with this definition.

1. **Currency with the public:** Notes and coins held by the public.
2. **Demand deposits:** Deposits held by the public with commercial banks and co-operative banks that are withdrawable on demand (e.g., savings accounts, current accounts).
3. **’Other’ deposits with Reserve Bank of India:** Demand deposits with RBI of entities other than banks and the government (e.g., deposits of quasi-government institutions, international financial institutions like IMF).
4. **Banker’s deposits with Reserve Bank of India:** Deposits of commercial banks with the RBI, which form a part of the reserves maintained by banks. These are included in the definition of M0 (Reserve Money) but not M1 in the standard Indian monetary aggregates.

The different measures of money supply (M0, M1, M2, M3, M4) represent different degrees of liquidity. M1 and M2 are considered Narrow Money, while M3 and M4 are considered Broad Money. M0 (Reserve Money) is the monetary base, representing the most liquid form of money.

19. Which of the following action(s) by the Government would lead to contr

Which of the following action(s) by the Government would lead to contraction of money supply in the economy ?

1. Purchase of Treasury Bills by the central bank from public
2. Sale of Treasury Bills by the central bank to public
3. Sale of foreign exchange by the central bank
4. Purchase of foreign exchange by the central bank

Select the correct answer using the code given below :

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1 and 4 only

1 and 3 only

2 and 3 only

2 only

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To contract the money supply in the economy, the central bank (like the Reserve Bank of India) needs to take actions that reduce the amount of money available with the public and commercial banks. Selling government securities and selling foreign exchange are tools used for monetary contraction.

1. **Purchase of Treasury Bills by the central bank from public:** The central bank pays money to the public in exchange for securities. This injects money into the economy, increasing money supply (expansionary).
2. **Sale of Treasury Bills by the central bank to public:** The central bank receives money from the public in exchange for securities. This withdraws money from the economy, decreasing money supply (contractionary). This is an Open Market Operation (OMO) used for contraction.
3. **Sale of foreign exchange by the central bank:** The central bank sells foreign currency and receives domestic currency in return. This takes domestic currency out of circulation, decreasing money supply (contractionary).
4. **Purchase of foreign exchange by the central bank:** The central bank buys foreign currency and pays domestic currency. This injects domestic currency into circulation, increasing money supply (expansionary).
Therefore, actions 2 and 3 lead to a contraction of the money supply.

Monetary policy tools used by central banks include OMOs (buying/selling government securities), adjusting policy rates (like repo rate, reverse repo rate), and varying reserve requirements (like Cash Reserve Ratio, Statutory Liquidity Ratio). Selling securities and selling foreign exchange are typically tightening measures.

20. Which one among the following is the highest mountain in Africa ?

Which one among the following is the highest mountain in Africa ?

Atlas Mountain

Mount Kilimanjaro

Mount Kenya

Mount Elgon

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UPSC CDS-2 – 2023

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Mount Kilimanjaro is the highest mountain in Africa. It is a dormant volcano in Tanzania.

Mount Kilimanjaro has three volcanic cones: Kibo, Mawenzi, and Shira. Its highest peak is Uhuru Peak on the Kibo cone, reaching an elevation of 5,895 metres (19,341 feet) above sea level.

The Atlas Mountains are a mountain range in Northwest Africa. Mount Kenya is the second highest mountain in Africa, located in Kenya. Mount Elgon is an extinct shield volcano on the border of Uganda and Kenya, one of the oldest and largest solitary volcanic mountains in East Africa, but not the highest.

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