CBSE Class 10 Science Model Question paper, Set 2

Contents
    CBSE Class 10 Science Model Question paper, Set 1
    SET - 2

    Class 10 Science Model Paper 2026

    Max Marks: 80 | Time: 3 Hours

    Instructions: This is the second practice set based on the new 2025-26 subject-wise pattern.
    • Section A: Biology (Q1-16)
    • Section B: Chemistry (Q17-29)
    • Section C: Physics (Q30-39)

    Section A: Biology

    Q1. 1 Mark
    Which of the following statements about the autotrophs is incorrect?
    A. They synthesize carbohydrates from $CO_2$ and water.
    B. They store carbohydrates in the form of starch.
    C. They convert carbon dioxide and water into carbohydrates in the absence of sunlight.
    D. They constitute the first trophic level in food chains.
    Check Answer
    Correct Option: C
    Autotrophs require sunlight (and chlorophyll) to convert $CO_2$ and water into carbohydrates. The statement "in the absence of sunlight" is incorrect.
    Q2. 1 Mark
    The growth of tendrils in pea plants is due to:
    A. Effect of light
    B. Effect of gravity
    C. Rapid cell divisions in tendrillar cells that are away from the support
    D. Rapid cell divisions in tendrillar cells in contact with the support
    Check Answer
    Correct Option: C
    Auxin accumulates on the side away from the support, causing cells there to grow faster, which makes the tendril curl around the support.
    Q3. 1 Mark
    In human males, the testes lie in the scrotum, because it helps in the:
    A. Process of mating
    B. Formation of sperm
    C. Easy transfer of gametes
    D. All of the above
    Check Answer
    Correct Option: B
    Sperm formation requires a temperature 2-3°C lower than the body temperature, which is provided by the scrotum.
    Q4. 1 Mark
    In a food chain, the third trophic level is always occupied by:
    A. Carnivores
    B. Herbivores
    C. Decomposers
    D. Producers
    Check Answer
    Correct Option: A
    1st Trophic Level = Producers.
    2nd Trophic Level = Herbivores (Primary Consumers).
    3rd Trophic Level = Carnivores (Secondary Consumers).
    Q5. 1 Mark
    Assertion (A): The accumulation of non-biodegradable pesticides in the food chain in increasing amount at each higher trophic level is known as bio-magnification.
    Reason (R): Humans occupy the top level in any food chain, so the maximum concentration of these chemicals gets accumulated in our bodies.
    A. Both A and R are true, and R is correct explanation of A
    B. Both A and R are true, but R is NOT correct explanation of A
    C. A is true but R is false
    D. A is false but R is true
    Check Answer
    Correct Option: B
    Both statements are true facts, but R explains the *consequence* for humans, not the *definition* of bio-magnification given in A. So, B is the better fit, though in some contexts A is accepted if R is seen as an example proving A. (For Class 10 CBSE, B is safer here as R is a specific case, not the cause).
    Q6. 1 Mark
    Which of the following is NOT a part of the female reproductive system in human beings?
    A. Ovary
    B. Uterus
    C. Vas deferens
    D. Fallopian tube
    Check Answer
    Correct Option: C
    Vas deferens is the sperm duct found in the male reproductive system.
    Q7. 1 Mark
    Which of the following groups contains only biodegradable items?
    A. Grass, flowers and leather
    B. Grass, wood and plastic
    C. Fruit-peels, cake and lime-juice
    D. Cake, wood and grass
    Check Answer
    Correct Option: A, C and D (All contain biodegradable items)
    In an exam, typically one option is distinct. Here, A, C, and D are all biodegradable. Option B contains plastic (non-biodegradable). (If you must choose the 'best' set often seen in books: D is commonly cited, but technically A, C, D are correct).
    Q8. 1 Mark
    Assertion (A): The sex of a child in humans is determined by the father.
    Reason (R): Males have one X and one Y chromosome.
    A. Both A and R are true, and R is correct explanation of A
    B. Both A and R are true, but R is NOT correct explanation of A
    C. A is true but R is false
    D. A is false but R is true
    Check Answer
    Correct Option: A
    Females produce only X eggs. Males produce X and Y sperms. It is the sperm (carrying X or Y) that determines the sex. Hence, the father determines the sex.
    Q9. 1 Mark
    Assertion (A): The inner lining of the small intestine has numerous finger-like projections called villi.
    Reason (R): Villi increase the surface area for absorption of digested food.
    A. Both A and R are true, and R is correct explanation of A
    B. Both A and R are true, but R is NOT correct explanation of A
    C. A is true but R is false
    D. A is false but R is true
    Check Answer
    Correct Option: A
    The primary function of villi is to maximize the surface area so that nutrients can be absorbed efficiently into the blood.
    Q10. 2 Marks
    Why is the rate of breathing in aquatic organisms much faster than in terrestrial organisms?
    Check Answer

    Aquatic organisms utilize oxygen dissolved in water. Since the amount of dissolved oxygen is fairly low compared to the amount of oxygen in the air, the rate of breathing in aquatic organisms is much faster to absorb sufficient oxygen.

    Q11. 2 Marks
    Attempt either option A or B.

    A. How does the chemical coordination take place in animals?
    OR
    B. What happens at the synapse between two neurons?
    Check Answer

    Answer A: Chemical coordination is maintained by hormones secreted by endocrine glands. These hormones are released directly into the blood and reach specific target organs (sites) to regulate physiological functions (growth, metabolism, etc.).


    Answer B: At the synapse, the electrical impulse reaches the axonal end of one neuron and releases chemicals called neurotransmitters. These chemicals cross the gap (synapse) and start a similar electrical impulse in the dendrite of the next neuron.

    Q12. 2 Marks
    State two methods to reduce the problem of waste disposal.
    Check Answer
    1. Segregation: Separating biodegradable (wet waste) and non-biodegradable (dry waste) at the source so they can be treated separately.
    2. Composting: Converting biodegradable kitchen waste into manure (compost) which reduces the volume of garbage and enriches the soil.
    Q13. 3 Marks
    (a) Name the plant hormone responsible for the following:
       (i) Elongation of cells
       (ii) Promoting cell division
       (iii) Inhibiting growth
    (b) What is a reflex arc? Draw a schematic flow chart of it.
    Check Answer

    (a) Hormones:
    (i) Auxin
    (ii) Cytokinins
    (iii) Abscisic Acid

    (b) Reflex Arc: The pathway taken by nerve impulses in a reflex action is called a reflex arc.
    Flow Chart:
    Stimulus $\rightarrow$ Receptor (Skin) $\rightarrow$ Sensory Neuron $\rightarrow$ Spinal Cord (Relay Neuron) $\rightarrow$ Motor Neuron $\rightarrow$ Effector (Muscle) $\rightarrow$ Response.

    Q14. 3 Marks
    Differentiate between 'Inherited traits' and 'Acquired traits'. Give one example of each.
    Check Answer
    Inherited Traits Acquired Traits
    Traits passed from parents to offspring via genes (DNA). Traits developed during the lifetime due to environment or practice.
    These can be passed to the next generation. These cannot be passed to the next generation.
    Ex: Eye colour, Skin colour. Ex: Swimming skills, cut on a finger.
    Q15. 4 Marks

    Case Study: Reproductive health is the state of physical, mental, and social well-being in all matters relating to the reproductive system. To maintain this, family planning and contraception are essential. A couple visited a doctor to understand methods to prevent unwanted pregnancies.

    Attempt either subpart A or B.

    A. (i) Name one mechanical barrier method of contraception. What is its additional benefit?
    (ii) How do oral contraceptive pills function to prevent pregnancy?

    OR

    B. (i) Name the surgical methods of contraception in males and females respectively.
    (ii) A woman uses a Copper-T loop. Will it protect her from Sexually Transmitted Diseases (STDs)? Justify.

    Check Answer

    Answer A:
    (i) Condoms. Additional Benefit: They prevent the transmission of Sexually Transmitted Diseases (STDs) like HIV/AIDS and Syphilis.
    (ii) Oral pills contain hormones (estrogen/progesterone) which prevent the release of eggs (ovulation) from the ovary. Without an egg, fertilization cannot occur.


    Answer B:
    (i) Male: Vasectomy. Female: Tubectomy.
    (ii) No. Copper-T prevents pregnancy by preventing implantation, but it does not provide a barrier against fluid exchange. Therefore, it cannot prevent STDs.

    Q16. 5 Marks
    Attempt either option A or B.

    A. (i) Draw a well-labelled diagram of the human excretory system.
    (ii) Explain the function of the Nephron.
    (iii) What is the difference between excretion in plants and animals?
    OR
    B. (i) Define Pollination. Distinguish between self-pollination and cross-pollination.
    (ii) What is the role of the tube nucleus in the pollen tube?
    (iii) Name the parts of the flower that develop into (a) Seed and (b) Fruit after fertilization.
    Check Answer

    Answer for A:
    (i) (Student must draw Kidneys, Ureters, Bladder, Urethra).
    (ii) Nephron: It filters the blood. The Bowman's capsule collects filtrate (glucose, amino acids, salts, water). Useful substances are reabsorbed in the tubular part, and waste (urea) remains as urine.
    (iii) Animals have specialized organs (kidneys), while plants excrete waste through falling leaves, bark, or secreting gums/resins.


    Answer for B:
    (i) Transfer of pollen from anther to stigma. Self: Same flower/plant. Cross: Different plant.
    (ii) Tube nucleus controls the growth of the pollen tube towards the ovary.
    (iii) (a) Seed: Ovule, (b) Fruit: Ovary.

    Section B: Chemistry

    Q17. 1 Mark
    Which of the following is an Amphoteric Oxide?
    A. $Na_2O$
    B. $SO_2$
    C. $Al_2O_3$
    D. $CaO$
    Check Answer
    Correct Option: C
    Aluminium oxide ($Al_2O_3$) and Zinc oxide ($ZnO$) react with both acids and bases to produce salt and water, hence called Amphoteric oxides.
    Q18. 1 Mark
    The acid present in the sting of a nettle plant leaf is:
    A. Acetic acid
    B. Citric acid
    C. Methanoic acid
    D. Oxalic acid
    Check Answer
    Correct Option: C
    Methanoic acid (Formic acid) causes the burning pain. Dock plant leaf is the traditional remedy.
    Q19. 1 Mark
    Which of the following observations is true when dilute Hydrochloric acid is added to Sodium Carbonate crystals in a test tube?
    A. A pop sound is heard.
    B. A brisk effervescence occurs and a gas turning lime water milky is evolved.
    C. A pungently smelling gas is evolved.
    D. No reaction takes place.
    Check Answer
    Correct Option: B
    Acids react with metal carbonates to release Carbon Dioxide ($CO_2$) gas, which creates brisk effervescence and turns lime water milky.
    Q20. 1 Mark
    The general formula of the homologous series of Alkynes is:
    A. $C_nH_{2n}$
    B. $C_nH_{2n+2}$
    C. $C_nH_{2n-2}$
    D. $C_nH_{2n+1}$
    Check Answer
    Correct Option: C
    Alkynes contain a triple bond and follow the formula $C_nH_{2n-2}$ (e.g., Ethyne $C_2H_2$).
    Q21. 1 Mark
    In the redox reaction: $CuO + H_2 \xrightarrow{Heat} Cu + H_2O$, the substance acting as the Oxidizing Agent is:
    A. $H_2$
    B. $Cu$
    C. $CuO$
    D. $H_2O$
    Check Answer
    Correct Option: C
    $CuO$ loses oxygen to become $Cu$. The substance that gives oxygen (or gets reduced) is the Oxidizing Agent.
    Q22. 1 Mark
    Which of the following non-metals is a good conductor of electricity?
    A. Sulphur
    B. Graphite
    C. Iodine
    D. Diamond
    Check Answer
    Correct Option: B
    Graphite is an allotrope of carbon. Due to the presence of free electrons in its structure, it can conduct electricity.
    Q23. 1 Mark
    What happens when Calcium is treated with water?
    A. It does not react with water.
    B. It reacts violently with water.
    C. It reacts less violently and bubbles of hydrogen gas stick to the surface of calcium.
    D. It reacts vigorously to form Calcium Oxide.
    Check Answer
    Correct Option: C
    The reaction is less violent than Sodium/Potassium. The heat is not enough for hydrogen to catch fire. The bubbles of $H_2$ stick to calcium metal, making it float.
    Q24. 1 Mark
    Assertion (A): White Silver Chloride turns grey in sunlight.
    Reason (R): Decomposition of Silver Chloride in presence of sunlight takes place to form Silver metal and Chlorine gas.
    A. Both A and R are true, and R is correct explanation of A
    B. Both A and R are true, but R is NOT correct explanation of A
    C. A is true but R is false
    D. A is false but R is true
    Check Answer
    Correct Option: A
    This is a photolytic decomposition reaction ($2AgCl \xrightarrow{Sunlight} 2Ag + Cl_2$). The grey colour is due to the formation of silver metal.
    Q25. 2 Marks
    When Potassium Iodide solution is added to a solution of Lead Nitrate in a test tube, a precipitate is formed.
    (i) What is the colour of the precipitate formed?
    (ii) Name the compound precipitated and write the balanced chemical equation.
    Check Answer

    (i) Colour: Yellow Precipitate.

    (ii) Compound: Lead Iodide ($PbI_2$).
    Equation:
    $Pb(NO_3)_2(aq) + 2KI(aq) \rightarrow PbI_2(s) + 2KNO_3(aq)$

    Q26. 3 Marks
    Attempt either option A or B.

    A. Differentiate between Roasting and Calcination with one example of each.
    OR
    B. (i) Draw the electron dot structure of Nitrogen molecule ($N_2$) and Methane ($CH_4$).
    (ii) Why do covalent compounds usually have low melting and boiling points?
    Check Answer

    Answer A:
    1. Roasting: Heating sulphide ores in excess air. (e.g., $2ZnS + 3O_2 \rightarrow 2ZnO + 2SO_2$).
    2. Calcination: Heating carbonate ores in limited/no air. (e.g., $ZnCO_3 \rightarrow ZnO + CO_2$).


    Answer B:
    (i) $N_2$: Triple bond between two N atoms ($:N \equiv N:$).
    $CH_4$: Carbon in center sharing 1 electron each with 4 Hydrogens.
    (ii) Covalent compounds have weak intermolecular forces of attraction, so less energy is required to break the bonds between molecules.

    Q27. 3 Marks
    (i) Explain the Thermite Reaction with a balanced chemical equation.
    (ii) Mention one practical application of this reaction.
    (iii) Why are ionic compounds usually hard solids?
    Check Answer

    (i) Thermite Reaction: The reaction of Iron(III) oxide with Aluminium powder is highly exothermic and produces molten iron.
    $Fe_2O_3(s) + 2Al(s) \rightarrow 2Fe(l) + Al_2O_3(s) + Heat$

    (ii) Application: Used to join railway tracks or cracked machine parts.

    (iii) Hardness: Due to the strong force of attraction between the positive and negative ions in the crystal lattice.

    Q28. 4 Marks

    Case Study: Plaster of Paris (POP) is a white powder. When it is mixed with water, it sets into a hard solid mass due to the formation of Gypsum. This property makes it very useful in the medical field for setting fractured bones in the right position.

    Attempt the following questions:

    A. Write the chemical name and formula of Plaster of Paris.

    B. Write the balanced chemical equation for the reaction of Plaster of Paris with water.

    Attempt either subpart C or D.

    C. Why should Plaster of Paris be stored in a moisture-proof container?

    OR

    D. How is Plaster of Paris prepared? Write the reaction temperature required.

    Check Answer

    Answer A:
    Chemical Name: Calcium Sulphate Hemihydrate.
    Formula: $CaSO_4 \cdot \frac{1}{2}H_2O$.

    Answer B (Equation):
    $CaSO_4 \cdot \frac{1}{2}H_2O + 1\frac{1}{2}H_2O \rightarrow CaSO_4 \cdot 2H_2O$ (Gypsum).


    Answer C:
    It should be stored in moisture-proof containers because it absorbs moisture from the atmosphere and hardens into Gypsum, becoming useless.


    Answer D (OR):
    It is prepared by heating Gypsum ($CaSO_4 \cdot 2H_2O$) at 373 K (100°C) carefully so that it loses 1.5 molecules of water.

    Q29. 5 Marks
    Attempt either option A or B.

    A. A neutral organic compound 'X' of molecular formula $C_2H_6O$ on oxidation with alkaline $KMnO_4$ gives an acidic compound 'Y'. Compound 'X' reacts with 'Y' on warming in the presence of Conc. $H_2SO_4$ to give a sweet-smelling substance 'Z'.
    (i) Identify X, Y, and Z.
    (ii) Write the chemical equations for all reactions involved.
    OR
    B. (i) What are Isomers? Draw structures of two isomers of Butane ($C_4H_{10}$).
    (ii) Differentiate between Soaps and Detergents based on their chemical composition and action in hard water.
    Check Answer

    Answer A:
    (i) X: Ethanol ($C_2H_5OH$), Y: Ethanoic Acid ($CH_3COOH$), Z: Ethyl Ethanoate (Ester).
    (ii) Oxidation: $CH_3CH_2OH \xrightarrow{Alk. KMnO_4} CH_3COOH$
    Esterification: $C_2H_5OH + CH_3COOH \xrightarrow{H^+} CH_3COOC_2H_5 + H_2O$


    Answer B:
    (i) Isomers: Compounds with same formula but different structures. (Draw n-Butane and Iso-butane).
    (ii) Soaps: Sodium salts of fatty acids. Do NOT work in hard water (form scum).
    Detergents: Ammonium/Sulphonate salts. Work well in hard water.

    Section C: Physics

    Q30. 1 Mark
    A spherical mirror and a thin spherical lens have each a focal length of $-15$ cm. The mirror and the lens are likely to be:
    A. Both concave
    B. Both convex
    C. Mirror is concave, lens is convex
    D. Mirror is convex, lens is concave
    Check Answer
    Correct Option: A
    According to the sign convention, the focal length is negative for both a concave mirror and a concave lens.
    Q31. 1 Mark
    The stars appear to twinkle while the planets do not. This is because:
    A. Stars are much closer to earth than planets.
    B. Stars are point sources of light, while planets are extended sources.
    C. Planets emit their own light.
    D. The atmosphere scatters star light but not planet light.
    Check Answer
    Correct Option: B
    Stars are far away and act as point sources. Atmospheric refraction causes their position to fluctuate (twinkle). Planets are closer extended sources; the variation in light from different points cancels out.
    Q32. 1 Mark
    Assertion (A): The magnetic field lines inside a current-carrying long solenoid are parallel straight lines.
    Reason (R): The magnetic field inside a solenoid is uniform at all points.
    A. Both A and R are true, and R is correct explanation of A
    B. Both A and R are true, but R is NOT correct explanation of A
    C. A is true but R is false
    D. A is false but R is true
    Check Answer
    Correct Option: A
    Parallel field lines indicate that the magnetic field strength is the same (uniform) throughout that region.
    Q33. 2 Marks
    An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.
    Check Answer

    Given: $u = -10$ cm, $f = +15$ cm (Convex mirror).
    Formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
    $\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{15} - \frac{1}{-10}$
    $\frac{1}{v} = \frac{1}{15} + \frac{1}{10} = \frac{2+3}{30} = \frac{5}{30} = \frac{1}{6}$
    $v = +6$ cm.
    Nature: Since $v$ is positive, the image is formed behind the mirror. It is Virtual and Erect.

    Q34. 2 Marks
    Attempt either option A or B.

    A. Calculate the cost of operating a heater of 500 W for 20 hours at the rate of ₹ 6.00 per unit.
    OR
    B. Explain Joule's Law of Heating. Write the mathematical expression for it.
    Check Answer

    Answer A:
    Energy = Power $\times$ Time = $500 W \times 20 h = 10,000 Wh = 10 kWh$.
    1 Unit = 1 kWh.
    Cost = $10 \times 6 = ₹ 60$.


    Answer B:
    Heat produced in a resistor is:
    1. Directly proportional to square of current ($I^2$).
    2. Directly proportional to resistance ($R$).
    3. Directly proportional to time ($t$).
    Formula: $H = I^2Rt$

    Q35. 3 Marks
    (i) Why does the sun appear reddish early in the morning?
    (ii) Why does the sky appear dark instead of blue to an astronaut?
    (iii) What is the function of the Iris in the human eye?
    Check Answer

    (i) At sunrise, sunlight travels a longer distance through the atmosphere. Blue light scatters away, leaving mainly red light (longer wavelength) to reach our eyes.

    (ii) At high altitudes (space), there is no atmosphere to scatter light. Since no scattering occurs, the sky appears black/dark.

    (iii) The Iris controls the size of the pupil and thereby regulates the amount of light entering the eye.

    Q36. 3 Marks
    Three resistors of $5 \Omega$, $10 \Omega$ and $30 \Omega$ are connected in parallel with a battery of 6V.
    (i) Calculate the total resistance of the circuit.
    (ii) Calculate the total current flowing in the circuit.
    (iii) Calculate the current flowing through the $30 \Omega$ resistor.
    Check Answer

    (i) Total Resistance ($R_p$):
    $\frac{1}{R_p} = \frac{1}{5} + \frac{1}{10} + \frac{1}{30} = \frac{6+3+1}{30} = \frac{10}{30} = \frac{1}{3}$.
    $R_p = 3 \Omega$.

    (ii) Total Current ($I$):
    $I = \frac{V}{R_p} = \frac{6}{3} = 2 A$.

    (iii) Current through $30 \Omega$ ($I_3$):
    Since it's parallel, Voltage is same (6V).
    $I_3 = \frac{V}{R_3} = \frac{6}{30} = 0.2 A$.

    Q37. 3 Marks
    A current-carrying conductor is placed in a magnetic field. Now answer the following:
    (i) List the factors on which the magnitude of force experienced by the conductor depends.
    (ii) Under what condition is the force experienced by the conductor maximum?
    (iii) State the rule used to find the direction of this force.
    Check Answer

    (i) Factors:
    - Strength of magnetic field ($B$).
    - Strength of electric current ($I$).
    - Length of conductor ($L$).

    (ii) Maximum Force: When the direction of current is perpendicular ($90^\circ$) to the direction of the magnetic field.

    (iii) Rule: Fleming's Left-Hand Rule.

    Q38. 4 Marks

    Case Study: Domestic Electric Circuits

    In our homes, we receive electric power supply through a main supply (mains). One of the wires has a red insulation cover and is called the Live wire, and the other has black insulation and is called the Neutral wire. The potential difference between the two is 220V. A third wire with green insulation is used for safety.

    Answer the following questions:

    A. What is the function of the Earth wire (green insulation)?

    B. Why is an electric fuse an important component of all domestic circuits?

    Attempt either subpart C or D.

    C. Two lamps, one rated 100W at 220V and the other 60W at 220V, are connected in parallel to the electric mains supply. What current is drawn from the line if the supply voltage is 220V?

    OR

    D. Why are copper and aluminium wires usually employed for electricity transmission? Explain why heating elements (like in toasters) are made of an alloy (nichrome) rather than pure metal.

    Check Answer

    Answer A: It provides a low-resistance path for the current. If there is any leakage of current to the metallic body of an appliance, it flows to the earth, protecting the user from electric shock.

    Answer B: A fuse breaks the circuit if the current exceeds a safe limit (due to short-circuit or overloading), thus preventing fire and damage to appliances.


    Answer C:
    Total Power $P = P_1 + P_2 = 100 + 60 = 160 W$.
    Current $I = \frac{P}{V} = \frac{160}{220} = \frac{8}{11} \approx 0.73 A$.


    Answer D (OR):
    1. Copper/Aluminium have very low resistivity, so they conduct electricity without much energy loss.
    2. Alloys (Nichrome) have higher resistivity and do not oxidize (burn) easily at high temperatures, making them ideal for heating elements.

    Q39. 5 Marks
    (i) State Ohm's Law.
    (ii) Draw a circuit diagram to verify Ohm's law (must include Ammeter, Voltmeter, Rheostat, Battery, Resistor).
    (iii) A student plots V vs I graph. What does the slope of this graph represent?
    (iv) If the voltage across a bulb is 220V and current is 0.5A, find its power and resistance.
    Check Answer

    (i) Ohm's Law: Potential difference (V) across the ends of a conductor is directly proportional to the current (I) flowing through it, provided temperature remains constant ($V = IR$).

    (ii) Diagram: (Student to draw circuit with Voltmeter in parallel and Ammeter in series).

    (iii) Slope: The slope of V-I graph represents Resistance (R).

    (iv) Calculation:
    $P = V \times I = 220 \times 0.5 = 110 W$.
    $R = V / I = 220 / 0.5 = 440 \Omega$.

    Good Job! You have practiced Set 2. Keep revising diagrams and formulas daily.
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