Mathematics and Science PYQs

The correct answer is Overcrowding

Explanation:-

Seed dispersal is a crucial mechanism that helps plants colonize new areas and ensure the survival and spread of their species. However, it does not directly benefit plants by causing overcrowding. In fact, overcrowding can lead to competition for resources such as sunlight, water, and minerals, which can be detrimental to plant growth and survival.

Produce new varieties: Seed dispersal can contribute to genetic diversity within plant populations by allowing seeds to be transported and germinate in different environments, potentially leading to the emergence of new varieties over time.

Overcrowding: Seed dispersal helps prevent overcrowding by spreading seeds away from the parent plant, allowing for better access to resources and reducing competition among offspring.

Avoid competition for sunlight, water, and minerals: Seed dispersal aids in distributing seeds over a wider area, reducing competition among offspring for resources and increasing their chances of accessing sunlight, water, and minerals.

Invade new habitats: Seed dispersal enables plants to colonize new habitats by dispersing seeds to distant locations, where they can germinate and establish new populations.

**Conclusion:-**Therefore, the correct answer is Overcrowding.

The correct option is periscope, reflection.

Explanation: 

Periscope, reflection​:

• A periscope uses mirrors or prisms at an angle to each other, positioned in such a way that light entering one end is reflected and exits out the other, thus allowing someone to see over or around obstacles.
• Dispersion refers to the process by which light separates into its constituent colors (spectral colors) when it passes through a medium, like a prism, due to different angles of refraction for different colors. This is not relevant to seeing around corners.

Telescope, Reflection:

• Telescopes are devices designed to observe distant objects by collecting electromagnetic radiation. Although the primary function of telescopes is not to see around corners, some telescopes use mirrors (reflecting telescopes). However, the main principle behind telescopes is not ideally suited for the described purpose.
• Reflection is the change in the direction of a wavefront at an interface between two different media so that the wavefront returns to the medium from which it originated. This is a principle used in a variety of optical devices, but it is not the primary function of telescopes in this context.

Kaleidoscope, Refraction:

• A kaleidoscope is an optical instrument with two or more reflecting surfaces tilted towards each other at an angle, so that one or more objects on one end of the mirrors are seen as a regular symmetrical pattern when viewed from the other end, due to repeated reflection.
• Refraction is the change in direction of wave propagation due to a change in its transmission medium. While refraction is an important optical principle, it is not the primary mechanism by which kaleidoscopes operate, nor is it suited for seeing around corners in the context described.

Periscope, Reflection:

• As previously mentioned, a periscope leverages the principle of reflection by using mirrors or prisms set at specific angles to redirect light from one end to the other, effectively allowing one to view objects from a location that does not have a direct line of sight. This perfectly aligns with the requirement to see around corners.

 Key Points

• Periscopes have crucial applications in submarines, allowing them to observe above water while remaining submerged.
• They have also been adapted for use in various fields, including surveillance and wildlife observation.
• The principle of reflection used in periscopes adheres to the law of reflection, which states that the angle of incidence is equal to the angle of reflection.
• Advanced variations of periscopes also employ electronic systems that use cameras and monitors to achieve the same effect without direct optical paths.

The correct answer is a - iv, b - vi, c - iii, d - v, e - i, f - ii

Concept:-

• Chemical Names and Formulas: Chemical substances have formal names that often reflect their composition. These names are part of the nomenclature established by the International Union of Pure and Applied Chemistry (IUPAC). Understanding chemical names involves knowing the elements involved and occasionally the structure of the compound.
• Common Names: Beyond systematic chemical names, substances often have common or trivial names. These names are usually historical or derived from the substance's source, appearance, or uses, and may not directly reflect the chemical composition.
• Ionic Compounds: Many of the substances listed are ionic compounds, formed from the electrostatic attraction between cations (positive ions) and anions (negative ions). Knowing the formula of these compounds helps in identifying the components involved—for example, (NaCl) (sodium chloride) is composed of sodium ions ((Na⁺)) and chloride ions ((Cl^-)).
• Chemical Reactions and Formulas: Some names hint at the chemical's formation or use in reactions. For example, "slaked lime" refers to the product of adding water to "quicklime," a process known as slaking.

Explanation:-

(a) Slaked lime - (iv) Calcium hydroxide

(b) Table salt - (vi) Sodium chloride

(c) Limestone - (iii) Calcium carbonate

(d) Caustic soda - (v) Sodium hydroxide

(e) Quick lime - (i) Calcium oxide

(f) Baking soda - (ii) Sodium bicarbonate

Conclusion:-

So the correct match is a - iv, b - vi, c - iii, d - v, e - i, f - ii

The correct answer is \(\frac{8}{9}\)Ω.

Concept:

For a combination of resistors, maximum resistance can be obtained when resistors are in series with each other and minimum resistance can be obtained if the resistors are in parallel with each other.

Calculation:

Given: 3 resistors of \(\frac{1}{3}\)Ω

Maximum resistance

We use series combination; equivalent resistance

Rne_t = R1 + R2 + R3

Rnet = \(\frac{1}{3}\)+\(\frac{1}{3}\)+\(\frac{1}{3}\)

Rnet = \(\frac{3}{3}\) = 1Ω

Minimum resistance

We use parallel combination; equivalent resistance

\(\frac {1}{R_{net}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\)

\(\frac {1}{R_{net}} = \frac{1}{\frac{1}{3}} + \frac{1}{\frac{1}{3}} + \frac{1}{\frac{1}{3}}\)

\(\frac {1}{R_{net}} = 3 + 3 + 3\)

\(\frac {1}{R_{net}} = 9\)

Rnet = \(\frac{1}{9}\)

The difference between maximum and minimum resistance:

(Rnet) max - (Rnet) min

1- \(\frac{1}{9}\)=  \(\frac{8}{9}\)Ω

Thus, The difference between maximum and minimum resistance that can be obtained by connecting three resistances of \(\frac{1}{3}\Omega\) each is \(\frac{8}{9}\) Ω.

The correct answer is (d) and (e)

Explanation:-

Acid rain is primarily caused by the emission of sulfur dioxide (SO₂) and nitrogen oxides (NO_x) into the atmosphere from human activities such as burning fossil fuels (coal, oil, and natural gas) in power plants, industrial processes, and vehicle emissions.

These gases undergo chemical reactions in the atmosphere to form sulfuric acid (H₂SO₄) and nitric acid (HNO₃), which then fall to the ground as acid rain.

Therefore, the correct answer is (d) Sulphur dioxide and (e) Nitric oxide.

The correct answer is (A) and (R) are both correct and (R) is the correct explanation for (A).

Explanation:-

Assertion (A): The stars in the night sky appear to move from east to west.

This assertion is correct. When we observe the night sky, it indeed seems like the stars move from the east towards the west over the course of the night. This apparent motion is due to the Earth's rotation, but the statement on its own doesn't specify the cause.

Reason (R) : The earth rotates from west to east.

This reason is also correct. The Earth rotates on its axis from west to east. This rotational direction is what causes the sun to rise in the east and set in the west for observers on Earth. Similarly, this eastward rotation of the Earth makes the stars (and other celestial objects) appear to move in the opposite direction, from east to west, in the sky.

Relationship

• The Earth's rotation from west to east, directly explains why the stars in the night sky appear to move from east to west, as asserted in (A). The Earth's rotation relative to the relatively fixed positions of the distant stars creates this apparent motion across the sky.
• Option 2 is the correct choice because both the assertion and the reason are factually correct, and moreover, the reason (R) directly explains the phenomenon described in the assertion (A). The Earth’s rotation from west to east is the fundamental reason behind the apparent east-to-west motion of the stars as seen from the Earth's surface. This specific cause-and-effect relationship is what makes option 2, stating that (R) is the correct explanation for (A), the right answer.

Conclusion:-

So, the correct statement is  (A) and (R) are both correct and (R) is the correct explanation for (A).

The correct answer is Zinc, Iron, Manganese

Explanation:-

Micronutrients: Micronutrients are essential nutrients required by plants in small quantities for their growth and development.

• They include elements such as zinc (Zn), iron (Fe), manganese (Mn), copper (Cu), molybdenum (Mo), boron (B), and chlorine (Cl).
• These micronutrients play crucial roles in enzyme activation, photosynthesis, nutrient uptake, and overall plant metabolism.

Macronutrients: Macronutrients are elements that plants require in relatively large quantities for their growth and development.

• The primary macronutrients are nitrogen (N), phosphorus (P), and potassium (K), often abbreviated as NPK.
• These nutrients are critical for various physiological processes in plants, including photosynthesis, energy transfer, and cell structure.

Conclusion:- Therefore, the correct answer is Zinc, Iron, Manganese, as these micronutrients are required by plants in small quantities for optimal growth and development.

The correct answer is guitar, tabla, shehnai.

Explanation:

Sound is produced by vibration and different musical instruments have specific vibrating parts. In a guitar (X) the sound is produced by stretched strings, in a tabla (Y) it is the stretched membrane that vibrates and in a shehnai (Z) the vibrating part that produces sound is the air column.

Guitar:

• In a guitar, sound is produced by stretched strings.
• When you pluck or strum the strings, they vibrate.
• These vibrations create sound waves that resonate through the hollow body of the guitar, amplifying and shaping the sound.
• The length, tension, and thickness of the strings determine the pitch and timbre of the notes produced.

Tabla:

• The tabla is a traditional Indian percussion instrument consisting of a pair of drums.
• The sound is produced by the stretched membrane (usually made of goat or cowhide) that covers the top of each drum.
• When the musician strikes the membranes with their fingers or hands, they vibrate, producing sound.
• The size and tension of the membranes, as well as the technique used to strike them, influence the pitch and tone of the sound produced by the tabla.

Shehnai:

• The shehnai is a type of Indian wind instrument similar to a flute.
• However, unlike a flute where the player blows across a hole in the side of the instrument, in a shehnai, the vibrating part that produces sound is the air column inside the instrument.
• The musician blows air into a double reed mouthpiece, causing the reeds to vibrate against each other.
• This vibration creates sound waves that resonate through the air column inside the shehnai, producing the characteristic rich and melodic sound of the instrument.

Thus, X, Y and Z can respectively be guitar, tabla, shehnai.

By employing observation and inductive reasoning, students can actively engage with the lesson content, develop their critical thinking skills, and deepen their understanding of body movements and the characteristics of objects in motion.

Key Points

• Observing: Observing involves using the senses, particularly sight in this case, to gather information about the objects presented.
• When the teacher shows images of a sailing boat, swimming fish, and flying aeroplane, students are expected to visually observe these images to understand their shapes and the manner of movement depicted.
• They will pay attention to details such as the structure of the boat, the shape of the fish, and the design of the aeroplane, as well as the depicted actions (sailing, swimming, flying).
• Through careful observation, students can gather information about the characteristics of each object and their movements.
• Inductive Reasoning: Inductive reasoning is a process of logical thinking that involves making generalizations based on specific observations or evidence.
• In this scenario, after observing the images provided by the teacher, students engage in inductive reasoning to draw conclusions or make generalizations about the shapes and movements of the objects.
• For example, based on their observations, students may infer that the sailing boat has a streamlined shape to move efficiently through the water, the fish has a streamlined body and fins for swimming, and the aeroplane has wings and engines for flying through the air.
• They may also generalize about the different ways these objects move: the boat uses wind to sail, the fish uses fins and tail for swimming, and the aeroplane uses engines and wings to fly.
• Inductive reasoning allows students to make connections between their observations and broader concepts or principles related to body movements.

Hence, we can conclude that observation and inductive reasoning are likely to be employed by students in answering.

The correct answer is Both (a) and (b)

Explanation:-

(a) Generally non-metals do not react with water. This statement is correct because non-metals typically lack the ability to donate electrons to hydrogen in the water, which would be necessary to replace the hydrogen and form a hydroxide. Their chemical properties do not favor the kind of displacement reaction that metals often engage in with water.

(b) Generally non-metals do not react with acids. This statement is also correct. Non-metals usually do not react with acids in a way that metals do because reactions between metals and acids often involve the metal displacing hydrogen from the acid to form a salt. Since non-metals are not keen to lose electrons (as opposed to metals which can more easily donate electrons to the hydrogen ions in the acid), they generally do not engage in similar displacement reactions with acids.

Therefore, both statements (a) and (b) correctly describe general tendencies in the reactive behaviors of non-metals with water and acids, respectively.

Conclusion:-

So,  the correct statements are Both (a) and (b)

The correct answer is Bitumen, Coal Tar

Concept:-

• Source and Derivation: Identifying substances based on their source—whether they are derived from petroleum or coal—is crucial. This differentiation helps in understanding their properties, uses, and how they are processed.
• Physical State: Recognizing the physical state (solid, liquid, gas) of a substance and its relevance to its described use, such as in road construction where a liquid or viscous material is required.
• Industrial Application: Knowledge of how certain materials are used in industry, particularly in construction and manufacturing, aids in identifying substances based on their described uses.
• Byproducts of Processes: Understanding the byproducts of industrial processes (like the coking of coal or the distillation of crude oil) allows us to connect substances with their sources.

Explanation:-

• X and Y are described as thick, black liquids used for metalling roads, indicating their use as binding agents in road construction for asphalt and similar applications.
• Petroleum and Coal Derivation: The description specifies that X is derived from petroleum and Y from coal. This clue is essential for identifying the substances correctly.
• Bitumen is a viscous liquid commonly used in road construction and waterproofing. It is refined from crude oil, making it a petroleum-derived product. Given its properties and applications, Bitumen fits the description of X.
• Coal Tar is a byproduct of the coal coking process, used in producing coke or gasified to produce coal gas. It is a thick, black liquid, used in industrial and medical applications, and also in sealing roads. Coal Tar matches the description of Y, as it is derived from coal.
• Charcoal is not a liquid; it's a porous form of carbon obtained from the carbonization of wood or other organic materials. Therefore, any option listing charcoal as either X or Y can be disregarded.

Conclusion:-

Given the descriptions and the process of elimination based on the provided concepts, the correct answer is Bitumen, Coal Tar

The correct answer is - There are unequal entries in column A and B.

The test item provided is poorly constructed because there is a mismatch between the items in Column A and Column B.

The correct matching is given below:

 

Now, let's identify the reason that cannot be given to justify that the item is poorly constructed:

• Unit of force matched with Joule: This is incorrect because the unit of force is Newton, not Joule.
• Symbol of iron matched with HCl: This is incorrect because the symbol of iron is Fe, not HCl.
• Formula of hydrochloric acid matched with Ag: This is incorrect because the formula of hydrochloric acid is HCl, not Ag.
• Unit of work matched with Battery: This is incorrect because the unit of work is Joule, not Battery.
• Symbol of silver matched with Calorie: This is incorrect because the symbol of silver is Ag, not Calorie.
• Symbol of battery matched with Fe Newton: This is incorrect because the symbol of battery is not Fe Newton; The battery symbols are represented as

.

The correct answer is (A) and (R) are both correct and (R) is the correct explanation for (A).

Explanation:

Assertion (A) states that dried raisins swell when left in plain water for some time due to osmosis.

• This is a correct statement. Osmosis is the process by which water molecules move across a semi-permeable membrane from a region of lower solute concentration to a region of higher solute concentration, leading to the swelling of raisins as water enters their cells.

Reason (R) correctly states that plant cells have a selectively permeable cell membrane.

• This means that the cell membrane allows certain substances, such as water, to pass through while restricting the passage of others based on their size and charge.
• This selective permeability is essential for regulating the movement of molecules in and out of the cell and is a key factor in osmosis.

Therefore, both assertion (A) and reason (R) are correct, and reason (R) provides the correct explanation for assertion (A). Thus, option 2) is the correct answer.

Concepts:-

• Linear Momentum: Reflects the quantity of motion an object has and is the product of its mass and velocity. This concept is foundational because it connects directly to both mass and velocity, which are integral to understanding kinetic energy.
• Kinetic Energy: Represents the energy of motion. The formula for kinetic energy (\((KE = \frac{1}{2}mv^2)\)) allows us to explore the relationship between an object's mass, its velocity, and the resulting energy from its state of motion.
• Relationship Between Momentum and Velocity: By expressing velocity ((v)) in terms of momentum ((p)) and mass ((m)), we bridge the connection between momentum and kinetic energy, providing a pathway to express (KE) in terms of (p) and (m).

Explanation:

The linear momentum ((p)) of a body is defined by the product of its mass ((m)) and velocity ((v)), which can be written as (p = mv).

Kinetic energy ((KE)), on the other hand, is the energy that a body possesses because of its motion, given by the equation (\(KE = \frac{1}{2}mv^2).\)

To express kinetic energy in terms of momentum, we manipulate the momentum equation to solve for velocity: (\(v = \frac{p}{m}\)). Substituting this expression for (v) into the kinetic energy equation gives:

[\(KE = \frac{1}{2}m\left(\frac{p}{m}\right)^2\)]

Upon simplification, we eliminate the mass squared in the denominator against one of the masses in the numerator:

[\(KE = \frac{1}{2}\frac{p^2}{m}\)]

This equation demonstrates that the kinetic energy of a body can be expressed in terms of its momentum and mass.

Conclusion:-

So, The kinetic energy of the body is given by \(\rm \frac{p^2}{2m}\)

The correct answer is Fertilisers are richer in specific nutrients as compared to manure.

Explanation:

Fertilisers increase the number of friendly microbes in soil:

• This statement is incorrect. Fertilisers primarily provide essential nutrients to plants, but they do not directly increase the number of friendly microbes in the soil.
• In fact, excessive use of chemical fertilisers can sometimes inhibit microbial activity in the soil.

Fertilisers are richer in specific nutrients as compared to manure:

• This statement is correct. Fertilisers are formulated to provide specific nutrients necessary for plant growth, such as nitrogen, phosphorus, and potassium, in readily available forms.
• In contrast, manure is organic matter derived from decomposed plant and animal materials, which provides a broader range of nutrients but typically in lower concentrations compared to fertilisers.

Fertilisers enhance the water holding capacity of the soil:

• This statement is incorrect. Fertilisers do not directly enhance the water holding capacity of the soil. However, organic amendments like compost and manure can improve soil structure and water retention.

Fertilisers provide a lot of humus to the soil:

• This statement is incorrect. Fertilisers primarily provide mineral nutrients to the soil, but they do not contribute to the formation of humus.
• Humus is formed from the decomposition of organic matter, such as plant residues and animal manure.

Conclusion:-Therefore, the correct statement is option 2) Fertilisers are richer in specific nutrients as compared to manure.

The correct answer is S1 is true and S2 is false

Explanation:-

Statement S1: Rayon is a synthetic fiber. It is produced through a chemical process involving regenerated cellulose derived from natural sources such as wood pulp or cotton linters.

Statement S2: This statement is false. Rayon is made using natural raw materials, primarily cellulose extracted from wood pulp or cotton linters. Cellulose is a natural polymer found in plant cell walls, and it serves as the primary component of rayon fibers.

Conclusion:-Therefore, the statement "Rayon is made without using any natural raw material" is incorrect.

A classroom demonstration is a teaching method where the instructor shows a process, experiment, or technique in real time to the students. 

Key PointsDesirable practices with respect to carrying out of a classroom demonstration by a teacher:

1. Follow up the demonstration with discussion:

• After a demonstration, engaging students in a discussion is highly beneficial. This follow-up allows students to process what they've observed, ask questions, and articulate their understanding or confusion.

2. Rehearse the demonstration before carrying it out in class:

• Rehearsal is key to ensuring that the demonstration goes as smoothly as possible. By practicing, a teacher can identify potential issues beforehand, refine the steps to make them more understandable, and ensure all necessary materials are prepared and functioning.

4. Supplement the demonstration with explanations:

• While demonstrations are excellent for showing concepts in action, supplementing these visual and practical elements with verbal explanations is crucial for deep learning.

Hint

• While emphasizing linkages beforehand is still a positive practice for setting context and goals, it could potentially limit the spontaneity of students' discoveries and inferences during the actual demonstration.
• In teaching methodologies that prioritize inquiry-based learning or constructivist approaches, the teacher might choose to let students observe the demonstration without strong preconceptions, fostering a more exploratory learning environment where students form linkages through discussion and reflection after the demonstration.

Hence, the correct answer is 'emphasizing beforehand the linkages that students are required to make'.

Key Points

• Scientists judge the validity of a claim based on objective empirical evidence: This statement accurately captures the essence of scepticism in science. Scientific scepticism involves questioning and evaluating claims based on empirical evidence, and scientists rely on objective observations and data.

Hint

• Scientists are open-minded and willing to modify their ideas:  While openness to modifying ideas is a characteristic of scientific inquiry, the statement 'science promotes scepticism' specifically refers to the critical evaluation of claims rather than scientists' personal openness.
• Science is purely inductive in nature: Inductive reasoning is one aspect of scientific inquiry, but it is not the sole basis for scepticism. Scepticism in science also involves critical thinking, experimentation, and verification.
• Scientists do not trust the findings of other scientists: While healthy scepticism encourages critical evaluation, the scientific community operates on trust but verifies principles. Peer review and replication of studies are essential components of the scientific process.

The correct answer is Scientists judge the validity of a claim based on objective empirical evidence

The correct answer is (a), (b) and (c)

Concept:-

• Chemical Reactions: Understanding that rusting is a chemical process where reactants (iron and oxygen) form a product (iron oxide).
• Thermodynamics: Recognizing rusting as an exothermic reaction, one that releases energy, highlights the importance of energy considerations in chemical reactions.
• Environmental Conditions: Knowing that certain reactions, like rusting, can happen under specific environmental conditions, such as the availability of water and suitable temperature.
• Reversibility of Reactions: Identifying whether a chemical reaction is reversible or not is key to understanding the permanence of the reaction's products and the feasibility of recovering the reactants.

Explanation:-

Rusting is a common chemical reaction where iron reacts with oxygen in the presence of water or moisture. This process leads to the formation of iron oxide (rust).

Nature of the Reaction (a): The statement that rusting involves a chemical reaction between iron and oxygen is true. The presence of water acts as a catalyst, accelerating the process. The chemical equation for rusting can be simplified as:

(4Fe + 3O₂ + 6H₂O→ 4Fe(OH)₃),

which upon dehydrating gives iron oxide, or rust.

Exothermic Reaction (b): Rusting is an exothermic reaction. Although the amount of heat released during the reaction is relatively low, it indeed releases energy to the surrounding environment, confirming that it is exothermic.

Room Temperature Reaction (c): Rusting can, and commonly does, occur at room temperature. The presence of moisture (water) and oxygen in the air at room temperature is sufficient to initiate and sustain the rusting process.

Reversibility (d): Rusting is not a reversible reaction under normal conditions. Once iron has oxidized to form rust, converting it back to pure iron requires a chemical process that involves reduction, typically not occurring spontaneously in nature.

Conclusion:-

The statements (a) It involves a chemical reaction between iron and oxygen, (b) It is an exothermic reaction, and (c) It can take place at room temperature, are all true regarding the rusting of iron.

The statement (d) It is a reversible reaction, is false since rusting does not easily reverse back to iron and oxygen under normal conditions.

Therefore, the correct answer is  (a), (b) and (c)

The correct answer is Frogs, fish, starfish

Explanation:-

• External fertilization is a reproductive process where fertilization occurs outside the body of the organism, typically in water or a moist environment.
• Organisms that exhibit external fertilization release their gametes (sperm and eggs) into the external environment, where they meet and fertilize. This process is common in aquatic animals and some terrestrial organisms.
• Frogs, fish, starfish: While frogs and fish exhibit external fertilization. Starfish also reproduce through external fertilization. Starfish release their gametes into the water, where fertilization occurs.
• Hens, lizards, butterflies: Hens,lizards and butterflies reproduce through internal fertilization, where fertilization occurs inside the female's body.Butterflies undergo internal fertilization, not external fertilization.
• During mating, male butterflies transfer sperm to the female's reproductive tract, where fertilization occurs internally. The female then lays fertilized eggs, usually on or near a suitable host plant for the larvae (caterpillars) to feed on after hatching.

Conclusion:- Frogs, fish, starfish is a set of animals in which all show external fertilization