Bihar Board Class 10 Science Question Paper 2025 PDF (Code 112 Set-J) is available for download here. The Science exam was conducted on February 21, 2025 in the Morning Shift from 9:30 AM to 12:15 PM and in the Evening Shift from 2:00 PM to 5:15 PM. The total marks for the theory paper are 100. Students reported the paper to be easy to moderate.

Bihar Board Class 10 Science Question Paper 2025 (Code 112 Set-J) with Solutions

Bihar Board Class Science Question Paper with Answer Key Download Check Solutions

Question 1:

Which of the following is a non-renewable source of energy?

  • (1) Sun
  • (2) Wind
  • (3) Petroleum
  • (4) Flowing water
Correct Answer: (3) Petroleum
View Solution



Step 1: Definition.

Non-renewable sources of energy are those which cannot be replenished in a short period of time. They take millions of years to form.

Step 2: Analysis of options.

- Sun, Wind, and Flowing water are renewable sources.

- Petroleum is formed from fossils over millions of years and once used cannot be replenished quickly.

Step 3: Conclusion.

Hence, petroleum is a non-renewable source.
Quick Tip: Petroleum, coal, and natural gas are non-renewable sources because they take millions of years to form.


Question 2:

The actual source of energy of fossil fuel is:

  • (1) Nuclear fusion
  • (2) Sun
  • (3) Moon
  • (4) None of these
Correct Answer: (2) Sun
View Solution



Step 1: Origin of fossil fuels.

Fossil fuels are formed from plants and animals buried under the earth millions of years ago.

Step 2: Energy source.

Plants get their energy through photosynthesis from the sun. That energy is trapped and stored in fossil fuels.

Step 3: Conclusion.

Thus, the Sun is the ultimate source of fossil fuel energy.
Quick Tip: All fossil fuels store ancient solar energy captured by plants.


Question 3:

Those which 'produce heat on combustion' are called:

  • (1) Engine
  • (2) Fuel
  • (3) Heater
  • (4) None of these
Correct Answer: (2) Fuel
View Solution



Step 1: Definition.

A fuel is any substance that produces heat and energy on combustion.

Step 2: Explanation of options.

- Engine uses fuel but is not itself fuel.

- Heater is a device, not a substance.

- Fuel like coal, petrol, LPG gives heat on burning.

Step 3: Conclusion.

Therefore, substances producing heat on combustion are called fuels.
Quick Tip: Petrol, diesel, coal, LPG are common fuels that release energy when burned.


Question 4:

Euro-II is related to:

  • (1) Air pollution
  • (2) Soil pollution
  • (3) Water pollution
  • (4) None of these
Correct Answer: (1) Air pollution
View Solution



Step 1: Background.

Euro norms are standards for controlling emissions from vehicles.

Step 2: Explanation.

Euro-II was introduced to reduce harmful gases like CO, NOx, SO2 from vehicles. It directly deals with air pollution.

Step 3: Conclusion.

Hence, Euro-II relates to air pollution control.
Quick Tip: Euro norms are emission standards for vehicles to reduce air pollution.


Question 5:

Dispersion of white light is produced by:

  • (1) Glass slab
  • (2) Plane mirror
  • (3) Spherical mirror
  • (4) Prism
Correct Answer: (4) Prism
View Solution



Step 1: Dispersion meaning.

Dispersion is the splitting of white light into seven colours (VIBGYOR).

Step 2: Device responsible.

A prism bends different colours at different angles due to refraction. This causes dispersion.

Step 3: Conclusion.

Hence, prism produces dispersion of light.
Quick Tip: Dispersion is best shown in Newton’s prism experiment.


Question 6:

The device which directly converts solar energy into electricity is known as:

  • (1) Daniel cell
  • (2) Leclanche cell
  • (3) Solar cell
  • (4) None of these
Correct Answer: (3) Solar cell
View Solution



Step 1: Definition.

A solar cell is a device that directly converts solar energy into electrical energy using photovoltaic effect.

Step 2: Options.

Daniel cell and Leclanche cell are chemical cells, not solar energy devices.

Step 3: Conclusion.

Hence, the correct device is solar cell.
Quick Tip: Solar cells work on the principle of photovoltaic effect.


Question 7:

Which one of the following is a strong base?

  • (1) NaOH
  • (2) Cu(OH)2
  • (3) NH4OH
  • (4) Mg(OH)2
Correct Answer: (1) NaOH
View Solution



Step 1: Definition.

Strong bases are those which completely dissociate in water.

Step 2: Explanation.

- NaOH dissociates completely, hence strong base.

- Cu(OH)2, NH4OH, Mg(OH)are weak bases because they dissociate partially.

Step 3: Conclusion.

Thus, NaOH is the correct answer.
Quick Tip: Strong bases are generally hydroxides of alkali metals like NaOH and KOH.


Question 8:

What is the chemical formula of dry ice?

  • (1) CO
  • (2) CO2
  • (3) H2O
  • (4) H2O2
Correct Answer: (2) CO2
View Solution



Step 1: Definition.

Dry ice is the solid form of carbon dioxide.

Step 2: Explanation.

It is called "dry" because it sublimates directly into gas without becoming liquid.

Step 3: Conclusion.

Thus, formula of dry ice is CO2.
Quick Tip: Dry ice is widely used for cooling and fog effects in stage shows.


Question 9:

Which one of the following proteins is responsible for the red colour of blood?

  • (1) Heparin
  • (2) Haemoglobin
  • (3) Thrombin
  • (4) Fibrinogen
Correct Answer: (2) Haemoglobin
View Solution



Step 1: Background.

Haemoglobin is a protein present in red blood cells. It binds oxygen and contains iron.

Step 2: Explanation.

The iron in haemoglobin gives blood its characteristic red colour.

Step 3: Conclusion.

Hence, haemoglobin is responsible for red colour.
Quick Tip: Haemoglobin carries oxygen from lungs to tissues.


Question 10:

The colour of chlorophyll pigment is:

  • (1) Black
  • (2) Yellow
  • (3) Blue
  • (4) Green
Correct Answer: (4) Green
View Solution



Step 1: Definition.

Chlorophyll is the green pigment present in plant leaves.

Step 2: Explanation.

It absorbs red and blue light for photosynthesis and reflects green light, making plants look green.

Step 3: Conclusion.

Thus, chlorophyll pigment is green.
Quick Tip: Chlorophyll is essential for photosynthesis as it traps solar energy.


Question 11:

The hardest part of the teeth is:

  • (1) dentine
  • (2) enamel
  • (3) pulp cavity
  • (4) canine
Correct Answer: (2) enamel
View Solution



Step 1: Fact.

Enamel is a highly mineralised layer (mainly hydroxyapatite) covering the crown of the tooth.

Step 2: Comparison.

Dentine lies below enamel and is softer; pulp cavity contains nerves and blood vessels; canine is a type of tooth, not a tissue.

Step 3: Conclusion.

Therefore, enamel is the hardest part of the tooth.
Quick Tip: Enamel is the hardest substance in the human body—harder than bone.


Question 12:

Which of the following is necessary in the synthesis of thyroxine hormone?

  • (1) Chlorine
  • (2) Iodine
  • (3) Manganese
  • (4) Iron
Correct Answer: (2) Iodine
View Solution



Step 1: Key idea.

Thyroxine (T4) and triiodothyronine (T3) are iodinated hormones of the thyroid gland.

Step 2: Application.

Iodine deficiency leads to reduced thyroxine, causing goitre and cretinism.

Step 3: Conclusion.

Hence iodine is essential for thyroxine synthesis.
Quick Tip: Use iodised salt to prevent iodine-deficiency disorders.


Question 13:

Which is an example of a decomposer?

  • (1) Cow
  • (2) Fungus
  • (3) Tiger
  • (4) Grass
Correct Answer: (2) Fungus
View Solution



Step 1: Definition.

Decomposers break down dead organic matter into simpler substances, recycling nutrients.

Step 2: Analysis.

Fungi (and many bacteria) are classic decomposers; cow and tiger are consumers; grass is a producer.

Step 3: Conclusion.

Therefore, fungus is a decomposer.
Quick Tip: Decomposers close the nutrient cycle by converting complex organics back to soil nutrients.


Question 14:

Which is the main source of energy on earth?

  • (1) Coal
  • (2) Wood
  • (3) Water
  • (4) Sun
Correct Answer: (4) Sun
View Solution



Step 1: Core concept.

Almost all natural energy on Earth originates from the Sun—directly (solar energy) or indirectly (wind, water cycle, biomass, fossil fuels).

Step 2: Conclusion.

Hence, the Sun is the ultimate/main source of energy on Earth.
Quick Tip: Even fossil fuels store ancient solar energy captured by plants.


Question 15:

Which of the following is/are a part of environment?

  • (1) Atmosphere
  • (2) Hydrosphere
  • (3) Lithosphere
  • (4) All of these
Correct Answer: (4) All of these
View Solution



Step 1: Understanding environment.

The environment includes air (atmosphere), water bodies (hydrosphere), and land/rocks (lithosphere), along with the biosphere.

Step 2: Conclusion.

Therefore, all listed spheres are components of the environment.
Quick Tip: Remember: Atmosphere + Hydrosphere + Lithosphere + Biosphere = Environment.


Question 16:

How many trophic levels are there in a forest ecosystem?

  • (1) 1
  • (2) 2
  • (3) 3
  • (4) 4
Correct Answer: (4) 4
View Solution



Step 1: Concept.

Typical forest food chains include: producers (plants), primary consumers (herbivores), secondary consumers (small carnivores), and tertiary consumers (top carnivores).

Step 2: Conclusion.

Thus, commonly we consider four trophic levels in a forest ecosystem.
Quick Tip: Energy decreases by about 90% at each successive trophic level (10% law).


Question 17:

The reaction in which ions are exchanged is called:

  • (1) displacement
  • (2) double displacement
  • (3) combination
  • (4) precipitation
Correct Answer: (2) double displacement
View Solution



Step 1: Definitions.

Double displacement reactions involve mutual exchange of ions between two compounds (AB + CD \(\rightarrow\) AD + CB).

Step 2: Note.

Precipitation is a type of double displacement where an insoluble solid forms.

Step 3: Conclusion.

Hence the general name is double displacement.
Quick Tip: If two ionic solutions react to form a precipitate, think “double displacement.”


Question 18:

Which of the following equations is not} balanced?

  • (1) 2H2 + O2 \(\rightarrow\) 2H2O
  • (2) 2KClO3 \(\rightarrow\) 2KCl + 3O2
  • (3) H2 + Cl2 \(\rightarrow\) 2HCl
  • (4) Pb(NO3)2 \(\rightarrow\) PbO + NO2 + O2
Correct Answer: (4) Pb(NO3)2 \(\rightarrow\) PbO + NO2 + O2
View Solution



Step 1: Count atoms on each side.

LHS: Pb=1, N=2, O=6.

RHS: Pb=1, N=1 (in NO2), O=5 (1 in PbO, 2 in NO2, 2 in O2).

Step 2: Observation.

N and O counts differ, so the equation is not balanced. Others are balanced.

Step 3: Conclusion.

Thus option (4) is not balanced.
Quick Tip: Always tally each element’s atoms on LHS and RHS to check balance.


Question 19:

The pH value of any neutral solution is:

  • (1) 0
  • (2) 4
  • (3) 7
  • (4) 14
Correct Answer: (3) 7
View Solution



Step 1: Concept.

Neutral solutions have equal concentrations of H+ and OH-- ions.

Step 2: Definition.

On the pH scale (0–14), neutrality corresponds to pH = 7 at 25\(^\circ\)C.

Step 3: Conclusion.

Hence, neutral solutions have pH 7.
Quick Tip: pH < 7 acidic; pH > 7 basic; pH = 7 neutral.


Question 20:

Which of the following is a natural indicator?

  • (1) Phenolphthalein
  • (2) Turmeric
  • (3) Methyl orange
  • (4) None of these
Correct Answer: (2) Turmeric
View Solution



Step 1: Idea.

Natural indicators are obtained from plants (e.g., litmus, red cabbage, turmeric).

Step 2: Analysis.

Phenolphthalein and methyl orange are synthetic indicators; turmeric is natural and turns reddish-brown in bases.

Step 3: Conclusion.

Therefore, turmeric is a natural indicator.
Quick Tip: Turmeric stains become reddish-brown with soap (basic), a quick home-test for bases.


Question 21:

What is the chemical formula of washing soda?

  • (1) Na2CO3.7H2O
  • (2) Na2CO3.5H2O
  • (3) Na2CO3.10H2O
  • (4) Na2CO3.H2O
Correct Answer: (3) Na2CO3.10H2O
View Solution



Step 1: Identification.

Washing soda is the decahydrate form of sodium carbonate.

Step 2: Formula.

Its correct chemical formula is Na2CO3.10H2O.

Step 3: Conclusion.

Thus, option (3) is correct.
Quick Tip: Washing soda is used for cleaning and water softening because it removes hardness.


Question 22:

Which of the following is a heterogeneous compound?

  • (1) Chalk
  • (2) Limestone
  • (3) Marble
  • (4) Plaster of Paris
Correct Answer: (3) Marble
View Solution



Step 1: Concept.

Heterogeneous compounds are those in which the composition is not uniform throughout.

Step 2: Explanation.

Marble (CaCO3 with impurities) has non-uniform distribution of minerals, making it heterogeneous.

Step 3: Conclusion.

Thus, marble is the heterogeneous compound among the given options.
Quick Tip: Impurities in marble cause its different colours and make it heterogeneous.


Question 23:

The hardest natural substance is:

  • (1) Iron
  • (2) Gold
  • (3) Silver
  • (4) Diamond
Correct Answer: (4) Diamond
View Solution



Step 1: Fact.

Diamond is made of pure carbon atoms arranged in a rigid tetrahedral structure.

Step 2: Hardness.

This structure makes diamond the hardest natural substance on Mohs hardness scale.

Step 3: Conclusion.

Hence, diamond is the hardest natural substance.
Quick Tip: Diamond is used in cutting tools due to its extreme hardness.


Question 24:

Which of the following ions can turn red litmus paper blue?

  • (1) H+
  • (2) OH--
  • (3) O2--
  • (4) None of these
Correct Answer: (2) OH--
View Solution



Step 1: Recall.

Red litmus turns blue in alkaline/basic medium.

Step 2: Explanation.

OH-- ions are responsible for basic nature. Thus, they turn red litmus paper blue.

Step 3: Conclusion.

So, the correct answer is OH--.
Quick Tip: Acids release H+ (turn blue litmus red), bases release OH-- (turn red litmus blue).


Question 25:

Fruit-ripening hormone is:

  • (1) Ethylene
  • (2) Auxin
  • (3) Gibberellin
  • (4) Cytokinin
Correct Answer: (1) Ethylene
View Solution



Step 1: Recall.

Ethylene is a gaseous plant hormone responsible for ripening of fruits like bananas and mangoes.

Step 2: Other hormones.

Auxins promote growth, gibberellins stimulate elongation, cytokinins promote cell division.

Step 3: Conclusion.

Thus, the fruit ripening hormone is ethylene.
Quick Tip: Ethylene gas is often used commercially to ripen fruits quickly.


Question 26:

Mushroom is:

  • (1) A saprophyte
  • (2) A parasite
  • (3) An autotroph
  • (4) An algae
Correct Answer: (1) A saprophyte
View Solution



Step 1: Recall.

Mushrooms feed on dead and decaying organic matter.

Step 2: Explanation.

This mode of nutrition is called saprophytic. Mushrooms cannot make their own food.

Step 3: Conclusion.

Hence, mushrooms are saprophytes.
Quick Tip: Fungi like mushrooms decompose organic matter and recycle nutrients.


Question 27:

The molecular formula of ozone is:

  • (1) O2
  • (2) O3
  • (3) O4
  • (4) O3
Correct Answer: (2) O3
View Solution



Step 1: Recall.

Ozone is an allotrope of oxygen formed by three oxygen atoms.

Step 2: Properties.

It forms the ozone layer which protects Earth from harmful UV radiation.

Step 3: Conclusion.

Thus, formula of ozone is O3.
Quick Tip: Ozone is less stable than O2 and has a sharp smell.


Question 28:

Which mode of nutrition is found in fungi?

  • (1) Autotrophic
  • (2) Holozoic
  • (3) Saprophytic
  • (4) None of these
Correct Answer: (3) Saprophytic
View Solution



Step 1: Definition.

Saprophytic nutrition means obtaining food from dead organic matter.

Step 2: Explanation.

Fungi cannot photosynthesise; they release enzymes and absorb nutrients.

Step 3: Conclusion.

Thus, fungi show saprophytic nutrition.
Quick Tip: Fungi recycle nutrients back to the ecosystem via saprophytic nutrition.


Question 29:

The flow of energy in an ecosystem is:

  • (1) Unidirectional
  • (2) Bidirectional
  • (3) Multidirectional
  • (4) Cyclic
Correct Answer: (1) Unidirectional
View Solution



Step 1: Recall.

Energy enters the ecosystem through sunlight (producers) and flows to herbivores, carnivores, and decomposers.

Step 2: Concept.

Unlike matter, energy cannot be recycled. It flows in one direction only.

Step 3: Conclusion.

Thus, energy flow in an ecosystem is unidirectional.
Quick Tip: Matter cycles in ecosystem, but energy flows in a single direction and eventually dissipates as heat.


Question 30:

How many chambers are found in human heart?

  • (1) 1
  • (2) 2
  • (3) 3
  • (4) 4
Correct Answer: (4) 4
View Solution



Step 1: Recall.

The human heart has four chambers: two atria (upper) and two ventricles (lower).

Step 2: Importance.

This separation allows efficient double circulation: oxygenated and deoxygenated blood remain separate.

Step 3: Conclusion.

Hence, human heart has 4 chambers.
Quick Tip: Four-chambered hearts are found in birds and mammals for efficient oxygen supply.


Question 31:

According to evolutionary view, we are more similar to:

  • (1) Chimpanzee
  • (2) Spider
  • (3) Orangutan
  • (4) Bacteria
Correct Answer: (1) Chimpanzee
View Solution



Step 1: Concept.

Humans share about 98–99% of DNA with chimpanzees, making them our closest relatives.

Step 2: Analysis of options.

Spiders are arthropods, bacteria are prokaryotes, orangutans are close but less similar than chimpanzees.

Step 3: Conclusion.

Thus, humans are most similar to chimpanzees.
Quick Tip: Chimpanzees are considered our evolutionary cousins.


Question 32:

Which one of the following reactions occurs in the formation of curd from milk?

  • (1) Dissociation
  • (2) Fermentation
  • (3) Excretion
  • (4) Photosynthesis
Correct Answer: (2) Fermentation
View Solution



Step 1: Process.

Curd forms when lactic acid bacteria ferment lactose sugar in milk.

Step 2: Explanation.

This is a fermentation process, not dissociation, excretion, or photosynthesis.

Step 3: Conclusion.

Hence, curd formation is due to fermentation.
Quick Tip: Lactobacillus bacteria ferment milk to form curd.


Question 33:

Which of the following lenses is called diverging lens?

  • (1) Concave lens
  • (2) Convex lens
  • (3) Convex lens and concave lens
  • (4) Bifocal lens
Correct Answer: (1) Concave lens
View Solution



Step 1: Recall.

Concave lenses spread out light rays (diverge them).

Step 2: Explanation.

Convex lens is converging, bifocal has both convex + concave parts.

Step 3: Conclusion.

Thus, concave lens is called a diverging lens.
Quick Tip: Concave lens is used in spectacles for myopia (short-sightedness).


Question 34:

Which colour has maximum wavelength in visible light?

  • (1) Yellow
  • (2) Violet
  • (3) Red
  • (4) Green
Correct Answer: (3) Red
View Solution



Step 1: Spectrum.

Visible spectrum: Violet (shortest wavelength, 400 nm) to Red (longest wavelength, 700 nm).

Step 2: Conclusion.

Hence, red light has maximum wavelength.
Quick Tip: That’s why red is used in danger signals—it scatters the least.


Question 35:

To increase the value of the resistance, resistors should be connected in:

  • (1) Series
  • (2) Parallel
  • (3) Both (A) and (B)
  • (4) None of these
Correct Answer: (1) Series
View Solution



Step 1: Concept.

In series: \(R_{eq} = R_1 + R_2 + R_3 ...\) (greater than individual).

In parallel: \(R_{eq} < R_{smallest}\).

Step 2: Conclusion.

So, to increase resistance, use series.
Quick Tip: Series = more resistance, Parallel = less resistance.


Question 36:

Which instrument does not have a positive (+) and a negative (-) sign?

  • (1) In voltmeter
  • (2) In ammeter
  • (3) In electric cell
  • (4) In coil
Correct Answer: (4) In coil
View Solution



Step 1: Explanation.

Voltmeter and ammeter have polarity signs; electric cell has positive and negative terminals.

Step 2: Note.

A coil is just a wire wound in loops, without polarity signs.

Step 3: Conclusion.

Thus, coil has no + or – sign.
Quick Tip: Only devices that measure or supply current/voltage need polarity marking.


Question 37:

A converging beam is incident on a plane mirror. The reflected beam will be:

  • (1) Diverging
  • (2) Converging
  • (3) Parallel
  • (4) None of these
Correct Answer: (2) Converging
View Solution



Step 1: Law of reflection.

Plane mirror simply reflects rays without changing their convergence/divergence.

Step 2: Application.

If a converging beam strikes a plane mirror, the reflected rays will remain converging.

Step 3: Conclusion.

Thus, the answer is converging.
Quick Tip: Plane mirrors change direction but not convergence/divergence of rays.


Question 38:

The SI unit of magnetic flux is:

  • (1) Watt
  • (2) Joule
  • (3) Weber
  • (4) Newton
Correct Answer: (3) Weber
View Solution



Step 1: Recall.

Magnetic flux \(\Phi = B \cdot A\) (Tesla \(\times\) m\(^2\)).

Step 2: SI unit.

Unit is weber (Wb).

Step 3: Conclusion.

Hence, the SI unit of magnetic flux is weber.
Quick Tip: 1 weber = magnetic flux producing 1 volt when reduced to zero in 1 second.


Question 39:

There are 20 divisions between the zero (0) and 2A number of an ammeter. What is the least count of the ammeter?

  • (1) 0.01 A
  • (2) 0.1 A
  • (3) 0.001 A
  • (4) 2 A
Correct Answer: (1) 0.01 A
View Solution



Step 1: Formula.

Least count = Range / Number of divisions.

Step 2: Substitution.

Range = 2A, divisions = 200 (20 major × 10 small).

So least count = 2 / 200 = 0.01 A.

Step 3: Conclusion.

Thus, least count is 0.01 A.
Quick Tip: Least count is the smallest value an instrument can measure.


Question 40:

If several resistances are parallel, their equivalent resistance will be:

  • (1) More than each resistance
  • (2) Less than each resistance
  • (3) Equal to each resistance
  • (4) None of these
Correct Answer: (2) Less than each resistance
View Solution



Step 1: Formula.

For parallel: \(\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + ...\)

Step 2: Property.
\(R_{eq}\) is always less than the smallest individual resistance.

Step 3: Conclusion.

Hence, equivalent resistance in parallel is less.
Quick Tip: Parallel connections reduce resistance, series increases it.


Question 41:

The pores of the stomata are surrounded by which of the following?

  • (1) Cuticle
  • (2) Guard cells
  • (3) Lenticels
  • (4) None of these
Correct Answer: (2) Guard cells
View Solution



Step 1: Structure.

Each stoma (pore) in a leaf epidermis is bordered by two kidney-shaped guard cells.

Step 2: Function.

Guard cells control opening and closing of stomata by changing turgor pressure, thus regulating gas exchange and transpiration.

Step 3: Conclusion.

Hence, stomatal pores are surrounded by guard cells.
Quick Tip: Lenticels are pores on woody stems, not on leaf epidermis.


Question 42:

Which gas is liberated during respiration?

  • (1) O2
  • (2) SO2
  • (3) NO2
  • (4) CO2
Correct Answer: (4) CO2
View Solution



Step 1: Concept.

In aerobic respiration, glucose is oxidised using oxygen to form carbon dioxide and water with release of energy.

Step 2: Equation.

C6H12O6 + 6O2 \(\rightarrow\) 6CO2 + 6H2O + Energy.

Step 3: Conclusion.

Therefore, CO2 is liberated.
Quick Tip: Exhaled air has higher CO2 and lower O2 than inhaled air.


Question 44:

What is liberated by complete oxidation of glucose?

  • (1) Only CO2
  • (2) Only energy
  • (3) Only H2O
  • (4) All of these
Correct Answer: (4) All of these
View Solution



Step 1: Reaction.

Complete oxidation: C6H12O6 + 6O2 \(\rightarrow\) 6CO2 + 6H2O + Energy (ATP).

Step 2: Output.

Products are CO2, H2O and energy.

Step 3: Conclusion.

Therefore, “All of these” is correct.
Quick Tip: Energy from glucose is captured mainly as ATP during respiration.


Question 45:

What type of membrane is the cell membrane?

  • (1) Permeable
  • (2) Impermeable
  • (3) Semi-permeable
  • (4) None of these
Correct Answer: (3) Semi-permeable
View Solution



Step 1: Idea.

The plasma membrane allows selective passage of substances—some pass easily, others are restricted.

Step 2: Term.

This property is called selective or semi-permeability.

Step 3: Conclusion.

Hence, the cell membrane is semi-permeable.
Quick Tip: “Selectively permeable” and “semi-permeable” are used interchangeably in Class 10 context.


Question 46:

Full form of ATP is:

  • (1) Adenine thymine phosphate
  • (2) Adenine triphosphate
  • (3) Adenosine triphosphate
  • (4) Adenine thymine diphosphate
Correct Answer: (3) Adenosine triphosphate
View Solution



Step 1: Definition.

ATP is the energy currency of the cell, consisting of adenine, ribose (together adenosine) and three phosphate groups.

Step 2: Clarify options.

It is not “adenine triphosphate”; the correct nucleoside is adenosine.

Step 3: Conclusion.

Thus, ATP stands for adenosine triphosphate.
Quick Tip: Breaking the terminal phosphate bond of ATP releases usable energy.


Question 47:

Which solution is used to test the presence of starch?

  • (1) Iodine
  • (2) Safranin
  • (3) Eosin
  • (4) Methylene blue
Correct Answer: (1) Iodine
View Solution



Step 1: Test.

Iodine solution turns blue-black in presence of starch due to formation of a starch–iodine complex.

Step 2: Others.

Safranin, eosin, and methylene blue are general stains, not specific starch indicators.

Step 3: Conclusion.

Therefore, iodine is used to test starch.
Quick Tip: A blue-black colour confirms starch; no colour change means no starch.


Question 48:

Rate of photosynthesis is dependent on which factors?

  • (1) Properties of light
  • (2) The amount of light
  • (3) Both (A) and (B)
  • (4) None of these
Correct Answer: (3) Both (A) and (B)
View Solution



Step 1: Factors.

Photosynthesis rate depends on light intensity (amount) and quality (wavelength/colour), among other factors (CO2, temperature).

Step 2: Application.

Red and blue light are more effective; higher intensity increases rate up to a limit.

Step 3: Conclusion.

So both properties and amount of light affect the rate.
Quick Tip: Red and blue wavelengths are most efficient for photosynthesis.


Question 49:

What is the common name of CaOCl2?

  • (1) Calcium chloro oxide
  • (2) Calcium oxy oxide
  • (3) Bleaching powder
  • (4) Calcium chloride
Correct Answer: (3) Bleaching powder
View Solution



Step 1: Identification.

Calcium oxychloride (CaOCl2) is commonly known as bleaching powder.

Step 2: Use.

It is used for bleaching, disinfection, and water treatment.

Step 3: Conclusion.

Thus, CaOCl2 is bleaching powder.
Quick Tip: Bleaching powder releases chlorine, which kills germs and bleaches fabrics.


Question 50:

Iodized salt is:

  • (1) NaCl + KIO3
  • (2) NaCl + KI
  • (3) both (A) and (B)
  • (4) none of these
Correct Answer: (3) both (A) and (B)
View Solution



Step 1: Composition.

Iodized salt contains table salt (NaCl) fortified with iodine—commonly as potassium iodate (KIO3) or potassium iodide (KI).

Step 2: Purpose.

It prevents iodine-deficiency disorders like goitre.

Step 3: Conclusion.

Therefore, both (A) and (B) correctly represent iodized salt.
Quick Tip: Check “iodized” on salt packets—fortified with KI or KIO3.


Question 51:

The alloy consisting of 90% Cu and 10% Sn is named as

  • (1) Solder
  • (2) Brass
  • (3) German silver
  • (4) Bronze
Correct Answer: (4) Bronze
View Solution



Step 1: Understanding alloys.

Bronze is an alloy mainly of copper (Cu) and tin (Sn).

Step 2: Percentage composition.

The given mixture has 90% Cu and 10% Sn, which is the typical composition of bronze.

Step 3: Eliminate others.

- Solder is an alloy of lead and tin.

- Brass is copper + zinc.

- German silver is copper + zinc + nickel.

Step 4: Conclusion.

Hence, the alloy is bronze.
Quick Tip: Bronze is historically important and used in making statues, medals, and tools.


Question 52:

How many bonds are there between two atoms of one molecule of oxygen gas?

  • (1) 1
  • (2) 2
  • (3) 3
  • (4) No bond
Correct Answer: (2) 2
View Solution



Step 1: Oxygen molecule structure.

Oxygen exists as O2. Each oxygen atom has 6 valence electrons.

Step 2: Bonding.

They share two pairs of electrons, forming a double bond (O=O).

Step 3: Conclusion.

Therefore, there are two covalent bonds between O atoms.
Quick Tip: O2 has a double bond, while N2 has a triple bond.


Question 53:

What is Philosopher’s wool?

  • (1) ZnO
  • (2) ZnS
  • (3) ZnCl2
  • (4) ZnSO4
Correct Answer: (1) ZnO
View Solution



Step 1: Concept.

Philosopher’s wool is the common name for zinc oxide (ZnO).

Step 2: Reason.

It forms as white fluffy wool-like substance when zinc metal is oxidized.

Step 3: Conclusion.

Hence, Philosopher’s wool = ZnO.
Quick Tip: ZnO is amphoteric – reacts with both acids and bases.


Question 54:

The sodium salts of higher fatty acids are called

  • (1) Rubber
  • (2) Plastic
  • (3) Soap
  • (4) Detergent
Correct Answer: (3) Soap
View Solution



Step 1: Reaction.

Saponification of fats and oils with NaOH gives sodium salts of fatty acids.

Step 2: Identification.

These sodium salts are soaps.

Step 3: Conclusion.

Therefore, the answer is soap.
Quick Tip: Soaps work well in soft water, but not in hard water due to scum formation.


Question 55:

Which of the following is a symbol of carbonyl group?

  • (1) –CHO
  • (2) –COOH
  • (3) >CO
  • (4) –O–
Correct Answer: (3) >CO
View Solution



Step 1: Carbonyl definition.

A carbonyl group is C=O, where carbon is double-bonded to oxygen.

Step 2: Elimination.

- –CHO is an aldehyde group.

- –COOH is a carboxyl group.

- –O– is ether linkage.

Step 3: Conclusion.

Thus, the correct symbol is >CO.
Quick Tip: Carbonyl group is common in aldehydes and ketones.


Question 56:

Which of the following organic compounds is an alkyne?

  • (1) Ethene
  • (2) Methane
  • (3) Acetylene
  • (4) Chloroform
Correct Answer: (3) Acetylene
View Solution



Step 1: Definition.

Alkynes are hydrocarbons with a triple bond.

Step 2: Options.

- Ethene: alkene (double bond).

- Methane: alkane (single bond).

- Acetylene (ethyne): C2H2, with a triple bond.

- Chloroform: not a hydrocarbon.

Step 3: Conclusion.

So acetylene is an alkyne.
Quick Tip: General formula of alkyne: CnH2n–2}.


Question 57:

The focal length of which mirror is taken as negative according to the convention of signs?

  • (1) Plane mirror
  • (2) Concave mirror
  • (3) Convex mirror
  • (4) None of these
Correct Answer: (2) Concave mirror
View Solution



Step 1: Sign convention.

In mirror formula, distances measured against incident light are taken negative.

Step 2: Mirrors.

For concave mirror, focal length is on the left side (against light), hence negative.

For convex mirror, focal length is positive.

Step 3: Conclusion.

So, concave mirror has negative focal length.
Quick Tip: Remember: Concave = negative focal length, Convex = positive focal length.


Question 58:

Where is the object placed to form a magnified virtual image in a concave mirror?

  • (1) Between focus and pole
  • (2) Beyond centre of curvature
  • (3) At focus
  • (4) Between centre of curvature and focus
Correct Answer: (1) Between focus and pole
View Solution



Step 1: Image formation.

Concave mirrors form different images depending on object position.

Step 2: For magnified virtual image.

When object is between focus (F) and pole (P), the mirror forms a virtual, erect, and magnified image.

Step 3: Conclusion.

Thus, the correct answer is “between focus and pole”.
Quick Tip: Concave mirrors are used in makeup mirrors for magnified virtual images.


Question 59:

How many laws of refraction of light are there?

  • (1) 1
  • (2) 2
  • (3) 3
  • (4) 4
Correct Answer: (2) 2
View Solution



Step 1: Definition.

Refraction is bending of light when it passes from one medium to another.

Step 2: Laws.

1. Incident ray, refracted ray and normal lie in the same plane.

2. Snell’s law: \(\dfrac{\sin i}{\sin r} = \mu\), a constant for given media.

Step 3: Conclusion.

Thus, there are 2 laws.
Quick Tip: Snell’s law is key to calculating refractive index.


Question 60:

What is the value of refractive index of a medium?

  • (1) \(\dfrac{\sin i}{\sin r}\)
  • (2) \(\dfrac{\sin r}{\sin i}\)
  • (3) \(\sin i + \sin r\)
  • (4) \(\sin i \times \sin r\)
Correct Answer: (1) \(\dfrac{\sin i}{\sin r}\)
View Solution



Step 1: Recall Snell’s law.
\(n = \dfrac{\sin i}{\sin r}\), where \(i =\) angle of incidence, \(r =\) angle of refraction.

Step 2: Concept.

This ratio remains constant for a given pair of media.

Step 3: Conclusion.

Therefore, refractive index is \(\dfrac{\sin i}{\sin r}\).
Quick Tip: Higher refractive index = light bends more towards normal.


Question 61:

What is the S.I. unit of power of lens?

  • (1) cm\(^{-1}\)
  • (2) m
  • (3) cm
  • (4) Dioptre
Correct Answer: (4) Dioptre
View Solution



Step 1: Understanding power of a lens.

The power of a lens is defined as the reciprocal of its focal length (in meters).
\[ P = \frac{100}{f \, (in cm)} = \frac{1}{f \, (in m)} \]

Step 2: Unit of power.

Since focal length is measured in meters, the unit of power is \( m^{-1} \). This unit is given a special name "Dioptre (D)".

Step 3: Conclusion.

Therefore, the SI unit of power of a lens is Dioptre.
Quick Tip: Power of lens increases when focal length decreases.


Question 62:

The magnification (m) in a concave lens is equal to:

  • (1) \(uv\)
  • (2) \(\frac{u}{v}\)
  • (3) \(\frac{v}{u}\)
  • (4) \(u+v\)
Correct Answer: (3) \(\frac{v}{u}\)
View Solution



Step 1: Definition of magnification.

Magnification produced by a lens is defined as the ratio of the image distance (\(v\)) to the object distance (\(u\)): \[ m = \frac{v}{u} \]

Step 2: Application in concave lens.

In concave lens, the image is always virtual, erect and diminished, hence \( m = \frac{v}{u} \) (always less than 1).

Step 3: Conclusion.

Thus, magnification in a concave lens is \(\frac{v}{u}\).
Quick Tip: For concave lens, the image formed is always virtual, erect and diminished.


Question 63:

What is the refractive index of diamond?

  • (1) 1.42
  • (2) 1.32
  • (3) 2.24
  • (4) 2.42
Correct Answer: (4) 2.42
View Solution



Step 1: Refractive index meaning.

Refractive index is the ratio of speed of light in vacuum to the speed of light in medium. Diamond has one of the highest refractive indices among natural substances.

Step 2: Known value.

The refractive index of diamond is 2.42.

Step 3: Conclusion.

Hence, correct answer is 2.42.
Quick Tip: Diamond’s high refractive index makes it sparkle brilliantly by causing total internal reflection.


Question 64:

A prism is bounded by how many surfaces?

  • (1) 2
  • (2) 3
  • (3) 4
  • (4) 5
Correct Answer: (2) 3
View Solution



Step 1: Understanding prism.

A prism is a transparent medium bounded by three rectangular surfaces and two triangular bases.

Step 2: Effective surfaces.

The prism is bounded by three surfaces (two triangular bases + one rectangular refracting surface).

Step 3: Conclusion.

So, a prism is bounded by 3 surfaces.
Quick Tip: Prism is used to study dispersion of light into seven colors (VIBGYOR).


Question 65:

The atomic number of potassium is 19. What is the valency?

  • (1) 1
  • (2) 2
  • (3) 3
  • (4) 4
Correct Answer: (1) 1
View Solution



Step 1: Electronic configuration.

Potassium (K) has atomic number 19. Its configuration is: \[ 2, 8, 8, 1 \]

Step 2: Valency concept.

Valency is determined by the number of electrons in the outermost shell. Here, it has 1 electron in outer shell.

Step 3: Conclusion.

So, valency of potassium is 1.
Quick Tip: Alkali metals (like Na, K, Li) all have valency 1.


Question 66:

What is the general formula of an alkane?

  • (1) \(C_nH_{2n}\)
  • (2) \(C_nH_{2n+2}\)
  • (3) \(C_nH_{2n-2}\)
  • (4) None of these
Correct Answer: (2) \(C_nH_{2n+2}\)
View Solution



Step 1: Understanding hydrocarbons.

Alkanes are saturated hydrocarbons with single bonds only.

Step 2: General formula.

For alkanes, the formula is: \[ C_nH_{2n+2} \]

Step 3: Examples.

Methane: \(CH_4\) (n=1), Ethane: \(C_2H_6\) (n=2).

Step 4: Conclusion.

Thus, correct general formula is \(C_nH_{2n+2}\).
Quick Tip: Remember: Alkanes – single bonds (\(C_nH_{2n+2}\)), Alkenes – double bonds (\(C_nH_{2n}\)), Alkynes – triple bonds (\(C_nH_{2n-2}\)).


Question 67:

What is the atomic number of fluorine?

  • (1) 9
  • (2) 19
  • (3) 29
  • (4) 39
Correct Answer: (1) 9
View Solution



Step 1: Recall periodic table.

Fluorine belongs to Group 17 (Halogens).

Step 2: Atomic number.

The atomic number of fluorine is 9. Its electronic configuration is \(2, 7\).

Step 3: Conclusion.

Thus, fluorine has atomic number 9.
Quick Tip: Halogens belong to group 17 and have 7 valence electrons.


Question 68:

A solution turns red litmus into blue. The pH value of this solution would be:

  • (1) 7
  • (2) More than 7
  • (3) Less than 7
  • (4) None of these
Correct Answer: (2) More than 7
View Solution



Step 1: Litmus test.

Red litmus turning blue indicates that the solution is basic.

Step 2: pH range.

Acidic solutions: \(pH < 7\)

Neutral solutions: \(pH = 7\)

Basic solutions: \(pH > 7\).

Step 3: Conclusion.

Since the solution is basic, its pH is more than 7.
Quick Tip: Always remember: Acids (\(<7\)), Neutral (=7), Bases (>7).


Question 69:

What is the atomic weight of oxygen?

  • (1) 8
  • (2) 12
  • (3) 16
  • (4) 18
Correct Answer: (3) 16
View Solution



Step 1: Recall oxygen details.

Oxygen has atomic number 8 and its most common isotope is \(O^{16}\).

Step 2: Atomic weight.

The relative atomic mass (atomic weight) of oxygen is 16 u.

Step 3: Conclusion.

Thus, the correct answer is 16.
Quick Tip: Atomic weight of oxygen = 16, hydrogen = 1 → so water \(H_2O\) has molar mass = 18 g/mol.


Question 70:

Bauxite is an ore of which of the following metals?

  • (1) Hg
  • (2) Fe
  • (3) Al
  • (4) Zn
Correct Answer: (3) Al
View Solution



Step 1: Understanding ores.

Bauxite is the principal ore of aluminium. It mainly contains hydrated aluminium oxides like \(Al_2O_3 \cdot 2H_2O\).

Step 2: Extraction.

Aluminium is extracted from bauxite using electrolytic reduction after refining by the Bayer’s process.

Step 3: Conclusion.

Hence, bauxite is an ore of Aluminium (Al).
Quick Tip: Important ores: Bauxite – Aluminium, Haematite – Iron, Galena – Lead, Cinnabar – Mercury.


Question 71:

The correct order of reactivity of metals is

  • (1) Na \(>\) Zn \(>\) Mg \(>\) Cu
  • (2) Na \(>\) Mg \(>\) Cu \(>\) Zn
  • (3) Mg \(<\) Na \(<\) Zn \(<\) Cu
  • (4) Na \(>\) Mg \(>\) Zn \(>\) Cu
Correct Answer: (4) Na \(>\) Mg \(>\) Zn \(>\) Cu
View Solution



Step 1: Activity series.

Standard reactivity series: K \(>\) Na \(>\) Ca \(>\) Mg \(>\) Al \(>\) Zn \(>\) Fe \(>\) Pb \(>\) H \(>\) Cu \(>\) Ag \(>\) Au.

Step 2: Pick the relative order.

Among Na, Mg, Zn, Cu the decreasing reactivity is Na \(>\) Mg \(>\) Zn \(>\) Cu.
Quick Tip: More reactive metals displace less reactive ones from their compounds.


Question 72:

\(\mathrm{Fe_2O_3 + 2Al \rightarrow Al_2O_3 + 2Fe}\) is which of the following types reaction?

  • (1) Combination
  • (2) Decomposition
  • (3) Displacement
  • (4) Double displacement
Correct Answer: (3) Displacement
View Solution



Step 1: Identify the change.

Aluminium replaces iron from iron(III) oxide to form aluminium oxide and iron.

Step 2: Type.

Replacement of one element by another is a single displacement reaction (Thermite reaction).
Quick Tip: In single displacement: \(A + BC \rightarrow AC + B\).


Question 73:

Carbon combines with hydrogen to form

  • (1) aqua regia
  • (2) halogen
  • (3) hydrocarbon
  • (4) ionic compound
Correct Answer: (3) hydrocarbon
View Solution



Step 1: Definition.

Compounds containing only carbon and hydrogen are called hydrocarbons (e.g., methane, ethane).
Quick Tip: Hydrocarbons are of three main types: alkanes, alkenes, alkynes.


Question 74:

Boron and aluminium belong to which group of elements in periodic table?

  • (1) 10
  • (2) 17
  • (3) 13
  • (4) 3
Correct Answer: (3) 13
View Solution



Step 1: Periodic position.

B and Al are in Group 13 (IIIA), called the boron family.
Quick Tip: Group 13: B, Al, Ga, In, Tl.


Question 75:

Which pigment makes the colour of urine yellow?

  • (1) Chromoplast
  • (2) Urochrome
  • (3) Chloroplast
  • (4) Leucoplast
Correct Answer: (2) Urochrome
View Solution



Step 1: Fact.

Urochrome (a breakdown product of haemoglobin) imparts the yellow colour to urine.
Quick Tip: Colour can vary with hydration; darker yellow indicates dehydration.


Question 76:

The tiger is a consumer of

  • (1) first trophic level
  • (2) second trophic level
  • (3) third trophic level
  • (4) none of these
Correct Answer: (3) third trophic level
View Solution



Step 1: Trophic levels.

Producers (1st), herbivores/primary consumers (2nd), carnivores/secondary consumers (3rd).

Step 2: Tiger’s role.

Tiger preys on herbivores (e.g., deer), so it is a secondary consumer at the 3rd trophic level.
Quick Tip: Some chains may add apex predators as 4th level, but in Class 10 context tiger is 3rd.


Question 77:

Bile juice is secreted by

  • (1) small intestine
  • (2) liver
  • (3) pancreas
  • (4) duodenum
Correct Answer: (2) liver
View Solution



Step 1: Production vs storage.

Bile is produced by the liver, stored in the gallbladder, and released into the duodenum.
Quick Tip: Bile emulsifies fats—mechanical aid to digestion; it has no enzymes.


Question 78:

The forelimbs of man, cat and bat are

  • (1) homologous organ
  • (2) analogous organs
  • (3) vestigial organ
  • (4) none of these
Correct Answer: (1) homologous organ
View Solution



Step 1: Concept.

Homologous organs have the same basic structure and origin but different functions.

Step 2: Application.

Human arm, cat’s foreleg and bat’s wing share the same bone arrangement—humerus, radius/ulna, carpals, etc.
Quick Tip: Homology evidences divergent evolution.


Question 79:

Which of the following is an example of regeneration?

  • (1) Hydra
  • (2) Frog
  • (3) Cow
  • (4) None of these
Correct Answer: (1) Hydra
View Solution



Step 1: Definition.

Regeneration is the ability to regrow lost body parts or a new organism from fragments.

Step 2: Example.

Hydra shows remarkable regeneration; frog and cow do not.
Quick Tip: Planaria and Hydra are classic regeneration examples.


Question 80:

The genic constitution of an individual organism is called

  • (1) genotype
  • (2) phenotype
  • (3) variation
  • (4) heredity
Correct Answer: (1) genotype
View Solution



Step 1: Terms.

Genotype = genetic makeup; phenotype = observable traits; variation = differences among individuals; heredity = transmission of traits.

Step 2: Conclusion.

Thus, the genic constitution is the genotype.
Quick Tip: Phenotype = Genotype + Environment (simplified view).


Question 81:

What is the source of energy of the Sun?

Correct Answer: The Sun’s energy is produced by nuclear fusion} in its core. At temperatures of about \(1.5\times10^{7}\,\mathrm{K}\) and enormous pressures, hydrogen nuclei fuse through the proton–proton chain to form helium. In each step, a small part of mass is lost and converted into energy by \(E=mc^{2}\). This energy leaves the Sun as photons (sunlight/heat) and neutrinos, powering almost all natural energy flows on Earth.
View Solution

Step 1: Conditions in the core.
The \( \sim \)200,000 km-wide solar core has \(T\approx1.5\times10^{7}\,\mathrm{K}\) and density \( \approx 150\,\mathrm{g\,cm^{-3}} \), enabling quantum tunnelling so protons overcome Coulomb repulsion.

Step 2: Fusion pathway.
In the p–p chain: \(p+p\rightarrow\,^2\!H+e^{+}+\nu_e\); \(^{2}\!H+p\rightarrow\,^{3}\!He+\gamma\); \(^{3}\!He+^{3}\!He\rightarrow\,^{4}\!He+2p\).
Net: \(4p\rightarrow\,^{4}\!He+2e^{+}+2\nu_e+\) energy (\(\approx 26.7\) MeV). The mass defect \( \Delta m \) transforms to energy via \(E=\Delta mc^{2}\).

Step 3: Energy transport.
Gamma photons random-walk outward, being repeatedly absorbed and re-emitted, and emerge at the photosphere as the solar spectrum (effective \(T\approx 5778\,\mathrm{K}\)). Neutrinos escape almost instantly, verifying fusion. Quick Tip: Fusion releases \(\sim 10^{7}\) times more energy per nucleon than chemical reactions—hence stars shine for billions of years.


Question 82:

What is nuclear fission?

Correct Answer: Nuclear fission is the splitting of a heavy nucleus (e.g., \(^{235}\mathrm{U}\) or \(^{239}\mathrm{Pu}\)) into two medium-mass nuclei when it absorbs a neutron, releasing \(2\!-\!3\) neutrons and a large amount of energy. Because the emitted neutrons can trigger further fissions, a chain reaction results. Controlled chain reactions in reactors generate electricity; uncontrolled ones cause nuclear explosions.
View Solution

Step 1: Mechanism.
A thermal neutron captured by \(^{235}\mathrm{U}\) produces an excited compound nucleus \(^{236}\mathrm{U}^{*}\) which deforms and splits, e.g. \[ ^{235}\mathrm{U}+n \rightarrow\,^{141}\mathrm{Ba}+^{92}\mathrm{Kr}+3n+Q, \]
with \(Q\approx 200\) MeV.

Step 2: Energy origin.
Products have higher total binding energy per nucleon than the parent; the mass defect converts to energy (\(E=mc^{2}\)), mostly as kinetic energy of fragments plus prompt \(\gamma\)-rays and delayed \(\beta\)-decays.

Step 3: Chain reaction control.
The average neutrons per fission sustain a chain reaction. Reactors keep the multiplication factor \(k_{\mathrm{eff}}=1\) using moderators (to slow neutrons) and control rods (B, Cd) that absorb excess neutrons; coolant removes heat to run turbines. If \(k_{\mathrm{eff}}>1\) and uncontrolled, the neutron population grows explosively. Quick Tip: Remember: fusion joins light nuclei; fission splits heavy nuclei—both release energy due to increased binding energy of the products.


Question 83:

How does a light ray proceed in a lens? Show by a diagram.

Correct Answer: Light refracts at both surfaces of a thin lens. Key rules: (i) A ray parallel to the principal axis passes through the focal point of a convex lens (or appears to diverge from the focus of a concave lens). (ii) A ray through the optical center travels undeviated. (iii) A ray directed toward the focus emerges parallel to the axis. Image position and size follow from the lens formula \( \tfrac{1}{f}=\tfrac{1}{v}-\tfrac{1}{u} \) and magnification \( m=\tfrac{v}{u} \).
View Solution

Step 1: Refraction at a thin lens.
Using the small-angle (paraxial) approximation, a lens redirects rays according to Snell’s law at each surface; for a convex lens, rays converge, for a concave lens, rays diverge.

Step 2: Principal rays (construction).
To locate images quickly:
1) Parallel ray \(\to\) through \(F\) (convex) / appears from \(F\) (concave).
2) Central ray through optical center \(O\) \(\to\) undeviated.
3) Focal ray aimed at \(F\) \(\to\) emerges parallel to axis.

Step 3: Nature of images.
Convex lens:
— Object beyond \(2F\): real, inverted, diminished (between \(F\) and \(2F\)).
— At \(2F\): real, inverted, same size (at \(2F\)).
— Between \(F\) and \(2F\): real, inverted, magnified (beyond \(2F\)).
— Inside \(F\): virtual, erect, magnified (same side).
Concave lens: always virtual, erect, diminished.


\begin{tikzpicture[scale=0.9]
\draw[-latex] (-4.5,0)--(4.8,0) node[right]{Principal axis;
% Convex lens
\draw ( -0.2,1.5) to[out=-90,in=90] (-0.2,-1.5);
\draw ( 0.2,1.5) to[out=-90,in=90] ( 0.2,-1.5);
\node at (0,1.8){Convex lens;
\foreach \x/\lab in {-2/\(F_1\),2/\(F_2\), -4/\(2F_1\), 4/\(2F_2\){
\draw (\x,0) -- ++(0,0.12) node[below=2pt]{\lab;

\draw[very thick] (-4,0)--(-4,1.0) node[above]{Object;
\draw[->,thick] (-4,1.0)--(0,1.0);
\draw[thick] (0,1.0)--(2,0);
\draw[->,thick] (-4,1.0)--(0,0.3);
\draw[thick] (0,0.3)--(1.6,-0.05);
\draw[very thick] (1.6,0)--(1.6,-0.35) node[below]{Image;
\end{tikzpicture Quick Tip: Sign convention (real is positive to the right of lens): \( \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \), \( m=\frac{v}{u}=\frac{h_i}{h_o} \).