Key Concept: Object Classification

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion states that a notebook and a glass bottle can be grouped together due to their smooth texture, which is true as many notebooks and glass bottles indeed have smooth surfaces. The reason given is also true because objects can be classified based on shared properties like texture. However, the reason does not correctly explain the assertion, since the assertion is more about the specific grouping of two objects rather than the general principle of classification by texture.

Key Concept: Classification of materials based on transparency

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that Sara hid behind a frosted glass door because it is translucent, making it difficult for others to see her clearly. This is true because frosted glass is a translucent material, which means it allows light to pass through but scatters the light, making objects appear blurry or unclear when viewed through it. The reason given is also correct; frosted glass indeed scatters light, which prevents clear visibility. Furthermore, the reason correctly explains why Sara chose the frosted glass door to hide behind—because it obscures clear vision due to its light-scattering property, aligning with the concept of translucency.
Both statements are true, and the Reason provides the correct explanation for the Assertion.

Key Concept: Classification, Properties of Materials

c) Lustrous vs non-lustrous
[Solution Description]
To classify these objects, we need to identify a common property that can divide them into two distinct groups. The wooden ruler and plastic comb are non-lustrous (dull in appearance), while the copper coin and iron nail are lustrous (shiny). Thus, the property "lustrous vs non-lustrous" can be used for classification.

Key Concept: Materials Around Us

c) Luster
[Solution Description]
The correct unscrambled form of "E R U S T L" is "LUSTER," which refers to a shiny surface. This property is commonly found in materials like polished metals.

Key Concept: Weight, Material Properties

c) Object A will appear heaviest
[Solution Description]
Iron is denser than water and will sink, appearing heavier when submerged due to minimal buoyancy effect. Plastic and wood are less dense than water and will float, seeming lighter or weightless in water. Thus, Object A (iron) will appear heaviest when submerged.

Key Concept: Object Composition

c) Objects can be made from one or more materials
[Solution Description]
The syllabus clearly states that objects can be made from a single material or combination of materials, and different materials can be used to make objects with similar functions.

Key Concept: Material Properties, Purpose-Based Selection

b) High melting point and non-porous structure
[Solution Description]
To safely hold boiling water (around $100^\circ C$), the container must:
1. Have high heat resistance to avoid melting.
2. Be non-porous to prevent leakage.
3. Withstand thermal shock (sudden temperature changes).
Materials like ceramics (terracotta) or certain metals (stainless steel) meet these criteria. Plastic melts at high temperatures, cloth is porous, and glass may crack under thermal shock unless specially treated. Thus, "High melting point and non-porous structure" is the correct combination.

Key Concept: Materials and Properties, Classification of Materials

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a tumbler cannot be made of cloth because it cannot hold water, which is correct as cloth is porous and allows water to pass through. The reason mentions that material selection depends on properties like solubility, transparency, and hardness, which is also true. Moreover, the reason correctly explains why cloth is unsuitable for making tumblers—due to its inability to hold water (a property-based limitation). Thus, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Purpose of material selection

b) It can hold water
[Solution Description]
Plastic is lightweight, durable, and capable of holding liquids without leaking, making it suitable for manufacturing water bottles.

Key Concept: Materials Around Us

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a notebook is made up of paper, which is correct as notebooks typically use paper for writing. The reason states that paper is a material commonly used to make notebooks, which is also true and correctly explains why the assertion is true.

Key Concept: Historical Materials, Properties

c) Clay, wheel-turned, slips applied, kiln-baked, red & black designs
[Solution Description]
The solution involves recalling historical facts:
1. Clay was the primary material.
2. Techniques included wheel-turning, pigmentation, and baking in kilns.
3. Slips (protective/decorative coats) of multiple colors were applied.
4. Pots had bright red surfaces with black geometric/animal designs.

Key Concept: Materials, Historical Context of Pottery

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the Harappan civilization used advanced pottery techniques such as wheel-turning and kiln-baking to produce durable storage jars. This is true as historical evidence shows that the Sindhu-Sarasvatī civilization (2600–1900 BCE) developed sophisticated pottery methods including wheel-turned production, pigmentation, and kiln-baking. The reason explains that these techniques made pottery both decorative and functional for long-term storage, which is also accurate because pots were indeed used for storing food grains, oil, and ghee. Moreover, the reason correctly justifies the assertion since durability and functionality were direct results of these advanced techniques.

Key Concept: Material Properties and Usage

c) Metal
[Solution Description]
Cooking pots need to withstand high temperatures and should not melt or catch fire. The material should also be a good conductor of heat. Among the given options, metal is the most suitable because it is durable, conducts heat well, and does not burn at cooking temperatures. Paper and plastic are unsuitable as they would burn or melt, while cloth cannot hold water.

Key Concept: Identifying materials of daily-use items

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a tumbler made of cloth cannot be used for storing water, which is true because cloth is not waterproof. The Reason explains that cloth is porous, meaning it has small holes that allow water to seep through, making it unsuitable for holding liquids. Therefore, the Reason correctly explains why the Assertion is true.

Key Concept: Classification of Objects

b) They are all household items
[Solution Description]
The objects listed are made from different materials: wood, steel, glass, and plastic. However, they all share a common usage—they are household items used daily. Alternatively, they could also be grouped based on their shape, but the most straightforward classification here is by their use as everyday items. Color and origin are irrelevant in this context.

Key Concept: Examples of Classification

b) By keeping similar utensils together
[Solution Description]
In a kitchen, utensils are usually stored by grouping similar items together. For example, all plates are kept in one place, and spoons in another, making it easier to find and use them. This is an example of classification based on type or function.

Key Concept: Classification of Materials

c) Classification
[Solution Description]
The process of arranging objects into groups based on their properties is known as classification. This method helps in organizing materials systematically for better understanding and usage.

Key Concept: Classification by Solubility

c) By whether they dissolve or not in water
[Solution Description]
Materials can be grouped based on their solubility in water. Sugar and salt dissolve in water (soluble), while sand and chalk powder do not dissolve (insoluble).

Key Concept: Classification based on color

b) Orange, carrot, pumpkin
[Solution Description]
Objects grouped by color share the same or similar colors. For example:
- Red: Apple, tomato, cherry
- Blue: Blueberry, blue pen, blue shirt
- Green: Leaf, cucumber, green crayon
The correct group must contain objects of the same color.

Key Concept: Classification based on material properties

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that grouping objects by transparency helps identify materials for windows, which is true because transparent materials are preferred for windows. The Reason explains why transparency is important for windows—it allows light to pass through, ensuring visibility. Both statements are correct, and the Reason directly justifies the Assertion.

Key Concept: Properties for grouping materials

c) Taste
[Solution Description]
According to the syllabus, materials can be grouped based on properties like shape, color, texture, luster, hardness, or softness. Taste is not mentioned as a property for grouping.

Key Concept: Classification based on properties, Ayurveda classification

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Both Assertion (A) and Reason (R) are true. The assertion correctly states that grouping helps in studying patterns in material properties, and it has been historically used, as seen in Ayurveda. The reason also correctly explains that Ayurveda's classification system (guṇa) includes properties like heavy/light, cold/hot, and soft/hard, which align with modern classification criteria such as feel and weight. Therefore, the reason is the correct explanation of the assertion.

Key Concept: Classification properties, Ayurvedic grouping

b) guru and hima
[Solution Description]
The question asks about classifying a material that has two specific properties from Ayurveda: heavy (guru) and cold (hima). Looking at the list of Ayurvedic property pairs, we need to identify which option contains both these characteristics. The first property 'heavy' corresponds to guru in the first pair (guru-laghu), and 'cold' corresponds to hima in the third pair (hima-uṣhṇa).

Key Concept: Classification based on properties

b) Gold and Silver
[Solution Description]
Lustrous materials are those that have a shiny appearance. Examples include metals like gold, silver, and aluminum. Non-lustrous materials do not shine, such as wood or plastic. Here, we need to identify a pair where both materials are lustrous.

Key Concept: Grouping Objects

c) Function of the utensils
[Solution Description]
Kitchens typically group utensils by function (e.g., cooking utensils, serving utensils, cutting tools) or frequency of use for efficiency. While color or material could theoretically be used, functionality is the most practical and commonly applied classification system in real-world kitchens.

Key Concept: Grouping, Real-world Applications

a) Metal spoons and forks
[Solution Description]
Classification based on material properties would involve grouping items by inherent characteristics like thermal conductivity or durability. Metal spoons and forks are grouped by material (metal). Glass jars are grouped by transparency and fragility, not function. Plates and bowls are typically grouped by shape/use, while cutting boards and knives are grouped by function. Hence, metal spoons and forks represent material-based grouping.

Key Concept: Material Properties, Classification

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion claims that a tennis ball and a rubber ball of the same size will bounce to the same height due to their elastic materials. However, this is false because although both materials are elastic, their elasticity differs. The reason states that elasticity determines bounce height, which is true, but it incorrectly assumes identical elasticity for both materials. Therefore, the assertion is false, but the reason is true.

Key Concept: Transparency Property

c) Because glass is transparent and wood is opaque
[Solution Description]
Glass is transparent, allowing light to pass through, so objects can be seen clearly. Wood is opaque and does not allow light to pass through, making it impossible to see anything behind it.

Key Concept: Lustrous and Non-Lustrous Materials

c) Assertion is true, but Reason is false.
[Solution Description]
The Assertion states that copper is a lustrous material because it has a shiny surface when freshly cut. This is true as metals like copper exhibit lustre on their freshly cut surfaces. However, the Reason claims that all materials with shiny surfaces are metals, which is false. Some non-metals can also appear shiny due to polishing or coating, but they are not metals. Therefore, the Assertion is true, but the Reason is false.

Key Concept: Lustrous appearance, Hardness

b) Iron nail is lustrous and hard; wooden stick is non-lustrous and soft.
[Solution Description]
The freshly cut iron nail will have a lustrous appearance because metals like iron are naturally shiny when freshly cut. However, the wooden stick is non-lustrous as it does not shine on its own. In terms of hardness, an iron nail is harder than a wooden stick since iron cannot be easily scratched or compressed compared to wood. Therefore, the correct answer must describe the iron nail as lustrous and hard while the wooden stick is non-lustrous and soft.

Key Concept: Lustre and Texture

d) Wooden block
[Solution Description]
Freshly cut metals like iron, copper, and aluminum have a shiny appearance (lustre). However, when exposed to air and moisture, these metals can react and form oxides or other compounds on their surface, making them appear dull or non-lustrous over time. Non-metallic materials like wood or paper do not show such changes in appearance as they are already non-lustrous.

Key Concept: Lustre, Effect of Air and Moisture

c) Both iron and copper lose their lustre due to oxidation over time.
[Solution Description]
Metals like iron and copper lose their lustre over time when exposed to air and moisture due to oxidation (rusting in iron, tarnishing in copper). Freshly cut surfaces would show inherent lustre, but exposed surfaces become dull.

Key Concept: Appearance Identification

c) Chalk and wood
[Solution Description]
All metals like copper and aluminum exhibit metallic lustre (shiny appearance), while non-metals like paper and cardboard do not. Grouping a metal with a non-metal would be incorrect based on their appearance properties as described in the syllabus.

Key Concept: Distinguishing Properties

c) Metals have natural lustre while plastics require surface treatment
[Solution Description]
The syllabus explains that while metals have intrinsic lustre, other materials can be made to look shiny through external treatments like coatings. The key difference is that the metal's shininess comes from its natural properties, while for the plastic it's an artificial coating.

Key Concept: Lustre distinction

b) React with air/moisture
[Solution Description]
Metals can lose their shine due to reaction with air and moisture over time, forming dull oxide layers. This makes them appear non-lustrous though they're actually metallic.

Key Concept: Lustrous vs Non-lustrous Materials

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that all metals are lustrous, which is generally true because metals like iron, copper, zinc, and aluminium have shiny surfaces when they are freshly cut or polished. However, some metals may lose their lustre over time due to exposure to air and moisture, but this does not make them non-lustrous in nature.
The Reason correctly explains why metals are considered lustrous by citing examples like iron and copper having shiny surfaces when freshly cut. Thus, the Reason provides a valid explanation for the Assertion.

Key Concept: Effect on Metals

b) Due to the effect of air and moisture
[Solution Description]
Metals can lose their shine due to the effect of air and moisture, which causes them to tarnish or corrode, making their surfaces look dull.

Key Concept: Non-Lustrous vs. Lustrous Materials

c) Wood
[Solution Description]
Non-lustrous materials do not have a shiny surface. Examples include wood, paper, rubber, and jute. Unlike metals such as gold or silver, these materials do not reflect light well, giving them a dull appearance.

Key Concept: Lustrous Properties of Materials

b) The formation of oxides or hydroxides due to reaction with air and moisture
[Solution Description]
Metals like iron, copper, and aluminium lose their shine when exposed to air and moisture because they react with oxygen and water vapour to form a dull layer of oxides or hydroxides on their surfaces. This process is called corrosion. For example, iron forms rust ($\text{Fe}_2\text{O}_3$), which lacks the shiny appearance of pure iron.

Key Concept: Compressibility, Relative Hardness

d) Steel rod
[Solution Description]
Hard materials resist both compression and scratching. A sponge is soft and can be compressed easily. A wooden block can be scratched but resists compression moderately. A brick resists scratching but may crack under high compression. A steel rod is hard and resists both compression and scratching effectively due to its metallic bonding and rigid structure.

Key Concept: Hardness Classification

c) Brick
[Solution Description]
The question asks about an object that would not show scratches when tested with a metal key. Objects that are hard resist scratching.
- From Table 6.3 in the syllabus, a brick is classified as hard (made of baked clay).
- A metal key is likely to leave scratches on softer materials like chalk or wood but not on very hard materials like brick.
- Thus, the brick is the least likely to show scratches because it is hard.

Key Concept: Relative Hardness

d) Iron
[Solution Description]
The syllabus states that rubber is softer than iron but harder than sponge; hence, iron is harder than rubber.

Key Concept: Hard vs Soft Materials

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that an iron nail can scratch a chalk piece easily, which is true because iron is harder than chalk. The reason provided is that chalk is softer than iron, which is also correct and directly explains why the iron nail can scratch the chalk piece. Hence, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Hard vs soft materials, Relative nature of hardness

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that a diamond cannot be scratched by any other material because it is the hardest known natural material. This is true as diamonds top the Mohs scale of hardness with a rating of 10. The Reason explains that hardness is a relative property, which is also correct since hardness is determined by comparing materials' ability to scratch or compress each other. However, the Reason does not explain why a diamond specifically cannot be scratched; it merely defines hardness as a relative property. Therefore, both statements are true, but the Reason does not correctly explain the Assertion.

Key Concept: Material properties, Real-world application

c) Hardness and compressive strength
[Solution Description]
Load-bearing structures require materials that are hard (resistant to scratching) and have high compressive strength. Hardness prevents surface damage, while compressive strength ensures structural integrity under weight.

Key Concept: Relative Hardness Properties

b) Mṛidu (\textit{soft}) - Kaṭhina (\textit{hard})
[Solution Description]
In Ayurveda, the property 'mṛidu' means soft, and its opposite is 'kaṭhina', meaning hard. This is one of the ten pairs of opposite properties described in ancient Indian texts for classifying matter.

Key Concept: Hardness and Material Classification

a) Chalk
[Solution Description]
Materials that are soft can be scratched easily with a metal key. Among the given options, chalk is known to be very soft compared to the others. Stone and iron are hard materials, while wood has moderate hardness but is still harder than chalk.

Key Concept: Material Properties, Comparative Hardness

c) Ceramic plate > Steel spoon > Plastic ruler > Wooden table
[Solution Description]
The metal pin scratches the wooden table and plastic ruler, meaning these are softer than the pin. Since the ceramic plate and steel spoon are not scratched, they are harder than the pin. Between ceramics and steel, ceramics are generally harder than steel. Among the scratched materials, wood is usually softer than plastic. Thus, the correct order is: ceramic plate > steel spoon > plastic ruler > wooden table.

Key Concept: Real-World Application, Material Properties

c) Translucent amber glass
[Solution Description]
The container must block harmful light (opaque) but allow visibility of the chemical level (transparent/translucent). Key points:
1. Opaque materials (e.g., wood) block all light and visibility.
2. Transparent materials (e.g., glass) expose the chemical to light.
3. Translucent materials (e.g., colored glass) filter light while permitting partial visibility.
A translucent material like amber glass is ideal as it blocks UV light (protecting the chemical) while allowing visual monitoring.

Key Concept: Transparent Materials

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Glass is indeed a transparent material as per the syllabus definition, allowing clear visibility. The reason correctly states that transparent materials enable clear visibility, which explains why glass is transparent. Both the assertion and reason are true, and the reason properly justifies the assertion.

Key Concept: Transparent Materials

c) Glass
[Solution Description]
Transparent materials allow clear visibility through them. Among the given options, glass is a transparent material as it allows light to pass through clearly.

Key Concept: Transparency, Translucency, Opacity

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that frosted glass allows some light to pass through but blurs the image. This is correct because frosted glass does let light pass but diffuses it, making images unclear. The Reason explains that frosted glass is translucent due to light scattering, which directly justifies why the image appears blurred. Hence, both Assertion and Reason are true, and Reason correctly explains the Assertion.

Key Concept: Properties of Opaque Materials

c) Does not allow light to pass at all
[Solution Description]
Opaque materials do not allow light to pass through them, making it impossible to see through them. Examples include wood, cardboard, and metals.

Key Concept: Transparency of Materials

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that glass is a transparent material. According to the syllabus, transparent materials like glass allow light to pass through them completely, enabling clear visibility of objects. The reason explains why glass is transparent: it allows light to pass through completely. Thus, the reason correctly explains the assertion.

Key Concept: Transparent, Translucent, Opaque Materials

b) Air is transparent and the wooden door is opaque
[Solution Description]
Air is transparent, meaning it allows almost all light to pass through without scattering, enabling clear visibility. A wooden door is opaque, blocking light completely and preventing us from seeing what's behind it. The difference lies in how much light each material transmits.

Key Concept: Transparent, Translucent, Opaque Materials

b) Translucent
[Solution Description]
If an object is faintly visible behind a material, it means the material allows some light to pass but not all, causing blurred vision. This property is characteristic of translucent materials, such as frosted glass or butter paper. Transparent materials would make the object clearly visible, while opaque materials would block visibility entirely.

Key Concept: Opaque Materials

c) Because wood is an opaque material
[Solution Description]
Opaque materials do not allow any light to pass through them, making objects behind them invisible. A wooden door is opaque, so we cannot see through it.

Key Concept: Transparent vs. Translucent, Real-world Application

c) Translucent
[Solution Description]
To allow sunlight to pass but diffuse it, the material needs to be translucent. Transparent materials let light pass clearly, while opaque materials block all light. Translucent materials scatter light, providing diffusion.

Key Concept: Transparent Materials, Multi-step Reasoning

a) A, D, B, C
[Solution Description]
Glass is transparent (highest transmission), butter paper is translucent (moderate), air is transparent (but negligible obstruction), and cardboard is opaque (no transmission). However, air is technically transparent but not a "material" in this context; glass is the primary reference.

Key Concept: Opaque vs. Translucent, Conceptual Complexity

a) P: Transparent, Q: Translucent, R: Opaque, S: Opaque
[Solution Description]
- Box P allows clear visibility: transparent.
- Box Q shows blurred images: translucent.
- Box R blocks all light: opaque.
- Box S reflects all light: also opaque.
Thus, the order is transparent $\rightarrow$ translucent $\rightarrow$ opaque.

Key Concept: Classification

a) Salt and sand
[Solution Description]
From the syllabus, sugar and salt are soluble, while chalk powder, sand, and sawdust are insoluble. The correct pair should have one from each category.

Key Concept: Solubility, Liquid Miscibility

b) Vinegar is soluble, but honey is insoluble in water.
[Solution Description]
Vinegar (acetic acid solution) is miscible with water due to its polar nature, forming a homogeneous mixture. Honey, however, contains high concentrations of sugars and other compounds that may exceed their solubility limits or form viscous suspensions, causing incomplete dissolution or settling. This shows that while vinegar is fully soluble, honey's solubility is limited under these conditions, leading to non-uniform mixing.

Key Concept: Insoluble Materials

c) Chalk powder
[Solution Description]
Insoluble materials like chalk powder, sand, and sawdust do not dissolve in water. The syllabus confirms that these materials do not disappear when mixed with water.

Key Concept: Definition of Soluble Materials

c) Sugar
[Solution Description]
Soluble materials completely disappear when mixed in water. From the syllabus examples, sugar and salt are soluble while chalk powder, sand and sawdust are insoluble.

Key Concept: Soluble vs Insoluble Materials

c) Assertion is true, but Reason is false.
[Solution Description]
The assertion states that sugar and salt dissolve in water (forming homogeneous solutions), which is true as observed in Table 6.5. However, the reasoning incorrectly attributes the insolubility of chalk powder to its "heterogeneous nature," which is not scientifically accurate. Chalk powder is insoluble due to its non-polar molecular structure, which does not interact well with polar water molecules. While the Assertion is true, the Reason is false because it misrepresents the scientific basis of solubility.

Key Concept: Soluble vs Insoluble Materials

b) It can dissolve many materials, aiding in transport
[Solution Description]
The syllabus mentions that water can dissolve a large number of materials, which is crucial for transporting nutrients and other substances within the body. This property makes water essential for bodily functions.

Key Concept: Solubility, Practical Application - ORS

c) 6 tsp sugar + 0.5 tsp salt in 500 mL water
[Solution Description]
Standard ORS contains 6 tsp sugar + 0.5 tsp salt per liter. For double concentration: need 12 tsp sugar and 1 tsp salt per liter. But only making 500 mL (half liter), so use half these amounts: 6 tsp sugar + 0.5 tsp salt in 500 mL water.

Key Concept: Solubility in Water

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, sugar is mentioned as a material that dissolves completely in water, making it soluble. The assertion states that sugar dissolves completely in water, which is true based on the activity described. The reason given is that sugar is a soluble substance in water, which is also true and directly explains why the assertion is correct. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Soluble vs. Insoluble

b) Sugar disappears, but sand does not.
[Solution Description]
Sugar is soluble in water, so it will disappear when stirred. Sand is insoluble, so it will not disappear. By checking the observations from Table 6.5, we see that sugar dissolves (disappears) while sand remains undissolved.

Key Concept: Mass Unit Consistency, Multi-Step Solution

b) 2.5 kg
[Solution Description]
Convert all masses to kg: $1500 \text{ g} = 1.5 \text{ kg}$, $0.75 \text{ kg} = 0.75 \text{ kg}$, $250 \text{ g} = 0.25 \text{ kg}$. Add them together: $1.5 \text{ kg} + 0.75 \text{ kg} + 0.25 \text{ kg} = 2.5 \text{ kg}$.

Key Concept: Mass Comparison, Real-World Application

b) 400 g
[Solution Description]
Convert 800 g to kg: $800 \text{ g} = 0.8 \text{ kg}$. The difference between the masses is $1.2 \text{ kg} - 0.8 \text{ kg} = 0.4 \text{ kg}$. Thus, an object of mass 400 g ($0.4 \text{ kg}$) is needed to balance the scale.

Key Concept: Mass and Units

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that mass measures the quantity of matter in an object, which is correct according to the syllabus. The reason correctly explains the units used for measuring mass (grams and kilograms) and their relationship (1 $kg$ = 1000 $g$). Since both statements are true and the reason provides a valid explanation for the assertion, the correct option is (a).

Key Concept: Mass measurement, Units

b) 150 g
[Solution Description]
Total mass = mass of cup + mass of sand. Given total mass = 200 g, cup mass = 50 g.
Step-by-step calculation:
1. Subtract the cup's mass from the total mass: $200\,\text{g} - 50\,\text{g} = 150\,\text{g}$.
2. The remaining 150 g is the mass of the sand.
Thus, the mass of sand alone is 150 g.

Key Concept: Volume Units

c) Cubic metre ($m^3$)
[Solution Description]
The International System of Units (SI) defines the standard unit for volume as cubic metre, abbreviated as $m^3$. Other units like litre ($L$) and millilitre ($mL$) are also used but are not the SI unit.

Key Concept: Units of Mass

d) 3 kg
[Solution Description]
According to the SI system, the unit for mass is kilogram ($kg$). It should be written without any space between 'k' and 'g', no full stop after 'kg', and a space between the number and the unit. Hence, the correct representation is $3$ $kg$.

Key Concept: Mass comparison

a) Bag of rice
[Solution Description]
To compare the masses, we need both quantities in the same unit. Convert $3000\ g$ to kilograms by dividing by $1000$ since $1\ kg = 1000\ g$.
Calculation: $3000\ g = 3000 \div 1000 = 3\ kg$.
Now, compare $5\ kg$ (rice) and $3\ kg$ (sugar). The bag of rice ($5\ kg$) is heavier.

Key Concept: Heavier/Lighter Objects

d) A heavier object has more mass than a lighter object.
[Solution Description]
A heavier object has more mass compared to a lighter object, as per the given syllabus. Mass determines whether an object is heavier or lighter.

Key Concept: Mass vs Weight

c) Weight
[Solution Description]
The syllabus states that weight is sometimes used in common language for mass, as it is determined by weighing.

Key Concept: Volume comparison, unit conversion

d) 150\%
[Solution Description]
First, convert the bottle's volume from millilitres to litres to match the container's unit:
$750 \text{ mL} = 0.75 \text{ L}$
The container has a capacity of 0.5 L. To find the percentage filled, divide the volume of water by the container's capacity and multiply by 100:
$\left( \frac{0.75 \text{ L}}{0.5 \text{ L}} \right) \times 100 = 150\%$
This means the container will be overfilled (150\%).

Key Concept: Volume and Space

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Assertion (A) states that increasing the amount of water in a container increases its volume. This is true because volume is the measure of space occupied by matter. Reason (R) correctly explains this by stating that volume is indeed the space occupied by matter, and adding more matter (water) will increase the occupied space. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Space and Volume

c) 2000 mL
[Solution Description]
To convert litres to millilitres, we use the conversion factor: 1 L = 1000 mL.
Therefore, for a 2 L bottle:
$2 \, \text{L} \times 1000 \, \frac{\text{mL}}{\text{L}} = 2000 \, \text{mL}$
The correct answer is 2000 mL.

Key Concept: Volume Conversion

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The Assertion states that the volume of a liquid is correctly written as $1 L$ because the abbreviation for litre is a capital L. According to the syllabus, litre is indeed abbreviated as a capital L, so the Assertion is true.
The Reason states that the SI unit for volume is cubic metre ($m^3$) and that $1 m^3 = 1000 L$. Both parts of the Reason are correct as per the syllabus. However, the Reason does not explain why the abbreviation for litre must be a capital L, which is what the Assertion claims.
Therefore, both Assertion and Reason are true, but Reason does not correctly explain Assertion.

Key Concept: Real-world application, Multi-step calculations

b) 2400 L
[Solution Description]
First, calculate the total volume of the reservoir: $2 m \times 1.5 m \times 1 m = 3 m^3$. Convert this to litres: $3 m^3 \times 1000 L/m^3 = 3000 L$. Since the reservoir is filled to 80\% of its capacity, the volume of water is $3000 L \times 0.8 = 2400 L$.

Key Concept: Comparing Volumes

c) 0.5 $L$
[Solution Description]
First, we need to know that $1 L = 1000 mL$. Therefore, to convert $500 mL$ to litres, we divide by 1000:
$500 mL = \frac{500}{1000} L = 0.5 L$
So, $500 mL$ is equal to $0.5 L$. This matches one of the given options.

Key Concept: Multi-concept problem

c) 0.0015 $m^3$
[Solution Description]
Convert all to $m^3$: 250 mL = 0.00025 $m^3$, 0.5 L = 0.0005 $m^3$, 750 cm³ = 0.00075 $m^3$. Sum them: $0.00025 + 0.0005 + 0.00075 = 0.0015 m^3$.

Key Concept: Volume Units

c) 750 mL
[Solution Description]
The correct abbreviation for millilitres is $mL$, with lowercase $m$ and uppercase $L$ without any space between them. Therefore, 750 millilitres is correctly written as 750 $mL$.

Key Concept: Volume Definition

b) The amount of space it occupies
[Solution Description]
Volume is defined as the amount of space occupied by any matter or object. It is measured in units like litre ($L$) or millilitre ($mL$), and the SI unit is cubic metre ($m^3$).

Key Concept: Volume and Space in Water-Filled Tumblers

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the volume of water in a half-filled tumbler is less than that in a fully-filled tumbler of the same capacity. This is true because volume measures the space occupied by the water, and a half-filled tumbler occupies less space compared to a fully-filled one. The reason explains that volume is indeed the measure of space occupied by a substance, which is correct. Moreover, the reason logically justifies the assertion since greater space occupied directly implies greater volume. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Key Observations

b) The water bottle has a smaller volume than the jug
[Solution Description]
This situation happens because the water bottle has a fixed volume. If the jug contains more water than the bottle's volume, only enough water to fill the bottle will fit, leaving some water behind in the jug. This demonstrates that objects (or containers) have limited space they can occupy.

Key Concept: Material Properties, Solubility

d) Lemon juice
[Solution Description]
The solubility of a substance determines its ability to dissolve in water. Sugar and salt are soluble in water, so they disappear when stirred. From the given options, chalk powder is insoluble, sand is insoluble, sawdust is insoluble, but lemon juice (which contains citric acid) is soluble.

Key Concept: Matter and Volume

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that the volume of a substance is always measured in litres or millilitres, which is not true because volume can also be measured in other units like cubic metres ($m^3$) as per the International System of Units (SI). The reason correctly states that the SI unit for volume is cubic metre ($m^3$), which is true. Therefore, the assertion is false, but the reason is true.

Key Concept: Mass and Volume Units

c) 25 kg
[Solution Description]
According to SI unit conventions for mass:
1. The symbol 'kg' must be written in lowercase letters without any space between 'k' and 'g'.
2. There should be no full stop after 'kg' unless at the end of a sentence.
3. A space must be left between the numerical value and the unit.
Therefore, the correct representation is "25 kg".

Key Concept: Units of Measurement

b) 0.0015 m$^3$
[Solution Description]
Given the conversion factor: 1 m$^3$ = 1000 L.
To convert 1.5 L to cubic meters:
1. Divide the volume in liters by 1000 to get cubic meters.
1.5 L $\div$ 1000 = 0.0015 m$^3$.
Therefore, 1.5 L equals 0.0015 m$^3$.

Key Concept: Units of Mass

c) 5 kg
[Solution Description]
The unit for mass in the International System of Units (SI) is kilogram, abbreviated as kg. There should be no space between 'k' and 'g', and no full stop after the symbol.

Key Concept: Units

b) 2 kg
[Solution Description]
According to the SI unit guidelines, the correct representation of mass in kilograms should have no space between 'k' and 'g'. It should also not have a full stop after the symbol. The numerical value and unit should be separated by a space.
$2 \, kg$

Key Concept: Definition of Matter

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, matter is defined as anything that occupies space and has mass. The syllabus also states that mass and volume are the fundamental properties of matter. Therefore, both the Assertion and the Reason are true, and the Reason correctly explains why the Assertion holds true.

Key Concept: Units of measurement

c) Assertion is true, but Reason is false.
[Solution Description]
The assertion states that the correct way to write 5 kilograms is $5$ $kg$, which is true as per the syllabus because there must be a space between the number and the unit symbol. The reason states that there should be no space between the numerical value and the unit symbol, which is false according to the syllabus because there must always be a space between the number and the unit symbol. Therefore, the assertion is true, but the reason is false.

Key Concept: Mass and Volume Relationship

d) 2 $g/mL$
[Solution Description]
First, convert mass from kilograms to grams: $12$ $kg = 12,\!000$ $g$.
Next, convert volume from litres to millilitres: $6$ $L = 6000$ $mL$.
Now, calculate density: $density = mass / volume = 12,\!000\, g / 6000\, mL = 2\, g/mL$.

Key Concept: Units of Mass

a) 5 kg
[Solution Description]
The syllabus specifies that the unit of mass, kilogram, should be abbreviated as $kg$ with no space between 'k' and 'g'. Additionally, there should be a space between the numerical value and the unit. Therefore, the correct representation is $5$ $kg$.

Key Concept: Mass and Volume

b) $5$ $kg$
[Solution Description]
The correct way to write 5 kilograms is by using the SI unit abbreviation for kilogram, which is $kg$. There should be no space between 'k' and 'g', no full stop after the symbol, and a space between the number and the unit. So, 5 kilograms is written as $5$ $kg$.