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Correct answer: 4)

Concept:

• The ability of carbon to reduce a metal is based upon its relative reactivity as compared to metal.
• Carbon can only reduce those metal oxides whose metals have less reactivity than carbon.

Explanation:

• Some metals involve the reduction of metal oxide by carbon at high temperatures.
• This process is known as smelting.
• Metal in the middle of the reactivity series, such as Zn, Fe, Pb and which are electropositive in nature are reduced to metals by using Carbon as a reducing agent.

Conclusion:

Thus, Some metals can be obtained by heating the metal oxide with Carbon. This process is called reduction.

Correct answer: 4)

Concept:

• Precipitation reactions occur when cations and anions in an aqueous solution combine to form an insoluble ionic solid called a precipitate.
• The precipitation reaction undergoes in aqueous solutions or medium in an ionic state.
• The reaction takes place between ions present in the aqueous solutions, forming the product.

Explanation:

• The reaction between silver nitrate (AgNO₃) and sodium chloride (NaCl), results in the formation of silver chloride (AgCl) which is an insoluble salt.

            AgNO3 + NaCl → AgCl↓ +NaNO3

• It is a Precipitation reaction.

Conclusion:

Thus, AgNO3 + NaCl → AgCl↓ +NaNO3 is an example of a Precipitation reaction.

Concept:

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. 

Calculation:

B = \({N \mu_0 I \over 2r}\)

Given:

r = 40 mm

N = 100 turns

I = 20 mA

B = \(100 \times 4\pi \times 10^{-7}\times 20 \times 10^{-3} \over 2 \times 40 \times 10^{-3} \)

= 0.00003141592 T

= 3.14×10-5 T

The correct answer is option (1).

CONCEPT:

Magnetic Induction in a Solenoid

• The magnetic field (B) at the center of a long solenoid is given by the formula:

B = μ₀ × n × I

• Where:
• B = Magnetic induction (T)
• μ₀ = Permeability of free space = 4π × 10⁻⁷ H/m
• n = Number of turns per meter = N / L
• I = Current (A)

EXPLANATION:

• Given:
• N = 2000 turns
• L = 0.5 m
• B = 0.08 T

n = N / L = 2000 / 0.5 = 4000 turns/m

0.08 = (4π × 10⁻⁷) × 4000 × I

I = 0.08 / [(4π × 10⁻⁷) × 4000]

I = 0.08 / (16π × 10⁻⁴)

I ≈ 0.08 / (0.005027) ≈ 15.91 A ≈ 16 A

Therefore, the correct answer is 16 A

Concept:

• The heating effect of electric current was discovered by James Prescott Joule in the 19^th century, which states that the amount of heat produced is directly proportional to the square of electric current flowing through it.
• It is directly proportional to the resistance of the conductor
• The relation b/w Heat & current is given by

​H = I²RT

• Magnetic effect of electric current was discovered by Hans Christian Oersted in 1820 which shows that current current-carrying conductor creates a magnetic field around it.
• The experiment used to show this effect is the Oersted experiment.
• Electromagnetic induction is a process in which a conductor is put in a particular position and the magnetic field keeps varying or the magnetic field is stationary and a conductor is moving.
• This produces a Voltage or  EMF (Electromotive Force) across the electrical conductor. Michael Faraday discovered the Law of electromagnetic induction in 1830.
• The potential difference between two points The electric potential difference between the two points refers to the work done in shifting a charge from one to another, which is given by Alessandro Volta.

Explanation:

From the above analysis, (A)-(ii), (B)-(iii), (C)-(i), (D)-(iv)

∴ The correct option is 3).

The correct answer is **As human grow older, their ears remains equally sensitive for all frequencies**.

**Key Points**

- As humans age, their hearing sensitivity decreases, especially for higher frequencies. This condition is known as **presbycusis**.
- **Presbycusis** typically affects individuals over the age of 65 and is a natural part of the aging process.
- High-frequency sounds become harder to hear, leading to difficulties in understanding speech, especially in noisy environments.
- The **audible range of sound** for humans is generally between 20 Hz to 20 kHz, but this range narrows with age.
- Various factors such as genetics, prolonged exposure to loud noises, and certain medical conditions can exacerbate hearing loss.

 **Additional Information**

- **The audible range of sound for human beings ranges between 20 Hz to 20 kHz**
- The typical human ear can detect sounds in the frequency range of 20 Hz to 20 kHz. This range is known as the **audible range**.
- **Sounds of frequencies below 20 Hz are called infrasonic waves**
- Infrasonic waves are sound waves with frequencies below the lower limit of human hearing (**20 Hz**).
- These waves can be produced by natural events like earthquakes and can be used for monitoring geological activities.
- **Dogs can hear sounds having frequencies up to 25 kHz**
- Dogs have a more acute sense of hearing compared to humans and can detect sounds up to **25 kHz** or even higher.
- This ability allows them to hear higher-pitched sounds that are inaudible to humans.

Concept:

Reflection from a plane mirror:

• The law of reflection states that the angle of incidence (\(i\)) is equal to the angle of reflection (\(r\)).
• When an angle rotates the mirror, the reflected ray rotates by an angle \(2\theta\).
• The angle of incidence is the angle between the incident ray and the normal to the mirror surface.

Formula used:

The change in the angle of the reflected ray is \(2 \times \theta\) when the mirror is rotated by an angle \(\theta\).

Calculation:

Given,

Initial angle of incidence = 25°

Mirror rotation = 7°

The new angle of incidence = 32°

The reflected ray will rotate by double the angle the mirror rotates.

⇒ Angle of rotation of the reflected ray = \(2 \times 7° = 14°\)

∴ The reflected ray is rotated by 14°.

Correct answer: 3)

Concept:

• A displacement reaction is one wherein the atom or a set of atoms is displaced by another atom in a molecule.
• For instance, when iron is added to a copper sulfate solution, it displaces the copper metal.
• A + B-C → A-C + B.
• The above equation exists when A is more reactive than B.

Explanation:

• Reactions in which two or more reactants combine to form one product are called Combination reactions. For example,
• Mg(s) + Cl₂(g) → MgCl₂(s)
• A neutralization reaction is a reaction of an acid and a base that results in an ionic compound and possibly water. For example,
• HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)
• A displacement reaction is a type of reaction that replaces part of one reactor with another. For example,
• CuSO₄(aq) + Fe(s) → FeSO₄(aq) + Cu(s)
• A decomposition reaction can be defined as a chemical reaction in which one reactant breaks down into two or more products. For example,
• 2PbNO₃(s)→ 2PbO(s) + 4NO₂(g) + O₂(g)

Conclusion:

Thus, CuSO4(aq) + Fe(s) → FeSO4(aq) + Cu(s) is a displacement reaction.

The correct answer is (A) and (C) only.

Key Points

• When coal (mainly carbon) burns in the presence of oxygen, it forms carbon dioxide and releases a large amount of heat and light.
• The chemical reaction is:

C + O₂ → CO₂ + Heat

• This is a combination reaction because two reactants (carbon and oxygen) combine to form a single product (carbon dioxide).
• It is also an exothermic reaction because heat is released during the reaction.
• It is not an endothermic reaction, as it does not absorb heat.
• It is not a decomposition reaction, since no compound breaks down into simpler substances.
• Hence, the correct answer is Option 3 – (A) and (C) only.

Additional Information

• Combination Reaction:
• Two or more substances combine to form a single product.
• Example: 2H₂ + O₂ → 2H₂O.
• Exothermic Reaction:
• A reaction that releases heat to the surroundings.
• Examples include combustion of coal, wood, LPG, and natural gas.
• Endothermic Reaction:
• A reaction that absorbs heat from the surroundings.
• Example: Thermal decomposition of calcium carbonate.
• Decomposition Reaction:
• A single compound breaks down into two or more simpler substances.
• Example: CaCO₃ → CaO + CO₂.

CONCEPT:

Calcium Chlorite vs. Bleaching Powder

• Bleaching powder commonly refers to Calcium hypochlorite, not chlorite, though in some contexts the term "chlorite" may refer to a salt of chlorous acid (HClO₂).
• Chlorite ion (ClO₂^-) has oxidation state +3.
• When forming a salt with calcium (Ca²⁺), two ClO₂^- ions are needed to balance one Ca²⁺ ion.

EXPLANATION:

• Ca(ClO₂)₂
• This is the correct formula for Calcium chlorite, as it contains two chlorite ions per calcium ion.
• CaClO₂
• Incorrect: does not balance calcium’s +2 charge properly.
• Ca(ClO₃)₂
• This is Calcium chlorate, not chlorite.
• Ca(ClO₄)₂
• This is Calcium perchlorate, not chlorite.

Therefore, the correct answer is Option 1) Ca(ClO₂)_2.