The CBSE Class 10 Sample paper 2025-26 serves as a vital introductory tool for students preparing for their board examinations. Its primary function is to familiarize students with the revised format, new types of questions, and the overall difficulty level they can expect. By analyzing this paper, students can gain a clear understanding of the weightage of different topics and sections, enabling them to strategize their study plan effectively.
This introductory document is not just a collection of questions; it’s a window into the pedagogical approach of the CBSE. It emphasizes a shift towards conceptual understanding and critical thinking, moving away from rote memorization. The paper features application-based questions, case studies, and integrated questions that test a student’s ability to apply scientific principles to real-world scenarios. It also introduces new formats, such as assertion-reasoning questions and image-based problems, which require a different kind of analytical skill.
Section A: Biology
1. Select the group in which all organisms have the same mode of nutrition.
- A. Cuscuta, yeast, legumes, leeches and tapeworm
- B. Cactus, ticks, lice, leeches and cow
- C. Cuscuta, ticks, lice, leeches and tapeworm
- D. Cactus, grass, lice, lion and tapeworm
Answer and Reason: The correct option is C. All organisms in this group are parasites, which have a parasitic mode of nutrition. Cuscuta is a parasitic plant, while ticks, lice, leeches, and tapeworms are all parasitic animals. They depend on a host for their nutrition.
2. Which of the following options indicates the products formed after breakdown of the glucose in our muscle cells when there is lack of oxygen?
- A. Ethanol + carbon dioxide + Energy
- B. Lactic acid + Energy
- C. Lactic acid + carbon monoxide + Energy
- D. Carbon dioxide + Water + Energy
Answer and Reason: The correct option is B. When there is a lack of oxygen in muscle cells, glucose breaks down into lactic acid and energy through anaerobic respiration.
3. Which of the following is a correct combination of function and part of the brain?
- A. Posture and balance: Cerebrum
- B. Salivation: Medulla in midbrain
- C. Hunger: Pons in hindbrain
- D. Blood pressure: Medulla in hindbrain
Answer and Reason: The correct option is D. The medulla, located in the hindbrain, is responsible for controlling involuntary actions, including blood pressure.
4. The blood glucose level in a patient was very high. It may be due to inadequate secretion of:
- A. growth hormone from pituitary gland
- B. oestrogen from ovary
- C. insulin from pituitary gland
- D. insulin from pancreas
Answer and Reason: The correct option is D. The hormone insulin, secreted by the pancreas, regulates blood glucose levels. Inadequate secretion of insulin leads to a high blood glucose level
5. In a cross between black furred rabbit (B) and white furred rabbit (b), all offspring were found to have black fur. What can be inferred about the genetic makeup of the parent rabbits?
- A. BB X bb
- B. Bb X Bb
- C. Bb X bb
- D. bb X bb
Answer and Reason: The correct option is A. The fact that all offspring have black fur indicates that the black fur allele (B) is completely dominant over the white fur allele (b). For all the offspring to exhibit the dominant trait (black fur), one parent must be homozygous dominant (BB) and the other must be homozygous recessive (bb). The cross BB x bb would produce all heterozygous Bb offspring, all of which would have black fur.
6. Which are the correct statements related to ozone?
- (i) Ozone layer helps in increasing the UV radiations reaching earth.
- (ii) Ozone is a deadly poison.
- (iii) Ozone layer shields the earth from UV radiations.
- (iv) Ozone layer prevents UV rays which cause skin cancer.
- (v) Ozone is formed with the help of Chloroflurocarbons.
- A. (i), (ii), (iii)
- B. (ii), (iii), (iv)
- C. (iii), (iv), (v)
- D. (i), (iv), (v)
Answer and Reason: The correct statements are (ii), (iii), and (iv). Ozone is a deadly poison. The ozone layer in the stratosphere acts as a shield, protecting the Earth from harmful ultraviolet (UV) radiation, which is known to cause skin cancer. Statements (i) and (v) are incorrect. The ozone layer
7. Which of the following human activities has resulted in an increase of non-biodegradable substances?
- A. Organic farming
- B. Increase in tree plantation
- C. Use of plastic as packaging material
- D. Composting of kitchen waste
Answer and Reason: The correct option is C. Plastic is a non-biodegradable substance. The widespread use of plastics for packaging has led to an increase in non-biodegradable waste in the environment.
8. Assertion (A): Tallness of a pea plant is controlled by an enzyme. Reason (R): The gene for that enzyme makes proteins which help the plant to be tall.
- A. Both A and R are true, and R is the correct explanation of A.
- B. Both A and R are true, and R is not the correct explanation of A.
- C. A is true but R is false.
- D. A is false but R is true.
Answer and Reason: The correct option is A. Both the assertion and the reason are true, and the reason provides the correct explanation for the assertion. A gene contains the information to synthesize proteins, some of which function as enzymes. These enzymes control metabolic pathways that determine physical traits like the tallness of a plant
9. Assertion (A): Vulture will always have the least amount of pesticides in a food chain. Reason (R): Vulture occupies the last trophic level and it gets only 10% of energy of the previous trophic level.
- A. Both A and R are true, and R is the correct explanation of A.
- B. Both A and R are true, and R is not the correct explanation of A.
- C. A is true but R is false.
- D. A is false but R is true.
Answer and Reason: The correct option is D. The assertion is false because of biomagnification; the concentration of pesticides increases at each successive trophic level. Therefore, a vulture, which is at the highest trophic level, will have the highest concentration of pesticides. The reason is a true statement, as only about 10% of the energy is transferred from one trophic level to the next.
10. Unlike animals, plants do not have any excretory products as they do not eat food. Comment upon the statement with justification.
Answer and Justification: The statement is incorrect. While plants do not eat food like animals do, they still perform metabolic activities, such as photosynthesis and respiration, which produce waste products
. They have several ways of getting rid of these waste products. Some waste products are stored in cellular vacuoles or in dead tissues like old xylem
. The plants can also excrete wastes through their leaves, which are later shed, or through their roots into the soil.
11. Students to attempt either option A or B. A. How many chambers are there in the heart of the following organisms? How is mixing of oxygenated and deoxygenated blood prevented in their body?
(i) Fishes
(ii) Humans
(i) The heart of a fish has two chambers. There is no mixing of oxygenated and deoxygenated blood because the heart pumps deoxygenated blood to the gills for oxygenation, and this blood then flows directly to the body.
(ii) The human heart has four chambers. The mixing of oxygenated and deoxygenated blood is prevented by the septum, a muscular wall that separates the left and right sides of the heart.
OR
B. Explain the mechanism by which the water is transported in plants?
Answer: Water is transported in plants through the xylem tissue. This transport is primarily driven by transpiration pull, where water vapor lost from the leaves creates a suction force that pulls water up from the roots. This process is aided by the cohesive and adhesive properties of water molecules, which help to maintain a continuous column of water in the xylem vessels
12. About 100 acres of forest land was declared as Natural reserve park. The following organisms were predominant in the Natural reserve park: rabbit, frog, grass, fish, fox, water insects, zebra, peacock, snake, trees, bird, owl, insects, tiger, vulture, duck. Create a food web comprising two separate food chains with different producers by using the above data.
Ans: Here are two food chains from the data provided:
- Food chain 1: Grass → Zebra → Lion
- Food chain 2: Trees → Water insects → Frog → Snake → Vulture
13. Draw and explain how the nerve cells help in transmission of impulses?
Ans: Nerve cells, also known as neurons, are specialized cells that transmit electrical impulses throughout the body. They are the fundamental units of the nervous system.
A neuron has three main parts:
- Dendrites: These are tree-like extensions that receive nerve impulses from other neurons.
- Cell Body (Soma): This part contains the nucleus and integrates the incoming signals.
- Axon: This is a long, slender projection that transmits the nerve impulse away from the cell body to other neurons or target cells.
Transmission of Impulses
The transmission of a nerve impulse is an electrochemical process.
- Signal Reception: An impulse is received by the dendrites of a neuron.
- Signal Integration: The impulse travels to the cell body, where the signals are processed.
- Signal Propagation: The impulse then moves down the axon as an electrical signal.
- Neurotransmitter Release: When the electrical signal reaches the end of the axon, called the axon terminal, it triggers the release of chemical messengers known as neurotransmitters into the synaptic cleft, the tiny gap between two neurons.
14. In a genetic experiment, plants with pure round green seeds (RRyy) were crossed with plants with wrinkled yellow seeds (rrYY). (i) Show the gametes formed when F1 was self-pollinated. (ii) A total of 144 seeds were produced which developed into saplings. Show the ratio in which these traits are independently inherited in these 144 sapling.
Answer:
- (i) A cross between a pure round green seed plant (RRyy) and a wrinkled yellow seed plant (rrYY) will result in a F₁ generation with the genotype RrYy (round and yellow). When this F₁ plant is self-pollinated, the gametes formed will be RY, Ry, rY, and ry.
- (ii) For a dihybrid cross, the phenotypic ratio for the traits that are independently inherited is 9:3:3:1.
- Round Yellow: (9/16) * 144 = 81
- Round Green: (3/16) * 144 = 27
- Wrinkled Yellow: (3/16) * 144 = 27
- Wrinkled Green: (1/16) * 144 = 9
15. Neha consumed boiled sweet potatoes and boiled eggs for breakfast…
A. Neha consumed boiled sweet potatoes and boiled eggs for breakfast. Help her to understand some steps in the process of digestion of the food taken by her by answering the questions given below. (Attempt either subpart A or B.)
Answer:
The part labeled O, which represents the small intestine, will contain the maximum amount of digested food. This is because the small intestine is the primary site for the completion of digestion and the absorption of nutrients into the bloodstream.
C. Which of these food items is rich in starch? How is its digestion initiated?
Sweet potatoes are rich in starch. The digestion of starch begins in the mouth, where it is broken down by the enzyme salivary amylase.
D. The figure given below represents parts of the human alimentary canal. Which of these parts will have the maximum amount of digested food as soon as the process of digestion is completed? *
OR
B. Which of these food items contains fats? How is it digested? C. Which of these food items is rich in starch? How is its digestion initiated? D. The figure given below represents parts of the human alimentary canal. Which of these parts will have the maximum amount of digested food as soon as the process of digestion is completed?
B. Boiled eggs contain fats. The digestion of fats begins in the small intestine, where large fat globules are emulsified by bile from the liver. The enzyme lipase, secreted by the pancreas, then breaks down these smaller fat droplets into fatty acids and glycerol.
C. Boiled sweet potatoes are rich in starch. The digestion of starch is initiated in the mouth, where it is broken down into simple sugars by the enzyme salivary amylase.
D. The part of the alimentary canal that has the maximum amount of digested food is the small intestine, labeled O in the figure. This is because it is the primary site of complete digestion and nutrient absorption.
16. Attempt either option A or B. A. Puneet wanted to grow banana plants… (i) Based on your knowledge on plant reproduction should he opt for seeds or any alternate method of reproduction. Justify your answer. (ii) Offsprings of a banana plant usually show very little variation. What causes variation and are variations good or bad? Justify.
(i) Puneet should opt for an alternate method of reproduction, such as vegetative propagation. Banana plants are typically sterile and produce few or no seeds. This method allows him to grow new plants that are genetically identical to the parent plant, ensuring consistent quality.
(ii) The lack of variation is due to asexual reproduction. Variations are primarily caused by sexual reproduction, as it involves the mixing of genes from two parents. They can also be caused by mutations. Variations are generally considered good, as they provide a species with the ability to adapt to changes in the environment, which is essential for survival.
OR
B. Annie was conducting research on the number of fruits produced by watermelon… (i) What difference will she observe in the number of fruits produced in the two glass houses? Explain with reason. (ii) List 3 changes that will occur in a flower once it gets fertilized.
(i) Annie will observe that glass house A will produce more fruits than glass house B. This is because glass house A had pollinators introduced, which are necessary for the transfer of pollen from the anther to the stigma. Without pollination, fertilization and subsequent fruit formation cannot occur.
(ii) After a flower is fertilized, three key changes occur:
- The ovary develops into the fruit.
- The ovules inside the ovary develop into seeds.
- Other parts of the flower, such as the petals and sepals, typically wither and fall off.
Section B: Chemistry
17. Which of the following equations represent redox reactions and what are the values for ‘p’ and ‘q’ in these equations? Equation 1: Fe2O3(s)+2Al(s)→Al2O3(s)+pFe(l)+heat Equation 2: 2C4H10(g)+13O2(g)→8CO2(g)+qH2O(g)
The correct answer is D. Both equations 1 and 2 are redox reactions, p=2 and q=10 . Both are redox reactions because oxidation and reduction occur simultaneously. In equation 1, aluminum is oxidized and iron is reduced. In equation 2, the hydrocarbon is oxidized and oxygen is reduced. By balancing the equations, we find p=2 and q=10.
18. Four statements about the reactions of oxides with dilute hydrochloric acid and aqueous sodium hydroxide are listed… Which statements are correct?
The correct answer is B. I and III . Statement I is correct as aluminum oxide is amphoteric and reacts with both acids and bases. Statement III is also correct as zinc oxide is amphoteric and reacts with both acids and bases. Calcium oxide is a basic oxide and only reacts with acids, and sulfur dioxide is an acidic oxide and only reacts with bases.
19. An iron nail is added to each of the two test tubes ‘P’ and ‘Q’ containing aqueous copper (II) sulphate, and aqueous silver nitrate respectively. Which of the following observation is correct?
The correct answer is B. Iron nail is coated with a brown coating in test tube ‘P’ and silver coating in test tube ‘Q’ . Iron is more reactive than both copper and silver. In test tube P, iron displaces copper, leading to a brown coating of copper on the nail. In test tube Q, iron displaces silver, resulting in a silver coating on the nail.
20. Methyl orange is added to dilute hydrochloric acid and to aqueous sodium hydroxide. What is the colour of the methyl orange in each solution?
The correct answer is D. Red, Yellow. Methyl orange is an indicator that turns red in acidic solutions, such as dilute hydrochloric acid, and yellow in basic solutions, such as aqueous sodium hydroxide.
21. Which of the following substances when dissolved in equal volume of water, will have the highest pH value?
The correct answer is D. Sodium hydroxide. Sodium hydroxide (NaOH) is a strong base, which dissociates completely in water to produce a high concentration of hydroxide ions, resulting in a high pH value.
22. When excess of carbon dioxide is passed through lime water, the milkiness disappears because
The correct answer is B. insoluble calcium carbonate converts to water soluble calcium bicarbonate. The initial milkiness is caused by the formation of insoluble calcium carbonate. When excess carbon dioxide is added, it reacts with the calcium carbonate and water to form soluble calcium bicarbonate, which makes the solution clear again.
23. In the reaction of aqueous solution of barium chloride with aqueous solution of sodium sulphate, the aqueous solution formed will be:
The correct answer is D. Sodium chloride (NaCl) . This is a double displacement reaction that produces an insoluble precipitate of barium sulfate (BaSO4) and a soluble aqueous solution of sodium chloride (NaCl).
24. Assertion (A): C4H8, C4H6 and C4H10 are members of the same homologous series. Reason (R): C4H8, C4H6, C3H4, C3H6, C2H4, C2H2 are unsaturated hydrocarbons.
The correct option is D. A is false but R is true. The assertion is false because the compounds have different general formulas for alkanes, alkenes, and alkynes, so they do not belong to the same homologous series. The reason is true, as all the listed compounds are hydrocarbons with double or triple bonds, making them unsaturated.
25. The following activity is set-up in the science lab by the teacher… A. If the teacher replaces aluminium wire by silver wire, will the students’ observation change? Justify your answer. B. Will the aluminium wire melt? Give reason for your answer.
A. The students’ observation will change. A silver wire is a better conductor of heat than an aluminum wire, so the heat will travel faster along the wire, and the wax will melt, causing the pin to fall off more quickly.
B. The aluminum wire will not melt. The melting point of aluminum is around 660°C, and the heat from a spirit lamp is not sufficient to reach this temperature. The wax melts because its melting point is much lower.
26. Attempt either option A or B. A. An element ‘X’ is stored in kerosene… (i) Can we store ‘X’ in water? Give reason to support your answer. (ii) Identify element ‘X’. Name the process used and write the equation for extraction of ‘X’ from its ore.
(i) No, we cannot store element ‘X’ in water. This is because ‘X’ is a highly reactive alkali metal that reacts vigorously and exothermically with water to produce hydrogen gas.
(ii) Element ‘X’ is Sodium (Na). The process used for its extraction is electrolysis of its molten chloride salt. The equation for the extraction is:
2NaCl→2Na+Cl2.
OR
B. The domes of many building in Europe are made of copper… (i) Why do the domes appear greenish though copper is orange-red in colour? (ii) In your opinion, should the copper domes be replaced by iron domes to overcome the problem of change of colour of copper domes? (iii) Domes used to be made from thin sheets of metals. Why did the ancient architects use copper to make domes?
(i) The domes appear greenish because a layer of basic copper carbonate is formed on the surface. This is a result of the copper reacting with carbon dioxide and moisture in the atmosphere.
(ii) No, the copper domes should not be replaced by iron domes. Iron rusts easily and extensively, while the greenish patina on copper is a protective layer that prevents further corrosion.
(iii) Ancient architects used copper because it is malleable and ductile, allowing it to be easily shaped into thin sheets. It is also a corrosion-resistant metal, which made it a durable building material.
27. Amrita electrolysed distilled water… A. Which gas was she expecting to be formed at the anode and which one at the cathode respectively? B. Why did the bulb not glow when Amrita passed electricity through distilled water? C. Which substance was added by Amrita to distilled water to get the expected result?
A. Amrita was expecting to get oxygen gas at the anode and hydrogen gas at the cathode.
B. The bulb did not glow because distilled water is a poor conductor of electricity. It does not contain enough free ions to carry the electric current.
C. Amrita likely added a substance such as a small amount of an acid (like sulphuric acid) or a base (like sodium hydroxide) to the water to make it a good conductor.
For visually impaired students Identify the type of reaction:
A. ZnO+C→Zn+CO This is a reduction reaction.
B. ZnCO3→ZnO+CO2 This is a decomposition reaction.
C. 2Mg+O2→2MgO+heat This is a combination and redox reaction.
28. Sara took 2 mL of dilute NaOH solution in a test tube and added two drops of phenolphthalein solution to it… A. If Sara used concentrated H2SO4 in place of dilute H2SO4 how many drops will be required for the change in colour to be observed? Justify your answer.
The correct answer is < 40 drops. This is because concentrated sulfuric acid contains more acid molecules per drop than the dilute solution. Therefore, fewer drops would be needed to neutralize the same amount of base and cause the color change.
B. Sara measured 20 drops of dil. H2SO4 and found its volume to be 1 mL. If Sara observed a change in colour of NaoH solution by using 3 mL of H2SO4, how many mL of NaOH did she add to the test tube initially?
From the provided table, 40 drops of dilute H2SO4 (2 mL) were used to neutralize 4 mL of NaOH solution. The ratio of H2SO4 to NaOH is 1:2. If Sara used 3 mL of H2SO4, she would have initially added 6 mL of NaOH solution to the test tube.
OR
Sara takes 10 drops of dilute H2SO4 in the test tube and adds two drops of phenolphthalein solution to it… What change in colour would she observe and why?
The solution would change from colorless to pink. The initial solution of dilute
H2SO4 and phenolphthalein is colorless because phenolphthalein is colorless in an acidic medium. When Sara adds 20 drops of NaOH, the solution becomes basic, and phenolphthalein turns pink in a basic solution.
C. Write a balanced chemical equation for the reaction… Which of the following is true and why?
The balanced chemical equation is: 2NaOH+H2SO4→Na2SO4+2H2O. The correct option is
(a) neutralisation and double displacement reaction. It is a neutralization reaction because an acid and a base react to form a salt and water. It is also a double displacement reaction because the ions of the two reactants are exchanged.
29. Attempt either option A or B. A. A hydrocarbon with the formula CxHy undergoes complete combustion… (a) What are the values of ‘x’ and ‘y’? (b) Give the chemical (IUPAC) name of the hydrocarbon. (c) Draw its electron dot structure. (d) Name the alcohol which on heating with conc. H2SO4 will produce the above hydrocarbon CxHy. (e) Write a balanced chemical equation for the reaction of CxHy with hydrogen gas in presence of Nickel.
(a) By balancing the equation, we find the values: 2x=6⟹x=3. 2y=12⟹y=6. The values are x=3 and y=6.
(b) The hydrocarbon is C3H6, which is propene.
(c) (d) The alcohol is propanol.
(e) The balanced chemical equation is: C3H6+H2→C3H8.
OR
B. The electronic structures of atoms P and Q are shown below… (a) If P and Q combine to form a compound, what type of bond is formed between them? (b) Give the chemical formula of the compound formed. (c) The compound so formed is dissolved in water. Is the resultant solution acidic or basic in nature? Justify your answer. (d) Write the chemical equation for the reaction between ‘Q’ and ethanol. (e) What will be the formula of the compound formed when ‘P’ undergoes bonding with carbon?
(a) Atom P has 6 valence electrons (non-metal), and Q has 1 valence electron (metal). They will form an ionic bond.
(b) The chemical formula is Q2P.
(c) The solution will be basic. The compound formed is a metallic oxide, which reacts with water to form a base.
(d) Assuming Q is Sodium (Na), the equation is: 2Na+2CH3CH2OH→2CH3CH2ONa+H2.
(e) P is similar to Oxygen, with a valency of 2. Carbon has a valency of 4. The formula for the compound is CO2.
Section C: Physics
30. Arnav was making notes and he wrote down the following statements from his understanding of reflection from curved surfaces… Choose from the following the correct option that lists the correct statements about reflection from curved surfaces.
The correct answer is D. I and III . Statement I is correct as concave mirrors can form both real and virtual images. Statement III is also correct, as the mirror formula is applicable to both types of curved mirrors. Statement II is incorrect because convex mirrors always form virtual, erect, and diminished images.
31. Choose the correct option from the below which explains the reason for us to perceive the day sky as blue.
The correct answer is A. As sunlight passes through the atmosphere, shorter wavelengths, such as blue are scattered more than other colors . This is known as Rayleigh scattering, where the shorter wavelength blue light is scattered in all directions by the fine particles in the atmosphere, making the sky appear blue.
32. Assertion (A): A point object is placed at a distance of 26 cm from a convex mirror of focal length 26 cm. The image will not form at infinity. Reason (R): For above given system the equation f1=v1+u1 gives v=∞. The correct option is C. A is true but R is false. The assertion is true because a convex mirror always forms a virtual image behind the mirror, and it cannot form an image at infinity. The reason is false because the focal length of a convex mirror is positive, and the calculation using the mirror formula does not result in
v=∞.
33. The above image shows the formation of an image with an optical instrument… A. Identify the optical instrument (shown schematically as a rectangle) in the image. B. What type of image is formed in this case? C. Based on the measurements given in the image, calculate the focal length of the instrument.
A. The optical instrument is a concave lens.
B. The image formed is virtual, erect, and diminished.
C. Using the lens formula:
1/f=1/v−1/u. We are given the object distance
u=−20 cm and the image distance v=−10 cm.
1/f=1/(−10)−1/(−20)=−1/10+1/20=−2/20+1/20=−1/20.
The focal length f is -20 cm.
For visually impaired students A. Under what conditions can a convex lens form a virtual image?
A convex lens can form a virtual image when the object is placed between the optical center and the principal focus of the lens.
B. Why does a piece of paper catch fire if we allow sunlight to pass through a convex lens onto the paper?
A convex lens converges parallel rays of sunlight to a single point called the principal focus. This concentration of light energy produces a large amount of heat at that point, causing the paper to burn.
34. Attempt either option A or B. A. Find out the following in the electric circuit given in the figure- (i) Effective resistance of two 8 ohm resistors in the combination. (ii) Current flowing through the 4-ohm resistor.
(i) The two 8 ohm resistors are connected in parallel. Their effective resistance is
Rp=(8×8)/(8+8)=64/16=∗∗4Ω∗∗.
(ii) The total resistance of the circuit is the sum of the parallel combination and the 4 ohm resistor: Rtotal=4+4=8Ω. The total current is I=V/Rtotal=8V/8Ω=∗∗1A∗∗.
This is the current flowing through the 4 ohm resistor as it is in series with the parallel combination.
OR
B. Study the circuit and find out- (i) Current in 12 ohm resistor. (ii) Difference in the readings of ammeter A1 and A2 if any.
(i) The 12 ohm resistor is in parallel with the 24 ohm resistor, so the voltage across it is 6V. The current is
I=V/R=6V/12Ω=∗∗0.5A∗∗.
(ii) Ammeter A1 measures the total current drawn from the battery.
The total resistance is Rtotal=1.5+(24×12)/(24+12)=1.5+8=9.5Ω.
The total current is I=V/Rtotal=6V/9.5Ω=0.63A.
Ammeter A2 measures the same total current.
Therefore, there is no difference in the readings of ammeter A1 and A2.
For visually impaired students A. You are given four resistors each having resistance of R ohm. Find the maximum and minimum resistance that can be made with these four resistors.
The maximum resistance is obtained when the resistors are connected in
series: Rmax=R+R+R+R=∗∗4R∗∗. The minimum resistance is obtained when they are connected in
parallel: 1/Rmin=1/R+1/R+1/R+1/R=4/R. So,
Rmin=∗∗R/4∗∗.
B. A copper wire has a length L=2 m… Calculate the resistance of another wire made of the same material whose length is twice the length of the wire but has the same cross-sectional area.
The resistance of a wire is directly proportional to its length. If the length is doubled and the material and cross-sectional area remain the same, the resistance will also be doubled.
35. The above image shows a corrective measure for a particular defect of vision… (i) Identify the defect of vision and state what kind of lens is used to correct this deficiency. (ii) Draw and label a ray diagram that shows the defect of vision in the above case before correction.
(i) The defect of vision is Hypermetropia or farsightedness. A convex lens is used to correct this deficiency.
(ii) Before correction, the image of a nearby object is formed behind the retina.
For visually impaired students (i) What is dispersion of light?
Dispersion of light is the phenomenon of splitting of white light into its constituent colors (VIBGYOR) when it passes through a transparent medium like a prism.
(ii) Explain the condition under which dispersion happens?
Dispersion occurs because the refractive index of the medium is different for different wavelengths (colors) of light.
(iii) Give one reason that causes presbyopia.
Presbyopia is caused by the weakening of the ciliary muscles and the loss of flexibility of the eye lens with age.
36. A student needs to make a 0.12 Ω resistor… (i) Determine the cross-sectional area of the wire. (ii) Calculate the length of wire required for the 0.12 Ω resistor.
(i) The diameter of the wire is 0.80 mm, so the radius is 0.40 mm or 0.40×10−3 m.
The cross-sectional area is A=πr2=3.14×(0.40×10−3)2=∗∗5.024×10−7m2∗∗.
(ii) The length is calculated using the formula R=ρL/A. Rearranging for L gives
L=(R×A)/ρ=(0.12Ω×5.024×10−7m2)/(1.8×10−8Ωm)=∗∗3.35m∗∗.
37. Magnetic field lines are shown in the given diagram… (i) Explain with reason if the student’s claim is correct. (ii) Also redraw the diagram and mark the direction of magnetic field lines.
(i) The student’s claim is correct. The magnetic field is stronger where the magnetic field lines are closer together or more crowded. In the diagram, the field lines are denser at point X than at point Y, indicating a stronger magnetic field at X.
(ii) The direction of the magnetic field lines is from the North pole to the South pole.
38. The above image is that of a Digital Single Lense Reflector (DSLR) Camera… A. What type of lens is used in the DSLR camera shown in the image? B. What type of image is formed on the sensor? C. A photographer is using a DSLR camera with a lens of focal length f=50 mm… Calculate the object distance (i.e., the distance between the object and the lens).
A. A convex lens is used in the DSLR camera.
B. A real, inverted, and diminished image is formed on the sensor.
C. We use the lens formula:
1/f=1/v−1/u. Given
f=+50 mm and v=+60 mm. 1/u=1/v−1/f=1/60−1/50=(5−6)/300=−1/300. The object distance u is -300 mm or 300 mm in front of the lens.
OR
D. A photographer is using a DSLR camera to take a picture of a flower… Calculate the focal length of the camera lens.
Given u=−150 mm, object height ho=80 mm, image height hi=−20 mm (inverted). Magnification
m=hi/ho=v/u=−20/80=−1/4.
v=m×u=(−1/4)×(−150)=37.5 mm. Using the lens formula:
1/f=1/v−1/u=1/37.5−1/(−150)=1/37.5+1/150=4/150+1/150=5/150=1/30.
The focal length
f is 30 mm.
39. Attempt either option A or B. A. The arrangement of resistors shown in the above figure is connected to a battery… The power dissipation in the 100 Ω resistor is 81 W. Calculate (i) the current in the circuit (ii) the reading in the voltmeter V2 (iii) the reading in the voltmeter V1.
(i) Using the formula P=I2R , we can find the current:
81=I2×100, so I=0.81=∗∗0.9A∗∗.
(ii) The two 25 Ω resistors are in parallel. Their equivalent resistance is Rp=(25×25)/(25+25)=12.5Ω. The reading of voltmeter V2 is the voltage across this parallel combination:
V2=I×Rp=0.9A×12.5Ω=∗∗11.25V∗∗.
(iii) The total resistance of the circuit is Rtotal=100Ω+12.5Ω=112.5Ω. The reading of voltmeter V1 is the total voltage of the battery:
V1=I×Rtotal=0.9A×112.5Ω=∗∗101.25V∗∗.
OR
B. An electric heater consists of three similar heating elements A, B and C… (i) Calculate the resistance of one heating element. (ii) Calculate the current in each resistor when only S1 and S3 are closed. (iii) Calculate the power dissipated across A when S1, S2 and S3 are closed.
(i) Using the formula
P=V2/R ,
we can calculate the resistance:
R=V2/P=(240)2/1200=57600/1200=∗∗48Ω∗∗.
(ii) When S1 and S3 are closed, elements A and C are connected in parallel to the 240V supply. The current in each resistor is
I=V/R=240V/48Ω=∗∗5A∗∗.
(iii) When all three switches are closed, all three elements are connected in parallel to the 240V supply. The power dissipated across element A will be its rated power, which is
1.2 kW or 1200 W.
For the official Class 10 Mathematics Solutions, you can visit:
- NCERT Textbooks (for Class 10):
Class-wise Solutions
Class 12:
Class 12 Physics – NCERT Solutions
Class 12 Chemistry – NCERT Solutions
Class 11:
- Class 11 Physics – NCERT Solutions
- Class 11 Chemistry – NCERT Solutions
- Class 11 Biology – NCERT Solutions
- Class 11 Math – NCERT Solutions
Class 10:
Class 9:
Class 8:
Class 7:
Class 6: