RRB Group D Official Paper (Held On: 04 Dec, 2025 Shift 2) (Previous Year Paper)

The correct answer is The total mass of all atoms in one formula unit of a compound.

Key Points

• The term formula unit mass refers to the total mass of all the atoms in one formula unit of a compound. It is expressed in atomic mass units (amu).
• A formula unit represents the simplest ratio of ions in an ionic compound. For example, in NaCl, one formula unit consists of one sodium ion (Na⁺) and one chloride ion (Cl⁻).
• The formula unit mass is calculated by summing the atomic masses of all atoms present in the chemical formula of the compound. For instance, in NaCl, the formula unit mass = atomic mass of Na + atomic mass of Cl = 23 + 35.5 = 58.5 amu.
• The formula unit mass is particularly used for ionic compounds because these do not exist as discrete molecules but as a lattice structure. Hence, the term "formula unit" is used instead of "molecule."
• This concept is essential in stoichiometry, allowing chemists to calculate the mass relationships in chemical reactions involving ionic compounds.

Additional Information

• Atomic Mass:
• The mass of an individual atom is expressed in atomic mass units (amu). For example, the atomic mass of sodium (Na) is approximately 23 amu, and that of chlorine (Cl) is 35.5 amu.
• The atomic mass is determined relative to the mass of one atom of carbon-12, which is defined as exactly 12 amu.
• Formula Unit:
• A formula unit is the smallest repeating unit of an ionic compound that represents its composition. For example, the formula unit of magnesium chloride is MgCl₂.
• It differs from a molecule because ionic compounds do not form discrete molecular entities but rather exist as a lattice of ions.
• Difference Between Formula Unit Mass and Molecular Mass:
• Formula unit mass is used for ionic compounds (e.g., NaCl, MgCl₂) and is based on the simplest ratio of ions.
• Molecular mass applies to covalent compounds (e.g., H₂O, CO₂) and is the sum of the atomic masses of all atoms in a molecule.
• Applications of Formula Unit Mass:
• It helps in calculating molar mass, which is crucial for stoichiometric calculations in chemistry.
• It is used to determine the proportions of elements in ionic compounds and their chemical behavior.
• Examples:
• The formula unit mass of NaCl: 23 + 35.5 = 58.5 amu.
• The formula unit mass of MgCl₂: 24.3 + (2 × 35.5) = 95.3 amu.

Important Points

• Option 1: "The mass of one mole of a substance" refers to molar mass, not formula unit mass. This is incorrect.
• Option 2: "The mass of a single atom of an element" refers to atomic mass, not formula unit mass. This is incorrect.
• Option 3: "The mass of a single molecule of an element" pertains to molecular mass, which is different from formula unit mass. This is incorrect.
• Option 4: "The total mass of all atoms in one formula unit of a compound" is the correct definition of formula unit mass. This is correct.

The correct answer is +4.0 D.

Key Points

• The power of a lens is the ability of the lens to converge or diverge light rays passing through it. It is measured in dioptres (D).
• The formula to calculate the power of a lens is:
  

P = 100 / f, where P is the power in dioptres and f is the focal length in centimeters.

• In the given question, the focal length of the convex lens is 25 cm. Substituting this into the formula:
  

P = 100 / 25 = +4.0 D.

• A positive power (+) indicates that the lens is a convex lens, which converges light rays.
• Hence, the power of the convex lens is +4.0 D, and this is the correct answer.

Additional Information

• Convex Lens:
• A convex lens is also known as a converging lens because it brings parallel rays of light to a focus.
• It is thicker at the center and thinner at the edges.
• Convex lenses are commonly used in devices like magnifying glasses, cameras, and projectors.
• Dioptre:
• The dioptre (D) is the unit of measurement for the optical power of a lens or a curved mirror.
• It is defined as the reciprocal of the focal length in meters (D = 1/f), where f is in meters.
• A positive dioptre value indicates a converging lens (convex), while a negative value indicates a diverging lens (concave).
• Lens Power and Focal Length:
• The focal length (f) of a lens is the distance from the center of the lens to the point where light rays converge or diverge.
• The shorter the focal length, the higher the optical power of the lens.
• For example, a lens with a focal length of 50 cm has a power of +2.0 D, while a lens with a focal length of 25 cm has a power of +4.0 D.
• Applications of Convex Lenses:
• Convex lenses are used in eyeglasses to correct farsightedness (hyperopia).
• They are also used in microscopes and telescopes for magnification purposes.
• Other applications include their use in optical instruments, cameras, and focusing systems.

Important Points

• Power of Concave Lens:
• A concave lens is a diverging lens, and its power is represented by a negative value.
• For example, if the focal length of a concave lens is 50 cm, its power is -2.0 D.
• Difference Between Convex and Concave Lenses:
• Convex Lens: Converges light rays, has positive power, and is thicker at the center.
• Concave Lens: Diverges light rays, has negative power, and is thinner at the center.
• Real and Virtual Images:
• A convex lens can form both real and virtual images, depending on the position of the object.
• A concave lens, however, always forms a virtual image.

The correct answer is Apical meristem.

Key Points

• Apical meristem is a type of meristematic tissue found at the tips of roots and shoots in plants.
• It is responsible for the primary growth of plants, leading to an increase in height or length.
• The cells in the apical meristem are actively dividing and undifferentiated, enabling the elongation of stems and roots.
• Apical meristems give rise to three primary meristems: protoderm (epidermis), procambium (vascular tissues), and ground meristem (ground tissues).
• This tissue ensures that plants grow taller or deeper by adding new cells at the apex of the plant body.

Additional Information

• Secondary meristem:
• This type of meristematic tissue is responsible for secondary growth, which leads to an increase in the thickness or girth of the plant body.
• Examples include the vascular cambium and cork cambium.
• It is found in woody plants and contributes to the formation of bark and wood.
• Cambium:
• Cambium is a type of secondary meristem that specifically produces vascular tissues like xylem and phloem.
• It is responsible for the lateral growth of plants, increasing the width of stems and roots.
• It is not involved in the increase in height but plays a crucial role in the plant's strength and transport system.
• Lateral meristem:
• Lateral meristems are located along the sides of stems and roots.
• Their function is to contribute to secondary growth by increasing the diameter or thickness of the plant body.
• Examples of lateral meristems include vascular cambium and cork cambium.
• Important Points:
• Meristematic tissues are responsible for the growth of plants due to their ability to divide continuously.
• Meristems are classified based on their location (apical, lateral, intercalary) and function (primary or secondary growth).
• Apical dominance: The apical bud suppresses the growth of lateral buds, ensuring that the plant grows upwards efficiently.
• Plants with active apical meristems typically exhibit elongation of roots and stems, allowing them to explore new areas for nutrients, water, and light.

The correct answer is Fallopian tube.

Key Points

• The Fallopian tube is a part of the female reproductive system that connects the ovaries to the uterus.
• During ovulation, the ovary releases an egg (ovum) into the Fallopian tube, where it may be fertilized by sperm.
• The movement of the egg through the Fallopian tube is facilitated by the coordinated actions of tiny hair-like structures called cilia and muscular contractions.
• The Fallopian tube is the typical site of fertilization, where the sperm meets the egg to form a zygote.
• Once fertilized, the zygote travels through the Fallopian tube to implant into the uterine lining, initiating pregnancy.

Additional Information

• Structure and Function of the Fallopian Tube:
• The Fallopian tube is approximately 10-12 cm long and consists of four parts: the infundibulum, ampulla, isthmus, and interstitial part.
• The infundibulum has finger-like projections called fimbriae that help capture the released egg from the ovary.
• The ampulla is the widest part and is the most common site for fertilization.
• The tube is lined with a mucous membrane containing ciliated epithelial cells that move the egg toward the uterus.
• Other Parts of the Female Reproductive System:
• The vagina is the muscular canal leading from the cervix to the outside of the body; it is not involved in transporting the egg.
• The cervix is the lower part of the uterus that opens into the vagina and plays no role in egg transportation.
• The ureter is part of the urinary system, transporting urine from the kidneys to the bladder, and is unrelated to reproduction.
• Common Disorders of the Fallopian Tube:
• Blocked Fallopian tubes can cause infertility as they prevent the egg from reaching the uterus.
• Ectopic pregnancy occurs when a fertilized egg implants in the Fallopian tube instead of the uterus, posing serious health risks.
• Infections like pelvic inflammatory disease (PID) can damage the Fallopian tubes, leading to infertility or complications.
• Fertilization and Implantation:
• Fertilization typically occurs within 24 hours of ovulation in the ampulla of the Fallopian tube.
• The fertilized egg (zygote) takes about 3-4 days to travel to the uterus, where it implants into the uterine lining.

Important Points

• The Fallopian tube is essential for natural conception, as it provides the environment for fertilization.
• Damage or blockage in the Fallopian tube can significantly reduce fertility and may require medical interventions like surgery or in-vitro fertilization (IVF).
• Maintaining reproductive health through regular check-ups and prompt treatment of infections is crucial for the proper functioning of the Fallopian tubes.

The correct answer is Ensure nectar-rich flowers bloom throughout the season.

Key Points

• Ensuring nectar-rich flowers bloom throughout the season is critical for honeybees as they rely on these flowers for nectar, their primary source of energy, and pollen, which provides essential proteins. This practice directly supports both the quantity and quality of honey production.
• By maintaining a variety of nectar-rich flowering plants, the farmer can ensure a continuous supply of food for bees, especially during different blooming periods throughout the year. This prevents seasonal gaps that could stress the bee colonies.
• Nectar-rich plants like sunflowers, lavender, clover, and wildflowers are known to produce high-quality nectar, which directly impacts the flavor, texture, and nutritional value of the honey produced.
• This approach also supports the overall health of the bee population by promoting biodiversity and reducing the risk of diseases or pests that can arise due to monoculture farming practices.
• Unlike other options, this method is sustainable and aligns with ecological farming practices, ensuring long-term benefits for both the farmer and the environment.

Additional Information

• Option 1: Reduce the number of flowering plants
• Reducing the number of flowering plants would decrease the availability of nectar and pollen for bees, leading to lower honey production and potentially weaker bee colonies.
• This approach is counterproductive for improving the quantity and quality of honey.
• Option 2: Remove all wildflowers from the area
• Wildflowers are often a rich source of diverse nectar and pollen. Removing them would eliminate a key food source for bees, negatively impacting honey production and biodiversity.
• Wildflowers also play a vital role in maintaining ecological balance, making their removal detrimental.
• Option 4: Keep the bees in shaded areas away from plants
• Keeping bees away from flowering plants would severely limit their access to nectar and pollen, directly reducing honey production.
• Bees thrive in areas with ample sunlight and easy access to flowers, making this option unsuitable for honey production improvement.
• Benefits of Nectar-Rich Plants:
• Plants like thyme, mint, borage, and marigolds are known to attract bees and support high-quality honey production.
• A diverse range of plants ensures year-round food availability, strengthening bee colonies and enhancing pollination efficiency.
• Such practices contribute to sustainable farming and boost crop yields through improved pollination.
• Importance of Sustainable Beekeeping:
• Maintaining biodiversity through nectar-rich plants ensures the health of bee populations and supports environmental conservation.
• Healthy bee colonies not only produce better honey but also play a crucial role in pollinating crops, which is essential for global food security.

Important Points

• Data and Facts:
• According to the Food and Agriculture Organization (FAO), bees are responsible for pollinating approximately 75% of global crops.
• Studies suggest that planting nectar-rich flowers can increase honey production by up to 30%, depending on the diversity and abundance of the plants.
• Government Initiatives:
• In India, programs like the National Beekeeping & Honey Mission (NBHM) under the Ministry of Agriculture aim to promote scientific beekeeping practices and improve honey production.
• Farmers are encouraged to integrate beekeeping with horticulture and ensure a continuous supply of nectar-producing plants to boost productivity.

The correct answer is To find speed, we need both the magnitude and direction of the object..

Key Points

• Statement 1: "Average speed only needs the magnitude, not direction" – This statement is correct. Average speed is a scalar quantity, meaning it is only concerned with the magnitude of distance traveled over time and does not consider direction.
• Statement 2: "Its SI unit is metres per second (m/s)" – This statement is correct. The SI unit of speed, including average speed, is metres per second (m/s), as it is derived from the formula of speed: distance (metres) divided by time (seconds).
• Statement 3: "To find speed, we need both the magnitude and direction of the object" – This statement is incorrect. Speed is a scalar quantity, and it does not depend on direction. If direction is included, it becomes velocity, which is a vector quantity. This is the correct answer as it is NOT true.
• Statement 4: "Speed is calculated as distance divided by time" – This statement is correct. The formula for speed is indeed distance ÷ time, which gives the rate at which an object covers distance.

Additional Information

• Difference Between Speed and Velocity:
• Speed: Speed is a scalar quantity that measures how fast an object is moving. It considers only the magnitude of the motion.
• Velocity: Velocity is a vector quantity that measures the rate of displacement of an object in a specific direction. It considers both magnitude and direction.
• Example: If a car travels 50 km north in one hour, the speed is 50 km/h, while the velocity is 50 km/h north.
• Formula for Average Speed:
• Average Speed = Total Distance / Total Time
• It does not take into account the direction of travel, making it different from average velocity.
• SI Unit of Speed:
• The SI unit of speed is metres per second (m/s).
• For practical purposes, speed is often measured in kilometres per hour (km/h) in daily life.
• Uniform and Non-Uniform Motion:
• Uniform Motion: When an object covers equal distances in equal intervals of time, it is said to be in uniform motion. In this case, the speed remains constant.
• Non-Uniform Motion: When an object covers unequal distances in equal intervals of time, it is said to be in non-uniform motion. The speed varies in this case.
• Applications of Speed in Real Life:
• Speed is used in transportation to measure how fast vehicles move.
• It is crucial in sports, especially in events like running and racing.
• Speed measurements are used in industries like aviation and shipping for navigation and logistics.

Important Points

• Scalar vs. Vector Quantities:
• Scalar: Quantities that have only magnitude (e.g., speed, distance, time).
• Vector: Quantities that have both magnitude and direction (e.g., velocity, displacement, force).
• Examples of Speed and Velocity:
• If a person runs 100 meters in 10 seconds, their speed is 10 m/s.
• If the same person runs 100 meters north in 10 seconds, their velocity is 10 m/s north.

The correct answer is HCl.

Key Points

• Acidic behavior in aqueous solutions: Acids are substances that release hydrogen ions (H⁺) when dissolved in water. The presence of H⁺ ions is responsible for the acidic nature of a solution.
• HCl (Hydrochloric Acid): HCl is a strong acid that completely dissociates in water, releasing a high concentration of hydrogen ions (H⁺). This dissociation contributes to the acidic behavior of HCl in aqueous solutions.
• Ca(OH)₂, NaOH, and KOH: These are strong bases that dissociate in water to release hydroxide ions (OH⁻), which neutralize hydrogen ions. Hence, they exhibit basic rather than acidic behavior in aqueous solutions.
• Acidity is measured using the pH scale: Solutions with a pH less than 7 are acidic. HCl solutions typically have a very low pH due to the high concentration of H⁺ ions.
• Example: In laboratories, HCl is commonly used as an acid for various chemical reactions, demonstrating its strong acidic properties.

Additional Information

• Hydrochloric Acid (HCl):
• HCl is a strong monoprotic acid, meaning it can donate one proton (H⁺) per molecule.
• It is widely used in industries for applications such as metal cleaning, pH adjustment, and chemical synthesis.
• Its molecular formula is HCl, and its aqueous solution is commonly referred to as hydrogen chloride.
• In the human body, HCl is produced in the stomach to aid digestion by breaking down food and killing pathogens.
• Calcium Hydroxide (Ca(OH)₂):
• Also known as slaked lime, it is a strong base and used in industries for neutralizing acids and water purification.
• It dissociates in water to release hydroxide ions (OH⁻), making the solution basic.
• Commonly used in construction as a component of mortar and plaster.
• Sodium Hydroxide (NaOH):
• NaOH, or caustic soda, is a strong base used in the manufacture of soap, paper, and textiles.
• It dissociates completely in water to produce hydroxide ions, contributing to its basic behavior.
• It is highly corrosive and must be handled with care.
• Potassium Hydroxide (KOH):
• KOH, commonly known as caustic potash, is a strong base used in fertilizers, soaps, and batteries.
• It releases hydroxide ions in aqueous solutions, leading to basic properties.
• It is also used in laboratories for titrations and chemical synthesis.

Important Points

• Acid-Base Behavior:
• Acids release H⁺ ions in water, while bases release OH⁻ ions.
• Strong acids like HCl fully dissociate in water, whereas weak acids partially dissociate.
• Strong bases like NaOH and KOH also fully dissociate in aqueous solutions.
• pH Scale:
• The pH scale ranges from 0 to 14, with values below 7 indicating acidic solutions and values above 7 indicating basic solutions.
• Neutral solutions have a pH of 7, such as pure water.
• HCl solutions typically have a pH of 1 to 3, depending on the concentration.
• Applications:
• HCl is used in laboratory experiments, industrial processes, and medical applications.
• Bases like NaOH and KOH are utilized in manufacturing, cleaning, and analytical procedures.
• Ca(OH)₂ is commonly used in agriculture to neutralize acidic soils.

The correct answer is Movement of tongue.

Key Points

• Voluntary muscles are those that can be consciously controlled by an individual. These muscles are attached to bones and are also known as skeletal muscles.
• The movement of the tongue is controlled by voluntary muscles. The tongue is made up of a group of skeletal muscles that allow for its precise and conscious movement, enabling activities like speaking, chewing, and swallowing.
• Movement in the intestines and movement of the stomach walls are controlled by involuntary muscles, specifically smooth muscles. These movements are part of the autonomic processes of digestion and cannot be controlled voluntarily. Hence, these statements are incorrect.
• The movement of the heart is governed by cardiac muscles, which are also involuntary. The heart's contractions are regulated by the autonomic nervous system and specialized pacemaker cells. Hence, this statement is incorrect.
• The tongue is unique because it combines voluntary control with some involuntary aspects, but its primary movements are voluntary. Hence, the correct answer is the movement of the tongue.

Additional Information

• Voluntary Muscles:
• These muscles are under conscious control and are primarily attached to the skeleton.
• They are striated in appearance and are responsible for enabling movements like walking, running, and grasping objects.
• Examples: Muscles of the arms, legs, and tongue.
• Involuntary Muscles:
• These muscles are not under conscious control and are regulated by the autonomic nervous system.
• They are smooth in structure and are found in internal organs like the intestines, stomach, and blood vessels.
• Examples: Muscles of the digestive tract and blood vessel walls.
• Cardiac Muscles:
• These muscles are found only in the heart and are responsible for pumping blood throughout the body.
• They are involuntary but have a striated appearance similar to skeletal muscles.
• Specialized pacemaker cells in the heart generate electrical impulses to regulate contractions.
• Function of the Tongue:
• The tongue is a muscular organ crucial for speech, taste, and food manipulation during chewing and swallowing.
• Its movements are controlled by extrinsic and intrinsic muscles, which work together to provide a wide range of motion.
• Intrinsic muscles change the shape of the tongue, while extrinsic muscles control its position.

Important Points

• Skeletal Muscles:
• These muscles form about 40% of body weight and enable body movements.
• They are composed of long fibers and are multinucleated.
• Autonomic Nervous System:
• This system controls involuntary actions like digestion, respiration, and heart rate.
• It has two divisions: the sympathetic and parasympathetic nervous systems.
• Heart’s Pacemaker:
• The SA node (Sinoatrial node) is known as the natural pacemaker of the heart.
• It generates electrical impulses that coordinate heart contractions.
• Digestive System Movements:
• Peristalsis is the rhythmic contraction of smooth muscles in the digestive tract, aiding in food movement.
• These movements are entirely involuntary and crucial for digestion.

The correct answer is Loudness depends on the amplitude..

Key Points

• Loudness of sound primarily depends on the amplitude of the sound wave. The larger the amplitude, the louder the sound perceived.
• Amplitude refers to the maximum displacement of particles in a medium due to the propagation of a sound wave. A higher amplitude causes greater energy transfer, resulting in a louder sound.
• The frequency of a sound wave determines the pitch, not loudness. Hence, the statement "Loudness depends on frequency" is incorrect.
• The speed of the wave is determined by the medium through which the sound travels and does not affect loudness. Therefore, the statement "Loudness depends on the speed of wave" is incorrect.
• Wavelength is inversely proportional to frequency in sound waves and does not directly affect loudness. Thus, the statement "Loudness depends on the wavelength" is incorrect.
• Loudness is also influenced by the sensitivity of the human ear and the duration of exposure to sound.

Additional Information

• Amplitude:
• Amplitude is measured in units like decibels (dB), which quantify the intensity of sound.
• For example, a typical conversation has an amplitude of about 60 dB, while a jet engine can reach over 120 dB.
• Higher amplitudes correspond to louder sounds, whereas lower amplitudes are associated with softer sounds.
• Frequency:
• Frequency is measured in Hertz (Hz) and determines the pitch of the sound.
• Humans can typically hear frequencies in the range of 20 Hz to 20,000 Hz, with higher frequencies perceived as higher-pitched sounds.
• While pitch and loudness are distinct qualities, they often interact in perception.
• Speed of Sound:
• The speed of sound varies with the medium, e.g., 343 m/s in air, 1,500 m/s in water, and 5,960 m/s in steel.
• Factors like temperature, pressure, and density of the medium influence the speed of sound.
• However, the speed does not directly impact loudness.
• Wavelength:
• Wavelength is the distance between successive crests or troughs in a sound wave.
• It is inversely proportional to frequency, as per the equation: wavelength = speed of sound / frequency.
• Like frequency, wavelength contributes to the tonal quality rather than loudness.
• Human Ear Sensitivity:
• The human ear is most sensitive to frequencies between 2,000 Hz and 5,000 Hz, where small changes in amplitude result in significant changes in perceived loudness.
• Prolonged exposure to loud sounds above 85 dB can cause hearing damage.

Important Points

• Threshold of Hearing:
• The quietest sound a human can hear is at 0 dB, known as the threshold of hearing.
• Sounds above 120 dB are painful and can cause immediate hearing loss.
• Applications of Loudness Measurement:
• Loudness is essential in audio engineering, designing sound systems, and acoustics.
• Devices like sound level meters are used to measure amplitude for safety and environmental purposes.
• Noise Pollution:
• Excessive loudness contributes to noise pollution, which can lead to health issues like stress, sleep disturbances, and hearing impairment.
• Regulations often enforce limits on noise levels in residential and industrial areas.
• Equal Loudness Contours:
• These are graphs showing the sound pressure levels required to produce the same perceived loudness at different frequencies.
• They highlight the frequency-dependent sensitivity of the human ear.

The correct answer is Work done by a constant force is zero if displacement is zero or perpendicular to force..

Key Points

• Definition of Work: Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. Mathematically, Work (W) = F × d × cos(θ), where:
• F is the magnitude of the applied force.
• d is the magnitude of displacement.
• θ is the angle between the force and displacement vectors.
• Condition for Zero Work: The work done by a constant force is zero when:
• Displacement (d) = 0: If the object does not move (no displacement), the work done is zero because W = F × 0 × cos(θ) = 0.
• Force and Displacement are Perpendicular (θ = 90°): When the angle between the force and displacement is 90°, cos(90°) = 0, leading to W = F × d × 0 = 0.
• Examples of Zero Work:
• A person holding a heavy box stationary does no work because there is no displacement.
• A satellite moving in a circular orbit under the influence of gravitational force does no work because the force is perpendicular to the displacement.
• Relevance of the Formula: The formula W = F × d × cos(θ) clearly shows that work depends on both the displacement and the angle between the force and displacement. If either displacement is zero or the angle is 90°, the work becomes zero.

Additional Information

• Characteristics of Work:
• Work is a scalar quantity, meaning it has magnitude but no direction.
• Positive work occurs when force and displacement are in the same direction (θ = 0°, cos(0°) = 1).
• Negative work occurs when force and displacement are in opposite directions (θ = 180°, cos(180°) = -1).
• Concept of Force and Displacement:
• For work to occur, there must be a displacement in the direction of the applied force.
• If there is no displacement, such as in static scenarios, no work is done regardless of the force applied.
• Work Done in Perpendicular Scenarios:
• When force is perpendicular to displacement, the angle θ is 90°, and cos(90°) = 0, leading to zero work.
• Examples: A person carrying a bag while walking horizontally (force exerted vertically while displacement is horizontal).
• Practical Applications:
• Understanding zero work is important in designing systems like pulleys and levers where forces need to be perpendicular to avoid unnecessary work.
• In physics problems, identifying cases of zero work helps simplify calculations and understand energy conservation principles.

Important Points

• Option 1: Displacement is small
• Even if the displacement is small, work is done as long as there is a component of force in the direction of displacement.
• Incorrect, as zero work depends on the angle and displacement being zero, not its magnitude.
• Option 2: Force is large
• The magnitude of force alone does not determine zero work.
• Incorrect, as work depends on both force and displacement.
• Option 3: Force is variable
• Variable force affects the calculation of work but does not inherently result in zero work.
• Incorrect, as zero work depends on displacement and angle.
• Option 4: Displacement is zero or perpendicular to force
• Zero displacement or perpendicularity between force and displacement results in zero work.
• Correct, as per the formula W = F × d × cos(θ).

The correct answer is reverses direction.

Key Points

• When a current-carrying conductor is placed in a magnetic field, it experiences a force according to the left-hand rule of Fleming.
• The direction of this force depends on the relative orientation of the current in the conductor and the magnetic field. The force is perpendicular to both the current and the magnetic field.
• When the direction of current in the conductor is reversed, the force acting on the conductor also reverses its direction. This is because the force is directly proportional to the current direction.
• This phenomenon is a direct application of the Lorentz Force, which states that the force on a charged particle moving in a magnetic field is given by F = q(v × B), where v represents velocity (current direction in this case).
• Hence, reversing the current in the conductor changes the direction of the force acting on it, but the magnitude remains the same. Hence, the correct answer is that the force reverses direction.

Additional Information

• Fleming's Left-Hand Rule:
• It is used to determine the direction of the force acting on a current-carrying conductor in a magnetic field.
• The thumb, forefinger, and middle finger of the left hand are stretched perpendicular to each other.
• Here, the thumb indicates the direction of force, the forefinger represents the magnetic field, and the middle finger denotes the direction of current.
• Lorentz Force:
• The total force experienced by a charged particle moving in electric and magnetic fields is called the Lorentz force.
• The formula for Lorentz force is F = q(E + v × B), where E is the electric field, v is the velocity of the particle, and B is the magnetic field.
• In this case, the magnetic component of the Lorentz force is responsible for the force on the conductor.
• Applications of Force on Current-Carrying Conductors:
• This principle is utilized in devices like electric motors, where current-carrying coils experience forces in a magnetic field to produce rotational motion.
• It is also employed in magnetic braking systems and electromagnetic actuators.
• Magnetic Field and Current Interaction:
• The interaction between the magnetic field and current is the basis of many electromechanical devices.
• The magnitude of the force can be calculated using the formula F = I × L × B × sin(θ), where I is the current, L is the length of the conductor, B is the magnetic field strength, and θ is the angle between the conductor and the magnetic field.

Important Points

• Option 1: Remains the Same: This is incorrect because reversing the current changes the direction of the force, not leaving it unchanged.
• Option 2: Doubles: This is incorrect as the magnitude of the force remains the same; only the direction changes.
• Option 3: Reverses Direction: This is the correct answer as reversing the current causes the force to act in the opposite direction.
• Option 4: Becomes Zero: This is incorrect because the force only becomes zero if the conductor is parallel to the magnetic field, which is not stated in the question.

The correct answer is copper sulphate.

Key Points

• Copper sulphate is the most commonly used electrolyte in the process of electrolytic refining of copper. It is used in a solution form, typically acidified with sulphuric acid (H₂SO₄).
• In electrolytic refining, the impure copper acts as the anode, a pure thin sheet of copper serves as the cathode, and the electrolyte is an aqueous solution of copper sulphate mixed with sulphuric acid.
• During the process, copper ions from the impure copper anode dissolve into the solution and then deposit onto the pure copper cathode, leaving impurities behind. This ensures the production of highly pure copper.
• The use of copper sulphate ensures a stable supply of Cu²⁺ ions in the electrolyte, which is crucial for the efficiency of the refining process.
• Other copper compounds like copper oxide, copper carbonate, or copper chloride are not suitable because they do not provide the required ionic stability or are not commonly used in industrial refining processes.

Additional Information

• Electrolytic Refining Process:
• This process is widely used for obtaining metals of high purity, such as copper, silver, gold, and aluminum.
• In the case of copper, the impurities like iron, nickel, and zinc are dissolved into the electrolyte, while noble metals like gold and silver settle at the bottom as anode mud.
• The chemical reaction involved is: Anode: Cu → Cu²⁺ + 2e⁻ Cathode: Cu²⁺ + 2e⁻ → Cu
• Properties of Copper Sulphate:
• Chemical formula: CuSO₄·5H₂O (pentahydrate form is most commonly used).
• It is a blue crystalline solid that is highly soluble in water.
• Copper sulphate provides a steady source of Cu²⁺ ions necessary for the electrolytic refining process.
• Why Acidified Copper Sulphate?
• Adding sulphuric acid (H₂SO₄) to the electrolyte improves the conductivity of the solution and stabilizes copper ions in the solution.
• It prevents hydrolysis of copper sulphate and ensures an efficient refining process.
• Industrial Applications of Electrolytic Copper:
• Pure electrolytic copper is used in manufacturing electrical wires, electronic components, and high-quality alloys due to its excellent conductivity.
• It is also used in plumbing, roofing, and industrial machinery.
• Characteristics of Other Copper Compounds:
• Copper Carbonate: Insoluble in water, not suitable for providing Cu²⁺ ions.
• Copper Oxide: Requires additional reactions to dissolve in water, making it inefficient.
• Copper Chloride: Though soluble, it is not commonly used due to cost and stability issues in the refining process.

Important Points

• The purity of copper obtained through electrolytic refining can reach up to 99.99%, making it suitable for critical applications.
• The anode mud collected during the refining process often contains valuable metals like gold, silver, and platinum, which can be recovered.
• Electrolytic refining is a highly controlled process that ensures minimal wastage of copper and other by-products.
• Copper's high conductivity makes its purity critical for industries like electronics and electrical engineering.

The correct answer is The force of attraction is different for different particles..

Key Points

• The force of attraction between particles of matter varies depending on the state of matter (solid, liquid, or gas). This directly supports the statement that the force of attraction is different for different particles.
• In solids, particles are tightly packed, and the force of attraction is the strongest. This is why solids maintain a fixed shape and volume.
• In liquids, the force of attraction is weaker compared to solids, allowing particles to flow and take the shape of their container, while still maintaining a definite volume.
• In gases, the force of attraction is the weakest, as particles are far apart and move freely. Gases neither have a fixed shape nor a fixed volume.
• The variation in the force of attraction between particles is the reason for the different physical properties of solids, liquids, and gases.

Additional Information

• Solids:
• In solids, particles are held together by strong intermolecular forces.
• This strong attraction leads to a definite shape and volume.
• Examples: Iron, wood, diamond.
• Liquids:
• In liquids, particles have a moderate force of attraction.
• Liquids do not have a fixed shape but have a definite volume.
• Examples: Water, oil, alcohol.
• Gases:
• In gases, particles are held together by very weak intermolecular forces.
• They neither have a definite shape nor a definite volume, and they expand to fill any container.
• Examples: Oxygen, nitrogen, carbon dioxide.
• Plasma:
• A state of matter where particles are ionized, and the force of attraction is negligible.
• Examples: Sun, lightning.
• Bose-Einstein Condensate (BEC):
• A state of matter formed at extremely low temperatures, where particles exhibit unique quantum properties.
• It was first observed in 1995 by scientists Eric Cornell and Carl Wieman.

Important Points

• Intermolecular Forces: These are forces of attraction or repulsion between neighboring particles, including Van der Waals forces, dipole-dipole interactions, hydrogen bonds, and others.
• Thermal Energy: The energy associated with the movement of particles. Higher thermal energy reduces the effect of intermolecular forces, allowing particles to move more freely.
• Phase Transition: Changes in state (e.g., solid to liquid, liquid to gas) occur due to variations in temperature and pressure, which alter the balance between intermolecular forces and thermal energy.
• Applications: Understanding the force of attraction helps in designing materials, studying fluid dynamics, and even predicting weather patterns.

The correct answer is Only (i).

Key Points

• Statement (i): "Fluids exert pressure on the base and walls of the container in which they are enclosed" is correct.
• Fluids, which include liquids and gases, exert pressure due to the random motion of their molecules.
• This pressure acts in all directions, including on the base and walls of any container they occupy.
• For example, water in a glass exerts pressure on the bottom and walls due to its weight and molecular motion.
• Statement (ii): "Pressure exerted in any confined mass of fluid is transmitted unequally in different directions" is incorrect.
• According to Pascal's Law, the pressure exerted in a confined fluid is transmitted equally in all directions.
• This principle is the basis for hydraulic systems, where a small force applied to a fluid results in an equal pressure transmitted to all parts of the system.
• The statement contradicts this fundamental principle, making it incorrect.

Additional Information

• Pascal's Law:
• It states that when a pressure is applied to a confined fluid, it is transmitted undiminished in all directions.
• This principle is widely used in hydraulic systems like hydraulic brakes, jacks, and presses.
• Fluid Pressure:
• It is defined as the force exerted by a fluid per unit area.
• The formula for pressure is P = F/A, where P is pressure, F is force, and A is area.
• Fluid pressure increases with depth due to the weight of the fluid above.
• Applications of Fluid Pressure:
• Hydraulic systems: Utilize fluid pressure to perform tasks, such as lifting heavy objects.
• Dams: Designed to withstand water pressure that increases with depth.
• Scuba diving: Divers experience higher pressure at greater depths due to the weight of water above them.
• Difference Between Liquid and Gas Pressure:
• Liquids: Pressure depends on depth and density, and is exerted only in the downward direction due to gravity.
• Gases: Pressure is exerted equally in all directions due to the random motion of gas molecules.

Important Points

• Key Characteristics of Fluid Pressure:
• It is scalar in nature, meaning it has magnitude but no specific direction.
• Pressure in a fluid at rest is the same at any given depth, regardless of the container shape.
• In a moving fluid, pressure varies with velocity (as per Bernoulli’s principle).
• Hydraulics: The science of transmitting force through liquids, based on Pascal's Law, is crucial in engineering and mechanical applications.
• Practical Examples:
• Car brakes, which use hydraulic fluid to transmit pressure from the pedal to the brake pads.
• Hydraulic lifts for elevating vehicles in workshops.

The correct answer is Neuron.

Key Points

• Neuron is a specialized cell in the nervous system that transmits information via electrical and chemical signals. It is the correct answer because it has dendrites on one end.
• Dendrites are branch-like structures present in neurons. Their primary function is to receive signals (electrical impulses) from other neurons and transmit them towards the cell body.
• Neurons are the structural and functional units of the nervous system. They are responsible for processing and transmitting information throughout the body.
• In contrast, the other options like monocytes, platelets, and red blood cells do not possess dendrites and are involved in completely different biological functions.
• Neurons have three main parts: dendrites, a cell body (soma), and an axon. Dendrites are specifically involved in receiving input signals.

Additional Information

• Monocyte:
• Monocytes are a type of white blood cell (WBC) and part of the immune system.
• They are primarily involved in engulfing pathogens and debris through a process called phagocytosis.
• Unlike neurons, they lack dendrites and are not involved in signal transmission.
• Platelet:
• Platelets, also known as thrombocytes, are small, disc-shaped cell fragments in the blood.
• They play a crucial role in blood clotting and preventing excessive bleeding.
• Platelets do not have a nucleus, dendrites, or any structures related to nerve signaling.
• Red Blood Cell (RBC):
• RBCs are responsible for transporting oxygen from the lungs to the tissues and carbon dioxide from the tissues to the lungs.
• They contain a protein called hemoglobin, which binds to oxygen molecules.
• RBCs lack a nucleus and other organelles, including dendrites.
• Neuron:
• Neurons are classified into three types based on their function: sensory neurons (carry signals to the brain), motor neurons (carry signals from the brain), and interneurons (connect neurons within the brain or spinal cord).
• The presence of dendrites allows neurons to integrate and process incoming information from other neurons or sensory inputs.
• The axon transmits the processed signal away from the cell body to other neurons, muscles, or glands.

Important Points

• Synapse: A synapse is the junction between two neurons where the axon terminal of one neuron communicates with the dendrites of another neuron through chemical signals.
• Signal Transmission: Neurons communicate via action potentials (electrical signals) and neurotransmitters (chemical signals).
• Nervous System: Neurons form the foundation of the nervous system, which is divided into the central nervous system (CNS) and the peripheral nervous system (PNS).
• Diseases: Disorders like Alzheimer's disease, Parkinson's disease, and multiple sclerosis affect neurons and disrupt their functioning.
• Research: Neurons are a major focus of research in neurobiology and neuroscience due to their critical role in controlling bodily functions and behavior.

The correct answer is Insoluble in water.

Key Points

• Ionic compounds are generally soluble in water: This is due to the polar nature of water molecules. The positive and negative ions in ionic compounds are attracted to the oppositely charged ends of water molecules, leading to their dissolution. Hence, the statement "Insoluble in water" is incorrect.
• High melting and boiling points: Ionic compounds have strong electrostatic forces of attraction between their oppositely charged ions, requiring a large amount of energy to break. Hence, statements "High melting point" and "High boiling point" are correct.
• Conductivity in molten state: Ionic compounds conduct electricity in the molten state or when dissolved in water because their ions become free to move. Hence, the statement "Conducts electricity in molten state" is correct.

Additional Information

• Physical Properties of Ionic Compounds:
• Solubility: Ionic compounds are typically soluble in polar solvents like water but insoluble in non-polar solvents like benzene or ether.
• Conductivity: In solid-state, ionic compounds do not conduct electricity due to fixed ions. In the molten state or aqueous solution, ions move freely, allowing conductivity.
• Melting and Boiling Points: Strong ionic bonds result in high melting and boiling points for ionic compounds.
• Hardness: Ionic compounds are generally hard due to the strong forces holding the ions together. However, they are brittle and can shatter under pressure.
• Examples of Ionic Compounds:
• Sodium chloride (NaCl): Common table salt, soluble in water and has a high melting point of 801°C.
• Magnesium oxide (MgO): Widely used in refractory materials, it has a melting point above 2800°C.
• Calcium chloride (CaCl₂): Used as a de-icing agent, it dissolves readily in water.
• Importance of Ionic Compounds:
• Industrial Applications: Used in batteries, ceramics, and electrolysis processes.
• Biological Significance: Ionic compounds like Na⁺ and K⁺ are essential for nerve impulse transmission and muscle contraction in living organisms.

Important Points

• Factors Affecting Solubility of Ionic Compounds:
• Lattice Energy: Higher lattice energy makes it harder for the ionic compound to dissolve in water.
• Hydration Energy: If the hydration energy of ions is greater than the lattice energy, the compound dissolves easily.
• Why Ionic Compounds are Brittle:
• When a force is applied, the layers of ions shift, causing like charges to align and repel each other, leading to shattering.
• Applications of Ionic Compounds:
• Sodium chloride: Used in food preservation and seasoning.
• Calcium carbonate: Utilized in construction (limestone and marble).
• Magnesium sulfate: Commonly known as Epsom salt, used in medicine and agriculture.

The correct answer is Myopia.

Key Points

• Myopia, also known as nearsightedness, is a common vision defect in which a person can see nearby objects clearly but struggles to see distant objects clearly.
• This occurs when the light rays converge in front of the retina rather than directly on it. This happens due to an elongated eyeball or an overly curved cornea.
• Myopia is commonly corrected using concave lenses (minus power lenses), which help focus the light directly on the retina.
• The condition is often hereditary and can appear in childhood, typically progressing until the late teens or early twenties.
• Symptoms include blurry distance vision, squinting, eye strain, and sometimes headaches. Regular eye exams can help detect and manage myopia effectively.

Additional Information

• Astigmatism:
• Astigmatism is a vision defect caused by an irregularly shaped cornea or lens, leading to blurred or distorted vision at all distances.
• This condition is often corrected using cylindrical lenses or through procedures like LASIK surgery.
• Presbyopia:
• Presbyopia is an age-related condition that makes it difficult to focus on nearby objects.
• It typically occurs after the age of 40 years due to the loss of elasticity in the eye's lens.
• This condition is corrected using bifocal or progressive lenses.
• Hypermetropia:
• Also known as farsightedness, hypermetropia is a condition where distant objects appear clear but nearby objects are blurry.
• It occurs when the eyeball is too short or the cornea has too little curvature, causing light rays to focus behind the retina.
• This condition is corrected using convex lenses.
• Important Points:
• Myopia is one of the most common refractive errors worldwide, with increasing prevalence due to factors like excessive screen time and reduced outdoor activities.
• Severe or high myopia can lead to complications such as retinal detachment, glaucoma, or macular degeneration.
• Preventive measures include maintaining proper lighting while reading, taking regular breaks from screens, and encouraging outdoor play for children.
• Modern corrective options include orthokeratology (special contact lenses), refractive surgery, and advanced spectacle designs.

The correct answer is Ca(ClO)₂.

Key Points

• The chemical formula of bleaching powder is CaOCl₂, which is also known as calcium oxychloride.
• Bleaching powder is prepared by passing chlorine gas (Cl₂) over dry slaked lime (Ca(OH)₂).
• The chemical reaction involved in the preparation of bleaching powder is: Ca(OH)₂ + Cl₂ → Ca(ClO)₂ + H₂O.
• Bleaching powder is commonly used as a disinfectant, oxidising agent, and for bleaching cotton, linen, and paper pulp.
• It releases chlorine when mixed with water, which provides its bleaching and germicidal properties.

Additional Information

• Bleaching Powder:
• Bleaching powder is an inorganic compound with the chemical name calcium oxychloride.
• It is a white powder with a characteristic smell of chlorine.
• It is generally represented by the formula Ca(ClO)₂.
• Preparation of Bleaching Powder:
• It is manufactured by the action of chlorine gas on dry slaked lime.
• The process is carried out in a Hasenclever plant for industrial production.
• The reaction produces bleaching powder along with water.
• Uses of Bleaching Powder:
• It is used for disinfection of drinking water due to its chlorine-releasing property.
• It is used in the textile industry for bleaching cotton and linen.
• It is also used for bleaching wood pulp in the paper industry.
• Important Chemical Compounds:
• Calcium hydroxide (Ca(OH)₂): Commonly known as slaked lime.
• Calcium oxide (CaO): Known as quicklime.
• Calcium carbonate (CaCO₃): Found in materials like limestone and marble.

Important Points

• Chemical name: Calcium oxychloride.
• Chemical formula: Ca(ClO)₂.
• Prepared by: Reaction of chlorine gas with dry slaked lime.
• Main active component: Chlorine, responsible for bleaching and disinfecting action.
• Major applications: Water purification, textile bleaching, paper industry, and sanitation.

The correct answer is Blue-green algae.

Key Points

• Blue-green algae, also known as cyanobacteria, reproduce asexually through a process called binary fission. This is a simple and efficient method of reproduction where a single cell divides into two identical daughter cells.
• In fission, the genetic material (DNA) of the parent cell is copied, and the cell divides into two, ensuring that both daughter cells are genetically identical to the parent cell.
• Cyanobacteria are prokaryotic organisms, meaning they lack a defined nucleus and other membrane-bound organelles, which facilitates their simpler mode of reproduction.
• These organisms are found in diverse environments, including freshwater, marine, and terrestrial ecosystems. They play a crucial role in ecosystems by contributing to nitrogen fixation and oxygen production.
• Unlike seed plants and flowering plants, which reproduce sexually, blue-green algae rely on asexual reproduction for their propagation. Hence, the correct answer is Blue-green algae.

Additional Information

• Asexual Reproduction:
• Asexual reproduction is a mode of reproduction where offspring are produced from a single organism, and there is no involvement of gametes or sexual processes.
• It is commonly observed in prokaryotes like bacteria and archaea, as well as in some eukaryotic organisms like fungi, algae, and certain plants and animals.
• Common methods of asexual reproduction include binary fission, budding, fragmentation, and spore formation.
• Characteristics of Blue-Green Algae (Cyanobacteria):
• Cyanobacteria are a group of photosynthetic prokaryotes capable of oxygenic photosynthesis, meaning they release oxygen as a byproduct.
• They are considered one of the earliest life forms on Earth and have played a significant role in shaping the planet’s atmosphere.
• Examples include Oscillatoria, Anabaena, and Nostoc.
• Some cyanobacteria can fix atmospheric nitrogen into a usable form, which is essential for nutrient cycling in ecosystems.
• Why Other Options Are Incorrect:
• All seed plants: Seed plants reproduce sexually through the formation of seeds, which involve the fusion of gametes. Asexual reproduction is not a characteristic of all seed plants.
• Flowering plants: These plants primarily reproduce sexually through flowers, which are specialized structures for sexual reproduction.
• All plants: While some plants (like algae or mosses) reproduce asexually, not all plants rely on this mode of reproduction. Most higher plants reproduce sexually.
• Importance of Cyanobacteria:
• They are crucial in aquatic and terrestrial ecosystems as primary producers.
• Cyanobacteria contribute significantly to the global nitrogen cycle and are used in biofertilizers to enhance soil fertility.
• They are also studied for their potential in biofuel production and other biotechnological applications.

Important Points

• Binary Fission:
• This is the most common form of asexual reproduction in unicellular organisms.
• It involves the replication of the genetic material, followed by the division of the parent cell into two identical cells.
• Binary fission is rapid and allows for exponential population growth under favorable conditions.
• Differences Between Asexual and Sexual Reproduction:
• Asexual reproduction: Involves a single parent, produces genetically identical offspring, and is faster but lacks genetic diversity.
• Sexual reproduction: Involves two parents, produces genetically diverse offspring, and is slower but enhances adaptability and evolution.
• Ecological Significance of Cyanobacteria:
• Cyanobacteria are crucial in maintaining the balance of oxygen and nutrients in aquatic ecosystems.
• They form symbiotic relationships with plants and fungi, aiding in nutrient exchange and ecosystem stability.

The correct answer is Catenation and Tetravalency.

Key Points

• Catenation: Carbon exhibits a unique ability to form long chains and rings by bonding with other carbon atoms. This property allows the formation of a wide variety of compounds, ranging from simple hydrocarbons to complex organic molecules. The strong covalent bonds between carbon atoms contribute to the stability of these structures.
• Tetravalency: Carbon has four valence electrons and requires four more electrons to complete its octet. This enables carbon to form four covalent bonds with other atoms (such as hydrogen, oxygen, nitrogen, etc.) or other carbon atoms, giving rise to a wide range of molecular configurations.
• Versatility in Bond Types: Carbon can form single, double, and triple bonds, allowing for diverse chemical structures and reactivities. This versatility enables the creation of functional groups and compounds essential for life, such as carbohydrates, proteins, and nucleic acids.
• Formation of Isomers: Due to its catenation and tetravalency, carbon compounds exhibit isomerism, where molecules with the same molecular formula have different structural arrangements. This adds to the diversity of organic compounds.
• Abundance and Role in Organic Chemistry: Carbon is a fundamental element in organic chemistry and life. Its ability to form a large number of compounds is a cornerstone in the study of chemistry, biology, and materials science.

Additional Information

• Explanation of Catenation:
• Catenation is the property of an element to form bonds with atoms of the same element, creating chains or rings. Carbon is exceptional in this regard due to its ability to form strong covalent bonds.
• This property is most prominent in carbon compared to other elements like silicon or sulfur, enabling the formation of complex organic molecules.
• Examples of catenation include alkanes (single bonds), alkenes (double bonds), and alkynes (triple bonds).
• Explanation of Tetravalency:
• Carbon's tetravalency arises from its electronic configuration (2s² 2p²), where four valence electrons are available for bonding.
• This allows carbon to bond with up to four other atoms, leading to the formation of stable molecules like methane (CH₄), ethane (C₂H₆), and ethanol (C₂H₅OH).
• Tetravalency enables the creation of diverse molecular geometries, such as linear, planar, and tetrahedral structures.
• Comparison with Other Elements:
• While elements like silicon also exhibit catenation and tetravalency, their bonds are weaker and less stable compared to carbon. This limits their ability to form complex structures.
• Carbon's small atomic size and high electronegativity contribute to the strength of its bonds, making it uniquely suited for forming stable, diverse compounds.
• Applications of Carbon's Properties:
• Carbon's versatility is utilized in the synthesis of polymers, fuels, pharmaceuticals, and biomolecules.
• Its compounds form the basis of life on Earth, including DNA, RNA, and proteins.
• Carbon is also used in materials science to develop substances like graphite, diamond, and carbon nanotubes.

Important Points

• Option Analysis:
• Option 1 (High melting point and ductility): These properties are irrelevant to carbon's versatility. They are more applicable to metals like iron and copper.
• Option 2 (Good conductivity and sonorous nature): These are metallic properties and do not apply to carbon, which is a non-metal.
• Option 3 (Isomerism and allotropy): While these are characteristics of carbon, they are a result of its catenation and tetravalency, not the primary reasons for its versatility.
• Option 4 (Catenation and tetravalency): Correct. These are the two main properties that enable carbon to form a vast number of compounds.
• Examples of Carbon Compounds:
• Simple hydrocarbons: Methane (CH₄), ethane (C₂H₆).
• Complex biomolecules: Glucose (C₆H₁₂O₆), DNA, proteins.
• Industrial compounds: Plastics, synthetic fibers, and fuels.

The correct answer is To transport the male germ cell to the female germ cell.

Key Points

• The pollen tube is a tubular structure that forms after a pollen grain lands on the stigma of a compatible flower.
• Its primary function is to transport the male germ cell (sperm cells) from the pollen grain to the ovule, where the female germ cell (egg cell) resides.
• The pollen tube grows through the style and into the ovary, navigating to the ovule via a specialized opening called the micropyle.
• Once the pollen tube reaches the ovule, it releases the sperm cells, enabling the process of fertilization, where one sperm cell fuses with the egg cell to form a zygote.
• The other sperm cell typically fuses with the central cell to form the endosperm, which provides nourishment to the developing embryo.

Additional Information

• Pollination:
• Pollination is the process of transferring pollen grains from the anther to the stigma of a flower.
• It can occur through various agents like wind, water, insects, or animals.
• The types of pollination include self-pollination (within the same flower or plant) and cross-pollination (between flowers of different plants).
• Fertilization in plants:
• Fertilization occurs when the male and female gametes (germ cells) fuse to form a zygote.
• This process leads to the formation of seeds, which contain the embryo and endosperm for nourishment.
• Structure of the pollen tube:
• The pollen tube is a microscopic, elongated structure that grows directionally, guided by chemical signals from the ovule.
• It has a tip-growing mechanism driven by the cytoskeleton and vesicle trafficking.
• Micropyle:
• The micropyle is a small opening in the ovule through which the pollen tube enters.
• It ensures that the sperm cells from the pollen tube reach the egg cell for fertilization.
• Double fertilization:
• Angiosperms exhibit a unique process called double fertilization.
• One sperm cell fuses with the egg cell to form a zygote, while the other fuses with two polar nuclei to form the endosperm.
• This process ensures both embryo formation and nutrient storage for seed development.

Important Points

• Option 1: To form the zygote
• This is incorrect because the formation of the zygote occurs after the sperm and egg cells fuse, not as a role of the pollen tube.
• Option 2: To produce the male germ cell
• This is incorrect as the male germ cells are already present within the pollen grain, not produced by the pollen tube.
• Option 3: To transport pollen grains to the stigma
• This is incorrect because pollen grains are transported to the stigma by pollination agents, not by the pollen tube.
• Option 4: To transport the male germ cell to the female germ cell
• This is correct because the pollen tube facilitates the movement of sperm cells to the ovule for fertilization.

The correct answer is A ball rolling on the ground and eventually stopping.

Key Points

• Unbalanced Force: An unbalanced force occurs when the net force acting on an object is not zero, causing a change in the object's state of motion (either speed, direction, or both).
• Correct Option Explanation: A ball rolling on the ground and eventually stopping involves an unbalanced force because friction acts as an opposing force, slowing down the ball until it comes to rest.
• Frictional Force: The friction between the ball and the ground is the unbalanced force responsible for reducing the ball's motion and eventually bringing it to a stop.
• Newton's First Law: According to Newton's First Law of Motion (Law of Inertia), an object in motion will remain in motion unless acted upon by an external unbalanced force. The rolling ball's motion changes due to the unbalanced frictional force, making the situation fit this law.
• Other Options: In the other scenarios provided (standing person, car moving at uniform speed, book on a table), the forces acting on the objects are balanced, meaning their state of motion remains unchanged. These are not examples of unbalanced forces.

Additional Information

• Balanced Forces:
• Balanced forces occur when the net force acting on an object is zero, meaning no change in the object's motion occurs.
• Examples include a person standing still on the ground (gravity and normal force cancel each other out) or a book resting on a table.
• Unbalanced Forces:
• Unbalanced forces result in a net force on an object, leading to a change in its motion (acceleration or deceleration).
• Examples include a rolling ball slowing down due to friction or a car accelerating forward when a greater force is applied by the engine than the opposing frictional forces.
• Friction:
• Friction is a force that opposes the relative motion of two surfaces in contact.
• It is a critical factor in real-world scenarios, as it often acts as the unbalanced force responsible for changes in motion.
• Newton's Laws of Motion:
• First Law: An object remains at rest or in uniform motion unless acted upon by an unbalanced external force.
• Second Law: The force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
• Third Law: For every action, there is an equal and opposite reaction.

Important Points

• Friction and Motion: Friction is essential for activities such as walking or driving, as it provides the necessary grip for movement. However, it also opposes motion, requiring additional force to maintain movement.
• Types of Friction:
• Static Friction: Acts on objects at rest, preventing them from starting to move.
• Kinetic Friction: Acts on moving objects, opposing their motion.
• Rolling Friction: Specific to rolling objects, like a ball or wheel, and typically lower than sliding friction.
• Applications: Understanding unbalanced forces is crucial in designing vehicles, machines, and other systems where motion control is essential.
• Real-Life Example: A bicycle slowing down when the rider stops pedaling is another instance of an unbalanced force (friction and air resistance) acting to reduce motion.

The correct answer is Approval given to a contractor to fell trees near the village.

Key Points

• The Chipko Movement, a historic environmental movement in India, began in the village of Reni in the Garhwal Himalayas of Uttarakhand in 1973.
• The movement was triggered when the government approved a contract to a sports goods company to fell trees in the forests near the village of Reni.
• When the men of the village were away, the women of Reni, led by Gaura Devi, organized themselves to protect the trees by physically hugging them, preventing the contractors from cutting them down.
• This act of hugging the trees, symbolizing a non-violent protest, drew significant attention to the environmental degradation caused by deforestation and highlighted the need for sustainable forest management.
• The Chipko Movement is considered one of the earliest and most successful environmental movements in India and inspired similar movements across the country.

Additional Information

• Background of the Chipko Movement:
• The term "Chipko" means "to hug" or "to cling" in Hindi, symbolizing the way villagers physically embraced the trees to protect them.
• The movement emerged as a response to commercial logging activities in the Himalayan region, which were causing significant environmental issues like soil erosion and loss of biodiversity.
• The movement was deeply rooted in the philosophy of Gandhian non-violence and emphasized the importance of community-driven conservation efforts.
• Role of Women:
• Women played a pivotal role in the Chipko Movement, as they were directly dependent on the forests for their livelihood, including firewood, fodder, and water.
• Gaura Devi, a local leader, mobilized the women of her village to stand against the contractors, making the movement a significant example of women's empowerment and environmental activism.
• Impact of the Movement:
• The Chipko Movement led to increased awareness about the importance of forests and the need for their conservation.
• In 1980, the Indian government imposed a 15-year ban on commercial logging in the Himalayan forests, largely due to the movement's influence.
• It also inspired other environmental movements in India, such as the Appiko Movement in Karnataka.
• Relevance Today:
• The Chipko Movement remains a symbol of grassroots environmental activism and the power of community action in addressing ecological issues.
• It highlights the interconnectedness between local communities and their natural environment, emphasizing the need for sustainable development practices.

Important Points

• Other Options Explained:
• Sale of forest by local residents: This was not the cause of the Chipko Movement; the issue arose due to government-approved commercial deforestation.
• Industrial development planned by villagers: There was no such industrial development planned by the villagers that led to the movement.
• Government decision to use forest land for farming: The movement was not against converting forest land for farming but was specifically against commercial logging.
• Key Figures:
• Sunderlal Bahuguna: A prominent environmentalist associated with the Chipko Movement who advocated for the conservation of forests.
• Chandi Prasad Bhatt: A key leader and founder of the Dasholi Gram Swarajya Sangh, which played a crucial role in organizing the movement.

The correct answer is Right-hand thumb rule gives the direction of magnetic field around a straight conductor..

Key Points

• Right-hand thumb rule: This rule is used to determine the direction of the magnetic field around a current-carrying conductor. If the thumb of the right hand points in the direction of the current, the curled fingers show the direction of the magnetic field lines. This statement is correct.
• Application to circular loops: The right-hand thumb rule is applicable to circular loops as well. Here, the thumb points in the direction of the current, and the fingers show the direction of the magnetic field along the circular path. Hence, the claim that it cannot be applied to circular loops is incorrect.
• Application to straight conductors: The rule is specifically meant for straight conductors, making the claim that it cannot be applied to straight conductors incorrect.
• Finding force on a conductor: The right-hand thumb rule is not used to determine the force on a conductor. Instead, the Fleming’s left-hand rule is applied for this purpose. Hence, this statement is incorrect.
• Correct statement: The right-hand thumb rule accurately gives the direction of the magnetic field around a straight current-carrying conductor. This is a fundamental concept in electromagnetism. Hence, option 1 is correct.

Additional Information

• Right-hand thumb rule:
• The rule was introduced to understand the relationship between current and magnetic fields in a conductor.
• It states: "If you hold a current-carrying conductor in your right hand such that the thumb points in the direction of the current, the direction of your curled fingers will indicate the direction of the magnetic field lines."
• This rule is derived from Maxwell's right-hand grip rule.
• Magnetic field around a conductor:
• When current flows through a conductor, it generates a magnetic field around it.
• The field lines form concentric circles around the conductor, and their direction is determined using the right-hand thumb rule.
• Fleming's left-hand rule:
• This rule is used to determine the direction of force on a current-carrying conductor in a magnetic field.
• According to this rule, if the thumb, forefinger, and middle finger of the left hand are stretched mutually perpendicular to each other:
• The thumb points in the direction of force (motion).
• The forefinger points in the direction of the magnetic field.
• The middle finger points in the direction of the current.
• Applications:
• The right-hand thumb rule is widely used in designing electrical devices like motors, generators, and transformers.
• It helps engineers understand how magnetic fields interact with electric currents to produce motion or induce current.

Important Points

• Hans Christian Ørsted: The discovery of the magnetic effect of electric current was made by Hans Christian Ørsted in 1820. This discovery formed the basis of electromagnetism.
• Magnetic field strength: The strength of the magnetic field generated by a current-carrying conductor depends on:
• The amount of current flowing through the conductor.
• The distance from the conductor; the field weakens as the distance increases.
• Practical examples: The right-hand thumb rule is applied in understanding the functioning of solenoids, electromagnets, and electric motors.
• Conceptual difference: While the right-hand thumb rule is used to determine the magnetic field direction, the Fleming’s left-hand rule is used to determine force direction, and the Fleming’s right-hand rule is used to find the direction of induced current.

The correct answer is Increase in humidity.

Key Points

• Evaporation is the process through which a liquid changes into a gas at a temperature below its boiling point.
• Evaporation is influenced by several factors such as temperature, surface area, wind speed, and humidity.
• Increase in temperature: Higher temperatures provide more energy to liquid molecules, making it easier for them to escape into the gaseous phase. Hence, this statement is correct.
• Increase in surface area: A larger surface area allows more liquid to be exposed to the air, facilitating faster evaporation. Hence, this statement is correct.
• Increase in wind speed: Faster winds remove water vapor from the surface, reducing humidity near the liquid and enhancing evaporation. Hence, this statement is correct.
• Increase in humidity: Higher humidity means more water vapor is already present in the air, making it harder for additional liquid to evaporate. Hence, this statement is incorrect.

Additional Information

• Evaporation and its Importance:
• Evaporation plays a key role in the water cycle, contributing to cloud formation and precipitation.
• It is also critical in cooling mechanisms such as sweating, which helps regulate body temperature.
• Factors Affecting Evaporation:
• Temperature: Higher temperatures increase molecular kinetic energy, leading to faster evaporation.
• Surface Area: A larger surface area provides more opportunities for molecules to escape into the air.
• Wind Speed: Wind removes saturated air near the liquid's surface, increasing the evaporation rate.
• Humidity: Higher humidity slows evaporation as the air is already saturated with water vapor.
• Applications of Evaporation:
• Used in industries such as salt production through seawater evaporation.
• Evaporation helps in cooling systems like air coolers and refrigeration.
• Real-World Examples:
• Clothes dry faster in dry and windy weather due to faster evaporation.
• Evaporation from oceans and lakes contributes to the formation of rain clouds.

Important Points

• Evaporation vs Boiling:
• Evaporation occurs at any temperature below the boiling point and only at the surface of the liquid.
• Boiling occurs at a fixed temperature (boiling point) and throughout the liquid.
• Role of Humidity:
• High humidity: Reduces the evaporation rate because the air is nearly saturated with water vapor.
• Low humidity: Increases evaporation since the air can absorb more water vapor.
• Scientific Insight: Evaporation is an endothermic process, meaning it absorbs heat from the surroundings, resulting in a cooling effect.

Shortcut Trick

Ratio of Surface Areas = 100 : 169

Ratio of Radii = √100 : √169 = 10 : 13

Ratio of Volumes = 10³ : 13³ = 1000 : 2197

Percentage increase in volume = ((2197 − 1000) ÷ 1000) × 100 = 119.7%

∴ The correct answer is 119.7%.

Alternate Method

Given:

Increase in surface area of the sphere = 69%

Formula Used:

Surface Area of a sphere (A) = 4 × π × r²

Volume of a sphere (V) = (4/3) × π × r³

Calculations:

⇒ Let the initial radius be r₁ and the new radius be r₂.

⇒ Initial Surface Area (A₁) = 4πr₁²

⇒ New Surface Area (A₂) = A₁ × (100 + 69)/100 = 1.69 A₁

⇒ 4πr₂² = 1.69 × 4πr₁²

⇒ (r₂/r₁)² = 1.69

⇒ r₂/r₁ = √1.69 = 1.3

⇒ Ratio of volumes (V₂/V₁) = (r₂/r₁)³ = (1.3)³ = 2.197

⇒ Percentage increase in volume = (V₂/V₁ − 1) × 100

⇒ Percentage increase = (2.197 − 1) × 100 = 119.7%

∴ The correct answer is 119.7%.

Additional Information

Properties of a Sphere

For a sphere of radius r, the Surface Area is 4πr² and the Volume is (4/3)πr³.

Hemisphere Formulas

For a hemisphere, Curved Surface Area (CSA) = 2πr², Total Surface Area (TSA) = 3πr², and Volume = (2/3)πr³.

Relationship between Ratios

If the radius changes by a factor k, the area changes by k² and the volume changes by k³.

Given:

$(57.6 \div 4.5 \times 1.5) = ? \times \frac{1}{5}$

Formula Used:

Basic arithmetic operations

Calculation:

$(57.6 \div 4.5 \times 1.5) = ? \times \frac{1}{5}$

⇒ $12.8 \times 1.5 = ? \times \frac{1}{5}$

⇒ $19.2 = ? \times \frac{1}{5}$

⇒ $? = 19.2 \times 5$

⇒ $? = 96$

∴ The correct answer is 96.

Shortcut Trick

Relation between Marked Price (MP) and Cost Price (CP): MP/CP = (100 + Profit%)/(100 − Discount%)

Given: MP is 33% above CP ⇒ MP/CP = 133/100

Formula: 133/100 = (100 + 13)/(100 − d)

133/100 = 113/(100 − d) ⇒ 100 − d = 11300/133 ≈ 84.962

d = 100 − 84.962 = 15.038% ≈ 15.04%

∴ The correct answer is 15.04%.

Alternate Method

Given: Marked Price (MP) = ���415, Markup Percentage = 33%, Profit Percentage = 13%.

Formula Used: CP = MP ÷ (1 + Markup%); SP = CP × (1 + Profit%); Discount% = (MP − SP) ÷ MP × 100.

⇒ Let Cost Price (CP) = 100 units

⇒ Marked Price (MP) = 100 + 33% of 100 = 133 units

⇒ Selling Price (SP) = 100 + 13% of 100 = 113 units

⇒ Discount = MP − SP = 133 − 113 = 20 units

⇒ Discount Percentage = (Discount ÷ MP) × 100

⇒ Discount Percentage = (20 ÷ 133) × 100 = 2000 ÷ 133

⇒ Discount Percentage ≈ 15.03759...

∴ The correct answer is 15.04%.

Additional Information

Markup Percentage

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

MP and CP Relationship

The direct ratio is MP/CP = (100 + P%)/(100 − D%). This eliminates the need to calculate the actual Selling Price.

Successive Percentage Change

Markup and Discount act as successive changes to reach the Profit/Loss percentage: Profit% = Markup% − Discount% − (Markup × Discount)/100.

Shortcut Trick In Set 1 {1, 7, 3, 7, 3, x}, 3 and 7 appear twice, so the mode is 3 (if x = 3) or 7 (if x = 7). In Set 2 {4, 8, 9, 8, 4, y}, 4 and 8 appear twice, so the mode is 4 (if y = 4) or 8 (if y = 8). Possible sums for 11 are (3 + 8) or (7 + 4). Given x > y, we choose x = 7 and y = 4. The relation is 7 − 4 = 3, which means x − y = 3. ∴ The correct answer is x − y = 3.

Alternate Method Given: Data sets A = {1, 7, 3, 7, 3, x} and B = {4, 8, 9, 8, 4, y}. Sum of modes = 11 and x > y. Concept: The mode is the value that appears most frequently in a data set. For a unique mode to exist in these sets, x and y must repeat an existing value.

⇒ For Set 1, if x = 7, then 7 appears 3 times ∴ Mode1 = 7. ⇒ For Set 1, if x = 3, then 3 appears 3 times ∴ Mode1 = 3. ⇒ For Set 2, if y = 4, then 4 appears 3 times ∴ Mode2 = 4. ⇒ For Set 2, if y = 8, then 8 appears 3 times ∴ Mode2 = 8. ⇒ Sum of modes = 11 ⇒ Possible combinations: (3 + 8) or (7 + 4). ⇒ Case 1: x = 3, y = 8. Here 3 < 8, so x < y (Violates x > y). ⇒ Case 2: x = 7, y = 4. Here 7 > 4, so x > y (Satisfies condition). ⇒ Finding relation: x − y = 7 − 4 = 3. ∴ The correct answer is x − y = 3.

Additional Information Mode Definition The value that occurs with the maximum frequency in a data set. A set can be unimodal, bimodal, or multimodal. Empirical Relationship For moderately skewed distributions: Mode = 3 × Median − 2 × Mean. Bimodal Data A dataset is bimodal if two different values share the highest frequency. In this problem, x and y were needed to create a unique majority frequency.

Shortcut Trick

Use the Successive Percentage formula: Net Change = a + b + (ab/100)

Here, Markup (a) = +76% and Discount (b) = −54%.

Net Change = 76 − 54 + (76 × (−54) / 100) = 22 − 41.04 = −19.04%.

Negative sign indicates a loss.

∴ The correct answer is 19.04%.

Alternate Method

Given: Markup % = 76%, Discount % = 54%.

Formula: SP = CP × (100 + Markup%)/100 × (100 − Discount%)/100

⇒ Let Cost Price (CP) = 100

⇒ Marked Price (MP) = 100 + 76% of 100 = 176

⇒ Selling Price (SP) = 176 − 54% of 176

⇒ SP = 176 × (46/100) = 80.96

⇒ Loss = CP − SP = 100 − 80.96 = 19.04

⇒ Loss % = (19.04 / 100) × 100 = 19.04%

∴ The correct answer is 19.04%.

Additional Information

Markup and Discount relation

The relationship between CP and MP is given by: MP/CP = (100 + Profit%) / (100 − Discount%).

Successive Percentage Change

If a value is changed by x% and then by y%, the net effective change is (x + y + xy/100)%.

Loss Percentage

Loss % = (Loss / CP) × 100, where Loss = CP − SP.

Shortcut Trick

The LCM of 7, 11, and 13 is 7 × 11 × 13 = 1001.

Any number divisible by 7, 11, and 13 must be a multiple of 1001.

Checking options: 1001 × 6 = 6006.

∴ The correct answer is 6006.

Alternate Method

Given numbers: 7, 11, 13

Concept: A number divisible by prime numbers 7, 11, and 13 is divisible by their product.

⇒ Product = 7 × 11 × 13

⇒ Product = 77 × 13 = 1001

⇒ Numbers in the form of xyzxyz (like 123123) are always divisible by 1001.

⇒ Check divisibility of options by 1001:

⇒ 2121 ÷ 1001 (Not divisible)

⇒ 3026 ÷ 1001 (Not divisible)

⇒ 1546 ÷ 1001 (Not divisible)

⇒ 6006 ÷ 1001 = 6 (Divisible)

∴ The correct answer is 6006.

Additional Information

Divisibility by 1001

Any 3-digit number written twice to form a 6-digit number (abcabc) is always divisible by 7, 11, and 13 because abcabc = abc × 1001.

Divisibility rule of 11

The difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.

Properties of Prime Numbers

Since 7, 11, and 13 are coprime, their LCM is simply the product of the three numbers.

Shortcut Trick

Since PQ = PR = 25 cm, ΔPQR is an isosceles triangle.

The altitude to the base QR bisects it, so half-base = 40 ÷ 2 = 20 cm.

In a right-angled triangle, use the Pythagorean triplet (3, 4, 5).

Scaling by 5: (3×5, 4×5, 5×5) → (15, 20, 25).

Comparing with sides (h, 20, 25), we get Altitude (h) = 15 cm.

∴ The correct answer is 15 cm.

Alternate Method

Given: PQ = 25 cm, PR = 25 cm, and QR = 40 cm.

Formula Used: In an isosceles triangle, the altitude (h) to the base (b) from the vertex joining equal sides (a) is given by: h = √(a² − (b/2)²).

Let PM be the altitude to QR. Since PQ = PR, M is the midpoint of QR.

⇒ QM = MR = QR ÷ 2 = 40 ÷ 2 = 20 cm

In right-angled triangle PMQ, by Pythagoras Theorem:

⇒ PQ² = PM² + QM²

⇒ 25² = h² + 20²

⇒ 625 = h² + 400

⇒ h² = 625 − 400

⇒ h² = 225

⇒ h = √225 = 15 cm

∴ The correct answer is 15 cm.

Additional Information

Isosceles Triangle Properties

In an isosceles triangle, the altitude to the base is also the median and the angle bisector of the vertex angle.

Area of Isosceles Triangle

The area can be calculated as (1/2) × base × altitude or using (b/4)√(4a² − b²) where 'a' is the equal side.

Pythagorean Theorem

For any right triangle with legs x, y and hypotenuse z, the relation is x² + y² = z².

Shortcut Trick

Pipe A empties 1/10 of the tank in 6 min → Full tank empty time = 60 min.

LCM of 60, 30, and 40 = 120 units (Total Capacity).

Efficiency: A = −2 (120/60), B = +4 (120/30), C = +3 (120/40).

Net Efficiency (A + B + C) = −2 + 4 + 3 = 5 units/min.

Total time to fill the empty tank = 120 ÷ 5 = 24 minutes.

∴ The correct answer is 24 minutes.

Alternate Method

Given:

Initial state: Tank 1/10 full.

Pipe A: Empties 1/10 tank in 6 minutes → Time for full tank = 60 minutes.

Pipe B: Fills tank in 30 minutes.

Pipe C: Fills tank in 40 minutes.

Condition: All pipes opened together after Pipe A empties the initial volume (Tank is now empty).

Formula Used:

Time = Total Capacity ÷ Net Efficiency

Inlet efficiency is positive (+), Outlet efficiency is negative (−).

Calculations:

⇒ Total Capacity = LCM of (60, 30, 40) = 120 units.

⇒ Efficiency of Pipe A = 120 ÷ 60 = −2 units/min.

⇒ Efficiency of Pipe B = 120 ÷ 30 = +4 units/min.

⇒ Efficiency of Pipe C = 120 ÷ 40 = +3 units/min.

⇒ Combined Efficiency = −2 + 4 + 3 = 5 units/min.

⇒ Time required to fill 120 units = 120 ÷ 5 = 24 minutes.

∴ The correct answer is 24 minutes.

Additional Information

Inlet and Outlet Pipes

A pipe used to fill a tank is called an Inlet (positive work), and a pipe used to empty it is called an Outlet (negative work).

Net Rate Formula

If an inlet fills in X hours and an outlet empties in Y hours, then net work in 1 hour = (1/X − 1/Y) if the tank is being filled.

Tank Capacity Calculation

Capacity = (Total time to fill/empty) × (Flow rate of the pipe in volume per unit time).

Shortcut Trick

Profit on Selling Price (SP) = 25% = 1/4.

Here, SP = 4 units and Profit = 1 unit.

Cost Price (CP) = SP − Profit = 4 − 1 = 3 units.

Actual Profit % = (Profit / CP) × 100 = (1 / 3) × 100 = 33.33%.

∴ The correct answer is 33.33%.

Alternate Method

Given: Profit percentage on Selling Price = 25%.

Formula Used: Actual Profit % = (Profit / Cost Price) × 100

⇒ Let the Selling Price (SP) = ₹100.

⇒ Profit = 25% of 100 = ₹25.

⇒ Cost Price (CP) = SP − Profit = 100 − 25 = ₹75.

⇒ Actual Profit % = (25 / 75) × 100

⇒ Actual Profit % = (1 / 3) × 100 = 33.33%.

∴ The correct answer is 33.33%.

Additional Information

Profit on CP vs SP

Standard Profit Percentage is always calculated on Cost Price unless specified otherwise.

Relationship Formula

If Profit on SP is x%, then Profit on CP = [x / (100 − x)] × 100.

Loss on SP

If Loss on SP is x%, then Loss on CP = [x / (100 + x)] × 100.

Shortcut Trick

In a 30°−60°−90° triangle, the ratio of sides is 1 : √3 : 2.

Side opposite to 30° (base) = 1115.4705 cm.

Side opposite to 60° (height) = Base × √3.

Height = 1115.4705 × 1.732 ≈ 1932 cm.

∴ The correct answer is 1932 cm.

Alternate Method

Given:

Distance of foot of ladder (Base) = 1115.4705 cm

Angle of elevation (θ) = 60°

Formula Used:

tan(θ) = Perpendicular (Height) / Base

Calculations:

⇒ tan(60°) = Height / 1115.4705

⇒ √3 = Height / 1115.4705

⇒ Height = 1115.4705 × 1.73205

⇒ Height = 1932.050... cm

⇒ Height ≈ 1932 cm (Rounding to the nearest integer)

∴ The correct answer is 1932 cm.

Additional Information

Trigonometric Ratios

For a right-angled triangle, sin θ = P/H, cos θ = B/H, and tan θ = P/B.

Special Triangle Ratios

In a 30°−60°−90° triangle, the sides are in the ratio 1 : √3 : 2 respectively.

Pythagoras Theorem

For any right triangle, H² = P² + B², where H is the hypotenuse.

Shortcut Trick

Successive percentage for 10% for 2 years = 10 + 10 + (10 × 10)/100 = 21%

Total Amount = 100% (Principal) + 21% (Interest) = 121% of Principal

Amount = 6800 × 1.21 = ₹8,228

∴ The correct answer is ₹8,228.

Alternate Method

Given:

Principal (P) = ₹6,800

Rate (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 6800 × (1 + 10/100)²

⇒ A = 6800 × (110/100)²

⇒ A = 6800 × (1.1) × (1.1)

⇒ A = 6800 × 1.21

⇒ A = 8228

∴ The correct answer is ₹8,228.

Additional Information

Effective Rate for Compound Interest

For 2 years, the effective rate of interest can be calculated using the formula x + y + (xy/100), where x and y are the rates for the first and second years.

Compound Interest (CI) vs Simple Interest (SI)

The difference between CI and SI for 2 years is given by the formula P(R/100)².

Amount Calculation

Amount is the sum of the Principal and the total Interest earned. A = P + CI.

Shortcut Trick

Speed ratio (New : Normal) = 1 : 3

Since distance is constant, Time ratio (New : Normal) = 3 : 1

Difference in time ratio units = 3 − 1 = 2 units

Given, 2 units = 50 minutes ⇒ 1 unit = 25 minutes

∴ The correct answer is 25 minutes.

Alternate Method

Given: New speed = 1/3 × Normal speed; Time delay = 50 minutes.

Formula Used: Distance = Speed × Time. For constant distance, S₁T₁ = S₂T₂.

⇒ Let normal speed be S and normal time be T.

⇒ New speed = S/3 and New time = T + 50

⇒ S × T = (S/3) × (T + 50)

⇒ 3T = T + 50

⇒ 2T = 50

⇒ T = 25 minutes

∴ The correct answer is 25 minutes.

Additional Information

Inverse Proportion Rule

When distance is constant, speed and time are inversely proportional (S ∝ 1/T). If speed becomes 1/n, time becomes n times the original.

Average Speed

For a round trip (A to B and B to A) with speeds x and y, Average Speed = 2xy/(x + y).

Relative Speed

Same direction: S₁ − S₂ | Opposite direction: S₁ + S₂.

Shortcut Trick

Investment Ratio = Profit Ratio

Prakhar's Profit = ₹1,400 | Total Profit = ₹5,400

Prakhar's Share of Profit = 1,400 / 5,400 = 7 / 27

Prakhar's Investment = (7 / 27) × 56,700 = 7 × 2,100 = ₹14,700

∴ The correct answer is ₹14,700.

Alternate Method

Given:

Total Investment = ₹56,700

Total Profit = ₹5,400

Prakhar's Profit Share = ₹1,400

Formula Used:

Profit Share of A / Profit Share of B = (Capital_A × Time_A) / (Capital_B × Time_B)

Calculations:

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

⇒ Riya's Profit = 5,400 − 1,400 = ₹4,000

⇒ Ratio of Profits (Prakhar : Riya) = 1,400 : 4,000 = 7 : 20

⇒ Since time period is same, Ratio of Investment = Ratio of Profits = 7 : 20

⇒ Sum of ratio parts = 7 + 20 = 27 units

⇒ 27 units = ₹56,700

⇒ 1 unit = 56,700 ÷ 27 = ₹2,100

⇒ Prakhar's Investment = 7 units = 7 × 2,100 = ₹14,700

∴ The correct answer is ₹14,700.

Additional Information

Partnership Basic Rule

Profit is always distributed in the ratio of the product of Capital and Time. If time is constant, Profit ∝ Capital.

Active vs Sleeping Partner

An Active Partner manages the business and may receive a salary or extra commission before the remaining profit is divided based on investment ratios.

Compound Partnership

When partners invest for different time periods, the ratio is calculated as (C₁×T₁) : (C₂×T₂) : (C₃×T₃).

Given:

180 ÷ A = 11 ÷ 44

Formula Used:

If a ÷ b = c ÷ d, then a × d = b × c

Calculation:

⇒ 180 × 44 = A × 11

⇒ 7920 = 11A

⇒ A = 7920 ÷ 11

⇒ A = 720

∴ The correct answer is 720.

Shortcut Trick

From 3 Pens = 5 Pencils, the price ratio of Pen : Pencil = 5 : 3.

Total cost for 5 pens and 3 pencils = (5 × 5) + (3 × 3) = 34 units.

Given 34 units = ₹34, so 1 unit = ₹1.

Required price for 3 pens and 5 pencils = (3 × 5) + (5 × 3) = 30 units.

30 units = 30 × 1 = ₹30.

∴ The correct answer is ₹30.

Alternate Method

Given:

Price of 3 Pens (P) = 5 Pencils (L)

Price of 5P + 3L = ₹34

Calculations:

⇒ Let the price of one pen be P and one pencil be L.

⇒ From the first condition: 3P = 5L ⇒ P = (5/3)L

⇒ Substitute P in the second equation: 5(5/3)L + 3L = 34

⇒ (25/3)L + 3L = 34

⇒ (25L + 9L) / 3 = 34

⇒ 34L / 3 = 34

⇒ L = 3

⇒ Now, substitute L in P = (5/3)L: P = (5/3) × 3 = 5

⇒ Cost of 3 pens and 5 pencils = 3P + 5L

⇒ 3(5) + 5(3) = 15 + 15 = 30

∴ The correct answer is ₹30.

Additional Information

Linear Equations in Two Variables

These are equations of the form ax + by = c. They can be solved using substitution, elimination, or cross-multiplication methods.

Ratio and Proportion Method

If mA = nB, then the ratio A : B = n : m. This allows for unit-based calculation which is often faster than algebra.

Unitary Method

Finding the value of a single unit (1 part) first and then multiplying it to find the required quantity.

Given:

(35x³y²z ÷ 7xy⁴) ÷ 25xy⁻²z

Formula Used:

a^m ÷ aⁿ = a^m−n

(a ÷ b) ÷ c = a ÷ (b × c)

Calculation:

⇒ 35 ÷ 7 = 5

⇒ x³ ÷ x = x²

⇒ y² ÷ y⁴ = y⁻²

⇒ Expression becomes = 5x²y⁻²z ÷ 25xy⁻²z

⇒ 5 ÷ 25 = 1 ÷ 5

⇒ x² ÷ x = x

⇒ y⁻² ÷ y⁻² = y⁰ = 1

⇒ z ÷ z = 1

⇒ Final value = x ÷ 5

∴ The correct answer is x ÷ 5.

Shortcut Trick

Remaining percentage = 100% − 60% = 40%

40% of salary = ₹33,200

100% of salary = (33,200 ÷ 40) × 100

Total Salary = 830 × 100 = ₹83,000

∴ The correct answer is ₹83,000.

Alternate Method

Given:

Spending = 60% of monthly salary

Savings (Remaining Amount) = ₹33,200

Let the total monthly salary be 'S'.

⇒ Household expenses = 60% of S = 0.60S

⇒ Remaining amount = S − 0.60S = 0.40S

⇒ 0.40S = 33,200

⇒ S = 33,200 ÷ 0.40

⇒ S = 3,32,000 ÷ 4

⇒ S = 83,000

∴ The correct answer is ₹83,000.

Additional Information

Percentage Change Formula

Percentage change = (New Value − Old Value) ÷ Old Value × 100.

Successive Percentage

If a value is changed by a% and then by b%, the net effective change is (a + b + ab/100)%.

Fraction to Percentage Conversion

To convert a fraction to a percentage, multiply by 100. Example: 2/5 = (2/5) × 100 = 40%.

Shortcut Trick

Speed = Difference in length ÷ Difference in time

⇒ Speed = (2492 − 1914) ÷ (81 − 64) = 578 ÷ 17 = 34 m/s

⇒ Length of train = (Speed × Time₁) − Tunnel₁

⇒ Length of train = (34 × 81) − 2492 = 2754 − 2492 = 262 m

∴ The correct answer is 262 m.

Alternate Method

Given: Length of Tunnel₁ (L₁) = 2492 m, Time₁ (T₁) = 81 s, Length of Tunnel₂ (L₂) = 1914 m, Time₂ (T₂) = 64 s.

Formula Used: Speed = (Length of Train + Length of Object) ÷ Time

⇒ Let L be the length of the train and V be the speed of the train.

⇒ Case 1: L + 2492 = V × 81 ... (i)

⇒ Case 2: L + 1914 = V × 64 ... (ii)

⇒ Subtracting (ii) from (i): 2492 − 1914 = 81V − 64V

⇒ 578 = 17V

⇒ V = 578 ÷ 17 = 34 m/s

⇒ Putting V in (ii): L + 1914 = 34 × 64

⇒ L + 1914 = 2176

⇒ L = 2176 − 1914 = 262 m

∴ The correct answer is 262 m.

Additional Information

Train Crossing Object with Length

When a train crosses a platform, tunnel, or bridge, the total distance covered is the sum of the train's length and the object's length.

Train Crossing Point Object

When a train crosses a pole or a standing man, the distance covered is equal to the length of the train itself.

Speed 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

Product of fractional values × Number = Result

30% = 3/10 and 50% = 1/2

⇒ (3/10) × (1/2) × (2/3) × Number = 325

⇒ (1/10) × Number = 325

∴ The correct answer is 3250.

Alternate Method

Given: Result = 325, Percentages = 30% and 50%, Fraction = 2/3

Formula Used: Percentage = (Value/100) × Total

Let the unknown number be x.

⇒ (30/100) × (50/100) × (2/3) × x = 325

⇒ (3/10) × (1/2) × (2/3) × x = 325

⇒ (3 × 1 × 2) / (10 × 2 × 3) × x = 325

⇒ (6 / 60) × x = 325

⇒ (1 / 10) × x = 325

⇒ x = 325 × 10

∴ The correct answer is 3250.

Additional Information

Percentage to Fraction Conversion

To convert a percentage to a fraction, divide the value by 100. Example: 25% = 25/100 = 1/4.

Successive Percentages

When multiple percentages are applied to a number of each other, they are multiplied directly as fractions or decimals.

Base Change Rule

If a value is increased by x%, to return to the original value, it must be decreased by [x/(100+x)] × 100%.

Shortcut Trick

Recognize that the numerator x² + 10x + 25 is a perfect square (x + 5)².

Divide by the denominator: (x + 5)² ÷ (x + 5) = (x + 5).

Subtract the remaining term: (x + 5) − 5 = x.

∴ The correct answer is x.

Alternate Method

Given: ((x² + 10x + 25) / (x + 5)) − 5

Formula Used: Algebraic Identity (a + b)² = a² + 2ab + b²

⇒ Step 1: Factorize the quadratic expression in the numerator.

⇒ x² + 10x + 25 = x² + 2(x)(5) + 5² = (x + 5)²

⇒ Step 2: Substitute the factored form back into the original expression.

⇒ [(x + 5)² / (x + 5)] − 5

⇒ Step 3: Simplify by canceling the common factor (x + 5).

⇒ (x + 5) − 5

⇒ x

∴ The correct answer is x.

Additional Information

Perfect Square Trinomials

An expression of the form a² ± 2ab + b² can always be simplified to the square of a binomial (a ± b)².

Division of Like Bases

When dividing powers with the same base, subtract the exponents: a^m ÷ aⁿ = a^m−n.

BODMAS Rule

Always perform division before subtraction in algebraic simplifications to ensure accuracy.

Shortcut Trick

Ratio of cost TV : Washing Machine = 4 : 3 (since 25% less means 3/4)

Total cost for 8 WM and 4 TV = (8 × 3) + (4 × 4) = 24 + 16 = 40 units

Net change = [(24 × 83) + (16 × −15)] ÷ 40

Net change = [1992 − 240] ÷ 40 = 1752 ÷ 40 = 43.8%

∴ The correct answer is Increase by 43.8%.

Alternate Method

Let the cost of TV = ₹400

⇒ Cost of Washing Machine (WM) = 400 − 25% of 400 = ₹300

⇒ Initial Total Cost (8 WM + 4 TV) = (8 × 300) + (4 × 400) = 2400 + 1600 = ₹4000

⇒ New cost of WM = 300 + 83% of 300 = 300 + 249 = ₹549

⇒ New cost of TV = 400 − 15% of 400 = 400 − 60 = ₹340

⇒ Final Total Cost = (8 × 549) + (4 × 340) = 4392 + 1360 = ₹5752

⇒ Increase in cost = 5752 − 4000 = ₹1752

⇒ Percentage change = (1752 ÷ 4000) × 100 = 43.8%

∴ The correct answer is Increase by 43.8%.

Additional Information

Percentage Change

Percentage change = [(Final Value − Initial Value) ÷ Initial Value] × 100.

Weighted Average Method

For mixed quantities, net % change = (n₁c₁ + n₂c₂) ÷ (n₁ + n₂), where n is quantity and c is % change.

Fractional Conversion

Always use fractions for quick calculations: 25% = 1/4, 20% = 1/5, etc.

Shortcut Trick

Base area = πr² = 169π ⇒ radius (r) = 13 cm.

Total Surface Area (TSA) = 2 × Base Area + Curved Surface Area

TSA = 2 × 169π + 2πrh = 2πr(r + h)

TSA = 2 × (22/7) × 13 × (13 + 15) = 2 × (22/7) × 13 × 28 = 2288 cm².

∴ The correct answer is 2288 cm².

Alternate Method

Given:

Height (h) of the cylinder = 15 cm

Base area = 169π cm²

Formula Used:

1. Area of base = πr²
2. Total Surface Area (TSA) = 2πr(r + h)

Calculations:

⇒ πr² = 169π

⇒ r² = 169

⇒ r = √169 = 13 cm

⇒ Total Surface Area = 2πr(r + h)

⇒ TSA = 2 × (22/7) × 13 × (13 + 15)

⇒ TSA = 2 × (22/7) × 13 × 28

⇒ TSA = 2 × 22 × 13 × 4

⇒ TSA = 2288 cm²

∴ The correct answer is 2288 cm².

Additional Information

Curved Surface Area of Cylinder

The area of the side surface of a cylinder is 2πrh, where r is the radius and h is the height.

Volume of Cylinder

The space occupied by a cylinder is calculated as Base Area × Height = πr²h.

Relation with Cone

A cylinder and a cone with the same base and height have a volume ratio of 3 : 1.

Shortcut Trick

Mode is defined as the observation that occurs most frequently in a data set.

By inspection of the given heights: 172, 173, 164, 178, 168, 169, 173, 172, 173, 164, 178, 168, 169, 173.

Frequency of 173 = 4 (Maximum occurrence).

Frequency of all other numbers (164, 168, 169, 172, 178) = 2 each.

∴ The correct answer is 173 cm.

Alternate Method

Given: A set of 14 observations representing the heights of gymnasts in cm.

Formula: Mode = Value with the highest frequency.

⇒ Frequency of 164 = 2

⇒ Frequency of 168 = 2

⇒ Frequency of 169 = 2

⇒ Frequency of 172 = 2

⇒ Frequency of 173 = 4

⇒ Frequency of 178 = 2

⇒ Comparing all frequencies, the maximum frequency is 4, which corresponds to the height 173 cm.

∴ The correct answer is 173 cm.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship between measures of central tendency is: Mode = 3 × Median − 2 × Mean.

Bimodal and Multimodal Data

If two or more values have the same maximum frequency, the data set is called bimodal (two modes) or multimodal.

Median Calculation

To find the Median, arrange data in ascending order. For N observations, if N is even, Median = Average of (N/2)^th and (N/2 + 1)^th terms.

Shortcut Trick

Sum of ages 5 years ago = 50 − (2 × 5) = 40 years.

Ratio of Ankita to Anushree was 3 : 1.

Total ratio parts = 3 + 1 = 4 units → 40 years.

1 unit = 10 years (Anushree's age 5 years ago).

Present age of Anushree = 10 + 5 = 15 years.

∴ The correct answer is 15 years.

Alternate Method

Given: Sum of ages = 50 years; 5 years ago Ankita = 3 × Anushree.

Let Anushree's present age be x.

Ankita's present age = 50 − x.

5 years ago:

⇒ (50 − x − 5) = 3 × (x − 5)

⇒ 45 − x = 3x − 15

⇒ 4x = 60

⇒ x = 15

∴ The correct answer is 15 years.

Additional Information

Age Difference Property

The difference between the ages of two people remains constant regardless of the number of years passed or preceding.

Sum of Ages Change

If there are n people, the sum of their ages increases or decreases by (n × t) years over a period of t years.

Ratio Method for Ages

When ratios at two different times are given, equate the parts by making the difference between ratio terms equal.

Shortcut Trick

Combined efficiency of A + B = 10 ÷ 5 = 2 units/day.

Efficiency of B alone = 10 ÷ 10 = 1 unit/day.

Efficiency of A = 2 − 1 = 1 unit/day.

Total work for A = Double work = 10 × 2 = 20 units.

Time taken by A = 20 ÷ 1 = 20 days.

∴ The correct answer is 20 days.

Alternate Method

Given:

Time taken by (A + B) = 5 days

Time taken by B = 10 days

Calculations:

⇒ Efficiency of A = Efficiency of (A + B) − Efficiency of B

⇒ Efficiency of A = 2 − 1 = 1 unit/day

⇒ New Total Work = 2 × Old Total Work

⇒ New Total Work = 2 × 10 = 20 units

⇒ Time taken by A alone = New Total Work ÷ Efficiency of A

⇒ Time taken by A alone = 20 ÷ 1 = 20 days

∴ The correct answer is 20 days.

Additional Information

Work-Efficiency Relationship

Total Work = Time taken × Efficiency. Efficiency is inversely proportional to time when work is constant.

Combined Work Formula

If two people A and B can do a work in x and y days respectively, then working together they finish it in (x × y) ÷ (x + y) days.

Efficiency Formula for Subtraction

If (A+B) take 't1' days and B takes 't2' days, then A takes (t1 × t2) ÷ (t2 − t1) days for the same work.

BODMAS Rule:

Decoding the given information:

Given equation: 187 − 4 ÷ 117 + 325 × 5 = ?

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 187 × 4 + 117 − 325 ÷ 5 = ?

⇒ 187 × 4 + 117 − 65 = ?

⇒ 748 + 117 − 65 = ?

⇒ 865 − 65 = ?

⇒ 800 = ?

Hence, the correct answer is "Option 4".

Given: In a certain code language, ‘we cook dinner’ is coded as ‘hn sh ai’ and ‘dinner is tasty’ is coded as ‘la tf sh’. How is 

Thus, ‘dinner’ is coded as 'sh' in that language.

Hence, the correct answer is "Option 1".

The position and positional values or English Alphabets are:

The pattern followed here is:

Each letter-cluster follows the pattern +2, -7.

1. FHA

This letter-cluster follows the pattern +2, -7.

2. SUN

This letter-cluster follows the pattern +2, -7.

3. PRK

This letter-cluster follows the pattern +2, -7.

4. KME

This letter-cluster does not follow the pattern +2, -7.

Thus, KME is the odd one out.

Hence, the correct answer is "Option 4".

Given: 835 836 839 844 851 ?

The logic followed here is:

Thus, 860 should come in place of the question mark (?) in the given series.

Hence, the correct answer is "Option 4".

Given: In a certain code language, ‘travel is exciting’ is coded as ‘ab op kj’ and ‘exciting and enjoyable’ is coded as ‘lm ab wv’.

Thus, ‘exciting’ is coded as 'ab' in the given language.

Hence, the correct answer is "Option 2".93

BODMAS Rule:

Decoding the given information:

Given equation: 88 × 8 ÷ 9 − 2 + 17 = ?

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 88 ÷ 8 + 9 × 2 − 17 = ?

⇒ 11 + 9 × 2 − 17 = ?

⇒ 11 + 18 − 17 = ?

⇒ 29 − 17 = ?

⇒ 12 = ?

Hence, the correct answer is "Option 1".

The position and positional values or English Alphabets are:

Given: KTV 12, IRT 24, GPR 36, ENP 48, ?

The logic followed here is:

Thus, CLN 60 will replace the question mark (?) in the given series to make it logically complete.

Hence, the correct answer is "Option 1".

Given: (Left) 4 3 5 2 9 7 2 8 7 2 1 8 7 4 5 5 2 3 5 5 6 9 6 3 3 (Right)

Now,

Odd digits, each of which is immediately preceded by an odd digit and also immediately followed by an odd digit.

So, the needed pattern is: Odd — Odd — Odd

Thus, there is one odd digit, which is immediately preceded by an odd digit and also immediately followed by an odd digit.

Hence, the correct answer is "Option 1".

Statements:

Some Llamas are Sheep.

All Sheep are Mules.

No Mules are Pigeons.

The least possible Venn diagram for the given statement is:

Conclusion:

(I) Some Llamas are Mules. - True (Because Some Llamas are Sheep and All Sheep are Mules, which means Some Llamas are Mules.)

(II) No Sheep are Pigeons. - True (Because All Sheep are Mules and No Mules are Pigeons, which means No Sheep are Pigeons.)

Thus, both conclusions (I) and (II) follow.

Hence, the correct answer is "Option 3".

Given: 5 9 17 29 45 65 ?

The logic followed here is:

Thus, 89 should come in place of the question mark (?) in the given series to make it logically complete.

Hence, the correct answer is "Option 1".

The position and positional values or English Alphabets are:

The logic followed here is:

Similarly,

Thus, BKIW is related to XDEP.

Hence, the correct answer is "Option 2".

Given: A, B, C, D, E, F and G are sitting around a circular table facing the centre.

1. E sits to the immediate right of D.
2. G sits second to the left of E.
3. B sits third to the right of E.
4. A is the immediate neighbour of C and B.

F, the only person left will occupy the vacant position.

Thus, two people sit between F and C when counted from the left of F.

Hence, the correct answer is "Option 4".

Given: (Left) 8 4 6 4 6 1 9 6 7 2 2 2 2 1 5 5 1 6 6 7 2 5 5 (Right)

Now,

Odd digits, each of which is immediately preceded by an odd digit and also immediately followed by an even digit.

So, the needed pattern is: Odd — Odd — Even

Thus, there are two odd digits, each of which is immediately preceded by an odd digit and also immediately followed by an even digit.​

Hence, the correct answer is "Option 4".

Given: Seven people B, C, D, I, J, K and L are sitting around a circular table facing the centre of the table.

1. K sits third to the left of L.
2. I sits to the immediate left of L.
3. D sits to the immediate left of J.
4. J sits second to the left of C.

Thus, K sits third to the right of B.

Hence, the correct answer is "Option 3".

Given: Seven boxes B, D, E, P, S, T and W are kept one over the other but not necessarily in the same order.

1. Only S is kept above P.
2. Only two boxes are kept between P and D.
3. Only E is kept below B.
4. T is not kept immediately above D.

W, the only person left will occupy the vacant position.

Thus, two boxes are kept between W and E.10

Hence, the correct answer is "Option 4".01

The logic followed here is:

Logic: a : b → a ÷ b = 7

14 : 2 → 14 ÷ 2 = 7

119 : 17 → 119 ÷ 17 = 7

Similarly,

105 : 15 → 105 ÷ 15 = 7 

Thus, 105 and 15 follow the same relationship.

Hence, the correct answer is "Option 1".

Given: Mr. Akai starts from Point A and drives 15 km towards south. He then takes a right turn, drives 18 km, turns right and drives 25 km. He then takes a right turn and drives 16 km, turns right drives 5 km. He then takes a left turn drives 6 km. He takes a final right turn, drives 5 km and stops at Point P.

Thus, he should drive 4 km to the west to reach point A from point P.

Hence, the correct answer is "Option 2".

Given: If 2 is added to each odd digit and 1 is subtracted from each even digit in the number 5147934, then:

Digit third from the left → 3

Digit second from the right → 5

Sum = 3 + 5 = 8

Thus, 8 will be the sum of the digits which are third from the left and second from the right.

Hence, the correct answer is "Option 4".

Given: A, B, C, D, W, X and Y are sitting in a straight line facing north.

1. Only two people sit to the left of C.
2. Only three people sit between C and W.
3. Only one person sits between W and X.
4. D sits to the immediate left of A.
5. Y is not an immediate neighbour of W.

So, Y sits between C and X.

B, the only person left will occupy the vacant position.

Thus, one people sit to the right of B.

Hence, the correct answer is "Option 1".

Given: Seven boxes A, B, C, D, E, F and G are kept one over the other but not necessarily in the same order.

1. Only E is kept above A. 2. Only two boxes are kept above G. 3. G is kept immediately above B. 4. D is kept immediately above F. 5. D is not kept at third position from the bottom.

C, the only person left will occupy the vacant position.

Thus, 5 boxes are kept above D.

Hence, the correct answer is "Option 1".5