Madhyamik Class 10 Physical Science Solved Paper 2026

(c) CO₂

Explanation

Carbon dioxide (CO₂) is a greenhouse gas that contributes to global warming, but it does not directly take part in the depletion of the ozone layer.

(b) 8.5 g

Explanation

At S.T.P., 1 mole of any gas occupies 22.4 L.

Therefore, 11.2 L of NH₃ = \frac{11.2}{22.4} = 0.5 mol

Molar mass of NH₃ = 14 + (1 × 3) = 17 g/mol

Mass of 0.5 mol NH₃ = 0.5 × 17 = 8.5 g

(a) 224 L

Explanation

CH₄ + 2O₂ → CO₂ + 2H₂O

From the balanced chemical equation,

1 mole of CH₄ requires 2 moles of O₂.

Therefore, 5 moles of CH₄ require = 5 × 2

= 10 moles of O₂

At S.T.P., 1 mole of any gas occupies 22.4 L.

Volume of 10 moles of O₂ = 10 × 22.4 = 224 L

(a) W m⁻¹ K⁻¹

Explanation

The SI unit of thermal conductivity is watt per metre per kelvin (W m⁻¹ K⁻¹).

Thermal conductivity is defined as the amount of heat conducted per second through unit area of a material of unit thickness when the temperature difference between its two faces is 1 K.

(a) 25 cm

Explanation

The least distance of distinct vision (near point) for a normal human eye is 25 cm.

It is the minimum distance from the eye at which an object can be seen clearly and distinctly without strain.

(a) 0°

Explanation

When a ray of light is incident normally on the surface of a glass slab, the angle of incidence is 0°.

According to Snell’s law, the ray passes undeviated along the normal. Therefore, the angle of refraction is also 0°.

(c) 6.25 × 10¹⁸

Explanation

Charge of one electron = 1.6 × 10⁻¹⁹ C

Number of electrons corresponding to 1 C = \frac{1}{1.6 \times 10^{-19}}

= 6.25 × 10¹⁸

(d) Silicon

Explanation

Silicon is a semiconductor. As its temperature increases, the number of free charge carriers also increases, causing its electrical resistance to decrease.

(a) m

Explanation

A β-particle (β⁻) is a high-speed electron emitted from the nucleus during beta decay.

Therefore, the mass of a β-particle is equal to the mass of an electron.

(a) Group 1

Explanation

An element with atomic number 19 is Potassium (K).

Electronic configuration of potassium: 2, 8, 8, 1

Since it has one electron in its outermost shell, it belongs to Group 1 (Alkali Metals) of the modern periodic table.

(b) CaO

Explanation

Quick lime (CaO) is used for drying ammonia gas (NH₃) because it absorbs moisture without reacting with ammonia.

Concentrated H₂SO₄ and P₂O₅ cannot be used because they react with ammonia.
Anhydrous CaCl₂ is also not suitable because it forms an addition compound with ammonia.

(b) Zn

Explanation

Duralumin is an alloy composed mainly of:

• Aluminium (Al)
• Copper (Cu)
• Magnesium (Mg)
• Manganese (Mn)

Zinc (Zn) is not a constituent of duralumin.

(d) Deep blue

Explanation

When excess aqueous ammonia (NH₄OH) is added to copper sulphate (CuSO₄) solution, a deep blue solution is formed due to the formation of the tetraammine copper(II) complex.

(d) None of these

Explanation

• Aqueous sugar solution: Sugar is a covalent compound that dissolves as neutral molecules, not ions.
• Pure water: Contains almost no free ions (extremely weak self-ionization).
• Liquid HCl: Pure covalent liquid without free ions (it only ionizes and conducts when dissolved in water).

(a) 109°28′

Explanation:

Methane (CH₄) has a tetrahedral structure with four identical single bonds around the central carbon atom. In a regular tetrahedron, the bond angle between any two bonds is 109°28′ (or about 109.5°).

Methane (CH₄)

Explanation

Biogas mainly contains methane, along with smaller amounts of gases such as carbon dioxide.

Carbon dioxide (CO₂)

Explanation

Carbon dioxide is involved in the breathing/respiration cycle and is also a greenhouse gas. An increase in its concentration in the atmosphere contributes to global warming.

The calorific value of natural gas is 50 kJ/g means that 50 kJ of heat energy is produced when 1 g of natural gas is completely burnt in oxygen.

False

Explanation

According to Avogadro’s Law, equal volumes of all gases at the same temperature and pressure contain an equal number of molecules, not necessarily an equal number of atoms.

The SI unit of the ideal gas constant R is: J mol⁻¹ K⁻¹

False

Explanation

The real expansion of a liquid is independent of the expansion of the vessel. It is the actual increase in the volume of the liquid due to heating.

Thermal resistance, R_t = \frac{\text{L}}{\text{K}\text{A}}

Since the length L and cross-sectional area A remain constant,

R_t ∝ \frac{1}{\text{K}}

Therefore, thermal resistance is inversely proportional to thermal conductivity.

Red light

Explanation

Red light has the longest wavelength among the colours of visible light. According to Rayleigh’s law, the intensity of scattering is inversely proportional to the fourth power of wavelength:

Scattering ∝ \frac{1}{\text{λ}^4}

Therefore, red light undergoes the minimum scattering.

Rainbow

Explanation

A rainbow is an example of a natural spectrum. It is formed due to the dispersion of sunlight by tiny water droplets present in the atmosphere.

Electric motor

The work required to move a charge Q through a potential difference V is QV joule.

Alpha (α) particle.

In a nuclear reactor, energy is produced by a controlled nuclear fission chain reaction.

2.11.1 – (c)

2.11.2 – (d)

2.11.3 – (b)

2.11.4 – (a)

Carbon tetrachloride (CCl₄)

Explanation

Carbon tetrachloride is a covalent compound because carbon and chlorine atoms form bonds by sharing electrons.

Potassium chloride (KCl) and sodium bromide (NaBr) are ionic compounds.

Potassium aurocyanide [K[Au(CN)₂]] solution is used as the electrolyte for gold plating.

In an aqueous solution of an electrolyte, electricity is conducted by the movement of positive and negative ions (cations and anions) towards the respective electrodes.

Alternating current (AC) cannot be used in electrolysis because its direction changes periodically. Hence, the electrodes continuously interchange their polarity and a continuous chemical reaction or deposition at a particular electrode cannot take place.

PbS (Lead sulphide)

Explanation

When H₂S gas is passed through an aqueous solution of lead nitrate, a black precipitate of lead sulphide (PbS) is formed.

Pb(NO₃)₂ + H₂S → PbS↓ + 2HNO₃

NH₂CONH₂ (Urea)

The reaction between ammonia gas (NH₃) and hydrogen chloride gas (HCl) produces solid ammonium chloride (NH₄Cl).

NH₃(g) + HCl(g) → NH₄Cl(s)

The product ammonium chloride is formed as a white solid.

Propan-2-ol

Explanation

The compound contains three carbon atoms and the –OH functional group is attached to the second carbon atom. Hence, its IUPAC name is propan-2-ol.

The structural formula of ethanoic acid is:

PVC (Polyvinyl Chloride) is used for making water pipes.

It is suitable for making pipes because it is durable, lightweight and resistant to corrosion.

Sustainable development means development that meets the needs of the present generation without compromising the ability of future generations to meet their own needs.

It aims at maintaining a proper balance between:

• Economic development
• Conservation of natural resources
• Protection of the environment

Initial temperature (T₁) = 0°C = 273 K

Let initial pressure = P₁ and initial volume = V₁

Final pressure (P₂) = 2P₁

Final volume (V₂) = 2V₁

From Combined Gas Law: \frac{\text{P₁V₁}}{\text{T₁}}=\frac{\text{P₂V₂}}{\text{T₂}}

⇒  \frac{\text{P₁V₁}}{273}=\frac{2\text{P₁}\times2\text{V₁}}{\text{T₂}}

⇒ T₂ = 4 × 273 = 1092 K

⇒ T₂ = 1092 − 273 = 819°C

Hence, the final temperature of the gas is 819°C.

Mass of gas (m) = 2 g

Volume (V) = 820 ml = 0.820 L

Temperature (T) = 7°C = 280 K

Pressure (P) = 2 atm

Gas constant (R) = 0.082 L atm mol⁻¹ K⁻¹

From Ideal Gas Equation: PV = nRT

Number of moles (n) = \frac{\text{PV}}{\text{RT}}

= \frac{2\times0.820}{0.082\times280}

= 0.0714 mol

Molar mass (M) = \frac{\text{Mass}}{\text{Number of moles}}

= \frac{2}{0.0714}

= 28 g mol⁻¹

Hence, the molar mass of the gas is 28 g mol⁻¹.

Refractive index of glass (μ) = 1.5

Speed of light in vacuum (c) = 3 × 10⁵ m s⁻¹

Speed of light in glass (v) = ?

We know, μ = \frac{\text{c}}{\text{v}}

Therefore,

v = \frac{\text{c}}{\text{μ}}

= \frac{3\times10^5}{1.5}

= 2 × 10⁵ m s⁻¹

Hence, the speed of light in the glass slab is 2 × 10⁵ m s⁻¹.

Magnification (m) = 10

Height of object (h₁) = 5 cm

Height of image (h₂) = ?

We know,

m = \frac{\text{h₂}}{\text{h₁}}

Therefore,

h₂ = m × h₁

= 10 × 5

= 50 cm

Hence, the length of the image is 50 cm.

Initial resistance (R₁) = 15 Ω

Let initial length = L₁

After stretching by 20%,

Final Length (L₂) = L₁ + 20% of L₁ = 1.2L₁

Since the volume of the wire remains constant,

A₁L₁ = A₂L₂

Therefore,

A₂ = \frac{\text{A₁L₁}}{\text{L₂}}

= \frac{\text{A₁}}{1.2}

We know,

R = \frac{\text{ρL}}{\text{A}}

Therefore, \frac{\text{R₂}}{\text{R₁}}=\frac{\text{L₂A₁}}{\text{L₁A₂}}

= 1.2 × 1.2

= 1.44

R₂ = 1.44 × 15

= 21.6 Ω

Hence, the new resistance of the wire is 21.6 Ω.

Liquid hydrogen chloride (HCl) is a covalent compound and does not contain free ions in the liquid state. Therefore, it cannot conduct electricity.

On the other hand, molten sodium chloride (NaCl) contains freely moving Na⁺ and Cl⁻ ions. These ions carry electric charge through the molten salt. Therefore, molten NaCl conducts electricity.

The octet rule is not obeyed by all ions. For example, lithium hydride (LiH) is an ionic compound.

Li → Li⁺ + e⁻

H + e⁻ → H⁻

The Li⁺ and H⁻ ions have only 2 electrons each in their outermost shell and attain a duplet configuration instead of an octet.

Thus, ions of some ionic compounds such as LiH attain a stable duplet configuration and do not obey the octet rule.

Solid covalent compound: Naphthalene (C₁₀H₈)

Liquid covalent compound: Carbon tetrachloride (CCl₄)

Both are covalent compounds in which atoms are bonded by the sharing of electrons.

Hydrogen sulphide (H₂S) can be prepared using Kipp’s apparatus.

It is prepared by the reaction of iron sulphide (FeS) with dilute sulphuric acid (H₂SO₄).

FeS + H₂SO₄ → FeSO₄ + H₂S↑

Hence, the gas prepared is hydrogen sulphide (H₂S).

Copper reacts slowly with moist air containing oxygen, carbon dioxide and water vapour and forms a green coating of basic copper carbonate [CuCO₃·Cu(OH)₂] on its surface.

Therefore, a copper vessel turns green when exposed to open air for a long time.

Curd and sour fruits contain acids. Therefore, they should not be kept in copper or brass vessels for a long time because:

• The acids react with the metals present in the vessels and form metal salts.
• These metal salts may be toxic and harmful to health, making the food unfit for consumption.

CH₃COOH (acetic acid) is an organic compound because it contains carbon bonded with hydrogen and possesses the characteristic –COOH functional group of organic carboxylic acids.

NaHCO₃ (sodium bicarbonate) is not an organic compound because it is an ionic salt containing the bicarbonate ion (HCO₃⁻) and is classified as an inorganic carbon compound.

Structural formula of ethylene (C₂H₄):

H₂C = CH₂

Ethylene contains a carbon-carbon double bond (C=C). Therefore, the valencies of carbon atoms are not fully saturated with hydrogen atoms.

Hence, ethylene is an unsaturated hydrocarbon.

Charles’s Law: At constant pressure, the volume of a fixed mass of gas increases or decreases by 1/273 of its volume at 0°C for every 1°C rise or fall in temperature.

If V₀ is the volume of a gas at 0°C, then its volume at t°C is:

V_t = V₀ \left(1+\frac{\text{t}}{273}\right)

or, V_t = \frac{\text{V₀}(273+\text{t})}{273}

Therefore, \frac{\text{Vₜ}}{273+\text{t}}=\frac{\text{V₀}}{273}

Hence, at constant pressure,

\frac{\text{V}}{\text{T}}=\text{Constant}

Determination of Absolute Zero

According to Charles’s law,

V_t = V₀ \left(1+\frac{\text{t}}{273}\right)

At absolute zero, the volume of an ideal gas theoretically becomes zero.

Therefore, 0 = V₀ \left(1+\frac{\text{t}}{273}\right)

or, 1 + \frac{\text{t}}{273} = 0

or, t = −273°C

Hence, the value of absolute zero on the Celsius scale is −273°C.

(i) From HgO

Balanced equation: 2HgO → 2Hg + O₂

Molar mass of HgO = 200 + 16 = 216 g/mol

From the equation,

2 × 216 g HgO produces 32 g O₂

Therefore, 216 g HgO produces = \frac{32\times216}{2\times216} = 16 g O₂

Now,

Balanced equation for KClO₃:

2KClO₃ → 2KCl + 3O₂

Molar mass of KClO₃ = 39 + 35.5 + (16 × 3)

= 122.5 g/mol

From the equation,

2 × 122.5 g KClO₃ produces 3 × 32 g O₂

Therefore, mass of KClO₃ required to produce 16 g O₂

= \frac{2\times122.5\times16}{3\times32}

= 40.83 g

Hence, 40.83 g of KClO₃ must be heated.

Mass of metallic carbonate = 200 g

Mass of metallic oxide = 112 g

Therefore, Mass of gaseous compound

= 200 − 112

= 88 g

Given, Vapour density = 22

Molar mass of gas = 2 × Vapour density

= 2 × 22

= 44 g/mol

Number of moles = \frac{\text{Mass}}{\text{Molar Mass}}

= \frac{88}{44}

= 2 mol

Hence, 2 moles of the gaseous compound are produced.

The coefficient of linear expansion of iron is 12 × 10⁻⁶ /°C means that for every 1°C rise in temperature, a unit length of iron increases in length by 12 × 10⁻⁶ of its original length.

For example, if the initial length of an iron rod is 1 m, then for a rise of temperature of 1°C, increase in length will be:

ΔL = 12 × 10⁻⁶ m

Coefficient of apparent expansion: The apparent increase in volume per unit original volume of a liquid for a rise in temperature of 1°C is called the coefficient of apparent expansion of the liquid.

Coefficient of real expansion: The actual increase in volume per unit original volume of a liquid for a rise in temperature of 1°C is called the coefficient of real expansion of the liquid.

The relationship is:

Coefficient of real expansion = Coefficient of apparent expansion + Coefficient of volume expansion of the vessel

or, γ_r = γ_a + γ_v

Let P, F and C be the pole, focus and centre of curvature of the convex mirror.

According to the law of reflection, ∠MQC’ = ∠NQC’

Since MQ ∥ PC, ∠CQC’ = ∠FCQ

Therefore, ∠FCQ = ∠FQC

Hence, FC = FQ

For paraxial rays, FQ ≈ FP = f

Therefore, FC = FP = f

Now, CP = CF + FP = 2f

Since CP = r,

r = 2f or, f = \frac{\text{r}}{2}

Use of concave mirror: It is used as a reflector in vehicle headlights.

For the same angle of incidence,

Angle of refraction in medium A = 30°

Angle of refraction in medium B = 45°

Angle of refraction in medium C = 60°

According to Snell’s law,

μ = \frac{\sin\text{i}}{\sin\text{r}}

Since the angle of incidence i is the same for all three media, the medium having the smallest angle of refraction has the highest refractive index.

Therefore,

μ_A > μ_B > μ_C

Also, v = \frac{\text{c}}{\text{μ}}

Thus, greater refractive index means lower speed of light.

Hence, the speed of light is minimum in medium A because it has the smallest angle of refraction (30°) and therefore the highest refractive index.

Myopia may occur due to:

1. Excessive curvature of the eye lens, which increases its converging power.
2. Elongation of the eyeball, which causes the image of a distant object to form in front of the retina.

Correction- Myopia is corrected by using a concave lens of suitable focal length.

Number of bulbs = 10

Power of each bulb = 50 W

Total power (P) = 10 × 50 = 500 W = 0.5 kW

Time used per day = 10 hours

Total time in 30 days (t) = 10 × 30 = 300 hours

Electrical energy consumed = 0.5 × 300

= 150 kWh = 150 B.O.T units

Total cost = 150 × 6 (Cost per unit = ₹6)

= ₹900

Hence, the total cost of electricity for 30 days is ₹900.

Let the resistances be R₁ and R₂.

For series combination:

R₁ + R₂ = 25 Ω …(1)

For parallel combination: 6 = \frac{\text{R₁R₂}}{\text{R₁}+\text{R₂}}

Using (1),

6 = \frac{\text{R₁R₂}}{25}

Therefore,

R₁R₂ = 150 …(2)

From (1), R₂ = 25 − R₁

Putting in (2), R₁(25 − R₁) = 150

25R₁ − R₁² = 150

⇒ R₁² − 25R₁ + 150 = 0

⇒ R₁² − 15R₁ − 10R₁ + 150 = 0

⇒ R₁(R₁ − 15) − 10(R₁ − 15) = 0

⇒ (R₁ − 15)(R₁ − 10) = 0

⇒ R₁ = 15 Ω or 10 Ω

Therefore, R₁ = 10 Ω, R₂ = 15 Ω

Two advantages of AC over DC

1. AC voltage can be easily increased or decreased using a transformer.
2. AC can be transmitted over long distances with less power loss by transmitting it at high voltage.

Hydroelectric power is more environmentally friendly because:

1. It uses flowing or stored water, which is a renewable source of energy.
2. It does not involve the burning of fossil fuels and hence produces almost no smoke, CO₂ or other harmful gases during electricity generation.

Nuclear Fission

The process in which a heavy atomic nucleus splits into two or more lighter nuclei, with the release of a large amount of energy and neutrons, is called nuclear fission.

For example:

²³⁵U + ¹n → ¹⁴¹Ba + ⁹²Kr + 3¹n + Energy

Nuclear fusion requires an extremely high temperature to occur. The large amount of heat produced by nuclear fission is used to provide this high temperature and initiate nuclear fusion.

Electronegativity is the tendency of an atom in a molecule to attract the shared pair of electrons towards itself.

In Group 1, electronegativity decreases from top to bottom. This is because down the group the atomic size increases. The attraction of the nucleus for the shared pair of electrons decreases.

Hence, Li > Na > K > Rb > Cs

From Moseley’s experiment, it was concluded that the atomic number, and not the atomic mass, is the fundamental property of an element.

Therefore, the modern periodic law is based on atomic number: The physical and chemical properties of elements are periodic functions of their atomic numbers.

This removed the defects caused by arranging elements according to their atomic masses.

Besides pure alumina (Al₂O₃), the molten mixture contains:

1. Cryolite (Na₃AlF₆)
2. Fluorspar (CaF₂)

In the electrolytic cell:

• Cathode: Carbon lining of the iron tank
• Anode: Graphite (carbon) rods

In the Ostwald process, ammonia is oxidised by atmospheric oxygen by passing a mixture of ammonia and air over a wired mesh of platinum or platinum–rhodium catalyst at a temperature of 750–900°C (1023–1173 K).

Nitric oxide is formed according to the reaction:

4NH₃ + 5O₂ → 4NO + 6H₂O + Heat

Thus, nitric oxide (NO) is obtained by the catalytic oxidation of ammonia with atmospheric oxygen.

Catalyst: Platinum or platinum–rhodium wired mesh

Temperature: 750–900°C (1023–1173 K)

Acetylene undergoes addition reaction with hydrogen to form ethane.

CH≡CH + H₂ {\overset{Ni}{\longrightarrow}}  CH₂=CH₂  + H₂ {\overset{Ni}{\longrightarrow}} CH₃–CH₃

Conditions:

1. Nickel (Ni) is used as a catalyst.
2. The reaction is carried out on heating.

Acetic acid reacts with sodium bicarbonate to form sodium acetate, water and carbon dioxide.

CH₃COOH + NaHCO₃ → CH₃COONa + H₂O + CO₂↑

Jute is more eco-friendly than polythene for packaging because:

1. Jute is biodegradable and decomposes naturally.
2. Polythene is non-biodegradable and causes environmental pollution.