UPSC NDA-2 Archives

31. If the focal length of a convex lens is 50 cm, which one of the follow

If the focal length of a convex lens is 50 cm, which one of the following is its power?

+2 dioptre

+0•02 dioptre

-0•5 dioptre

+0•5 dioptre

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The power of the convex lens with a focal length of 50 cm is +2 dioptre.

– The power of a lens (P) is the reciprocal of its focal length (f).
– The focal length must be expressed in meters when calculating power in dioptres.
– Given focal length f = 50 cm.
– Convert focal length to meters: 50 cm = 0.50 m.
– Power P = 1 / f (in meters).
– P = 1 / 0.50 m = 2 dioptres.
– A convex lens has a positive focal length and therefore a positive power.

– The unit of power of a lens is the dioptre (D), which is equal to m⁻¹.
– Convex lenses are converging lenses and are used to correct hypermetropia (far-sightedness).

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32. Consider the following velocity and time graph: Which one of the follo

Consider the following velocity and time graph:
Which one of the following is the value of average acceleration from 8 s to 12 s?

8 m/s²

12 m/s²

2 m/s²

-1 m/s²

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The correct value of average acceleration from 8 s to 12 s is -1 m/s².

– Average acceleration is defined as the change in velocity divided by the time interval.
– From the given velocity-time graph, the velocity at t = 8 s is approximately 10 m/s.
– From the graph, the velocity at t = 12 s is approximately 6 m/s.
– The time interval is Δt = 12 s – 8 s = 4 s.
– The change in velocity is Δv = v(12s) – v(8s) = 6 m/s – 10 m/s = -4 m/s.
– Average acceleration = Δv / Δt = (-4 m/s) / (4 s) = -1 m/s².

– A negative acceleration indicates that the velocity is decreasing.
– In a velocity-time graph, the slope of the line represents instantaneous acceleration. For average acceleration over an interval, we consider the endpoints of the interval.

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33. The wavelength of X-rays is of the order of

The wavelength of X-rays is of the order of

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1 Å

1 μm

1 mm

1 cm

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X-rays are a form of electromagnetic radiation with wavelengths ranging approximately from 0.01 to 10 nanometers (nm). An Angstrom (Å) is a unit of length equal to 0.1 nanometers, or 10⁻¹⁰ meters. Therefore, the wavelength of X-rays is of the order of Angstroms (1 Å = 0.1 nm). The other options represent much longer wavelengths: 1 μm (micrometer) = 1000 nm (infrared), 1 mm (millimeter) = 1,000,000 nm (microwave/radio), 1 cm (centimeter) = 10,000,000 nm (radio).

The electromagnetic spectrum covers a wide range of wavelengths and frequencies. Different types of radiation (radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays) are characterized by their distinct wavelength ranges. X-rays are high-energy, short-wavelength radiation.

X-rays are commonly used in medical imaging (radiography) due to their ability to penetrate soft tissues but be absorbed by denser materials like bones. They are also used in crystallography (X-ray diffraction) to determine the atomic and molecular structure of crystals, as the wavelengths of X-rays are comparable to the spacing between atoms in crystal lattices.

34. Which one of the following statements about the law of conservation of

Which one of the following statements about the law of conservation of mass is correct?

A given compound always contains exactly same proportion of elements.

When gases combine in a reaction, they do so in a simple ratio by volume provided all gases are at room temperature.

Matter can neither be created nor destroyed.

Equal volumes of all gases at same temperature and pressure contain equal number of molecules.

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The Law of Conservation of Mass, first stated by Antoine Lavoisier, posits that mass is conserved in a chemical reaction or physical change. This means that the total mass of the reactants before a chemical reaction is equal to the total mass of the products after the reaction. The statement “Matter can neither be created nor destroyed” is a fundamental principle expressing this law.

The Law of Conservation of Mass is a cornerstone of classical chemistry, stating that the total quantity of matter remains constant in an isolated system. It is often expressed as matter cannot be created or destroyed, though it can change form.

Option A describes the Law of Definite Proportions (Proust). Option B describes Gay-Lussac’s Law of Combining Volumes. Option D describes Avogadro’s Law. These are different fundamental laws of chemistry. While related to how matter behaves in chemical reactions, they are distinct from the Law of Conservation of Mass.

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35. Which one of the following is the chemical formula of gypsum?

Which one of the following is the chemical formula of gypsum?

CaSO₄·2H₂O

Ca₂SiO₄

2CaSO₄·H₂O

CaSO₄

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Gypsum is a mineral commonly found in evaporite deposits. Its chemical composition is calcium sulfate dihydrate, meaning it contains calcium sulfate (CaSO₄) and two molecules of water of crystallization per formula unit. The chemical formula for gypsum is CaSO₄·2H₂O.

The degree of hydration of calcium sulfate determines whether it is gypsum (dihydrate), plaster of Paris (hemihydrate), or anhydrite (anhydrous).

When gypsum (CaSO₄·2H₂O) is heated, it loses water to form calcium sulfate hemihydrate (CaSO₄·½H₂O), which is commonly known as Plaster of Paris. Further heating removes all water, resulting in anhydrous calcium sulfate (CaSO₄), or anhydrite. Gypsum is widely used in plaster, drywall (gypsum board), cement production, and as a soil conditioner.

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36. Which one of the following is not used as fertilizer?

Which one of the following is not used as fertilizer?

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Ammonium nitrate

Ammonium sulphide

Ammonium phosphate

Ammonium sulphate

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Fertilizers are substances used to provide essential nutrients to plants, primarily nitrogen (N), phosphorus (P), and potassium (K).
A) Ammonium nitrate (NH₄NO₃) is a common nitrogen fertilizer.
B) Ammonium sulphide ((NH₄)₂S) contains nitrogen and sulfur, but it is highly unstable and decomposes easily to ammonia and hydrogen sulfide gas. Due to its instability and potential toxicity (hydrogen sulfide), it is not used as a common agricultural fertilizer.
C) Ammonium phosphate (e.g., (NH₄)₂HPO₄ or NH₄H₂PO₄) are common fertilizers (like DAP and MAP) providing both nitrogen and phosphorus.
D) Ammonium sulphate ((NH₄)₂SO₄) is a common fertilizer providing nitrogen and sulfur.
Therefore, Ammonium sulphide is not used as a fertilizer.

Common fertilizers contain essential plant nutrients, primarily nitrogen, phosphorus, and potassium, often in the form of stable salts. Ammonium compounds are often used as sources of nitrogen, but their suitability as fertilizers depends on their stability and chemical properties in soil.

While ammonium sulphide contains nitrogen and sulfur, its instability makes it unsuitable for agricultural application. It is more relevant in laboratory chemistry or specific industrial processes rather than widespread use as a soil nutrient source.

37. Which one of the following is an oxidation-reduction reaction?

Which one of the following is an oxidation-reduction reaction?

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NaOH + HCl → NaCl + H₂O

CaO + H₂O → Ca(OH)₂

2Mg + O₂ → 2MgO

Na₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl

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An oxidation-reduction (redox) reaction is a chemical reaction in which the oxidation states of atoms are changed. This involves the transfer of electrons.
Let’s check the oxidation states of elements in each reaction:
A) NaOH + HCl → NaCl + H₂O: Na (+1→+1), O (-2→-2), H (+1→+1), Cl (-1→-1). No change in oxidation states. This is an acid-base neutralization reaction.
B) CaO + H₂O → Ca(OH)₂: Ca (+2→+2), O (-2→-2), H (+1→+1). No change in oxidation states. This is a combination reaction.
C) 2Mg + O₂ → 2MgO: Mg (0→+2), O (0→-2). Magnesium’s oxidation state increases from 0 to +2 (oxidation). Oxygen’s oxidation state decreases from 0 to -2 (reduction). This is a redox reaction.
D) Na₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl: Na (+1→+1), S (+6→+6), O (-2→-2), Ba (+2→+2), Cl (-1→-1). No change in oxidation states. This is a double displacement (precipitation) reaction.

Redox reactions are characterized by changes in the oxidation states of the participating atoms. Oxidation is the loss of electrons (increase in oxidation state), and reduction is the gain of electrons (decrease in oxidation state). Elemental substances (like Mg and O₂) have an oxidation state of 0.

Many common reactions are redox reactions, including combustion, corrosion, and cellular respiration. Acid-base neutralization and simple precipitation reactions typically do not involve changes in oxidation states and are therefore not redox reactions.

38. The solution of which one of the following will have pH less than 7?

The solution of which one of the following will have pH less than 7?

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NaOH

KCl

FeCl₃

NaCl

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The pH of a solution indicates its acidity or alkalinity. A pH less than 7 is acidic, pH equal to 7 is neutral, and pH greater than 7 is alkaline (basic). Let’s analyze the given options:
A) NaOH (Sodium hydroxide) is a strong base. Its solution is alkaline (pH > 7).
B) KCl (Potassium chloride) is a salt formed from a strong acid (HCl) and a strong base (KOH). Its solution is neutral (pH ≈ 7).
C) FeCl₃ (Iron(III) chloride) is a salt formed from a weak base (Fe(OH)₃) and a strong acid (HCl). When dissolved in water, metal ions with high charge density, like Fe³⁺, undergo hydrolysis, reacting with water to produce hydrated metal ions and release H⁺ ions, making the solution acidic: FeCl₃(aq) + 3H₂O(l) ⇌ Fe(OH)₃(s) + 3H⁺(aq) + 3Cl⁻(aq). Therefore, its solution will have a pH less than 7.
D) NaCl (Sodium chloride) is a salt formed from a strong acid (HCl) and a strong base (NaOH). Its solution is neutral (pH ≈ 7).

The pH of a salt solution depends on the strength of the acid and base from which the salt is formed. Salts of strong acid and strong base are neutral, salts of strong acid and weak base are acidic, and salts of weak acid and strong base are alkaline.

Hydrolysis is the reaction of a substance with water. In the case of salts formed from weak acids or bases, the ions can react with water, affecting the pH of the solution. Cations from weak bases and anions from weak acids are the ones that undergo significant hydrolysis.

39. Which one of the following is not an agent of metamorphism?

Which one of the following is not an agent of metamorphism?

Heat

Compression

Decomposition

Solution

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Metamorphism is the process by which existing rocks are transformed into new types of rock by high temperature, high pressure, and/or chemically active fluids. Heat, pressure (often resulting in compression), and chemically active fluids (which can involve solution and redeposition of minerals) are the primary agents of metamorphism. Decomposition, which is the breakdown of substances, typically organic matter, is not a process that drives the transformation of rocks under metamorphic conditions.

The three main agents of metamorphism are heat, pressure, and chemically active fluids. These agents cause mineralogical, textural, and/or chemical changes in the parent rock without complete melting.

Heat can be provided by geothermal gradient, contact with magma, or friction along faults. Pressure can be lithostatic (confining pressure from overlying rocks) or directed pressure (differential stress). Chemically active fluids are typically hot water or gas mixtures that circulate through the rock, dissolving and transporting ions, leading to the formation of new minerals. Decomposition is a biological and chemical process associated with weathering and breakdown, distinct from the high-energy transformations of metamorphism.

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40. Match List-I with List-II and select the correct answer using the code

Match List-I with List-II and select the correct answer using the code given below the Lists :

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List-I (Major Port)	List-II (Location)
A. Kolkata	1. Landlocked area
B. Mormugao	2. In the delta region
C. Visakhapatnam	3. On the riverside
D. Paradip	4. On the entrance of the estuary

A-3 B-1 C-4 D-2

A-3 B-4 C-1 D-2

A-2 B-4 C-1 D-3

A-2 B-1 C-4 D-3

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A. Kolkata Port is located on the Hooghly River, a tributary of the Ganges, making it a riverine port. This matches with ‘On the riverside’ (3).
B. Mormugao Port is located in Goa at the entrance of the Zuari River estuary. This matches with ‘On the entrance of the estuary’ (4).
C. Visakhapatnam Port is often described as a protected or landlocked harbour, with the harbour basin partially enclosed by landforms. This matches with ‘Landlocked area’ (1).
D. Paradip Port is located in Odisha at the confluence of the Mahanadi River and the Bay of Bengal, situated in the Mahanadi delta region. This matches with ‘In the delta region’ (2).
Thus, the correct match is A-3, B-4, C-1, D-2.

Understanding the geographical location and characteristics of major Indian ports is crucial for geography and economic studies. Ports have distinct locations based on their natural setting (coast, river, estuary, delta) and infrastructure development.

Kolkata is India’s only major riverine port. Visakhapatnam is known for its natural harbour sheltered by the Dolphin’s Nose hill. Mormugao is a significant iron ore exporting port. Paradip is a deep-water port handling various cargo, including iron ore, coal, and petroleum.