Mathematics and Science PYQs

Cardinal numbers indicate "how many" of something there are. They represent quantity and are used for counting.

Key Points

• In simpler terms, if you can use the number to answer the question, "How many?", then you're likely dealing with a cardinal number.
• There are five team members in each group. Cardinal numbers represent quantities.
• In the above statement, "five" indicates the quantity or number of team members in each group.
• On the other hand, ordinal numbers (like "fifth") indicate position or order in a sequence. The other statements use "5" or "fifth" in ordinal or nominal senses.

Hence, we can conclude that in "There are five team members in each group" the number 5 is used in the cardinal sense.

Formative assessment is an ongoing process that uses a variety of techniques to evaluate students' comprehension, learning needs, and academic progress during a lesson, unit, or course. 

Key Points

• Siddhi's approach, which involves making careful observations of her classroom, providing regular worksheets, and offering feedback on student errors and alternate conceptions, aligns with continuous evaluation and improvement.
• The assessment technique that Siddhi uses is formative assessment.
• The primary purpose is to provide feedback to both the instructor and the student to improve the learning process.
• This type of assessment is aimed at enhancing the learning process in real-time by identifying strengths, weaknesses, and misconceptions as they arise.

Hence, we can conclude that Siddhi uses Formative Assessment.

Creating a positive classroom environment is a major responsibility of teachers" emphasizes the importance of fostering an environment conducive to learning and positive interactions.

Key Points

• When both teachers and students are actively involved, it results in a dynamic and responsive classroom where learning becomes a two-way process.
• Active involvement fosters mutual trust and respect. When students feel their voice matters, they develop a greater respect for the teacher and the learning process.
• An active role encourages students to ask questions, explore concepts, and delve deeper into topics, fostering critical thinking and problem-solving skills.
• An active classroom environment better prepares students for real-world situations where initiative, collaboration, and problem-solving are crucial.
• Active involvement promotes other aspects of development, such as emotional intelligence, social skills, and moral values.

Hence, we can conclude that teachers and students should have an active role in the teaching-learning process that most appropriately depicts the above situation.

The error the student made ​​(2/3)+(1/5)=(3/8)  indicates a fundamental misunderstanding of how to add fractions, especially those with different denominators (unlike fractions).

Key Points

• Give different pictorial representations to clear the concept of addition of unlike fractions, this is the most appropriate remedial action for Jyoti to take.
• Pictorial representations can help students visually see how fractions are combined, especially when the denominators are different.
• By starting with a picture, the student may better grasp the abstract arithmetic of adding fractions.
• Pictorial representations can clarify why this method is incorrect and demonstrate the correct process of finding a common denominator.

Hence, we can conclude that Jyoti should Give different pictorial representations to clear the concept of addition of unlike fractions.

Proportional thinking involves recognizing and understanding the multiplicative relationships between quantities.

Key Points

• Firoze's ability to read the scale on a map and determine the correct distance between two places indicates Proportional thinking.
• When reading a map, a scale might indicate, for example, that 1 inch on the map represents 10 miles in reality.
• If Firoze measures 3 inches between two places on the map, using proportional thinking, he would determine that the actual distance is 30 miles.
• Initially, children think in additive terms (just adding or subtracting amounts).
• As they mature and with proper instruction, they transition to thinking in multiplicative or proportional terms.

Hence, we can conclude that He is displaying Proportional thinking.

Deductive reasoning is a process that starts with a general statement or hypothesis and examines the possibilities to reach a specific, logical conclusion.

Key Points

Here's a brief explanation of each step:

• Theory: This is the foundation of the reasoning process. It's a well-established explanation for a phenomenon or set of observations.
• Hypothesis: Based on the theory, you formulate a specific prediction about what you expect to observe under certain conditions. This prediction is your hypothesis.
• Patterns: This step involves collecting data and analyzing it to see if it supports or contradicts the hypothesis.
• Confirmation: Based on the observed patterns, you either confirm or reject the hypothesis.
• If the patterns consistently support the hypothesis, you can conclude that it has been confirmed.

Hence, we can conclude that the correct sequence of steps in deductive reasoning is Theory → Hypothesis → Patterns → Confirmation.

Intuitive knowledge is often described as the knowledge one possesses without conscious reasoning or analysis.

Key Points

• Intuitive knowledge comes from experiences, innate abilities, or even patterns that one's brain unconsciously recognizes.
• Intuitive knowledge in mathematics is a kind of understanding that is immediate and not the result of conscious thought or reasoning.
• Intuitive knowledge is more about inherent understanding or "gut feelings" rather than something that is explicitly based on empirical evidence.

Hence, we can conclude that It is a kind of knowledge that is generally based on scientific empirical evidence and is least appropriate for intuitive knowledge in mathematics.

The Van Hiele model of geometric thinking is a theory of how students come to understand geometric concepts, advancing through five distinct levels of understanding. 

Key Points

Level 0 (Visualisation)

• At this initial level, students recognize geometric shapes and figures based on their overall appearance, rather than by analyzing their properties.
• The focus is on the holistic view of the shape. For example:
• A student might recognize a triangle because it "looks like" a triangle, not because it has three straight sides or angles.
• As in Reena's case, rectangles and squares might be seen as the same because they both appear to have similar attributes at a cursory glance.
• At this stage, students might not recognize that a square is a specific type of rectangle where all sides are of equal length.

Hence, we can conclude that She is at Level 0( Visualisation) of Van Hieles geometric thinking.

When a child in class V claims that 1/2 is less than 1/3 it indicates a misunderstanding or overgeneralization about Natural numbers.

Key Points

• The child seems to be confusing the concept of fractions with natural numbers.
• In natural numbers, a larger denominator means a larger value, but with fractions, the relationship is reversed: the larger the denominator (with the same numerator), the smaller the fraction's value.
• This misconception shows that the child hasn't yet fully grasped how fractions differ from natural numbers in terms of their relative values.

Hence, we can conclude that the child is over-generalizing the idea of Natural Numbers.

A composition of transformations means you're applying multiple transformations to a figure, one after the other.

Key Points

• When a geometrical figure is transformed through multiple transformations (like reflection over a line followed by a rotation about a point), this sequence of transformations is referred to as a Composition.
• Similarity: Refers to figures that have the same shape but not necessarily the same size.
• Congruency: Refers to figures that have the exact same size and shape.
• Tessellation: Refers to a collection of plane figures that fill the plane with no overlaps and no gaps.

Hence, we can conclude that this geometrical transformation is called Composition.

The correct answer is human beings do not have cellulose-digesting enzymes.

Explanation:

• Cellulose-rich food substances are a good source of roughage for human beings because human beings do not have cellulose-digesting enzymes.
• Cellulose is a polymeric polysaccharide consisting of only one type of monosaccharide i.e., glucose.
• Cellulose plays an important role in the human body because it is an excellent source of fiber.
• Except for cellulose, enzymes secreted from the human mouth, liver, and stomach can digest any type of sugar.
• Cellulose is digested by the enzyme cellulase which is absent in human beings.
• Humans do not have the cellulose-digesting enzyme (cellulase) to degrade the beta-1, 4 glycosidic bonds of cellulose.
• Thus, it cannot be digested by humans and acts as a good source of roughage.
• Roughage helps our body to get rid of undigested food.

Additional Information

• A balanced diet provides all the nutrients that our body needs, in the right quantities, along with an adequate amount of roughage and water.
• The major nutrients in our food are carbohydrates, proteins, fats, vitamins, and minerals.
• In addition, food also contains dietary fibers and water.
• Carbohydrates and fats mainly provide energy to our body.
• Proteins and minerals are needed for the growth and maintenance of our body.
• Vitamins help in protecting our bodies against diseases.

The Correct answer is Level of water will be same in both A and B.

Concept:

Archimedes principle: The principle of Archimedes states “When a body is immersed in a liquid, an upward thrust, equal to the weight of the liquid displaced, acts on it.”

Thus, when a solid is fully immersed in a liquid, it loses weight which is equal to the weight of the liquid it displaces.

Apparent weight = Actual weight - buoyant force = mg - ρgV

• Hence if there is no gravity, there is no Upward Thrust.
• The upward force applied to the object is called the buoyant force.

Where m = Mass of the object, ρ = Density of liquid, g = Acceleration due to gravity, V = Volume of liquid displaced by the object

Explanation:

• The level of water in the glasses depends on the volume of the objects submerged in them, not their mass or density. As Archimedes' principle states, any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.
• In simpler terms, when an object is submerged in a fluid, it displaces an amount of fluid equivalent to its volume, not its mass or density.
• Both metal balls X and Y have the same volume, so they would displace the same volume of water in each glass. Hence, the levels of water in both glasses A and B would be the same, even though the mass and density of ball X are greater than that of ball Y.

Hence, the correct choice is: The level of water will be the same in both A and B.

The Correct answer is YZ.

Concept:

• Elements form compounds by gaining, losing, or sharing electrons to achieve stability, usually by having a full outer electron shell.
• The types of bonds that can form depend on how the elements achieve this stability.

Explanation:

• Element X has an electronic configuration of 2, 4. This means it has 4 electrons in its outer shell and it would like to lose these 4 electrons to achieve a full outer electron shell, making it a metal.
• Element Y has an electronic configuration of 2, 7. This means it has 7 electrons in its outer shell and it would like to gain 1 electron to achieve a full outer electron shell, making it a non-metal.
• Element Z has an electronic configuration of 2, 1. This means it has 1 electron in its outer shell and it would like to lose this 1 electron to achieve a full outer electron shell, making it a metal.

The possible compounds would be:

• X and Y would form a compound by ionic bonding. X will lose its 4 electrons to achieve a full outer shell. Y will need to find 1 electron, meaning it can bond with 1 X element and play a part in the formation of the compound XY
• X and Z could form a compound by ionic bonding. X can lose its 4 electrons and Z can lose its 1 electron. The ratio will be XZ₄ to reflect the number of electrons getting involved from each side.
• Y and Z would form a compound by ionic bonding. Y will gain 1 electron that Z loses. So that compound would be YZ.

Hence the correct answer is YZ

The Correct answer is Both S1 and S2 are correct and S2 is the correct explanation for S1.

Explanation:

• Based on the information provided, polio drops should not be given to children suffering from diarrhea because they can be eliminated before they have a chance to provide protection.
• Statement S₁: "Polio drops should not be given to children suffering from diarrhea." This is largely in line with the aforementioned fact, as the oral vaccine may not be fully effective in the case of diarrhea.
• Statement S₂: "Polio drops are eliminated due to diarrhea." This statement is also correct. Diarrhea can prevent the body from fully absorbing the polio drops, leading to them being expelled from the body before they can take effect.

Therefore, both S1 and S2 appear to be accurate, and S2 is the correct explanation for S₁.

The Correct answer is (a) - (iii), (b) - (i), (c) - (iv), (d) - (ii).

Explanation:

• Bacterial infections, inorganic impurities, organic impurities, and nutrients, each have different characteristics and relate to different types of substances or illnesses.
• (a) Bacterial Infections - Bacterial infections are caused by harmful bacteria and can result in various diseases. Cholera is a bacterial infection,
• (b) Inorganic Impurities - These are non-organic (non-carbon based) substances that can contaminate water or other substances. Nitrates are an example of inorganic impurities
• (c) Organic Impurities - Organic impurities refer to substances that are carbon-based, here the relevant match would be Pesticides, which usually contain carbon and are organic in nature.
• (d) Nutrients - Nutrients are substances used by an organism to survive, grow, and reproduce. They include compounds containing nitrogen and phosphorus, which in certain quantities, can promote the growth of harmful algal blooms in water bodies.

The Correct answer is (a) - Veins, (b) - Arteries, (c) - Arteries, (d) - Veins.

Explanation:

• The circulatory system of the body is made up of blood vessels including arteries, veins, and capillaries.

Each type of blood vessel has its structure and function.

• (a) Veins: These are blood vessels that carry blood toward the heart. Most veins carry deoxygenated blood from the tissues back to the heart. Veins have thin walls relative to their diameter and are less muscular than arteries.
• (b) Arteries: These are blood vessels that carry blood away from the heart. They carry oxygenated blood to the tissues (except for the pulmonary artery). Being high-pressure vessels, arteries have thicker, more elastic walls.
• (c) Arteries: Blood flows at high pressure in arteries because they carry blood being pushed from the heart, which is a powerful muscle. This high-pressure flow allows blood to reach all parts of the body.
• (d) Veins: Valves are present in veins to prevent backflow of blood. Because the pressure in veins is much lower, these valves help to keep the blood flowing in one direction towards the heart.

The Correct answer is (C)

Explanation:

• In the selection of a fuse wire, two primary factors need to be considered based on statements.
• Melting Point - The fuse wire needs to have a relatively low melting point, where it would melt and hence break the circuit whenever the current exceeds the safe value.
• Conductivity - The fuse also needs to be a good conductor of electricity. While exact thresholds can vary, a higher conductivity would generally make a wire more suitable for use in a fuse.
• Using these criteria, you can evaluate the materials as follows:
• Material 'A' has high conductivity but also a very high melting point, which makes it less suitable as it may not melt quickly when the current exceeds the safe threshold.
• Material 'B' also has a high melting point, although its conductivity is somewhat lower. Its high melting point makes it less suitable as a fuse wire.
• Material 'C' has the lowest melting point, and while it has lower conductivity than the other two, it is not so low as to disqualify direct utility. Given the balance of these factors, this suggests it's the most suitable as a fuse wire.

Therefore: Material 'C' would be the most appropriate choice for a fuse.

The Correct answer is A - Red, B - Red, C - Blue, D - Red.

Explanation:

• Chemical substances can affect litmus paper differently based on their acidic or basic nature.
• Litmus paper is a pH indicator that changes color depending on the nature of the solution:
• An aqueous solution of milk: Generally, milk tends to be neutral to slightly acidic, so the red litmus paper might not change at all, or it might turn slightly more intense red if the acidity level is higher.
• An aqueous solution of glucose: As glucose is neutral, the red litmus paper, when dipped in this solution, should remain red without any color change.
• An aqueous solution of calamine: calamine's basic nature, the red litmus paper should turn blue upon reacting with this solution.
• An aqueous solution of amla (gooseberry): Amla is acidic, which means red litmus paper will maintain its color and possibly become a more pronounced red if the amla is particularly acidic.
• An aqueous solution of amla: No change or redder as amla is acidic

The Correct answer is electromagnetism

Explanation:

• Electrolysis: It is an application of the chemical effects of electric current. By passing an electric current through an electrolyte (a conductive liquid, often a solution of salts or other compounds), chemical reactions are induced, including those that cause the electrolyte to decompose.
• Electroplating: This also directly involves the chemical effects of electric current. In electroplating, a metal object is coated with a layer of a different metal. This is achieved by passing an electric current through a solution that contains ions of the coating metal, causing these ions to adhere to the object.
• Electromagnetism: This is NOT considered an application of the chemical effects of electric current. Electromagnetism involves the generation of a magnetic field around a current-carrying conductor, which is a different kind of effect - a physical one, not a chemical one.
• Galvanization: This involves the use of electric current to apply a protective layer of zinc to iron or steel, to prevent rusting. Therefore, it's a type of electroplating and IS a result of the chemical effects of electric current.

The Correct answer is Multiple reflections of light.

Explanation:

• Multiple Reflections of Light: This concept Is demonstrated by a periscope. A periscope operates based on the principle of multiple reflections of light. It has mirrors placed at a 45-degree angle at each end. When light from an object strikes the top mirror, it is reflected down to the second mirror and then reflected again into the viewer's eye. This is why periscopes are used in submarines and armored vehicles for viewing things over, around, or through obstacles.
• Refraction of Sound: This concept IS NOT demonstrated by a periscope. A periscope involves the reflection of light, not sound. There's no sound manipulation happening inside a periscope.
• Refraction of Light: While this is a fundamental concept in optics, a periscope DOES NOT demonstrate refraction of light. Refraction involves the bending of light as it passes from one medium to another medium with a different refractive index. In a periscope, the light is reflected, not refracted.
• Total Internal Reflection: This principle IS NOT shown in a periscope. Total internal reflection occurs when light traveling from one medium with a higher refractive index to another with a lower refractive index hits the boundary at an angle larger than a particular critical angle. In a periscope, light is simply reflected off of mirrors - it does not undergo total internal reflection.