Mathematics and Science PYQs

National Curriculum Framework, 2005 advocates for a learning process without stress or undue burden on the students. It emphasizes understanding and learning over rote memorization.

Key Points

• According to the National Curriculum Framework (NCF) 2005, the primary goal of math education is to develop children's abilities to think and reason mathematically, to pursue assumptions to their logical conclusions, and to handle abstraction.
• It also emphasizes the need to relate classroom learning to the child’s physical and social environment.
• Statement (c) - "When real-life situations are given, I could connect them with mathematical concepts" - is aligned with these objectives.
• It shows the learner's ability to apply mathematical concepts to real-life situations, which is one of the main goals of the NCF.
• On the other hand, statements (a) and (b) mainly focus on rote learning, memorizing formulae, and learning proofs, which are not the primary focus of the NCF's approach to mathematics education.

Hence, we can conclude that the statement (c) is the most appropriate by a mathematics learner.

A context-based question is a question that cannot be answered without considering the context in which it is asked.

Key Points

• 144 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
• This question is a context-based question because it involves a real-life situation that requires the concept of square roots to solve.
• The question asks for the number of rows and plants in each row, and because the number of plants is equal to the number of rows, we are essentially taking the square root of the total number of plants (144) to find the answer.
• The other options are more straightforward, calculation-based questions.

Hence, we can conclude that option 3 is the correct answer.

Open-ended questions in mathematics are questions that do not have a single correct answer, or that require more than simply performing a calculation to answer.

Key Points

• These types of questions promote deep thinking, problem-solving, creativity, and mathematical communication.
• They allow students to explore different approaches, discuss their thinking process, and justify their solutions, all of which are essential skills in mathematics.
• Open-ended questions can also be used throughout the learning process, not just after the syllabus has been completed.
• While open-ended questions might require more effort from teachers in terms of assessment, and might initially be challenging for students who are accustomed to straightforward calculation-based tasks, they don't necessarily create confusion or burden if used and managed appropriately.

Hence, we can conclude that giving open-ended questions in mathematics provides scope for mathematical communication.

Euclid's algorithm, named after the ancient Greek mathematician Euclid, is an efficient method used to find the greatest common divisor (GCD) of two numbers. 

Key Points

• The greatest common divisor of two integers is the largest number that divides both of them without leaving a remainder.
• The algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number.
• The process is repeated until the numbers become equal, that is until we find the greatest common divisor.

Hence, we can conclude that 'It is a way to find the greatest common divisor of any two positive integers' is true for Euclid's algorithm.

Ask the students to measure the top of their tables using notebooks, books, dusters, etc., and then compare the results.

Key Points

• This activity involves students actively engaging with the concept of area in a hands-on, tangible way.
• It connects mathematical concepts to real-world objects that students are familiar with, which can help them to understand and remember the concept better.
• After students have some intuitive understanding of what "area" means through these practical measurements, the formula for the area of a rectangle can be introduced as a more efficient way to calculate it.
• The other options focus more on procedural knowledge and the formula, without giving students the chance to first develop their conceptual understanding of what area is.

Hence, we can conclude that option 4 is the correct answer.

The problem-solving method of teaching is an instructional strategy where significant problems are used as the basis for the development and implementation of learning activities. 

Key PointsGeorge Polya promoted the idea of heuristics in mathematical problem-solving and mathematics education. 

The problem-solving method follows a general sequence of steps, which are:

• Identify the problem: This is where the problem is understood and defined. The problem may be presented by the teacher or derived from the students’ experiences.
• Analyze the problem: This involves breaking down the problem into simpler parts or elements.
• Develop possible solutions: This step involves brainstorming and developing as many solutions as possible, without evaluating them at first.
• Implement a solution: Select the most promising solution from those that were developed, and then apply it to the problem.
• Evaluate the solution: This is where students analyze the results to see if the problem has been solved or needs further investigation.

Hence, we can conclude that George Polya promoted the idea of heuristics in mathematical problem-solving and mathematics education.

Mathematical communication is the process of expressing, discussing, interpreting, and clarifying mathematical ideas.

Key Points

• The least appropriate for mathematical communication in a classroom among the provided options is a teacher should emphasize students explain mathematical ideas using standard algorithms only.
• Mathematics can be understood and explained in a variety of ways, not just through standard algorithms.

Some students might find other methods more intuitive or easier to understand.

• A strong mathematical education encourages students to explain their thinking in different ways, including through diagrams, words, and alternative methods or algorithms.
• This not only helps them understand the subject more deeply but also builds their problem-solving skills as they find multiple ways to approach a problem.

Hence, we can conclude that 'A teacher should emphasize students to explain mathematical ideas using standard algorithm only' is least appropriate for mathematical communication in a classroom.

A mathematical proof is a logical argument demonstrating that a specific mathematical statement or theorem is universally true, assuming certain premises or axioms. 

Key Points

• Observations can help in formulating hypotheses or discovering patterns, but they are not typically involved in formal mathematical proofs.
• In mathematics, a proof is a deductive argument for a mathematical statement, often built upon axioms and previously proven statements through deductive reasoning, not just mere observation.
• In the context of formal mathematics, proofs rely on precise logical reasoning, not on observational or empirical evidence as in the natural sciences.

Hence, we can conclude that Mathematical proofs are least likely to involve Observations.

The most appropriate educational aim for having students create polygons with matchsticks is to let students discover the various attributes of polygons.

Key Points

• Hands-on activities like creating polygons with matchsticks allow students to explore and understand mathematical concepts in a tactile and visual way.
• This can help them internalize the attributes of polygons, such as the number of sides, vertices, and angles, and how these change as they manipulate the matchsticks to form different polygons.
• Through such activities, students can make observations, test their hypotheses, and draw conclusions, promoting a deeper understanding of the concepts at hand.
• Breaking the monotony is a positive effect of varied teaching methods, but should not be the primary aim.
• Checking if students copy from others isn't a productive learning goal.
• Learning the names of polygons is important, but the activity can serve to facilitate a much deeper understanding than just terminology.

Hence, we can conclude that 'To let students discover the various attributes of polygons' is the most appropriate aim for doing this activity.

The National Curriculum Framework, 2005 emphasizes problem-solving as a key aspect of learning.

Key Points

• The aim of posing meaningful problems is to help students see the relevance of what they're learning, understand the application of mathematical concepts in real-world situations, and enhance their problem-solving skills.
• By tackling problems that reflect real-life situations, students can see the practical uses of math, which can boost their interest and motivation, as well as deepen their understanding.
• While other options might be components of a well-rounded mathematical education, they don't necessarily align with the idea of "meaningful problems".

Hence, we can conclude that meaningful problems are problems that use mathematical skills of problem-solving in daily life situations.

The Correct answer is Parasite.

Explanation:

• Cuscuta, commonly known as dodder or amarbel, is a parasitic plant that does not have chlorophyll. Unlike typical plants that can photosynthesize and produce their own food using sunlight, cuscuta lacks this ability. Instead, it relies on other host plants for its nutrition.
• No chlorophyll: Chlorophyll is a green pigment found in plants that is essential for photosynthesis, the process of converting sunlight into energy (food) for the plant. Since cuscuta lacks chlorophyll, it cannot perform photosynthesis.
• Obtains ready-made food: Cuscuta has specialized structures called haustoria that penetrate the host plant's tissue. Through these haustoria, cuscuta extracts water, minerals, and nutrients directly from the host plant. It essentially "steals" the food that the host plant has produced through photosynthesis.
• Dependence on host plants: Cuscuta cannot survive on its own and depends entirely on the host plant for its nutrition. It wraps itself around the host plant, twining and climbing as it grows, to access more nutrients from different parts of the host.
• Impact on host plant: The parasitic nature of cuscuta can harm the host plant. As cuscuta extracts nutrients from the host, it weakens the host's growth and may cause reduced vigor, stunting, or even death of the host plant if the infestation is severe.
• Reproductive strategy: Cuscuta produces seeds that are dispersed to nearby vegetation. When these seeds land on a suitable host plant, they germinate, and the young cuscuta starts to grow and establish its parasitic connection to the host.
• cuscuta is classified as a parasitic plant due to its inability to photosynthesize and its dependence on other plants for nutrition. This parasitic relationship can be detrimental to the host plant, making cuscuta an interesting but potentially harmful species in ecological contexts.

The Correct answer is  (B) and (D)

Explanation:

• It is a thick wall bag: This statement is correct. The stomach is a muscular organ located in the upper abdomen. It has a thick, muscular wall that helps it contract and mix the food with gastric juices during digestion. The stomach can expand and accommodate varying amounts of food, and its muscularity aids in the churning and breakdown of food.
• Its shape is like a flattened 'S': This statement is incorrect. The shape of the stomach is more accurately described as a J-shaped pouch. It is not a flattened 'S' but rather resembles the letter "J." The stomach has two main parts: the cardiac (or upper) part and the pyloric (or lower) part. The cardiac part receives food from the esophagus, while the pyloric part connects to the small intestine.
• It lies between the food pipe and the small intestine: This statement is correct. The stomach is located between the food pipe (esophagus) and the small intestine. Food travels from the mouth through the esophagus and into the stomach for further digestion before being released into the small intestine for the absorption of nutrients.
• It is the narrowest part of the alimentary canal: This statement is incorrect. The narrowest part of the alimentary canal is not the stomach; it is the small intestine. The small intestine is a long, narrow tube that follows the stomach in the digestive tract and is the site where most of the nutrient absorption occurs.

so the incorrect statements are (B) "Its shape is like a flattened 'S'" and (D) "It is the narrowest part of the alimentary canal."

Additional Information Stomach: it is a muscular pouch-like sac that lies slightly to the left of the abdomen to store food temporarily.

The stomach is divided into four regions:

1. The cardia, which surrounds the openings of the esophagus into the stomach.
2. The fundus of the stomach, which is the area above the level of the cardiac orifice.
3. The body of the stomach, which is the largest region of the stomach.
4. The pyloric part, which is divided into the pyloric canal and is the distal end of the stomach.

Functions of the stomach:

• Digestion of food
• Secretion of gastric juices, digestive enzymes, and hydrochloric acid.
• Secretion of gastric hormones and intrinsic factors.
• Regulation of the rate and delivery of partially digested food to the small intestine.
• Absorption of small quantities of water and dissolved substances.

The Correct answer is Breaking down into a powdery mass on tapping with a hammer.

Concept:

• Non-metals generally have certain properties that distinguish them from metals. One of the key properties of non-metals is that they are brittle. When subjected to mechanical force, such as tapping with a hammer, non-metals tend to break down into a powdery mass or may shatter into pieces.

Explanation:

• Sonorous and hard: This property is more characteristic of metals, not non-metals. Metals are known for being sonorous (producing a ringing sound when struck) and hard, whereas non-metals are generally not sonorous and are often less hard than metals.
• Lustrous and malleable: Lustrousness refers to the property of being shiny or reflective. Metals are typically lustrous, whereas non-metals are not. Malleability, which means the ability to be hammered into thin sheets without breaking, is another property of metals, not non-metals. Non-metals are usually not lustrous and are not malleable.
• Good conductor of heat and electricity: This property is also primarily associated with metals. Metals are excellent conductors of heat and electricity due to the mobility of their free electrons, while non-metals are generally poor conductors of heat and electricity.
• The property of "breaking down into a powdery mass on tapping with a hammer" is more characteristic of non-metals.

Additional Information Physical Properties of Metals and Non-metals

The Correct answer is (i) - (B), (ii) - (A), (iii) - (D), (iv) - (C).

Explanation:

• An acid is a substance that typically has a sour taste, turns blue litmus paper red, and can react with metals to produce hydrogen gas. One of the common household acids is found in window cleaner, which is used to clean glass surfaces.
• A base is a substance that typically has a bitter taste, turns red litmus paper blue, and can feel slippery or soapy to the touch. Tamarind is a natural source of tartaric acid, which is a weak organic acid and is commonly used in cooking as a base or souring agent.
• Neutral substances are neither acidic nor basic. They do not show any significant color change with litmus paper. Water is a neutral substance with a pH of 7.
• Indicators are the substances that are used to identify whether the given substance is an acid or a base.
• An indicator is a substance that changes its color in response to changes in the acidity or basicity of a solution. Turmeric is a natural indicator that turns reddish-brown in acidic solutions and yellow in basic solutions.

Additional Information

• An indicator does not change the nature of the substance or the solution but only helps to indicate the acidic or basic nature of the solution by showing a color change.
• For example, litmus paper turns red in acidic conditions and blue in basic conditions. Similarly, phenolphthalein turns colorless in acidic solution and pink in basic/alkaline solution.

 

The correct answer is The colour of solution changes from green to blue.

 

Concept:

• In the experiment where an iron nail is dipped into a blue color solution of copper sulfate (CuSO4)

Theory of the chemical reaction 

• Iron displaces copper ions from an aqueous solution of copper sulfate as it is a single displacement reaction of one metal by another metal.
• Iron is placed above copper in the activity series & elements placed above in this series are more reactive than those placed below them. Thus iron is more reactive than copper.
• In this reaction, metallic iron is converted into a ferrous ion (Fe2+), and a cupric ion (Cu2+) is converted into metallic copper.
• Fe (s) + Cu2+ (aq) → Fe2+ (aq) + Cu (s)

Observations:

• The color of the solution changes from blue to green color.
• The green color is due to the formation of ferrous sulfate (FeSO4).
• A reddish-brown layer of copper is deposited on the nail.

Explanation:

• When copper sulfate reacts with iron, the color of the solution does not change from green to blue. In fact, the copper sulfate solution is already blue in color. The blue color of copper sulfate is due to the presence of copper ions (Cu²⁺⁾ in the solution.
• The reaction between copper sulfate (CuSO₄₎ and iron (Fe) proceeds as follows:
• CuSO₄ (aq) + Fe (s) → FeSO₄ (aq) + Cu (s)
• In this reaction, iron displaces copper from copper sulfate, forming iron sulfate (FeSO₄) and solid copper (Cu). The iron sulfate formed is also in solution and can appear colorless or light green, depending on the concentration.

Additional Information

The Correct answer is Chromium.

Explanation:

• Stainless steel is an alloy that contains iron, carbon, and other elements, primarily chromium. The addition of chromium is what makes stainless steel "stainless" or resistant to corrosion and rust. The primary reason for the addition of chromium is to form a protective oxide layer on the surface of the steel, which prevents further oxidation or rusting.
• When chromium is added to iron to form stainless steel, it combines with oxygen from the air to form a thin, invisible, and protective layer of chromium oxide (Cr₂O₃) on the surface of the steel. This layer acts as a barrier, protecting the underlying steel from corrosion and giving stainless steel its unique property of being resistant to stains, rust, and corrosion.
• The proportion of chromium in stainless steel can vary, but it is typically present in significant amounts, usually ranging from 10% to 25% of the alloy's composition. Other elements like nickel, molybdenum, and sometimes manganese are also added to enhance specific properties of stainless steel.

Additional Information

• Iron (Fe): Iron is the primary component of stainless steel. It provides strength and structural integrity to the alloy.
• Carbon (C): Carbon is another essential element in stainless steel, although it is generally present in low amounts. It enhances the hardness and strength of the alloy.
• Chromium (Cr): Chromium is the critical component that distinguishes stainless steel from other types of steel. It forms a thin and invisible layer of chromium oxide on the surface of the steel, known as the passive layer. This passive layer provides excellent corrosion resistance and prevents the steel from rusting.
• Nickel (Ni): Improves ductility, toughness, and resistance to corrosion.
• Molybdenum (Mo): Enhances resistance to corrosion in specific environments.
• Titanium (Ti): Provides improved welding and fabrication characteristics.
• Copper (Cu): Improves resistance to certain corrosive environments.
• The precise composition of stainless steel can vary based on the specific grade or type of stainless steel being produced. There are numerous grades of stainless steel, each with its own unique combination of elements and properties to suit various applications, such as kitchenware, cutlery, medical instruments, construction materials, industrial equipment, and more.

The Correct answer is It does not hold air.

Explanation:

• Loamy soil does hold air in addition to its other properties. Loamy soil is considered the best type of soil for plant growth because it has a balanced mixture of sand, clay, and silt.
• The air spaces within the soil are crucial for plant roots to access oxygen, which is necessary for their respiration.
• A mixture of sand, clay, and silt: Loamy soil is a well-balanced combination of sand, clay, and silt. This composition provides good drainage while retaining enough moisture for plant roots.
• Presence of humus: Loamy soil contains organic matter, including humus, which is the decomposed remains of plants and animals. Humus enhances soil fertility and improves its water-holding capacity.
• Water-holding capacity: Loamy soil has good water-holding capacity due to the presence of silt and clay particles. It can retain moisture for plant roots without becoming waterlogged.
• Air-holding capacity: Loamy soil also has adequate air spaces between its particles. These air spaces allow oxygen to reach plant roots, promoting healthy root growth and respiration.

The Correct answer is (i) - (C), (ii) - (B), (iii) - (A), (iv) - (D).

Explanation;

• Cockroaches have a system of tubes called tracheae that extend throughout their body. These tracheae allow the direct exchange of gases (oxygen and carbon dioxide) with the tissues without the need for specialized respiratory organs like the lungs.
• Earthworms breathe through their skin. Their skin is thin and moist, which allows oxygen and carbon dioxide to pass through and exchange gases with the environment.
• Fish have gills as their respiratory organs. Gills are feathery structures located on both sides of the fish's head, and they are responsible for extracting oxygen from the water and expelling carbon dioxide.
• Lizards have lungs as their respiratory organs. They breathe air through their nostrils, and the air enters their lungs for gas exchange, similar to how mammals breathe.

The Correct answer is (A) and (B) only

Concept:

• Blood circulates throughout your body through the blood vessels.
• The three major kinds of blood vessels are -
• arteries
• veins
• capillaries
• They majorly help in delivering oxygen to vital organs and tissues, and also help in the removal of waste products.
• Arteries and veins are tubes of muscle that our blood flows through.
• Arteries are the ones that carry blood away from the heart.
• Veins are the ones that carry blood toward the heart
• Except for the pulmonary blood vessels, arteries carry oxygenated blood and veins carry deoxygenated blood.
• Capillaries are the smallest blood vessels that connect arteries and veins.

Explanation:

• (A) Arteries carry oxygen-rich blood from the heart to all parts of the body: Arteries are blood vessels that carry oxygenated blood away from the heart to various organs and tissues in the body. The blood in arteries is rich in oxygen, which is essential for providing oxygen and nutrients to body tissues for their proper functioning.
• (B) Veins carry carbon dioxide-rich blood from all parts of the body back to the heart:  Veins are blood vessels that carry deoxygenated or carbon dioxide-rich blood from various parts of the body back to the heart. After tissues and organs have used the oxygen from the blood, the blood becomes deoxygenated and carries carbon dioxide, waste products, and other metabolic byproducts back to the heart for eventual elimination from the body.
• (C) Blood flow is rapid and at high pressure, thus, veins have thick elastic walls: This statement is incorrect. Blood flow in the circulatory system is rapid and at high pressure in arteries, not in veins. Arteries have thick, elastic walls that can withstand the pressure generated by the heart's pumping action, helping to propel blood throughout the body. In contrast, veins have thinner walls and contain valves to prevent the backward flow of blood (backflow) and assist in the return of blood to the heart, but they do not have thick elastic walls.
• (D) The valves present in arteries allow blood to flow in one direction only: This statement is incorrect. While the circulatory system does have valves, these valves are primarily present in veins, not arteries. Veins have one-way valves that help maintain blood flow in one direction, preventing the backflow of blood and aiding in the return of blood to the heart. Arteries, on the other hand, do not have valves.

Additional Information Arteries

• Arteries are blood vessels that distribute oxygen-rich blood to the whole body.
• It carries blood from the heart to all other parts of the body.
• Except the pulmonary artery which carries deoxygenated blood from the heart to the lungs.
• Arteries have thicker walls with muscle tissue when compared to veins.
• They don’t have valves.
• The force of the blood coming from the heart helps the blood to flow in one direction.

Veins

• Veins bring back the oxygen-poor blood or deoxygenated blood from the body’s cells and tissues to the heart.
• Veins have thinner walls.
• They have valves to keep the blood flowing and prevent the blood to move in the wrong direction.
• Types of Veins - 
• Pulmonary veins carry oxygenated blood from the lungs to the left atrium of the heart.
• Systemic veins return oxygen-depleted blood from the rest of the body to the right atrium of the heart.

The Correct answer is Only (A).

Concept:

• Vascular tissue is an arrangement of multiple cell types in vascular plants that allows for the transport of water, minerals, and products of photosynthesis to be transported throughout the plant.
• Types of vascular tissue are :
• Xylem: It is a specialized type of vascular tissue created in vascular plants to transport water and nutrients from the roots of a plant to the tips of the leaves.
• Phloem: Through the channel of the phloem cells sugar is transported throughout the plant. The phloem requires inputs of water from the xylem and specialized proteins to help quickly pass the sugars through the plant.

Explanation:

• (A) Plants have pipe-like vessels to transport water and nutrients from the soil: This statement is true. Plants have specialized tissues called xylem and phloem that function as pipe-like vessels to transport water, minerals, and nutrients throughout the plant. Xylem is responsible for upward water movement from the roots to the aerial parts of the plant, while the phloem is responsible for the bidirectional transport of sugars, nutrients, and other organic compounds.
• (B) Phloem transports water in plants: This statement is incorrect. Phloem primarily transports sugars (carbohydrates) and other organic compounds, not water. The movement of water in plants is primarily facilitated by the xylem.
• (C) Food is transported by xylem in all parts of plants: This statement is incorrect. Food, which includes sugars and other organic compounds produced during photosynthesis, is primarily transported by the phloem, not the xylem. The phloem is responsible for translocating food from the leaves, where it is synthesized, to other parts of the plant for growth, storage, and energy utilization.
• (D) Photosynthesis generates energy, which helps in pulling water from roots to different parts of plants: This statement is incorrect. Photosynthesis is the process by which plants convert light energy into chemical energy in the form of glucose (a sugar). However, photosynthesis itself does not directly pull water from the roots to different parts of the plant. Instead, water is transported through the xylem by a process called transpiration. Transpiration is the evaporation of water from the aerial parts of the plant, primarily from the leaves, which creates a "pull" or negative pressure, known as tension, that draws water up from the roots to replace the water lost.