RRB Group D Official Paper (Held On: 09 Feb, 2026 Shift 3) (Previous Year Paper)

The correct answer is It resists the current and gets hot.

Key Points

• The heating wire in a toaster glows red due to the Heating Effect of Electric Current, also known as Joule Heating. This phenomenon occurs when an electric current passes through a conductor with significant resistance, converting electrical energy into thermal energy.
• Resistance is the property of a material that opposes the flow of electrons. When electrons collide with the ions/atoms of the conductor (the heating wire), they transfer kinetic energy, which manifests as heat. Hence, statement 4 is correct.
• If the wire had zero resistance, it would be a superconductor. In such a case, no heat would be generated because there is no opposition to the current flow (H = I²Rt, where R=0 leads to H=0). Hence, statement 1 is incorrect.
• Heating elements must have a high melting point to ensure they do not melt or deform while operating at temperatures high enough to glow red (typically above 500°C to 1000°C). A low melting point is a characteristic of a fuse wire, not a heating element. Hence, statement 2 is incorrect.
• While the current flowing through the toaster is substantial, the "glowing red" is specifically the result of that current meeting high resistance. High current alone in a low-resistance thick copper wire would not cause it to glow red under normal household conditions. Hence, statement 3 is incorrect.

Additional Information

• Nichrome: The most common material used for heating wires in toasters and space heaters is Nichrome, which is an alloy consisting of approximately 80% Nickel and 20% Chromium.
• High Resistivity: Nichrome is chosen because it has relatively high electrical resistivity compared to copper or aluminum, allowing it to generate significant heat in a compact space.
• Oxidation Resistance: When heated to high temperatures, Nichrome forms a protective layer of chromium oxide on its surface, which prevents the wire from further oxidation and breaking down in the open air.
• Incandescence: The "red glow" is a form of incandescence. As the temperature of the wire increases, it begins to emit electromagnetic radiation in the visible spectrum, starting with long-wavelength red light.
• Applications: Apart from toasters, this principle is utilized in electric irons, geysers, hair dryers, and room heaters.

Important Points

• Joule's Law of Heating: The heat produced (H) in a conductor is directly proportional to the square of the current (I²), the resistance (R), and the time (t) for which the current flows. The formula is expressed as H = I²Rt.
• Material Comparison:
• Heating Element: High resistance and High melting point (e.g., Nichrome, melting point ~1400°C).
• Fuse Wire: High resistance and Low melting point (e.g., Tin-Lead alloy, melting point ~183°C to 230°C) to protect circuits by melting during a power surge.
• Bulb Filament: Extremely high melting point (e.g., Tungsten, melting point ~3422°C) to withstand temperatures high enough to emit white light.

The correct answer is The volume of air decreases and its pressure increases.

Key Points

• When a sealed syringe is pressed, the plunger moves inward, which directly reduces the physical space available for the air trapped inside. This results in a decrease in volume.
• According to Boyle's Law, discovered by Robert Boyle in 1662, for a fixed amount of gas at a constant temperature, the pressure and volume are inversely proportional. This means as the volume decreases, the pressure increases simultaneously. Hence, option 4 is correct.
• Air is a mixture of gases, and gases possess high compressibility because of the large intermolecular spaces between their particles. In a sealed system, pressing the plunger forces these particles closer together.
• The temperature of the air would not drop significantly; in fact, if compressed rapidly, the temperature might increase slightly due to the work done on the gas molecules. Hence, option 1 is incorrect.
• Because the syringe is closed at the other end and properly sealed, the mass of the air remains constant, and it cannot escape the container. Hence, option 2 is incorrect.
• The action of pressing the plunger is a physical reduction of the container's size, which contradicts the idea of an increase in volume. Hence, option 3 is incorrect.

Additional Information

• Kinetic Molecular Theory: This theory explains that gas pressure is caused by the frequent collisions of gas molecules against the walls of their container. When the volume is reduced, the molecules have less space to travel and hit the walls more often, thus increasing the measured pressure.
• States of Matter: Unlike solids and liquids, which have fixed volumes and are almost incompressible, gases do not have a fixed shape or volume and can be easily compressed into smaller containers.
• Applications: This principle is utilized in various pneumatic systems, bicycle pumps, medical syringes, and even in the functioning of internal combustion engines where the air-fuel mixture is compressed by a piston before ignition.
• Isothermal vs. Adiabatic: If the compression happens slowly enough for heat to exchange with the surroundings, it is an isothermal process (constant temperature). If it happens very fast, it is an adiabatic process, where the internal energy and temperature of the air increase.

Important Points

• Ideal Gas Law: The relationship between these variables is summarized by the formula PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature.
• Direct and Inverse Proportions: In science, it is vital to distinguish between these. In a syringe, the inverse proportion between P and V is a fundamental concept taught in General Science and Physics to explain the behavior of matter.
• Standard Units: Pressure is often measured in Pascals (Pa) or Atmospheres (atm), while volume in the context of a syringe is usually measured in milliliters (ml) or cubic centimeters (cm³).

The correct answer is P.

Key Points

• The chemical symbol for the element Phosphorus is P. It is derived from the first letter of its name, following the standard IUPAC (International Union of Pure and Applied Chemistry) nomenclature where symbols for many elements consist of a single capitalized letter.
• Phosphorus is a chemical element with the atomic number 15. It belongs to Group 15 of the periodic table, which is also known as the Pnictogens.
• The name phosphorus originates from the Greek word phosphoros, which means "bringing light" or "light-bearer." This name was given due to its property of glowing in the dark when exposed to oxygen.
• In its elemental form, it is highly reactive and is never found as a free element on Earth. It is essential for life, appearing in DNA, RNA, ATP, and the phospholipids that form all cell membranes.
• The correct symbol is not Ph, Ps, or Pr. While Pr is a valid atomic symbol, it represents Praseodymium, not phosphorus. Ph is frequently used in organic chemistry as a shorthand for the phenyl group, but it is not an atomic symbol for a single element.

Additional Information

• Discovery and History:
• Phosphorus was discovered by the German alchemist Hennig Brand in the year 1669. He isolated it from human urine, making it the first element to be discovered that was not known since ancient times.
• Allotropes of Phosphorus:
• White Phosphorus: A waxy, dangerous solid that is highly flammable and toxic. It glows in the dark (chemiluminescence).
• Red Phosphorus: More stable than white phosphorus and is used in the striking surface of matchboxes. It is non-toxic compared to the white variety.
• Black Phosphorus: The most stable form and is produced by heating white phosphorus under high pressure. It resembles graphite in its structure and properties.
• Physical and Chemical Characteristics:
• Atomic Mass: Approximately 30.974 u.
• Location: It is situated in Period 3 and p-block of the Periodic Table.
• State at Room Temperature: It exists as a solid.
• Industrial and Biological Uses:
• The largest industrial use of phosphorus compounds is in the production of fertilizers (such as phosphates) to replace the phosphorus that plants remove from the soil.
• It is also used in the manufacture of detergents, pesticides, steel, and safety matches.

Important Points

• Rules for Atomic Symbols:
• According to the Dalton’s and later Berzelius's suggestions, symbols of elements are represented by the first letter (in Uppercase) or the first and second letter (second being lowercase) of the element's name in English, Latin, or Greek.
• Examples: Hydrogen (H), Carbon (C), Oxygen (O), and Iron (Fe from Latin Ferrum).
• Comparison of the Options:
• Ph: Not an element symbol; used for Phenyl functional groups.
• P: Correct symbol for Phosphorus.
• Ps: Not a standard atomic symbol for a naturally occurring element.
• Pr: Symbol for Praseodymium, a rare earth metal with atomic number 59.
• Phosphate Cycle: In the environment, phosphorus is most commonly found as the phosphate ion (PO4³⁻). It is a critical limiting nutrient in many ecosystems, especially aquatic ones.

The correct answer is Areolar tissue.

Key Points

• Areolar tissue is the most widely distributed connective tissue in the animal body. It acts as a supporting and packing tissue between most of the organs.
• It is found located between the skin and muscles, around blood vessels and nerves, and in the bone marrow.
• The primary functions of areolar tissue include filling the space inside the organs, providing support to internal organs, and assisting in the repair of tissues after injury. Hence, the correct answer is Areolar tissue.
• This tissue consists of a semifluid ground substance (matrix) that contains three types of cells: fibroblasts, macrophages, and mast cells.
• It also contains two types of protein fibers: white collagen fibers, which provide tensile strength, and yellow elastic fibers (elastin), which allow for flexibility and recoil.

Additional Information

• Squamous epithelium:
• Unlike areolar tissue, this is an epithelial tissue, not a connective tissue. It is composed of a single thin layer of flattened cells with irregular boundaries.
• It is primarily found in the walls of blood vessels and the alveoli (air sacs) of the lungs.
• Its main function is to form a diffusion boundary for the exchange of gases and nutrients.
• Tendon:
• Tendons are a type of dense regular connective tissue characterized by great strength but limited flexibility.
• Their specific function is to connect skeletal muscles to bones, facilitating movement of the skeleton when muscles contract.
• Ligament:
• Ligaments are also dense connective tissues, but they are highly elastic and possess significant strength.
• They contain very little matrix and serve the crucial role of connecting one bone to another bone at joints, maintaining structural stability.
• Adipose Tissue:
• This is another type of loose connective tissue located mainly beneath the skin and between internal organs.
• The cells of this tissue (adipocytes) are specialized to store fats, which acts as an insulator and an energy reservoir for the body.

Important Points

• Connective Tissues are categorized into three main types: Loose connective tissue (e.g., Areolar and Adipose), Dense connective tissue (e.g., Tendons and Ligaments), and Specialized connective tissue (e.g., Cartilage, Bone, and Blood).
• The matrix is a non-living material secreted by the cells of the connective tissue, which can be fluid, jelly-like, or solid depending on the tissue's function.
• In Areolar tissue, the loose arrangement of fibers allows the tissue to be flexible yet strong enough to bind different tissue types together, such as connecting the epithelial tissue to the underlying structures.
• Fibroblasts within the areolar tissue are the cells responsible for secreting the fibers (collagen and elastin) and the polysaccharides that make up the ground substance.

The correct answer is The space increases as matter changes from solid to gas.

Key Points

• According to the Kinetic Molecular Theory, all matter is made of particles that are in constant motion, and the space between these particles determines the state of matter.
• In a solid, particles are tightly packed in a fixed, regular lattice structure with very little intermolecular space between them.
• As a substance transitions to a liquid state, the particles gain energy and move further apart, creating moderate gaps that allow them to slide past each other.
• In the gaseous state, particles have high kinetic energy and are widely separated, occupying much larger volumes compared to their solid or liquid forms.
• The intermolecular distance is greatest in gases and smallest in solids. Hence, the statement that the space increases as matter changes from solid to gas is correct.
• Statement 1: Solids and gases always have equal spacing. This statement is incorrect as gases have significantly more void space than solids.
• Statement 2: The space remains unchanged during the change in states of matter. This statement is incorrect because phase changes (like melting or evaporation) are fundamentally defined by the change in particle arrangement and distance.
• Statement 4: The space decreases as matter changes from solid to gas. This statement is incorrect as this describes condensation or freezing (gas to liquid/solid), not the transition to a gas.

Additional Information

• Intermolecular Forces: These are the attractive forces between molecules. They are strongest in solids, keeping the particles in fixed positions, and weakest (almost negligible) in gases, allowing particles to move independently.
• Kinetic Energy and Temperature: The transition from solid to gas usually occurs by increasing temperature. Adding heat increases the kinetic energy of the particles, allowing them to overcome intermolecular attractions and increase their separation.
• Compressibility: Because gases have large intermolecular spaces, they are highly compressible. Solids have very little empty space, making them virtually incompressible.
• Density: For most substances, density is highest in the solid phase and lowest in the gas phase because the same mass occupies a much larger volume in the gaseous state due to increased particle spacing.
• Shape and Volume: Solids have a definite shape and fixed volume due to lack of space between particles. Gases have no definite shape or volume, expanding to fill the entire container they occupy.

Important Points

• Sublimation: This is the direct transition of a substance from solid to gas without passing through the liquid phase (e.g., dry ice or naphthalene), which results in a massive and rapid increase in intermolecular space.
• Thermal Expansion: Even within a single state, increasing temperature generally causes a slight increase in intermolecular distance, leading to the expansion of the material.
• Pressure Effects: Increasing pressure on a gas reduces the space between particles, which can eventually force a phase change back into a liquid state through liquefaction.

The correct answer is 14 m/s.

Key Points

• The problem involves Newton's Second Law of Motion and the Equations of Motion to determine how a constant force affects an object's velocity over time.
• In the first scenario, an object of mass 4 kg has an initial velocity (u) of 2 m/s and reaches a final velocity (v) of 8 m/s in a time duration (t) of 2 s.
• We first calculate the acceleration (a) using the formula: a = (v - u) / t. Plugging in the values: a = (8 m/s - 2 m/s) / 2 s = 6 / 2 = 3 m/s². This means the constant force produces a steady acceleration of 3 m/s².
• The magnitude of the force (F) can be found using F = m * a. Thus, F = 4 kg * 3 m/s² = 12 N.
• In the second scenario, the same force is applied for a duration of 4 s. Assuming it starts from the same initial velocity of 2 m/s, we calculate the new final velocity using v = u + at.
• Calculation: v = 2 m/s + (3 m/s² * 4 s) = 2 + 12 = 14 m/s. Hence, the final velocity is 14 m/s.

Additional Information

• Newton's Second Law of Motion: This law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. The formula is F = ma.
• Force: It is defined as a push or pull upon an object resulting from the object's interaction with another object. The SI unit of force is the Newton (N), named after Sir Isaac Newton. One Newton is equal to 1 kg.m/s².
• Acceleration: This is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity. The SI unit for acceleration is m/s².
• Equations of Motion: These equations relate the displacement, velocity, acceleration, and time of a moving object. The three primary equations for constant acceleration are v = u + at, s = ut + 0.5at², and v² = u² + 2as.

Important Points

• Constant Force: When a constant force acts on a body of constant mass, it results in a constant acceleration. This allows for the use of the linear equations of motion.
• Mass vs. Weight: Mass is a fundamental property of an object (measured in kg) and does not change based on location, while weight is the force of gravity acting on that mass. In this problem, the mass is 4 kg.
• Initial and Final Velocity: Initial velocity is the velocity at which motion begins (at t = 0), and final velocity is the velocity after a specific time interval has elapsed.
• Relationship with Time: If the acceleration is constant, the change in velocity is directly proportional to the time for which the force is applied. Doubling the time from 2 s to 4 s (if starting from rest) would double the velocity change, but since there is an initial velocity, we must add it to the total change.

The correct answer is Phloem.

Key Points

• Phloem is a complex permanent tissue in plants that acts as the primary conduction system for organic nutrients, especially sucrose, which is produced during photosynthesis.
• The transport of food in plants is known as translocation. This process occurs from the source (usually the leaves) to the sink (areas of growth or storage like roots, stems, and fruits).
• Unlike xylem, the movement of food through phloem is bidirectional, meaning it can move both upwards and downwards to reach all parts of the plant depending on the seasonal or metabolic needs.
• Phloem is composed of four distinct types of cells: sieve tubes, companion cells, phloem parenchyma, and phloem fibers. Out of these, only phloem fibers are dead cells at maturity, while the others are living cells.
• The process of translocation in phloem is an active process that requires energy in the form of ATP (Adenosine Triphosphate) to load sucrose into the sieve tubes, creating an osmotic pressure that facilitates the flow of materials.

Additional Information

• Xylem:
• It is the complex tissue responsible for the conduction of water and minerals from the soil through the roots to the rest of the plant.
• The flow of water in xylem is unidirectional (only upwards). It consists of tracheids, vessels, xylem parenchyma, and xylem fibers. Most of the cells in xylem (except parenchyma) are dead at maturity to facilitate efficient water transport.
• Collenchyma:
• This is a simple permanent tissue made of living cells. It provides mechanical support and flexibility to the plant, allowing parts like petioles (leaf stalks) and young stems to bend without breaking.
• The cells are characterized by irregularly thickened walls at the corners due to the deposition of cellulose and pectin.
• Sclerenchyma:
• It is a simple permanent tissue composed of dead cells with extremely thickened secondary walls containing lignin.
• Its primary function is to provide strength, stiffness, and structural rigidity to the plant. It is found in the husk of coconut, the hard shells of nuts, and the grit in fruits like pear (sclereids).
• Vascular Bundles:
• In higher plants, xylem and phloem are grouped together to form vascular bundles. These tissues are essential for the survival of terrestrial plants, allowing them to grow tall by facilitating the transport of nutrients and water over long distances.

Important Points

• Sieve Tubes: These are tubular cells with perforated walls called sieve plates. Although they are living, they lack a nucleus at maturity and rely on companion cells for metabolic functions.
• Companion Cells: These are specialized parenchyma cells that are closely associated with sieve tubes and help in regulating the pressure gradient during translocation.
• Lignin: A complex polymer found in sclerenchyma and xylem that acts as a cementing material, making the cell walls waterproof and extremely strong.
• Difference between Simple and Complex Tissue: Simple tissues (like Collenchyma and Sclerenchyma) consist of only one type of cell, whereas complex tissues (like Xylem and Phloem) are made of more than one type of cell working together as a unit.

The correct answer is Binary Fission.

Key Points

• Binary Fission is a primary method of asexual reproduction typically observed in unicellular organisms, where a single cell divides into two approximately equal and genetically identical daughter cells.
• Since the scientist is observing a multicellular organism, it possesses complex structures and specialized tissues that cannot simply split into two through cellular fission to reproduce the entire organism. Hence, the statement that the organism would NOT use binary fission is correct.
• Multicellular organisms, particularly plants, utilize more complex mechanisms for asexual reproduction such as budding, fragmentation, and vegetative propagation, which involve the growth of new tissues from specialized regions.
• In Binary Fission, the genetic material (DNA) replicates and the cytoplasm divides, a process common in prokaryotes like bacteria and some eukaryotic protists like Amoeba.
• The other options—Budding, Fragmentation, and Vegetative Propagation—are all viable methods for various multicellular plants and simple multicellular animals.

Additional Information

• Budding:
• In this process, a small outgrowth or bud develops on the parent body due to repeated cell division at one specific site.
• These buds develop into tiny individuals and, when fully mature, detach from the parent body to become new independent individuals.
• Examples include Hydra (a multicellular animal) and Yeast (a unicellular fungus).
• Fragmentation:
• This occurs when a multicellular organism simply breaks up into smaller pieces upon maturation.
• Each piece, or fragment, grows into a new complete individual through regeneration of missing parts.
• Examples include filamentous algae like Spirogyra and some flatworms like Planaria.
• Vegetative Propagation:
• This is a form of asexual reproduction in plants where new plants are produced from vegetative parts such as roots, stems, and leaves rather than seeds.
• Methods include tubers (potato), runners (strawberry), and leaf notches (Bryophyllum).
• It allows for the rapid production of genetically uniform offspring and is widely used in horticulture.
• Binary Fission Details:
• It is the simplest form of reproduction. In Amoeba, the division can take place in any plane, whereas in Leishmania (which causes Kala-azar), it occurs in a definite orientation in relation to whip-like structures.
• Because it involves the division of a single cell into two, it is biologically impossible for a complex multicellular plant to undergo this process as a whole.

Important Points

• Complexity and Reproduction: As organisms become more complex (multicellular), their reproductive strategies shift from simple cell division to processes involving specialized reproductive cells or tissues.
• Asexual vs. Sexual: All methods mentioned in the options are types of asexual reproduction, meaning they do not involve the fusion of gametes and result in offspring that are clones of the parent.
• Environmental Adaptation: Vegetative propagation and fragmentation are often advantageous in stable environments where the parent's traits are already well-suited for survival.

The correct answer is Neutralisation.

Key Points

• A Neutralisation reaction is a specific type of chemical reaction where an acid and a base react with each other to produce salt and water.
• In aqueous solutions, this reaction occurs when H+ ions (hydrogen ions) from the acid combine with OH- ions (hydroxyl ions) from the base to form H2O (water) molecules.
• The general chemical equation representing this process is: Acid + Base → Salt + Water. For example, the reaction between Hydrochloric acid (HCl) and Sodium hydroxide (NaOH) produces Sodium chloride (NaCl) and water.
• Neutralisation reactions are generally exothermic in nature, meaning they involve the evolution of heat during the process.
• The resulting pH of the solution depends on the strength of the reactants; a reaction between a strong acid and a strong base typically results in a solution with a pH of 7 (neutral). Hence, the correct answer is Neutralisation.

Additional Information

• Decomposition Reaction:
• This is a chemical reaction in which a single compound breaks down into two or more simpler substances or elements.
• It usually requires an external energy source such as heat (thermal decomposition), light (photolysis), or electricity (electrolysis) to break the chemical bonds.
• An example is the decomposition of Calcium Carbonate (CaCO3) into Calcium Oxide (CaO) and Carbon Dioxide (CO2) upon heating. Hence, option 1 is incorrect.
• Combustion Reaction:
• Combustion is a high-temperature exothermic reaction between a fuel and an oxidant (usually atmospheric oxygen).
• This reaction typically produces smoke, heat, and light, along with oxidized gaseous products like Carbon dioxide and Water vapor.
• The burning of methane (CH4) in the presence of oxygen is a classic example of a combustion reaction. Hence, option 2 is incorrect.
• Oxidation Reaction:
• In classical chemistry, Oxidation refers to the addition of oxygen to a substance or the removal of hydrogen.
• In modern electronic terms, it is defined as the process where an atom, ion, or molecule loses electrons during a reaction.
• It is always accompanied by reduction (gain of electrons) in what is collectively known as a Redox reaction. Hence, option 3 is incorrect.

Important Points

• Practical Applications of Neutralisation:
• Indigestion: Human stomachs produce Hydrochloric acid to help digest food, but excess acid causes pain. This is treated with antacids like Milk of Magnesia (Magnesium Hydroxide), which is a mild base that neutralizes the acid.
• Soil Treatment: Plants do not grow well if the soil is too acidic or too basic. If soil is acidic, it is treated with bases like quick lime (Calcium Oxide) or slaked lime (Calcium Hydroxide).
• Ant Stings: When an ant bites, it injects formic acid into the skin. The effect of the sting can be neutralized by rubbing moist baking soda (Sodium Hydrogen Carbonate) or calamine solution (containing Zinc Carbonate).
• Factory Waste: The waste of many factories contains acids. If allowed to flow into water bodies, they kill fish. These wastes are neutralized by adding basic substances before disposal.

The correct answer is Work done by the force of gravity.

Key Points

• Work is defined in physics as the product of the force applied to an object and the displacement of the object in the direction of that force. The formula is W = F d cos(theta), where theta is the angle between the force and displacement vectors.
• When a boy lifts an object above his head, the displacement of the object is in the upward direction.
• The force of gravity (weight) acts on the object vertically downward toward the center of the Earth.
• Because the displacement is upward and the force of gravity is downward, the angle theta between them is 180 degrees.
• The value of cos(180) is -1; therefore, the work done by the force of gravity is negative. Hence, option 1 is the correct answer.
• Conversely, the applied force exerted by the boy is in the upward direction, the same as the displacement. This means the angle is 0 degrees, and since cos(0) is 1, the work done by the boy is positive.

Additional Information

• Positive Work: This occurs when the force and the displacement are in the same direction (angle between 0 and 90 degrees). A common example is a horse pulling a cart or a person pushing a car forward.
• Zero Work: Work is zero if the force is perpendicular to the displacement (90 degrees) or if there is no displacement. For example, a person holding a heavy box stationary or a satellite moving in a circular orbit (where centripetal force is perpendicular to velocity) does no work.
• SI Unit of Work: The standard unit is the Joule (J). One Joule is the work done when a force of 1 Newton moves an object through a distance of 1 meter.
• Nature of Work: Work is a scalar quantity, meaning it only has magnitude and no specific direction in space, even though force and displacement are vectors.
• Dimensions: The dimensional formula for work is [M1 L2 T-2], which is the same as the dimensions of energy.

Important Points

• Work-Energy Theorem: This theorem states that the net work done on an object is equal to the change in its kinetic energy. When gravity does negative work, it often results in an increase in the object's potential energy.
• Power: Related to work, power is the rate at which work is done. It is measured in Watts (W), where 1 Watt = 1 Joule per second.
• Conservative Forces: Gravity is a conservative force, meaning the work done by it depends only on the initial and final positions of the object, not the path taken.
• Mechanical Energy: In the absence of friction, the sum of kinetic energy and potential energy remains constant. In this lifting scenario, the positive work from the boy is stored as gravitational potential energy because gravity is "resisting" the motion with negative work.

The correct answer is Axon terminal → Dendrite of another neuron.

Key Points

• A synapse is the specialized junction through which neurons signal to each other or to non-neuronal cells such as those in muscles or glands. In a chemical synapse, the process involves the transmission of neurotransmitters.
• The transmission begins when an electrical impulse (action potential) reaches the axon terminal of the presynaptic neuron. This terminal contains synaptic vesicles filled with chemical messengers.
• Upon reaching the end of the axon, the nerve impulse triggers the release of these neurotransmitters into a fluid-filled gap known as the synaptic cleft, which is typically 20 to 50 nanometers wide.
• The neurotransmitters diffuse across the gap and bind to specific protein receptors located on the dendrite or the cell body of the postsynaptic neuron. This binding action generates a new electrical signal in the receiving neuron. Hence, the primary chemical communication occurs from the Axon terminal to the Dendrite of another neuron.
• The options describing communication within the same neuron or involving the myelin sheath do not represent the standard mechanism of intercellular chemical signaling. Hence, statement 3 is correct.

Additional Information

• Structural Components of a Neuron:
• Cell Body (Soma): Contains the nucleus and cytoplasm; it serves as the metabolic center of the cell.
• Dendrites: These are highly branched, short fibers that receive incoming signals from other neurons and carry them toward the cell body.
• Axon: A single, long, cylindrical fiber that transmits impulses away from the cell body toward other neurons or effectors.
• Myelin Sheath and Conduction:
• Many axons are covered by a fatty insulating layer called the myelin sheath, produced by Schwann cells in the PNS and oligodendrocytes in the CNS.
• It facilitates saltatory conduction, where the impulse "jumps" between Nodes of Ranvier, significantly increasing the speed of transmission.
• Common Neurotransmitters:
• Acetylcholine (ACh): Essential for muscle stimulation and memory.
• Dopamine: Associated with the reward system, motivation, and motor control.
• Serotonin: Plays a key role in mood regulation, sleep, and digestion.
• Types of Synapses:
• Chemical Synapse: Uses chemicals to bridge the gap; it is the most common type and allows for complex signal modulation.
• Electrical Synapse: Neurons are connected by gap junctions, allowing ions to flow directly between cells, resulting in faster, near-instantaneous transmission.

Important Points

• Unidirectional Flow: Nerve impulses in a chemical synapse travel in only one direction because neurotransmitter receptors are located only on the postsynaptic side (dendrites), while vesicles are on the presynaptic side (axon terminals).
• Synaptic Delay: There is a brief time interval (approx 0.3 to 0.5 milliseconds) required for the neurotransmitter to be released, cross the cleft, and bind to receptors.
• Exocytosis: The specific biological process where synaptic vesicles fuse with the presynaptic membrane to dump neurotransmitters into the extracellular space.
• Reuptake: After signaling, neurotransmitters are often cleared from the synaptic cleft through enzymatic degradation or reuptake back into the presynaptic neuron to terminate the signal.

The correct answer is Both A and R are true, and R is the correct explanation of A.

Key Points

• Assertion (A) states that keeping oily food in airtight containers prevents rancidity. This is based on the principle of limiting the exposure of food items to atmospheric oxygen. Hence, statement A is correct.
• Reason (R) explains that airtight containers slow down the oxidation of fats and oils. Since the supply of oxygen is restricted within a sealed environment, the chemical reaction between oxygen and the fat molecules occurs much more slowly. Hence, statement R is correct.
• Rancidity is the process of aerial oxidation of unsaturated fats and oils present in food materials, which results in an unpleasant smell and taste.
• The primary cause of oxidative rancidity is the reaction of oxygen with the double bonds of fatty acid chains. By using an airtight container, the volume of oxygen available for this reaction is significantly reduced.
• Because the mechanism described in the reason (slowing down oxidation) directly leads to the effect described in the assertion (prevention of rancidity), Reason (R) is the correct explanation of Assertion (A).
• Hence, the correct answer is Both A and R are true, and R is the correct explanation of A.

Additional Information

• Types of Rancidity:
• Oxidative Rancidity: This occurs when oxygen damages the food by breaking the long-chain fatty acids into smaller compounds like aldehydes and ketones.
• Hydrolytic Rancidity: This happens when water (moisture) splits fatty acid chains away from the glycerol backbone in triglycerides, often catalyzed by enzymes like lipase.
• Microbial Rancidity: This is caused by microorganisms such as bacteria or molds that use enzymes to break down chemical structures in fats.
• Methods to Prevent Rancidity:
• Antioxidants: Chemicals such as Butylated Hydroxyanisole (BHA) and Butylated Hydroxytoluene (BHT) are often added to fat-containing foods to inhibit oxidation.
• Nitrogen Flushing: Manufacturers of potato chips and other snacks flush the bags with Nitrogen gas (an inert gas) to displace oxygen and prevent the chips from turning rancid.
• Vacuum Packaging: Removing all air from the packaging before sealing effectively stops the oxidation process.
• Refrigeration: Storing food at low temperatures reduces the rate of chemical reactions, including oxidation and microbial growth.
• Light Protection: Storing oily food in dark places or opaque containers helps because Ultraviolet (UV) light can act as a catalyst for the oxidation process.

Important Points

• Chemical Reaction: The process of rancidity is a redox reaction (specifically oxidation) where the fatty acids lose electrons to oxygen.
• Impact on Health: Consuming rancid food is not only unpleasant due to the off-flavor but can also lead to the formation of free radicals, which are linked to various health issues and cellular damage.
• Detection: Rancidity is typically detected through sensory evaluation (smell and taste) or chemical tests like the Peroxide Value (PV) test, which measures the extent of primary oxidation.
• Saturated vs. Unsaturated Fats: Unsaturated fats (like vegetable oils) are much more susceptible to rancidity than saturated fats (like butter or lard) because of the presence of carbon-carbon double bonds that react easily with oxygen.

The correct answer is Catenation.

Key Points

• Catenation is the unique property of an element to form covalent bonds with other atoms of the same element, resulting in the formation of long chains, branched structures, or rings.
• Among all known elements, Carbon exhibits the maximum tendency for catenation due to the high strength and stability of the Carbon-Carbon (C-C) bond.
• This property allows carbon to form an almost infinite variety of molecules, ranging from simple hydrocarbons to complex biological macromolecules like DNA and proteins.
• The ability to form single, double, and triple bonds between carbon atoms further enhances the structural diversity enabled by catenation.
• It is because of catenation and tetravalency that carbon forms such a large number of compounds, leading to the dedicated branch of science known as Organic Chemistry.

Additional Information

• Tetravalency:
• Carbon has four valence electrons in its outermost shell, allowing it to form four covalent bonds with other atoms.
• This characteristic enables carbon to link with a wide variety of other elements like hydrogen, oxygen, nitrogen, and sulfur, as well as other carbon atoms.
• Isomerism:
• This is the phenomenon where compounds have the same molecular formula but different structural arrangements or spatial orientations.
• Since catenation allows for different chain lengths and branching, isomers are very common in organic compounds, contributing to their vast chemical variety.
• Polymerisation:
• This is a chemical process in which small units called monomers join together to form a very large molecule called a polymer.
• While catenation is the inherent atomic property, polymerisation is the process used to create materials like plastics (polyethene), rubber, and nylon.
• Comparison with Silicon:
• Silicon also shows catenation properties but to a much lesser extent than carbon.
• Silicon can form chains with hydrogen (silanes) up to about 7 or 8 atoms, but these compounds are highly reactive and unstable because the Si-Si bond is significantly weaker than the C-C bond.

Important Points

• Bond Energy: The stability of carbon chains is attributed to the high bond enthalpy of the C-C bond, which is approximately 348 kJ/mol. In contrast, the Si-Si bond energy is only about 222 kJ/mol.
• Atomic Size: Carbon is a small-sized atom, which allows the nucleus to hold the shared pair of electrons in the covalent bond more tightly, leading to a strong and stable bond.
• Allotropes of Carbon: Catenation is also responsible for the different forms of carbon, such as Diamond (3D network), Graphite (layered hexagonal sheets), and Fullerenes (spherical cages like C60).

The correct answer is Phloem, companion cells.

Key Points

• Phloem is a complex permanent tissue in vascular plants responsible for the translocation of food (mainly sucrose) from the leaves, where it is produced during photosynthesis, to other parts of the plant like roots, fruits, and storage organs.
• It consists of four main components: sieve tube elements, companion cells, phloem parenchyma, and phloem fibers. Out of these, only the phloem fibers are dead cells, while the rest are living cells.
• Sieve tubes are long, tubular structures with perforated end walls known as sieve plates. Interestingly, while they are living cells at maturity, they lack a nucleus, ribosomes, and vacuoles to allow for the efficient flow of nutrients.
• Companion cells are specialized parenchyma cells that are closely associated with sieve tube elements. They possess a dense cytoplasm and a prominent nucleus, which regulates the metabolic activities of the enucleated sieve tubes.
• The relationship between sieve tubes and companion cells is vital; they are connected by plasmodesmata, and the companion cells help in the loading and unloading of sugars into the sieve tube elements. Hence, the first option is correct.

Additional Information

• Xylem:
• This is another complex tissue primarily responsible for the unidirectional transport of water and minerals from the roots to the aerial parts of the plant.
• It consists of tracheids, vessels, xylem parenchyma, and xylem fibers. In xylem, only the xylem parenchyma is a living cell, while the others are dead at maturity. Hence, options 3 and 4 are incorrect.
• Simple Plant Tissues:
• Collenchyma: Provides mechanical support and flexibility to young plant parts like the petiole of a leaf. It consists of living cells with localized cellulose thickening at corners.
• Sclerenchyma: Composed of dead cells with highly thickened, lignified walls, providing structural rigidity and strength to the plant. Hence, option 2 is incorrect.
• Bidirectional Transport: Unlike the xylem, which moves water only upwards, the phloem facilitates bidirectional movement. This ensures that food can move both downwards to the roots and upwards to developing buds or fruits.

Important Points

• Vascular Bundles: The xylem and phloem together form vascular bundles. In dicotyledonous stems, there is a layer of cambium between them, allowing for secondary growth (increase in girth).
• Sugar Source and Sink: The "source" is usually the leaves (where food is synthesized), and the "sink" is the part that needs or stores the food. The phloem transport is driven by a pressure gradient created by the active loading of solutes.
• Evolutionary Context: The development of vascular tissues (xylem and phloem) was a critical adaptation that allowed Tracheophytes (vascular plants) to colonize land and grow to significant heights, unlike non-vascular plants like mosses.

The correct answer is m/s.

Key Points

• Average speed is defined as the total distance traveled by an object divided by the total time taken to cover that distance.
• In the International System of Units (SI), which was established in 1960, the standard unit for length (distance) is the meter (m) and the standard unit for time is the second (s).
• By using the formula Speed = Distance / Time, the derived SI unit becomes meters per second, mathematically expressed as m/s or m s⁻¹.
• Option 1 (km/h²): This is not a recognized standard unit for speed or average speed in the SI system, though km/h is a common metric unit for speed. Hence, this statement is incorrect.
• Option 2 (m/s²): This is the SI unit of acceleration, which measures the rate of change of velocity over time. Hence, this statement is incorrect.
• Option 3 (s/m²): This unit does not represent any standard physical quantity in classical mechanics. Hence, this statement is incorrect.
• Option 4 (m/s): This is the correct SI unit for both instantaneous speed and average speed. Hence, this statement is correct.

Additional Information

• Scalar vs Vector: Speed is a scalar quantity because it possesses only magnitude and no direction. Velocity, which is the displacement divided by time, is a vector quantity as it includes both magnitude and direction.
• Measuring Instruments: In automobiles, the speedometer is used to measure the instantaneous speed of the vehicle at any given moment, while the odometer records the total distance traveled.
• Unit Conversion: In daily life, speed is often expressed in kilometers per hour (km/h). To convert 1 km/h to m/s, we multiply by 5/18 (since 1000m / 3600s = 5/18). For example, 36 km/h is equal to 10 m/s.
• Dimensional Formula: The dimensional formula for speed is [M⁰ L¹ T⁻¹], indicating it is independent of mass (M) and depends on length (L) and time (T).
• Types of Speed: Apart from average speed, there is Uniform speed (covering equal distances in equal intervals of time) and Variable speed (covering unequal distances in equal intervals of time).

Important Points

• CGS System: In the Centimetre-Gram-Second (CGS) system of units, the unit of speed is centimeter per second (cm/s).
• FPS System: In the Foot-Pound-Second (FPS) system, speed is measured in feet per second (ft/s).
• Speed of Light: The ultimate speed limit in the universe is the speed of light in a vacuum, which is approximately 299,792,458 m/s (often rounded to 3 x 10⁸ m/s).
• Supersonic Speeds: Speeds exceeding the speed of sound (approx. 343 m/s in air) are referred to as supersonic and are often measured using Mach numbers.

The correct answer is - 3/4.

Key Points

• Magnification (m) produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size.
• It is expressed as the ratio of the height of the image to the height of the object. It is also related to the object distance (u) and image distance (v) by the formula: m = -v / u.
• According to the New Cartesian Sign Convention, the object distance (u) is always negative. In this case, u = - 40 cm.
• Since the image is real and inverted and formed in front of the concave mirror, the image distance (v) is also negative. Here, v = - 30 cm.
• Substituting the values into the formula: m = - (- 30) / (- 40). This simplifies to m = 30 / (- 40), which equals - 3/4.
• The negative sign in the result signifies that the image is real and inverted. Hence, the correct answer is - 3/4.

Additional Information

• Concave Mirror: A spherical mirror whose reflecting surface is curved inwards (towards the center of the sphere). It is also known as a converging mirror because it converges light rays at a single point called the focus.
• Sign Convention Rules:
• The Pole (P) is taken as the origin.
• Distances measured in the direction of incident light are positive.
• Distances measured opposite to the direction of incident light are negative.
• Heights measured upwards and perpendicular to the principal axis are positive, while those measured downwards are negative.
• Nature of Magnification:
• If m is negative, the image is real and inverted.
• If m is positive, the image is virtual and erect.
• If |m| > 1, the image is magnified (larger than the object).
• If |m| < 1, the image is diminished (smaller than the object).

Important Points

• Mirror Formula: The relationship between focal length (f), object distance (u), and image distance (v) is given by 1/f = 1/v + 1/u.
• In this specific question, since |m| = 3/4 (0.75), which is less than 1, the image is diminished.
• For a concave mirror, real images are always inverted, and virtual images (formed when the object is between the Focus and Pole) are always erect and magnified.
• The radius of curvature (R) is twice the focal length (f), denoted as R = 2f.

The correct answer is 800 Hz.

Key Points

• The relationship between the speed, frequency, and wavelength of a wave is governed by the universal wave equation: Speed (v) = Frequency (f) × Wavelength (λ).
• In the given problem, the speed of the sound wave (v) is 320 m/s and the wavelength (λ) is 0.4 m.
• To calculate the frequency (f), the formula is rearranged as f = v / λ.
• By substituting the provided numerical values into the equation: f = 320 / 0.4.
• The calculation 320 / 0.4 equals 800. Thus, the frequency of the sound wave is 800 Hz. Hence, the correct answer is 800 Hz.

Additional Information

• Frequency:
• Frequency refers to the number of complete oscillations or wave cycles that pass a fixed point in one second.
• The SI unit of frequency is the Hertz (Hz), named after the physicist Heinrich Hertz. One Hertz is equivalent to one cycle per second.
• Wavelength:
• Wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
• In longitudinal waves like sound, it is the distance between the centers of two consecutive compressions or two consecutive rarefactions. It is measured in meters (m).
• Nature of Sound Waves:
• Sound is a mechanical wave, meaning it requires a medium (solid, liquid, or gas) to travel. It cannot propagate through a vacuum.
• It is also a longitudinal wave, where the particles of the medium vibrate parallel to the direction of energy transport.

Important Points

• Human Audibility: The standard audible range for humans is between 20 Hz and 20,000 Hz (20 kHz). Since 800 Hz falls within this range, it is an audible sound to the human ear.
• Pitch and Frequency: The pitch of a sound is directly proportional to its frequency. A wave with a higher frequency is perceived as having a higher pitch (shrill), while a lower frequency is perceived as a lower pitch (grave).
• Speed of Sound in Air: The speed of sound is not constant; it varies with temperature and humidity. For example, at 0 degrees Celsius, the speed is approximately 331 m/s, whereas at 20 degrees Celsius, it increases to about 343 m/s.
• Medium Density: Sound travels fastest in solids (due to high elasticity and density), slower in liquids, and slowest in gases. In steel, the speed can reach approximately 5960 m/s.

The correct answer is Only immature eggs.

Key Points

• At the time of birth, the ovaries of a human female child already contain all the eggs she will ever have throughout her lifetime.
• These eggs are in an immature state and are scientifically referred to as primary oocytes. Hence, statement 1 is correct.
• Unlike the male reproductive system, which produces sperm continuously after puberty, the female reproductive system does not produce any new eggs after the birth of the child.
• The process of egg maturation does not begin until the girl reaches puberty, which typically occurs between the ages of 10 and 14 years. Hence, statement 2 is incorrect.
• Because the ovaries are fully formed and populated with follicles during fetal development, it is false to say they contain no eggs at birth. Hence, statement 3 is incorrect.
• Since the maturation process is triggered by hormonal changes later in life, a newborn cannot possess mature eggs (secondary oocytes) ready for fertilization. Hence, statement 4 is incorrect.

Additional Information

• Oogenesis:
• This is the biological process of the formation of a mature female gamete or ovum.
• It begins during the embryonic development stage when a couple of million gamete mother cells (oogonia) are formed within each fetal ovary.
• These cells start cell division and enter into prophase-I of the meiotic division and get temporarily arrested at that stage, called primary oocytes.
• Puberty and Ovulation:
• Upon reaching puberty, the hypothalamus releases Gonadotropin-releasing hormone (GnRH), which stimulates the pituitary gland.
• The pituitary gland secretes Follicle Stimulating Hormone (FSH) and Luteinizing Hormone (LH), which trigger the maturation of a few immature eggs each month.
• Usually, only one follicle matures fully to release a mature egg during the menstrual cycle, a process known as ovulation.
• Menopause:
• The supply of eggs decreases over time due to a process called atresia.
• When the store of oocytes is eventually exhausted, usually around the age of 45 to 55, the female reaches menopause, marking the end of reproductive capability.

Important Points

• Numerical Data: A female child is born with approximately 1 to 2 million immature eggs. By the time she reaches puberty, only about 300,000 to 400,000 remain.
• During a woman's entire reproductive life, only about 400 to 500 of these eggs will actually mature and be released during ovulation.
• Cellular Stage: The immature eggs are specifically arrested in the diplotene stage of Prophase I of Meiosis I. Completion of the first meiotic division occurs just before ovulation.
• Location: These eggs are housed within structures called ovarian follicles located in the cortex of the ovaries.

The correct answer is Au (gold).

Key Points

• The reactivity series is a sequence of metals arranged in the decreasing order of their chemical reactivity. It helps in predicting how metals will behave in displacement reactions and their interaction with water, oxygen, and acids.
• Gold (Au) is located at the very bottom of the reactivity series. This indicates that it is the most stable and the least reactive metal among the given options. Because of its inert nature, gold does not react with oxygen or water even at high temperatures.
• Potassium (K) is placed at the top of the reactivity series. It is an alkali metal that reacts violently with cold water to produce hydrogen gas and heat. It is so reactive that it must be stored under kerosene oil to prevent reaction with atmospheric moisture.
• Calcium (Ca) is also a highly reactive metal, although less so than potassium. It reacts readily with cold water to form calcium hydroxide and hydrogen bubbles, which often cause the metal to float.
• Iron (Fe) is a moderately reactive metal found in the middle of the series. It does not react with cold water but reacts with steam to form iron oxide. It also reacts slowly with oxygen and moisture to form rust (hydrated ferric oxide).
• Comparing the positions, Potassium (K) > Calcium (Ca) > Iron (Fe) > Gold (Au). Hence, Gold (Au) is the least reactive metal.

Additional Information

• Concept of Reactivity: The reactivity of a metal is determined by its tendency to lose electrons and form positive ions (cations). Metals like Potassium and Sodium have one electron in their outermost shell, which they lose very easily, making them highly electropositive.
• Noble Metals: Metals like Gold (Au), Silver (Ag), and Platinum (Pt) are often referred to as noble metals. Because they are least reactive, they are found in nature in their native state (free state) rather than in combined forms like oxides or sulfides. This property makes them ideal for jewelry and electronic components as they do not corrode.
• Displacement Reactions: A metal higher in the reactivity series can displace a metal lower in the series from its salt solution. For example, Iron (Fe) can displace Copper (Cu) from a copper sulfate solution, but Gold (Au) cannot displace any of the metals mentioned in the options.
• Extraction Methods: The position in the reactivity series dictates the method of extraction. Highly reactive metals (K, Na, Ca, Mg, Al) are extracted through electrolysis of their molten chlorides or oxides. Moderately reactive metals (Zn, Fe, Pb) are reduced using Carbon (C). The least reactive metals (Au, Ag) are found in their pure form and require only physical separation.
• Reaction with Acids: Metals above Hydrogen (H) in the series can displace hydrogen from dilute acids (like HCl or H2SO4). Gold, being below hydrogen, does not react with dilute acids and can only be dissolved in Aqua Regia (a mixture of concentrated nitric acid and hydrochloric acid in a 1:3 ratio).

The correct answer is Sporangia.

Key Points

• Rhizopus is a genus of saprophytic fungi, commonly known as bread mold, which belongs to the phylum Zygomycota.
• The Sporangia (singular: sporangium) are the spherical, sac-like structures specifically responsible for asexual reproduction through the production of spores. Hence, statement 2 is correct.
• These structures develop at the tips of specialized upright hyphae known as sporangiophores.
• Inside the sporangium, the protoplasm undergoes cleavage to form thousands of minute, multinucleate, and non-motile sporangiospores.
• When the spores mature, the outer wall of the sporangium ruptures due to internal pressure or environmental factors, dispersing the spores into the air to colonize new substrates.

Additional Information

• Hyphae:
• These are the individual, thread-like filaments that make up the body of the fungus. In Rhizopus, the hyphae are coenocytic, meaning they are continuous tubes filled with multinucleated cytoplasm without septa (cross-walls).
• While they form the structural basis, they are not the direct site of spore formation. Hence, statement 1 is incorrect.
• Mycelium:
• The mycelium refers to the entire collective network or mass of hyphae that constitutes the vegetative part of the fungus.
• It is responsible for nutrient absorption and spreading across the substrate (like bread or fruit). Hence, statement 3 is incorrect.
• Rhizoids:
• Rhizoids are root-like, branching hyphae that grow downward into the food source.
• Their primary functions include anchoring the fungus to the substrate and secreting digestive enzymes to absorb organic nutrients. Hence, statement 4 is incorrect.
• Stolons:
• These are horizontal hyphae that grow along the surface of the substrate, connecting different clusters of rhizoids and sporangiophores.

Important Points

• Asexual Reproduction: This is the most common method of reproduction in Rhizopus, occurring rapidly under favorable conditions of moisture and temperature (typically 25°C to 30°C).
• Sexual Reproduction: While sporangia handle asexual cycles, Rhizopus can also undergo sexual reproduction through the fusion of two compatible gametangia, leading to the formation of a thick-walled zygospore.
• Columella: This is the central sterile portion found inside the sporangium. It plays a role in nutrient exchange for the developing spores.
• Economic Importance: Some species like Rhizopus stolonifer cause food spoilage, while others like Rhizopus oryzae are used in the industrial production of lactic acid and cortisone.

The correct answer is Only weight changes on the Moon.

Key Points

• Mass is defined as the total quantity of matter contained in an object. It is an intrinsic property of the body and remains constant regardless of the location in the universe, whether on Earth, the Moon, or in deep space.
• Weight is the gravitational force exerted on an object by a celestial body. It is calculated using the formula W = m × g, where m is mass and g is the acceleration due to gravity.
• The acceleration due to gravity on the Moon is approximately 1.62 m/s², which is about 1/6th (or 16.6%) of the gravity on Earth (9.8 m/s²). Since g changes, the weight of an object will change when moved to the Moon.
• The statement "Both mass and weight change on the Moon" is incorrect because mass is a scalar quantity that does not depend on gravity. Hence, statement 1 is incorrect.
• The statement "Only mass changes on the Moon" is incorrect because mass remains invariant, while weight is the property that actually fluctuates. Hence, statement 2 is incorrect.
• The statement "Neither mass nor weight changes on the Moon" is incorrect because while mass is constant, the gravitational pull of the Moon is significantly weaker than Earth's, causing weight to decrease. Hence, statement 3 is incorrect.
• The statement "Only weight changes on the Moon" is correct because an object's matter stays the same, but the force of gravity acting upon it decreases to 1/6th of its Earth value. Hence, statement 4 is correct.

Additional Information

• Detailed Comparison of Mass and Weight:
• Measurement Units: The SI unit of mass is the kilogram (kg), whereas the SI unit of weight is the Newton (N), as it is a measure of force.
• Nature of Quantity: Mass is a scalar quantity (it has only magnitude), while weight is a vector quantity because it acts in a specific direction (towards the center of the gravity source).
• Measuring Instruments: Mass is typically measured using a physical balance or beam balance, while weight is measured using a spring balance.
• Gravity on Different Celestial Bodies:
• On Jupiter, which has a much higher mass than Earth, the acceleration due to gravity is about 24.79 m/s². Consequently, an object's weight would increase by more than 2.5 times, even though its mass remains exactly the same.
• In a state of free fall or in outer space far from any planet, an object can become weightless (Weight = 0), but it will still possess its original mass.
• Practical Example:
• If a person has a mass of 60 kg on Earth, their weight on Earth would be 60 kg × 9.8 m/s² = 588 Newtons.
• On the Moon, that same person’s mass remains 60 kg, but their weight becomes 60 kg × 1.62 m/s² ≈ 98 Newtons.

Important Points

• Inertia: Mass is often described as a measure of inertia, which is the resistance of an object to any change in its state of motion. The higher the mass, the higher the inertia.
• Variation of 'g' on Earth: Even on Earth, weight can vary slightly because the Earth is an oblate spheroid. Gravity is slightly stronger at the poles (where you are closer to the center) and slightly weaker at the equator.
• Newton's Law of Universal Gravitation: This law states that every point mass attracts every other point mass by a force acting along the line intersecting both points. This force is what we perceive as weight.

The correct answer is Litmus.

Key Points

• Olfactory indicators are substances whose odor or smell changes depending on whether they are mixed with an acidic or basic solution.
• Onion is a well-known olfactory indicator. When treated with a base like sodium hydroxide (NaOH), the characteristic sharp smell of onion cannot be detected. however, its smell does not vanish when treated with an acid. Hence, it is an olfactory indicator.
• Vanilla essence has a characteristic pleasant smell. If we add a few drops of dilute Hydrochloric acid (HCl), the smell persists, but if we add dilute NaOH, the smell of vanilla vanishes. Hence, it is an olfactory indicator.
• Clove oil also acts as an olfactory indicator. Its distinct smell changes or disappears in the presence of a base, while it remains detectable in acidic conditions. Hence, it is an olfactory indicator.
• Litmus is a natural indicator but it is a visual indicator rather than an olfactory one. It changes its color in different media; it turns red in acidic solutions and blue in basic solutions. It does not rely on a change in smell for detection. Hence, it is NOT an olfactory indicator and is the correct answer.

Additional Information

• Natural Indicators:
• These are indicators obtained from natural sources like plants.
• Litmus is extracted from Lichens (a symbiotic relationship between algae and fungi). It is the most commonly used indicator in laboratories.
• Turmeric is another natural indicator. It remains yellow in acidic solutions but turns reddish-brown in basic solutions (often seen when soap, which is basic, touches a turmeric stain).
• Synthetic Indicators:
• These are laboratory-synthesized chemical indicators used to test acidity or alkalinity.
• Phenolphthalein is a popular synthetic indicator that remains colorless in acidic solutions and turns pink in basic solutions.
• Methyl Orange turns red in acidic media and yellow in basic media.
• Significance of Olfactory Indicators:
• Olfactory indicators are particularly useful for visually impaired students in chemistry laboratories, as they can identify the nature of a substance (acid or base) through the sense of smell rather than sight.
• pH Scale:
• The pH scale was introduced by S.P.L. Sorensen in 1909 to measure the concentration of hydrogen ions in a solution.
• The scale ranges from 0 to 14, where 7 is neutral, values below 7 are acidic, and values above 7 are basic or alkaline.

The correct answer is Concave lens cannot form a real image.

Key Points

• A concave lens is also known as a diverging lens because it diverges the parallel rays of light incident on it after refraction.
• For any position of a real object, a concave lens always forms a virtual, erect, and diminished image.
• A virtual image is formed when light rays appear to meet at a point but do not actually intersect; therefore, such images cannot be obtained on a screen. Hence, the student's claim of forming an image on a screen is a fundamental mistake.
• While a concave lens does indeed form diminished images, the impossibility of it being real (and thus projectable on a screen) is the primary error in the student's observation. Hence, statement 4 is the correct identification of the mistake.
• The image in a concave lens is always formed between the Optical Centre (O) and the Principal Focus (F1) on the same side as the object.

Additional Information

• Lens Formula and Sign Convention:
• The relationship between object distance (u), image distance (v), and focal length (f) is given by 1/v - 1/u = 1/f.
• For a concave lens, the focal length (f) is always taken as negative according to the Cartesian sign convention.
• Magnification (m):
• It is the ratio of the height of the image to the height of the object (h'/h) or v/u.
• For a concave lens, the magnification is always positive (indicating an erect image) and less than 1 (indicating a diminished image).
• Applications of Concave Lenses:
• They are primarily used in spectacles to correct Myopia (near-sightedness), as they help shift the image back onto the retina.
• They are also used in peepholes of house doors, flashlights, and telescopes to provide a wider field of view or to manipulate light beams.
• Comparison with Convex Lenses:
• A convex lens is a converging lens that can form both real and virtual images depending on the object's position.
• A real, diminished image can be formed by a convex lens when the object is placed beyond 2F1.

Important Points

• The Power of a lens is the reciprocal of its focal length in meters (P = 1/f). The SI unit of power is Dioptre (D).
• Since the focal length of a concave lens is negative, its power is also always negative.
• Light passing through the optical centre of any lens emerges without any deviation.
• The refractive index of the material and the curvature of the lens surfaces determine the focal length of the lens.

The correct answer is Both Soil and Air.

Key Points

• Plant pathogens are biological agents such as fungi, bacteria, viruses, and nematodes that cause diseases in plants, leading to significant agricultural loss worldwide.
• Soil transmission occurs when pathogens reside in the soil and infect plant roots or the base of the stem. Soil-borne pathogens can survive for long periods in the absence of a host by forming dormant structures. Hence, statement 1 is correct.
• Air transmission involves the movement of pathogen propagules, primarily spores, through wind currents. These spores can travel short distances within a field or thousands of miles across continents. Hence, statement 3 is correct.
• The transmission of diseases is a complex process where pathogens utilize multiple media, including water (rain splash/irrigation), insect vectors, and contaminated seeds, but soil and air remain the primary environmental pathways for dispersal.
• Because pathogens can utilize both the subterranean environment (soil) and the atmosphere (air) to find new hosts, the disease spread is categorized as both soil-borne and air-borne. Hence, the correct answer is Both Soil and Air.

Additional Information

• Soil-borne Diseases:
• These diseases are often caused by fungi like Fusarium, Rhizoctonia, and Pythium.
• They typically cause root rot, damping-off, and vascular wilts.
• Pathogens in the soil can remain viable for 5 to 10 years or more in the form of chlamydospores or sclerotia.
• Prevention: Techniques like crop rotation and soil solarization are used to manage these pathogens.
• Air-borne Diseases:
• Fungal rusts, smuts, and mildews are classic examples of air-borne plant diseases.
• Puccinia graminis (Wheat Rust) is a famous air-borne pathogen that produces millions of urediniospores that are carried by the wind.
• Environmental factors like relative humidity and wind velocity play a crucial role in the successful dispersal and germination of air-borne spores.
• Late Blight of Potato, caused by Phytophthora infestans, spread rapidly across Ireland in the 1840s due to air-borne and water-borne transmission.
• Other Transmission Modes:
• Vector-borne: Many plant viruses (e.g., Tobacco Mosaic Virus) are transmitted by insects like aphids, whiteflies, and leafhoppers.
• Seed-borne: Pathogens can be carried on the surface of or inside seeds, ensuring the disease is present when the plant begins to grow.

Important Points

• Disease Triangle: For a plant disease to occur, three factors must coincide: a susceptible host, a virulent pathogen, and a favorable environment.
• Impact on Economy: It is estimated that plant diseases reduce global crop yields by approximately 10% to 16% annually, affecting food security.
• Modern Detection: Farmers now use spore traps and remote sensing to monitor air-borne pathogens and DNA-based soil testing to identify soil-borne threats before planting.

The correct answer is High resistance and high melting point.

Key Points

• The filament of an incandescent light bulb is made of Tungsten (chemical symbol W) because it possesses a high melting point and high resistance.
• High Melting Point: Tungsten has the highest melting point of all metallic elements, recorded at approximately 3422°C (6192°F). This characteristic is crucial because the filament must reach temperatures above 2000°C to emit visible light through incandescence without melting or deforming.
• High Resistivity: Tungsten provides significant electrical resistance. When an electric current passes through the thin tungsten wire, the Joule heating effect (expressed as Heat = I²Rt) converts electrical energy into intense thermal energy, causing the filament to glow.
• Low Vapor Pressure: At elevated temperatures, tungsten exhibits a very low vapor pressure, which minimizes the rate of sublimation. This prevents the filament from thinning too quickly and reduces the darkening of the glass bulb caused by metal deposits.
• Ductility and Strength: Tungsten is highly ductile, meaning it can be drawn into very fine wires. It also maintains great tensile strength even at high temperatures, which is necessary for the stability of the coiled filament structure.
• Hence, the correct answer is High resistance and high melting point.

Additional Information

• Composition of a Light Bulb:
• A standard incandescent bulb consists of a glass envelope, a tungsten filament, and contact wires.
• The bulb is typically filled with an inert gas such as Argon or Nitrogen (sometimes Krypton) to prevent the oxidation of the tungsten filament, which would otherwise burn up instantly in the presence of oxygen.
• Historical Context:
• Early light bulbs used carbon filaments, but they had a lower melting point and shorter lifespan. Tungsten filaments were introduced around 1904-1906, revolutionizing the lighting industry due to their superior durability and brightness.
• The transition to tungsten was significantly advanced by William Coolidge in 1910, who developed a method to make tungsten more ductile.
• Energy Efficiency:
• Incandescent bulbs are relatively inefficient compared to modern LED (Light Emitting Diode) or CFL (Compact Fluorescent Lamp) technology.
• Approximately 90% to 95% of the energy consumed by a tungsten bulb is released as heat, while only 5% to 10% is converted into visible light.

Important Points

• Tungsten Properties: It has an atomic number of 74 and is found in minerals like Wolframite and Scheelite. Its name "Tungsten" is derived from the Swedish words for heavy stone.
• Resistance and Temperature: The electrical resistance of tungsten increases as the temperature rises. When the bulb is first switched on, the "cold" resistance is low, leading to a brief inrush current before the filament heats up and the resistance stabilizes.
• Evaporation and Life Span: Over time, even with inert gas, tungsten atoms slowly evaporate from the filament. This leads to "hot spots" where the wire becomes thinner, has higher resistance, gets even hotter, and eventually breaks, which is why a bulb "burns out."
• Halogen Bulbs: In a Halogen lamp, a small amount of halogen gas (like Iodine or Bromine) is added. This triggers a chemical reaction that returns evaporated tungsten back to the filament, allowing it to operate at higher temperatures and last longer than standard bulbs.

Shortcut Trick

Expenditure % = 100% − Savings % = 100% − 88% = 12%

Monthly Expenditure = 12% of ₹9475

⇒ 12/100 × 9475 = 3/25 × 9475

⇒ 3 × 379 = ₹1137

∴ The correct answer is ₹1137.

Alternate Method

Given:Monthly Salary = ₹9475, Savings Percentage = 88%

Formula Used:Expenditure = Salary − Savings

⇒ Savings amount = 88% of 9475 = (88 × 9475) ÷ 100

⇒ Savings amount = 0.88 × 9475 = ₹8338

⇒ Expenditure = 9475 − 8338

⇒ Expenditure = ₹1137

∴ The correct answer is ₹1137.

Additional Information

Percentage Change

Percentage change is calculated as (New Value − Old Value) / Old Value × 100. In income problems, if income increases by r%, new income = Original × (1 + r/100).

Income-Expenditure Relation

Total Income is always the sum of Total Expenditure and Total Savings. If any two are known, the third can be calculated directly.

Base Value in Percentage

In salary-based questions, the Total Salary is always considered as the base (100%) for calculating percentage savings or expenses.

Shortcut Trick

Using the trigonometric identity: If A + B = 90°, then tan A × tan B = 1.

Here, (10° + 80° = 90°) ⇒ tan 10° × tan 80° = 1.

And, (18° + 72° = 90°) ⇒ tan 18° × tan 72° = 1.

Therefore, the product is 1 × 1 = 1.

∴ The correct answer is 1.

Alternate Method

Given: tan 10° tan 18° tan 72° tan 80°

Formula Used: tan(90° − θ) = cot θ and tan θ × cot θ = 1

⇒ tan 80° = tan(90° − 10°) = cot 10°

⇒ tan 72° = tan(90° − 18°) = cot 18°

Substitute these values back into the expression:

⇒ tan 10° × tan 18° × cot 18° × cot 10°

⇒ (tan 10° × cot 10°) × (tan 18° × cot 18°)

⇒ 1 × 1 = 1

∴ The correct answer is 1.

Additional Information

Complementary Angle Identities

For any angle θ, sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, and tan(90° − θ) = cot θ.

Reciprocal Identities

The product of trigonometric terms that are reciprocals of each other is 1, such as tan θ × cot θ = 1 and sin θ × cosec θ = 1.

Shortcut Trick

Effective Rate of Interest for 2 years at 20% = 20 + 20 + (20 × 20)/100 = 44%.

Amount = 100% + 44% = 144% of Principal.

Amount = 1.44 × 9400 = 13536.

∴ The correct answer is ₹13,536.

Alternate Method

Given:

Principal (P) = ₹9,400

Rate (R) = 20% p.a.

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 9400(1 + 20/100)²

⇒ A = 9400(1 + 1/5)²

⇒ A = 9400(6/5)²

⇒ A = 9400 × (36/25)

⇒ A = 376 × 36

⇒ A = 13536

∴ The correct answer is ₹13,536.

Additional Information

Effective Rate for Compound Interest

For 2 years, the effective rate is x + y + (xy/100)%, where x and y are the rates for the first and second years.

Compound Interest vs Simple Interest

The difference for 2 years is given by the formula D = P(R/100)².

Compounding Half-Yearly

If interest is compounded half-yearly, the rate is halved (R/2) and the time is doubled (2n).

Shortcut Trick

Identify the smallest two-digit prime numbers: 11 and 13.

Check if they are twin primes: 13 − 11 = 2 (Yes).

Calculate the sum: 11 + 13 = 24.

∴ The correct answer is 24.

Alternate Method

Given: We need to find the sum of the first pair of two-digit twin prime numbers.

Definition: Twin primes are pairs of prime numbers that have a difference of 2.

⇒ Prime numbers starting from 10 are: 11, 13, 17, 19, 23, 29, ...

⇒ The first two-digit prime number is 11.

⇒ The next prime number is 13.

⇒ Difference = 13 − 11 = 2.

⇒ Since the difference is 2, (11, 13) is the first pair of two-digit twin primes.

⇒ Sum = 11 + 13 = 24.

∴ The correct answer is 24.

Additional Information

Twin Prime Pairs

Common twin prime pairs include (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), and (41, 43).

Prime Number Properties

Except for (3, 5), all twin prime pairs are of the form (6n − 1, 6n + 1) for some integer n.

Smallest Two-Digit Prime

The smallest two-digit prime number is 11, and the largest is 97.

Shortcut Trick

Difference in costs after doubling the second set:

Cost of 1 cookie = (2 × 23) − 36 = 46 − 36 = ₹ 10.

Cost of 1 chocolate = 23 − (2 × 10) = ₹ 3.

Required cost of 4 chocolates and 5 cookies = (4 × 3) + (5 × 10) = 12 + 50 = ₹ 62.

∴ The correct answer is ₹ 62.

Alternate Method

Given:

Case 1: 2 Chocolates + 3 Cookies = ₹ 36

Case 2: 1 Chocolate + 2 Cookies = ₹ 23

Let the cost of one chocolate be ₹ x and one cookie be ₹ y.

⇒ 2x + 3y = 36 ....(i)

⇒ x + 2y = 23 ....(ii)

Multiplying equation (ii) by 2:

⇒ 2x + 4y = 46 ....(iii)

Subtracting equation (i) from equation (iii):

⇒ (2x + 4y) − (2x + 3y) = 46 − 36

⇒ y = 10

Substitute y = 10 in equation (ii):

⇒ x + 2(10) = 23

⇒ x + 20 = 23

⇒ x = 3

Cost of 4 chocolates and 5 cookies:

⇒ 4x + 5y = 4(3) + 5(10)

⇒ 12 + 50 = 62

∴ The correct answer is ₹ 62.

Additional Information

Linear Equations in Two Variables

Equations of the form ax + by = c represent a straight line. Solving two such equations finds the intersection point (x, y).

Elimination Method

A technique to solve a system of equations by making the coefficients of one variable equal and then adding or subtracting the equations.

Substitution Method

Solve one equation for one variable and substitute that expression into the second equation to find the value of the other variable.

Shortcut Trick

Apply BODMAS directly by adding like terms first, then dividing:

⇒ (3x² + 4x²) ÷ 7x

⇒ 7x² ÷ 7x

⇒ x

∴ The correct answer is x.

Alternate Method

Given:

Expression: (3x² + 4x²) ÷ 7x

Formula Used:

Addition of like terms: axⁿ + bxⁿ = (a + b)xⁿ

Law of exponents for division: a^m ÷ aⁿ = a^m−n

Calculations:

⇒ According to the BODMAS rule, solve the bracket first.

⇒ 3x² + 4x² = 7x²

⇒ Now, divide the result by 7x.

⇒ 7x² ÷ 7x = (7 ÷ 7) × (x² ÷ x¹)

⇒ 1 × x²⁻¹

⇒ x

∴ The correct answer is x.

Additional Information

BODMAS Rule

It stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Always solve expressions inside parentheses first.

Law of Exponents (Multiplication)

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

Law of Exponents (Division)

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

Shortcut Trick

Net discount multiplier = (100 − 20)% × (100 − 11)% = 0.80 × 0.89 = 0.712.

Marked Price (MP) = Selling Price ÷ 0.712.

MP = 8,900 ÷ 0.712 = 12,500.

∴ The correct answer is ₹12,500.

Alternate Method

Given → Selling Price (SP) = ₹8,900 | Discount₁ = 20% | Discount₂ = 11%. Formulas: SP = MP × (100 − D₁)% × (100 − D₂)% | Successive = a + b − ab ÷ 100.

⇒ Let the Marked Price be x. ⇒ First discount of 20%: Price becomes x × (80/100). ⇒ Second discount of 11%: Price becomes x × (80/100) × (89/100). ⇒ Set equation: x × 0.8 × 0.89 = 8,900. ⇒ x × 0.712 = 8,900. ⇒ x = 8,900 ÷ 0.712 = 12,500.

∴ The correct answer is ₹12,500.

Additional Information

Marked Price & Discount

The Marked Price (MP) is the price listed on the label. Discount is always calculated on the MP unless stated otherwise. SP = MP − Discount.

Successive Discount Formula

To find a single equivalent discount for two discounts a% and b%, use: Equivalent Discount = (a + b − ab/100)%.

Shortcut Trick

Ratio of Father : Daughter

Present → 4 : 1 (Difference = 3)

5 years ago → 7 : 1 (Difference = 6)

Make differences equal: Present ratio × 2 → 8 : 2

Change in units: 8 − 7 = 1 unit or 2 − 1 = 1 unit

1 unit = 5 years ∴ Daughter's present age = 2 units = 2 × 5 = 10 years

∴ The correct answer is 10 years.

Alternate Method

Given:

Present age ratio Father : Daughter = 4 : 1

Age ratio 5 years ago = 7 : 1

Let daughter's present age be x years.

⇒ Father's present age = 4x years.

⇒ 5 years ago, daughter's age = x − 5

⇒ 5 years ago, father's age = 4x − 5

⇒ According to question: (4x − 5) = 7 × (x − 5)

⇒ 4x − 5 = 7x − 35

⇒ 3x = 30

⇒ x = 10

∴ The correct answer is 10 years.

Additional Information

Age Difference Property

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

Ratio Balancing

To solve age problems using ratios, multiply the ratios by the difference of the other ratio to balance the units representing time intervals.

Shortcut Trick

When two objects meet and then travel towards their destinations, the ratio of their speeds is the inverse square root of the ratio of time taken to reach the destinations.

Speed Ratio S_A : S_B = √T_B : √T_A

Given: S_B = 1.5 × S_A ⇒ S_A/S_B = 1/1.5 = 2/3

2/3 = √(p / 95.4) ⇒ 4/9 = p / 95.4

p = (95.4 × 4) ÷ 9 = 10.6 × 4 = 42.4 hours

∴ The correct answer is 42.4 hours.

Alternate Method

Given:

Time taken by A after meeting (T_A) = 95.4 hours

Time taken by B after meeting (T_B) = p hours

Speed of B (S_B) = Speed of A (S_A) + 50% of S_A = 1.5 S_A

Formula Used:

S_A / S_B = √(T_B / T_A)

Calculations:

⇒ S_A / 1.5S_A = √(p / 95.4)

⇒ 1 / 1.5 = √(p / 95.4)

⇒ 10 / 15 = √(p / 95.4)

⇒ 2 / 3 = √(p / 95.4)

Squaring both sides:

⇒ 4 / 9 = p / 95.4

⇒ p = (4 × 95.4) / 9

⇒ p = 4 × 10.6

⇒ p = 42.4

∴ The correct answer is 42.4 hours.

Additional Information

Post-Meeting Time Theorem

If two bodies start at the same time and meet at a point, then take T₁ and T₂ time to reach their destinations, their speed ratio is S₁/S₂ = √(T₂/T₁).

Meeting Time Formula

The time they took to meet each other from the start is given by T_meet = √(T₁ × T₂).

Relative Speed

When two objects move towards each other, their relative speed is the sum of their individual speeds: S_rel = S_A + S_B.

Shortcut Trick

Mean proportion M = √(a × b)

Given M = 66, a = x, and b = 99

66² = x × 99

x = (66 × 66) ÷ 99 = (2 × 33 × 2 × 33) ÷ (3 × 33) = (2 × 2 × 33) ÷ 3 = 4 × 11 = 44

∴ The correct answer is 44.

Alternate Method

Given:

Mean Proportion = 66

First and Third terms are x and 99 respectively.

Formula Used:

In a continued proportion a, b, c, the mean proportion b² = ac.

Calculations:

⇒ x : 66 = 66 : 99

⇒ x ÷ 66 = 66 ÷ 99

⇒ x = (66 × 66) ÷ 99

⇒ x = 4356 ÷ 99

⇒ x = 44

∴ The correct answer is 44.

Additional Information

Third Proportional

If a, b, c are in continued proportion, then c is called the third proportional to a and b, where c = b² ÷ a.

Fourth Proportional

If a : b :: c : d, then d is the fourth proportional to a, b, and c, calculated as d = (b × c) ÷ a.

Duplicate Ratio

The duplicate ratio of a : b is a² : b², and the sub-duplicate ratio is √a : √b.

Shortcut Trick

Total votes = 100%

Votes for N = 100% − (42% + 34%) = 24%

Votes for N = 24% of 37,700 = 24 × 377

Votes for N = 9048

∴ The correct answer is 9048 votes.

Alternate Method

Given: Total votes = 37,700 | Votes for M = 42% | Votes for R = 34%

⇒ Total percentage = Percentage(M) + Percentage(N) + Percentage(R)

⇒ 100% = 42% + Percentage(N) + 34%

⇒ Percentage(N) = 100% − 76% = 24%

⇒ Number of votes for N = (24 ÷ 100) × 37,700

⇒ Number of votes for N = 24 × 377 = 9048

∴ The correct answer is 9048 votes.

Additional Information

Total vs Valid Votes

In election problems, Total Votes = Valid Votes + Invalid Votes. If all votes are valid, then total polled equals valid.

Winner Margin

The margin of victory is the difference between the votes of the first and second-place candidates.

Percentage Calculation

To find the absolute value from a percentage: Value = (Percentage ÷ 100) × Total.

Shortcut Trick

Efficiency Ratio (Rishi : Shan) = 100 : 120 = 5 : 6.

Time Ratio is the inverse of Efficiency Ratio = 6 : 5.

If 6 units = 12 days (Rishi), then 1 unit = 2 days.

Days for Shan = 5 units = 5 × 2 = 10 days.

∴ The correct answer is 10 days.

Alternate Method

Given: Rishi takes 12 days. Shan is 20% more efficient.

Formula Used: Total Work = Efficiency × Time; Days = Total Work ÷ Efficiency

⇒ Let Efficiency of Rishi = 5 units/day.

⇒ Efficiency of Shan = 5 + (20% of 5) = 5 + 1 = 6 units/day.

⇒ Total Work = Efficiency of Rishi × Days = 5 × 12 = 60 units.

⇒ Days taken by Shan = Total Work ÷ Efficiency of Shan = 60 ÷ 6 = 10 days.

∴ The correct answer is 10 days.

Additional Information

Inverse Proportionality

For a constant work, Time is inversely proportional to Efficiency (T ∝ 1/E). If efficiency increases, time taken decreases.

Combined Work

If two people work together, their combined efficiency is the sum of their individual efficiencies (E_total = E₁ + E₂).

Percentage to Fraction

20% more efficiency means a ratio of 120/100 or 6/5. This fractional approach simplifies ratio calculations significantly.

Shortcut Trick

Area of wet surface = Area of base + Lateral surface area

Area of wet surface = (length × width) + 2 × depth × (length + width)

Area of wet surface = (5 × 3) + 2 × 1.5 × (5 + 3)

Area of wet surface = 15 + 3 × 8 = 15 + 24 = 39 m²

∴ The correct answer is 39 m².

Alternate Method

Given:

Length (l) = 5 m

Width (w) = 3 m

Depth (h) = 1.50 m

Formula: Wet surface area = Area of bottom + Area of 4 vertical sides

⇒ Area of bottom = l × w = 5 × 3 = 15 m²

⇒ Area of 2 long sides = 2 × (l × h) = 2 × (5 × 1.5) = 2 × 7.5 = 15 m²

⇒ Area of 2 wide sides = 2 × (w × h) = 2 × (3 × 1.5) = 2 × 4.5 = 9 m²

⇒ Total wet area = 15 + 15 + 9 = 39 m²

∴ The correct answer is 39 m².

Additional Information

Total Surface Area of Cuboid

The total area of all six faces is given by 2(lb + bh + hl).

Lateral Surface Area (Area of 4 walls)

The area of the four vertical faces is 2h(l + b).

Volume of Rectangular Tank

The volume of water or capacity is calculated as Length × Width × Height.

Shortcut Trick

The Cost Price (CP) represents 100%.

Since there is a loss of 6%, the Selling Price (SP) represents 100% − 6% = 94%.

SP = 1,400 × (94 ÷ 100)

SP = 14 × 94 = 1,316.

∴ The correct answer is ₹1,316.

Alternate Method

Given: Cost Price (CP) = ₹1,400 and Loss Percentage = 6%.

Formula: Loss = (Loss% × CP) ÷ 100 | SP = CP − Loss

⇒ Loss Amount = (6 × 1,400) ÷ 100

⇒ Loss Amount = 6 × 14 = ₹84

⇒ Selling Price (SP) = Cost Price − Loss

⇒ SP = 1,400 − 84 = ₹1,316

∴ The correct answer is ₹1,316.

Additional Information

Loss and Profit

Profit occurs when SP > CP. Loss occurs when CP > SP. Both are always calculated on the Cost Price unless stated otherwise.

Percentage Change

To find the new value after a percentage decrease: New Value = Original Value × (100 − decrease%) ÷ 100.

Shortcut Trick

Combine ratios A:B (2:3), B:C (4:5), and C:D (6:7) by making common terms equal.

Ratio A:B:C:D = (2×4×6) : (3×4×6) : (3×5×6) : (3×5×7) = 48 : 72 : 90 : 105.

Simplified Ratio A:B:C:D = 16 : 24 : 30 : 35 (Dividing by 3).

Total units = 16 + 24 + 30 + 35 = 105 units → ₹9,975. So, 1 unit = ₹95.

Share of A = 16 units = 16 × 95 = ₹1,520.

∴ The correct answer is ₹1,520.

Alternate Method

Given: Total Amount = ₹9,975. Ratios A:B = 2:3, B:C = 4:5, C:D = 6:7.

Formula: Joint Ratio calculation and Unitary method.

⇒ To find A:B:C:D, multiply terms vertically and diagonally:

⇒ A = 2 × 4 × 6 = 48

⇒ B = 3 × 4 × 6 = 72

⇒ C = 3 × 5 × 6 = 90

⇒ D = 3 × 5 × 7 = 105

⇒ Ratio A:B:C:D = 48 : 72 : 90 : 105 = 16 : 24 : 30 : 35

⇒ Total components = 16 + 24 + 30 + 35 = 105

⇒ Value of 1 part = 9975 ÷ 105 = ₹95

⇒ Share of A = 16 × 95 = ₹1,520

∴ The correct answer is ₹1,520.

Additional Information

Combined Ratio Rule

If A:B = a:b, B:C = c:d, and C:D = e:f, then A:B:C:D = (a×c×e) : (b×c×e) : (b×d×e) : (b×d×f).

Compound Ratio

The compound ratio of (a:b), (c:d) and (e:f) is simply (a×c×e) : (b×d×f).

Proportional Division

To divide an amount S in the ratio a:b:c, the shares are [a/(a+b+c)]×S, [b/(a+b+c)]×S, and [c/(a+b+c)]×S.

Shortcut Trick

In any data set, the Mode is the observation with the maximum frequency (the value that repeats the most).

By observation: 86 appears 4 times, while 65, 85, 71, and 90 appear only 2 times each, and others appear once.

Since 86 has the highest repetition, it is the mode.

∴ The correct answer is 86.

Alternate Method

Given: Data set = 65, 86, 86, 85, 69, 90, 71, 60, 86, 71, 86, 65, 81, 82, 67, 72, 84, 66, 75, 85, 68, 78, 61, 64, 74, 90.

Formula Used: Mode = Value with the Highest Frequency.

Calculating the frequency of each observation from the given data:

⇒ Frequency of 60 = 1

⇒ Frequency of 65 = 2

⇒ Frequency of 71 = 2

⇒ Frequency of 85 = 2

⇒ Frequency of 90 = 2

⇒ Frequency of 86 = 4 (appears at positions 2, 3, 9, and 11)

⇒ All other values (61, 64, 66, 67, 68, 69, 72, 74, 75, 78, 81, 82, 84) appear only 1 time.

⇒ Maximum frequency = 4, which corresponds to the value 86.

∴ The correct answer is 86.

Additional Information

Mean (Average)

It is the sum of all observations divided by the total number of observations: Mean = (Σx_i) ÷ n.

Median

It is the middle-most value of the data when arranged in ascending or descending order.

Empirical Relationship

For moderately skewed distributions: Mode = 3 × Median − 2 × Mean.

Types of Mode

Data can be Unimodal (one mode), Bimodal (two modes), or Multimodal (more than two modes).

Shortcut Trick

Interior angle of regular polygon with n sides = [(n − 2) × 180°] ÷ n

For n = 8, A = (6 × 180°) ÷ 8 = 135° ⇒ A/3 = 45°

For n = 10, B = (8 × 180°) ÷ 10 = 144° ⇒ 5B/6 = 120°

Value = sin²(45°) + cos³(120°) = (1/√2)² + (−1/2)³ = 1/2 − 1/8 = 3/8

∴ The correct answer is 3/8.

Alternate Method

Given: Sides of first polygon n₁ = 8, Sides of second polygon n₂ = 10.

Formula Used: Interior angle = 180° − (360°/n); sin 45° = 1/√2; cos 120° = −1/2.

A (n=8)A = 135°B (n=10)B = 144°Expression: sin²(A/3) + cos³(5B/6)

⇒ Angle A = 180° − (360° ÷ 8) = 180° − 45° = 135°

⇒ Angle B = 180° − (360° ÷ 10) = 180° − 36° = 144°

⇒ A/3 = 135° ÷ 3 = 45°

⇒ 5B/6 = (5 × 144°) ÷ 6 = 5 × 24° = 120°

⇒ sin²(45°) + cos³(120°) = (1/√2)² + (cos(180°−60°))³

⇒ 1/2 + (−cos 60°)³ = 1/2 + (−1/2)³

⇒ 1/2 − 1/8 = 4/8 − 1/8 = 3/8

∴ The correct answer is 3/8.

Additional Information

Interior and Exterior Angles

For any regular polygon, Interior Angle + Exterior Angle = 180°. Sum of all exterior angles is always 360°.

Trigonometric Ratios of Obtuse Angles

cos(180° − θ) = −cos θ. Since 120° is in the second quadrant, cosine is negative.

Sum of Interior Angles

The sum of all interior angles of a polygon with n sides is given by (n − 2) × 180°.

Shortcut Trick

Total distance = Length of Train + Length of Platform = 200 + 600 = 800 m

Speed in m/sec = 50 × (5/18) = 125/9 m/sec

Time = Distance ÷ Speed = 800 ÷ (125/9) = (800 × 9) ÷ 125

Time = 6.4 × 9 = 57.6 sec

∴ The correct answer is 57.6 sec.

Alternate Method

Given:

Length of Train (L₁) = 200 m

Length of Platform (L₂) = 600 m

Speed (S) = 50 km/hr

Formula Used:

Time = Total Distance ÷ Speed

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

Calculations:

⇒ Total Distance = 200 + 600 = 800 m

⇒ Speed in m/s = 50 × (5/18) = 250/18 = 125/9 m/s

⇒ Time = 800 ÷ (125/9)

⇒ Time = (800 × 9) ÷ 125

⇒ Time = 7200 ÷ 125 = 57.6 sec

∴ The correct answer is 57.6 sec.

Additional Information

Unit Conversion

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

Relative Speed (Same Direction)

When two objects move in the same direction, the relative speed is the difference of their speeds (S₁ − S₂).

Relative Speed (Opposite Direction)

When two objects move in opposite directions, the relative speed is the sum of their speeds (S₁ + S₂).

Shortcut Trick

Total discount on First Article = a + b − (ab ÷ 100) = 30 + 18 − (30 × 18 ÷ 100) = 48% − 5.4% = 42.6%.

Total discount on Second Article = 48%.

The shopkeeper gets more benefit where the discount is lower (First Article).

Difference in discount % = 48% − 42.6% = 5.4%.

More benefit amount = 5.4% of 2,40,000 = 0.054 × 2,40,000 = 12,960.

∴ The correct answer is First article; ₹12,960.

Alternate Method

Given → Marked Price (MP) = ₹2,40,000. Case 1: Successive discounts 30% and 18%. Case 2: Single discount 48%. Formulas: SP = MP × (100 − D₁)% × (100 − D₂)% | Profit is higher when SP is higher.

⇒ SP of First Article = 2,40,000 × (70 ÷ 100) × (82 ÷ 100) = 2,400 × 0.7 × 82 = ₹1,37,760. ⇒ SP of Second Article = 2,40,000 × (52 ÷ 100) = 2,400 × 52 = ₹1,24,800. ⇒ Shopkeeper benefit is higher when selling price is higher ∴ First Article. ⇒ Difference in benefit = 1,37,760 − 1,24,800 = ₹12,960.

∴ The correct answer is First article; ₹12,960.

Additional Information

Successive Discounts

Two successive discounts of x% and y% are equivalent to a single discount of (x + y − xy/100)%.

Shopkeeper Perspective

For a seller, a smaller total discount results in a higher Selling Price, thus yielding more benefit.

Shortcut Trick

The relationship between Mode, Median, and Mean is expressed as: Mode − Median = 2/3 × (Mode − Mean).

Given: Mode − Mean = 34.8

Applying the trick: Mode − Median = 2/3 × 34.8

Calculation: 2 × 11.6 = 23.2

∴ The correct answer is 23.2.

Alternate Method

Given: Difference between Mode and Mean = 34.8

Formula used: Empirical Relationship → Mode = 3 × Median − 2 × Mean

⇒ Let Mean = x

⇒ Mode = x + 34.8

⇒ Substituting in formula: x + 34.8 = 3 × Median − 2x

⇒ 3x + 34.8 = 3 × Median

⇒ Median = (3x + 34.8) ÷ 3

⇒ Median = x + 11.6

⇒ Difference (Mode − Median) = (x + 34.8) − (x + 11.6)

⇒ Mode − Median = 23.2

∴ The correct answer is 23.2.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship is: Mode = 3 × Median − 2 × Mean.

Symmetric Distribution

In a perfectly symmetrical distribution, the values of Mean, Median, and Mode are identical (Mean = Median = Mode).

Mean - Mode Relation

Another variation of the formula is: Mean − Mode = 3 × (Mean − Median).

Shortcut Trick

Total Work (LCM of 33, 22, 55) = 330 units.

Efficiency of A = 10, B = 15, Combined (A + B − C) = 6.

Efficiency of C = (10 + 15) − 6 = 19.

Time taken by C = 330 ÷ 19 = 17(7/19) minutes.

∴ The correct answer is 17(7/19) minutes.

Alternate Method

Given: Time for Pipe A = 33 min, Pipe B = 22 min, Combined (A+B-C) = 55 min.

⇒ Efficiency of Pipe A + Efficiency of Pipe B − Efficiency of Pipe C = Combined Efficiency

⇒ 10 + 15 − Efficiency of Pipe C = 6

⇒ 25 − Efficiency of Pipe C = 6

⇒ Efficiency of Pipe C = 25 − 6 = 19

⇒ Time taken by Pipe C to empty the tank = Total Work ÷ Efficiency of C

⇒ Time = 330 ÷ 19

⇒ Time = 17(7/19) minutes

∴ The correct answer is 17(7/19) minutes.

Additional Information

Negative Work Concept

In Pipes and Cisterns, an outlet pipe (emptying pipe) performs negative work, so its efficiency is subtracted from the total efficiency of inlet pipes.

Efficiency and Time Relationship

Efficiency is inversely proportional to Time when the total work is constant. Efficiency = Total Work ÷ Time.

Formula Method

For three pipes where C is an outlet: (1/T_A) + (1/T_B) − (1/T_C) = (1/T_Total). Solve for T_C directly.

Shortcut Trick

We can separate the square roots directly using the property √(a × b) = √a × √b:

⇒ (11 × 7) + (8 × 6) − (10 × 4)

⇒ 77 + 48 − 40

⇒ 125 − 40 = 85

∴ The correct answer is 85.

Alternate Method

Given:

Expression: √(121 × 49) + √(64 × 36) − √(100 × 16)

Formula Used:

√(x × y) = √x × √y

Calculation:

⇒ √(121 × 49) = √121 × √49 = 11 × 7 = 77

⇒ √(64 × 36) = √64 × √36 = 8 × 6 = 48

⇒ √(100 × 16) = √100 × √16 = 10 × 4 = 40

Substituting the calculated values back into the main expression:

⇒ 77 + 48 − 40

⇒ 125 − 40

⇒ 85

∴ The correct answer is 85.

Additional Information

BODMAS Rule

Always follow the strict sequence of Brackets, Order (Powers/Roots), Division/Multiplication, and Addition/Subtraction from left to right to ensure an accurate result.

Properties of Radicals

The product of two square roots is equivalent to the square root of their product: √a × √b = √(a × b). This property is universally valid for all non-negative real numbers.

Common Perfect Squares

Memorizing squares up to 30 heavily aids in faster calculation during simplification questions (e.g., 11² = 121, 15² = 225, 25² = 625).

Shortcut Trick

Find LCM of 28, 24, 56, and 29.

LCM (28, 24, 56, 29) = LCM(56, 24, 29) = 168 × 29 = 4872.

Multiples of 4872 near 9054: 4872 × 2 = 9744.

Required number = (Next Multiple + Remainder) − Given Number = (9744 + 6) − 9054 = 9750 − 9054 = 696.

∴ The correct answer is 696.

Alternate Method

Given: Numbers 28, 24, 56, 29; Remainder = 6; Target number > 9054.

Formula Used: Required number = [n × LCM(divisors) + Remainder] − 9054

⇒ Step 1: Prime factorization of divisors:

⇒ 28 = 2² × 7

⇒ 24 = 2³ × 3

⇒ 56 = 2³ × 7

⇒ 29 = 29 (Prime number)

⇒ LCM = 2³ × 3 × 7 × 29 = 8 × 3 × 7 × 29 = 168 × 29 = 4872

⇒ To find a number just greater than 9054, we take the 2^nd multiple:

⇒ 4872 × 2 = 9744

⇒ To leave a remainder of 6: 9744 + 6 = 9750

⇒ Smallest number to be added = 9750 − 9054 = 696

∴ The correct answer is 696.

Additional Information

LCM and Remainder Concept

The general form of a number that leaves a remainder 'r' when divided by x, y, and z is [k × LCM(x, y, z) + r].

Divisibility Rules

For large numbers, check divisibility of the final sum (9054 + x − 6) by simpler factors like 3 or 8 from the LCM set.

Prime Numbers

If one of the divisors is a prime number (like 29), it must be a direct factor of the LCM.

Shortcut Trick

Ratio of Expenditure to Savings = 200 : 100 = 2 : 1

Using Alligation/Weighted Average method:

Net Income change = (Expenditure % × E-ratio + Savings % × S-ratio) ÷ (E-ratio + S-ratio)

Income increase = (−4% × 2 + 35% × 1) ÷ (2 + 1) = (−8 + 35) ÷ 3 = 27 ÷ 3 = 9%

∴ The correct answer is 9%.

Alternate Method

Given:Expenditure is 100% more than Savings.

Formula Used:Income = Expenditure + Savings

⇒ Let Savings = 100

⇒ Expenditure = 100 + 100% of 100 = 200

⇒ Initial Income = 200 + 100 = 300

⇒ New Expenditure = 200 − 4% of 200 = 200 − 8 = 192

⇒ New Savings = 100 + 35% of 100 = 135

⇒ New Income = 192 + 135 = 327

⇒ Increase in Income = 327 − 300 = 27

⇒ % Increase = (27 ÷ 300) × 100 = 9%

∴ The correct answer is 9%.

Additional Information

Income, Expenditure and Savings Relationship

The fundamental identity is Income = Expenditure + Savings. Any percentage change in two components directly determines the change in the third.

Weighted Average Concept

If components A and B change by x% and y%, the total change is (A×x + B×y) ÷ (A+B). This is the fastest way to solve income-expenditure problems.

Percentage Base Change

When a value is x% more than another, the ratio is (100+x) : 100. Always identify the base correctly before calculating increments or decrements.

Shortcut Trick

Let Length = L and Breadth = B.

From conditions: (L − 7)(B + 5) = LB − 21 ⇒ 5L − 7B = 14

From second condition: (L + 4)(B + 5) = LB + 67 ⇒ 5L + 4B = 47

Subtracting both: 11B = 33 ⇒ B = 3 m. Putting B in first: 5L − 21 = 14 ⇒ 5L = 35 ⇒ L = 7 m.

Original Area = L × B = 7 × 3 = 21 m².

∴ The correct answer is 21 m².

Alternate Method

Given: Reduction in area = 21 m², Increase in area = 67 m².

Formula: Area of Rectangle = Length (L) × Breadth (B).

⇒ Case 1: (L − 7)(B + 5) = LB − 21

⇒ LB + 5L − 7B − 35 = LB − 21

⇒ 5L − 7B = 14 ----(i)

⇒ Case 2: (L + 4)(B + 5) = LB + 67

⇒ LB + 5L + 4B + 20 = LB + 67

⇒ 5L + 4B = 47 ----(ii)

⇒ Subtracting (i) from (ii): (5L + 4B) − (5L − 7B) = 47 − 14

⇒ 11B = 33 ⇒ B = 3 m

⇒ Substituting B in (i): 5L − 7(3) = 14 ⇒ 5L − 21 = 14 ⇒ 5L = 35 ⇒ L = 7 m

⇒ Area = 7 × 3 = 21 m²

∴ The correct answer is 21 m².

Additional Information

Perimeter of Rectangle

The total boundary length is given by P = 2 × (Length + Breadth).

Diagonal of Rectangle

The length of the diagonal is calculated using Pythagoras theorem: d = √(L² + B²).

Percentage Change in Area

If length changes by x% and breadth by y%, net area change % = x + y + (xy/100).

The logic followed here is:

So, 'DHG 40' will replace the question mark in the given series.

Hence, the correct answer is "Option 3".

Given Statements:

All rods are hooks.

Some hooks are baits.

The least possible Venn diagram for the given statements is:

Conclusions:

I. All rods are baits  → Does not follow (Rods are inside hooks, and only some hooks are baits; no definite inclusion or overlap of rods with baits is given.)

II. Some baits are rods → Does not follow  (There is no established intersection between rods and baits.)

So, neither conclusion I nor II follows.

Hence, the correct answer is "Option 2".

The logic followed here is based on the alphabetical position pattern:

Option 1: SK - XP

Option 2: DY - IC

Option 3: EZ - JE

Option 4: JQ - OV

Thus, DY - IC does not follow this uniform shift.

Hence, the odd one out is Option 2.

Given:

 “she is lovely” → “kl pc cp”

“lovely paint here” → “lk cp no”

So, the code for lovely = cp

Hence, the correct answer is Option 1.

The logic followed here is:

thus, "91" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

The logic followed here is:

For, KGLO → QMRU

For, NJOR → TPUX

Now, applying the same pattern to EAFI:

So, EAFI → KGLO

Hence, the correct answer is Option 1.

Given: (Left) / 8 & + ^ 1 + < # @ ^ \ 2 # $8 9 * 7 2$ (Right)

Now,

We need to find numbers that are immediately preceded by a symbol and immediately followed by a symbol.

So, Needed pattern is: Symbol - Number - Symbol.

(Left) / 8 & + ^ 1 + < # @ ^ \ 2 # $8 9 * 7 2$ (Right)

Total valid numbers satisfying the condition = 3.

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Given sequence: 324, 286, 472, 539, 731

Logic: Arrange the numbers in ascending order and compare their positions with the original sequence.

Arranging in ascending order: 286, 324, 472, 539, 731

Numbers that remain in the same position: 472, 539, 731

Hence, the correct answer is Option 2.

Family Chart:

Decoding the Symbols:

Given: M + N x O - P ÷ Q

It means: M is the father of N, N is the sister of O, O is the brother of P, and P is the wife of Q.

Thus, M is Q’s wife’s father.

Hence, the correct answer is "Option 3".

Given:

Andy’s rank from the top = 11th, rank from the bottom = 15th.

Total number of students = 11 + 15 – 1 = 25.

So, there are 25 students in the class.

Hence, the correct answer is "Option 1".

BODMAS Table: 

Decoding the given information:

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

⇒ 154 × 2 + 49 × 7 − 10 ÷ 5 − 28 ÷ 7 + 25 × 5 = ?

⇒ 308 + 343 − 2 − 4 + 125 = ?

⇒ (308 + 343 + 125) − (2 + 4) = ?

⇒ 776 − 6 = ?

⇒ 770

Hence, the correct option is "Option 3".

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

Now,

We need to find an odd number which is immediately preceded by an even number and immediately followed by an even number.

So, Needed pattern is: Even - Odd - Even.

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

No occurrence satisfies Even - Odd - Even.

Hence, the correct answer is 'Option 2'.

The logic followed here is based on the alphabetical position pattern:

Option 1: QK - VH

Option 2: WH - BD

Option 3: GQ - LN

Option 4: AE - FB

Thus, WH - BD does not follow this uniform pattern.

Hence, the odd one out is Option 2.

The logic followed here is:

thus, "114" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

Given:

Total people = 119, Mr. Ihg is 29th from the left,

and Mr. Lkj is 7th from the right.

Number of people between them = 119 − (29 + 7) = 119 − 36 = 83.

So, there are 83 people between Mr. Ihg and Mr. Lkj.

Hence, the correct answer is "Option 3".

The logic followed here is:

thus, "208" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

Given number: 3652497

Logic:

Arrange the digits in descending order (highest to lowest), then find the product of the 2nd digit from the left and the 2nd digit from the right.

Original number: 3 6 5 2 4 9 7

Now arranging in descending order:

Rearranged number: 9 7 6 5 4 3 2 → 9765432

Second from the left = 7

Second from the right = 3

Product 7 × 3 = 21

Hence, the correct answer is Option 4.

BODMAS Table: 

Decoding the given information:

 

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

⇒ 53 × 13 − 391 ÷ 17 + 289 = ?

⇒ 689 − 23 + 289 = ?

⇒ 689 + 289 = 978

⇒ 978 − 23 = ?

⇒ 955

Hence, the correct option is "Option 3".

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

E sits third to the left of B.

D sits second to the right of B.

C sits to the immediate right of F.

G sits second to the right of A.

Total people between C and G = 2

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: Third Number = (First Number + Second Number) × 3.

For, (24, 11, 105)

⇒ 24 + 11 = 35

⇒ 35 × 3 = 105

For, (38, 42, 240)

⇒ 38 + 42 = 80

⇒ 80 × 3 = 240

Now, checking the options using the same pattern:

Option 1) (34, 62, 286)

⇒ 34 + 62 = 96

⇒ 96 × 3 = 288 ≠ 286

Option 2) (46, 53, 287)

⇒ 46 + 53 = 99

⇒ 99 × 3 = 297 ≠ 287

Option 3) (74, 34, 324)

⇒ 74 + 34 = 108

⇒ 108 × 3 = 324

Option 4) (93, 12, 318)

⇒ 93 + 12 = 105

⇒ 105 × 3 = 315 ≠ 318

Hence, the correct answer is Option 3.

Given: Seven people S, Q, U, A, R, E and D are sitting in a row facing north.

Only S sits to the left of Q.

Only four people sit between S and U.

Only A sits between E and R, and E is not an immediate neighbor of U.

Now, the person at the extreme right is: D

Hence, the correct answer is "Option 3".

The logic followed here is:

For, QOHY → WJLV

For, NRBT → TMFQ

Now, applying the same pattern to JRUF:

So, JRUF → PMYC

Hence, the correct answer is Option 3.

The logic followed here is:

For, JUNC → QBUJ

For, LWPE → SDWL

Now, applying the same pattern to GRKZ:

So, GRKZ → NYRG

Hence, the correct answer is Option 3.

The logic followed here is:

Given:

City A is to the North of City B.

City D is to the East of City A.

City D is to the South of City E.

City E is to the West of City C.

Thus, City B lies to the South-West of City E.

Hence, the correct answer is Option 2.

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

D sits to the immediate right of B.

E sits third to the right of B.

G sits third to the left of D.

C is the immediate neighbour of D and E.

A is not an immediate neighbour of B.

Total people between F and D = 4

Hence, the correct answer is "Option 3".

The logic followed here is:

Given:

Aarav drives 13 km East

He turns left → 8 km North

He turns left → 15 km West

He turns left → 11 km South

He turns left → 2 km East

So, To reach Point A, he must go 3 km North.

Hence, the correct answer is Option 1.

The logic followed here is:

So, 'WR49' will replace the question mark in the given series.

Hence, the correct answer is "Option 4".

Given:

VOLT is coded as 6428

LIFE is coded as 5761

So, the code for L = 6

Hence, the correct answer is Option 3.

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

Now,

We need to find an odd number which is immediately preceded by an odd number and immediately followed by an odd number.

So, Needed pattern is: Odd - Odd - Odd.

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

Only one valid triplet satisfies the condition

Hence, the correct answer is 'Option 1'.