Mathematics and Science PYQs

Divergent Questions are open-ended questions that allow for multiple answers and encourage students to think broadly and creatively.

Key Points

• To promote critical thinking: Divergent questions encourage students to think beyond standard answers, allowing for multiple solutions or perspectives. This fosters critical thinking as students must analyze, evaluate, and synthesize information to respond effectively.
• To develop communication: These questions foster discussions and debates, improving students' ability to express their ideas clearly and effectively.
• To identify alternate conceptions: As students respond to divergent questions, they often reveal misconceptions or alternate conceptions they may hold. Teachers can use these responses to address and correct misunderstandings in the learning process.
• To appreciate subjectivity in science: Divergent questions can highlight that science is not always black and white, and that there can be multiple valid interpretations of scientific phenomena.

Hence, we can conclude that (a), (c), (e) and (f) describes the purpose of divergent questions in science classroom.

The correct answer is closed, double circulation

Explanation

The human circulatory system is characterized by being a closed and double circulation system.

• Closed Circulatory System: In a closed circulatory system, the blood is enclosed within blood vessels and is pumped throughout the body by the heart. This system allows for more efficient transport of nutrients, gases, and wastes compared to an open circulatory system where the blood is not enclosed in vessels.
• Double Circulation: Double circulation means that the blood passes through the heart twice during one complete circuit of the body.
• Humans have two separate loops in their circulatory system: the pulmonary circulation (between the heart and lungs) and the systemic circulation (between the heart and the rest of the body).
• This allows efficient oxygenation of blood and supply of oxygenated blood to the tissues.

Other Options:

• 1) closed, single circulation: This is not correct. Single circulation is characteristic of fish where the heart pumps blood to the gills and then it directly goes to the rest of the body.
• 3) open, single circulation: This is not correct. An open circulatory system is found in some invertebrates like arthropods and mollusks, where the blood is not always contained within vessels.
• 4) open, double circulation: This is not correct. Open circulation systems do not involve double circulation.

Therefore, the correct answer is 2) closed, double circulation.

CONCEPT:

Scientific Laws

• Scientific laws are concise statements that describe relationships or patterns found in nature based on repeated experimental observations.
• They do not provide explanations or reasoning for the phenomena they describe.
• Scientific laws are different from scientific theories, which offer explanations of the underlying causes of observed phenomena.
• Scientific laws can be tested and potentially challenged if new evidence or observations contradict them.

Explanation:

• 1. They can't be challenged - False. Scientific laws can be challenged and revised if new evidence emerges.
• 2. They provide reasoning for physical phenomena - False. Scientific laws describe relationships but do not explain the reasoning behind them; that is the role of scientific theories.
• 3. They describe relationships between observable phenomena - True. Scientific laws describe consistent relationships or patterns observed in nature.
• 4. They are formed from scientific theories - False. Scientific laws and theories serve different purposes; laws describe what happens, while theories explain why things happen.

Conclusion:-

So the correct answer is They describe relationships between observable phenomena.

The correct answer is Both (A) and (R) are false.

Concept:

• Aquatic Animals' Breathing Rate: The rate of breathing in aquatic animals is generally faster, not slower, compared to land animals. This is because water contains less dissolved oxygen than air, so aquatic animals need to breathe more frequently to obtain the oxygen they need.
• Dissolved Oxygen in Water: The amount of dissolved oxygen in water is lower than the oxygen available in the atmosphere, making it more challenging for aquatic animals to get sufficient oxygen.

Explanation:

• Assertion (A): The rate of breathing in aquatic animals is slower than land animals. This statement is false because aquatic animals breathe more frequently due to lower oxygen levels in water.
• Reason (R): Presence of large amounts of dissolved oxygen affects the rate of breathing of aquatic animals. This statement is also false because large amounts of dissolved oxygen would actually facilitate breathing, not require a higher breathing rate.

Therefore,Both (A) and (R) are false.

CONCEPT:

Acoustics in Architecture

• The design of ceilings in cinema halls and concert halls often takes acoustics into account to ensure sound is distributed evenly across the space.
• Curved surfaces help in reflecting sound waves in multiple directions, enhancing the acoustics by dispersing sound evenly.
• The claim in the assertion and the reason provided both align with principles of sound reflection.

Explanation:-

• Assertion (A): The ceilings of cinema halls and concert halls are generally curved - True.
• Reason (R): Sound waves after striking a curved surface get reflected in all directions - True. This helps in uniform sound distribution.
• Explanation: The reason correctly explains why curved ceilings are used, as it addresses the principle of sound reflection and dispersion.

Conclusion:-

• so the correct answer is  Both (A) and (R) are true and (R) is correct explanation for (A).

The correct answer is Soil erosion

Concept:

• Eutrophication: This is caused by the excessive use of fertilizers. Nutrients like nitrogen and phosphorus run off into water bodies, leading to excessive growth of algae and depletion of oxygen in the water.
• Bio-magnification: This occurs when pesticides accumulate in the tissues of organisms at each trophic level of the food chain, leading to higher concentrations in top predators.
• Nitrification: This is a natural process where soil bacteria convert ammonia into nitrites and then into nitrates, which are nutrients for plants. It is not directly caused by the excessive use of fertilizers and pesticides but is relevant to the nitrogen cycle in the soil.
• Soil erosion: This refers to the removal of topsoil by wind or water. It is generally caused by factors like deforestation, unsuitable agricultural practices, and climate conditions, rather than the excessive use of fertilizers and pesticides.

Explanation:

The key effects of excessive use of fertilizers and pesticides are:

• Eutrophication (1): Caused by the runoff of nutrients from fertilizers into water bodies, leading to algal blooms and oxygen depletion.
• Bio-magnification (2): Caused by the accumulation of pesticides in organisms, becoming more concentrated at higher trophic levels in the food chain.
• Nitrification (4): Though part of the nitrogen cycle, it is not a direct consequence of excessive use of fertilizers; rather, it's a natural soil process.

Soil erosion (3) is not directly caused by excessive use of fertilizers and pesticides. While poor agricultural practices can contribute to soil erosion, this phenomenon is more directly linked to physical processes like wind and water movement.

CONCEPT:

Odometer Function in a Car

• The odometer is an instrument used in vehicles to measure the distance travelled.
• It records the total distance a vehicle has driven since it was manufactured or since it was last reset.
• It does not measure speed, acceleration, or instantaneous speed.

EXPLANATION:

• An odometer is typically found on the dashboard of a car and displays how many miles or kilometers the vehicle has traveled.
• It is important for tracking the vehicle's usage and scheduling maintenance such as oil changes, tire rotations, and other service intervals.
• Other instruments, like the speedometer, measure instantaneous speed, while devices like accelerometers measure acceleration.

Explanation:-

• So the correct answer is distance travelled by the car

CONCEPT:

Types of Mirrors and Image Formation

• Plane Mirror: Always forms virtual, erect, and same-sized images.
• Concave Mirror:
• Forms real, inverted images when the object is placed beyond the focal point.
• Can form enlarged images if the object is placed between the focal point and the center of curvature.
• Convex Mirror: Forms virtual, erect, and diminished images.

EXPLANATION:

• A (Nature: virtual and erect, Size: same as object): Plane mirror fits this description.
• B (Nature: real and inverted, Size: same as object): A concave mirror with the object at the center of curvature forms this type of image.
• C (Nature: real and inverted, Size: enlarged): A concave mirror with the object placed between the focal point and the center of curvature fits this description.
• D (Nature: virtual and erect, Size: diminished): A convex mirror fits this description.

Conclusion:-

• So, the correct answer is A - Plane mirror, B - Concave, C - Concave, D - Convex

CONCEPT:

Hydrostatic Pressure and Fluid Dynamics

• Hydrostatic pressure in a fluid increases with depth.
• The velocity of water exiting a hole due to hydrostatic pressure is governed by Torricelli's law, which states \( v = \sqrt{2gh} \) .
• The force with which water exits a hole is greater at greater depths due to higher pressure.
• The distance water falls from a hole is influenced by both the exit velocity and the height of the hole from the ground.

EXPLANATION:

• (a) Water from lowest hole comes out with greatest force: True. The pressure is greatest at the lowest hole, hence the greatest force.
• (b) Water from highest hole comes out with greatest force: False. The pressure is lowest at the highest hole.
• (c) Water from all holes comes out with equal force: False. Pressure varies with depth.
• (d) Water from lowest hole falls at maximum distance: True. The higher exit velocity and lower initial height combine for maximum horizontal distance.
• (e) Water from highest hole falls at maximum distance: False. Lower exit velocity results in less horizontal distance.
• (f) Water from all holes falls at same distance: False. Different pressures and heights result in different distances.

So the correct answer is (a) and (d)

CONCEPT:

Factors Affecting the Color of Flame

• Nature of Combustible Substance: Different substances emit different colors when they combust due to the varying chemical properties and the presence of certain elements.
• Oxygen Supply: The amount of oxygen available can affect the color of the flame. For example, a limited oxygen supply can produce a yellow, sooty flame, while a sufficient oxygen supply can produce a blue flame.
• Temperature of the Surroundings: The ambient temperature can influence the flame's color to a lesser extent, but is not a primary determining factor.

EXPLANATION:

• (a) Nature of combustible substance: True. Different materials produce different flame colors when they burn.
• (b) Oxygen supply: True. The flame color varies with different oxygen concentrations.
• (c) Temperature of the surroundings: False. While temperature can influence the combustion process, it is not a primary factor in the color of the flame.

So the correct answer is 1) (a) and (b)

Alternate conceptions, also known as misconceptions, are ideas or understandings that students develop based on their experiences or prior knowledge but are scientifically inaccurate or incomplete.

Key Points

• Diagnostic questionnaire: This helps the teacher assess students' prior knowledge and uncover any misconceptions they may have about the topic. It is a direct way to identify alternate conceptions.
• Interview: Interviews allow the teacher to delve deeper into students' thinking and reasoning, providing insights into their understanding and misconceptions.
• Drawings: Students' drawings can visually reflect their conceptions of adaptations in plants and animals. Misconceptions often appear clearly in the way students depict these adaptations.
• This combination of strategies allows the teacher to assess both verbal and non-verbal representations of student understanding, providing a comprehensive approach to identifying alternate conceptions.

Hence, we can conclude that Diagnostic questionnaire, interview, and drawings strategies are best suited for this purpose.

Confusion Points

• Both options 1 and 4 are considered as the correct answer by the board.

CONCEPT:

Reaction of Potassium with Water

• Hydrogen Gas Evolution: When potassium reacts with water, it produces potassium hydroxide and hydrogen gas.
• Pop Sound: The hydrogen gas evolved can create a popping sound when it ignites in the presence of air.
• Violent Reaction: Potassium reacts violently with water due to the highly exothermic nature of the reaction.
• Endothermic Reaction: An endothermic reaction absorbs heat from the surroundings, which is not the case here.

EXPLANATION:

REACTION:

\(\text{2K} + \text{2H}_2\text{O} \rightarrow \text{2KOH} + \text{H}_2 + heat\)

• 1) Hydrogen gas is evolved: Correct. Hydrogen gas is produced during the reaction.
• 2) Pop sound is heard: Correct. The hydrogen gas can ignite and produce a popping sound.
• 3) Potassium reacts violently with water: Correct. The reaction is highly exothermic and vigorous.
• 4) It is endothermic reaction: Incorrect. The reaction is exothermic, releasing a significant amount of heat.

Concluison:-

• The correct answer is It is endothermic reaction.

CONCEPT:

Colour Changes in Indicators in Acidic and Basic Solutions

• Turmeric:
• In acids: No change (stays yellow).
• In bases: Changes to reddish brown.
• China rose:
• In acids: Changes to dark pink.
• In bases: Changes to green.
• Phenolphthalein:
• In acids: Colourless.
• In bases: Pink.
• Methyl orange:
• In acids: Red or orange.
• In bases: Pink or yellow.

EXPLANATION:

• A (Turmeric in bases): Changes to reddish brown.
• B (China rose in bases): Changes to green.
• C (Phenolphthalein in acids): Colourless.
• D (Methyl orange in acids): Changes to red or orange.

So the correct answer is  reddish brown, green, colourless, orange

The correct answer is fraternal

Explanation:

• Twins can be either identical (monozygotic) or fraternal (dizygotic).
• Identical twins are formed from one sperm fusing with one egg, then the resulting zygote splits into two embryos.They share the same genetic material and are of the same sex.
• Fraternal twins are formed when two separate sperms fertilize two separate eggs, resulting in two genetically unique zygotes, just like ordinary siblings, and can be of the same or different sexes.

CONCEPT:

Science as Inquiry

• The concept of 'science as inquiry' involves investigating, exploring, and questioning the natural world through scientific processes and methods.
• It emphasizes the importance of asking questions, conducting investigations, and collecting data to understand natural phenomena.

EXPLANATION:

• 1) List five uses of coconut tree: This is a factual recall task, not inquiry-based.
• 2) Observe the types of venation in various leaves: This involves observation, but doesn't fully engage in the process of inquiry or investigation.
• 3) Classify the given plants into herbs, shrubs and trees: This is a classification task based on pre-existing knowledge.
• 4) Explore factors which affect the rate of germination in gram seeds: This involves formulating questions, conducting experiments, and making observations to gather data—an excellent example of 'science as inquiry'.

Conclusion:-

So the correct answer is Explore factors which affect the rate of germination in gram seeds

The correct answer is Both S1 and S2 are true.

Concept:

• Photosynthesis is an endothermic reaction because it requires energy from sunlight to convert carbon dioxide (CO₂) and water (H₂O) into glucose (C₆H₁₂O₆) and oxygen (O₂).
• Respiration is an exothermic reaction because it releases energy by breaking down glucose into carbon dioxide and water.

Explanation:

1. Photosynthesis (S1):

• Endothermic Reaction: Photosynthesis is classified as an endothermic reaction because it absorbs energy. Specifically, plants and other photosynthetic organisms harness light energy from the sun to drive the conversion of CO₂ and H₂O into glucose and O₂.
• Chemical Equation: The overall balanced chemical equation for photosynthesis can be written as:

6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂

• Energy Absorption: Chlorophyll in the chloroplasts of plant cells captures light energy, which initiates a series of reactions that ultimately produce glucose. The energy absorbed is stored in the chemical bonds of glucose molecules, signifying the endothermic nature of the process.

2. Respiration (S2):

• Exothermic Reaction: Respiration is an exothermic process because it releases energy. During cellular respiration, glucose is broken down, and the chemical energy stored in glucose is released to produce ATP (adenosine triphosphate), which cells use for various functions.
• Chemical Equation: The overall balanced chemical equation for aerobic respiration can be written as:

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP)

• Energy Release: The breakdown of glucose involves a series of metabolic pathways that release energy, which is captured in the form of ATP. This release of energy characterizes respiration as an exothermic process.

Conclusion:

In summary, both S1 and S2 are correct statements. Photosynthesis is endothermic because it absorbs energy in the form of sunlight. Respiration is exothermic because it releases energy by breaking down glucose.

Inductive reasoning involves making generalizations based on specific observations or experiments.

Key Points 

• Asking students to measure the angle of reflection for various angles of incidence in a plane mirror encourages them to observe patterns and derive general principles or rules from their data.
• This process helps them develop inductive reasoning by allowing them to infer laws or general rules from specific examples.

Hint

• Verify laws of reflection experimentally is more about confirming established principles rather than developing inductive reasoning from scratch.
• Solve numerical problems based on the law of reflection involves applying known principles, not necessarily discovering them through inductive reasoning.
• Asking students to state laws of reflection is about recalling information rather than developing reasoning skills.

Hence, the correct answer is asking students to measure angle of reflection for various cases of angle of incidence in a plane mirror.

CONCEPT:

Chemical Bonding and Valency

• The atomic number of A is 13, meaning A is Aluminum (Al) with the electronic configuration 2, 8, 3. This means Aluminum has a valency of 3.
• The atomic number of B is 17, meaning B is Chlorine (Cl) with the electronic configuration 2, 8, 7. This means Chlorine has a valency of 1.
• In forming a compound, the total positive charge must balance the total negative charge.
• Aluminum (Al) can lose 3 electrons to form Al³⁺ ions.
• Chlorine (Cl) can gain 1 electron to form Cl^- ions.

EXPLANATION:

• To balance the charges, 1 Aluminum ion (Al³⁺) will need 3 Chlorine ions (Cl^-) to form a neutral compound.
• Thus, the chemical formula of the compound will be AlCl₃.

Conclusion:-

• 4. AB₃

CONCEPT:

Safety in Chemistry: Dilution of Acids

• Assertion A: It is recommended that acid should be added to water for diluting the acid and not vice-versa.
• Reason R: Dilution of acid is a highly exothermic reaction.
• When an acid is diluted, heat is released. If water is added to acid, the heat can cause the water to vaporize rapidly, potentially splashing the acid and causing burns or injuries.
• By adding acid to water slowly, the heat is absorbed by the larger volume of water, reducing the risk of splashing and ensuring safer handling.

EXPLANATION:

• Both Assertion A and Reason R are true. The assertion correctly describes the recommended method for diluting acids to ensure safety.
• Reason R correctly explains why this method is recommended, as the dilution process releases a significant amount of heat (it is exothermic), making safe practices essential.

Concluion:-

• 3. Both (A) and (R) are true and (R) is correct explanation of (A)

Alternate conceptions in science refer to ideas or understandings that students develop based on their everyday experiences or observations, but these ideas may not align with scientifically accepted concepts. 

Key Points

• Alternate conceptions arise because learners try to make sense of the world using their direct, observable experiences.
• For example, students may observe the sun moving across the sky and conclude that the sun revolves around the Earth.
• Alternate conceptions are often stable, meaning that once these ideas form, they tend to persist unless directly challenged by new, more accurate information.
• Alternate conceptions are resistant to change because they are deeply ingrained in a student’s worldview, often built upon repeated personal experiences.
• Many alternate conceptions do involve cause-and-effect reasoning, but the reasoning is often flawed or incomplete.
• Students tend to form logical relationships between events based on their observations, even though these relationships might not align with scientific principles.

Hence, we can conclude that the ideas do not demonstrate cause and effect reasoning is not a feature of alternate conceptions in science.