RRB Group D Official Paper (Held On: 03 Feb, 2026 Shift 3) (Previous Year Paper)

The correct answer is Binary fission.

Key Points

• Binary fission is a method of asexual reproduction where a single parent cell divides into two approximately equal daughter cells.
• It is the primary mode of reproduction in prokaryotic organisms, specifically bacteria and archaea.
• The process begins with the replication of the circular DNA (nucleoid) of the bacterium. The two DNA molecules then move to opposite ends of the cell.
• As the cell elongates, a septum (a new cell wall) forms in the middle of the cell, eventually leading to cytokinesis, which splits the cytoplasm.
• This results in two genetically identical offspring that are clones of the original parent.
• Because bacteria lack a nucleus and membrane-bound organelles, this process is significantly faster and simpler than mitosis seen in eukaryotes. For instance, Escherichia coli can undergo this division every 20 minutes under optimal temperature and nutrient conditions.

Additional Information

• Fragmentation:
• This is a form of asexual reproduction where the body of the parent organism breaks into several fragments, and each fragment develops into a new, complete individual.
• It is common in multicellular organisms like filamentous algae (e.g., Spirogyra), fungi, and some invertebrates like Planaria (flatworms).
• Budding:
• In this process, a small outgrowth or bud develops on the body of the parent organism due to repeated cell division at one specific site.
• The bud gradually grows, receives nutrients from the parent, and eventually detaches to lead an independent life.
• Classic examples include unicellular fungi like Yeast and multicellular organisms like Hydra.
• Spore Formation:
• Organisms produce specialized reproductive structures called spores, which are typically unicellular and encased in a protective thick wall to survive harsh environmental conditions.
• When conditions become favorable (adequate moisture and warmth), these spores germinate into new individuals.
• This method is common in Fungi (e.g., Rhizopus or bread mold), Ferns, and Mosses. Note that in bacteria, endospores are primarily a survival mechanism rather than a reproductive one.

Important Points

• Asexual Reproduction: This mode involves only one parent and occurs without the fusion of gametes, ensuring that the genetic makeup remains consistent across generations, except in cases of mutation.
• Generation Time: In the context of binary fission, the time required for a bacterial population to double is called the generation time or doubling time, which is a critical factor in microbiology and infection control.
• Horizontal Gene Transfer: While binary fission produces identical clones, bacteria achieve genetic diversity through other mechanisms like conjugation, transformation, and transduction, rather than through their primary reproductive method.

The correct answer is A group of atoms carrying a net charge is called a polyatomic ion.

Key Points

• An ion is a charged particle formed by the loss or gain of electrons by an atom or a group of atoms. These can be classified into two types: cations and anions.
• A cation is a positively charged species formed when an atom loses one or more electrons. For example, Sodium (Na+). Hence, statement 1 is incorrect.
• A polyatomic ion consists of a group of atoms joined together by covalent bonds, behaving as a single unit that carries a specific net electrical charge. Common examples include the Ammonium ion (NH4+), Hydroxide ion (OH-), and Carbonate ion (CO3 2-). Hence, statement 2 is correct.
• Ions are formed from both metal and non-metal atoms. Usually, metals form cations (positive ions) by losing electrons, while non-metals form anions (negative ions) by gaining electrons. Hence, statement 3 is incorrect.
• Sodium chloride (NaCl) is a classic example of an ionic compound. It does not consist of neutral atoms; instead, it is composed of Sodium cations (Na+) and Chloride anions (Cl-) held together by strong electrostatic forces of attraction. Hence, statement 4 is incorrect.
• Hence, the correct answer is A group of atoms carrying a net charge is called a polyatomic ion.

Additional Information

• Formation of Ions:
• Atoms participate in ion formation to achieve a stable noble gas configuration (octet rule).
• The energy required to remove an electron from a neutral atom is known as Ionization Potential, whereas the energy released when an electron is added is Electron Affinity.
• Types of Polyatomic Ions:
• Oxyanions: These are polyatomic ions that contain oxygen, such as Sulfate (SO4 2-), Nitrate (NO3-), and Phosphate (PO4 3-).
• Monatomic Ions: Unlike polyatomic ions, these consist of only a single atom with a charge, such as Magnesium ion (Mg2+) or Fluoride ion (F-).
• Chemical Formulas of Ionic Compounds:
• When writing formulas for compounds containing polyatomic ions, the ion is often enclosed in brackets if a subscript is needed to indicate its numerical ratio (e.g., Mg(OH)2).
• The total positive charge must balance the total negative charge to ensure the compound is electrically neutral.

Important Points

• Valency: This refers to the combining capacity of an atom or a group of atoms. For ions, the valency is equal to the magnitude of the charge it carries. For instance, the valency of Aluminum (Al3+) is 3.
• Size Comparison:
• A cation is always smaller than its parent neutral atom because the loss of electrons reduces electron-electron repulsion and often results in the loss of an entire shell.
• An anion is always larger than its parent neutral atom due to increased repulsion between the extra electrons.
• Electrolytes: Substances that dissociate into ions when dissolved in water or melted are called electrolytes. These ions act as charge carriers, allowing the solution to conduct electricity.

The correct answer is Ureters.

Key Points

• The Ureters are narrow, hollow, muscular tubes that connect the kidneys to the urinary bladder. Each person typically has two ureters, one attached to each kidney.
• The primary function of the ureter is to transport urine, which is continuously formed by the kidneys, down to the urinary bladder for storage. Hence, the correct answer is Ureters.
• Urine does not simply flow down due to gravity; the walls of the ureters contract and relax in peristaltic waves. These rhythmic contractions occur about one to five times per minute to push urine toward the bladder.
• In an adult, the ureters are approximately 25 to 30 cm (10 to 12 inches) long and have a diameter of about 3 to 4 mm.
• The ureters enter the urinary bladder at an oblique angle through the bladder wall. This specific anatomical arrangement acts like a valve, preventing the backflow (reflux) of urine from the bladder back into the kidneys when the bladder is full or during micturition (urination).

Additional Information

• Vena Cava:
• The Vena Cava is the largest vein in the human body. There are two parts: the Superior Vena Cava (carrying blood from the upper body) and the Inferior Vena Cava (carrying blood from the lower body).
• Its primary function is to transport deoxygenated blood from various parts of the body back to the right atrium of the heart. It is part of the circulatory system, not the urinary system.
• Artery:
• Arteries are blood vessels that carry oxygenated blood away from the heart to the rest of the body (except for the pulmonary artery).
• In the context of the renal system, the Renal Artery supplies oxygen-rich and unfiltered blood from the Aorta to the kidneys.
• Vein:
• Veins are blood vessels that carry deoxygenated blood toward the heart.
• The Renal Vein carries filtered, deoxygenated blood away from the kidneys to the Inferior Vena Cava. Neither arteries nor veins carry urine; they carry blood.
• Urinary Bladder:
• The Urinary Bladder is a muscular, pear-shaped sac located in the pelvic cavity. It serves as a temporary reservoir for urine.
• The bladder wall contains the detrusor muscle, which contracts to expel urine during urination. An average adult bladder can hold between 400 to 600 ml of urine.

Important Points

• The Human Excretory System:
• The main components include a pair of kidneys, a pair of ureters, a urinary bladder, and a urethra.
• The Kidneys are the primary organs for homeostasis, filtering approximately 120 to 150 quarts of blood daily to produce about 1 to 2 quarts of urine.
• The Urethra is the tube that conveys urine from the urinary bladder to the outside of the body. In males, it also serves as a passage for semen, whereas in females, it is strictly part of the urinary system.
• Renal Pelvis: This is the funnel-like dilated proximal part of the ureter in the kidney where urine collects before entering the tube.

The correct answer is A mixture retains the individual properties of its constituents.

Key Points

• A mixture is a substance made by combining two or more different materials in such a way that no chemical reaction occurs. Because no new chemical bonds are formed, each constituent substance in a mixture keeps its own physical and chemical properties. For example, in a mixture of iron filings and sulfur powder, the iron remains magnetic and the sulfur remains yellow. Hence, statement 4 is correct.
• A compound is a substance formed when two or more chemical elements are chemically bonded together. Once bonded, the constituent elements lose their original properties and the resulting compound has entirely new characteristics. For instance, Liquid Water (H2O) is formed from Hydrogen and Oxygen, which are both gases at room temperature. Hence, statement 2 is incorrect.
• Compounds cannot be separated into their constituents by physical methods such as filtration, distillation, or decantation. They require chemical methods or electrochemical reactions (like electrolysis) to break the chemical bonds. Hence, statement 1 is incorrect.
• A mixture does not have a fixed ratio; its composition is variable. You can mix salt and sand in any proportion. In contrast, compounds always contain elements in a fixed, definite proportion by mass, according to the Law of Definite Proportions. Hence, statement 3 is incorrect.

Additional Information

• Classification of Mixtures:
• Homogeneous Mixtures: These have a uniform composition throughout. Examples include Air, Alloys like Brass, and Salt solutions.
• Heterogeneous Mixtures: These have a non-uniform composition and visible boundaries of separation. Examples include Oil and Water, Soil, and Mixture of pulses and stones.
• Energy Changes:
• During the formation of a mixture, energy (in the form of heat, light, or sound) is usually neither absorbed nor evolved.
• In the formation of a compound, energy is almost always involved as chemical bonds are either broken or created.
• Melting and Boiling Points:
• Compounds have sharp and fixed melting and boiling points because of their definite structure.
• Mixtures do not have fixed melting or boiling points; they melt or boil over a range of temperatures depending on the concentration of their components.

Important Points

• Law of Constant Proportions: Proposed by Joseph Proust in 1799, it states that a chemical compound always contains exactly the same proportion of elements by mass. This is a fundamental differentiator from mixtures.
• Constituent Identity: In Chemistry, the "identity" of a substance refers to its molecular structure. In a mixture, the molecules of substance A and substance B simply coexist. In a compound, substance A and B react to form a new molecule C.
• Separation Techniques: Mixtures are separated using physical properties like solubility, density, boiling point, or magnetism. For example, fractional distillation is used to separate crude oil (a mixture) into its components.

The correct answer is Black.

Key Points

• Silver articles react with sulfur compounds, specifically hydrogen sulphide (H2S), present in the air to undergo a chemical process called tarnishing.
• This reaction results in the formation of a layer of silver sulphide (Ag2S) on the surface of the metal. Hence, the statement regarding the formation of a coating is correct.
• The physical appearance of this silver sulphide coating is distinctly Black, which causes the silver to lose its shiny, metallic luster. Hence, the option "Black" is correct.
• The chemical equation for this process is typically represented as: 4Ag + 2H2S + O2 → 2Ag2S + 2H2O. This indicates that oxygen also plays a role in the oxidation of silver in the presence of moisture.
• Unlike the rusting of iron, which can eat away the entire metal, the corrosion of silver is generally a surface phenomenon that provides a protective layer against further deep oxidation, although it is aesthetically undesirable.

Additional Information

• Corrosion of Iron (Rusting):
• When iron is exposed to moist air for a long time, it acquires a coating of a reddish-brown flaky substance called rust.
• Rust is chemically known as hydrated ferric oxide [Fe2O3.xH2O]. This process requires both oxygen and water.
• Corrosion of Copper:
• Copper reacts with moist carbon dioxide in the air and slowly loses its shiny brown surface.
• It gains a green coating consisting of basic copper carbonate [CuCO3.Cu(OH)2]. This is often seen on old copper statues or coins.
• Prevention of Corrosion:
• Various methods are used to protect metals, such as Galvanization (coating iron with zinc), Anodizing, Painting, Greasing, and Alloying.
• Stainless steel is an alloy of iron, nickel, and chromium, which does not rust easily and is widely used in kitchenware.
• Reactivity Series:
• Metals like Gold and Platinum are found at the bottom of the reactivity series and do not corrode easily because they are chemically inert under normal atmospheric conditions.
• Silver is slightly more reactive than gold, which is why it reacts with sulfur but not readily with pure oxygen at room temperature.

Important Points

• Hydrogen Sulphide (H2S): This gas is often found in the atmosphere due to industrial pollution, decaying organic matter, or volcanic activity. Higher concentrations of H2S lead to faster tarnishing of silver.
• Redox Reaction: Corrosion is a redox reaction where the metal acts as a reducing agent (loses electrons) and is oxidized by the environment.
• Cleaning Silver: The black coating can be removed by reacting it with aluminum foil in a solution of baking soda and hot water; this is an electrochemical process where the sulfur is transferred from the silver to the aluminum.

The correct answer is Submergence of forests.

Key Points

• Environmental Impact: The construction of big dams requires the creation of massive reservoirs. To accommodate these reservoirs, vast areas of natural forests and agricultural land are permanently flooded. Hence, the statement regarding the submergence of forests is correct.
• Loss of Biodiversity: When forests are submerged, the natural habitat of countless species of flora and fauna is destroyed. This leads to a significant decrease in biological diversity, as many endemic species may face local extinction. Hence, the statement regarding increased biodiversity is incorrect as dams lead to a decrease.
• Greenhouse Gas Emissions: The submerged vegetation undergoes anaerobic decomposition under the water. This process releases significant amounts of methane (CH4) and carbon dioxide (CO2), which are potent greenhouse gases contributing to global warming.
• Disruption of River Flow: Big dams alter the natural flow of rivers, which affects the aquatic ecosystem. It prevents the migration of fish and other aquatic organisms, disrupting their breeding cycles and life history.
• Sedimentation: Dams trap sediments that would naturally flow downstream. This leads to siltation in the reservoir, reducing its capacity over time, and deprives downstream floodplains of nutrient-rich alluvial soil.

Additional Information

• Social Impacts and Displacement: One of the biggest challenges of large dam projects like the Narmada Sarovar Project is the displacement of large populations, especially tribal communities and rural poor, who lose their livelihood and cultural heritage.
• Seismic Sensitivity: Large reservoirs exert immense pressure on the earth's crust. In seismically active zones, such as the Himalayan region (e.g., the Tehri Dam in Uttarakhand), this can potentially trigger Reservoir Induced Seismicity (RIS), leading to earthquakes.
• Waterlogging and Salinity: In the command areas of large dams, excessive irrigation often leads to waterlogging. This brings salts to the surface, making the soil saline and unfit for agriculture over the long term.
• Recreational and Economic Benefits: While dams provide hydroelectric power, flood control, and water conservation (which are advantages), they are often critiqued because the ecological costs far outweigh these benefits in many environmental impact assessments. Hence, water conservation and recreational spaces are considered advantages, not disadvantages.

Important Points

• Case Study: Narmada Bachao Andolan: This is a famous environmental movement in India led by activists like Medha Patkar. It protested against the Sardar Sarovar Dam on the Narmada River due to the massive submergence of forests and the lack of proper rehabilitation for displaced people.
• International Commission on Large Dams (ICOLD): This organization sets standards for dam construction globally, emphasizing the need for sustainable development and minimizing environmental degradation.
• Sustainable Alternatives: To mitigate these disadvantages, environmentalists often suggest small-scale check dams, rainwater harvesting, and watershed management as more eco-friendly ways to ensure water security without destroying forest ecosystems.

The correct answer is A sharp, sour smell and taste.

Key Points

• Ethanoic acid, which is widely known by its common name Acetic acid, is a colorless liquid organic compound with the chemical formula CH3COOH.
• It belongs to the group of carboxylic acids and is characterized by a very distinctive pungent and sharp odor, similar to the smell of concentrated vinegar.
• The taste of ethanoic acid is sour, which is a fundamental property of most acids; this sourness is what gives vinegar its characteristic flavor profile. Hence, statement 1 is correct.
• In everyday life, vinegar is actually a dilute solution of ethanoic acid in water, usually containing between 5% and 8% of the acid by volume.
• The name "acetic" is derived from the Latin word acetum, which translates directly to vinegar.

Additional Information

• Acidity and Litmus Test: Ethanoic acid is a weak acid, meaning it does not fully dissociate in water. However, it still exhibits acidic properties and will turn blue litmus paper red. It also reacts with reactive metals like magnesium or zinc to evolve Hydrogen gas. Hence, statement 2 is incorrect.
• pH and Texture: Substances that feel slippery and have a basic pH (greater than 7) are bases (alkalis). Ethanoic acid has an acidic pH (typically around 2.4 for a 1.0 M solution) and does not possess a soapy or slippery texture. Hence, statement 3 is incorrect.
• Odor Profile: While acetic acid has a sharp, vinegar-like smell, it is the esters (formed by the reaction of the acid with alcohols) that are famous for having a sweet, fruity smell. Pure ethanoic acid itself does not smell fruity. Hence, statement 4 is incorrect.
• Glacial Acetic Acid: The melting point of pure ethanoic acid is 290 K (or 17 degrees Celsius). Because this temperature is close to room temperature, the acid often freezes during winter in cold climates, forming ice-like crystals. For this reason, pure ethanoic acid is frequently called Glacial Acetic Acid.

Important Points

• Chemical Reactions:
• Esterification: When ethanoic acid reacts with absolute ethanol in the presence of an acid catalyst, it forms an ester (Ethyl ethanoate), which is used in making perfumes and flavoring agents.
• Saponification: Esters can react with Sodium hydroxide (NaOH) to be converted back into alcohol and the sodium salt of the carboxylic acid; this reaction is the basis for soap manufacturing.
• Reaction with Bases: Like other acids, it reacts with bases to form a salt and water. For example, reacting with NaOH produces Sodium ethanoate (Sodium acetate).
• Industrial Uses: Beyond its use as a food preservative, it is a vital industrial chemical used in the production of cellulose acetate for photographic film, polyvinyl acetate for wood glue, and various synthetic fibers and fabrics.

The correct answer is A is true, but R is false.

Key Points

• Assertion (A) states that monoculture plantations often fail to meet the diverse needs of forest-dependent villagers. This is because these communities rely on a wide variety of forest products such as fodder, fruits, tubers, and honey for their daily survival, which a single-species plantation cannot provide. Hence, statement A is correct.
• Reason (R) claims that these plantations provide medicinal herbs, food, and fuel for villagers. In reality, monocultures (like Teak, Pine, or Eucalyptus) are usually established for commercial timber or industrial raw materials and do not support the undergrowth of herbs and shrubs that villagers use. Hence, statement R is false.
• Monoculture refers to the practice of growing a single species of tree over a large area, which significantly reduces the ecological diversity of the region.
• Forest-dependent communities, including various tribal groups in India, have traditionally managed natural forests that offer a mix of species, ensuring a sustenance-based economy rather than a purely profit-based one.
• The transition from diverse natural forests to managed plantations has historically led to the displacement of local traditional knowledge and livelihood resources.

Additional Information

• Scientific Forestry: This system was introduced in India by the British under the guidance of Dietrich Brandis, the first Inspector General of Forests, in the 1860s. It promoted the cutting down of natural forests with diverse species to replace them with planned plantations of trees like Teak and Sal, which were useful for railways and shipbuilding.
• Biodiversity Loss: Monoculture plantations lack the canopy layers and species richness found in tropical or temperate natural forests. This leads to a decline in pollinators, birds, and soil microorganisms, ultimately weakening the ecosystem services.
• Fuel and Fodder Needs: Villagers require fuelwood from specific broad-leaved trees that burn well and fodder for their livestock. Commercial species like Eucalyptus are often unsuitable for fodder and can even deplete the groundwater table in semi-arid regions.
• Economic Impact: While monocultures generate revenue for the Forest Department or private industries through the sale of timber, they often lead to the impoverishment of local communities who lose access to Non-Timber Forest Products (NTFPs).

Important Points

• Environmental Risks: Monocultures are highly susceptible to pests and diseases. If a specific pathogen attacks the chosen species, the entire plantation can be wiped out, whereas mixed forests are more resilient.
• Joint Forest Management (JFM): To rectify the failures of exclusionary forestry, the Government of India introduced JFM in the 1980s (formally via the National Forest Policy, 1988). This initiative aims to involve local communities in forest conservation and ensure they have a share in forest produce.
• Forest Rights Act (2006): This Act was a landmark piece of legislation that recognized the customary rights of Scheduled Tribes and Other Traditional Forest Dwellers, acknowledging that their diverse needs are best met through community-led forest management rather than state-imposed monocultures.

The correct answer is 16 m.

Key Points

• The problem states that the car produces an acceleration of 8 m/s² opposite to its motion. In physics, when acceleration is opposite to the direction of velocity, it is termed retardation or deceleration. Therefore, we take the numerical value of acceleration (a) as -8 m/s².
• Since the car comes to a complete halt, its final velocity (v) is 0 m/s. The time (t) taken to stop is given as 2 seconds.
• To find the distance (s), we first need to determine the initial velocity (u) using the first equation of motion: v = u + at. Substituting the values, 0 = u + (-8 × 2), which gives u = 16 m/s.
• Once the initial velocity is known, we apply the second equation of motion: s = ut + ½at² to find the distance. Hence, the calculation becomes s = (16 × 2) + ½ × (-8) × (2)².
• Solving this yields s = 32 - 16 = 16 meters. This represents the total displacement of the car from the moment the brakes were applied until it reached a standstill. Hence, the calculated distance is correct.
• Alternatively, the third equation of motion (v² = u² + 2as) can be used. Plugging in the values: 0² = 16² + 2 × (-8) × s, which results in 0 = 256 - 16s, or s = 16 m. Hence, the correct answer is 16 m.

Additional Information

• Kinematic Equations: These equations describe the motion of objects under constant acceleration. They relate five variables: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
• Uniform Acceleration: This refers to a scenario where the velocity of an object changes by the same numerical value in every equal interval of time. In this question, the car slows down uniformly, meaning the rate of change of velocity remains constant at 8 m/s².
• Retardation: Also known as negative acceleration, it occurs when the force applied (like braking force) is in the direction opposite to the displacement. It results in a decrease in the magnitude of velocity over time.
• SI Units: In physics, it is crucial to use standard International System of Units. Here, distance is measured in meters (m), time in seconds (s), velocity in meters per second (m/s), and acceleration in meters per second squared (m/s²).

Important Points

• Sign Convention: While solving mechanics problems, assigning the correct sign (+ or -) to vectors is vital. If motion is taken as positive, then braking acceleration must be negative.
• Area under V-T Graph: The distance covered can also be calculated by finding the area under a velocity-time graph. For a car slowing down from 16 m/s to 0 m/s in 2 seconds, the graph forms a triangle. Area = ½ × base × height = ½ × 2 × 16 = 16 m.
• Braking Distance: The distance covered after applying brakes is influenced by the initial speed and the braking efficiency (acceleration). In real-world automotive engineering, this is a key safety metric.

The correct answer is Pollination and fertilisation.

Key Points

• The stigma is the uppermost part of the carpel (the female reproductive organ of a flower) and serves as the receptive platform for pollen grains during the process of pollination.
• Pollination is the physical transfer of pollen from the anther (male part) to the stigma; if the stigma is damaged or removed, the pollen cannot land or be recognized, effectively halting the reproductive cycle. Hence, statement 2 is correct.
• Following a successful landing, the stigma provides the necessary nutrients and moisture for the pollen grain to germinate and grow a pollen tube down the style to reach the ovary for fertilisation.
• Seed dispersal is the mechanism by which seeds are spread away from the parent plant, which occurs only after the ovules have been successfully fertilised and developed into seeds. Hence, statement 1 is incorrect.
• Fruit ripening is a physiological process that follows fertilisation, where the ovary wall transforms into a pericarp; this stage is not directly dependent on the stigma's integrity once fertilisation has occurred. Hence, statement 3 is incorrect.
• The formation of petals and sepals happens during the bud development stage (pre-anthesis) and is controlled by floral meristem identity genes, occurring well before the stigma becomes functional for pollination. Hence, statement 4 is incorrect.

Additional Information

• Structure of the Gynoecium:
• The Gynoecium represents the female reproductive unit of a flower, consisting of one or more carpels. Each carpel is divided into three distinct regions: the stigma, style, and ovary.
• The stigma often has a sticky or feathery surface to efficiently trap pollen grains from various pollinating agents like wind, water, or insects.
• The Process of Fertilisation:
• Once pollen germinates on the stigma, the pollen tube carries two male gametes. In angiosperms, this leads to double fertilisation, a unique feature where one gamete fuses with the egg to form a zygote (2n) and the other fuses with polar nuclei to form the endosperm (3n).
• The ovary eventually matures into the fruit, while the ovules mature into seeds.
• Types of Pollination:
• Self-pollination: Transfer of pollen from the anther to the stigma of the same flower or another flower on the same plant.
• Cross-pollination (Xenogamy): Transfer of pollen from the anther of one flower to the stigma of a flower on a different plant of the same species, increasing genetic diversity.

Important Points

• Stigmatic Compatibility: The stigma performs a "chemically-mediated" recognition check to ensure only compatible pollen of the same species (and sometimes avoiding self-pollen to prevent inbreeding) is allowed to grow.
• Environmental Factors: Factors such as extreme temperature, heavy rain, or pesticide exposure can damage the stigma, leading to crop failure due to poor fruit set and lack of fertilisation.
• Morphological Adaptations: In wind-pollinated plants (like maize), the stigma is often long and tassel-like to maximize the surface area for catching airborne pollen.

The correct answer is m, g and h.

Key Points

• Gravitational Potential Energy is the energy possessed by an object by virtue of its position in a gravitational field. It represents the potential to do work when the object is released.
• The formula for calculating potential energy (U) is given by the product of mass (m), acceleration due to gravity (g), and height (h): U = mgh.
• Mass (m): The energy is directly proportional to the mass of the body. An object with a larger mass will possess higher potential energy compared to a lighter object at the same height.
• Acceleration due to gravity (g): The energy depends on the strength of the gravitational field. On Earth, the average value of g is approximately 9.8 m/s². If the same object were taken to the Moon, where g is roughly 1.62 m/s², its potential energy would decrease even if the height remained the same.
• Height (h): This refers to the vertical displacement from a chosen reference level (datum). The higher the body is raised, the more potential energy it accumulates.
• Since the energy formula contains all three variables as multipliers, the potential energy depends on m, g, and h simultaneously. Hence, the correct answer is m, g and h.

Additional Information

• Work-Energy Principle: When a body is lifted, work is done against the force of gravity. This work done (W = Force × Displacement) is stored in the body as Gravitational Potential Energy. Since Force = mg and Displacement = h, the work done is mgh.
• SI Unit and Dimensions: The Standard International (SI) unit of potential energy is the Joule (J), which is equivalent to kg·m²/s². The dimensional formula is [ML²T⁻²], which is the same as that for work and kinetic energy.
• Reference Point: Potential energy is a relative quantity. It is usually measured relative to the ground, where h = 0 and U = 0. However, any arbitrary level can be chosen as the zero-potential level.
• Conservative Nature: The gravitational force is a conservative force. This means the potential energy depends only on the initial and final positions (the vertical height h) and is independent of the path taken to reach that height.

Important Points

• Variations in g: While g is often treated as a constant (9.8 m/s²), it actually varies slightly depending on the latitude (it is higher at the poles than at the equator) and altitude (it decreases as you go higher above sea level).
• Energy Transformation: According to the Law of Conservation of Energy, when an object falls, its potential energy is converted into kinetic energy (the energy of motion). At any point during a free fall (neglecting air resistance), the total mechanical energy (sum of PE and KE) remains constant.
• Sign Convention: If an object is moved upward, the potential energy increases (positive work done against gravity). If an object moves below the reference level, its potential energy is considered negative.

The correct answer is 360 kg and 360 kg wt.

Key Points

• Weight changes with gravity, but mass remains the same everywhere.
• On the Moon: Weight = 60 kg-wt
• Since the Moon's gravity is 1/6 of Earth's gravity, 
• Weight on Earth = 6× Weight on Moon
• = 6 × 60 = 360 Kg-Wt
• Now, A kilogram-weight (kg-wt) represents the gravitational pull of the Earth on a mass of 1 kg.
• For this question, 1 kg-wt is equal to 10N. (g on Earth 10 m/s²)
• 360 Kg-Wt = 360 × 10 = 3600N. (Convert to SI un it)
• Mass = weight on Earth / acceleration due to gravity on Earth
• ​Mass = 3600/10 = 360 kg
• Hence, the correct answer is,
• Mass on Earth = 360 kg
• Weight on Earth = 360 kg-wt

Additional Information

• Mass:
• It is the intrinsic property of a body that determines its inertia.
• The S.I. unit of mass is the kilogram (kg).
• It is a scalar quantity, meaning it has only magnitude and no direction. It remains the same on Earth, the Moon, or even in outer space.
• Weight:
• It is the gravitational force acting on an object. The formula is W = m x g, where m is mass and g is the acceleration due to gravity.
• The S.I. unit of weight is the Newton (N), but it is often expressed in kg wt for practical purposes.
• It is a vector quantity because it always acts vertically downwards towards the center of the planet.

The correct answer is to ensure uniform sound distribution.

Key Points

• The primary objective of using curved ceilings and walls in large auditoriums, concert halls, and cinema theaters is to utilize the reflection of sound effectively.
• When sound waves strike a curved surface (specifically a concave surface), they are reflected in a way that allows the waves to spread out and reach all corners of the hall.
• This design ensures that the sound is distributed uniformly throughout the entire audience area, preventing the formation of "dead spots" where the sound might be faint or inaudible. Hence, statement 2 is correct.
• The curved ceiling acts like a large reflector, redirecting sound waves that travel upwards back down toward the listeners sitting at the back of the hall.
• Contrary to some misconceptions, the shape of the walls does not reduce the speed of sound, as the speed of sound is a property of the medium (like air) and depends on factors like temperature and humidity, not the shape of the container. Hence, statement 1 is incorrect.
• The purpose is to make the sound audible to the entire audience, not just to make it louder near the stage. Hence, statement 3 is incorrect.
• While architectural beauty is a factor in construction, the specific curved geometry in a hall's design is dictated by acoustical engineering requirements rather than purely aesthetic reasons. Hence, statement 4 is incorrect.

Additional Information

• Soundboard: In many large halls, a curved soundboard is placed behind the speaker or the stage. The source of sound is placed at the focus of this board so that the reflected sound waves emerge as parallel beams, ensuring they travel long distances across the hall.
• Reflection of Sound: Just like light, sound follows the laws of reflection, where the angle of incidence is equal to the angle of reflection. This principle is fundamental in acoustics for designing functional spaces.
• Reverberation: While reflection is necessary for audibility, excessive reflection can lead to reverberation, which is the persistence of sound after the source has stopped. To control this, halls often use sound-absorbent materials like compressed fiberboard, heavy curtains, or plaster on the non-curved surfaces.
• Echo: An echo is a distinct repetition of sound caused by reflection. For an echo to be heard clearly by the human ear, the minimum distance between the source and the reflecting surface must be approximately 17.2 meters (at 22 degrees Celsius).
• Multiple Reflection: Curved surfaces utilize the concept of multiple reflection. This same principle is used in instruments like megaphones, horns, and stethoscopes to direct sound in a specific direction without it spreading in all directions prematurely.

Important Points

• Acoustics of Buildings: This is a branch of physics that deals with the design and construction of buildings to provide the best possible audible sound to the audience.
• Concave vs. Convex: While concave surfaces (like curved ceilings) converge or direct sound toward the audience, convex surfaces would diverge sound waves, potentially making the sound thinner and harder to hear in large spaces.
• Intensity of Sound: The use of curved reflectors helps in maintaining the intensity of the sound over a larger area, reducing the attenuation (loss of energy) that occurs as sound waves travel.

The correct answer is Real, inverted, and diminished.

Key Points

• When an object is placed beyond the Centre of Curvature (C) of a concave mirror, the rays of light originating from the object follow specific paths according to the laws of reflection.
• A ray of light starting from the top of the object and traveling parallel to the principal axis will, after reflection, pass through the Principal Focus (F).
• Another ray passing through the Centre of Curvature (C) strikes the mirror normally and reflects back along the same path.
• The point where these two reflected rays intersect is the location of the image. In this specific case, the intersection occurs between the Centre of Curvature (C) and the Focus (F).
• The image formed is Real because the reflected rays actually meet at a point. It is Inverted (upside down) relative to the object and Diminished (smaller in size) compared to the original object. Hence, the correct answer is Real, inverted, and diminished.

Additional Information

• Concave Mirror: It is a spherical mirror with a reflecting surface that curves inwards (like a spoon). It is also known as a converging mirror because it converges parallel rays of light after reflection.
• Important Terms:
• Pole (P): The center of the reflecting surface of the mirror.
• Centre of Curvature (C): The center of the hollow sphere of which the mirror is a part.
• Principal Focus (F): The point on the principal axis where all parallel rays converge after reflection.
• Focal Length (f): The distance between the Pole and the Focus. It is exactly half of the Radius of Curvature (R), given by f = R/2.
• Mirror Formula: The relationship between object distance (u), image distance (v), and focal length (f) is expressed as 1/v + 1/u = 1/f.
• Magnification (m): It is the ratio of the height of the image to the height of the object. It is also given by m = -v/u. For a diminished image, the absolute value of magnification is less than 1.
• Uses: Concave mirrors are widely used in shaving mirrors, dentists' mirrors, solar furnaces, and car headlights to produce powerful parallel beams of light.

Important Points

• Other Cases of Image Formation by Concave Mirror:
• If the object is at Infinity, the image is formed at Focus (F) and is highly diminished, real, and inverted.
• If the object is at C, the image is formed at C and is of the same size, real, and inverted. Statement 3 is incorrect for the given question.
• If the object is between C and F, the image is formed beyond C and is magnified, real, and inverted. Statement 4 is incorrect for the given question.
• If the object is at F, the image is formed at Infinity and is highly magnified.
• If the object is between F and Pole (P), the image is formed behind the mirror and is Virtual, erect, and magnified. Statement 2 is incorrect for the given question.
• A Real image can be obtained on a screen, whereas a Virtual image cannot.
• The nature of the image changes from real to virtual only when the object moves within the focal length of the concave mirror.

The correct answer is Nucleus.

Key Points

• Binary fission in Amoeba is a method of asexual reproduction where a single parent cell divides into two equal daughter cells.
• The very first step in this process is the division of the nucleus, a biological stage known as karyokinesis.
• During karyokinesis, the nucleus of the Amoeba begins to elongate and develop a constriction in the middle, eventually splitting the genetic material into two separate parts.
• Once the nucleus has successfully divided into two daughter nuclei, the second stage, called cytokinesis, begins. This is the division of the cytoplasm.
• In cytokinesis, the cell body constricts and pinches off, resulting in the formation of two distinct, independent Amoeba individuals. Hence, the nucleus is the first organelle to divide during this process.

Additional Information

• Amoeba:
• It is a unicellular eukaryote belonging to the kingdom Protista.
• Amoeba proteus is one of the most common species studied in biology. It was first discovered in 1755 by August Johann Rösel von Rosenhof.
• It lacks a cell wall and instead possesses a flexible plasma membrane, which allows it to change shape and move using pseudopodia (false feet).
• Cytoplasm:
• The cytoplasm is the jelly-like substance where most metabolic activities occur. During binary fission, it only begins its division after the nucleus has finished its separation to ensure each daughter cell receives a copy of the DNA.
• Vacuole:
• Amoebae contain contractile vacuoles for osmoregulation and food vacuoles for digestion. While these may be replicated or distributed during fission, they are not the primary drivers or the first to initiate the division process.
• Cell Wall:
• This option is incorrect because Amoeba is an animal-like protist and does not possess a cell wall. Cell walls are typically found in plants, fungi, and bacteria.

Important Points

• Asexual Reproduction: Since only one parent is involved and the offspring are genetically identical to the parent, the daughter cells are often referred to as clones.
• Environmental Conditions: Binary fission typically occurs during favorable conditions (adequate food and temperature). During unfavorable conditions, Amoeba may undergo multiple fission or encystment.
• Irregular Binary Fission: In Amoeba, binary fission is described as "irregular" because the plane of cytoplasmic division can occur in any direction, unlike in Leishmania (longitudinal) or Paramecium (transverse).
• Mitosis: The nuclear division in Amoeba involves a process similar to mitosis, where the chromosomes are replicated and distributed equally, ensuring the continuity of biological information across generations.

The correct answer is They release energy due to stable product formation.

Key Points

• A combination reaction (also known as a synthesis reaction) is a reaction where two or more elements or compounds combine to form a single compound. The general form is A + B → AB.
• In any chemical reaction, energy is required to break existing bonds in the reactants (an endothermic process), and energy is released when new bonds are formed in the products (an exothermic process).
• Combination reactions are generally exothermic because the energy released during the formation of new bonds in the product is greater than the energy absorbed to break the bonds of the reactants. Hence, statement 3 is correct.
• The formation of a stable product means the system moves to a lower energy state. This excess internal energy is liberated into the surroundings, usually in the form of heat or light.
• Statement 1 is incorrect because bond formation always releases energy, while bond breaking absorbs it. Statement 4 is incorrect as combination reactions primarily focus on bond formation to create a complex molecule from simpler ones.

Additional Information

• Common Examples of Combination Reactions:
• Burning of Coal: When carbon (C) burns in the presence of oxygen (O2), it forms carbon dioxide (CO2) and releases a significant amount of heat. (C + O2 → CO2 + Heat).
• Formation of Water: The reaction between hydrogen gas (H2) and oxygen gas (O2) to form liquid water (H2O) is highly exothermic.
• Slaking of Lime: The reaction of Quick Lime (Calcium Oxide - CaO) with water (H2O) to form Slaked Lime (Calcium Hydroxide - Ca(OH)2) produces a large amount of heat, making the container hot.
• Thermodynamic Perspective:
• In an exothermic reaction, the change in enthalpy (ΔH) is negative. This indicates that the enthalpy of the products is lower than the enthalpy of the reactants.
• Most spontaneous combination reactions occur because the universe tends toward states of lower energy and higher stability.
• Contrast with Decomposition Reactions:
• Unlike combination reactions, decomposition reactions involve the breaking down of a single compound into two or more simpler substances. These typically require an input of energy (heat, light, or electricity) and are therefore endothermic.

Important Points

• Bond Energy: The strength of the bonds in the product determines how much energy is released. Stronger bonds in the product compared to the reactants lead to a more exothermic reaction.
• Stability: In chemistry, lower energy is synonymous with higher stability. Therefore, the drive to form more stable chemical species is the primary reason why these reactions release energy.
• Activation Energy: Even though combination reactions release energy, they may still require a small amount of initial energy (activation energy), such as a spark or flame, to start the process.

The correct answer is catenation.

Key Points

• Catenation is the unique property of carbon atoms to link with one another through covalent bonds to form long chains, branched chains, and closed ring structures.
• This property is primarily due to the small size of the carbon atom and the high strength of the carbon-carbon (C-C) bond.
• The bond energy of the C-C bond is approximately 348 kJ/mol, which is significantly higher than that of other elements like silicon or sulfur, allowing for stable, long-chain molecules.
• Because of catenation, carbon forms the structural backbone of millions of organic compounds, including hydrocarbons, proteins, and DNA. Hence, option 2 is correct.
• The tetravalency of carbon (valency of 4) further supports catenation by allowing each carbon atom to bond with up to four other atoms, facilitating complex molecular architectures.

Additional Information

• Addition Reaction:
• In organic chemistry, an addition reaction occurs when two or more molecules combine to form a larger one. This typically happens in unsaturated compounds like alkenes and alkynes.
• For example, the hydrogenation of ethene to ethane is an addition reaction. It does not refer to the property of atoms linking to themselves. Hence, statement 1 is incorrect.
• Conjugation:
• Conjugation refers to the overlap of p-orbitals across an adjacent sigma bond, typically in a system of alternating single and multiple bonds.
• This leads to the delocalization of electrons, which increases the stability of the molecule (e.g., in benzene). While it involves carbon bonding, it is a specific electronic arrangement rather than the basic property of forming large molecules. Hence, statement 4 is incorrect.
• Unification:
• Unification is not a standard chemical term used to describe the bonding properties or the molecular structural ability of carbon atoms. Hence, statement 3 is incorrect.
• Other Elements showing Catenation:
• While carbon is the leader in catenation, Silicon also shows this property but can only form chains of up to 7 or 8 atoms because the Si-Si bonds are weaker and more reactive toward oxygen and water.
• Sulfur shows catenation in the form of S8 rings and long chains in plastic sulfur, but it lacks the structural variety found in carbon compounds.

Important Points

• Allotropes of Carbon: The property of catenation is vividly seen in carbon's allotropes such as Diamond (3D network), Graphite (hexagonal layers), and Fullerenes (spherical cages like C60).
• Isomerism: Catenation allows for different arrangements of the same number of atoms, leading to structural isomerism. For instance, butane and isobutane have the same formula (C4H10) but different linkages.
• Economic and Biological Importance: The ability of carbon to form stable chains is the reason for the existence of fossil fuels (long-chain alkanes) and the complex biopolymers that make up living organisms.
• Atomic Number: Carbon has an atomic number of 6 and its electronic configuration is 2, 4, which provides the perfect balance for forming stable covalent bonds.

The correct answer is Urea.

Key Points

• The Nephron is the basic functional and structural unit of the Kidney, responsible for filtering the blood and forming urine.
• Urine formation involves three main processes: Glomerular Filtration, Selective Reabsorption, and Tubular Secretion.
• Selective Reabsorption is the process where the renal tubule reclaims useful substances from the Glomerular Filtrate back into the bloodstream. This occurs primarily in the Proximal Convoluted Tubule (PCT).
• Substances like Glucose, Amino acids, and certain Salts are highly useful to the body and are almost entirely reabsorbed via active or passive transport. Hence, options 1, 2, and 4 are selectively re-absorbed.
• Urea is a nitrogenous waste product formed in the Liver. The primary function of the kidney is to excrete urea from the body. While a small amount may passively diffuse back to maintain medullary osmotic pressure, it is NOT selectively re-absorbed for conservation like nutrients. Hence, statement 3 is the correct answer.

Additional Information

• Glucose Reabsorption:
• Under normal physiological conditions, 100% of the filtered Glucose is reabsorbed in the PCT.
• If blood glucose levels exceed the Renal Threshold (approximately 180 mg/dL), the transport carriers become saturated, and glucose is excreted in the urine, a condition known as Glycosuria, often associated with Diabetes Mellitus.
• Amino Acids:
• Like glucose, Amino acids are vital nutrients. They are completely reabsorbed in the Proximal Convoluted Tubule through Secondary Active Transport mechanisms.
• Salts and Electrolytes:
• The body reabsorbs Sodium (Na+), Potassium (K+), and Chloride (Cl-) to maintain Electrolyte Balance and blood pressure.
• About 65-70% of filtered Sodium is reabsorbed in the PCT, while the Distal Convoluted Tubule (DCT) performs conditional reabsorption under the influence of the hormone Aldosterone.
• Urea and Waste Excretion:
• Urea is produced through the Ornithine Cycle in the liver to detoxify ammonia.
• The concentration of Urea increases as the filtrate moves down the tubule because water is reabsorbed, ensuring that the majority of this waste is eliminated in Urine.

Important Points

• Glomerular Filtration Rate (GFR): This is the volume of filtrate formed by both kidneys per minute, typically about 125 mL/min in a healthy adult.
• Tubular Secretion: This is the opposite of reabsorption, where substances like Hydrogen ions (H+), Potassium (K+), and Ammonia (NH3) are moved from the blood into the tubule to maintain Ionic Balance and pH of body fluids.
• Antidiuretic Hormone (ADH): Also known as Vasopressin, it acts on the Collecting Ducts to increase water reabsorption, thereby concentrating the urine and preventing dehydration.
• Henle's Loop: Plays a critical role in the Counter-Current Mechanism, which helps in concentrating the urine by creating an osmotic gradient in the kidney medulla.

The correct answer is Remain same.

Key Points

• The Resistance (R) of a conductor is a property that opposes the flow of electric current. It is mathematically defined by the formula R = ρ(L/A), where ρ represents the resistivity of the material, L is the length, and A is the cross-sectional area.
• In the given scenario, the length of the conductor is halved, which means the new length is L/2 or 0.5L.
• Similarly, the cross-sectional area is also halved, making the new area A/2 or 0.5A.
• When these new values are substituted into the resistance formula, the expression becomes R' = ρ × (L/2) / (A/2). The numerical value of 1/2 in the numerator and 1/2 in the denominator cancel each other out completely.
• Since the material remains the same, the resistivity (ρ) remains constant. As a result, the new resistance R' is exactly equal to the original resistance R. Hence, the statement that the resistance remains the same is correct.

Additional Information

• Resistivity (ρ):
• It is an intrinsic property of a material that quantifies how strongly it resists electric current. Its SI unit is the Ohm-meter (Ω·m).
• Unlike resistance, resistivity does not depend on the dimensions (length or area) of the object; it only depends on the nature of the material and the temperature.
• Ohm's Law:
• Discovered by George Simon Ohm in 1827, this law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points, provided physical conditions like temperature remain constant. The constant of proportionality is Resistance (R).
• Factors Affecting Resistance:
• Length: Resistance is directly proportional to the length of the conductor. Doubling the length doubles the resistance.
• Area: Resistance is inversely proportional to the cross-sectional area. Increasing the thickness of a wire reduces its resistance.
• Nature of Material: Different materials have different concentrations of free electrons. For example, Silver has lower resistance than Iron.
• Temperature: For metallic conductors, resistance generally increases with an increase in temperature.

Important Points

• Distinction between Independent Change and Stretching:
• It is important to distinguish between changing dimensions independently and stretching a wire. If a wire is stretched to double its length, its volume remains constant, causing the area to decrease. In such cases, the resistance would change by a factor of 4 (square of the change in length).
• However, in this specific question, both length and area are explicitly and independently halved, resulting in no net change to the resistance.
• Conductance and Conductivity:
• The reciprocal of resistance is known as conductance (G), measured in Siemens (S).
• The reciprocal of resistivity is known as electrical conductivity (σ), which indicates how easily a material allows current to flow. Its SI unit is Siemens per meter (S/m).

The correct answer is It causes a change in speed or direction of motion.

Key Points

• An unbalanced force is defined as a force where the net force acting on an object is not zero. When such a force is applied to a moving object, it disrupts the state of equilibrium.
• According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. This means an unbalanced force always results in acceleration.
• Because acceleration is a change in velocity, and velocity is a vector quantity consisting of both speed and direction, an unbalanced force can cause the object to speed up, slow down (decelerate), or change its direction of travel. Hence, statement 4 is correct.
• If the forces acting on an object were balanced, the object would continue to move at a constant velocity or remain at rest. An unbalanced force is required to change that state of motion. Hence, statement 1 is incorrect.
• While an unbalanced force can stop an object, it does not necessarily stop it immediately; the time taken to stop depends on the magnitude of the force and the mass of the object. Hence, statement 2 is incorrect.
• The weight of an object is the force of gravity acting on its mass (W = mg). Applying an external horizontal or vertical unbalanced force does not change the inherent mass or the gravitational constant of the object. Hence, statement 3 is incorrect.

Additional Information

• Newton's First Law of Motion: Often called the Law of Inertia, it states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external unbalanced force. This law was first formulated by Sir Isaac Newton and published in 1687.
• Types of Forces: Forces can be categorized as contact forces (like friction, tension, and normal force) or non-contact forces (like gravitational, electrostatic, and magnetic forces). Any of these can contribute to an unbalanced net force.
• Vector Nature: Since force is a vector, the direction of the unbalanced force determines the direction of the resulting acceleration. If the force is applied perpendicular to the direction of motion, only the direction changes (as seen in uniform circular motion).
• SI Unit: The standard unit of force is the Newton (N), defined as the force needed to provide a mass of 1 kilogram with an acceleration of 1 meter per second squared.

Important Points

• Inertia: This is the inherent property of matter by which it resists any change in its state of rest or motion. Mass is a quantitative measure of an object's inertia.
• Friction as an Unbalanced Force: In real-world scenarios, a rolling ball eventually stops because of friction and air resistance, which act as unbalanced forces opposing the direction of motion.
• Mathematical Expression: The relationship is expressed by the formula F = ma, where F is the net unbalanced force, m is the mass, and a is the acceleration. This fundamental equation is the cornerstone of Classical Mechanics.
• Centripetal Force: This is a specific type of unbalanced force that acts toward the center of a circular path, causing a moving object to change direction continuously without necessarily changing its speed.

The correct answer is Both (i) and (ii).

Key Points

• Statement (i): The amount of light scattering is highly dependent on the size of the particles in the medium. If the particles are very small compared to the wavelength of light (like nitrogen and oxygen molecules in the air), Rayleigh scattering occurs. If the particles are large (like water droplets in clouds), they scatter all wavelengths almost equally. Hence, statement (i) is incorrect.
• Statement (ii): According to Rayleigh's Law of Scattering, the intensity of scattered light is inversely proportional to the fourth power of its wavelength (Scattering ∝ 1/λ⁴). This means shorter wavelengths scatter much more than longer wavelengths. It is not directly proportional. Hence, statement (ii) is incorrect.
• Statement (iii): Blue light has a shorter wavelength compared to red light. As light from the Sun enters the Earth's atmosphere, the molecules in the air scatter the blue light more strongly in all directions. This is why the sky appears blue to an observer on the ground. Hence, statement (iii) is correct.
• Statement (iv): Red light has the longest wavelength in the visible spectrum. Due to its long wavelength, it is scattered the least by air molecules, fog, or smoke. This allows the red color to travel longer distances without being dispersed, making it ideal for danger signals. Hence, statement (iv) is correct.
• Since statements (i) and (ii) are the ones that are not true, the correct option is Both (i) and (ii).

Additional Information

• Rayleigh Scattering: Formulated by Lord Rayleigh in 1871, this phenomenon explains why the sky is blue. It occurs when the scattering particles have a diameter significantly smaller (less than 1/10^th) than the wavelength of the incident light.
• The Visible Spectrum: Human eyes can detect wavelengths approximately between 400 nm (violet) and 700 nm (red). Within this range, violet and blue have the highest frequencies and shortest wavelengths, while red has the lowest frequency and longest wavelength.
• Tyndall Effect: This is the scattering of a beam of light by colloidal particles or particles in a very fine suspension. It is often observed when sunlight passes through a canopy of a dense forest where mist or dust particles scatter the light.
• Color of the Sun at Sunrise and Sunset: During these times, sunlight must travel a longer distance through the atmosphere to reach our eyes. Most of the shorter wavelengths (blue and violet) are scattered away, leaving only the longer wavelengths (red and orange) to reach the observer.
• Mie Scattering: Unlike Rayleigh scattering, Mie scattering occurs when the particles are of a similar size to the wavelength of light. This is why clouds appear white, as large water droplets scatter all colors of light equally.

Important Points

• Wavelength Relationship: The relationship between wavelength and scattering explains many natural phenomena. Because red scatters the least, it is used in tail lights and stop signs for maximum visibility in adverse weather conditions like rain or fog.
• Atmospheric Composition: If the Earth had no atmosphere, there would be no scattering of light, and the sky would appear black even during the daytime, similar to what astronauts see in outer space.
• Numerical Fact: Because scattering is proportional to 1/λ⁴, blue light (wavelength approx 450 nm) is scattered about 10 times more efficiently than red light (wavelength approx 650 nm).

The correct answer is 3.6 x 10^6 joules.

Key Points

• Kilowatt-hour (kWh) is the commercial unit of electrical energy. It represents the amount of energy consumed by an electrical appliance of 1 kilowatt power in one hour.
• To convert 1 kWh into Joules, we must break down the units into their SI base units. 1 kilowatt is equal to 1000 Watts, and 1 hour is equal to 3600 seconds (60 minutes × 60 seconds).
• By definition, 1 Watt is equal to 1 Joule per second (1 J/s). Therefore, the total energy in joules is calculated by multiplying power in watts by time in seconds: 1000 W × 3600 s.
• Performing the calculation: 1000 × 3600 = 3,600,000 Joules. In scientific notation, this value is expressed as 3.6 × 10^6 Joules.
• The statement in option 1 claims 1 kWh = 3.6 × 10^3 joules, which is incorrect as it represents only 3600 joules. Hence, statement 1 is incorrect.
• The statement in option 2 claims 1 kWh = 360 joules, which is a significant undervaluation of the energy unit. Hence, statement 2 is incorrect.
• The statement in option 3 claims 1 kWh = 36 × 10^-6 joules, which suggests a microscopic amount of energy. Hence, statement 3 is incorrect.
• The statement in option 4 claims 1 kWh = 3.6 × 10^6 joules, which matches the derived mathematical conversion. Hence, statement 4 is correct.

Additional Information

• Difference between Power and Energy: Power is the rate at which work is done or energy is transformed, measured in Watts (W). Energy is the total capacity to do work, measured in Joules (J) or kilowatt-hours (kWh).
• Commercial Usage: In many countries, including India, the electricity bill is calculated based on "units" of electricity. 1 Unit is exactly equal to 1 kilowatt-hour (kWh).
• SI Unit of Energy: The Joule is the Standard International (SI) unit for energy, named after the English physicist James Prescott Joule. It is a derived unit equivalent to 1 Newton-meter.
• Other Units: Energy can also be measured in Calories (often used in nutrition) or electron-volts (eV) (used in atomic physics). 1 calorie is approximately equal to 4.184 Joules.

Important Points

• Dimensional Formula: The dimensional formula for energy (and work) is [M^1 L^2 T^-2]. This is derived from Force × Displacement.
• Mega Joules: Because 3.6 × 10^6 is a large number, 1 kWh is often referred to as 3.6 Mega Joules (MJ).
• Historical Context: The term Board of Trade Unit (B.O.T.U.) was previously used in the United Kingdom to describe 1 kilowatt-hour before the metric terminology became standardized.
• Practical Example: If a 100-Watt light bulb is left on for 10 hours, it consumes 1 kWh of energy (100W × 10h = 1000Wh = 1kWh).

The correct answer is Methane, Ethane, Propane.

Key Points

• A homologous series is a sequence of organic compounds that have the same functional group and similar chemical properties in which the successive members differ by a CH2 unit.
• Methane (CH4), Ethane (C2H6), and Propane (C3H8) all belong to the Alkane series, which follows the general formula CnH2n+2. Hence, statement 3 is correct.
• In Methane, Methanol, and Methanoic acid, the compounds have different functional groups (alkane, alcohol, and carboxylic acid respectively), meaning they do not belong to the same series. Hence, statement 1 is incorrect.
• In Ethene, Ethyne, and Ethane, the compounds have different degrees of saturation (alkene, alkyne, and alkane), resulting in different general formulas. Hence, statement 2 is incorrect.
• In Methane, Ethane, and Ethene, the first two are alkanes while the third is an alkene, so they do not form a single homologous series. Hence, statement 4 is incorrect.
• Successive members of a homologous series like alkanes have a difference of 14 atomic mass units (u) in their molecular mass.

Additional Information

• Characteristics of Homologous Series:
• All members of a series can be represented by the same general molecular formula. For example, Alkenes follow CnH2n and Alkynes follow CnH2n-2.
• Any two adjacent members differ by a -CH2- group in their molecular formula.
• The chemical properties of the members are similar because they contain the same functional group (such as -OH for alcohols or -CHO for aldehydes).
• There is a gradual change in physical properties like melting point, boiling point, and solubility as the molecular mass increases.
• Alkanes:
• These are saturated hydrocarbons where all carbon-carbon bonds are single bonds.
• Methane is the simplest alkane, often called marsh gas, and is a primary component of natural gas.
• As the number of carbon atoms increases, the boiling point increases due to stronger Van der Waals forces.
• Alkenes and Alkynes:
• Alkenes contain at least one double bond (unsaturated) and start from Ethene (C2H4).
• Alkynes contain at least one triple bond (unsaturated) and start from Ethyne (C2H2), also known as acetylene.

Important Points

• The concept of homology was developed to simplify the study of millions of organic chemistry compounds by grouping them based on structural similarities.
• Isomers are compounds with the same molecular formula but different structural arrangements; they should not be confused with members of a homologous series.
• The substitution reaction is a characteristic chemical property of alkanes, while addition reactions are characteristic of alkenes and alkynes.
• In the homologous series of alcohols, the members would be Methanol (CH3OH), Ethanol (C2H5OH), Propanol (C3H7OH), and so on, all differing by -CH2-.

The correct answer is 10^-10.

Key Points

• According to the Rutherford model of the atom, the radius of an atom is approximately 10^-10 metres. This value is also commonly referred to as 1 Angstrom (Å) in atomic physics.
• In contrast, the radius of the nucleus is much smaller, estimated to be about 10^-15 metres, which is equivalent to 1 femtometre or 1 Fermi.
• This implies that the atom is about 10⁵ (100,000) times larger than its nucleus. If an atom were expanded to the size of a large football stadium, the nucleus would be about the size of a small marble placed at the center.
• Ernest Rutherford derived these dimensions based on his famous Alpha-particle scattering experiment conducted in 1911, where he observed how alpha particles interacted with a thin gold foil.
• The model concluded that since most alpha particles passed through the foil undeflected, the vast majority of an atom's volume is empty space. Hence, the statement regarding the radius being 10^-10 metres is correct.

Additional Information

• Rutherford’s Gold Foil Experiment:
• In this experiment, high-energy alpha particles (Helium nuclei) were directed at a thin gold foil of about 100 nm thickness.
• Observations showed that about 99% of the particles passed straight through, while a very small fraction was deflected by large angles, and about 1 in 12,000 particles rebounded completely (180 degrees).
• This led to the discovery of the Atomic Nucleus, proving that the positive charge and most of the mass of the atom are concentrated in a tiny central region.
• Key Features of Rutherford's Atomic Model:
• The nucleus is positively charged and contains nearly all the mass of the atom.
• The electrons revolve around the nucleus in well-defined circular orbits, much like planets revolving around the Sun. This is why it is often called the Planetary Model.
• The electrostatic force of attraction between the nucleus and the electrons holds the atom together.
• Limitations of the Model:
• The primary drawback was its inability to explain atomic stability. According to Maxwell’s electromagnetic theory, an accelerating charged particle (like an orbiting electron) should radiate energy.
• If an electron continuously lost energy, its orbital radius would decrease, eventually causing it to spiral into the nucleus, making the atom unstable. This was later addressed by Niels Bohr in 1913.
• Scientific Legacy of Ernest Rutherford:
• Ernest Rutherford is hailed as the Father of Nuclear Physics.
• He was awarded the Nobel Prize in Chemistry in 1908 for his investigations into the disintegration of elements and the chemistry of radioactive substances.
• He also successfully performed the first artificial transmutation of an element in 1919, converting nitrogen into oxygen by bombarding it with alpha particles.

Important Points

• Comparison of Scales: While the atom is 10^-10 m, the Proton has a radius of approximately 0.84 to 0.87 femtometres.
• Measurement Units: 1 Angstrom (Å) = 10^-10 metres = 0.1 nanometres. This scale is fundamental for measuring bond lengths and atomic sizes in chemistry.
• Density of the Nucleus: Because almost all mass is in the tiny nucleus, the density of the nucleus is extremely high, approximately 2.3 x 10¹⁷ kg/m³.

The correct answer is Growth, repair, and replacement of damaged or old cells.

Key Points

• Cell division is a fundamental biological process by which a parent cell divides into two or more daughter cells, primarily serving the needs of growth and maintenance in multicellular organisms.
• Growth: Every multicellular organism starts its life as a single cell called a zygote. Through successive rounds of mitotic cell division, the number of cells increases, leading to the development of tissues, organs, and the overall body structure.
• Repair: When an organism suffers an injury, such as a cut on the skin or a broken bone, cell division is activated at the site of the damage to produce new cells that fill the wound and restore the structural integrity of the tissue.
• Replacement: Cells in a multicellular body have a finite lifespan and are constantly being worn out. For example, Red Blood Cells (RBCs) in humans have a lifespan of approximately 120 days, and skin cells are shed regularly; hence, cell division is essential to replace these dead or damaged cells to keep the organism healthy.
• Genetic Continuity: It ensures that the genetic information (DNA) is accurately passed from one generation of cells to the next, maintaining the biological blueprint of the organism.

Additional Information

• Types of Cell Division:
• Mitosis: Also known as equational division, it occurs in somatic cells (body cells). It results in two daughter cells that are genetically identical to the parent cell, each containing a diploid (2n) number of chromosomes.
• Meiosis: Known as reduction division, it occurs in germ cells to produce gametes (sperm and eggs). It reduces the chromosome number by half to haploid (n), ensuring that the diploid number is restored upon fertilization.
• The Cell Cycle: The process of division is part of a larger cycle comprising Interphase (the growth and DNA replication phase) and the M-phase (the actual division phase). The S-phase within Interphase is critical as it is the period when DNA synthesis occurs.
• Regulation of Cell Division: In healthy organisms, cell division is strictly regulated by proteins and checkpoints. If this regulation fails, cells may divide uncontrollably, which is the primary cause of cancer and tumor formation.
• Analysis of Other Options:
• Vacuoles and Turgidity: This is a function of the cell organelle (specifically in plants), not the purpose of division. Hence, statement 1 is incorrect.
• Transport of substances: This is managed by the cell membrane through osmosis, diffusion, and active transport. Hence, statement 2 is incorrect.
• Absorption and Waste Release: These are metabolic and excretory functions performed by the cell during its interphase life. Hence, statement 3 is incorrect.

Important Points

• Chromosomes: During division, chromatin condenses into visible chromosomes. Humans have 23 pairs (total 46) of chromosomes.
• Cytokinesis: This is the physical process of cytoplasmic division that follows karyokinesis (nuclear division) to finally split one cell into two.
• Regeneration: Some organisms, like Planaria or Starfish, use specialized cell division to regrow entire lost body parts, showing an extreme form of the repair function.

Shortcut Trick

Side (a) = 20 cm, Half-diagonal (d₁/2) = 12 cm.

Using Pythagoras triplet (12, 16, 20), the other half-diagonal (d₂/2) = 16 cm.

Full diagonal d₂ = 16 × 2 = 32 cm.

Area = (1/2) × d₁ × d₂ = (1/2) × 24 × 32 = 384 cm².

∴ The correct answer is 384 cm².

Alternate Method

Given:

Side of rhombus (a) = 20 cm

Diagonal 1 (d₁) = 24 cm

Formula Used:

Area of rhombus = (1/2) × d₁ × d₂

Relation between side and diagonals: 4a² = d₁² + d₂²

Side = 20 d1 = 24 d2 = ?  12 cm 16 cm

Calculations:

⇒ In a rhombus, diagonals bisect each other at 90°.

⇒ Let half of d₂ be x.

⇒ Using Pythagoras theorem in the small right triangle: (d₁/2)² + x² = a²

⇒ (24/2)² + x² = 20²

⇒ 12² + x² = 400

⇒ 144 + x² = 400

⇒ x² = 400 − 144 = 256

⇒ x = √256 = 16 cm

⇒ Second diagonal d₂ = 2 × x = 2 × 16 = 32 cm

⇒ Area of rhombus = (1/2) × 24 × 32

⇒ Area = 12 × 32 = 384 cm²

∴ The correct answer is 384 cm².

Additional Information

Properties of Rhombus

All sides are equal, opposite angles are equal, and diagonals bisect each other at right angles (90°).

Perimeter of Rhombus

Perimeter = 4 × side = 4a. Also, 4a² = d₁² + d₂².

Area using Trigonometry

Area = a² × sin(θ), where θ is any internal angle of the rhombus.

Shortcut Trick

For a Mean Proportional in the form x : A :: A : y, the value is calculated as A = √(x × y).

Here, x = 54 and y = 150.

A = √(54 × 150) = √(8100) = 90.

∴ The correct answer is 90.

Alternate Method

Given: The continued proportion 54 : A :: A : 150.

Formula Used: Product of Means = Product of Extremes.

⇒ 54/A = A/150

⇒ A² = 54 × 150

⇒ A² = 8100

⇒ A = √8100

⇒ A = 90

∴ The correct answer is 90.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b). It is the middle term in a continued proportion.

Third Proportional

If a : b :: b : c, then c is called the third proportional to a and b, where c = b² / a.

Fourth Proportional

In the ratio a : b :: c : d, d is the fourth proportional and is calculated as d = (b × c) / a.

Shortcut Trick

Initial Price = 100

Final Price = 100 × 0.65 × 0.60 × 0.50 × 1.45

Final Price = 28.275

Change % = 100 − 28.275 = 71.725% ≈ 71.73%

∴ The correct answer is Decreases by 71.73%.

Alternate Method

Given: Successive changes are −35%, −40%, −50%, and +45%.

Formula Used: Final Value = Initial Value × (100 ± r₁)/100 × (100 ± r₂)/100 × ...

⇒ Let original price be 100.

⇒ Price after 1^st month = 100 − 35% of 100 = 65.

⇒ Price after 2^nd month = 65 − 40% of 65 = 65 − 26 = 39.

⇒ Price after 3^rd month = 39 − 50% of 39 = 39 − 19.5 = 19.5.

⇒ Price after 4^th month = 19.5 + 45% of 19.5 = 19.5 + 8.775 = 28.275.

⇒ Total decrease = 100 − 28.275 = 71.725%.

⇒ Rounding off to two decimal places, we get 71.73%.

∴ The correct answer is Decreases by 71.73%.

Additional Information

Successive Percentage Formula

For two changes a% and b%, effective change is (a + b + ab/100)%. For decrease, use negative values.

Multiplier Method

A decrease of x% is equivalent to multiplying by (1 − x/100), and an increase is multiplying by (1 + x/100).

Rounding Off Rule

If the third decimal digit is 5 or more, increase the second decimal digit by 1 (e.g., 71.725 becomes 71.73).

Shortcut Trick

Ratio of Income (Vijay : Mohan) = 5 : 9

Ratio of Expenditure (Vijay : Mohan) = 2 : 4 = 1 : 2

Since Savings are equal (₹42,000), make the ratio difference equal: (5−1) ≠ (9−2).

Adjust Expenditure ratio by multiplying with (5−9) difference → 1:2 × 4 = 4 : 8.

Income 5 : 9 and Exp 4 : 8 → Savings = 1 unit = ₹42,000.

Vijay's Income = 5 units = 5 × 42,000 = ₹2,10,000.

∴ The correct answer is ₹2,10,000.

Alternate Method

Given: Ratio of incomes = 5 : 9, Each saving = ₹42,000, Ratio of expenditures = 2 : 4.

Formula: Income − Saving = Expenditure

⇒ (5x − 42,000) ÷ (9x − 42,000) = 2 ÷ 4

⇒ (5x − 42,000) ÷ (9x − 42,000) = 1 ÷ 2

⇒ 2 × (5x − 42,000) = 1 × (9x − 42,000)

⇒ 10x − 84,000 = 9x − 42,000

⇒ 10x − 9x = 84,000 − 42,000

⇒ x = 42,000

⇒ Vijay's Income = 5x = 5 × 42,000 = ₹2,10,000

∴ The correct answer is ₹2,10,000.

Additional Information

Income, Expenditure, and Saving Relationship

The fundamental equation is Income = Expenditure + Savings. For two people with fixed savings, the change in income units must correspond to the change in expenditure units.

Ratio Balancing Method

If Savings are equal, the numerical difference between the income ratio parts and expenditure ratio parts must be the same. If not, multiply the ratios by the cross-difference of the other ratio.

Cross Multiplication Trick

For problems with different savings: (I₁ × E₂ − I₂ × E₁) units = (S₁ × E₂ − S₂ × E₁) value.

Shortcut Trick

Relative Speed in same direction = 60 − 24 = 36 km/h.

Convert to m/s: 36 × (5/18) = 10 m/s.

Combined Length = Relative Speed × Time = 10 × 30 = 300 m.

∴ The correct answer is 300 m.

Alternate Method

Given:

Speed of Train 1 (S₁) = 60 km/h

Speed of Train 2 (S₂) = 24 km/h

Time taken to cross (t) = 30 sec

Formula Used:

Distance = Speed × Time

Relative Speed (Same Direction) = S₁ − S₂

Calculations:

⇒ Relative Speed = 60 − 24 = 36 km/h

⇒ Convert km/h to m/s: 36 × (5/18) m/s

⇒ Relative Speed = 2 × 5 = 10 m/s

⇒ Combined Length = Relative Speed × Time

⇒ Combined Length = 10 × 30

⇒ Combined Length = 300 m

∴ The correct answer is 300 m.

Additional Information

Relative Speed Concept

When two objects move in the same direction, relative speed is S₁ − S₂. When they move in opposite directions, it is S₁ + S₂.

Unit Conversion

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

Crossing Objects

When a train crosses another train, the total distance covered is always the sum of the lengths of both trains.

Shortcut Trick

In a right-angled triangle with an angle of elevation of 45°, the height and the base are always equal.

Since the distance from the base (base) is 20 m, the height of the pole must also be 20 m.

Ratio of sides in 45°-45°-90° triangle is 1 : 1 : √2.

∴ The correct answer is 20 m.

Alternate Method

Given:

Distance from the base (BC) = 20 m

Angle of elevation (θ) = 45°

Formula Used:

tan θ = Perpendicular (Height) ÷ Base

Calculations:

⇒ tan 45° = Height (h) ÷ 20

⇒ 1 = h ÷ 20

⇒ h = 20 × 1

⇒ h = 20 m

∴ The correct answer is 20 m.

Additional Information

Trigonometric Ratios for Standard Angles

For 30°, tan 30° = 1/√3; For 60°, tan 60° = √3; For 45°, tan 45° = 1.

Angle of Elevation and Depression

The angle of elevation is the angle between the horizontal line and the line of sight when looking up at an object.

Right-Angled Triangle Properties

Pythagoras Theorem: Hypotenuse² = Base² + Perpendicular².

Shortcut Trick

Effective Rate of Interest for 2 years at 10% compounded annually = 10 + 10 + (10 × 10) ÷ 100 = 21%.

The Amount is 100% (Principal) + 21% (Interest) = 121% of the Principal.

Amount = 121% × 7,100 = 1.21 × 7,100.

Amount = 121 × 71 = ₹8,591.

∴ The correct answer is ₹8,591.

Alternate Method

Given:

Principal (P) = ₹7,100

Rate (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P × (1 + R/100)ⁿ

Calculations:

⇒ A = 7100 × (1 + 10/100)²

⇒ A = 7100 × (1 + 1/10)²

⇒ A = 7100 × (11/10) × (11/10)

⇒ A = 71 × 11 × 11

⇒ A = 71 × 121

⇒ A = ₹8,591

∴ The correct answer is ₹8,591.

Additional Information

Compound Interest Formula

Interest (CI) = Amount − Principal = P[(1 + R/100)ⁿ − 1].

Difference between CI and SI

For 2 years, the difference D = P(R/100)².

Successive Percentage Method

If interest is compounded annually, the effective rate for 't' years is the successive percentage change of 'R' for 't' times.

Shortcut Trick

Net discount = a + b − (a × b) ÷ 100 = 16 + 20 − (16 × 20) ÷ 100 = 32.8%.

Multiplier for SP = CP × (100 + P%) ÷ 100 = 7700 × 1.32.

Relationship: CP × (100 + P%) = MP × (100 − D%).

MP = 7700 × 132 ÷ (100 − 32.8) = 7700 × 132 ÷ 67.2.

MP = 7700 × 1320 ÷ 672 = 15125.

∴ The correct answer is ₹15,125.

Alternate Method

Given → Cost Price (CP) = ₹7,700, Gain% = 32%, Successive Discounts = 16% and 20%. Formulas: SP = CP × (100 + P%) ÷ 100 | MP = SP × 100 ÷ (100 − D%) | Net Discount = a + b − ab ÷ 100.

⇒ Calculate Selling Price (SP): SP = 7700 × (132 ÷ 100) = 77 × 132 = ₹10,164. ⇒ Let Marked Price be MP. After 16% discount, Price = 0.84MP. ⇒ After second discount of 20%, SP = 0.84MP × 0.80 = 0.672MP. ⇒ Equating SP: 0.672MP = 10164. ⇒ MP = 10164 ÷ 0.672 = 10164000 ÷ 672. ⇒ MP = ₹15,125. ∴ The correct answer is ₹15,125.

Additional Information

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount.

Successive Discounts

Two discounts d₁ and d₂ are equivalent to a single discount of (d₁ + d₂ − d₁d₂/100)%.

Shortcut Trick

Convert the given equation x² − 3x − 1 = 0 into the form (x − 1/x) by dividing by x.

x − 3 − 1/x = 0 ⇒ x − 1/x = 3.

Use the algebraic shortcut: If (x − 1/x) = k, then (x² + 1/x²) = k² + 2.

Here, k = 3, so x² + 1/x² = 3² + 2 = 11.

Required value = (x² + 1/x²) − 6 = 11 − 6 = 5.

∴ The correct answer is 5.

Alternate Method

Given: x² − 3x − 1 = 0

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

Calculations:

⇒ x² − 1 = 3x

⇒ (x² − 1) ÷ x = 3

⇒ x − 1/x = 3

Squaring both sides of the equation:

⇒ (x − 1/x)² = 3²

⇒ x² + 1/x² − 2(x)(1/x) = 9

⇒ x² + 1/x² − 2 = 9

⇒ x² + 1/x² = 11

Now, find the value of the expression x² + 1/x² − 6:

⇒ (x² + 1/x²) − 6 = 11 − 6

⇒ 5

∴ The correct answer is 5.

Additional Information

Square Algebraic Identities

x² + 1/x² can be expressed as (x + 1/x)² − 2 or (x − 1/x)² + 2.

Cube Algebraic Identities

x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) and x³ − 1/x³ = (x − 1/x)³ + 3(x − 1/x).

Relationship between Sum and Difference

(x + 1/x)² = (x − 1/x)² + 4, which is useful for switching between addition and subtraction forms.

Shortcut Trick

Loss of 10% means the Selling Price (SP) is 90% of the Cost Price (CP).

Ratio method: 10% = 1/10 (Loss/CP).

If CP = 10 units and Loss = 1 unit, then SP = 9 units.

Given 10 units = ₹1,200, so 1 unit = ₹120.

∴ SP = 9 × 120 = ₹1,080.

∴ The correct answer is ₹1,080.

Alternate Method

Given: Cost Price (CP) = ₹1,200, Loss% = 10%. Formulas: Loss = (Loss% ÷ 100) × CP | SP = CP − Loss

⇒ Calculate Loss amount = (10 ÷ 100) × 1,200 ⇒ Loss = 0.10 × 1,200 = ₹120 ⇒ Selling Price (SP) = CP − Loss ⇒ SP = 1,200 − 120 = ₹1,080

∴ The correct answer is ₹1,080.

Additional Information

Relationship between CP and SP

When there is a loss, the Cost Price is always greater than the Selling Price (CP > SP). Formula: SP = CP × (100 − Loss%) ÷ 100.

Profit Scenario

If the watch was sold at a 10% profit, the SP would be CP × (100 + Profit%) ÷ 100 = 1,200 × 1.1 = ₹1,320.

Shortcut Trick

Increase in average = (New score − Old average) ÷ Total number of innings

Increase = (193 − 76) ÷ 11

Increase = 117 ÷ 11 = 10.636...

Rounding 10.636 to the nearest whole number, we get 11.

∴ The correct answer is 11.

Alternate Method

Given:

Average of 10 innings = 76 runs

Runs in 11^th inning = 193 runs

Formula Used:

Average = Total Runs ÷ Total Innings

Increase in Average = New Average − Old Average

Calculations:

⇒ Total runs in 10 innings = 10 × 76 = 760 runs

⇒ Total runs in 11 innings = 760 + 193 = 953 runs

⇒ New average = 953 ÷ 11 = 86.6363...

⇒ Increase in average = 86.6363 − 76 = 10.6363...

⇒ Rounding to the nearest whole number ≈ 11

∴ The correct answer is 11.

Additional Information

Effect of New Entry on Average

If a new value is added, New Average = (Old Sum + New Value) ÷ (n + 1). If New Value > Old Average, the average increases.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Deviation Method

The sum of deviations of all observations from their mean is always zero. This property helps in finding missing values quickly.

Shortcut Trick

60% of First Number = 12 → 100% of First Number = 20.

Ratio value 10 units = 20 → 1 unit = 2.

Difference of Third and Second (21 − 16) = 5 units = 10.

40% of 10 = 4.

∴ The correct answer is 4.

Alternate Method

Given: Ratio = 10 : 21 : 16 | 60% of 1^st = 12

Formula Used: Number = (Given Value ÷ Percentage) × 100

⇒ Let the numbers be 10x, 21x, and 16x.

⇒ 60% of 10x = 12

⇒ 0.6 × 10x = 12 ⇒ 6x = 12 ⇒ x = 2

⇒ Second number = 21 × 2 = 42

⇒ Third number = 16 × 2 = 32

⇒ Difference = 42 − 32 = 10

⇒ Required value = 40% of 10 = 0.4 × 10 = 4

∴ The correct answer is 4.

Additional Information

Percentage to Fraction Conversion

To simplify calculations, use 60% = 3/5 and 40% = 2/5.

Ratio Scaling

If a : b : c is the ratio, any change in one part according to a multiplier x applies to all parts to maintain the proportion.

Shortcut Trick

Assume an average of 40 to find deviations: −22, +34, −7, −24, −5, +56, 0, +28, +3.

Net deviation = (−22 − 7 − 24 − 5) + (34 + 56 + 28 + 3) = −58 + 121 = +63.

Average deviation = 63 ÷ 9 = +7.

Actual Arithmetic Mean = 40 + 7 = 47.

∴ The correct answer is 47.

Alternate Method

Given: Observations = 18, 74, 33, 16, 35, 96, 40, 68, 43

Total count (n) = 9

Formula: Arithmetic Mean = (Sum of all observations) ÷ (Total number of observations)

⇒ Sum = 18 + 74 + 33 + 16 + 35 + 96 + 40 + 68 + 43

⇒ Sum = 423

⇒ Mean = 423 ÷ 9

⇒ Mean = 47

∴ The correct answer is 47.

Additional Information

Properties of Arithmetic Mean

The sum of the deviations of all observations from their arithmetic mean is always zero. ∑(x_i − mean) = 0.

Effect of Constant on Mean

If every observation is increased or decreased by a constant k, the mean also increases or decreases by k. If multiplied by k, the mean is multiplied by k.

Weighted Mean Formula

When observations have different weights, the mean is calculated as ∑(w_i × x_i) ÷ ∑w_i.

Shortcut Trick

Use the successive discount formula: Equivalent Discount = a + b − (a × b) ÷ 100.

Here, a = 20% and b = 29%.

Equivalent Discount = 20 + 29 − (20 × 29) ÷ 100.

Equivalent Discount = 49 − (580 ÷ 100) = 49 − 5.8 = 43.2%.

∴ The correct answer is 43.2%.

Alternate Method

Given: First discount = 20%, Second discount = 29%.

Formula: Net SP = MP × (100 − d₁)% × (100 − d₂)%

⇒ Let the Marked Price (MP) be 100.

⇒ Price after 20% discount = 100 − 20 = 80.

⇒ Price after 29% discount on 80 = 80 − (29% of 80).

⇒ 29% of 80 = (29 × 80) ÷ 100 = 23.2.

⇒ Final Selling Price (SP) = 80 − 23.2 = 56.8.

⇒ Total Discount = MP − SP = 100 − 56.8 = 43.2.

∴ The correct answer is 43.2%.

Additional Information

Successive Discounts

When two or more discounts are applied one after another on the reduced price, they are called successive discounts. The total effective discount is always less than the sum of individual discounts.

Marked Price & Selling Price

Marked Price is the price printed on the label. Selling Price is the final amount paid after subtracting the discount from the MP: SP = MP × (1 − d/100).

Shortcut Trick

To find percentage of A with respect to B, use: (A ÷ B) × 100.

Required % = (1/30 ÷ 1/100) × 100 = (100/30) × 100.

Required % = (10/3) × 100 = 1000/3 %.

Required % = 333.33%.

∴ The correct answer is 333.33%.

Alternate Method

Given: First fraction = 1/30, Second fraction = 1/100.

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

⇒ Required Percentage = [(1/30) / (1/100)] × 100

⇒ Required Percentage = (1/30 × 100/1) × 100

⇒ Required Percentage = (100/30) × 100

⇒ Required Percentage = (10/3) × 100

⇒ Required Percentage = 1000 / 3

⇒ Required Percentage = 333.333...

∴ The correct answer is 333.33%.

Additional Information

Fraction to Percentage Conversion

To convert any fraction to percentage, multiply the fraction by 100 and add the % symbol.

Reciprocal Percentages

Common reciprocals: 1/3 ≈ 33.33%, 1/6 ≈ 16.67%, 1/9 ≈ 11.11%.

Rounding Off Rules

When rounding to two decimal places, if the third decimal digit is 5 or more, increase the second decimal digit by 1.

Shortcut Trick

Combined efficiency of A, B, and C = 8 + 3 + 1 = 12 units/day (taking total work as 24 units).

To complete twice the work (48 units), they will take 48 ÷ 12 = 4 days.

∴ The correct answer is 4 days.

Alternate Method

Given:

Time taken by A = 3 days

Time taken by B = 8 days

Time taken by C = 24 days

Formula Used:

Total Work = LCM of individual times

Efficiency = Total Work ÷ Days

Time taken = Work ÷ Combined Efficiency

Calculations:

⇒ Total original work = 24 units

⇒ Twice the work = 2 × 24 = 48 units

⇒ Combined efficiency of A, B and C = 8 + 3 + 1 = 12 units/day

⇒ Time taken to complete twice the work = 48 ÷ 12 = 4 days

∴ The correct answer is 4 days.

Additional Information

LCM Method in Time and Work

Using the LCM of individual days as the total work helps avoid working with complex fractions, simplifying calculations into whole number efficiencies.

Work and Wages Relation

Wages are always distributed in the proportion of the total work done by each individual, or in the ratio of their efficiencies if they work for the same duration.

Shortcut Trick

For a number to be divisible by 8, its last three digits must be divisible by 8.

The last three digits of 130A1568 are 568.

Check: 568 ÷ 8 = 71 (Exactly divisible).

Since 568 is already divisible by 8, the value of A does not affect the divisibility of the last three digits.

The question asks for the minimum value of A.

∴ The correct answer is 0.

Alternate Method

Given: The 8-digit number is 130A1568.

Divisibility Rule for 8: A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8.

⇒ Last three digits of 130A1568 = 568

⇒ 568 ÷ 8 = 71

⇒ Since 568 is divisible by 8, the entire number 130A1568 is divisible by 8 regardless of the value of A.

⇒ Possible values for digit A are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

⇒ The minimum value among these is 0.

∴ The correct answer is 0.

Additional Information

Divisibility by 2ⁿ

A number is divisible by 2ⁿ if its last n digits are divisible by 2ⁿ. For 2 (2¹), check last 1 digit; for 4 (2²), check last 2 digits; for 8 (2³), check last 3 digits.

Divisibility by 3 and 9

A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9 respectively.

Divisibility by 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.

Shortcut Trick

When the distance for two journeys is equal (A to B and B to A), use the harmonic mean formula.

Average Speed = [2 × S₁ × S₂] ÷ [S₁ + S₂]

Average Speed = [2 × 48 × 52] ÷ [48 + 52] = 4992 ÷ 100 = 49.92 km/hr.

∴ The correct answer is 49.92 km/hr.

Alternate Method

Given: Distance (D) = 964 km, Speed A to B (S₁) = 48 km/hr, Speed B to A (S₂) = 52 km/hr.

Formula Used: Average Speed = Total Distance ÷ Total Time

⇒ Total Distance = 964 + 964 = 1928 km

⇒ Time taken (A to B) = 964 ÷ 48 = 241 ÷ 12 hours

⇒ Time taken (B to A) = 964 ÷ 52 = 241 ÷ 13 hours

⇒ Total Time = (241 ÷ 12) + (241 ÷ 13) = [241 × (13 + 12)] ÷ (12 × 13)

⇒ Total Time = (241 × 25) ÷ 156 hours

⇒ Average Speed = 1928 ÷ [(241 × 25) ÷ 156] = (1928 × 156) ÷ (241 × 25)

⇒ Average Speed = (8 × 156) ÷ 25 = 1248 ÷ 25 = 49.92 km/hr

∴ The correct answer is 49.92 km/hr.

Additional Information

Average Speed for Equal Distances

When an object covers two equal distances at speeds x and y, the average speed is given by [2xy] ÷ [x + y]. Note that the actual distance value does not affect the final result.

Three Equal Distances

For three equal distances covered at speeds x, y, and z, the average speed formula is [3xyz] ÷ [xy + yz + zx].

General Average Speed

Always defined as Total Distance ÷ Total Time. If the distances are not equal, individual times must be calculated and summed up.

Shortcut Trick

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

∠DOC = (∠A + ∠B) ÷ 2

∠DOC = (62° + 19°) ÷ 2

∠DOC = 81° ÷ 2 = 40.5°

∴ The correct answer is 40.5°.

Alternate Method

Given: ∠A = 62°, ∠B = 19°, CO and DO are angle bisectors.

Formula Used: Sum of interior angles of a quadrilateral = 360° | Sum of angles in a triangle = 180°.

⇒ In quadrilateral ABCD, ∠A + ∠B + ∠C + ∠D = 360°

⇒ 62° + 19° + ∠C + ∠D = 360°

⇒ ∠C + ∠D = 360° − 81° = 279°

⇒ In ΔDOC, ∠DOC + ∠OCD + ∠ODC = 180°

⇒ Since CO and DO are bisectors, ∠OCD = ∠C ÷ 2 and ∠ODC = ∠D ÷ 2

⇒ ∠DOC + (∠C + ∠D) ÷ 2 = 180°

⇒ ∠DOC + 279° ÷ 2 = 180°

⇒ ∠DOC + 139.5° = 180°

⇒ ∠DOC = 180° − 139.5° = 40.5°

∴ The correct answer is 40.5°.

Additional Information

Angle Sum Property

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

Angle Bisector Property

An angle bisector divides an angle into two equal parts. In any triangle, the sum of the angles is 180°, which is used to find the third angle when the other two (or their sum) are known.

1

Shortcut Trick

LCM of 12, 15, 18 = 180 units (Total Capacity).

Efficiencies: A = 15, B = 12, C = 10.

Hour 1 (A+B): 15 + 12 = 27 units | Hour 2 (A+C): 15 + 10 = 25 units.

2-hour cycle = 27 + 25 = 52 units. In 3 cycles (6 hours), work done = 52 × 3 = 156 units.

Remaining 24 units filled by (A+B) in 24/27 = 8/9 hours. Total = 6 + 8/9 = 6 8/9 hours.

∴ The correct answer is 6 8/9 hr.

Alternate Method

⇒ Hour 1 (A and B are open): Efficiency = 15 + 12 = 27 units/hr

⇒ Hour 2 (A and C are open): Efficiency = 15 + 10 = 25 units/hr

⇒ Work done in 2 hours = 27 + 25 = 52 units

⇒ Work done in 6 hours (3 cycles) = 52 × 3 = 156 units

⇒ Remaining work = 180 − 156 = 24 units

⇒ Time taken for remaining work (by A+B) = 24 ÷ 27 = 8/9 hr

⇒ Total time = 6 + 8/9 = 6 8/9 hr

∴ The correct answer is 6 8/9 hr.

Additional Information

Pipes and Cisterns Efficiency

Efficiency is inversely proportional to the time taken. If a pipe fills a tank in 'x' hours, its 1-hour work is 1/x.

Alternate Work Principle

In alternate timing problems, calculate the work done in one complete cycle (sum of individual hours) before multiplying to reach the target capacity.

Inlet and Outlet Pipes

Inlet pipe efficiency is taken as positive, while outlet (leakage) pipe efficiency is taken as negative during net efficiency calculation.

Shortcut Trick

Substitute the options into the equation 25^{(r − 1)} + 100 = 5^{(2r − 1)} to see which one satisfies it.

Checking for r = 2:

⇒ 25^{(2 − 1)} + 100 = 5^{(2 × 2 − 1)}

⇒ 25¹ + 100 = 5³

⇒ 125 = 125 (Satisfied)

∴ The correct answer is 2.

Alternate Method

Given:

25^{(r − 1)} + 100 = 5^{(2r − 1)}

Formula Used:

(a^m)ⁿ = a^{m × n}

Calculation:

⇒ (5²)^{(r − 1)} + 100 = 5^{(2r − 1)}

⇒ 5^{(2r − 2)} + 100 = 5^{(2r − 1)}

Rearranging the terms by taking base 5 values to one side:

⇒ 100 = 5^{(2r − 1)} − 5^{(2r − 2)}

Taking 5^{(2r − 2)} common on the right hand side:

⇒ 100 = 5^{(2r − 2)} × (5¹ − 1)

⇒ 100 = 5^{(2r − 2)} × 4

⇒ 25 = 5^{(2r − 2)}

⇒ 5² = 5^{(2r − 2)}

Equating the exponents since the bases are equal:

⇒ 2r − 2 = 2

⇒ 2r = 4

⇒ r = 2

∴ The correct answer is 2.

Additional Information

Law of Product

When multiplying expressions with the same base, add their exponents: a^m × aⁿ = a^{m + n}.

Law of Quotient

When dividing expressions with the same base, subtract their exponents: a^m ÷ aⁿ = a^{m − n}.

Law of Power of a Power

When raising a power to another power, multiply the exponents: (a^m)ⁿ = a^{m × n}.

Equality of Exponents

If a^m = aⁿ (where a > 0 and a ≠ 1), then m = n.

Shortcut Trick

To find the two numbers quickly using Sum (S) and Difference (D):

Larger number = (S + D) ÷ 2 = (24 + 8) ÷ 2 = 16

Smaller number = (S − D) ÷ 2 = (24 − 8) ÷ 2 = 8

Product = 16 × 8 = 128

∴ The correct answer is 128.

Alternate Method

Given:

Sum of two numbers (x + y) = 24

Difference of two numbers (x − y) = 8

Formula Used:

Algebraic product identity: xy = ((x + y)² − (x − y)²) ÷ 4

Calculations:

⇒ x + y = 24 --- (Equation 1)

⇒ x − y = 8 --- (Equation 2)

⇒ Adding both equations: (x + y) + (x − y) = 24 + 8

⇒ 2x = 32

⇒ x = 32 ÷ 2 = 16

⇒ Substitute x = 16 in Equation 1: 16 + y = 24

⇒ y = 24 − 16 = 8

⇒ Product = x × y = 16 × 8 = 128

∴ The correct answer is 128.

Additional Information

Product-Sum-Difference Identity

The product of two numbers can be directly calculated using the identity: Product = [(Sum)² − (Difference)²] ÷ 4.

Sum of Squares Relationship

The sum of the squares of two numbers is given by: x² + y² = [(Sum)² + (Difference)²] ÷ 2.

Relationship with Arithmetic Mean

The Average of the two numbers is always exactly half of their sum (S ÷ 2). The numbers are (Average + D/2) and (Average − D/2).

Shortcut Trick

To find the larger value (Sister) when the sum and difference are known:

Sister age = (Sum + Difference) ÷ 2

Sister age = (26 + 2) ÷ 2 = 28 ÷ 2 = 14

∴ The correct answer is 14 years.

Alternate Method

Given:

Sum of ages = 26 years

Age difference = 2 years

Formula Used:

Linear Equation solving for two variables.

Let the age of the Sister be S and the age of the Brother be B.

⇒ S + B = 26 --- (Equation 1)

⇒ S − B = 2 --- (Equation 2)

Adding Equation 1 and Equation 2:

⇒ (S + B) + (S − B) = 26 + 2

⇒ 2S = 28

⇒ S = 28 ÷ 2

⇒ S = 14

∴ The correct answer is 14 years.

Additional Information

Sum and Difference Rule

If sum (S) and difference (D) of two numbers are given, Larger = (S+D)/2 and Smaller = (S−D)/2.

Age Constant Property

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

Shortcut Trick

Total Surface Area (TSA) = CSA of cylinder + CSA of hemisphere + CSA of cone + Area of annular base.

TSA = 2πRH + 2πR² + πrl + (πR² − πr²) = π[2RH + 3R² + rl − r²]

Substitute R=14, H=48, r=7, h=24, l=25: TSA = (22/7) × [2(14)(48) + 3(14²) + 7(25) − 7²]

TSA = (22/7) × [1344 + 588 + 175 − 49] = (22/7) × 2058 = 22 × 294 = 6468 cm².

∴ The correct answer is 6468 cm².

Alternate Method

Given:

Height of cylinder (H) = 48 cm, Radius of cylinder (R) = 14 cm

Radius of conical cavity (r) = 7 cm, Height of conical cavity (h) = 24 cm

Radius of hemisphere (R_h) = 14 cm

Formula Used:

Curved Surface Area (CSA) of cylinder = 2πRH

CSA of cone = πrl, where l = √(r² + h²)

CSA of hemisphere = 2πR²

Calculations:

⇒ Slant height of cone (l) = √(7² + 24²) = √(49 + 576) = √625 = 25 cm

⇒ CSA of cylinder = 2 × (22/7) × 14 × 48 = 2 × 22 × 2 × 48 = 4224 cm²

⇒ CSA of cone = (22/7) × 7 × 25 = 550 cm²

⇒ CSA of hemisphere = 2 × (22/7) × 14 × 14 = 1232 cm²

⇒ Area of top annular region = πR² − πr² = (22/7) × (14² − 7²) = (22/7) × (196 − 49) = (22/7) × 147 = 462 cm²

⇒ Total Surface Area = 4224 + 550 + 1232 + 462

⇒ Total Surface Area = 6468 cm²

∴ The correct answer is 6468 cm².

Additional Information

Volume of Remaining Solid

The volume is calculated by subtracting the volumes of the cavities: V = πR²H − (1/3)πr²h − (2/3)πR³.

Surface Area Change

When a cavity is made, the Total Surface Area usually increases as the internal curved surface of the cavity is added, while only the flat base area of the cavity is removed.

Hemisphere Surface Area

For a solid hemisphere, TSA = 3πR² (Curved + Base), but for a hemispherical cavity, only the curved part 2πR² is added to the internal surface.

Shortcut Trick

The given expression follows the algebraic identity (a² − b²) ÷ c.

Notice that (75983 − 45983) = 30000, which is exactly the denominator.

Since (a² − b²) = (a + b)(a − b), the expression reduces to (a + b) when (a − b) is the divisor.

Result = 75983 + 45983 = 121966.

∴ The correct answer is 121966.

Alternate Method

Given: Expression = (75983 × 75983 − 45983 × 45983) ÷ 30000

Formula Used: a² − b² = (a + b)(a − b)

⇒ Let a = 75983 and b = 45983.

⇒ a² − b² = (75983 + 45983) × (75983 − 45983)

⇒ a² − b² = 121966 × 30000

⇒ Expression = (121966 × 30000) ÷ 30000

⇒ Expression = 121966

∴ The correct answer is 121966.

Additional Information

Difference of Squares

The identity a² − b² = (a + b)(a − b) is used to simplify the multiplication and division of large square terms.

Sum and Difference Cubes

Similarly, a³ − b³ = (a − b)(a² + ab + b²) and a³ + b³ = (a + b)(a² − ab + b²).

BODMAS Rule

Always follow the order of operations: Brackets, Orders, Division, Multiplication, Addition, and Subtraction for correct results.

Given: G, H, I, Q, R and S are sitting in a straight line facing north.

No one is seated to the left of R.

Only three people are seated between R and G.

Only three people are seated to the right of H.

Q is seated to the immediate left of H.

S is not an immediate neighbor of H.

 

So, number of people between S and I = 1

Hence, the correct answer is Option 2.

Given Statements:

All potatoes are bananas.

All bananas are apples.

The least possible Venn diagram for the given statements is:

Conclusions:

I. All potatoes are apples – Follows (Since all potatoes are bananas and all bananas are apples, all potatoes must be apples).

II. Some apples are bananas – Follows (All bananas are apples, so at least some apples are definitely bananas).

So, both conclusion I and II follow.

Hence, the correct answer is Option 2.

Given:

Total people = 52

Dimple’s position from left = 17^th

15 people sit to the right of Avni

Avni’s position from right = 15 + 1 = 16^th

Avni’s position from left = (52 − 16) + 1 = 37^th

Now, number of people between Dimple and Avni = |37 − 17| − 1

= 20 − 1

= 19

Here, the number of people sitting between Dimple and Avni is 19.

Hence, the correct answer is "Option 2".

The logic followed here is:

So, 'IMQ 38' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

Given:

The shopping complex of A is 6 km West of B.

The shopping complex of C is 4 km North of B.

The shopping complex of D is 6 km West of C.

 

Therefore, the shopping complex of D is to the North of the shopping complex of A.

Hence, the correct answer is Option 1.

The logic followed here is:

thus, "237" will replace the question mark in the given series.

Hence, the correct option is "Option 4".

Given: (Left) 562, 428, 653, 154, 749 (Right)

Now,

We need to identify the second highest and second lowest numbers from the given list, extract the specified digits, and find their sum.

(Left) 562, 428, 653, 154, 749 (Right)

Now, arranging numbers in ascending order: 154 428 562 653 749

Now identifying:

Second lowest number = 428

Second highest number = 653

Second digit of second highest number = 5

Third digit of second lowest number = 8

Now,

Value 1 = 5

Value 2 = 8

Sum = 5 + 8 = 13

Hence, the correct answer is "Option 3".

The logic followed here is:

Given:

‘rain hall pig’ → kq zz nl

‘pig bean error’ → hu mt zz

So, pig → zz

Hence, the correct answer is Option 3.

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

Only two people sit between A and G when counted from the left of G.

B sits to the immediate left of G.

Only three people sit between C and B when counted from the left of C.

E sits to the immediate right of D.

F is not an immediate neighbour of B.

 

Therefore, the person sitting second to the right of H is G.

Hence, the correct answer is Option 1.