Madhyamik Class 10 Physical Science Solved Paper 2024

(a) CH₄

Explanation

Biogas primarily consists of methane (CH₄), with small amounts of other gases like carbon dioxide (CO₂). Methane is the main combustible component.

(c) Low pressure and high temperature

Explanation

At low pressure and high temperature, intermolecular forces become negligible, and gas molecules move more freely, making a real gas behave like an ideal gas.

(c) 2

Explanation

At STP, 1 mole of any gas occupies 22.4 litres.

Given volume of CO2 = 44.8 litres.

Number of moles = 44.8 ÷ 22.4 = 2

(d) 1

Explanation

For an ideal gas, the ratio of the volume coefficient to the pressure coefficient is 1, as they are directly proportional and follow the ideal gas law.

(d) μ = A + B/λ²

Explanation

The refractive index (μ) of light is inversely proportional to the square of the wavelength (λ). This is represented by the equation μ = A + B/λ².

(d) concave lens

Explanation

A concave lens forms a magnified virtual image when the object is placed between the lens and the focus.

(b) will decrease

Explanation

When the wire is stretched, its length increases and its area of cross-section decreases.

As a result, its resistance increases.

(b) 150 coulomb

Explanation

The total charge (Q) is given by

Q = I × t,

where I is current (5 A) and

t is time (30 seconds).

So, Q = 5 × 30 = 150 coulombs.

(b) 3α, 4β

Expansion

Mass number drops from 222 to 210 → 12 decrease → 3 α particles.
Atomic number drops from 86 to 84. After 3 α emissions it becomes 80, so 4 β emissions raise it to 84.

(b) C > N > 0 > F

Explanation

Electropositivity decreases from left to right across a period. Therefore, carbon (C) is more electropositive than nitrogen (N), oxygen (O), and fluorine (F).

(c) Na – 2, 8, 1 : Cl – 2, 8, 7

Explanation

Sodium (Na) has an electron configuration of 2, 8, 1, and chlorine (Cl) has an electron configuration of 2, 8, 7. In NaCl, Na loses one electron and Cl gains one electron to form a stable ionic bond.

(c) Resistance usually increases with the increase in temperature

Explanation

This statement is incorrect. In electrolytes, conductivity generally increases with temperature due to higher ion mobility, while resistance decreases.

(d) NH₃

Explanation

Nessler’s reagent is used to detect ammonia (NH₃) gas. It forms a yellow-brown color when ammonia is present.

(c) Fe

Explanation

Iron (Fe) is extracted by thermal reduction (reduction of iron ore with carbon) in a blast furnace.

(c) CH₂Cl₂ + Cl₂

Explanation

Chloroform (CHCl₃) is produced by the chlorination of dichloromethane (CH₂Cl₂) in the presence of chlorine gas.

CH₂Cl₂ + Cl₂ → CHCl₃ + HCl

Chlorine reacts with ozone:

Cl + O₃ → ClO + O₂

Chlorine monoxide reacts with another ozone molecule:

ClO + O₃ → Cl + 2O₂

Minimum temperature is noted in the mesosphere (-95ºC).

OR

The orbit of the International Space Station lies in the thermosphere.

The nature of the P vs 1/V graph is hyperbolic.

Density (ρ) ∝ 1/Temperature (T), when pressure is constant.

Coefficient of linear expansion of aluminium = 24 × 10⁻⁶ °C⁻¹.
Since 1 °C change = 1 K change, its SI unit value is 24 × 10⁻⁶ K⁻¹.

OR

The value of the volume expansion coefficient of a gas is obtained from Charles’ law.

The refractive index of a medium is independent of the angle of incidence.

beyond 2f

First, calculate the equivalent resistance of the two resistors in parallel (6 Ω and 3 Ω):

The formula for parallel resistors is:

1/R_parallel = 1\over \text{R}_1 + 1\over \text{R}_2

Substituting the values:

1/R_parallel = 1\over6 + 1\over3

1/R_parallel = 1\over6 + 2\over6 = 3/6

R_parallel = 6\over3 = 2 Ω

Now, add the series resistor (1 Ω) to the equivalent resistance of the parallel resistors:

R_total = R_parallel + R_Series

R_total = 2 Ω + 1 Ω = 3 Ω

So, the total equivalent resistance is 3 Ω.

The direction of rotation of Barlow’s wheel is determined by Fleming’s Left-Hand Rule.

One practical application of a controlled chain reaction is in nuclear power plants.

OR

Nuclear fission is conducted before nuclear fusion because fission reactions release a large amount of energy that can be used to achieve the extremely high temperatures and pressures required for nuclear fusion to occur.

KCl is soluble in water but insoluble in benzene.

During the electrolysis of water, oxidation takes place at the anode.

OR

DC (Direct Current) is used in electrolysis.

An aqueous solution of HCl gas conducts electricity because HCl dissociates into hydrogen ions (H⁺) and chloride ions (Cl⁻) when dissolved in water. These ions are charged particles that can move, allowing the solution to conduct electricity.

Organic Fertilizer produced from ammonia:

Name: Urea

Formula: CO(NH₂)₂

OR

Black Precipitate formed when H₂S gas is passed through an aqueous solution of silver nitrate:

The black precipitate formed is silver sulfide.

Formula: Ag₂S

The compound used to prepare melamine is urea.

Two organic compounds with the formula C₂H₆O but different functional groups are:

• Ethanol (alcohol) – CH₃CH₂OH
• Ether (dimethyl ether) – CH₃OCH₃

The principal constituent of LPG (Liquefied Petroleum Gas) is propane. The structural formula of propane is:

CH₃CH₂CH₃

OR

The structural formula of 1,1,2,2-tetrabromoethane is:

CHBr₂-CHBr₂

Fire ice is the common name for methane hydrate.

Chemical formula: CH₄·nH₂O

Methane gas is obtained from fire ice by heating or by reducing pressure.

Given

• V₁ = 750 cc (initial volume)
• T₁ = -3°C = 270 K (initial temperature in Kelvin)
• V₂ = 1 litre = 1000 cc (final volume)
• T₂ is the final temperature in Kelvin.

Using the formula:

750over270 = 1000overtext{T}_2

or, T₂ = (1000 × 270) over 750

T₂ = 360 K

Converting T2 back to Celsius:

T₂ = 360 K – 273 = 87°C

So, the final temperature is 87°C.

OR

Given

• Pressure (P) = 4 atm
• Volume = V (what we need to find)
• number of moles = n
• R = 0.082 L·atm·mol⁻¹·K⁻¹
• Temperature (T) = 27°C + 273 = 300 K

Number of moles (n) = 8over2 = 4 mol

PV = nRT

or, 4 × V = 4 × 0.082 × 300

or, V = 4 × 0.082 × 300over 4 = 24.6 L

So, the volume of 8 g of H₂ gas is 24.6 liters.

Angle of the prism = 60°

Angle of minimum deviation (δ) = 20°

We know,

Angle of minimum deviation (δ) = 2i – A

or, δ = 2i – A

or, 2i = δ + A = 20° + 60° = 80°

or, i = 40°

OR

Given

• Distance = 2 mm = 2 × 10⁻³ m
• Speed of light in vacuum (c) = 3 × 10⁸ m/s
• Refractive index of glass (μ) = 1.5

μ = \text{c}\over\text{v}

or, v = \text{c}\over\text{μ}

= \text{3 × 10⁸}\over\text{1.5}

= 2 × 10⁸ m/s

Current (I) = \text{EMF}\over \text{Total Resistance}

Current (I) = \text{E}\over \text{(R + r)}

∴ E = I (R + r)

Octet Rule: Atoms tend to gain, lose, or share electrons to achieve 8 electrons in their outer shell.

Exceptions:

1. BeCl₂: Beryllium has 4 electrons in its outer shell.
2. BF₃: Boron has 6 electrons in its outer shell.

OR

The differences between ionic and covalent compounds:

The formula weight is used for ionic compounds because they don’t consist of discrete molecules. Instead, they form a crystal lattice with repeating units, and the formula weight is the sum of the atomic weights of the ions in the formula unit. Molecular weight applies to covalent compounds, where discrete molecules exist.

Concentrated H₂SO₄ is not used to dry ammonia gas because it reacts with ammonia to form ammonium bisulfate (NH₄HSO₄). This reaction absorbs the ammonia gas, making H₂SO₄ ineffective as a drying agent.

Dehydrated calcium chloride (CaCl₂) is added during the electrolysis of sodium chloride (NaCl) because it lowers the melting point of sodium chloride. Sodium chloride has a high melting point, and adding CaCl₂ helps to keep the electrolyte in a molten state at lower temperatures, making the process more efficient.

OR

Two ways of preventing the rusting of iron:

1. Galvanization: Coating iron with a layer of zinc to protect it from exposure to moisture and air.
2. Paint coating: Applying a layer of paint to prevent direct contact between iron and the environment.

Denatured spirit is ethanol (ethyl alcohol) that has been mixed with chemicals (denaturants) to make it undrinkable. This is done to avoid the consumption tax on alcohol while still allowing it to be used as a solvent or fuel.

OR

Uses:

1. Ethyl alcohol: It is used as a solvent in industries and laboratories.
2. Acetic acid: It is used in the production of vinegar for culinary purposes.

Phenomenon: Brownian motion shows that gas molecules are in constant motion.

Two incorrect postulates of Kinetic Theory of Gases:

1. The volume of gas molecules is negligible compared to the volume of the container.
2. There are no forces of attraction or repulsion between gas molecules.

Balanced Eq: 3Fe + 4H₂O → Fe₃O₄ + 4H₂

.                  3 × 56 g  = 168 g                  4 × 2 = 8 g

Amount of H₂ produced by 168 g of Fe = 8 g

or, Amount of H₂ produced by 21 g of Fe = 8\over168 × 21 g = 1 g

Volume of 2 g of H₂ = 22.4 liters

∴ Volume of 1 g of H₂ = 22.4 / 2 = 11.2 liters

OR

Balanced Eq: 2SO₂ + O₂ → 2SO₃

.                             64 g    32 g     80 g

To produce 80 g of SO₃, 64 g of SO₂ is required.

∴ To produce 40 g of SO₃, 32 g of SO₂ is required.

Thermal Conductivity is the ability of a material to conduct heat. It indicates how easily heat passes through a substance.

The SI unit of Thermal Resistance is kelvin per watt (K/W). It measures how much a material resists the flow of heat.

OR

Volume expansion coefficient: The coefficient of volume expansion of a gas at constant pressure is defined as the fraction of its volume at 0°C by which the volume of a fixed mass of gas expands per degree Celsius rise in temperature.

According to Charles’ law, the volume of a given mass of gas at constant pressure expands or contracts by a fixed fraction 1/273 of its volume at 0°C for each degree Celsius rise or fall in temperature.

we get γₚ = 1 \over 273 °C^-1

= 0.00366°C^-1

Relative refractive index of medium 2 with respect to medium 1:

₁μ₂ = μ₂ / μ₁

where μ₂ and μ₁ are absolute refractive indices of medium 2 and medium 1.

Factors on which relative refractive index depends:

1. Nature of the two media.
2. Wavelength (or colour) of the light.

OR

Let the angle of prism A = 60°.

For minimum deviation, the light ray passes symmetrically, i.e. angle

of incidence i = angle of emergence e.

So, angle of refraction r = A/2 = 30°.

Relation:

δmin = 2i – A

Since i = r when symmetrical,

i = A/2 + δmin/2.

Thus, δmin occurs when the ray passes symmetrically through the prism.

Dispersion of Light is the phenomenon where light splits into its constituent colors (spectrum) when passing through a medium, such as a prism.

Identifying Monochromatic and Composite Light with a Prism:

1. Monochromatic Light: It passes through the prism without splitting, remaining as a single color.
2. Composite Light: It splits into a spectrum of colors when passed through the prism.

If the light remains a single color, it’s monochromatic; if it spreads out into a rainbow, it’s composite light.

For Series: R₁ + R₂ = 9 or, R₁ = 9 – R₂ — (i)

For Parallel: 1\over R_\text{parallel} = 1\over R_1 + 1\over R_2

or, 1\over 2 = R_1×R_2\over R_1 + R_2

or, 1\over 2 = (9 – R_2)×R_2\over 9

or, 9R₂ – R₂² = 18

or, R₂² – 9R₂ – 18 = 0

or, R₂² – (6 + 3)R₂ – 18 = 0

or, R₂(R₂ – 6) – 3(R₂ – 6) = 0

or, (R₂ – 6)(R₂ – 3) = 0

or, R₂ = 6Ω or 3 Ω

Put R₂ in eq (i) we get: R₁ = 6Ω or 3 Ω

The resistances of the two conductors are 3Ω and 6Ω.

OR

The 2 Ω and 3 Ω resistors are connected in parallel.

1\over \text{R}_{\text{Parallel}}= 1\over \text{R}_1 + 1\over \text{R}_2

1\over \text{R}_{\text{Parallel}}= 1\over 2 + 1\over 3

1\over \text{R}_{\text{Parallel}}= 3 + 2\over 6 = 5\over 6

or, R_parallel = 6\over 5 = 1.2 Ω

∴ R_total = R_parallel + R₃ = 1 Ω + 1.2 Ω = 2.2 Ω

Difference between Dynamo and Electric Motor:

Earthing is the process of connecting the electrical circuit or equipment to the ground (earth). It provides a safe path for the current to flow into the earth in case of a fault, reducing the risk of electrical shock and preventing damage to electrical devices.

Comparison between α rays and γ rays based on charge, penetrating power, and ionising power:

Ionisation energy is the amount of energy required to remove an electron from an isolated atom in the gaseous state.

Rb < Cs < Na < Li

OR

Group of A and C:

• A (atomic number n-2) is in Group 1 (alkali metals).
• C (atomic number n+1) is in Group 17 (halogens).

Highest Reductive Power:

• A (an alkali metal) has the highest reductive power.

Formula of the Compound:

• The formula of the compound formed between A (Group 1) and C (Group 17) will be AC, such as NaCl, LiCl, etc.

The purpose of electroplating is:

1. To improve the appearance of the surface.
2. To provide protection against corrosion, wear, and tear.

To plate gold on a substance, the electrolyte used is typically a solution containing gold chloride (AuCl3) or gold cyanide (Au(CN)₂⁻).

Chemicals Used:

1. Ammonia (NH₃)
2. Carbon dioxide (CO₂)

Balanced Chemical Equation:

2NH₃ + CO₂ → NH₂CONH₂ + H₂O

CH₃CH₂OH (Vapour) \overset {Al_2O_3,\ 350°C} {\longrightarrow} H₂C = CH₂ (Ethylene) + H₂O

The two uses of Ethylene are:

1. To ripen fruit and for fruit preservation.
2. To make plastic polyethylene.

OR

Carbon tetrachloride (CCl₄) is produced by chlorinating methane (CH₄) in several steps:

CH₄ + Cl₂ → CH₃Cl + HCl

CH₃Cl + Cl₂ → CH₂Cl₂ + HCl

CH₂Cl₂ + Cl₂ → CHCl₃ + HCl

CHCl₃ + Cl₂ → CCl₄ + HCl