RRB Group D Official Paper (Held On: 02 Dec, 2025 Shift 2) (Previous Year Paper)

The correct answer is reflection of sound.

Key Points

• The working principle of a stethoscope is based on the reflection and amplification of sound waves. This enables the doctor to hear internal body sounds such as heartbeats or lung sounds clearly.
• The stethoscope consists of a chest piece, a tube, and earpieces. When the chest piece is placed on the body, the sound waves are reflected and transmitted through the tube to the doctor's ears.
• Sound waves from internal organs such as the heart and lungs reflect off the walls of the stethoscope’s diaphragm, enhancing the clarity of the sound.
• The stethoscope diaphragm vibrates in response to sound waves, and these vibrations are transmitted through the hollow tube to the earpieces.
• The reflection of sound is critical because it concentrates the sound waves and eliminates noise interference, allowing the physician to detect abnormalities effectively.
• This principle can detect sounds at low frequencies, which are crucial for diagnosing conditions like heart murmurs or respiratory issues.

Additional Information

• Reflection of Sound:
• Sound waves, like light waves, can reflect when they hit a surface. This phenomenon is used in many applications such as stethoscopes, sonar, and ultrasound devices.
• In stethoscopes, the curved diaphragm acts as a reflecting surface that collects and transmits sound waves efficiently.
• The reflection of sound allows the focusing of sound waves, making faint noises from internal organs more audible.
• Components of a Stethoscope:
• The chest piece contains a diaphragm (for high-frequency sounds) and a bell (for low-frequency sounds).
• The tubing transmits sound without significant loss, ensuring that the doctor hears clear and amplified internal body sounds.
• The earpieces are designed to fit snugly into the ear canal, eliminating external noise interference.
• Applications of Stethoscopes:
• Used to listen to heartbeats for diagnosing conditions like arrhythmias, valve abnormalities, and murmurs.
• Helps in monitoring respiratory sounds, aiding in the diagnosis of lung infections, asthma, or pneumonia.
• Used during blood pressure measurement to detect Korotkoff sounds.
• Important Characteristics of Sound Reflection:
• Reflection occurs when sound waves hit a surface and bounce back.
• It is influenced by the nature of the surface (smooth surfaces reflect sound more efficiently).
• This principle is used in both mechanical and electronic medical devices.

Important Points

• Option 1: Absorption of high-frequency sound – This is incorrect as stethoscopes primarily reflect and amplify sound waves rather than absorb them.
• Option 2: Conversion of sound into electric signals only – This is incorrect because traditional stethoscopes are mechanical devices and do not convert sound into electrical signals.
• Option 3: Conversion of sound into light for observation – This is incorrect as stethoscopes do not involve the use of light for sound detection.
• Option 4: Reflection of sound – Correct as stethoscopes work on the principle of sound reflection to amplify internal body sounds.

The correct answer is Image is always virtual, erect, and on the same side as the object.

Key Points

• A concave lens always forms an image that is virtual, erect, and smaller than the object. The image is formed on the same side as the object, irrespective of the object's position.
• The focal length of a concave lens is negative, and it diverges light rays, making them appear to originate from a point on the same side as the object.
• Virtual images are formed because the light rays diverge after passing through the lens and do not actually converge to form a real image.
• Concave lenses are used in devices like glasses for correcting myopia (nearsightedness), cameras, and telescopes, where the formation of a smaller virtual image is required.
• Real images cannot be formed by concave lenses as they only diverge light rays. Hence, statements about real images are incorrect.

Additional Information

• Concave Lens Characteristics:
• A concave lens is thinner at the center and thicker at the edges.
• It is also known as a diverging lens because it spreads out light rays that pass through it.
• The focal length of a concave lens is represented by a negative value, indicating the divergent nature.
• Applications of Concave Lens:
• Used in glasses for correcting myopia, where distant objects appear blurry.
• In binoculars, telescopes, and cameras, concave lenses help focus and adjust the light rays.
• Used in projectors to spread light uniformly.
• Comparison with Convex Lens:
• While concave lenses produce virtual images, convex lenses can produce both real and virtual images depending on the object's position.
• Convex lenses converge light rays, while concave lenses diverge them.
• Convex lenses are used in magnifying glasses and cameras to create real images.
• Important Facts:
• In physics, the study of lenses falls under the branch of optics, which explores how light interacts with different mediums.
• The behavior of concave lenses is explained using the principles of ray diagrams and geometrical optics.
• Concave lenses are often paired with convex lenses in optical instruments for corrective purposes.

Important Points

• Statement Analysis:
• Statement 1 (Image is always virtual, erect, and on the same side as the object): Correct. Concave lenses always produce virtual images on the same side as the object.
• Statement 2 (Image is always real): Incorrect. Concave lenses never produce real images as they diverge light rays.
• Statement 3 (Image is always virtual and on the opposite side): Incorrect. Virtual images formed by concave lenses are always on the same side as the object.
• Statement 4 (Image is much larger than the object): Incorrect. The image formed by concave lenses is smaller than the object.
• Use in Scientific Instruments:
• Concave lenses are integral to designing microscopes, telescopes, and other optical devices.
• They are often combined with convex lenses to achieve better focus and image clarity.

The correct answer is They never intersect.

Key Points

• Electric field lines never intersect: This is because, at any given point in space, the electric field has a unique direction. If two field lines were to intersect, it would mean that the electric field has two directions at that point, which is not possible. Hence, this statement is correct.
• Electric field lines do not form closed loops: Electric field lines originate from positive charges and terminate on negative charges. They cannot form closed loops, as this would violate the principle that electric fields have sources (positive charges) and sinks (negative charges). Hence, this statement is incorrect.
• Electric field lines start on negative charges and end on positive charges: This is incorrect. Electric field lines originate from positive charges and terminate on negative charges. Hence, this statement is incorrect.
• Electric field lines are not always straight lines: The shape of electric field lines depends on the configuration of charges. For example, in the case of a single point charge, the lines are radial, but in the case of a dipole, the lines are curved. Hence, this statement is incorrect.

Additional Information

• Electric Field Lines:
• Electric field lines are an abstract representation of the electric field. They provide a visual way to understand the strength and direction of the field at various points in space.
• The density of electric field lines represents the magnitude of the electric field. Closer lines indicate a stronger field, while lines farther apart indicate a weaker field.
• Properties of Electric Field Lines:
• They originate from positive charges and terminate on negative charges.
• They never intersect because the electric field at any point has a unique direction.
• They do not form closed loops because electric fields are conservative in nature.
• In a uniform electric field, the field lines are parallel and equidistant.
• Applications of Electric Field Lines:
• They help in visualizing electric fields around charge distributions.
• They are used in understanding the behavior of charges in electric fields, such as in capacitors and dipoles.
• They are crucial in designing devices like electric motors, generators, and capacitors.
• Examples of Electric Field Configurations:
• Single Charge: Electric field lines radiate outward for a positive charge and inward for a negative charge.
• Dipole: Electric field lines are curved and originate from the positive charge to terminate on the negative charge.
• Parallel Plates: The electric field is uniform, with straight, parallel lines between the plates.

Important Points

• Mathematical Representation: The electric field at a point is represented as E = F/q, where F is the force on a test charge q.
• Superposition Principle: The net electric field at a point due to multiple charges is the vector sum of the electric fields due to individual charges.
• Electric Dipole: It consists of two equal and opposite charges separated by a small distance. The electric field lines of a dipole are distinctive and curved.
• Conservative Nature: The work done in moving a charge in an electric field depends only on the initial and final positions, not on the path taken.

The correct answer is Metals are sonorous and produce sound when struck..

Key Points

• Sonority of Metals: Metals are sonorous, meaning they produce a ringing sound when struck. This is due to their ability to vibrate uniformly, which is a distinctive physical property of metals.
• Low Melting and Boiling Points: The statement that metals have low melting and boiling points is incorrect. Most metals, such as iron and tungsten, have very high melting and boiling points, making them suitable for high-temperature applications.
• Brittleness: Metals are generally malleable and ductile, meaning they can be hammered or drawn into wires without breaking. The statement that metals are brittle is incorrect, as brittleness is a property of non-metals like sulfur or phosphorus.
• Conductivity: Metals are excellent conductors of heat and electricity due to the presence of free electrons. The statement that metals are poor conductors is incorrect.
• Practical Examples: The sonorous nature of metals is utilized in making bells, gongs, and musical instruments like cymbals, where the production of a clear sound is essential.

Additional Information

• Malleability and Ductility: Metals like gold and silver are highly malleable and ductile, allowing them to be shaped into thin sheets or drawn into wires. These properties are crucial for jewelry and electrical wiring.
• Electrical Conductivity: Metals like copper and aluminum are extensively used in electrical circuits due to their high conductivity. Their free electrons facilitate the easy flow of electricity.
• Thermal Conductivity: Metals like silver and copper are excellent thermal conductors, making them ideal for cookware and heat exchangers.
• High Density: Most metals have a high density, meaning they are heavy for their size. For example, iron and lead are significantly denser than non-metals like carbon.
• Melting Points: Metals generally have high melting points. For instance, tungsten has the highest melting point among metals, at approximately 3422°C, making it useful in light bulb filaments.

Important Points

• Applications of Sonorous Metals: The sonorous property of metals is utilized in making bells, church gongs, and tuning forks, where the production of a resonating sound is essential.
• Exceptions: While most metals are sonorous, some metals like mercury, which is in liquid form at room temperature, do not exhibit sonority.
• Industrial Usage: Sonorous metals like bronze and brass are widely used in musical instruments due to their ability to produce clear and resonating sounds.

The correct answer is Lead(II) iodide (PbI₂).

Key Points

• Reaction Overview: When lead nitrate (Pb(NO₃)₂) reacts with potassium iodide (KI), a double displacement reaction occurs, forming a yellow precipitate of Lead(II) iodide (PbI₂). This reaction is represented as: Pb(NO₃)₂ + 2KI → PbI₂ (yellow precipitate) + 2KNO₃.
• Formation of Precipitate: Lead(II) iodide (PbI₂) is insoluble in water, which is why it forms a solid yellow precipitate during the reaction.
• Potassium nitrate: Potassium nitrate (KNO₃) remains dissolved in the solution as it is highly soluble in water, and does not form a precipitate.
• Double Displacement Reaction: The reaction between lead nitrate and potassium iodide is classified as a double displacement reaction where ions exchange places to form new compounds.
• Color of PbI₂: The distinct yellow color of Lead(II) iodide makes the identification of the precipitate straightforward and is a characteristic property of this compound.

Additional Information

• Lead(II) iodide (PbI₂):
• PbI₂ is a yellow crystalline solid that is sparingly soluble in water but soluble in hot water.
• It is commonly used in laboratory experiments to demonstrate precipitation reactions and is also used in applications like solar cells.
• PbI₂ exhibits interesting optical properties and has been studied for its potential in optoelectronic devices.
• Potassium nitrate (KNO₃):
• KNO₃ is a soluble ionic compound and does not form a precipitate in the reaction.
• It is widely used in fertilizers, food preservation, and pyrotechnics.
• Its role in this reaction is as a by-product, remaining dissolved in the aqueous medium.
• Double Displacement Reactions:
• These reactions involve the exchange of ions between two reacting compounds to form two new compounds.
• One of the products is often a precipitate, gas, or water, making it easy to identify such reactions.
• Common examples include reactions between salts, acids, and bases.
• Solubility Rules:
• According to solubility rules, nitrates (NO₃^-) are generally soluble in water, which explains why KNO₃ remains in solution.
• Halides of lead, such as PbI₂, tend to be insoluble, leading to the formation of a precipitate.

Important Points

• Laboratory Demonstrations: The reaction between lead nitrate and potassium iodide is often demonstrated in chemistry laboratories to teach concepts of precipitation and solubility.
• Environmental Concerns: Lead compounds, including PbI₂, are toxic and must be handled with care. Disposal should follow proper guidelines to avoid environmental harm.
• Applications of PbI₂: Due to its optical properties, PbI₂ has been explored for use in perovskite solar cells and radiation detectors.
• Reaction Classification: The reaction is a clear example of a double displacement reaction and highlights the importance of solubility rules in predicting reaction outcomes.
• Precipitation Reactions: These reactions are crucial in analytical chemistry for the qualitative and quantitative determination of ions in solution.

The correct answer is 5 m/s².

Key Points

• Acceleration is the rate of change of velocity of an object per unit time. The formula to calculate acceleration is:
  

a = (v - u) / t, where:

• a is acceleration,
• v is the final velocity,
• u is the initial velocity, and
• t is the time taken.
• Here, the car starts from rest, so the initial velocity (u) = 0 m/s.
• The final velocity (v) attained by the car is 20 m/s.
• The time taken (t) for this change is 4 seconds.
• Substituting these values into the formula:
  

a = (20 - 0) / 4 = 20 / 4 = 5 m/s².

• Hence, the acceleration of the car is 5 m/s², which matches the given option.

Additional Information

• Acceleration:
• It is a vector quantity, meaning it has both magnitude and direction.
• If an object speeds up, the acceleration is positive; if it slows down, the acceleration is negative (also called deceleration).
• Units of acceleration are typically expressed as meters per second squared (m/s²).
• Types of Acceleration:
• Uniform Acceleration: When the rate of change of velocity remains constant over time (e.g., free fall under gravity).
• Non-uniform Acceleration: When the rate of change of velocity varies over time (e.g., a car accelerating unevenly).
• Real-life Applications of Acceleration:
• Used in designing vehicles to ensure optimal speed and safety during acceleration.
• Helps astronauts understand forces during rocket launches.
• Essential in physics experiments to study motion and forces.
• Newton's Second Law of Motion:
• The concept of acceleration is closely tied to Newton's Second Law, which states:
  

F = ma, where:

• F is the force applied,
• m is the mass of the object, and
• a is the acceleration produced.
• This law explains the relationship between force, mass, and acceleration.

Important Points

• SI Units: Always ensure the units are consistent when solving equations involving velocity, time, and acceleration. For instance, use seconds for time and meters/second for velocity.
• Motion Equations: Other equations used in motion analysis include:
• v = u + at
• s = ut + 1/2 at²
• v² = u² + 2as
• Practical Example: A rocket taking off from the ground or a car speeding up on a highway are examples of acceleration in real life.

The correct answer is Density decreases.

Key Points

• Density is defined as the mass per unit volume of a substance, expressed mathematically as Density = Mass/Volume.
• When the temperature of a substance increases, its volume typically expands due to the increase in kinetic energy of the particles. This phenomenon is more pronounced in gases and liquids.
• Since density is inversely proportional to volume, an increase in volume leads to a decrease in density. Hence, option 3 is correct.
• This behavior is most commonly observed in liquids and gases, where particles move more freely compared to solids. In solids, the effect is minimal due to their rigid structure.
• For example, when water is heated, its molecules move faster, causing the liquid to expand, resulting in a lower density.

Additional Information

• Density and Temperature Relationship:
• Solids: The density of solids is minimally affected by temperature changes due to their rigid molecular structure.
• Liquids: Liquids expand more noticeably when heated, leading to a decrease in density. For example, hot water is less dense than cold water.
• Gases: Gases exhibit the greatest change in density with temperature. When heated, gases expand significantly, causing their density to drop. This is governed by the **Ideal Gas Law (PV = nRT).
• Applications of Density Changes:
• Hot Air Balloons: Heated air inside the balloon becomes less dense than the cooler air outside, enabling the balloon to rise.
• Ocean Currents: Temperature-induced density changes in seawater contribute to the formation of ocean currents.
• Expansion of Metals: In engineering, temperature-induced density changes are considered when designing structures like bridges and pipelines.
• Anomalous Behavior of Water:
• Unlike most substances, water exhibits an anomalous expansion where its density decreases as it is cooled below 4°C, leading to ice floating on water.
• This unique property plays a crucial role in maintaining aquatic ecosystems during winter.
• Thermal Expansion Coefficient:
• The rate at which a substance expands with temperature is quantified by its thermal expansion coefficient.
• Substances with a high thermal expansion coefficient experience greater density changes when heated.

Important Points

• Ideal Gas Law: The density (ρ) of a gas is given by the formula ρ = P/(RT), where P is pressure, R is the gas constant, and T is temperature.
• In engineering, temperature-induced density changes must be considered for materials exposed to heat, such as turbine blades and engine parts.
• Thermal Expansion in Liquids: This property is utilized in thermometers, where the liquid expands with rising temperature to indicate the reading.
• Environmental Implications: Density changes in air and water due to temperature variations are significant in weather patterns, climate dynamics, and ecological balance.

The correct answer is It kills pests and insects that could otherwise damage stored grains..

Key Points

• Fumigation is a process used in the safe storage of food grains to eliminate pests, insects, and other biological threats that can damage the grains. This ensures the quality and longevity of the stored grains.
• The method involves the use of chemical fumigants, such as phosphine, methyl bromide, or sulfuryl fluoride, which are released in a controlled environment to destroy pests at all life stages, including eggs, larvae, pupae, and adults.
• Fumigation is particularly effective in protecting grains during long-term storage by preventing infestations that can lead to spoilage and economic losses.
• This practice is crucial for maintaining the food security of a nation, as it prevents wastage and ensures that grains remain fit for consumption.
• It is important to note that fumigation does not alter the nutritional value, weight, or moisture content of the grains, but solely targets pests and insects.

Additional Information

• Purpose of Fumigation:
• The primary purpose of fumigation is to eliminate infestations by killing pests such as weevils, beetles, moths, and mites in stored grains.
• It is a preventive measure to ensure that food grains remain free from contamination.
• Commonly Used Fumigants:
• Phosphine: This is one of the most widely used fumigants due to its high efficacy and low residue levels.
• Methyl Bromide: Although effective, its use is restricted in many countries due to its potential environmental and health hazards.
• Carbon Dioxide: Often used as a natural alternative for organic fumigation.
• Fumigation Process:
• The grains are stored in airtight containers or silos before the fumigant is introduced.
• The fumigant is allowed to circulate for a specific period to ensure complete pest eradication.
• After fumigation, the storage area is ventilated to remove any remaining traces of the chemical.
• Legal and Safety Regulations:
• Fumigation is regulated by government guidelines to ensure safe and effective use of chemicals.
• For example, in India, the Insecticides Act, 1968 governs the use of fumigants to prevent misuse and safeguard public health.
• Importance in Agriculture:
• Fumigation plays a critical role in maintaining the quality of stored grains, especially in agricultural economies where grains are stored for extended periods.
• It helps reduce post-harvest losses, which account for a significant portion of food wastage globally.

Important Points

• Option 2: "It increases the weight of the grains" is incorrect as fumigation does not affect the physical weight or mass of the grains.
• Option 3: "It prevents moisture loss from grains" is incorrect because fumigation does not impact the moisture levels of the grains.
• Option 4: "It adds nutrients to the grains" is incorrect since fumigation is not intended to alter the nutritional composition of the grains.
• Fumigation is purely a pest control method, ensuring that the grains remain safe for human consumption and free from infestations.

The correct answer is its kinetic energy.

Key Points

• The work-energy principle states that the work done by all forces acting on a body is equal to the change in its kinetic energy. This is a fundamental concept in physics.
• The moving body possesses kinetic energy, which is defined as KE = (1/2)mv², where m is the mass of the body, and v is its velocity.
• When an external force is applied to bring the moving body to rest, it does negative work on the body by reducing its velocity to zero.
• The amount of work required to stop the body is equal to the initial kinetic energy of the body because the kinetic energy is converted into work done by the external force.
• Other quantities like weight, momentum, or potential energy are not directly involved in the process of stopping a moving object unless specifically mentioned in the context.
• Hence, the work done by the external force to stop the moving body is equal to its kinetic energy.

Additional Information

• Kinetic Energy:
• Kinetic energy is the energy possessed by a body due to its motion.
• The formula is KE = (1/2)mv², where m is mass and v is velocity.
• It is a scalar quantity, meaning it has magnitude but no direction.
• Kinetic energy is measured in joules (J) in the SI system.
• Work-Energy Theorem:
• The work-energy theorem states that the work done by the net force acting on an object is equal to the change in its kinetic energy.
• Mathematically, W = ΔKE = KE_final - KE_initial.
• When a moving object is brought to rest, its final kinetic energy is zero, and the work done equals its initial kinetic energy.
• Weight:
• Weight is the force exerted by gravity on a body, calculated as W = mg, where m is the mass of the body and g is the acceleration due to gravity.
• Weight is unrelated to the kinetic energy unless the context involves motion against gravity.
• Momentum:
• Momentum is the product of the mass and velocity of an object, given by p = mv.
• While momentum is conserved in a closed system, it is not directly equal to the work done to stop a moving body.
• Potential Energy:
• Potential energy is the energy possessed by a body due to its position in a force field, such as gravity or elasticity.
• It is calculated as PE = mgh for gravitational potential energy.
• Potential energy is not relevant in the context of stopping a moving object unless the object is moving in a potential energy field.

Important Points

• The conversion of energy is fundamental in physics. In this case, the kinetic energy of the moving object is converted into work done by the external force to bring it to rest.
• The negative work done by the external force reduces the velocity of the object to zero.
• Understanding the distinction between kinetic energy, momentum, and potential energy is crucial for solving problems related to motion and forces.
• Real-world examples of this concept include applying brakes to a moving vehicle, where the brakes do work to reduce the car's kinetic energy to zero.

The correct answer is Health education and medical care.

Key Points

• Health education and medical care are crucial components in maintaining reproductive health. They provide awareness and preventive measures to avoid diseases and promote overall well-being.
• Health education ensures individuals have the knowledge to make informed decisions about contraception, family planning, sexually transmitted infections (STIs), and safe sexual practices.
• Access to medical care, such as routine health check-ups, vaccinations, and treatment for diseases, plays a vital role in reducing reproductive health issues.
• Proper health education empowers people to recognize the importance of hygiene, nutrition, and regular medical check-ups, which are essential for reproductive health.
• Government and non-governmental organizations often implement programs focusing on reproductive health awareness, particularly for adolescents and women in rural areas, to reduce maternal and infant mortality rates.

Additional Information

• Hygiene: Maintaining personal hygiene, particularly during menstruation, pregnancy, and post-pregnancy, is critical for avoiding infections and promoting reproductive health.
• Impact of Early Marriage: Early marriage can negatively affect reproductive health as it often leads to early pregnancies, which increase the risk of maternal and infant mortality. Hence, it should be avoided.
• Junk Food: Regular consumption of junk food can lead to malnutrition, obesity, and hormonal imbalances, adversely impacting reproductive health.
• Reproductive Health Programs in India: Initiatives such as the National Reproductive and Child Health (RCH) Program aim to improve maternal and child health by providing essential services like antenatal care, safe delivery, and contraception.
• Adolescent Health: Programs like the Rashtriya Kishor Swasthya Karyakram (RKSK) focus on improving adolescent health, which includes components of reproductive health education and services.

Important Points

• Government Schemes: In India, schemes like Janani Suraksha Yojana and Pradhan Mantri Matru Vandana Yojana aim to improve reproductive health by providing financial incentives for institutional deliveries and maternal nutrition.
• Data and Statistics: According to the National Family Health Survey (NFHS-5), maternal health indicators such as institutional delivery rates and antenatal care coverage have significantly improved in recent years.
• Role of NGOs: Non-governmental organizations such as Population Foundation of India and PATH work extensively in creating awareness and providing resources for reproductive health, especially in underserved communities.
• Global Perspective: According to the World Health Organization (WHO), comprehensive sexual and reproductive health services are integral to achieving the Sustainable Development Goals (SDG) 3, which target ensuring healthy lives and promoting well-being.

The correct answer is Manufacture of lipids.

Key Points

• The Smooth Endoplasmic Reticulum (SER) is primarily responsible for the manufacture of lipids. Lipids are essential for cell membrane formation, energy storage, and signaling.
• Unlike the Rough Endoplasmic Reticulum (RER), the SER lacks ribosomes, which gives it a smooth appearance under the microscope.
• The SER is involved in the synthesis of steroid hormones in endocrine cells, such as those in the adrenal glands and gonads.
• It also plays a crucial role in the detoxification of drugs and harmful substances in liver cells.
• In muscle cells, the SER is referred to as the sarcoplasmic reticulum and is responsible for regulating calcium ion storage and release, which is vital for muscle contraction.

Additional Information

• Protein Synthesis (Option 1):
• Protein synthesis is a function of the Rough Endoplasmic Reticulum (RER), not the SER. The RER is studded with ribosomes, which facilitate the production of proteins.
• Proteins synthesized in the RER are often destined for secretion or incorporation into the cell membrane.
• Assembly of Ribosomes (Option 2):
• Ribosome assembly occurs in the nucleolus, a structure within the nucleus of the cell. This process is independent of both the RER and SER.
• Once assembled, ribosomes may either float freely in the cytoplasm or attach to the RER for protein synthesis.
• Modification of Sugars (Option 3):
• The modification of sugars is typically a function of the Golgi apparatus, not the SER. The Golgi apparatus processes and packages carbohydrates for incorporation into glycoproteins and glycolipids.
• This organelle plays a key role in the transport of macromolecules within the cell.
• Manufacture of Lipids (Correct Answer - Option 4):
• The SER synthesizes phospholipids, which are critical components of cellular membranes.
• It also produces cholesterol and steroid hormones, which are essential for various physiological functions.

Important Points

• The SER is abundant in cells specialized for lipid metabolism, such as liver cells and adipocytes.
• It also plays a role in the storage of ions, particularly calcium ions in muscle cells, which is critical for muscle function.
• The SER detoxifies substances like alcohol and drugs through enzymatic reactions, making it vital for maintaining cellular health.
• The balance of lipid production and metabolism in the SER is crucial for maintaining the structural integrity of membranes and proper cellular function.

The correct answer is rate of flow of electric charge.

Key Points

• Electric current is defined as the rate at which electric charge flows through a conductor or a circuit. It is typically measured in amperes (A).
• Current is expressed mathematically as I = Q / t, where Q represents the electric charge in coulombs, and t is the time in seconds during which the charge flows.
• The direction of current flow is conventionally taken to be from the positive terminal to the negative terminal, even though electrons flow in the opposite direction.
• Electric current arises due to the movement of electrons or charged particles, and it can be classified into direct current (DC), where the flow is unidirectional, or alternating current (AC), where the direction periodically reverses.
• In practical applications, current can be generated by various sources such as batteries, generators, or solar cells, depending on the requirement.

Additional Information

• Option 1: Amount of charge per unit length:
• This statement is incorrect because electric current is not defined in terms of charge per unit length. Instead, it is based on the rate of charge flow over time.
• Charge per unit length may be relevant in specific contexts like linear charge density in physics, but it does not define electric current.
• Option 2: Energy consumed per unit time:
• This statement is incorrect as it refers to power, not current. Power is defined as the rate at which energy is transferred or consumed, and it is given by P = IV, where I is current and V is voltage.
• While power is closely related to current, it does not define electric current itself.
• Option 3: Rate of flow of electric charge:
• This is the correct definition of electric current. It quantifies how much charge passes through a given point in a circuit over a specified time.
• Current is a fundamental concept in electrical and electronic systems, and it forms the basis of various applications, from powering devices to signal transmission.
• Option 4: Amount of charge per unit area:
• This statement is incorrect as it refers to surface charge density, which is used in electrostatics to describe the distribution of charge on surfaces.
• Electric current, however, is not described in terms of charge per unit area.

Important Points

• Types of Current:
• Direct Current (DC): The flow of charge is unidirectional and constant over time. Batteries are common sources of DC.
• Alternating Current (AC): The flow of charge periodically reverses direction. Household electricity is typically AC, delivered at a frequency of 50 Hz in countries like India.
• Measurement of Electric Current:
• Current is measured using an instrument called an ammeter, which is connected in series in a circuit.
• The unit of current is the ampere (A), named after the French scientist André-Marie Ampère.
• Sources of Current:
• Electric current can be generated from various sources, such as chemical reactions in batteries, electromagnetic induction in generators, or photovoltaic effects in solar cells.
• In industrial applications, large generators produce currents that are distributed through power grids.
• Applications of Electric Current:
• Current plays a crucial role in powering electronic devices, lighting systems, motors, and communication networks.
• In medical applications, controlled electric currents are used in devices like ECGs and defibrillators.

The correct answer is 5 m/s.

Key Points

• Displacement: The displacement of the body is given as 50 m. Displacement is the shortest distance between the initial and final positions of the body in a straight line.
• Time Taken: The total time taken by the body to cover the displacement is 10 seconds.
• Average Velocity Formula: The formula for average velocity is:
  

Average Velocity = Total Displacement / Total Time

• Calculation:
  

Substituting the given values:

Average Velocity = 50 m / 10 s = 5 m/s.

• Interpretation: The body moves along a straight line with varying speed, but average velocity depends only on the total displacement and total time, not the actual speed variations. Hence, the correct answer is 5 m/s.

Additional Information

• Difference Between Speed and Velocity:
• Speed is a scalar quantity and measures how fast an object is moving. It does not consider direction.
• Velocity is a vector quantity, meaning it includes both magnitude and direction. Average velocity is determined by dividing total displacement by total time.
• Uniform vs. Non-Uniform Motion:
• Uniform Motion: The object covers equal distances in equal intervals of time, and speed remains constant.
• Non-Uniform Motion: The speed of the object changes, leading to varying distances covered in equal intervals of time.
• Importance of Displacement:
• Displacement is a vector quantity that reflects the overall change in position.
• It is crucial for calculating average velocity, as opposed to average speed, which uses total distance.
• SI Units:
• The SI unit of displacement is meter (m).
• The SI unit of time is second (s).
• The SI unit of velocity is meter per second (m/s).

Important Points

• Average Velocity:
• It depends only on total displacement and total time, irrespective of how the speed varies during motion.
• It can be positive, negative, or zero depending on the direction of displacement.
• Instantaneous Velocity: Unlike average velocity, it refers to the velocity of an object at a specific moment during its motion.
• Relation Between Velocity and Speed:
• For straight-line motion in one direction, average speed and average velocity are equal if the motion does not reverse direction.
• If the motion involves changes in direction, average speed will always be greater than or equal to the average velocity.

The correct answer is -CHO.

Key Points

• Aldehydes are organic compounds characterized by the presence of the -CHO functional group, also called the aldehyde group. This group is fundamental to their chemical properties.
• The -CHO group consists of a carbon atom double-bonded to an oxygen atom (C=O) and single-bonded to a hydrogen atom (H), making it a carbonyl group with a hydrogen attached.
• The -CHO group is always located at the end of the carbon chain because it requires a terminal carbon atom to attach the hydrogen and oxygen atoms.
• Aldehydes are distinct from other carbonyl-containing compounds like ketones because ketones have the carbonyl group bonded to two carbon atoms, while aldehydes have one hydrogen atom attached to the carbonyl group.
• The correct answer is -CHO because this functional group is unique to aldehydes and defines their chemical behavior. Hence, the correct option is -CHO.

Additional Information

• Explanation of Other Functional Groups:
• -OH (Hydroxyl Group): This is the functional group of alcohols. It consists of an oxygen atom bonded to a hydrogen atom. Alcohols do not contain a carbonyl group like aldehydes, and hence this option is incorrect.
• -COOH (Carboxylic Acid Group): This functional group is present in carboxylic acids. It consists of a carbon atom double-bonded to an oxygen atom (C=O) and single-bonded to a hydroxyl group (-OH). Aldehydes do not have this structure, so this option is incorrect.
• -CO (Carbonyl Group): While aldehydes do contain a carbonyl group, this option is too generic. The specific functional group for aldehydes is -CHO, which includes the carbonyl group bonded to a hydrogen atom. Hence, this option is not specific enough to be correct.
• Applications of Aldehydes:
• Aldehydes are widely used in the chemical industry for the production of resins, dyes, and perfumes.
• Formaldehyde (the simplest aldehyde) is used in the production of plastics and disinfectants.
• Acetaldehyde is used in the synthesis of acetic acid and as a precursor in the production of certain flavors and fragrances.
• Reactions of Aldehydes:
• Aldehydes undergo oxidation reactions to form carboxylic acids.
• They also participate in nucleophilic addition reactions, such as the addition of alcohols to form hemiacetals and acetals.
• Their reactivity is influenced by the electron-withdrawing nature of the carbonyl group, making the carbon atom electrophilic.
• Examples of Aldehydes:
• Formaldehyde (HCHO): Used in the production of polymers and as a disinfectant.
• Acetaldehyde (CH3CHO): Used as an intermediate in the synthesis of acetic acid and in the production of perfumes.
• Benzaldehyde (C6H5CHO): Found in almond oil and used in the food and fragrance industries.

Important Points

• Distinguishing Aldehydes:
• Aldehydes can be distinguished from ketones using Tollens' Test, where aldehydes reduce Tollens' reagent (ammoniacal silver nitrate) to form a silver mirror.
• The Fehling's Test also distinguishes aldehydes, as they reduce Fehling's solution to form a brick-red precipitate of cuprous oxide (Cu2O).
• Importance of Functional Groups: Functional groups like -CHO play a crucial role in determining the chemical reactivity, physical properties, and biological activity of organic compounds.

The correct answer is Ethanol.

Key Points

• Ethanol is a widely used alcohol as a fuel or fuel additive because of its renewable and eco-friendly nature.
• It is primarily produced from the fermentation of crops like sugarcane, corn, and other biomass materials, making it a renewable energy source.
• When blended with gasoline, ethanol reduces harmful emissions such as carbon monoxide and particulate matter, thereby improving air quality and promoting cleaner combustion.
• Many countries, including India, the United States, and Brazil, have adopted ethanol-blended fuels to reduce reliance on fossil fuels and improve energy security. For example, India has set a target of achieving a 20% ethanol blend with petrol by 2025.
• Ethanol has a high octane number, enhancing engine performance and reducing knocking in internal combustion engines.

Additional Information

• Methanol:
• Also known as wood alcohol, methanol is sometimes used as a fuel but is less common than ethanol because it is toxic and corrosive.
• It is primarily used in industrial applications, such as in the production of formaldehyde, acetic acid, and as a solvent.
• Propanol:
• Propanol is not commonly used as a fuel due to its higher production costs and less favorable combustion properties compared to ethanol and methanol.
• It finds its use mainly in the pharmaceutical and cosmetics industries as a solvent.
• Butanol:
• Butanol can also be used as a fuel or fuel additive, but its production is less efficient compared to ethanol.
• However, it has some advantages, such as higher energy content and lower volatility, making it a potential alternative in the future.
• Advantages of Ethanol-Blended Fuel:
• It helps reduce greenhouse gas emissions, supporting global efforts to combat climate change.
• Using ethanol reduces dependency on imported crude oil, promoting energy independence in countries like India.
• It supports the agricultural sector by creating demand for crops like sugarcane and corn.
• Blending ethanol in fuels leads to cleaner air by reducing harmful pollutants.

Important Points

• Ethanol Production in India:
• In India, ethanol production is primarily derived from sugarcane molasses under the National Bio-Energy Mission.
• The Ethanol Blended Petrol (EBP) Programme was launched in India to promote the use of ethanol as an alternative fuel.
• Global Leaders in Ethanol Use:
• Brazil is one of the largest producers and consumers of ethanol, with its fuel market dominated by ethanol-blended gasoline.
• The United States also heavily uses ethanol, primarily sourced from corn, under its Renewable Fuel Standard (RFS) program.
• Challenges of Ethanol Use:
• Large-scale production of ethanol can lead to competition for agricultural resources, affecting food security.
• It requires substantial water resources for crop cultivation and ethanol processing.

The correct answer is Oxygen mixed with Nitrogen in air.

Key Points

• Homogeneous Solution: A solution is homogeneous when its composition is uniform throughout. Gaseous mixtures like air, where oxygen (solute) is mixed with nitrogen (solvent), are classic examples of this. Air is a homogeneous mixture, and the gases are mixed uniformly, making it a solution.
• Solute and Solvent as Elements: Both oxygen (O₂) and nitrogen (N₂) are elements. In air, oxygen acts as the solute, while nitrogen, being the most abundant gas, is the solvent. This fits the requirement of a solution where both the solute and solvent are elements.
• Physical State: In this case, both the solute and solvent are in the gaseous state, making it easier to form a homogeneous mixture. The properties of gases allow them to mix thoroughly without any barriers.
• Incorrect Options: Other options involve either heterogeneous mixtures or solutions where the solute/solvent are not both elements. For example, sugar dissolved in water involves a compound (sugar) and a compound (water), not two elements.
• Relevance of Air: Air is a natural example of a homogeneous solution where gases like oxygen, nitrogen, argon, and carbon dioxide coexist in a single phase. Hence, this scenario aligns perfectly with the question's requirement.

Additional Information

• Iron Filings Mixed with Sulphur: This is a heterogeneous mixture because the components do not mix uniformly. Iron filings and sulfur retain their individual properties and can be separated easily by physical methods such as using a magnet. Hence, this is not a homogeneous solution.
• Sugar Dissolved in Water: Sugar (a compound) dissolves in water (another compound), forming a homogeneous solution. However, the solute and solvent are not both elements, which disqualifies this option based on the question's criteria.
• Carbon Dissolved in Water: Carbon in its solid form (e.g., graphite) does not dissolve in water to form a homogeneous solution. This makes it an incorrect example for the given question.
• Definition of Homogeneous Mixture: A homogeneous mixture has a uniform composition and phase throughout. Examples include salt dissolved in water, alcohol mixed with water, and gases like air. These solutions are stable and do not separate over time.
• Gaseous Mixtures: Gases mix freely and form homogeneous solutions due to their high kinetic energy and the lack of intermolecular forces. Air is a prime example, where oxygen and nitrogen are uniformly distributed.

Important Points

• Key Characteristics of Solutions:
• Homogeneous solutions have a single phase and uniform composition.
• Solutes and solvents can exist in various states (solid, liquid, or gas).
• In gaseous solutions, all components are gases, as seen in air.
• Air Composition:
• Air is approximately 78% nitrogen, 21% oxygen, and small amounts of other gases like carbon dioxide and argon.
• It is a prime example of a homogeneous mixture where individual gases retain their properties but are evenly mixed.
• Solutions in Different Phases:
• Solid in Liquid: Salt in water.
• Liquid in Liquid: Alcohol in water.
• Gas in Gas: Oxygen in nitrogen (air).
• Scientific Applications: Understanding homogeneous solutions is crucial in fields like chemistry, environmental science, and industrial processes where uniformity in composition is necessary.

The correct answer is Protein.

Key Points

• The DNA in the cell nucleus contains the genetic instructions necessary for the synthesis of proteins. Proteins are crucial for the structure, function, and regulation of the body's tissues and organs.
• DNA is transcribed into mRNA (messenger RNA) in the cell nucleus. This mRNA serves as a template for protein synthesis during the process called translation.
• Proteins are composed of chains of amino acids, which are arranged in specific sequences as dictated by the genetic code in the DNA. This sequence determines the protein's structure and function.
• Unlike proteins, substances like lipids, glucose, and fructose are not directly synthesized using the instructions from DNA. Their production involves enzymatic pathways influenced by proteins.
• Thus, the DNA in the nucleus primarily directs the production of proteins, making it the central molecule in biological information transfer and cellular function.

Additional Information

• Protein Synthesis Process:
• The process begins with transcription, where the DNA sequence of a gene is copied into mRNA.
• The mRNA exits the nucleus and binds to a ribosome in the cytoplasm, initiating translation.
• During translation, tRNA (transfer RNA) molecules bring specific amino acids to the ribosome, where they are assembled into a protein chain based on the mRNA sequence.
• Importance of Proteins:
• Proteins serve as enzymes, which catalyze biochemical reactions essential for life.
• They act as structural components, like collagen in connective tissues and keratin in hair and nails.
• Proteins play a role in transport, such as hemoglobin carrying oxygen in blood, and in defense mechanisms, like antibodies in the immune system.
• Substances Not Synthesized Directly by DNA:
• Lipids: Lipids are synthesized through enzymatic pathways involving acetyl-CoA and are not directly encoded by DNA.
• Glucose and Fructose: These are carbohydrates metabolized via pathways such as glycolysis, gluconeogenesis, and the Calvin cycle in plants.
• Central Dogma of Molecular Biology:
• The central dogma describes the flow of genetic information: DNA → RNA → Protein.
• This principle highlights how genetic instructions in DNA are used to synthesize functional proteins that drive cellular activities.

Important Points

• Gene Expression:
• Gene expression is the process by which the information in a gene is used to produce a functional product, typically a protein.
• It involves two main steps: transcription (DNA to RNA) and translation (RNA to protein).
• Codons:
• A codon is a sequence of three nucleotides in mRNA that specifies a particular amino acid or a stop signal during protein synthesis.
• For example, the codon AUG codes for the amino acid methionine and also serves as the start codon for translation.
• Role of Ribosomes:
• Ribosomes are the cellular organelles where protein synthesis occurs. They consist of ribosomal RNA (rRNA) and proteins.
• They facilitate the binding of mRNA and tRNA, ensuring the correct sequence of amino acids in the protein.

The correct answer is Density of object.

Key Points

• Buoyant Force is determined by Archimedes' Principle, which states that the upward buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
• The density of the fluid is crucial because the buoyant force depends on the weight of the displaced fluid, which is directly proportional to the fluid's density. Hence, this affects buoyant force.
• Gravitational acceleration influences the buoyant force because it directly affects the weight of the displaced fluid. The formula for buoyant force involves gravitational acceleration (g), making it a significant factor. Hence, this affects buoyant force.
• Volume of displaced fluid is key in calculating buoyant force. The larger the volume displaced, the greater the buoyant force. Hence, this affects buoyant force.
• Density of the object, however, does not directly influence the buoyant force. The buoyant force depends only on the density of the fluid and the volume displaced, not on the object's density. Hence, this does NOT affect buoyant force.

Additional Information

• Archimedes' Principle:
• Formulated by ancient Greek scientist Archimedes, this principle explains the behavior of objects submerged in a fluid.
• The principle states that the buoyant force is equal to the weight of the displaced fluid, which can be calculated using the formula: Buoyant Force = ρ × V × g, where:
• ρ = density of fluid
• V = volume of displaced fluid
• g = gravitational acceleration
• This principle is used in applications such as ship design, submarines, and measuring densities.
• Factors Affecting Buoyant Force:
• Density of fluid: Higher fluid density results in a greater buoyant force.
• Volume of displaced fluid: A larger displaced volume increases the buoyant force.
• Gravitational acceleration: The buoyant force is proportional to the acceleration due to gravity.
• Applications of Buoyant Force:
• Ships and boats: Designed to displace sufficient water to counteract their weight.
• Submarines: Adjust buoyancy by controlling the volume of water in ballast tanks.
• Hot air balloons: Use the principle of buoyancy to rise by displacing cooler air.
• Density of Object:
• The object's density determines whether it will float or sink, but it does not affect the buoyant force directly.
• If the object's density is less than the fluid's density, it will float. If greater, it will sink.
• Example: A wooden block floats in water because its density is lower than water, while a metal block sinks.

Important Points

• Weight vs Buoyant Force:
• The buoyant force acts upward, opposing the weight of the object acting downward.
• When the buoyant force equals the object's weight, the object floats. If less, the object sinks.
• Neutral Buoyancy:
• Occurs when an object's weight is equal to the buoyant force, causing it to remain suspended in the fluid.
• Example: Scuba divers achieve neutral buoyancy by adjusting their buoyancy compensators.
• Real-life Examples:
• Icebergs float in water despite their massive size because ice has a lower density than water.
• Oil spills float on water due to the lower density of oil compared to water.

The correct answer is Cell body.

Key Points

• The cell body, also known as the soma, is a key structural part of the neuron that contains the nucleus and surrounding cytoplasm.
• The nucleus inside the cell body contains the genetic material (DNA), which directs the activities of the neuron, such as protein synthesis.
• The cytoplasm of the cell body is rich in organelles like mitochondria, ribosomes, and the endoplasmic reticulum, which are essential for maintaining cellular functions and generating energy.
• The cell body is responsible for integrating signals received from the dendrites and generating an appropriate response that is transmitted to the axon.
• This part of the neuron also plays a critical role in the growth, repair, and survival of the neuron by coordinating various metabolic activities.

Additional Information

• Structure of a Neuron:
• Neurons are specialized cells that transmit electrical and chemical signals in the nervous system.
• They consist of three main parts: dendrites, cell body (soma), and axon.
• Dendrites: These are branched structures that receive signals from other neurons or sensory receptors.
• Axon: A long, slender projection that transmits signals away from the cell body to other neurons or effector cells.
• Functions of the Cell Body:
• Acts as the control center of the neuron, regulating vital activities.
• Processes incoming signals from dendrites and determines whether an action potential should be generated.
• Provides metabolic support and maintains the structural integrity of the neuron.
• Comparison of Other Options:
• Dendrites: They do not contain the nucleus but are responsible for receiving signals.
• Nerve endings: These are specialized structures for transmitting signals to other neurons, muscles, or glands.
• Axon: It transmits signals but does not house the nucleus or cytoplasm.
• Importance of Neurons:
• Neurons are critical for the functioning of the brain, spinal cord, and peripheral nervous system.
• They enable communication between different parts of the body and the brain, allowing processes like movement, sensation, and cognition.

Important Points

• Neurotransmission:
• Neurons communicate via electrical signals and chemical messengers known as neurotransmitters.
• Neurotransmitters are released at the synaptic cleft, enabling signal transmission between neurons.
• Types of Neurons:
• Sensory neurons: Transmit sensory information from receptors to the brain and spinal cord.
• Motor neurons: Send signals from the brain and spinal cord to muscles and glands.
• Interneurons: Connect sensory and motor neurons and facilitate communication within the central nervous system.
• Diseases Affecting Neurons:
• Diseases like Alzheimer's disease, Parkinson's disease, and multiple sclerosis impact neuron functionality.
• Understanding the structure and function of neurons is crucial for developing treatments for these conditions.

The correct answer is Vas deferens.

Key Points

• The vas deferens is the duct responsible for transporting sperm from the testicles to the urethra during ejaculation. Altering this structure prevents sperm from being included in semen.
• The surgical procedure commonly performed to block or cut the vas deferens is called a vasectomy. It is a minor operation used as a method of permanent contraception for males.
• During a vasectomy, the vas deferens is either tied, cut, or sealed to prevent sperm from entering the ejaculate. This ensures that the semen released during ejaculation does not contain sperm, effectively preventing fertilization.
• The vas deferens is located within the male reproductive system and connects the epididymis (where sperm mature and are stored) to the urethra.
• This procedure does not affect the production of sperm in the testicles or the volume of semen ejaculated, as sperm constitutes only a small portion of the semen. Hence, the man’s sexual function remains normal post-procedure.

Additional Information

• Testis:
• The testis is responsible for producing sperm and the male hormone testosterone. Alteration to the testis would impact sperm production, but this is not the structure modified during a vasectomy.
• The testis is located within the scrotum and serves as the primary site for spermatogenesis (sperm production).
• Damage or removal of the testes would lead to infertility and hormonal imbalance, unlike a vasectomy which preserves hormonal function.
• Urethra:
• The urethra is the tube that carries urine from the bladder and semen from the reproductive system out of the body. It is not altered during a vasectomy.
• It functions as a passageway for both urine and ejaculate in males, but it does not directly influence the composition of semen.
• Penis:
• The penis is the external male genital organ responsible for delivering semen and urine outside the body.
• It is not surgically altered during a vasectomy, as the procedure focuses on the internal vas deferens ducts.
• Any surgical alteration to the penis would impact sexual or urinary function, which is not the case with vasectomy.
• Additional Facts about Vasectomy:
• Vasectomy is considered a highly effective method of contraception, with a failure rate of less than 1%.
• The procedure is minimally invasive, typically performed under local anesthesia, and recovery is quick, often within a few days.
• It does not protect against sexually transmitted infections (STIs), and individuals are advised to use condoms for STI prevention.
• Vasectomy can be reversed in some cases through a procedure called vasovasostomy, although reversal is not always successful.

Important Points

• Vasectomy does not affect the production of testosterone, libido, or sexual ability in males. These functions remain intact post-procedure.
• The semen released during ejaculation after a vasectomy is visually and functionally normal, except it does not contain sperm.
• The vasectomy procedure is a safe and reliable form of permanent contraception, but individuals must be informed about its irreversible nature in most cases.
• In rare cases, the vas deferens can spontaneously reconnect, leading to the potential for pregnancy, though this is extremely uncommon.
• Vasectomy is widely practiced globally and is considered one of the simplest and safest methods of permanent male sterilization.

The correct answer is is considered positive.

Key Points

• Height of an image in a concave mirror is considered positive when the image is formed above the principal axis. This is based on the standard sign convention used in optics.
• In the Cartesian sign convention, all distances measured above the principal axis are positive, while those below it are negative.
• When the object is placed within the focal length of a concave mirror, the image is virtual, erect, and formed above the principal axis, hence its height is considered positive.
• For example, if a ray diagram shows an image formed above the principal axis, the corresponding height value will be positive. This adheres to the general rules of image formation in concave mirrors.
• The height of an image depends on the position of the object, but the sign of the height (positive or negative) is determined by its orientation relative to the principal axis.

Additional Information

• Concave Mirror:
• A concave mirror is a spherical mirror with the reflecting surface curved inward, resembling the interior of a sphere.
• It is also known as a converging mirror because it converges light rays that are incident parallel to its principal axis to a single focal point.
• Applications include telescopes, shaving mirrors, and headlights due to their ability to focus light.
• Sign Convention in Optics:
• In the Cartesian sign convention:
• Distances measured in the direction of the incident light are considered positive.
• Distances measured against the direction of the incident light are considered negative.
• Heights above the principal axis are positive, and those below are negative.
• This convention ensures consistency in calculations and diagrams.
• Image Formation in Concave Mirrors:
• The nature, position, and size of the image depend on the object's position relative to the mirror's focal point (F) and center of curvature (C).
• When the object is placed:
• Beyond C: The image is real, inverted, and smaller.
• At C: The image is real, inverted, and of the same size.
• Between C and F: The image is real, inverted, and larger.
• At F: No image is formed as the reflected rays are parallel.
• Between F and the mirror: The image is virtual, erect, and larger.
• Applications of Concave Mirrors:
• In solar furnaces to focus sunlight and generate heat.
• In torches, searchlights, and car headlights for producing parallel beams of light.
• In shaving or makeup mirrors to provide a magnified view.
• In optical devices such as microscopes and telescopes for focusing light.

Important Points

• Position of Object and Image Properties:
• The position of the object significantly affects the image's size, orientation, and type (real or virtual).
• For example, moving the object closer to the mirror changes the image from real and inverted to virtual and erect.
• Magnification:
• The magnification (M) of a mirror is the ratio of the height of the image to the height of the object.
• A positive magnification indicates a virtual and erect image, while a negative magnification indicates a real and inverted image.
• Focal Length and Radius of Curvature:
• The focal length (f) of a concave mirror is half of its radius of curvature (R), i.e., f = R/2.
• The relationship between object distance (u), image distance (v), and focal length is given by the mirror formula: 1/f = 1/v + 1/u.

The correct answer is Hydroxyl group.

Key Points

• Ethanol is miscible with water due to the presence of a hydroxyl group (-OH), which can form hydrogen bonds with water molecules.
• The hydroxyl group is a polar functional group, meaning it has a partial positive charge on hydrogen and a partial negative charge on oxygen, enabling it to interact with the polar water molecules.
• This hydrogen bonding is responsible for the high solubility of ethanol in water, as the intermolecular forces between ethanol and water molecules are strong enough to overcome the forces within each substance.
• The carbon chain in ethanol is relatively short, which further facilitates its miscibility. Longer carbon chains tend to reduce solubility in water due to increased hydrophobic characteristics.
• Ethanol's chemical structure (C₂H₅OH) includes both a non-polar carbon chain and a polar hydroxyl group. The hydroxyl group dominates, making ethanol hydrophilic and miscible with water.

Additional Information

• Hydroxyl Group (-OH):
• It is a functional group consisting of an oxygen atom bonded to a hydrogen atom.
• The oxygen atom in the hydroxyl group is highly electronegative, which makes the bond polar.
• The polarity of the hydroxyl group allows it to form hydrogen bonds, which are critical for the solubility of alcohols like ethanol in water.
• Hydrogen Bonding:
• Hydrogen bonding occurs when a hydrogen atom covalently bonded to a highly electronegative atom (like oxygen, nitrogen, or fluorine) interacts with another electronegative atom.
• This bonding is responsible for the miscibility of ethanol in water, as the hydroxyl group in ethanol forms bonds with water molecules.
• Solubility of Alcohols:
• Alcohols with shorter carbon chains are more soluble in water due to the dominance of the hydroxyl group's hydrophilic nature.
• As the length of the carbon chain increases, the hydrophobic nature of the carbon chain begins to dominate, reducing solubility.
• Ethanol, with only two carbon atoms, is highly miscible with water.
• Other Functional Groups:
• Carbon chain: Non-polar and hydrophobic, does not contribute to ethanol's miscibility with water.
• Double bonds: Found in alkenes, they do not directly influence solubility in water as they are non-polar.
• Carboxyl group (-COOH): Found in carboxylic acids, it also contributes to solubility in water but is not present in ethanol.

Important Points

• Ethanol's Applications:
• Used as a solvent in industries due to its miscibility with both water and many organic compounds.
• Acts as a fuel or fuel additive in vehicles (e.g., ethanol-blended petrol).
• Used in alcoholic beverages due to its ability to dissolve in water and provide desired properties.
• Miscibility Principle:
• “Like dissolves like” is a fundamental principle of solubility. Polar substances like ethanol are miscible with polar solvents like water.

The correct answer is The individual substances retain their properties.

Key Points

• A heterogeneous mixture is a type of mixture in which the individual components are not uniformly distributed, and they retain their distinct properties. Hence, the statement is correct.
• The substances in a heterogeneous mixture can usually be identified visually, as the mixture consists of physically distinct components. For example, a salad or a mixture of sand and iron filings. This supports the correctness of the option.
• Unlike compounds, the components in a heterogeneous mixture do not combine chemically but rather remain physically separate. This means each component retains its individual characteristics, such as taste, color, and texture. This reinforces the correct answer.
• The components of a heterogeneous mixture can often be separated by simple physical methods, such as filtration, decantation, or sieving. Thus, the statement "components cannot be separated" is incorrect.
• The composition of a heterogeneous mixture is not uniform throughout. For instance, in a mixture of oil and water, the oil forms a distinct layer above the water due to differences in density. Hence, the statement "composition is the same throughout" is incorrect.

Additional Information

• Heterogeneous Mixture:
• A heterogeneous mixture consists of two or more substances that are not uniformly distributed. Examples include mixtures like sand and salt, oil and water, or granite.
• Heterogeneous mixtures are classified into two categories: suspensions (e.g., muddy water) and colloids (e.g., milk).
• The components of these mixtures can typically be separated by physical methods such as filtration, centrifugation, or magnetic separation.
• Unlike homogeneous mixtures (e.g., salt dissolved in water), the properties of heterogeneous mixtures vary throughout the mixture.
• Comparison with Compounds:
• In a compound, elements combine chemically in a fixed ratio, forming a substance with new properties. For example, water (H₂O) is a compound where hydrogen and oxygen chemically bond.
• In contrast, a heterogeneous mixture retains the original properties of its components, as there is no chemical bonding involved.
• Separation Techniques:
• Filtration: Used to separate insoluble solids from liquids (e.g., sand from water).
• Decantation: Employed to separate liquids of different densities, such as oil from water.
• Sieving: Used to separate particles of different sizes, such as sand from gravel.
• Examples of Heterogeneous Mixtures:
• Concrete: A mixture of cement, sand, gravel, and water, where the components are visibly distinct.
• Trail Mix: A combination of nuts, raisins, and chocolate chips, where each component is easily identifiable.

Important Points

• Homogeneous vs. Heterogeneous Mixtures:
• Homogeneous mixtures have a uniform composition throughout, such as saltwater or air.
• Heterogeneous mixtures have visibly distinct components, such as salad or a mixture of sand and iron filings.
• Properties of Heterogeneous Mixtures:
• They do not have a fixed composition.
• Each component retains its physical properties.
• The mixture can often be separated into its original components using physical methods.

The correct answer is It promotes digestion by increasing blood flow to the stomach..

Key Points

• Adrenaline, also known as epinephrine, is a hormone secreted by the adrenal glands during stress or emergency situations. It plays a key role in the body's "fight or flight" response.
• Adrenaline reduces blood supply to the digestive system and redirects it to essential areas like the skeletal muscles, brain, and heart, preparing the body for action. Hence, statement 1 is correct.
• It does not promote digestion. Instead, it suppresses digestive activities by reducing blood flow to the stomach and intestines, conserving energy for more critical functions. Hence, statement 2 is incorrect.
• Adrenaline increases heart rate and breathing rate, ensuring a higher oxygen supply to muscles and other vital organs during stress. Hence, statement 3 is correct.
• It triggers the "fight or flight" response, enabling the body to respond swiftly to emergencies by increasing energy availability, sharpening focus, and enhancing physical performance. Hence, statement 4 is correct.
• This hormone's actions are crucial for responding to acute stress but can have detrimental effects if released excessively over long periods.

Additional Information

• Functions of Adrenaline:
• Adrenaline increases blood glucose levels by stimulating glycogen breakdown in the liver and muscles, providing energy for immediate use.
• It dilates the airways in the lungs, improving oxygen intake and making breathing easier during stress.
• It causes vasoconstriction in certain areas, such as the skin and digestive system, and vasodilation in others, such as the muscles, to optimize blood flow.
• Adrenal Glands:
• Adrenal glands are small, triangular organs located on top of each kidney.
• They are divided into two parts: the adrenal cortex (outer part) and the adrenal medulla (inner part).
• The adrenal medulla produces adrenaline and noradrenaline, which are crucial in stress responses.
• Fight or Flight Response:
• This is an automatic physiological reaction to a perceived threat or danger.
• It involves the release of adrenaline, which prepares the body to either confront the threat (fight) or escape from it (flight).
• Key effects include increased heart rate, pupil dilation, elevated glucose levels, and suppressed non-essential functions like digestion.
• Health Implications of Excess Adrenaline:
• Prolonged stress or excessive adrenaline release can lead to health issues like hypertension, anxiety, insomnia, and cardiovascular problems.
• Chronic stress can also suppress the immune system and impair digestion.
• Examples of Adrenaline Use in Medicine:
• Adrenaline is used in emergency treatments, such as anaphylaxis (severe allergic reactions) and cardiac arrest.
• It is administered via injection to rapidly counteract life-threatening conditions.

Important Points

• Adrenaline vs. Noradrenaline:
• Both are stress hormones, but their effects differ slightly.
• Adrenaline has a more significant impact on the "fight or flight" response, while noradrenaline primarily acts as a neurotransmitter and regulates blood pressure.
• Historical Discovery:
• Adrenaline was first isolated in 1901 by Jokichi Takamine, a Japanese chemist.
• Its discovery revolutionized the understanding of stress responses and led to the development of life-saving drugs.
• Applications in Sports:
• Adrenaline enhances physical performance by boosting energy and focus.
• However, excessive reliance on adrenaline during high-pressure situations can lead to burnout or stress-related injuries.

The correct answer is Introducing pest predators.

Key Points

• Biological method of crop protection involves the use of natural organisms or their products to control pests and diseases in agriculture. Introducing pest predators is a key example of this approach.
• Predators such as ladybirds (Coccinellidae), spiders, and lacewings are used to control populations of pests like aphids and mites, which harm crops.
• This method is environmentally friendly as it reduces the reliance on chemical pesticides, which can cause soil and water pollution.
• Biological pest control is a part of Integrated Pest Management (IPM), which combines biological, cultural, and mechanical techniques for sustainable crop protection.
• Unlike chemical methods like spraying DDT or burning residues, the use of pest predators ensures a natural balance in the ecosystem, promoting biodiversity and long-term agricultural sustainability.

Additional Information

• Option 1: Spraying DDT
• DDT (Dichlorodiphenyltrichloroethane) is a synthetic chemical pesticide used to kill pests but has severe environmental and health impacts.
• Its excessive use leads to soil contamination, bioaccumulation in food chains, and harm to non-target organisms like birds and aquatic life.
• DDT is not a biological method and is discouraged due to its long-term adverse effects.
• Option 2: Burning crop residues
• This method is not biological and is primarily employed to clear fields of leftover plant material after harvest.
• Burning crop residues releases carbon dioxide (CO2) and other harmful gases into the atmosphere, contributing to air pollution and global warming.
• Option 3: Introducing pest predators
• This is a biological control method that involves introducing natural enemies of pests, such as predators, parasitoids, or pathogens.
• Examples include releasing Trichogramma wasps to control caterpillar populations and using Bt (Bacillus thuringiensis) to target insect larvae.
• It is a sustainable and eco-friendly approach that minimizes environmental harm.
• Option 4: Ploughing
• Ploughing is a mechanical method used to prepare the soil for sowing and to bury weeds or crop residues. It is not considered a biological method.
• While ploughing can disrupt pest habitats, it is not a direct method of biological pest control.

Important Points

• Advantages of biological pest control:
• Minimizes environmental pollution and reduces the use of harmful chemicals.
• Maintains ecological balance by promoting biodiversity.
• Cost-effective in the long term as natural predators multiply and sustain themselves.
• Challenges:
• Requires careful selection of predators to avoid harm to non-target species.
• May take longer to show results compared to chemical pesticides.
• Effectiveness can depend on environmental factors like temperature and habitat availability.
• Examples of biological pest control:
• Using beetles to control water hyacinth in aquatic systems.
• Releasing parasitic wasps to target crop-damaging pests in fields.

Shortcut Trick

Use the direct relation between Cost Price (CP) and Marked Price (MP):

CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%)

CP ÷ 5360 = (100 − 8) ÷ (100 + 34) = 92 ÷ 134

CP = 5360 × (92 ÷ 134) = 40 × 92 = ₹3,680

∴ The correct answer is ₹3,680.

Alternate Method

Given:

Marked Price (MP) = ₹5,360

Discount = 8%

Profit = 34%

Calculations:

⇒ Selling Price (SP) = MP × (100 − Discount%) ÷ 100

⇒ SP = 5360 × (92 ÷ 100) = ₹4,931.2

⇒ Cost Price (CP) = [SP ÷ (100 + Profit%)] × 100

⇒ CP = [4931.2 ÷ 134] × 100

⇒ CP = 36.8 × 100 = ₹3,680

∴ The correct answer is ₹3,680.

Additional Information

Markup Percentage

It is the percentage by which the cost price is increased to set the marked price. Markup% = [(MP − CP) ÷ CP] × 100.

Successive Discounts

If two successive discounts of a% and b% are given, the effective discount is (a + b − ab/100)%.

Relation between CP and MP

The ratio CP : MP is always (100 − D%) : (100 + P%) where D is discount and P is profit percentage.

Shortcut Trick

In any quadrilateral, the angle formed by the bisectors of two adjacent angles is equal to half the sum of the other two angles.

∠STR = (∠P + ∠Q) ÷ 2

⇒ ∠P + ∠Q = 2 × ∠STR = 2 × 24° = 48°

Given the ratio of ∠P : ∠Q = 3 : 5, the total parts = 3 + 5 = 8 parts.

The difference between ∠Q and ∠P = 5 − 3 = 2 parts.

⇒ Difference = (2 ÷ 8) × 48° = 12°.

∴ The correct answer is 12°.

Alternate Method

Given:

⇒ In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at point T.

⇒ ∠STR = 24°

⇒ Ratio of ∠P : ∠Q = 3 : 5

Calculations:

In triangle STR, the sum of angles is 180°:

⇒ ∠STR + ∠TSR + ∠TRS = 180°

Since ST and RT are the angle bisectors of ∠S and ∠R respectively:

⇒ ∠TSR = ∠S ÷ 2

⇒ ∠TRS = ∠R ÷ 2

Substitute these into the triangle angle sum equation:

⇒ 24° + (∠S ÷ 2) + (∠R ÷ 2) = 180°

⇒ (∠S + ∠R) ÷ 2 = 180° − 24°

⇒ (∠S + ∠R) ÷ 2 = 156°

⇒ ∠S + ∠R = 312°

In quadrilateral PQRS, the sum of all interior angles is 360°:

⇒ ∠P + ∠Q + ∠R + ∠S = 360°

⇒ ∠P + ∠Q + 312° = 360°

⇒ ∠P + ∠Q = 360° − 312°

⇒ ∠P + ∠Q = 48°

Given that the ratio of ∠P to ∠Q is 3 : 5:

Let ∠P = 3x and ∠Q = 5x

⇒ 3x + 5x = 48°

⇒ 8x = 48°

⇒ x = 6°

Now, find the difference between the measures of ∠Q and ∠P:

⇒ Difference = ∠Q − ∠P = 5x − 3x = 2x

⇒ Difference = 2 × 6° = 12°

∴ The correct answer is 12°.

Additional Information

Angle Bisector Theorem in Quadrilaterals

The angle formed by the bisectors of two adjacent angles of a quadrilateral is equal to half the sum of the remaining two angles: ∠STR = (∠P + ∠Q) ÷ 2.

Sum of Interior Angles of a Polygon

The sum of the interior angles of any n-sided polygon is given by the formula (n − 2) × 180°. For a quadrilateral (n = 4), the sum is always 360°.

Opposite Angle Bisectors

If the bisectors of two opposite angles of a quadrilateral intersect, the angle between them is equal to half the difference of the other two opposite angles.

Shortcut Trick

CP_Manufacturer = 840 × (100/120) = ₹700

CP_Customer = 840 × (110/100) = ₹924

Difference = 924 − 700 = ₹224

∴ The correct answer is ₹224.

Alternate Method

Given:

Selling Price by Manufacturer = ₹840

Profit% of Manufacturer = 20%

Profit% of Shopkeeper = 10%

Calculations:

⇒ Cost Price to Manufacturer = 840 ÷ (1 + 20/100)

⇒ CP_M = 840 ÷ 1.2 = ₹700

⇒ Cost Price to Customer = Selling Price of Shopkeeper

⇒ CP_C = 840 × (1 + 10/100)

⇒ CP_C = 840 × 1.1 = ₹924

⇒ Required Difference = CP_C − CP_M

⇒ Difference = 924 − 700 = ₹224

∴ The correct answer is ₹224.

Additional Information

Successive Percentage Formula

When there are successive changes of a% and b%, the effective change is (a + b + ab/100)%.

Cost Price from Selling Price

CP = [SP × 100] / [100 + Profit%] or [SP × 100] / [100 − Loss%].

Marked Price and Discount

SP = MP × (1 − Discount/100). Profit is always calculated on CP unless stated otherwise.

Given:

999.99 + 99.99 + 9.99

Formula Used:

Direct addition of decimal numbers

Calculation:

⇒ 999.99 + 99.99 = 1099.98

⇒ 1099.98 + 9.99 = 1109.97

∴ The correct answer is 1109.97.

Given:

$(2^4)^3 \times (2^5)^2 \div 2^7$

Formula Used:

$(a^m)^n = a^{mn}$

$a^m \times a^n = a^{m+n}$

$a^m \div a^n = a^{m-n}$

Calculation:

$(2^4)^3 \times (2^5)^2 \div 2^7$

⇒ $2^{12} \times 2^{10} \div 2^7$

⇒ $2^{12+10-7}$

⇒ $2^{15}$

∴ The correct answer is $2^{15}$.

Shortcut Trick

Ratio of profit = Ratio of investments

Aakash : Suman : Raj = 1720 : 1690 : 1240 = 172 : 169 : 124

Total units = 172 + 169 + 124 = 465 units

Raj's share = (124 ÷ 465) × 1440 = 384

∴ The correct answer is ₹384.

Alternate Method

Given:

Investment of Aakash (C_A) = ₹1720

Investment of Suman (C_S) = ₹1690

Investment of Raj (C_R) = ₹1240

Total Profit = ₹1440

Formula Used:

Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂)

Calculations:

⇒ Since time is same for all, Profit Ratio = 1720 : 1690 : 1240

⇒ Profit Ratio = 172 : 169 : 124

⇒ Total Ratio sum = 172 + 169 + 124 = 465

⇒ Raj's Profit Share = (124 / 465) × 1440

⇒ Raj's Profit Share = 124 × (1440 / 465) = 124 × 3.0967... ≈ 384

⇒ Raj's Profit Share = ₹384

∴ The correct answer is ₹384.

Additional Information

Partnership Profit Distribution

When investment periods are equal, the profit is divided in the ratio of the capitals invested by the partners.

Compound Partnership

If partners invest for different time periods, Profit Ratio = (C₁ × T₁) : (C₂ × T₂) : (C₃ × T₃).

Active vs Sleeping Partner

An active partner may receive an additional salary or percentage of profit before the remaining profit is shared among all partners.

Shortcut Trick

Time from A to B = 150 ÷ 60 = 2.5 hours.

Total Time = 7.5 hours (7 hours 30 min).

Return Time = 7.5 − 2.5 = 5 hours.

Return Speed = 150 ÷ 5 = 30 km/hr.

∴ The correct answer is 30 km/hr.

Alternate Method

Given:

Distance (D) = 150 km

Forward Speed (S₁) = 60 km/hr

Total Time (T_total) = 7 hours 30 min = 7.5 hours

Formula Used:

Time = Distance ÷ Speed

Calculations:

⇒ Time taken from A to B (T₁) = 150 ÷ 60

⇒ T₁ = 2.5 hours

⇒ Time taken for return trip (T₂) = T_total − T₁

⇒ T₂ = 7.5 − 2.5 = 5 hours

⇒ Return Speed (S₂) = Distance ÷ T₂

⇒ S₂ = 150 ÷ 5

⇒ S₂ = 30 km/hr

∴ The correct answer is 30 km/hr.

Additional Information

Average Speed for Round Trip

When distances are equal, Average Speed = (2 × S₁ × S₂) ÷ (S₁ + S₂).

Time-Speed Inversely Proportional

For a constant distance, the ratio of speeds is the inverse of the ratio of times (S₁/S₂ = T₂/T₁).

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Shortcut Trick

Convert fractions to decimals for quick comparison.

1/20 = 0.05

10/100 = 1/10 = 0.1

Percentage = (0.05 ÷ 0.1) × 100 = 50%

∴ The correct answer is 50%.

Alternate Method

Given: First value = 1/20, Second value = 10/100

Formula Used: Percentage = (Part ÷ Whole) × 100

⇒ Required % = [(1/20) ÷ (10/100)] × 100

⇒ Required % = [(1/20) ÷ (1/10)] × 100

⇒ Required % = (1/20 × 10/1) × 100

⇒ Required % = (10/20) × 100

⇒ Required % = (1/2) × 100

⇒ Required % = 50%

∴ The correct answer is 50%.

Additional Information

Percentage Change

Percentage change is calculated as [(New Value − Old Value) ÷ Old Value] × 100.

Fraction to Percentage

To convert any fraction x/y into percentage, multiply it by 100 and add the % sign.

Decimal Conversion

Moving the decimal point two places to the right converts a decimal to a percentage (e.g., 0.5 → 50%).

Shortcut Trick

Investment ratio is equal to the profit ratio when time is constant.

Total Profit = ₹6,700 | Prakhar's Profit = ₹2,000 | Riya's Profit = ₹4,700.

Prakhar's Investment = (Prakhar's Profit ÷ Total Profit) × Total Investment

Prakhar's Investment = (2,000 ÷ 6,700) × 33,500 = 20 ÷ 67 × 33,500 = 20 × 500 = ₹10,000.

∴ The correct answer is ₹10,000.

Alternate Method

Given:

Total Investment = ₹33,500

Total Profit = ₹6,700

Prakhar's Profit Share = ₹2,000

Formula: Profit Ratio = Investment Ratio (for same time period)

⇒ Riya's Profit = Total Profit − Prakhar's Profit

⇒ Riya's Profit = 6,700 − 2,000 = ₹4,700

⇒ Ratio of Profits (Prakhar : Riya) = 2,000 : 4,700 = 20 : 47

⇒ Sum of ratio parts = 20 + 47 = 67 units

⇒ 67 units = ₹33,500

⇒ 1 unit = 33,500 ÷ 67 = ₹500

⇒ Prakhar's Investment = 20 units = 20 × 500 = ₹10,000

∴ The correct answer is ₹10,000.

Additional Information

Partnership Basic Law

Profit is distributed in the ratio of the product of Capital and Time: P₁:P₂ = C₁×T₁ : C₂×T₂.

Active vs Sleeping Partner

An active partner may receive a salary or fixed percentage of profit before the remaining profit is divided based on investment ratios.

Constant Time Case

If all partners invest for the same duration, the Profit Ratio is directly proportional to the Investment Ratio (P₁:P₂ = C₁:C₂).

Shortcut Trick

Ratio of Father : Ravi presently is 4 : 1 (Difference = 3 units).

After 5 years, ratio becomes 3 : 1 (Difference = 2 units).

Equalize differences: Present (8 : 2) and After 5 years (9 : 3).

Ratio increase of 1 unit = 5 years.

Ravi present age = 2 units × 5 = 10 years.

∴ The correct answer is 10 years.

Alternate Method

Given: Present age ratio 4:1, Age after 5 years ratio 3:1.

Formula Used: Age Equation Method.

⇒ Let Ravi’s present age be x years.

⇒ Father’s present age = 4x years.

⇒ According to the condition: (4x + 5) = 3(x + 5)

⇒ 4x + 5 = 3x + 15

⇒ 4x − 3x = 15 − 5

⇒ x = 10

∴ The correct answer is 10 years.

Additional Information

Ratio Difference Constant

In age problems, the absolute difference between two people's ages remains constant over any number of years.

Linear Equations in Ages

Most age problems can be solved by setting up a linear equation: Age_future = Age_present + n years.

Shortcut Trick

Net efficiency of filling the tank = 4 − 1 = 3 units/minute.

Time to fill the whole tank = 12 ÷ 3 = 4 minutes.

Time to fill one-fourth of the tank = 4 × (1/4) = 1 minute.

∴ The correct answer is 1 minute.

Alternate Method

Given:

Time taken by the first pipe to fill the tank = 3 minutes

Time taken by the second pipe to empty the tank = 12 minutes

Formula Used:

Total Work = LCM of individual times

Efficiency = Total Work ÷ Time

Calculations:

⇒ Net efficiency of both pipes combined = 4 − 1 = 3 units/minute

⇒ One-fourth of the total capacity of the tank = 12 ÷ 4 = 3 units

⇒ Time required to fill one-fourth of the tank = 3 units ÷ 3 units/minute = 1 minute

∴ The correct answer is 1 minute.

Additional Information

Inlet and Outlet Pipes

An inlet pipe fills a tank (positive work/efficiency), while an outlet pipe empties it (negative work/efficiency).

Combined Rate Formula

If an inlet pipe fills a tank in x hours and an outlet pipe empties it in y hours, the net rate of work when both are open is (1/x − 1/y) per hour.

Shortcut Trick

Ratio of LCM : HCF is given as 4 : 1.

Sum of ratios → 4 + 1 = 5 units.

5 units = 140 ⇒ 1 unit (HCF) = 28.

LCM = 4 × 28 = 112.

Since Product of numbers = LCM × HCF, and one number is 112, the other must be the HCF.

∴ The correct answer is 28.

Alternate Method

Given:

LCM = 4 × HCF

LCM + HCF = 140

First number (a) = 112

Formula Used:

Product of two numbers = LCM × HCF

Calculations:

⇒ Let HCF be x, then LCM = 4x

⇒ x + 4x = 140

⇒ 5x = 140

⇒ x = 28

⇒ HCF = 28 and LCM = 4 × 28 = 112

⇒ Let the second number be b

⇒ a × b = LCM × HCF

⇒ 112 × b = 112 × 28

⇒ b = 28

∴ The correct answer is 28.

Additional Information

Fundamental Property of HCF and LCM

For any two positive integers a and b, the product of the numbers is always equal to the product of their Greatest Common Divisor (HCF) and Least Common Multiple (LCM): a × b = HCF(a, b) × LCM(a, b).

HCF as a Factor

The HCF of two or more numbers is always a factor of their LCM. This means LCM ÷ HCF will always result in an integer.

Co-prime Numbers

If two numbers are co-prime, their HCF is 1 and their LCM is simply the product of the two numbers.

Shortcut Trick

Present ages: Thomas = 38, Nephew = 38 − 26 = 12 years.

Let n years pass. Condition: 38 + n = 3(12 + n) − 14.

Solve: 38 + n = 36 + 3n − 14 ⇒ 38 + n = 22 + 3n.

2n = 16 ⇒ n = 8 years.

∴ The correct answer is 8 years.

Alternate Method

Given:

Thomas's age = 38 years.

Nephew's age = 38 − 26 = 12 years.

Calculations:

Let the required number of years be x.

⇒ Age of Thomas after x years = 38 + x.

⇒ Age of nephew after x years = 12 + x.

According to the question:

⇒ 38 + x = 3 × (12 + x) − 14

⇒ 38 + x = 36 + 3x − 14

⇒ 38 + x = 22 + 3x

⇒ 3x − x = 38 − 22

⇒ 2x = 16

⇒ x = 8 years.

∴ The correct answer is 8 years.

Additional Information

Constant Age Difference

The difference between the ages of two persons remains constant regardless of how many years pass.

Linear Equations in Ages

Most age problems can be solved by representing unknown years as 'x' and forming a linear equation based on the given ratio or comparison.

Verification Method

In multiple-choice exams, plugging in options into the final condition is often faster than solving the algebraic equation.

Shortcut Trick

If 20% of a number is added to 84 to get the same number (100%), then 84 represents the remaining 80%.

80% → 84

1% → 84 ÷ 80 = 1.05

65% → 1.05 × 65 = 68.25

∴ The correct answer is 68.25.

Alternate Method

Given: 20% of x + 84 = x

⇒ Let the number be x.

⇒ 0.20x + 84 = x

⇒ x − 0.20x = 84

⇒ 0.80x = 84

⇒ x = 84 ÷ 0.80 = 105

⇒ Required value = 65% of 105

⇒ Required value = (65 ÷ 100) × 105 = 0.65 × 105

⇒ Required value = 68.25

∴ The correct answer is 68.25.

Additional Information

Percentage Base Change

When a part (P%) of a value is removed, the remaining part is (100 − P)%. Here, 100% − 20% = 80%.

Fraction Equivalents

20% = 1/5 and 80% = 4/5. Using fractions: 4/5 of x = 84 ⇒ x = 105.

Percentage to Decimal

To convert a percentage to a decimal, divide by 100. Example: 65% = 65/100 = 0.65.

Shortcut Trick

If the value of a + 1/a = k, then the value of a² + 1/a² = k² − 2.

Given: k = 12

Applying the trick: 12² − 2 = 144 − 2 = 142.

∴ The correct answer is 142.

Alternate Method

Given: a + 1/a = 12

Formula Used: (x + y)² = x² + y² + 2xy

⇒ a + 1/a = 12

Squaring both sides:

⇒ (a + 1/a)² = (12)²

⇒ a² + (1/a)² + 2 × a × (1/a) = 144

⇒ a² + 1/a² + 2 = 144

⇒ a² + 1/a² = 144 − 2

⇒ a² + 1/a² = 142

∴ The correct answer is 142.

Additional Information

Algebraic Identity for Squares

The square of a binomial sum is given by (x + y)² = x² + y² + 2xy.

Reciprocal Square Relation (Minus Sign)

If a − 1/a = k, then the value of a² + 1/a² = k² + 2.

Sum of Cubes Shortcut

If a + 1/a = k, then the value of a³ + 1/a³ = k³ − 3k.

Product of Reciprocals

The product of a variable and its reciprocal (a × 1/a) is always equal to 1.

Shortcut Trick

Given cos α = 5/13. In a Pythagorean triplet (5, 12, 13), Base = 5, Perpendicular = 12, Hypotenuse = 13.

sec α = Hypotenuse / Base = 13/5.

tan α = Perpendicular / Base = 12/5.

sec α − tan α = 13/5 − 12/5 = 1/5.

∴ The correct answer is 1/5.

Alternate Method

Given: cos α = 5/13

Formula Used: sin²α + cos²α = 1 | sec α = 1/cos α | tan α = sin α / cos α

⇒ sin α = √(1 − cos²α)

⇒ sin α = √(1 − (5/13)²) = √(1 − 25/169) = √(144/169) = 12/13

⇒ sec α = 1 / (5/13) = 13/5

⇒ tan α = (12/13) / (5/13) = 12/5

⇒ sec α − tan α = 13/5 − 12/5 = 1/5

∴ The correct answer is 1/5.

Additional Information

Trigonometric Identity

sec²α − tan²α = 1, which implies (sec α − tan α)(sec α + tan α) = 1.

Reciprocal Relationship

If sec α + tan α = x, then sec α − tan α = 1/x.

Pythagorean Triplets

Common triplets used in exams include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Shortcut Trick

The ratio of Volume to Curved Surface Area of a cylinder is r/2.

r/2 = 1848 ÷ 528 = 3.5 ⇒ Radius (r) = 7 m.

Total Surface Area = Curved Surface Area + 2 × Base Area

TSA = 528 + 2 × (22/7 × 7 × 7) = 528 + 308 = 836 m².

∴ The correct answer is 836 m².

Alternate Method

Given:

Curved Surface Area (CSA) = 528 m²

Volume (V) = 1848 m³

Formula Used:

CSA = 2 × π × r × h

Volume = π × r² × h

Total Surface Area (TSA) = 2 × π × r × (r + h) = CSA + 2 × π × r²

Calculations:

⇒ V / CSA = (π × r² × h) / (2 × π × r × h) = r / 2

⇒ 1848 / 528 = r / 2

⇒ 3.5 = r / 2

⇒ r = 7 m

⇒ Base Area (πr²) = 22/7 × 7 × 7 = 154 m²

⇒ TSA = CSA + 2 × (Base Area)

⇒ TSA = 528 + 2 × 154

⇒ TSA = 528 + 308

⇒ TSA = 836 m²

∴ The correct answer is 836 m².

Additional Information

Curved Surface Area of Cylinder

It is the area of only the side surface, calculated as 2πrh.

Total Surface Area of Cylinder

It includes the curved surface and the areas of the two circular bases: 2πrh + 2πr².

Volume of Cylinder

The space occupied by the cylinder is given by the formula πr²h.

Relation between Volume and CSA

Volume = (CSA × r) ÷ 2, which allows finding the radius if V and CSA are known.

Shortcut Trick Scheme A: Discount % = (Free ÷ Total) × 100 ⇒ (6 ÷ 11) × 100 ≈ 54.54%. Scheme B: Single discount = 82%. Scheme C: Successive discounts 11% and 24% ≈ 11 + 24 − (11 × 24)/100 ≈ 32.36%. Comparing the values: 32.36% (C) < 54.54% (A) < 82% (B). ∴ The correct answer is C, A, B.

Alternate Method

Given: Scheme A: Buy 5 get 6 free. Scheme B: 82% discount. Scheme C: Successive 11% and 24%. Calculations: ⇒ Discount A = (Free items / Total items) × 100 ⇒ Discount A = (6 / (5 + 6)) × 100 = 600 / 11 = 54.54% ⇒ Discount B = 82% ⇒ Discount C = [x + y − (xy/100)]% ⇒ Discount C = 11 + 24 − (11 × 24 / 100) = 35 − 2.64 = 32.36% ⇒ Arranging in Ascending Order: 32.36% < 54.54% < 82% ∴ The correct answer is C, A, B.

Additional Information Buy X Get Y Free The effective discount percentage is calculated as [Y / (X + Y)] × 100. Always use the total quantity in the denominator. Successive Discounts For two successive discounts a% and b%, the equivalent single discount is given by the formula (a + b − ab/100)%. Marked Price and Selling Price Selling Price (SP) = Marked Price (MP) × (100 − Discount%)/100. Discount is always calculated on the Marked Price.

Shortcut Trick

Ratio of Males to Females = 58% : 42% = 29 : 21.

Assume base average = 72 kg.

Net deviation for males = 29 × (82 − 72) = +290.

Average increase = 290 ÷ (29 + 21) = 290 ÷ 50 = 5.8 kg.

Final Average Weight = 72 + 5.8 = 77.8 kg.

∴ The correct answer is 77.8 kg.

Alternate Method

Given: Total players = 150, Male percentage = 58%, Male avg weight = 82 kg, Female avg weight = 72 kg.

⇒ Number of male players = 58% of 150 = 0.58 × 150 = 87

⇒ Number of female players = 150 − 87 = 63

⇒ Total weight of males = 87 × 82 = 7134 kg

⇒ Total weight of females = 63 × 72 = 4536 kg

⇒ Total weight of all players = 7134 + 4536 = 11670 kg

⇒ Average weight of the group = 11670 ÷ 150 = 77.8 kg

∴ The correct answer is 77.8 kg.

Additional Information

Weighted Average Formula

The weighted average is calculated as (n₁w₁ + n₂w₂) ÷ (n₁ + n₂), where n represents the quantity and w represents the weight/value.

Deviation Method

To simplify calculations, assume a base value (usually the smaller average) and distribute the total excess or deficit over the entire group size.

Ratio Principle in Averages

When calculating average weights or scores, the actual number of people is not required if the percentage distribution or ratio is known.

Shortcut Trick

Let Appeared students from School X be 100.

Qualified from X = 80% of 100 = 80.

Appeared from Y = 100 + 15% = 115.

Qualified from Y = 80 + 30% of 80 = 80 + 24 = 104.

Required % for Y = (104 ÷ 115) × 100 ≈ 90.4%.

∴ The correct answer is 90.4%.

Alternate Method

Given:

⇒ Qualified % X = 80%

⇒ Appeared Y = Appeared X × (115/100)

⇒ Qualified Y = Qualified X × (130/100)

Calculations:

⇒ Let Appeared X = 100

⇒ Qualified X = 0.80 × 100 = 80

⇒ Appeared Y = 100 × 1.15 = 115

⇒ Qualified Y = 80 × 1.30 = 104

⇒ Required % = (Qualified Y ÷ Appeared Y) × 100

⇒ Required % = (104 ÷ 115) × 100

⇒ Required % = 90.434...

∴ The correct answer is 90.4%.

Additional Information

Percentage Increase

To increase a value by x%, multiply the original value by (1 + x/100).

Successive Percentage

When a value changes by a% and then b%, the net change is [a + b + (ab/100)]%.

Rounding Off Rules

If the digit after the decimal is 5 or more, round up; otherwise, keep the digit as is.

Shortcut Trick

Time = (Volume of Rectangular Tank) ÷ (Volume flow per hour through Cylindrical Pipe)

Volume of Tank = 50 × 44 × 0.21 = 462 m³

Volume flow per hour = (22/7) × (0.07)² × 15000 = 231 m³

Time = 462 ÷ 231 = 2 hr

∴ The correct answer is 2 hr.

Alternate Method

Given:

Diameter of pipe = 14 cm ⇒ Radius (r) = 7 cm = 0.07 m

Speed of water (v) = 15 km/hr = 15,000 m/hr

Dimensions of tank: Length (L) = 50 m, Width (W) = 44 m

Required rise in Water Level (h) = 21 cm = 0.21 m

Calculations:

⇒ Volume of water needed in the tank = L × W × h

⇒ Volume = 50 × 44 × 0.21 = 462 m³

⇒ Area of cross-section of the pipe = πr² = (22/7) × 0.07 × 0.07

⇒ Area = (22/7) × 0.0049 = 0.0154 m²

⇒ Volume of water flowing through the pipe in 1 hour = Area × Speed

⇒ Volume per hr = 0.0154 × 15,000 = 231 m³/hr

⇒ Time required = (Total Volume needed) ÷ (Volume per hr)

⇒ Time = 462 ÷ 231 = 2 hours

∴ The correct answer is 2 hr.

Additional Information

Volume of Cylinder

The volume of a cylindrical pipe is calculated as V = πr²h, where r is the radius and h is the length of water column (distance covered by speed).

Volume of Cuboid

The volume of a rectangular tank is V = length × width × height.

Unit Conversion

Always ensure all units are consistent: 1 km = 1000 m and 1 m = 100 cm.

Rate of Flow

Rate of flow = Area of cross-section × velocity of fluid flow.

Shortcut Trick

Apply the Man-Days formula: M₁D₁ = M₂D₂.

Initial men = X, Initial days = 28.

Final men = X − 5, Final days = 30.

28X = 30(X − 5) ⇒ 28X = 30X − 150 ⇒ 2X = 150.

X = 75.

∴ The correct answer is 75 people.

Alternate Method

Given: Initial people = X, Initial time = 28 days, Absent people = 5, Final time = 30 days.

Formula Used: Total Work = Number of People × Number of Days.

⇒ Total Work = X × 28

⇒ Total Work = (X − 5) × 30

⇒ 28X = 30X − 150

⇒ 30X − 28X = 150

⇒ 2X = 150

⇒ X = 150 ÷ 2

⇒ X = 75

∴ The correct answer is 75 people.

Additional Information

Chain Rule Formula

The general formula for work is (M₁×D₁×H₁)/W₁ = (M₂×D₂×H₂)/W₂ where M is men, D is days, H is hours, and W is work.

Inverse Proportion

When work is constant, the number of people is inversely proportional to the time taken (M ∝ 1/D).

Efficiency and Time

If efficiency increases, the time required to complete the same work decreases proportionally.

Shortcut Trick

The increase in interest is due to the 3% higher rate per annum for 4 years.

Total percentage increase in interest = 3% × 4 = 12%

According to the question, this 12% increase is equal to ₹960.

⇒ 12% of Principal = ₹960

⇒ 100% of Principal = (960 ÷ 12) × 100 = ₹8,000

∴ The correct answer is ₹8,000.

Alternate Method

Given:

Time (T) = 4 years

Increase in rate of interest (R_diff) = 3% per annum

Increase in Simple Interest (I_diff) = ₹960

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Difference in Simple Interest (I_diff) = (P × R_diff × T) ÷ 100

Calculations:

⇒ 960 = (P × 3 × 4) ÷ 100

⇒ 960 = (P × 12) ÷ 100

⇒ P × 12 = 960 × 100

⇒ P = 96000 ÷ 12

⇒ P = 8,000

Thus, the principal sum is ₹8,000.

Verification of Options:

Option (1) ₹7,500: Extra interest = (7500 × 3 × 4) ÷ 100 = ₹900 (Incorrect)

Option (2) ₹7,800: Extra interest = (7800 × 3 × 4) ÷ 100 = ₹936 (Incorrect)

Option (3) ₹8,300: Extra interest = (8300 × 3 × 4) ÷ 100 = ₹996 (Incorrect)

Option (4) ₹8,000: Extra interest = (8000 × 3 × 4) ÷ 100 = ₹960 (Correct)

∴ The correct answer is ₹8,000.

Additional Information

Simple Interest Formula

SI = (P × R × T) ÷ 100, where P is the principal, R is the rate of interest per annum, and T is the time in years.

Direct Proportionality of Interest

Simple Interest is directly proportional to the rate of interest and time. Thus, any change in rate (ΔR) leads to a direct change in interest (ΔI) given by ΔI = (P × ΔR × T) ÷ 100.

Compound Interest vs Simple Interest

For the first year, Simple Interest and Compound Interest are equal (when compounded annually). From the second year onwards, Compound Interest is higher due to interest being earned on interest.

Shortcut Trick

Teacher age = New Average + (Initial Count × Increase in Average)

Given: Initial students = 40, Initial average = 33, New average = 34

Increase in average = 34 − 33 = 1 year

Teacher age = 34 + (40 × 1) = 34 + 40 = 74 years

∴ The correct answer is 74 years.

Alternate Method

Given:

Number of students (n₁) = 40

Average age of students (A₁) = 33 years

Total number of people including teacher (n₂) = 40 + 1 = 41

New average age (A₂) = 34 years

Formula Used:

Total Age = Average × Number of persons

Calculations:

⇒ Total age of 40 students = 40 × 33 = 1320 years

⇒ Total age of 41 persons (including teacher) = 41 × 34

⇒ Total age of 41 persons = 1394 years

⇒ Teacher age = Total age (41) − Total age (40)

⇒ Teacher age = 1394 − 1320

⇒ Teacher age = 74 years

∴ The correct answer is 74 years.

Additional Information

Average Concept

The average is the sum of observations divided by the total number of observations: Average = Sum ÷ Number.

Inclusion/Exclusion Rule

When a new person joins, their value = (New Number of People × Change in Average) + Old Average.

Net Deviation Method

The sum of deviations from the average is always zero. If the average increases, the new entry must be higher than the previous average by (Count × Increase).

Shortcut Trick

Total distance = Speed × Time

Total distance = 59 m/sec × 9 sec = 531 m

X (Train length) = Total distance − Platform length

X = 531 − 279 = 252 m

∴ The correct answer is 252 m.

Alternate Method

Given:

Speed of train = 59 m/sec

Time taken to cross = 9 sec

Length of platform = 279 m

Length of train = X m

Formula Used:

Distance = Speed × Time

When a train crosses a platform, Total Distance = Length of Train + Length of Platform

Calculations:

⇒ Total Distance = (X + 279) m

⇒ Total Distance = Speed × Time

⇒ X + 279 = 59 × 9

⇒ X + 279 = 531

⇒ X = 531 − 279

⇒ X = 252 m

∴ The correct answer is 252 m.

Additional Information

Unit Conversion

To convert km/hr to m/sec, multiply by 5/18. To convert m/sec to km/hr, multiply by 18/5.

Crossing Stationary Objects

When crossing a point object (pole, man), distance = length of train. When crossing a platform/bridge, distance = length of train + length of object.

Relative Speed

In same direction, Relative Speed = S₁ − S₂. In opposite direction, Relative Speed = S₁ + S₂.

Preparing the family tree using the following symbols:

According to the given information,

The given expression is :

'P – Q * R + S ÷ T' → P is mother of Q, Q is sister of R, R is father of S and S is brother of T.

 

P is T's father's mother.

Hence, the correct answer is “Option 3”.

Series: 23, 40, 57, 74, 91, ?

Step 1: Difference check karo

40 − 23 = 17

57 − 40 = 17

74 − 57 = 17

91 − 74 = 17

Pattern: +17

Step 2: Next number

91 + 17 = 108

Hence, the correct answer is 108

Given:

Shantanu starts from Point A and drives 4 km towards the north.

He then takes a right turn and drives 5 km.

He then turns right and drives 7 km.

He then takes a right turn and drives 10 km.

He takes a final right turn, drives 3 km, and stops at Point P.

Hence, the correct answer is option 3

CLAW → 3948

FLAW → 9748

Common letters in both words: LAW

Common codes in both numbers: 948

So mapping:

L → 9

A → 4

W → 8

In FLAW = 9748, remaining number 7 corresponds to F.

Hence, the correct answer is 7.

Given:

B sits to the immediate left of F.

C sits second to the right of F.

E sits third to the left of B.

D sits to the immediate right of A.

Hence, the correct answer is option 3

ILL → LKN → OJP → RIR

Pattern:

First letters: I → L → O → R → U (+3 each time)

Second letters: L → K → J → I → H (−1 each time)

Third letters: L → N → P → R → T (+2 each time)

So the ne×t cluster is UHT.

Hence, the correct answer is UHT.

Series:

4 8 2 7 3 9 8 5 3 9 4 1 4 8 9 8 3 8 5 6 4 8 4 5 8 4 6

Condition: Odd – Even – Even

Valid cases:

1 4 8

5 6 4

5 8 4

Total such even numbers = 3

Hence, the correct answer is 3.

Given:

No one sits to the left of D → D is at the leftmost end 

Only four people sit between D and G → G is 5th from D

Only three people sit to the right of M → 7 seats total → M = 4.

L sits immediate left of E → L–E are consecutive with L on the left.

N is not an immediate neighbour of M → N

D — L — E — M — F — G — N

Hence, the correct answer is N

Logic:

1st word → last, first, third, second

2nd word → swap 1↔2 and 3↔4

Example check:

MANY → YMNA → MYAN

WING → GWNI → WGIN

Now check options:

UNIT

UNIT → TUIN (last, first, third, second)

TUIN → UTNI (swap 1↔2 and 3↔4)

Hence, the correct answer is Option 2: UNIT – TUIN – UTNI.

Operators interchange:

• ↔ −
  

× ↔ ÷

Equation becomes:

428 × 2 − 183 ÷ 3 + 127

Now solve (BODMAS):

428 × 2 = 856

183 ÷ 3 = 61

856 − 61 + 127 = 795 + 127 = 922

Hence, the correct answer is 922.

Series:

310, 320, 321, 331, 332, 342, ?

Pattern: +10, +1, +10, +1, +10

310 → 320 (+10)

320 → 321 (+1)

321 → 331 (+10)

331 → 332 (+1)

332 → 342 (+10)

Next:

342 → 343 (+1)

Hence, the correct answer is 343.

FIRE → 2739

RISE → 3978

Common letters: R, I, E

Common digits: 3, 7, 9

Matching positions:

R → 3

I → 7

E → 9

In RISE = 3978, remaining digit 8 corresponds to S.

Hence, the correct answer is 8.

Riddhima’s rank from top = 18

Riddhima’s rank from bottom = 43

Total students = 18 + 43 − 1 = 60

Hence, the correct answer is 60.

Statements:

All denims are trousers.

All trousers are shoes.

From this: Denims ⊆ Trousers ⊆ Shoes

Conclusion I: Some shoes are trousers

Since all trousers are shoes, at least some shoes must be trousers. ✔️ Follows

Conclusion II: All denims are shoes

Denims → Trousers → Shoes, so all denims are shoes. ✔️ Follows

Hence, both conclusions I and II follow.

Given:

Only I above C → I is directly above C 

Only L between C and J → C–L–J sequence 

Only K below D → D–K sequence 

B and I positions: B = 3, I = 7 → boxes between them = 3

Top

7. I
8. C
9. L
10. J
11. B
12. D
13. K

Bottom

Hence, the correct answer is 3

Statements:

All chalan are tax.

All chalan are rebate.

So, Chalan ⊆ Tax and Chalan ⊆ Rebate

Conclusion I: Some tax are rebate

Since all chalan are both tax and rebate, some tax must be rebate. ✔️ Follows

Conclusion II: All rebate are chalan

This cannot be concluded because rebate may contain elements other than chalan. ❌ Does not follow

Hence, only conclusion I follows.

Given:

Only two people sit to the right of X.

Only two people sit between X and C.

Only two people sit between A and D.

D sits to the immediate left of X.

B sits to the immediate right of Y.

A — C — W — D — X — Y — B

Hence, the correct answer is W

Given words:

TOK, THE, HAS, ALL, COW

Each letter is replaced by the next alphabet letter.

TOK → UPL (U is vowel)

THE → UIF (U, I are vowels)

HAS → IBT (I is vowel)

ALL → BMM (no vowel)

COW → DPX (no vowel)

Words with no vowel: BMM, DPX

Total = 2

Hence, the correct answer is 2.

Pairs:

DG–BE

JM–HL

HK–FJ

FI–DH

Pattern (alphabet position shift):

DG → BE

D → B (−2)

G → E (−2)

JM → HL

J → H (−2)

M → L (−1) ❌

HK → FJ

H → F (−2)

K → J (−1) ❌

FI → DH

F → D (−2)

I → H (−1) ❌

Group pattern: both letters decrease by 2.

Only DG → BE follows −2, −2 rule.

Hence, the correct answer is Option 1 (DG–BE).