Mathematics and Science PYQs

The concept that can be most appropriately explained by an example of the most easily available size of a particular garment in garment shops or garment factories is Mode.

Key Points

• The mode is the value that appears most frequently in a dataset.
• In the context of the example you provided, the most easily available size of a particular garment would likely be the size that is most frequently produced or stocked, which aligns with the concept of mode in statistics.

Word problems require a strong understanding of the problem statement and the ability to extract relevant information.

Key Points

• Students may struggle with comprehending the problem, identifying the key details, and translating them into a mathematical representation.
• Without a solid comprehension skill, students may find it challenging to solve word problems, even when the teacher provides the necessary operation.
• Building comprehension skills, such as reading and analyzing information effectively, is crucial for students to successfully solve word problems.
• Teachers can support students in developing these skills through guided practice, explicit instruction, and providing scaffolding techniques.

Hence, it can be concluded that option 2 is the correct answer.

The correct option is 1. Both (A) and (R) are true and (R) is the correct reason of (A).

Key Points

Assertion (A) is true because an ambitious mathematics curriculum will challenge students to think and reason at a higher level. This will help them to develop their mathematical skills and to become more creative thinkers.

Reason (R) is also true because the aim of mathematics education is to develop students' inner resources to think and reason mathematically. An ambitious curriculum will help to achieve this aim by providing students with opportunities to solve challenging problems and to explore mathematical concepts in depth.

Therefore, both statements are true and (R) is the correct reason for (A).

The statement "All right-angles are equal" is an axiom.

Key Points

• An axiom is a fundamental and self-evident statement or principle that is accepted without proof as a basis for reasoning and building a mathematical system.
• In this case, the axiom asserts that all right-angles, which are angles measuring 90 degrees, are equal to each other.
• It is considered self-evident and does not require any proof or justification.
• Axioms form the foundation of geometry and mathematics, providing the starting point for constructing logical deductions and theorems.
• They are assumed to be true and are used as the building blocks for developing mathematical concepts and reasoning.

Hence, it can be concluded that axiom is the correct answer.

The most appropriate pedagogical approach to introduce the algebraic identity (a + b)2 = a2 + b2 + 2ab in class VIII is to let students solve (a + b) × (a + b) and arrive at the identity.

Key Points

• This approach fosters active learning as students engage in the process of multiplication and observe the resulting terms.
• By expanding the expression and simplifying it, students can recognize the pattern that leads to the identity.
• This hands-on exploration allows them to understand the concept intuitively and gain a deeper grasp of algebraic manipulations.
• Furthermore, it promotes critical thinking, logical reasoning, and problem-solving skills as students apply the identity to solve related exercises and develop confidence in their mathematical abilities.

Hence, it can be concluded that Let students solve (a + b) × (a + b) and arrive at the identity is the correct approach.

While a mathematics dictionary is a valuable resource for students to look up definitions and explanations of mathematical terms, it may not directly contribute to experimentation and exploration.

Key Points

• While a dictionary is a valuable reference tool for understanding mathematical terms and concepts, it primarily provides definitions and explanations.
• It does not offer hands-on experiences or interactive activities that actively engage students in experimentation and exploration.
• The dictionary serves as a passive resource for accessing information rather than promoting active learning.

Additional Information

• In contrast, options like digital learning games, mathematics laboratories, and educational board games provide students with opportunities to actively engage with mathematical concepts, apply their knowledge, and explore mathematical ideas in a more interactive and experiential manner.

By using examples of other shapes such as trapezium, rhombus, and open figures along with pentagonal shapes, Janet is providing a comparative context for her students.

Key Points

• This approach helps address any alternate conceptions or misconceptions that students may have about the pentagonal shape.
• By highlighting the distinguishing features of each shape and comparing them, Janet can clarify the specific characteristics of pentagonal shapes and help students understand them better.
• This pedagogical method promotes conceptual clarity and ensures that students have a clear understanding of pentagonal shapes in relation to other geometric shapes.

 Hence, it can be concluded that the pedagogy used by Janet would most likely address the alternate conceptions regarding a pentagonal shape.

The teacher's question regarding the quantity of milk required to make 4 cups of tea demonstrates the concept of proportionality.

Key Points

• In the given scenario, it is stated that 2 cups of tea require 3/4^th cup of milk.
• By setting up a proportion, students can determine the quantity of milk needed for 4 cups of tea. Proportions involve comparing two ratios, where the quantities are directly related.
• In this case, the ratio of cups of tea to cups of milk remains constant, and students can use this relationship to solve the problem.
• Understanding proportionality is crucial for solving various real-life situations that involve scaling or adjusting quantities based on a given ratio.

Hence, it can be concluded that proportionality is the correct answer.

Portfolios in mathematics are typically not group-centered assessments. Instead, they focus on individual student work and achievements.

Key Points

• Portfolios are designed to reflect the progress and growth of an individual student over a period of time.
• They provide opportunities for students to showcase their work, demonstrate their understanding, and reflect on their learning.
• Portfolios emphasize qualitative assessments, such as reflective self-assessments and the presentation of a collection of artifacts that showcase a student's mathematical thinking and problem-solving abilities.
• They are often used as a formative assessment tool to inform instruction and promote student self-reflection.

Hence, it can be concluded that option 4 is the correct answer.

Discussion in a mathematics classroom can be a valuable method to connect mathematical concepts to real-life contexts.

Key Points

• It allows students to explore the practical applications of mathematics and understand how it relates to their daily lives.
• Through discussions, students can share their perspectives, ask questions, and engage in critical thinking.
• This approach encourages active participation, fosters a deeper understanding of mathematical concepts, and promotes problem-solving skills.
• By bringing real-life contexts into the discussion, students can see the relevance of mathematics and develop a stronger connection to the subject.

Hence, it can be concluded that Discussion as one of the teaching-learning methods in a mathematics classroom should be used to bring real-life contexts in mathematics classroom.

The correct answer is Ginger, Turmeric.

Concept :

Modified stem :

• The stem is the central axis that provides support to all the aerial parts of the plant.
• In some plants, these also help in perennation, vegetative propagation, food storage, and photosynthesis through various modifications.
• Their morphology and structure have been modified to suit the function they perform.
• Stem modifications can be seen in potatoes, ginger, garlic, yam, etc.

Explanation:

Ginger:

• Ginger is a modified stem
• It grows under the soil by forming a structure called a rhizome.

Turmeric:

• Turmeric is a plant with a modified stem called a rhizome.
• Rhizomes are horizontal, underground stems that grow horizontally below the surface of the soil.

Onion:

• An onion is an underground modified stem with fleshy overlapping leaves.
• The scales of the onion are modified into the leaves to prevent the loss of water.

Sweet potato :

• Sweet potato is a modified adventitious root.
• It stores the food.

Carrot:

• Carrots are modified taproots.
• It stores the food

Turnip:

• It is a root vegetable, and the enlarged, fleshy part of the turnip that we consume is actually a modified taproot.

The correct answer is Those which are volatile or contain volatile substances.

Concept:

• Fuels that burn with a flame typically have two key characteristics:
• they are volatile or contain volatile substances, and they undergo combustion reactions that release heat and light energy.

Explanation:

• Those that are solid and have high calorific value: While solid fuels with high calorific value can release significant heat energy when burned, they may not necessarily burn with a visible flame.
• Examples of solid fuels include coal and wood, which can produce a glowing or smoldering effect rather than a visible flame.
• Those which are volatile or contain volatile substances: Volatile fuels are those that easily vaporize or evaporate at relatively low temperatures.
• These fuels have a high tendency to form flammable vapors or gases that can burn with a visible flame.
• Examples of volatile fuels include gasoline, natural gas, propane, and ethanol.
• When these fuels are ignited, their volatile components vaporize and react with oxygen, resulting in a flame.
• Those that are liquid and have high calorific value: Liquid fuels with high calorific value, such as diesel or kerosene, can release substantial heat energy when burned.
• However, whether they burn with a visible flame depends on their volatility and the presence of flammable vapors.
• Some liquid fuels may produce a flame, while others may only emit a glowing effect.
• Those that contain carbon and hydrogen: Fuels that contain carbon and hydrogen, such as hydrocarbons, have the potential to burn with a flame.
• When hydrocarbon fuels are combusted, carbon and hydrogen react with oxygen to form carbon dioxide (CO₂) and water vapor (H₂O).
• The combustion process releases heat energy and produces a visible flame, provided there is a sufficient supply of oxygen.

The correct answer is Polio, Hepatitis-A.

Concept:

• The organisms which cannot be seen through the naked eyes are called microorganisms.
• Microorganisms are classified into four major groups. These groups are bacteria, fungi, protozoa and some algae.
• Viruses are also microscopic.
• Microorganisms are both beneficial as well as harmful.

Explanation:

• Microorganisms are harmful in many ways.

Some of the microorganisms cause diseases in human beings, plants and animals.

• Such disease-causing microorganisms are called pathogens.
• On the basis of these pathogens, diseases can be categorised as - Viral diseases, Bacterial diseases, Nematode diseases, etc.
• Some of the viral diseases include - Measles, Chickenpox, Polio, Common cold, AIDS, etc.
• Hepatitis A is an inflammation of the liver caused by the hepatitis A virus (HAV). The virus is primarily spread when an uninfected (and unvaccinated) person ingests food or water that is contaminated with the faces of an infected person

Additional Information 

 Common Human Diseases are caused by Microorganisms.

The correct answer is -  A - iii, B - iv, C - ii, D - i

Explanation:

The processes match the descriptions as follows:

• Ginning - Separation of fibres from cotton seeds. Ginning is the process of removing the seeds from cotton bolls.
• Spinning - Making yarns from fibres. Spinning is the process of twisting together fibres to form yarn.
• Knitting - Making a piece of fabric from a single yarn. Knitting involves creating fabric by interlocking loops of yarn.
• Weaving - Arrange two sets of yarns together to make a fabric. Weaving is a method of textile production in which two distinct sets of yarns or threads are interlaced at right angles to form a fabric or cloth.

The Correct answer is The pole strength of each new piece will be one-ninth of the original.

 CONCEPT:

Magnet:

• An object which is capable of producing a magnetic field, attracting Ni, Co, Fe, etc, and aligning in the geographical north-south direction when suspended freely is called a magnet.

Pole strength:

• The strength of a magnetic pole to attract magnetic material towards itself is known as pole strength.
• It is a scalar quantity.
• Its SI unit is amp×m.

Poles of magnet:

• The point on the magnet which has maximum attraction property is called the pole of the magnet.
• The poles of the magnet lie slightly inside from the end.
• If a magnet is cut perpendicular to its axis then its pole strength does not change.
• If a magnet is cut along its axis then its pole strength decreases.
• If a magnet is cut into two equal parts along its length then the pole strength of each part becomes half of the given original magnet.

Explanation:

• The bar magnet has been cut into nine equal pieces, both lengthwise and widthwise. This effectively means each piece is a smaller magnet with the same magnetic properties but with a reduced pole strength. Notably, each of the components will still maintain a north and a south pole, but the strength of these poles reduces as the size of the magnet decreases.
• In this situation, the pole strength of each new piece will be one-ninth of the original. When a magnet is cut, the pole strength becomes divided equally among the pieces. The magnet is not losing its magnetic properties, but rather they are being distributed among the smaller pieces. So, by dividing the original magnet into nine parts, the pole strength of each piece is one-ninth of the original magnet's pole strength.
• The third option suggests that the pole strength of the new pieces depends on the region from where they were cut. This is not typically the case with a uniformly magnetized bar magnet, which maintains consistent magnetic properties throughout. Hence, each properly cut piece would have equal pole strength.

 "The pole strength of each new piece will be one-ninth of the original", accurately reflects the scenario according to the basic principles of magnetism

The correct answer is It will be 35°C 

Explanation:

• When the water from both glasses is transferred into the larger jar, the individual water molecules mix together.
• The molecules in the glasses collide with each other and spread out in the larger jar.
• However, during this transfer, the temperature of the water in each glass is assumed to remain constant.
• This means that the average kinetic energy, and thus the average speed of the water molecules, remains the same.
• Since the water molecules from both glasses mix together in the larger jar, their speeds and kinetic energies also mix together.
• This mixing process ensures that the average kinetic energy, and hence the temperature, of the water in the jar remains the same.
• Therefore, the temperature of the water in the jar immediately after the transfer will still be 35°C, assuming no heat is gained or lost during the transfer process.

The correct answer is:  3) Kharif, maize, soyabean.

Explanation:

• In India, the Kharif season starts with the onset of the monsoon and lasts till September or October.
• Crops are sown at the beginning of the monsoon and harvested at the end of the season.
• Major Kharif crops include maize and soyabean, among others.
• The other cropping season in India is the Rabi season, which starts after the monsoon i.e., around November, and the crops are harvested in spring i.e., around April. Major Rabi crops include wheat and mustard.

Explanation:

• The data represents a city with high temperatures throughout the year, even in what would traditionally be considered winter months, and rainfall that increases substantially from January to July.
• This suggests a tropical climate, which would be found near the equator.
• Out of the given options, Kanyakumari, being the southernmost tip of the Indian mainland, has a tropical climate and the temperatures and precipitation in the table align with what we might expect for this region.
• The other cities - Bikaner, Shimla, and New Delhi - do not have such climates.
• Bikaner is a desert city in Rajasthan with very little rainfall.
• Shimla is a hill station in Himachal Pradesh with cooler temperatures, especially in winter.
• New Delhi has a monsoon-influenced humid subtropical climate with significant variation in temperature across seasons.
• So, the correct answer is:  Kanyakumari

The Correct answer is (A) is false but (R) is true. 

Key Points

Sodium metal, being highly reactive is kept under kerosene.

• Sodium reacts when it directly comes in contact with air hence it cannot be kept in the air openly.
• It can be stored in mineral oils to avoid direct contact with chemical compounds present in the air.
• Although Kerosene is preferred because of its low volatility and cost-effectiveness.

Reaction with air:

• Sodium is highly reactive and reacts with air at even room temperature to give Sodium oxide and Sodium peroxide.
• This change can be easily noticed when lustrous white sodium metal starts getting dull because of the formation of oxides of Sodium.

Reaction with water:

• Sodium also reacts explosively with water giving out flames.
• When added to water Sodium reacts to give Sodium hydroxide and highly inflammable Hydrogen gas.

The correct answer is Gravitational force and Normal force.

Concept:

• Gravitational force: The; gravitational force is a; force that attracts any two objects with mass.
• It is called attractive because it always tries to pull masses together, it never pushes them apart.
• Its value is 9.8 m/s2 on Earth, that is to say, the acceleration due to gravity on the surface of the Earth at sea level is 9.8 m/s2.
• The normal force: The normal force is the force exerted by a surface to support the weight of an object resting on it.
• It acts perpendicular to the surface of contact between the block and the table.
• In this case, the table exerts an upward normal force on the block to balance the downward force of gravity.
• The normal force prevents the block from sinking into the table.

Explanation:

• Gravitational force, Normal force, and Static friction: Static friction is a force that opposes the relative motion between two surfaces in contact when there is no relative motion.
• In this scenario, since the block is at rest and not sliding or moving, there is no relative motion between the block and the table.
• Therefore, there is no static friction acting on the block. Thus, this option is incorrect.
• Gravitational force, Normal force, and Sliding friction: Sliding friction is a force that opposes the motion between two surfaces in contact when they are sliding past each other.
• In this case, since the block is lying at rest on the table and not sliding or moving, there is no sliding friction acting on the block. Hence, this option is also incorrect.