RRB Group D Official Paper (Held On: 10 Feb, 2026 Shift 3) (Previous Year Paper)

The correct answer is Zinc metal only.

Key Points

• Galvanisation is a metallurgical process used to protect Iron and Steel from Rusting by applying a thin, protective coating of Zinc.
• The process is highly effective because Zinc acts as a physical barrier between the metal and the atmosphere, preventing Oxygen and Moisture from reaching the surface of the Iron.
• The most common method utilized in industries is Hot-dip galvanizing, where the metal components are submerged in a bath of molten Zinc at temperatures typically around 450 degrees Celsius (842 degrees Fahrenheit).
• A unique feature of this process is Sacrificial Protection; since Zinc is more chemically active (electropositive) than Iron, it corrodes in preference to the Iron, even if the coating is scratched or damaged.
• While other metals like Nickel, Chromium, or Tin can be used for coating (in processes like electroplating), the specific term Galvanisation refers exclusively to the application of Zinc.

Additional Information

• Rusting of Iron:
• Rusting is an oxidation reaction that occurs when Iron reacts with Oxygen in the presence of Water or Moisture.
• The chemical formula for rust is Fe2O3.nH2O, which is known as Hydrated Iron(III) Oxide. It is a reddish-brown flaky substance that weakens the structural integrity of the metal.
• Other Methods of Rust Prevention:
• Painting and Greasing: Provides a simple barrier to block Air and Water.
• Alloying: Mixing Iron with elements like Chromium (at least 10.5%) and Nickel produces Stainless Steel, which is highly resistant to corrosion.
• Anodizing: Primarily used for Aluminium, it thickens the natural oxide layer on the metal surface.
• Tinning: Coating Iron or Steel with Tin, often used for food containers as Tin is non-toxic.
• Comparison of Options:
• Silver: It is an expensive precious metal and would be economically unviable for industrial rust protection.
• Copper: If used as a coating, it can actually accelerate the corrosion of Iron if the coating is breached because Iron is more reactive than Copper.
• Nickel: Used in Electroplating to provide a shiny finish and corrosion resistance, but it does not provide the same sacrificial protection as Zinc.

Important Points

• The term Galvanisation is named after the Italian scientist Luigi Galvani, who studied the effects of electricity on biological tissues, though the industrial coating process was developed later in the 19th Century.
• In a Galvanic Cell setup, the Zinc acts as the Anode and the Iron acts as the Cathode, ensuring the base metal remains protected as long as the Zinc is present.
• Common applications of galvanized Iron include Roofing sheets, Water pipes, Fencing, and Automotive body parts.

The correct answer is No, because the two forces act on the same object.

Key Points

• Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. A fundamental criterion for these forces to be considered an action-reaction pair is that they must act on two different objects.
• In the given scenario, the force of gravity (the Earth pulling the person downward) and the normal force (the ground pushing the person upward) both act on the same object—the person.
• Because both forces are applied to the person, they cannot constitute an action-reaction pair according to the Third Law. Instead, they represent a state of static equilibrium. Hence, statement 4 is correct.
• Statement 1 suggests they are a pair because they balance each other. However, balancing forces that prevent motion are related to Newton's First Law (equilibrium) and specifically act on a single body, which contradicts the definition of a Third Law pair. Hence, statement 1 is incorrect.
• Statement 2 is factually incorrect in its premise regarding the specific forces mentioned; the gravity and normal force in this example are both exerted on the person, not on different objects. Hence, statement 2 is incorrect.
• Statement 3 claims they are a pair simply because they are equal and opposite. While action-reaction pairs are indeed equal and opposite, not all equal and opposite forces are action-reaction pairs. They must also act on different bodies and be of the same physical nature. Hence, statement 3 is incorrect.

Additional Information

• Identifying True Action-Reaction Pairs:
• The reaction to the Earth's gravitational pull on the person is the person's gravitational pull on the Earth. These two forces act on different bodies (Person and Earth).
• The reaction to the ground pushing up on the person (Normal Force) is the person pushing down on the ground. These two forces act on different bodies (Person and Ground).
• Nature of Forces: Action-reaction pairs must be of the same nature. Gravity is a field force (non-contact), whereas the normal force is a contact force (electromagnetic in origin at the atomic level). A field force and a contact force can never form a Newtonian pair.
• Equilibrium vs. Third Law:
• Equilibrium involves multiple forces acting on one object that sum to a net force of zero, resulting in zero acceleration.
• Newton's Third Law describes a symmetry in nature where forces always occur in pairs acting on interacting objects. These forces never cancel each other out because they act on different systems.
• Simultaneity: In an action-reaction pair, there is no time delay. The action does not "cause" the reaction after a lapse of time; both forces appear and disappear simultaneously.

Important Points

• Mathematical Representation: Newton's Third Law is often expressed as F_AB = -F_BA, where F_AB is the force exerted by object A on object B, and F_BA is the force exerted by object B on object A.
• Independence of Motion: The Third Law holds true whether the objects are stationary, moving at a constant velocity, or accelerating.
• Common Examples:
• Recoil of a Gun: The gun exerts a forward force on the bullet (action), and the bullet exerts an equal backward force on the gun (reaction).
• Swimming: A swimmer pushes the water backward (action), and the water pushes the swimmer forward (reaction).
• Walking: A person pushes the ground backward with their feet (action), and the ground pushes the person forward (reaction).
• Mass Influence: Although the forces are equal in magnitude, the resulting accelerations can be vastly different depending on the mass of the objects (a = F/m). This is why we don't see the Earth move when we jump, even though we pull on it with the same force it pulls on us.

The correct answer is Copper sulphate is converted into iron sulphate.

Key Points

• When an iron nail is placed in a copper sulphate (CuSO4) solution, a single displacement reaction takes place. In this process, iron, being a more reactive metal, displaces copper from its salt solution.
• The chemical equation for this reaction is: Fe (s) + CuSO4 (aq) -> FeSO4 (aq) + Cu (s). This shows that copper sulphate is converted into iron (II) sulphate (also known as ferrous sulphate). Hence, the statement that copper sulphate is converted into iron sulphate is correct.
• The blue colour of the copper sulphate solution is due to the presence of Cu2+ ions. As the reaction proceeds, the concentration of these ions decreases, causing the blue colour to fade and eventually turn light green.
• Iron sulphate (FeSO4), which is formed in the solution, imparts a light green colour to the liquid. Hence, the statement that iron sulphate is colourless is incorrect.
• The displaced copper metal does not dissolve; instead, it settles on the surface of the iron nail as a reddish-brown coating. Hence, the statement that copper dissolves in water is incorrect.
• This reaction is not a decomposition; it is a redox reaction where iron is oxidized and copper is reduced. Hence, the statement that copper sulphate decomposes is incorrect.

Additional Information

• Reactivity Series: This is a list of metals arranged in the order of their decreasing chemical reactivity. In this series, Iron (Fe) is placed above Copper (Cu), which explains why iron can displace copper from its compounds.
• Copper Sulphate (CuSO4): Often called Blue Vitriol, it typically exists as a pentahydrate (CuSO4.5H2O). It is widely used in agriculture as a fungicide and in educational laboratories to demonstrate displacement reactions.
• Ferrous Sulphate (FeSO4): Known as Green Vitriol, it is used industrially in the manufacture of inks and as a reducing agent in chemical processes. In medicine, it is used to treat iron deficiency anemia.
• Redox Reactions: In the given reaction, Iron loses two electrons (oxidation) to become Fe2+, while the Copper ions gain two electrons (reduction) to become solid Copper.

Important Points

• Visual Observations: During this experiment, two distinct changes are observed: the blue colour of the solution changes to light green, and the greyish iron nail acquires a brownish texture.
• Duration: Usually, the fading of the blue colour is observable within 20 to 30 minutes of immersion, depending on the molarity (concentration) of the solution.
• Law of Conservation of Mass: The total mass of the reactants (Iron + Copper Sulphate) remains equal to the total mass of the products (Ferrous Sulphate + Copper) in a closed system.

The correct answer is When the current and field are perpendicular to each other.

Key Points

• The magnitude of the magnetic force acting on a current-carrying conductor placed in a uniform magnetic field is determined by the formula F = BIL sin θ, where F is the force, B is the magnetic field strength, I is the current, L is the length of the conductor, and θ is the angle between the conductor and the field.
• The force is observed to be the highest (maximum) when the angle θ is 90 degrees. This occurs because the value of sin 90° is 1, which is the maximum possible value for the sine function. Hence, statement 4 is correct.
• When the current and the magnetic field are parallel or anti-parallel to each other, the angle θ is 0 degrees or 180 degrees. Since sin 0° and sin 180° are both 0, the magnetic force acting on the conductor is zero. Hence, statement 1 is incorrect.
• Varying the current instantaneously may change the magnitude of the force over time, but it does not represent the spatial condition (alignment) required for the maximum force to be exerted at any given moment. Hence, statement 2 is incorrect.
• The direction of current flowing towards a specific pole (like the south pole) does not inherently define the angle θ unless the orientation of the magnetic field lines relative to that pole is specified as being perpendicular. Hence, statement 3 is incorrect.

Additional Information

• Magnetic Flux Density (B): It represents the strength of the magnetic field. The SI unit for magnetic flux density is the Tesla (T). One Tesla is defined as one Newton of force per Ampere-meter.
• Fleming’s Left-Hand Rule: This rule is used to determine the direction of the mechanical force exerted on a conductor. If the forefinger points in the direction of the magnetic field and the middle finger points in the direction of the current, then the thumb represents the direction of the force (motion).
• Lorentz Force: While the formula F = BIL sin θ applies to conductors, the fundamental force on a single moving charge (q) with velocity (v) in a magnetic field is F = qvB sin θ.
• Factors Affecting Force: The force is directly proportional to the magnitude of current (I), the length of the conductor (L), and the strength of the magnetic field (B). If any of these values increase, the force acting on the conductor also increases proportionally.

Important Points

• Vector Representation: The force is mathematically expressed as a vector product (cross product): F = I (L × B). This implies that the resulting force is always perpendicular to both the direction of the current and the direction of the magnetic field.
• Applications: This principle is the foundational mechanism behind the operation of electric motors, galvanometers, and loudspeakers, where electrical energy is converted into mechanical work via magnetic interaction.
• Maximum Condition: In most practical motor designs, the armature is configured to ensure the current-carrying wires move perpendicular to the magnetic field as much as possible to maintain peak torque and efficiency.

The correct answer is It must be an aqueous or molten solution of a suitable metal salt.

Key Points

• The process of electrolytic refining is used to obtain highly pure metals from impure samples. In this process, the electrolyte must be a medium that allows the movement of metal ions between the electrodes.
• A necessary property of the electrolyte is that it must be an aqueous or molten solution of a suitable metal salt. This ensures that the electrolyte contains the same metal ions as the metal being purified, facilitating the transfer of pure metal to the cathode. Hence, statement 1 is correct.
• The electrolyte cannot remain completely non-reactive. In fact, it must actively participate in the ion exchange process, where metal ions from the solution are reduced at the cathode and metal atoms from the anode are oxidized into the solution. Hence, statement 2 is incorrect.
• While electrolysis may generate heat due to resistance (Joule heating), the primary required property is ionic conductivity (the ability to conduct electricity via ions), not specifically the efficiency of conducting heat. Hence, statement 3 is incorrect.
• The electrolyte must be a homogeneous conductive medium. Using a layer of neutral oil would act as an insulator and prevent the flow of electric current, thus halting the refining process. Hence, statement 4 is incorrect.

Additional Information

• Definition of Electrolytic Refining:
• It is a technique used for the extraction and purification of metals like Copper (Cu), Zinc (Zn), Tin (Sn), Nickel (Ni), Silver (Ag), and Gold (Au).
• In this setup, a thick block of the impure metal is made the anode (positive electrode), and a thin strip of pure metal is made the cathode (negative electrode).
• Role of the Electrolyte:
• The electrolyte is typically a water-soluble salt of the metal being refined. For example, in copper refining, acidified Copper Sulphate (CuSO4) is used.
• When electric current is passed through the electrolyte, the impure metal from the anode dissolves into the electrolyte as cations.
• An equivalent amount of pure metal ions from the electrolyte are then deposited onto the cathode.
• Fate of Impurities:
• Soluble impurities go into the solution during the process.
• Insoluble impurities settle down at the bottom of the anode and are known as anode mud. This mud often contains precious metals like Gold and Silver, which can be recovered later.

Important Points

• Chemical Equations:
• At the Anode (Oxidation): M → Mⁿ⁺ + ne^- (Metal atoms lose electrons and enter the solution).
• At the Cathode (Reduction): Mⁿ⁺ + ne^- → M (Metal ions gain electrons and deposit as pure metal).
• Conductivity: The electrolyte must have high ionic conductivity to ensure the process is energy efficient. The concentration of the metal salt and the pH of the solution are carefully maintained during industrial operations.
• Purity Levels: Electrolytic refining is capable of producing metals with a purity of up to 99.99%, which is essential for electrical applications (like copper wiring) where impurities significantly increase resistance.

The correct answer is Chloroplasts.

Key Points

• Chloroplasts are specialized organelles found in plant cells and algae that conduct photosynthesis. They contain the green pigment called chlorophyll, which captures the energy from sunlight to convert water and carbon dioxide into food (glucose). Hence, option 1 is correct.
• The Nucleus serves as the control center of the cell and contains the genetic material (DNA). It is responsible for regulating gene expression and cell division, but it does not contain chlorophyll or participate directly in photosynthesis. Hence, option 2 is incorrect.
• Mitochondria are known as the powerhouse of the cell. Their primary function is to perform cellular respiration, which involves breaking down nutrients to generate energy in the form of ATP (Adenosine Triphosphate). While plants have mitochondria, these organelles do not produce chlorophyll. Hence, option 3 is incorrect.
• The Vacuole is a storage sac within the cell. In plant cells, a large central vacuole maintains turgor pressure against the cell wall and stores water, enzymes, and waste products. It does not play a role in the absorption of light for photosynthesis. Hence, option 4 is incorrect.

Additional Information

• Structure of Chloroplasts:
• Double Membrane: Chloroplasts are bounded by an inner and outer membrane with an intermembrane space between them.
• Thylakoids: These are disc-like sacs arranged in stacks called grana. The light-dependent reactions of photosynthesis occur here because the chlorophyll is embedded in the thylakoid membranes.
• Stroma: This is the alkaline, aqueous fluid surrounding the grana. The light-independent reactions (Calvin Cycle) occur in the stroma, where carbon dioxide is converted into sugar.
• Types of Chlorophyll:
• Chlorophyll a is the primary pigment involved in photosynthesis, reflecting blue-green light.
• Chlorophyll b is an accessory pigment that collects energy and passes it to chlorophyll a, reflecting yellow-green light.
• Photosynthesis Process:
• The overall chemical reaction can be summarized as: 6 Carbon Dioxide + 6 Water + Light Energy results in 1 Glucose + 6 Oxygen.
• This process is vital for life on Earth as it provides the primary source of energy for nearly all food chains and releases oxygen into the atmosphere.

Important Points

• Endosymbiotic Theory: It is widely believed by biologists that chloroplasts (and mitochondria) originated from free-living bacteria that were engulfed by ancestral eukaryotic cells. Evidence for this includes the fact that chloroplasts have their own circular DNA and 70S ribosomes.
• Location: While chloroplasts are found throughout the green parts of a plant, they are most concentrated in the mesophyll cells of the leaves. A single mesophyll cell can contain anywhere from 20 to 100 chloroplasts.
• Other Plastids: Chloroplasts belong to a family of organelles known as plastids. Other types include Chromoplasts (which contain carotenoid pigments giving fruits and flowers red, orange, or yellow colors) and Leucoplasts (which are colorless and used for storing starch, oils, or proteins).

The correct answer is Aqua Culture.

Key Points

• Aqua Culture is the primary method of fish production in the Kashmir region due to its vast freshwater resources, including rivers, lakes, and springs. It involves the breeding and harvesting of fish in controlled aquatic environments. Hence, the correct answer is Aqua Culture.
• Marine Fisheries refer to fishing activities in oceans and seas. Since Kashmir is a landlocked mountainous region located far from any coastline, marine fishing is geographically impossible. Hence, statement 3 is incorrect.
• Brackish Water Fisheries involve the farming of fish in water that has more salinity than fresh water but less than seawater, typically found in estuaries and mangrove swamps. The water bodies in Kashmir are predominantly fresh, lacking the salinity required for brackish water fish production. Hence, statement 2 is incorrect.
• Pearl Culture is the process of producing pearls by nurturing pearl oysters or freshwater mussels. While freshwater pearl culture exists in some parts of India, it is not a traditional or significant fish production method in the cold climatic conditions of the Kashmir Valley. Hence, statement 1 is incorrect.
• The Department of Fisheries in Jammu & Kashmir focuses extensively on Cold Water Fisheries, leveraging the oxygen-rich, running waters of the Himalayas to boost the local economy.

Additional Information

• Trout Farming: Kashmir is globally renowned for its Trout production. Two main species are cultivated: Brown Trout (Salmo trutta fario) and Rainbow Trout (Oncorhynchus mykiss).
• Historical Context: Trout was first introduced to Kashmir by the British in the year 1900. The first batch of Trout ova arrived from the United Kingdom as a gift to the then Maharaja.
• Geographical Advantages: The region possesses perennial water sources such as the Jhelum River, Sindh River, and high-altitude lakes like Gangabal and Vishansar, which maintain the low temperatures (below 20°C) necessary for cold-water Aqua Culture.
• Native Species: Apart from exotic trout, the region is home to indigenous species known as Schizothorax (locally called Kashir Gaad or Snow Trout), which are well-adapted to the torrential mountain streams.
• Economic Impact: The fish industry in Jammu & Kashmir provides a livelihood to thousands of people, with major markets in Srinagar and exports to other parts of India.

Important Points

• Kokernag Trout Farm: Located in Anantnag district, it is considered Asia's largest trout fishery farm. It serves as a major hub for seed production and distribution.
• Major Lakes: Wular Lake and Dal Lake are significant centers for capture fisheries in the valley, contributing a large percentage of the total fish catch in the Union Territory.
• Government Schemes: The Pradhan Mantri Matsya Sampada Yojana (PMMSY) is being actively implemented in the region to modernize Aqua Culture infrastructure, including the construction of RAS (Recirculatory Aquaculture Systems) and cold storage facilities.
• Blue Revolution: The initiative to increase fish production in Kashmir is a part of the broader Blue Revolution in India, aimed at achieving self-sufficiency in protein sources and doubling farmers' income by 2024-25.

The correct answer is The v–t graph is always curved.

Key Points

• In a velocity-time (v–t) graph, the slope of the line represents the acceleration of the object. A positive slope indicates that the velocity is increasing with time, which signifies positive acceleration. Hence, statement 1 is correct.
• The area under the v–t graph within a specific time interval represents the displacement of the object during that period. This is because displacement is the product of velocity and time (integrated over the interval). Hence, statement 2 is correct.
• For uniform acceleration, the rate of change of velocity is constant. Since the slope of a v–t graph represents acceleration, a constant acceleration results in a constant slope throughout the motion. Hence, statement 3 is correct.
• A v–t graph for uniform acceleration is represented by a straight line (either horizontal for zero acceleration or inclined for constant non-zero acceleration). A curved graph indicates non-uniform acceleration, where the acceleration changes at different points in time. Hence, statement 4 is incorrect.
• Therefore, the statement that the v–t graph is always curved is not correct in the context of uniform acceleration.

Additional Information

• Uniform Acceleration: This occurs when an object's velocity changes by equal amounts in equal intervals of time. The most common example is an object in free fall near the Earth's surface, accelerating at approximately 9.8 m/s².
• Types of v–t Graphs:
• Zero Acceleration: The graph is a horizontal straight line parallel to the time axis, meaning the object moves with constant velocity.
• Positive Uniform Acceleration: The graph is a straight line sloping upwards from left to right.
• Negative Uniform Acceleration (Retardation): The graph is a straight line sloping downwards, indicating that the object is slowing down.
• Equations of Motion: For an object moving with uniform acceleration (a), the relationship between initial velocity (u), final velocity (v), time (t), and displacement (s) is given by:
• v = u + at
• s = ut + 0.5at²
• v² = u² + 2as

Important Points

• Slope Calculation: The slope is calculated as the change in velocity divided by the change in time (rise over run). The unit of the slope is meters per second squared (m/s²).
• Distance vs. Displacement: While the area under the v–t graph gives displacement, the total area (treating areas below the time axis as positive) gives the total distance traveled.
• Origin of the Graph: If the straight line passes through the origin (0,0), it implies the object started from rest (initial velocity u = 0) at time t = 0.
• Non-Uniform Motion: If the acceleration is not constant, the v–t graph will be curved. The instantaneous acceleration at any point on such a curve is found by drawing a tangent to the curve at that point and finding its slope.

The correct answer is Fallopian Tube.

Key Points

• Fertilization is the biological process of the fusion of a haploid male gamete (sperm) and a haploid female gamete (ovum) to form a diploid zygote.
• In the human female reproductive system, the location where fertilization usually occurs is the Fallopian tube, also commonly referred to as the oviduct.
• Specifically, the fusion typically takes place in the ampulla region, which is the widest and longest part of the tube, or at the ampullary-isthmic junction.
• During ovulation, a mature egg is released from the ovary and is swept into the tube by the fimbriae (finger-like projections).
• The sperm must travel through the vagina, cervix, and uterus to reach the Fallopian tube to encounter the egg.
• The ovum remains viable for fertilization for approximately 12 to 24 hours after being released.

Additional Information

• Ovary:
• The ovaries are the primary female sex organs responsible for producing ova (eggs).
• They also secrete essential hormones such as estrogen and progesterone which regulate the menstrual cycle.
• In a typical 28-day cycle, one egg is released from one of the two ovaries.
• Uterus (Womb):
• The uterus is a hollow, pear-shaped muscular organ located in the pelvic cavity.
• Its primary function is to support the development of the fetus during pregnancy.
• The inner lining, called the endometrium, is where the embryo implants itself after traveling down from the tube.
• Vagina:
• The vagina is a muscular, elastic canal that serves as the birth canal during delivery.
• It acts as the receptacle for sperm during sexual intercourse and provides a pathway for menstrual flow to leave the body.
• Fallopian Tube Structure:
• There are two Fallopian tubes, each measuring about 10 to 12 cm in length.
• They consist of four parts: the infundibulum (with fimbriae), the ampulla, the isthmus, and the uterine part.

Important Points

• Implantation: After fertilization in the tube, the zygote undergoes cleavage (cell division) as it moves toward the uterus. It takes about 6 to 10 days for the resulting blastocyst to attach to the uterine wall.
• Ectopic Pregnancy: This is a medical condition where the fertilized egg implants outside the uterus, most commonly within the Fallopian tube itself. This is a dangerous condition as the tube is not designed to hold a growing embryo.
• Zygote to Embryo: The single-celled zygote represents the first stage of a new individual, containing a complete set of 46 chromosomes (in humans).
• Ciliary Action: The inner lining of the Fallopian tube contains ciliated epithelium. The rhythmic movement of these cilia helps transport the non-motile egg toward the uterus.

The correct answer is 1 – c, 2 – a, 3 – d, 4 – b.

Key Points

• Dandelions (Wind Dispersal): Dandelions produce seeds that are attached to light, feathery bristles called a pappus. These structures function like tiny parachutes, enabling the seeds to be easily lifted and carried over long distances by the wind (Anemochory). Hence, 1 matches with c.
• Lotus (Water Dispersal): The Lotus plant grows in aquatic environments and has a unique, spongy thalamus (the seed head). This spongy structure, along with a fibrous outer covering, allows the fruit to float on water surfaces for a long period until it eventually sinks or reaches a bank to germinate (Hydrochory). Hence, 2 matches with a.
• Mango (Animal Dispersal): Mango is a fleshy fruit designed to attract animals and humans. The sweet, pulpy mesocarp is consumed, and the large, hard seed is typically discarded in a different location. In some cases, smaller seeds of other fruits are ingested and passed through the digestive tract of birds or mammals (Zoochory). Hence, 3 matches with d.
• Castor (Explosion Mechanism): Castor plants utilize a method known as ballochory or explosive mechanism. The fruit of the Castor is a capsule that creates internal tension as it dries out. When the tension reaches a certain point, the pod bursts open with a sudden force, shooting the seeds away from the mother plant. Hence, 4 matches with b.

Additional Information

• Modes of Seed Dispersal: Dispersal is the process by which seeds are spread away from the parent plant to prevent overcrowding and reduce competition for sunlight, water, and minerals.
• Anemochory (Wind): Plants like Drumstick and Maple have winged seeds, while Madar (Aak) has hairy seeds. These adaptations increase the surface area, making them buoyant in the air.
• Hydrochory (Water): This is common in plants living near water bodies. The Coconut is a prime example, possessing a fibrous husk that provides buoyancy, allowing it to travel across oceans.
• Zoochory (Animals): Some seeds have evolved hooks or spines to facilitate transport. For instance, Xanthium and Urena seeds have hooks that get attached to the fur of animals or the clothes of humans, carrying them to distant locations.
• Autochory (Self-Dispersal): Apart from Castor, plants like Balsam and Pea also show explosive fruit dehiscence. When the pods ripen and dry, they burst open, scattering the seeds effectively.

Important Points

• Ecological Significance: Seed dispersal is a critical ecological process that allows plant species to colonize new habitats and ensures genetic diversity within a population.
• Adaptations: The features of a seed (weight, shape, presence of wings/hooks) are specifically evolved to match the primary agent of dispersal available in the plant's environment.
• Survival Rate: By moving away from the parent plant, seedlings avoid the pathogens and pests that often accumulate in high densities near the mother plant.

The correct answer is One atom or group of atoms being replaced by another.

Key Points

• A substitution reaction (also known as a single displacement reaction) is a chemical reaction during which a functional group or an atom in a chemical compound is replaced by another functional group or atom. Hence, statement 3 is correct.
• These reactions are highly significant in organic chemistry. Saturated hydrocarbons, such as alkanes, primarily undergo substitution reactions because they contain single covalent bonds that are stable and do not allow for the addition of more atoms without removing existing ones.
• The process involves the cleavage of an existing sigma bond and the simultaneous or sequential formation of a new sigma bond with the substituting species.
• A common example is the halogenation of methane (CH4). When methane reacts with chlorine (Cl2) in the presence of ultraviolet light or heat, one or more hydrogen atoms are replaced by chlorine atoms to form chloromethane (CH3Cl) and hydrogen chloride (HCl).
• Unlike addition reactions, the saturation level of the molecule typically remains unchanged in a simple substitution reaction. Hence, statement 1 is incorrect as it describes addition reactions.

Additional Information

• Types of Substitution Reactions:
• Nucleophilic Substitution: This occurs when the "attacking" species is a nucleophile (an electron-rich species like OH- or CN-). It is common in alkyl halides and is further divided into Sn1 (unimolecular) and Sn2 (bimolecular) mechanisms based on the reaction kinetics.
• Electrophilic Substitution: This occurs when an electrophile (an electron-deficient species) displaces an atom. This is the characteristic reaction of aromatic compounds like benzene, where a hydrogen atom on the ring is replaced (e.g., nitration or sulfonation).
• Radical Substitution: This involves free radicals as intermediates. It usually requires UV radiation to initiate the process by breaking bonds homolytically, as seen in the chlorination of alkanes.
• Comparison with other reaction types:
• Addition Reactions: These involve atoms being added to unsaturated molecules containing double or triple bonds (alkenes or alkynes), resulting in a more saturated product.
• Elimination Reactions: These involve the removal of atoms or groups from a molecule, often resulting in the formation of pi bonds (double or triple bonds). Hence, statement 4 is incorrect.
• Replacement of Carbon: Organic substitution reactions generally involve replacing hydrogen or a functional group attached to a carbon atom, rather than replacing the carbon atom itself. Hence, statement 2 is incorrect.

Important Points

• Leaving Group: In a substitution reaction, the atom or group that is detached is called the leaving group. The efficiency of the reaction often depends on how stable the leaving group is after it departs.
• Catalysts: Many electrophilic aromatic substitutions require a Lewis acid catalyst, such as FeCl3 or AlCl3, to generate a strong enough electrophile to attack the stable benzene ring.
• Industrial Use: Substitution reactions are used extensively in the pharmaceutical industry, the production of polymers, and the synthesis of dyes and pesticides.
• Reactivity Series: In inorganic chemistry, a metal higher in the reactivity series can substitute (displace) a metal lower in the series from its salt solution (e.g., Zinc replacing Copper in copper sulfate).

The correct answer is Tertiary Consumer.

Key Points

• Biological Magnification (or biomagnification) refers to the process where the concentration of toxic substances, such as pesticides or heavy metals, increases progressively at each successive trophic level of a food chain.
• The Tertiary Consumer occupies the highest trophic level in the provided options. Because these organisms consume secondary consumers, they accumulate the total chemical load from all the lower levels combined. Hence, statement 1 is correct.
• Primary Consumers, which are herbivores, occupy the second trophic level. They ingest pesticides directly from producers, but their body concentration is significantly lower than that of top predators. Hence, statement 2 is incorrect.
• Producers (such as green plants) represent the first trophic level. They absorb non-biodegradable chemicals from the soil or water. While they are the entry point for toxins, they contain the lowest concentration compared to consumers. Hence, statement 3 is incorrect.
• Secondary Consumers are carnivores that feed on primary consumers. While their toxin levels are higher than those of herbivores, they still possess a lower concentration than the Tertiary Consumers who prey upon them. Hence, statement 4 is incorrect.

Additional Information

• Characteristics of Biomagnified Substances:
• To undergo biomagnification, a substance must be long-lived (persistent), mobile, soluble in fats (lipophilic), and biologically active.
• Examples include DDT (Dichlorodiphenyltrichloroethane), BHC, and heavy metals like mercury, arsenic, and cadmium.
• Because these substances are fat-soluble, they are not excreted easily through urine and instead accumulate in the adipose tissues of organisms.
• Impact on Apex Predators:
• Apex predators at the Tertiary Consumer level often suffer from reproductive failure or population decline due to high toxic loads.
• In the year 1962, scientist Rachel Carson highlighted the dangers of DDT in her book "Silent Spring," noting how it led to the thinning of eggshells in birds of prey like eagles and falcons.
• This phenomenon eventually led to a ban on DDT for agricultural use in many countries, including the United States in 1972.

Important Points

• The 10% Energy Law vs. Biomagnification:
• According to Raymond Lindeman's 10% Law (proposed in 1942), only about 10 percent of energy is transferred from one trophic level to the next.
• While energy decreases as we go up the pyramid, the concentration of non-biodegradable chemicals increases. This inverse relationship is critical for understanding ecosystem health.
• Bioaccumulation occurs within a single organism over its lifetime, whereas Biomagnification occurs across multiple trophic levels in a food web.
• Human Health Implications:
• As humans often act as Tertiary Consumers (eating fish, poultry, or meat), they are highly susceptible to the effects of biological magnification.
• Consumption of mercury-contaminated fish led to the famous Minamata disease in Japan during the 1950s, showcasing the lethal potential of high-trophic level toxin accumulation.

The correct answer is A chemical change occurs as a new substance is formed.

Key Points

• When iron filings and sulfur powder are simply mixed together at room temperature, they form a heterogeneous mixture. This is a physical change because no chemical bonds are broken or formed, and the iron retains its magnetic properties.
• When the mixture is heated, a chemical reaction occurs between the two elements to form a new compound called Iron(II) sulfide (FeS). This substance is a black solid that has entirely different chemical and physical properties compared to the original reactants. Hence, statement 1 is correct.
• The formation of Iron sulfide is a chemical change because a new substance is created with a fixed chemical composition. Unlike the initial mixture, the components of the compound cannot be separated by simple physical means such as using a magnet. Hence, statement 2 is incorrect.
• Chemical changes are generally irreversible by physical methods. Once Iron sulfide is formed, you cannot retrieve the iron and sulfur by cooling it or filtering it. Hence, statement 3 is incorrect.
• Iron does not dissolve in sulfur to form a solution; instead, the atoms undergo a chemical bonding process (ionic/covalent character) to form a crystal lattice of FeS. A solution is a homogeneous mixture where no chemical reaction occurs. Hence, statement 4 is incorrect.

Additional Information

• Chemical vs. Physical Changes:
• A physical change alters the form of a substance but does not change its molecular identity. Examples include melting, shredding, or mixing.
• A chemical change results in the formation of new chemical substances. Signs of a chemical change include color change, temperature change (evolution of heat), and the formation of a precipitate or gas.
• Properties of Reactants:
• Iron (Fe) is a greyish-metallic element that is ferromagnetic, meaning it is strongly attracted to magnets.
• Sulfur (S) is a bright yellow non-metal powder that is insoluble in water but soluble in solvents like carbon disulfide (CS2).
• Properties of the Product (Iron Sulfide):
• Iron(II) sulfide is a non-magnetic black solid.
• It reacts with dilute hydrochloric acid to produce hydrogen sulfide gas (H2S), which has a characteristic rotten egg smell, whereas the original mixture of Fe and S would produce hydrogen gas when reacted with acid.

Important Points

• Exothermic Nature: The reaction between iron and sulfur is exothermic, meaning it releases energy in the form of heat and light once the activation energy is provided by initial heating.
• Law of Constant Proportions: In the compound Iron sulfide, iron and sulfur are always present in a fixed ratio by mass (approximately 7:4), regardless of how much of each was initially mixed.
• Separation Techniques: In the mixture stage, iron can be separated using a magnet and sulfur can be separated by dissolving it in carbon disulfide. These techniques fail once the chemical change into FeS has occurred.

The correct answer is 225 J.

Key Points

• Kinetic Energy (KE) is the energy possessed by an object due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.
• The mathematical formula for Kinetic Energy is K.E. = 1/2 mv^2, where m represents the mass of the object and v represents its velocity.
• According to the question, the initial kinetic energy of the object with mass m and velocity v is 25 J. Therefore, 1/2 mv^2 = 25 Joules.
• When the velocity is increased three times, the new velocity becomes 3v.
• Substituting the new velocity into the formula: New Kinetic Energy = 1/2 m(3v)^2. Since (3v)^2 = 9v^2, the expression becomes 9 * (1/2 mv^2).
• Given that the value of 1/2 mv^2 is 25 J, the new kinetic energy is calculated as 9 * 25 = 225 J. Hence, the calculation shows the final kinetic energy is 225 J.

Additional Information

• Relationship between Velocity and Energy: Kinetic energy is directly proportional to the square of the velocity. This means that if the velocity doubles, the energy increases by 4 times (2^2), and if the velocity triples, the energy increases by 9 times (3^2).
• SI Unit: The standard unit of energy is the Joule (J), named after the English physicist James Prescott Joule. One Joule is equivalent to 1 kg.m^2/s^2.
• Mass Dependency: Kinetic energy is also linearly proportional to the mass of the object. If the mass of the object is doubled while keeping the velocity constant, the kinetic energy will also double.
• Scalar Quantity: Kinetic energy is a scalar quantity, meaning it has only magnitude and no direction. It is always a non-negative value (zero or positive) because mass is positive and the square of velocity is always positive.
• Work-Energy Theorem: This principle states that the net work done on an object is equal to the change in its kinetic energy. This is a fundamental concept in classical mechanics used to solve various physics problems involving force and displacement.

Important Points

• Frame of Reference: While the mass of an object is constant, its velocity (and thus its kinetic energy) depends on the frame of reference from which it is measured.
• Types of Kinetic Energy: In addition to translational kinetic energy (studied here), there is also rotational kinetic energy (1/2 Iw^2) for spinning objects and vibrational kinetic energy.
• Relativistic Effects: At extremely high speeds approaching the speed of light (c), the classical formula 1/2 mv^2 becomes inaccurate, and Einstein's theory of special relativity must be applied to calculate energy.
• Conversion: Kinetic energy can be converted into other forms of energy, such as potential energy (e.g., a ball thrown upwards) or thermal energy (e.g., through friction).

The correct answer is Onion extract changes smell in bases.

Key Points

• Olfactory indicators are substances whose odour or smell changes depending on whether they are mixed with an acidic or basic solution.
• Onion extract is a classic example of an olfactory indicator. When a basic solution like Sodium Hydroxide (NaOH) is added to onion extract, the characteristic smell of the onion cannot be detected or vanishes. Hence, statement 1 is correct.
• Turmeric is a natural indicator that changes color in different media. It remains yellow in acidic solutions but turns reddish-brown in basic solutions. It does not turn blue. Hence, statement 2 is incorrect.
• Phenolphthalein is a synthetic indicator. It is colorless in acidic solutions and turns pink in basic solutions. The statement claims it turns pink in acids, which is factually wrong. Hence, statement 3 is incorrect.
• Methyl orange is another synthetic indicator that shows a distinct color change. it turns red in acidic media and yellow in basic media. It is not an olfactory indicator and does not rely on producing or changing odour to indicate pH. Hence, statement 4 is incorrect.
• Hence, the correct answer is Onion extract changes smell in bases.

Additional Information

• Types of Olfactory Indicators:
• Vanilla Essence: The pleasant smell of vanilla is retained in acidic solutions but is destroyed or lost when added to a base.
• Clove Oil: In acidic solutions, the smell of clove oil remains, but it changes or disappears in basic solutions.
• These indicators are particularly useful in chemistry laboratories for visually impaired students, as they can identify the nature of a substance through the sense of smell rather than sight.
• Natural Indicators:
• Litmus: Derived from Lichens, it is purple in neutral solutions, red in acids, and blue in bases.
• China Rose (Gudhal): It turns dark pink (magenta) in acidic solutions and green in basic solutions.
• Red Cabbage Extract: It remains red in acids but turns green or yellow in basic solutions.
• Synthetic Indicators:
• These are man-made chemicals used to detect pH. Common examples include Phenolphthalein and Methyl orange.
• Phenolphthalein is often used in acid-base titrations because of its sharp color change at a pH range of approximately 8.2 to 10.0.

Important Points

• pH Scale: The acidity or basicity is measured on a pH scale ranging from 0 to 14. A pH of 7 is neutral (like pure water), a pH less than 7 is acidic, and a pH greater than 7 is basic.
• Neutralization Reaction: When an acid and a base react, they form salt and water. Indicators are used to find the equivalence point of these reactions.
• Chemical Nature of Olfactory Change: The change in smell occurs because the odorous molecules (which are often weak acids themselves) react with the hydroxide ions (OH-) in a base to form odorless salts.

The correct answer is Number of electrons.

Key Points

• The size of an atom is primarily determined by the space occupied by its electrons. While the nucleus contains more than 99.9% of the atom's mass, it occupies an insignificantly small volume compared to the total size of the atom.
• The volume of an atom is defined by the electron cloud, which is the region where electrons are likely to be found. As the number of electrons increases, they occupy more energy levels or shells, which significantly expands the atomic radius.
• The atomic radius is the distance from the center of the nucleus to the outermost stable electron shell. Therefore, the physical boundary that determines "size" is essentially the limit of the electron distribution. Hence, option 1 is the primary factor.
• While the number of protons (atomic number) affects the pull on the electrons, and the mass of the nucleus and number of neutrons affect the weight and stability, they do not define the physical dimensions or volume of the atom in the same way electrons do. Hence, options 2, 3, and 4 are incorrect as primary determinants of size.

Additional Information

• Atomic Radius Trends:
• Down a Group: In the Periodic Table, the atomic size increases as you move down a group. This is because a new electron shell is added for each succeeding element, moving the outermost electrons further from the nucleus.
• Across a Period: Atomic size generally decreases from left to right across a period. This occurs because the number of protons increases, creating a stronger positive charge that pulls the electron cloud closer to the nucleus, despite the number of shells remaining the same.
• The Nucleus vs. The Atom:
• To visualize the scale, if an atom were expanded to the size of a football stadium, the nucleus would be about the size of a small marble placed at the center, while the electrons would define the outer perimeter of the stands.
• The nucleus consists of protons and neutrons, which are much heavier than electrons, but they are packed into an extremely dense, tiny area of roughly 10^-15 meters in diameter.
• Shielding Effect:
• This is a phenomenon where inner electrons act as a shield, reducing the attractive force between the positive nucleus and the outermost electrons. This effect allows the electron cloud to expand, further influencing the overall atomic size.
• Effective Nuclear Charge (Zeff):
• This refers to the net positive charge experienced by an electron in a multi-electron atom. It is a crucial concept in General Chemistry that explains why atoms with more protons aren't always larger; the increased Zeff pulls the electrons inward, counteracting the size increase.

The correct answer is 5 x 10¹⁴ Hz.

Key Points

• The relationship between the speed of light, its frequency, and its wavelength is governed by the fundamental wave equation: c = f λ, where c is the speed, f is the frequency, and λ is the wavelength.
• In this problem, the wavelength (λ) is given as 600 nm. To perform calculations in SI units, this must be converted to meters. Since 1 nanometer (nm) equals 10^-9 meters, the wavelength is 600 x 10^-9 m, which simplifies to 6 x 10^-7 m.
• The speed of light (c) is provided as 3 x 10⁸ m/s, which is the standard speed of electromagnetic radiation in a vacuum.
• To find the frequency (f), the formula is rearranged to f = c / λ. Substituting the values: f = (3 x 10⁸) / (6 x 10^-7).
• Performing the division yields 0.5 x 10¹⁵, which is scientifically expressed as 5 x 10¹⁴ Hz. Hence, the frequency of the light is 5 x 10¹⁴ Hz, making this the correct statement.

Additional Information

• The Visible Spectrum: Light with a wavelength of 600 nm falls within the orange part of the visible light spectrum. The human eye typically perceives light in the range of 400 nm (violet) to 700 nm (red).
• Electromagnetic Wave Nature: Light is an electromagnetic wave consisting of oscillating electric and magnetic fields. Unlike sound waves, it does not require a material medium for propagation and can travel through a vacuum.
• Inverse Relationship: Frequency and wavelength are inversely proportional. As the wavelength of light increases (shifting toward the red end), its frequency decreases. Conversely, shorter wavelengths (toward the violet end) correspond to higher frequencies.
• Medium Transition: When light enters a different medium (like glass or water), its speed and wavelength change, but its frequency remains constant because frequency is determined by the source of the wave.

Important Points

• Unit of Frequency: The Hertz (Hz) is the SI unit for frequency, named after Heinrich Hertz. One Hertz corresponds to one cycle per second.
• Photon Energy: The energy (E) of a light photon is directly proportional to its frequency, defined by the equation E = hf, where h is Planck’s constant (6.626 x 10^-34 J·s). Higher frequency light carries more energy.
• Scientific Notation: In physics, power-of-ten notation is essential for managing very large values (like speed) and very small values (like wavelength) accurately during algebraic manipulation.

The correct answer is Hydrometer.

Key Points

• Archimedes’ Principle states that when a body is immersed fully or partially in a fluid, it experiences an upward force (buoyant force) that is equal to the weight of the fluid displaced by it.
• A Hydrometer is a device specifically designed to measure the relative density or specific gravity of liquids based on the concept of buoyancy. Hence, the correct answer is Hydrometer.
• The working of a hydrometer depends on the Law of Flotation, which is a direct application of Archimedes' principle. It consists of a weighted glass bulb and a thin stem with a graduated scale.
• When placed in a liquid, the hydrometer sinks until it displaces a volume of liquid exactly equal to its own weight. In a low-density liquid, the device sinks deeper, whereas in a high-density liquid, it floats higher.
• This principle is also utilized in other instruments like the Lactometer, which is used to determine the purity of milk by measuring its density.

Additional Information

• Sphygmomanometer:
• This is a medical instrument used to measure blood pressure. It was invented by Samuel Siegfried Karl Ritter von Basch in 1881.
• It typically consists of an inflatable cuff, a measuring unit (mercury manometer or aneroid gauge), and a mechanism for inflation. It measures pressure in millimeters of mercury (mmHg).
• Altimeter:
• An Altimeter is an instrument used to measure the altitude of an object above a fixed level, most commonly mean sea level.
• In aircraft, the barometric altimeter is most common; it works by measuring the atmospheric pressure, which decreases as altitude increases. It does not work on Archimedes' principle but on pressure-height relationship.
• Aneroid Barometer:
• This device is used to measure atmospheric pressure. It was invented by Lucien Vidi in 1844.
• Unlike the mercury barometer, it uses no liquid. Instead, it utilizes a small, flexible metal box called an aneroid cell (capsule) that expands or contracts with changes in air pressure.
• It is widely used in meteorology for weather forecasting and as a portable tool for surveying.

Important Points

• Archimedes of Syracuse: The principle is named after the Greek mathematician Archimedes, who discovered it in the 3rd century BC.
• Buoyant Force: This is the net upward force exerted by a fluid on an object. Its magnitude is given by the formula Fb = ρVg, where ρ is the density of the fluid, V is the displaced volume, and g is the acceleration due to gravity.
• Applications: Archimedes' principle is fundamental in designing ships, submarines, and hot air balloons. It explains why a heavy iron ship floats on water while a small iron nail sinks.

The correct answer is Plasma membrane.

Key Points

• Amoeba is a unicellular eukaryotic organism that does not have a fixed shape. It relies entirely on its plasma membrane (or cell membrane) to interact with its external environment.
• The process by which Amoeba acquires its food is known as endocytosis. This is possible because the plasma membrane is highly flexible and composed of lipids and proteins, allowing it to deform and engulf particles.
• To capture food, the Amoeba extends temporary, finger-like projections of the plasma membrane called pseudopodia (meaning "false feet"). These extensions surround the food particle until they fuse together.
• Once the pseudopodia fuse, the food particle is trapped inside a small, membrane-bound cavity within the cell called a food vacuole. This specific type of ingestion of solid matter is often referred to as phagocytosis.
• The plasma membrane serves as the primary interface for nutrition, as the organism lacks specialized mouth-like structures found in more complex multicellular animals.

Additional Information

• Plasma Membrane:
• It is a selectively permeable membrane that regulates the movement of substances in and out of the cell.
• In addition to food acquisition, it provides protection to the internal cellular contents and maintains the cell's integrity.
• Cilia:
• These are short, hair-like structures found on the surface of some cells. In organisms like Paramecium, cilia help in movement and in pushing food into a specific "mouth" area called the cytostome. Amoeba does not possess cilia.
• Flagella:
• These are long, whip-like structures used primarily for locomotion in certain bacteria and protists like Euglena. While they can help create currents to move food, they are not the primary structure for food engulfment in Amoeba.
• Nuclear Membrane:
• This is a double-layered membrane that surrounds the nucleus of a eukaryotic cell. Its function is to protect the genetic material (DNA) and regulate the flow of information between the nucleus and cytoplasm. It has no role in the external acquisition of food.

Important Points

• Digestion: Once the food is inside the food vacuole, digestive enzymes from the cytoplasm are secreted into the vacuole to break down the food into simpler, diffusible nutrients.
• Exocytosis: After the nutrients are absorbed, the undigested waste is moved toward the plasma membrane. The membrane then ruptures at any point to expel the waste outside the body, a process known as egestion.
• Habitat: Amoeba are typically found in freshwater bodies like ponds, lakes, and slow-moving rivers, where they feed on bacteria, algae, and other microscopic organisms.
• Discovery: The Amoeba was first discovered by August Johann Rösel von Rosenhof in the year 1755.

The correct answer is Both possess their own DNA and 70S Ribosome.

Key Points

• Chloroplasts and Mitochondria are both semi-autonomous organelles because they contain their own genetic material and protein-synthesizing machinery.
• Statement 1: Both perform photosynthesis. This statement is incorrect because photosynthesis is a process exclusive to chloroplasts (found in plants and algae). Mitochondria do not perform photosynthesis; they are involved in breaking down nutrients. Hence, statement 1 is incorrect.
• Statement 2: Both possess their own DNA and 70S Ribosome. Both organelles contain extra-chromosomal DNA (usually circular) and 70S ribosomes, which are similar to those found in prokaryotic cells. This allows them to produce some of their own enzymes and proteins. Hence, statement 2 is correct.
• Statement 3: Both perform respiration. While both are energy-transducing organelles, the process of aerobic cellular respiration (ATP production via the Krebs cycle and Electron Transport Chain) is the primary function of mitochondria. Chloroplasts are primarily for carbon fixation. Hence, statement 3 is incorrect.
• Statement 4: Both have chlorophyll. Chlorophyll is the green pigment essential for capturing light energy during photosynthesis and is located within the thylakoids of chloroplasts. Mitochondria do not contain chlorophyll. Hence, statement 4 is incorrect.
• Hence, the correct answer is Both possess their own DNA and 70S Ribosome.

Additional Information

• Mitochondria:
• Commonly referred to as the "Powerhouse of the cell", they are found in almost all eukaryotic cells.
• Their main function is the synthesis of ATP (Adenosine Triphosphate) through cellular respiration.
• They have a double-membrane structure where the inner membrane is folded into cristae to increase surface area for oxidative phosphorylation.
• Chloroplasts:
• These are a type of plastid primarily found in the mesophyll cells of leaves in green plants.
• They contain chlorophyll and carotenoid pigments responsible for trapping light energy for photosynthesis.
• Like mitochondria, they are double-membrane bound and contain a fluid matrix called stroma and stacked sacs called grana.
• The Endosymbiotic Theory:
• This evolutionary theory, popularized by Lynn Margulis in the 1960s, suggests that mitochondria and chloroplasts originated as free-living prokaryotic organisms.
• The presence of 70S ribosomes and circular DNA inside these organelles is strong evidence of their bacterial ancestry, as eukaryotic cytoplasm typically contains 80S ribosomes.
• Both organelles reproduce independently of the cell nucleus through a process similar to binary fission.

Important Points

• Comparison of Ribosomes: In a eukaryotic cell, the cytoplasmic ribosomes are 80S (composed of 60S and 40S subunits), whereas the organellar ribosomes (mitochondrial and plastidial) are 70S (composed of 50S and 30S subunits).
• DNA Type: The DNA found in these organelles is typically naked (not associated with histone proteins) and circular, mirroring the structure of plasmid DNA in bacteria.
• Energy Transformation: While mitochondria convert chemical energy (glucose) into metabolic energy (ATP), chloroplasts convert solar energy into chemical energy (sugar).

The correct answer is 14 u.

Key Points

• The molecular mass of a substance is the sum of the atomic masses of all the atoms in a molecule of that substance. It is therefore the relative mass of a molecule expressed in atomic mass units (u).
• In the given problem, the total molecular mass of the compound is 63 u. The compound consists of one hydrogen atom, three oxygen atoms, and one unknown element.
• The atomic mass of Hydrogen (H) is 1 u. Since there is one hydrogen atom, its contribution to the total mass is 1 u.
• The atomic mass of Oxygen (O) is 16 u. Since the compound contains three oxygen atoms, their total contribution is calculated as 3 x 16 u = 48 u.
• To find the atomic mass of the remaining element, we subtract the masses of the known components from the total molecular mass: 63 u - (1 u + 48 u) = 63 u - 49 u = 14 u. Hence, the calculated mass is 14 u.
• The element that possesses an atomic mass of 14 u is Nitrogen (N). Therefore, the compound is Nitric Acid, which has the chemical formula HNO3. Hence, the correct option is 14 u.

Additional Information

• Nitric Acid (HNO3):
• It is a highly corrosive mineral acid, also known as aqua fortis or the spirit of niter.
• In its pure form, it is colorless, but older samples tend to acquire a yellow cast due to decomposition into oxides of nitrogen and water.
• It is widely used in the manufacture of fertilizers (like ammonium nitrate), explosives (like TNT and nitroglycerin), and in metal refining.
• Atomic Mass Unit (u):
• The atomic mass unit is defined as a mass exactly equal to one-twelfth (1/12th) of the mass of one carbon-12 atom.
• The unified atomic mass unit (u) has replaced the older amu designation in modern scientific literature.
• It allows chemists to calculate formula mass and molar mass, facilitating the study of stoichiometry in chemical reactions.
• Characteristics of constituent elements:
• Hydrogen: The lightest element in the periodic table with atomic number 1. It usually exists as a diatomic gas (H2).
• Oxygen: A highly reactive nonmetal and oxidizing agent. It is the third-most abundant element in the universe by mass.
• Nitrogen: A colorless, odorless gas that makes up about 78% of Earth's atmosphere. It is essential for life as a component of amino acids and DNA.

Important Points

• Calculation Summary:
• Total Mass: 63
• Mass of H: 1
• Mass of 3 O: 48 (3 x 16)
• Equation: 1 + X + 48 = 63
• Result: X = 14
• Comparison with other options:
• 32 u is the atomic mass of Sulfur (S). If the element were sulfur, the molecular mass would have been 81 u (HSO3 - hypothetical radical).
• 16 u is the atomic mass of Oxygen (O).
• 12 u is the atomic mass of Carbon (C). For a compound like HCO3 (Bicarbonate), the mass would be 61 u.
• Date of Discovery: Nitric acid was first synthesized by the alchemist Jabir ibn Hayyan around 800 AD. Its composition was accurately determined by Henry Cavendish in 1785.

The correct answer is The screen should be placed 80 cm from the lens.

Key Points

• A convex lens is a converging lens. According to the lens formula, 1/v - 1/u = 1/f, where f is the focal length, u is the object distance, and v is the image distance.
• In the given problem, the focal length (f) of the convex lens is +40 cm and the object distance (u) is -80 cm (since the object is placed to the left of the lens).
• By substituting these values into the lens formula: 1/v - 1/(-80) = 1/40, which simplifies to 1/v + 1/80 = 1/40. Solving for v, we get 1/v = 1/40 - 1/80, which equals 1/80. Thus, v = +80 cm.
• The positive sign indicates that the image is formed on the right side of the lens at a distance of 80 cm. This is exactly where the screen should be placed to capture the image. Hence, the statement that the screen should be placed 80 cm from the lens is correct.
• The magnification (m) is given by the ratio v/u. Here, m = 80 / (-80) = -1. A magnification of -1 signifies that the image is real, inverted, and of the same size as the object.
• This specific condition occurs when the object is placed at 2f (twice the focal length). Since f = 40 cm, 2f = 80 cm. When an object is at 2f, the image is always formed at 2f on the opposite side.

Additional Information

• Nature of Convex Lens:
• A convex lens is thicker at the center than at the edges. It converges parallel rays of light passing through it to a point called the principal focus.
• The power of a convex lens is positive, measured in Diopters (D), and is calculated as the reciprocal of the focal length in meters (P = 1/f).
• Image Formation Rules for Convex Lenses:
• If the object is at infinity, the image is formed at the focus (F), and it is highly diminished and real.
• If the object is beyond 2F, the image is formed between F and 2F on the other side, and it is diminished, real, and inverted.
• If the object is at 2F, the image is formed at 2F on the other side, and it is the same size, real, and inverted.
• If the object is between F and 2F, the image is formed beyond 2F, and it is magnified, real, and inverted.
• If the object is at F, the image is formed at infinity.
• If the object is between the optical center and F, the image is virtual, erect, and magnified on the same side as the object.

Important Points

• Sign Convention: According to the New Cartesian Sign Convention, distances measured in the direction of incident light (to the right of the optical center) are taken as positive, while distances measured against the direction of incident light (to the left) are negative.
• Real vs Virtual Image: A real image is formed when light rays actually intersect and can be projected onto a screen. An inverted image always accompanies a real image in single-lens systems.
• Applications: Convex lenses are used in eyeglasses to correct hypermetropia (farsightedness), in cameras, microscopes, and telescopes to magnify or focus images.
• Focal Length Fact: For the same material, a lens with more curvature (thicker) has a shorter focal length and higher optical power compared to a flatter lens.

The correct answer is 1 ohm.

Key Points

• The relationship between voltage, current, and resistance in an electrical circuit is defined by Ohm's Law, which states that the current flowing through a conductor is directly proportional to the potential difference applied across its ends, provided physical conditions like temperature remain constant.
• Mathematically, Ohm's Law is expressed as V = IR, where V is the potential difference, I is the current, and R is the resistance of the conductor.
• In this specific problem, the given potential difference (V) is 1 volt and the electric current (I) is 1 ampere.
• To calculate the resistance, we use the formula R = V / I. Substituting the values: R = 1 volt / 1 ampere.
• The resulting calculation gives R = 1 ohm. This implies that 1 ohm is the resistance of a conductor when a potential difference of 1 volt results in a current of 1 ampere. Hence, the correct option is 1 ohm.

Additional Information

• Electrical Resistance (R):
• Resistance is the property of a conductor by virtue of which it opposes the flow of electric current through it.
• The SI unit of resistance is the Ohm, represented by the Greek symbol Ω (omega).
• The value of resistance depends on the length of the conductor, its area of cross-section, the nature of the material, and the temperature.
• Georg Simon Ohm:
• The law and the unit of resistance are named after the German physicist Georg Simon Ohm, who published his findings in 1827.
• His work was fundamental in the development of the theory of electricity and circuits.
• Potential Difference (V):
• It is defined as the work done to move a unit charge from one point to another in an electric field. Its SI unit is the Volt.
• A device used to measure potential difference is called a voltmeter, which is always connected in parallel across the points where the voltage is to be measured.
• Electric Current (I):
• It is the rate of flow of electric charges (usually electrons) through a conductor. The SI unit is the Ampere.
• An ammeter is used to measure current in a circuit and is always connected in series.

Important Points

• Ohmic and Non-Ohmic Conductors:
• Ohmic Conductors: Materials that obey Ohm's Law (where V is proportional to I) are called ohmic. Examples include copper, silver, and aluminum. Their V-I graph is a straight line.
• Non-Ohmic Conductors: Devices that do not follow Ohm's Law are non-ohmic. Examples include semiconductors, diodes, transistors, and vacuum tubes.
• Resistivity (ρ):
• While resistance changes with shape, resistivity is a characteristic property of the material. It is measured in ohm-meter (Ωm).
• Insulators like glass and rubber have very high resistivity (10^12 to 10^17 Ωm), whereas metals have low resistivity (10^-8 to 10^-6 Ωm).
• Effect of Temperature:
• For pure metals, resistance increases with an increase in temperature. However, for semiconductors like silicon and germanium, resistance decreases as temperature increases.

The correct answer is They converge at a point on the opposite side of the lens.

• A convex lens is also known as a converging lens because of its ability to bring parallel rays of light together after refraction.
• When rays of light travel parallel to the principal axis and strike the surface of a convex lens, they are bent inward toward the center of the lens. This occurs because the lens is thicker at the middle than at the edges.
• According to the laws of refraction, these parallel rays intersect at a single point on the principal axis on the opposite side of the lens. This specific point is known as the Principal Focus (F). Hence, statement 3 is correct.
• If rays were to pass without any deviation, it would mean the lens has no refractive power or the ray is passing exactly through the optical center. Hence, statement 1 is incorrect.
• Rays meet at infinity only when the source of light is placed exactly at the focus of the lens, creating a parallel beam after refraction. Hence, statement 2 is incorrect.
• Rays diverge as if coming from the principal focus in the case of a concave lens, which is a diverging lens. Hence, statement 4 is incorrect.
• Structure of Convex Lens: A convex lens is usually made of glass or transparent plastic and is bounded by two spherical surfaces bulging outwards. It can be categorized into double convex (bi-convex), plano-convex, and concavo-convex lenses.
• Image Formation: Depending on the position of the object, a convex lens can form both real and inverted images or virtual and erect images. For instance, when an object is placed beyond the focus, the image formed is real.
• Focal Length: The distance between the optical center of the lens and the principal focus is called the focal length (f). For a convex lens, the focal length is traditionally taken as positive in the Cartesian sign convention.
• Applications: Because of its converging properties, the convex lens is widely used in magnifying glasses, microscopes, telescopes, and camera lenses.
• Medical Use: In ophthalmology, convex lenses are used in spectacles to correct Hypermetropia (long-sightedness), where the eye cannot focus on nearby objects because the image forms behind the retina.

Important Points

• Power of a Lens: The degree of convergence or divergence of light rays achieved by a lens is expressed as its Power (P). It is the reciprocal of the focal length (P = 1/f). The SI unit of power is the Dioptre (D).
• Optical Center: This is the central point of the lens. Any ray of light passing through the optical center emerges without any deviation from its original path.
• Refraction Basics: The phenomenon of bending light occurs due to the change in the speed of light when it moves from one medium (like air) to another (like glass). This is governed by Snell's Law.
• Aperture: The effective diameter of the light-transmitting area of the lens is called the aperture. It determines the intensity of the light passing through and the brightness of the resulting image.

The correct answer is Cracking of voice.

Key Points

• Sexual maturation in human males is primarily driven by the onset of puberty, typically occurring between the ages of 11 and 16 years.
• One of the most distinct physical changes is the Cracking of voice. This happens because the Larynx (voice box) grows significantly larger during this period. Hence, statement 2 is correct.
• As the Larynx grows, it begins to protrude at the front of the neck, forming what is commonly known as the Adam's apple.
• During this transition, the Vocal Cords become longer and thicker. Before they fully adjust to the new size, the voice may "crack" or fluctuate between high and low pitches before settling into a deeper tone.
• While an Increase in weight and Increase in height occur during the adolescent growth spurt, they are general developmental changes seen in both sexes and are not exclusive indicators of male sexual maturation. Hence, statements 3 and 4 are not the most specific answers for sexual maturation.
• Deposition of fat in hips is a secondary sexual characteristic typically associated with female maturation to facilitate childbirth. Hence, statement 1 is incorrect.

Additional Information

• Testosterone: This is the primary androgen (male sex hormone) secreted by the Testes. It is responsible for the development of male Secondary Sexual Characteristics and the stimulation of Spermatogenesis (production of sperm).
• Secondary Sexual Characteristics in Males: These include the appearance of facial hair (mustache and beard), pubic hair, axillary hair (underarm), and the broadening of the shoulders and chest.
• Pituitary Gland: The process of maturation begins when the Pituitary Gland releases Luteinizing Hormone (LH) and Follicle-Stimulating Hormone (FSH), which signal the testes to produce testosterone.
• Physical Composition: Unlike females, who experience fat deposition in the pelvic region, males typically experience an increase in Muscle Mass and a decrease in body fat percentage relative to muscle during puberty.
• Primary vs. Secondary Characteristics: Primary characteristics are the reproductive organs themselves (testes, penis), while Secondary characteristics (like voice deepening) are the physical signs of sexual maturity that do not involve the reproductive tract directly.

Important Points

• Timing: The onset of these changes can vary based on Genetics, Nutrition, and Environmental factors. In recent decades, studies have shown a slight trend toward earlier onset of puberty in some populations.
• Growth Spurt: The Peak Height Velocity (PHV) in boys usually occurs about two years later than in girls. During this time, bones grow rapidly, and the Epiphyseal plates eventually close, marking the end of height growth.
• Skin Changes: Increased activity of Sebaceous Glands (oil glands) often leads to Acne during the phase of sexual maturation due to hormonal fluctuations.

Shortcut Trick

The age difference between two people remains constant throughout their lives.

Ratio 5 years ago (Priya : Meera) = 3 : 2 → Difference in ratio units = 3 − 2 = 1 unit.

Given, 1 unit = 10 years. ∴ Meera's age 5 years ago = 2 × 10 = 20 years.

Meera's present age = 20 + 5 = 25 years.

∴ The correct answer is 25 years.

Alternate Method

Given:

Ratio of Priya and Meera (5 years ago) = 3 : 2

Difference in their present ages = 10 years

Calculations:

⇒ Let ages 5 years ago be 3x and 2x.

⇒ Present age of Priya = 3x + 5

⇒ Present age of Meera = 2x + 5

⇒ Difference = (3x + 5) − (2x + 5) = 10

⇒ x = 10

⇒ Meera's present age = 2(10) + 5

⇒ Meera's present age = 20 + 5 = 25 years

∴ The correct answer is 25 years.

Additional Information

Constant Difference Rule

The difference between the ages of two people is always constant, whether it is 10 years ago, present, or 10 years in the future.

Ratio Scaling

If the difference in ratio units is 'd' and the actual difference is 'D', then 1 ratio unit = D/d. This multiplier is used to find all related age values.

Shortcut Trick

Convert bases to 2: 16 = 2⁴ and 64 = 2⁶.

Equate the exponents: 3y + x = 4 and 2y − x = 6.

Add both equations to eliminate x: 5y = 10.

Solve for y: y = 2.

∴ The correct answer is 2.

Alternate Method

Given:

2^{3y + x} = 16

2^{2y − x} = 64

Formula Used:

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

Calculations:

⇒ 2^{3y + x} = 2⁴

⇒ 3y + x = 4 ---(Equation 1)

⇒ 2^{2y − x} = 2⁶

⇒ 2y − x = 6 ---(Equation 2)

⇒ Adding (Equation 1) and (Equation 2):

⇒ (3y + x) + (2y − x) = 4 + 6

⇒ 5y = 10

⇒ y = 10 ÷ 5

⇒ y = 2

∴ The correct answer is 2.

Additional Information

Laws of Indices

When the bases are equal, their powers can be equated. Also, a^m × aⁿ = a^m+n and (a^m)ⁿ = a^m×n.

Linear Equations in Two Variables

To find the value of one variable, use the elimination method by adding or subtracting equations to remove the other variable.

Powers of 2

Recognizing standard powers like 2⁴ = 16, 2⁵ = 32, and 2⁶ = 64 is essential for quick calculation in exponential equations.

Shortcut Trick

Ratio of speeds S_A : S_B = 100 : 150 = 2 : 3.

Using the meeting point formula: S_A / S_B = √(T_B / T_A).

2 / 3 = √(p / 90.9)

Squaring both sides: 4 / 9 = p / 90.9

p = 4 × 10.1 = 40.4 hours.

∴ The correct answer is 40.4 hours.

Alternate Method

Given:

Time taken by A after meeting (T_A) = 90.9 hours

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

Speed of B (S_B) = 1.5 × Speed of A (S_A)

Formula Used:

For two objects starting simultaneously from opposite ends and meeting at a point, the ratio of their speeds is inversely proportional to the square root of the time taken to reach the opposite destinations after meeting: S_A / S_B = √(T_B / T_A)

Calculations:

⇒ S_A / S_B = 1 / 1.5 = 1 / (3/2) = 2/3

⇒ 2/3 = √(p / 90.9)

⇒ (2/3)² = p / 90.9

⇒ 4 / 9 = p / 90.9

⇒ p = (4 × 90.9) ÷ 9

⇒ p = 4 × 10.1

⇒ p = 40.4

∴ The correct answer is 40.4 hours.

Additional Information

Meeting Point Time

The time when they meet (T_M) is given by the geometric mean of the remaining times: T_M = √(T_A × T_B).

Relative Speed

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

Speed-Time Relationship

For a constant distance, speed is inversely proportional to time (S ∝ 1/T).

Shortcut Trick

Let Total Work (LCM of 10 and 15) = 30 units.

Efficiency of M = 3; Efficiency of N = 2.

Work done by M + N in 5 minutes = (3 + 2) × 5 = 25 units.

Remaining work = 30 − 25 = 5 units, filled by N in 5 ÷ 2 = 2.5 minutes.

Total time = 5 + 2.5 = 7.5 minutes.

∴ The correct answer is 7.5 min.

Alternate Method

Given: Time for Pipe M = 10 min, Time for Pipe N = 15 min.

Calculations:

⇒ Both pipes M and N opened for first 5 minutes.

⇒ Work done in 5 min = (Efficiency of M + Efficiency of N) × 5

⇒ Work done = (3 + 2) × 5 = 25 units

⇒ Remaining work = Total Work − Completed Work = 30 − 25 = 5 units

⇒ Time taken by Pipe N to fill remaining part = 5 ÷ 2 = 2.5 minutes

⇒ Total time required = 5 min + 2.5 min = 7.5 minutes

∴ The correct answer is 7.5 min.

Additional Information

Pipes & Cisterns Efficiency

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

Inlet and Outlet Pipes

Inlet pipe efficiency is taken as positive (+), while outlet (leakage) pipe efficiency is taken as negative (−).

Total Work Concept

Total work is the LCM of individual times taken by the pipes to fill or empty the tank independently.

Shortcut Trick

Bina SP (Shyam CP) = 81% of Bina CP = ₹4,860.

Bina CP = 4,860 ÷ 0.81 = ₹6,000.

Shyam SP (Bina 17% Profit Price) = 117% of 6,000 = ₹7,020.

Shyam Profit = Shyam SP − Shyam CP = 7,020 − 4,860 = ₹2,160.

∴ The correct answer is ₹2,160.

Alternate Method

Given → Bina SP = ₹4,860, Bina Loss = 19%, Target Profit = 17%. Formulas: CP = SP × 100 ÷ (100 − Loss%), New SP = CP × (100 + Profit%) ÷ 100.

⇒ Cost Price (CP) of article for Bina = 4,860 × 100 ÷ (100 − 19) = 4,860 × 100 ÷ 81 = ₹6,000. ⇒ Selling Price (SP) for Shyam (Bina 17% profit price) = 6,000 × 117 ÷ 100 = ₹7,020. ⇒ Cost Price (CP) for Shyam = ₹4,860. ⇒ Profit for Shyam = 7,020 − 4,860 = ₹2,160.

∴ The correct answer is ₹2,160.

Additional Information

Chain Sale Calculations

In chain sales, the Selling Price for one person becomes the Cost Price for the next person in the sequence.

Profit and Loss Relation

SP = CP × (100 ± Gain/Loss)% ÷ 100. Always calculate the profit or loss percentage on the Cost Price unless stated otherwise.

Shortcut Trick

Ratio of Cost Price (CP) to Marked Price (MP) is given by (100 − Discount%) : (100 + Profit%).

CP : MP = (100 − 20) : (100 + 10) = 80 : 110 = 8 : 11.

Given MP = 11 units = 880, so 1 unit = 880 ÷ 11 = 80.

CP = 8 units = 8 × 80 = 640.

∴ The correct answer is ₹ 640.

Alternate Method

Given: Marked Price (MP) = ₹ 880, Discount = 20%, Profit = 10%.

Formulas: SP = MP × (100 − Discount%) ÷ 100 | CP = SP × 100 ÷ (100 + Profit%).

⇒ Selling Price (SP) = 880 × (100 − 20) ÷ 100 = 880 × 0.8 = ₹ 704.

⇒ Cost Price (CP) = 704 × 100 ÷ (100 + 10) = 704 × 100 ÷ 110.

⇒ CP = 7040 ÷ 11 = ₹ 640.

∴ The correct answer is ₹ 640.

Additional Information

Marked Price & Discount

The Marked Price is the price listed on the label. Discount is always calculated on the MP to arrive at the Selling Price (SP).

Relation between CP and MP

When both profit percentage and discount percentage are known, use the direct relation CP/MP = (100 − D%)/(100 + P%).

Shortcut Trick

Apply the Empirical Formula: Mode = 3 × Median − 2 × Mean.

46.2 = 3 × 40 − 2 × Mean

46.2 = 120 − 2 × Mean

2 × Mean = 120 − 46.2 = 73.8

Mean = 36.9

∴ The correct answer is 36.9.

Alternate Method

Given:

Mode = 46.2

Median = 40

Formula Used:

The relationship between the three measures of central tendency is given by: Mode = 3(Median) − 2(Mean)

Calculations:

⇒ 46.2 = 3 × 40 − 2 × Mean

⇒ 46.2 = 120 − 2 × Mean

⇒ 2 × Mean = 120 − 46.2

⇒ 2 × Mean = 73.8

⇒ Mean = 73.8 ÷ 2

⇒ Mean = 36.9

∴ The correct answer is 36.9.

Additional Information

Empirical Formula

It is used for moderately skewed distributions where the relationship is Mode = 3 Median − 2 Mean.

Symmetric Distribution

In a perfectly symmetrical distribution (like the Normal Distribution), Mean = Median = Mode.

Mean Calculation

Mean can also be calculated as Mean = Median − (Mode − Median) ÷ 2, which is a derivation of the same formula.

Skewness Relation

If Mean > Median > Mode, the data is positively skewed; if Mode > Median > Mean, the data is negatively skewed.

Shortcut Trick

Using Alligation method: Difference between Type A (30%) and Mean (42%) is 12.

Difference between Type B (50%) and Mean (42%) is 8.

Ratio of A : B = 8 : 12 = 2 : 3.

Total parts = 2 + 3 = 5 parts = 20 kg → 1 part = 4 kg.

Type A = 2 × 4 = 8 kg and Type B = 3 × 4 = 12 kg.

∴ The correct answer is 8 kg of A, 12 kg of B.

Alternate Method

Given: Total mixture = 20 kg, Nitrogen required = 42%. Nitrogen in A = 30%, Nitrogen in B = 50%.

⇒ Ratio of quantity of A to B = 8 : 12 = 2 : 3.

⇒ Let the quantities be 2x and 3x.

⇒ 2x + 3x = 20 kg

⇒ 5x = 20 kg ⇒ x = 4 kg.

⇒ Quantity of Fertiliser A = 2 × 4 = 8 kg.

⇒ Quantity of Fertiliser B = 3 × 4 = 12 kg.

∴ The correct answer is 8 kg of A, 12 kg of B.

Additional Information

Alligation Rule

It states that (Quantity of Cheaper / Quantity of Dearer) = (CP of Dearer − Mean Price) / (Mean Price − CP of Cheaper).

Weighted Average Formula

The final concentration C = (n₁c₁ + n₂c₂) / (n₁ + n₂), where n is quantity and c is concentration.

Mixture Applications

This method is widely used in profit/loss, average speed, simple interest rates, and solution concentrations.

Shortcut Trick

Product of H.C.F. and L.C.M. = Product of the two numbers.

Other number = (18 × 1296) ÷ 162

Other number = 1296 ÷ 9 = 144

∴ The correct answer is 144.

Alternate Method

Given:

H.C.F. = 18

L.C.M. = 1296

First Number (A) = 162

Formula Used:

H.C.F. × L.C.M. = A × B

Calculations:

⇒ 18 × 1296 = 162 × B

⇒ B = (18 × 1296) ÷ 162

⇒ B = 23328 ÷ 162

⇒ B = 144

∴ The correct answer is 144.

Additional Information

H.C.F. and L.C.M. Property

For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b. This property holds true only for two numbers.

Co-prime Numbers

If two numbers are co-prime, their H.C.F. is always 1 and their L.C.M. is equal to the product of the two numbers.

H.C.F. of Fractions

H.C.F. = (H.C.F. of Numerators) ÷ (L.C.M. of Denominators).

L.C.M. of Fractions

L.C.M. = (L.C.M. of Numerators) ÷ (H.C.F. of Denominators).

Shortcut Trick

Surface Area of Sphere = 4πr² = 5544 cm².

r² = 5544 ÷ (4 × 22/7) = 5544 × 7 ÷ 88 = 441.

r = √441 = 21 cm.

Diameter = 2r = 2 × 21 = 42 cm.

∴ The correct answer is 42 cm.

Alternate Method

Given: Surface Area of sphere = 5544 cm², π = 22/7.

Formula Used: Surface Area of Sphere = 4πr² and Diameter (d) = 2r.

⇒ 4 × (22/7) × r² = 5544

⇒ r² = (5544 × 7) ÷ (4 × 22)

⇒ r² = (5544 × 7) ÷ 88

⇒ r² = 63 × 7 = 441

⇒ r = √441 = 21 cm

⇒ Diameter = 2 × 21 = 42 cm

∴ The correct answer is 42 cm.

Additional Information

Volume of a Sphere

The total space occupied by a sphere is given by Volume = (4/3)πr³.

Hemisphere Properties

For a hemisphere of radius r, Curved Surface Area = 2πr² and Total Surface Area = 3πr².

Relation between Radius and Diameter

The diameter is the longest chord of a sphere passing through the center, where d = 2r.

Shortcut Trick

When A finishes the race in 36 seconds, B is still running and takes 9 more seconds (45 − 36) to finish.

Distance B covers in those 9 seconds is the distance by which A beats B.

Distance = (Total Distance ÷ B's Time) × Time Difference

Distance = (100 ÷ 45) × 9 = 20 m.

∴ The correct answer is 20 metres.

Alternate Method

Given:

Distance = 100 m

Time taken by A = 36 seconds

Time taken by B = 45 seconds

Formula Used:

Speed = Distance ÷ Time

Distance = Speed × Time

Calculations:

⇒ Speed of B = 100 ÷ 45 m/s

⇒ Speed of B = 20/9 m/s

⇒ Distance covered by B in 36 seconds = (20/9) × 36

⇒ Distance covered by B = 20 × 4 = 80 m

⇒ Distance by which A beats B = Total Distance − Distance covered by B in 36 seconds

⇒ Beating distance = 100 − 80 = 20 m

∴ The correct answer is 20 metres.

Additional Information

Beating by Distance

If A beats B by x metres, it means when A reaches the finish line, B is x metres behind.

Beating by Time

If A beats B by t seconds, it means B takes t more seconds than A to complete the same distance.

Relative Speed in Races

In a linear race starting at the same time, the ratio of distances covered is equal to the ratio of their speeds: D₁/D₂ = S₁/S₂.

Shortcut Trick

Ratio of Expenditure to Savings = 275 : 100 = 11 : 4

Net change in Income = [(11 × −12) + (4 × 40.5)] ÷ (11 + 4)

Net change = [−132 + 162] ÷ 15 = 30 ÷ 15 = 2%

∴ The correct answer is 2%.

Alternate Method

Given: Expenditure is 175% more than Savings.

Formula Used: Income = Expenditure + Savings

⇒ Let Savings = 100 units

⇒ Expenditure = 100 + 175 = 275 units

⇒ Initial Income = 275 + 100 = 375 units

⇒ New Expenditure (12% decrease) = 275 − (12% of 275) = 275 − 33 = 242 units

⇒ New Savings (40.5% increase) = 100 + 40.5 = 140.5 units

⇒ New Income = 242 + 140.5 = 382.5 units

⇒ Increase in Income = 382.5 − 375 = 7.5 units

⇒ Percentage Increase = (7.5 ÷ 375) × 100 = 2%

∴ The correct answer is 2%.

Additional Information

Percentage Change Rule

Income change can be calculated using the weighted average of expenditure and savings changes: %ΔI = (%ΔE × E + %ΔS × S) ÷ (E + S).

Base Value Concept

Always identify the base correctly; "175% more than x" means the new value is 2.75x, whereas "175% of x" means 1.75x.

Shortcut Trick

Effective Compound Interest rate for 2 years at 10% = 10 + 10 + (10 × 10)/100 = 21%.

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

Amount = 1.21 × 3,300 = 3,993.

∴ The correct answer is ₹ 3,993.

Alternate Method

Given:

Principal (P) = ₹ 3,300

Rate of Interest (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 3300(1 + 10/100)²

⇒ A = 3300(1 + 1/10)²

⇒ A = 3300(11/10)²

⇒ A = 3300 × (121/100)

⇒ A = 33 × 121

⇒ A = 3,993

∴ The correct answer is ₹ 3,993.

Additional Information

Effective Rate for Successive Periods

The effective interest rate for two successive periods with rates r₁ and r₂ is given by [r₁ + r₂ + (r₁ × r₂)/100]%.

Compound Interest Formula

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

Difference between CI and SI

For 2 years, the difference between CI and SI = P(R/100)².

Shortcut Trick

Compare the amounts: ₹ 13,600 is exactly double of ₹ 6,800.

Since Price and Quantity are directly proportional, the number of stands will also double.

⇒ Number of stands = 34 × 2 = 68

∴ The correct answer is 68 mobile stands.

Alternate Method

Given: Cost Price of 34 mobile stands = ₹ 6,800. New Total Amount = ₹ 13,600.

Formula Used: Unitary Method (Value of 1 item = Total Cost ÷ Total Quantity)

⇒ Cost of 1 mobile stand = 6,800 ÷ 34

⇒ Cost of 1 mobile stand = ₹ 200

⇒ Number of stands for ₹ 13,600 = 13,600 ÷ 200

⇒ Number of stands = 68

∴ The correct answer is 68 mobile stands.

Additional Information

Direct Proportion

When two quantities increase or decrease together at the same rate, they are in direct proportion (x/y = k).

Unitary Method

A technique used to find the value of a single unit first, and then multiply by the desired quantity to find the final value.

Inverse Proportion

When one quantity increases while the other decreases (e.g., speed and time), the product remains constant (x × y = k).

Shortcut Trick

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

Here, a = 2% and b = 21%.

Equivalent Discount = 2 + 21 − (2 × 21) ÷ 100.

Equivalent Discount = 23 − 42 ÷ 100 = 23 − 0.42 = 22.58%.

∴ The correct answer is 22.58%.

Alternate Method

Given: First discount = 2%, Second discount = 21%.

Formula: Single equivalent discount = [1 − (1 − d₁/100) × (1 − d₂/100)] × 100

⇒ Let the Marked Price (MP) be 100.

⇒ Price after 1st discount = 100 − 2% of 100 = 98.

⇒ Price after 2nd discount = 98 − 21% of 98 = 98 − 20.58 = 77.42.

⇒ Total Discount = 100 − 77.42 = 22.58.

⇒ Discount percentage = (22.58 ÷ 100) × 100 = 22.58%.

∴ The correct answer is 22.58%.

Additional Information

Successive Discounts

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

Effective Discount Rate

For three successive discounts a%, b%, and c%, the net discount can be calculated by applying the formula twice or using the multiplier method: 1 − [(100−a)/100 × (100−b)/100 × (100−c)/100].

Shortcut Trick

Use identities: sec² A = 1 + tan² A and cosec² A = 1 + cot² A.

Substitute these into the given equation: (1 + tan² A) + (1 + cot² A) = 13.

⇒ 2 + tan² A + cot² A = 13.

⇒ tan² A + cot² A = 13 − 2 = 11.

∴ The correct answer is 11.

Alternate Method

Given: sec² A + cosec² A = 13

Formula Used: 1 + tan² θ = sec² θ | 1 + cot² θ = cosec² θ

⇒ sec² A + cosec² A = 13

⇒ (1 + tan² A) + (1 + cot² A) = 13

⇒ 1 + 1 + tan² A + cot² A = 13

⇒ 2 + tan² A + cot² A = 13

⇒ tan² A + cot² A = 13 − 2

⇒ tan² A + cot² A = 11

∴ The correct answer is 11.

Additional Information

Trigonometric Identities

Fundamental identities include sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Reciprocal Relations

tan θ = 1 / cot θ and sec θ = 1 / cos θ, which are useful for simplifying algebraic expressions in trigonometry.

Product Form of sec and cosec

Note that sec² A + cosec² A is also equal to sec² A × cosec² A.

Shortcut Trick

Outer radius R = 5 cm, Inner radius r = 3 cm, Length h = 21 cm.

Total Surface Area = 2π(R + r)(h + R − r)

⇒ 2π(5 + 3)(21 + 5 − 3) = 2π × 8 × 23

⇒ 16 × 23 × π = 368π cm².

∴ The correct answer is 368π cm².

Alternate Method

Given:

Outer Diameter = 10 cm ⇒ Outer Radius (R) = 5 cm

Inner Diameter = 6 cm ⇒ Inner Radius (r) = 3 cm

Length of pipe (h) = 21 cm

Formula Used:

Total Surface Area (TSA) of a hollow cylinder = CSA_outer + CSA_inner + 2 × Area of circular rings

TSA = 2πRh + 2πrh + 2π(R² − r²)

Calculations:

⇒ TSA = 2πh(R + r) + 2π(R + r)(R − r)

⇒ TSA = 2π(R + r) [h + R − r]

⇒ TSA = 2π(5 + 3) [21 + 5 − 3]

⇒ TSA = 2π(8) [23]

⇒ TSA = 16π × 23

⇒ TSA = 368π cm²

∴ The correct answer is 368π cm².

Additional Information

Volume of Hollow Cylinder

The space occupied by the material is Volume = π(R² − r²)h.

Curved Surface Area

The total curved area (inner + outer) is 2πh(R + r).

Area of Cross-section

The area of the base ring is π(R² − r²).

Shortcut Trick

Combined efficiency (P + Q) = 1/3 and P efficiency = 1/12.

Q efficiency = 1/3 − 1/12 = 3/12 = 1/4 cistern per hour.

Time for Q to fill 1/4 cistern = (1/4 cistern) ÷ (1/4 cistern/hour) = 1 hour.

∴ The correct answer is 1 hour.

Alternate Method

Given: Time (P + Q) = 3 hours, Time (P) = 12 hours.

Formula Used: Total Work = LCM of time; Efficiency = Total Work ÷ Time.

⇒ Efficiency of Q = Efficiency of (P + Q) − Efficiency of P

⇒ Efficiency of Q = 4 − 1 = 3 units/hour

⇒ Required work = 1/4 of total work = 1/4 × 12 = 3 units

⇒ Time taken by Q = Required work ÷ Efficiency of Q = 3 ÷ 3 = 1 hour

∴ The correct answer is 1 hour.

Additional Information

Pipes & Cisterns Efficiency

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

Inlet and Outlet Pipes

Inlet pipes have positive efficiency (+), while outlet pipes (leaks) have negative efficiency (−).

Combined Work Formula

If A takes 'a' days and B takes 'b' days, together they take (a × b) ÷ (a + b) days.

Shortcut Trick

Expenditure = 75% → Savings = 100% − 75% = 25%

25% of Income = ₹ 10,000

Income (100%) = 10,000 × 4 = ₹ 40,000

∴ The correct answer is ₹ 40,000.

Alternate Method

Given:

Monthly Expenditure = 75% of Monthly Income

Monthly Savings = ₹ 10,000

Formula Used:

Income = Expenditure + Savings

Calculations:

⇒ Let the total Monthly Income be 100 units.

⇒ Expenditure = 75% of 100 = 75 units.

⇒ Savings = 100 − 75 = 25 units.

⇒ According to the question, 25 units = ₹ 10,000.

⇒ 1 unit = 10,000 ÷ 25 = ₹ 400.

⇒ Total Monthly Income = 100 × 400 = ₹ 40,000.

∴ The correct answer is ₹ 40,000.

Additional Information

Percentage Change

To find the percentage of a value: (Value ÷ Base) × 100. In income problems, Income is always the base (100%).

Ratio Representation

75% can be written as 3/4. This means for every ₹ 4 of Income, ₹ 3 is Expenditure and ₹ 1 is Savings.

Successive Percentage

If income increases by x% and expenditure increases by y%, the new savings are calculated using the Net Change formula or component-wise calculation.

Shortcut Trick

Let x = p − q, y = q − r, and z = r − p.

Observe that their sum is x + y + z = (p − q) + (q − r) + (r − p) = 0.

According to the algebraic property, if x + y + z = 0, then x³ + y³ + z³ = 3xyz.

The numerator becomes 3(p − q)(q − r)(r − p), which when divided by the denominator (p − q)(q − r)(r − p), equals 3.

∴ The correct answer is 3.

Alternate Method

Given: The expression to simplify is ((p − q)³ + (q − r)³ + (r − p)³) ÷ ((p − q)(q − r)(r − p)).

Formula Used: a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca).

⇒ Let a = p − q, b = q − r, and c = r − p.

⇒ First, calculate a + b + c = (p − q) + (q − r) + (r − p) = 0.

⇒ Substituting a + b + c = 0 into the algebraic identity:

⇒ a³ + b³ + c³ − 3abc = 0 × (a² + b² + c² − ab − bc − ca) = 0.

⇒ Therefore, a³ + b³ + c³ = 3abc.

⇒ The given expression simplifies to [3(p − q)(q − r)(r − p)] ÷ [(p − q)(q − r)(r − p)].

⇒ By cancelling common terms, the result is 3.

∴ The correct answer is 3.

Additional Information

Algebraic Identity for Three Variables

The formula a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) is a fundamental polynomial identity used in factorization.

Conditional Cube Identity

A special case arises when a + b + c = 0; in this scenario, the sum of cubes a³ + b³ + c³ is always equal to 3abc.

Square of a Trinomial

Relatedly, the square of a trinomial is given by (a + b + c)² = a² + b² + c² + 2(ab + bc + ca).

Shortcut Trick

Let the total salary be S.

Using the multiplying factor for successive deductions: S × 0.9 × 0.8 × 0.8 × 0.9 = 23328

S × (9/10) × (4/5) × (4/5) × (9/10) = 23328

S × (1296 / 2500) = 23328

S = 18 × 2500 = 45000

∴ The correct answer is ₹45,000.

Alternate Method

Given: Remaining amount = ₹23,328

⇒ Let Total Salary = 100x

⇒ After House Rent (10%): 100x − 10x = 90x

⇒ After Conveyance (20% of 90x): 90x − 18x = 72x

⇒ After Income Tax (20% of 72x): 72x − 14.4x = 57.6x

⇒ After Clothes (10% of 57.6x): 57.6x − 5.76x = 51.84x

⇒ 51.84x = 23328

⇒ x = 23328 ÷ 51.84 = 450

⇒ Total Salary = 100 × 450 = 45000

∴ The correct answer is ₹45,000.

Additional Information

Successive Percentage Change

When multiple deductions are made on the remaining balance, use the formula: Final Value = Initial Value × (1 − r₁/100) × (1 − r₂/100)...

Percentage to Fraction Conversion

10% = 1/10 (Remaining = 9/10) and 20% = 1/5 (Remaining = 4/5). These fractions simplify complex calculations significantly.

Shortcut Trick

Number of diagonals = n(n − 3) ÷ 2 = 9 ⇒ n(n − 3) = 18 ⇒ n = 6 (regular hexagon)

One exterior angle of a regular hexagon = 360° ÷ 6 = 60°

One interior angle of a regular hexagon = 180° − 60° = 120°

Difference between interior and exterior angle = 120° − 60° = 60°

∴ The correct answer is 60°.

Alternate Method

Given:

The number of diagonals of a regular polygon = 9

Formula Used:

1. Number of diagonals of an n-sided polygon = n(n − 3) ÷ 2
2. Each exterior angle of a regular polygon = 360° ÷ n
3. Each interior angle of a regular polygon = 180° − (Each exterior angle)

Calculations:

⇒ n(n − 3) ÷ 2 = 9

⇒ n(n − 3) = 18

⇒ n² − 3n − 18 = 0

⇒ n² − 6n + 3n − 18 = 0

⇒ n(n − 6) + 3(n − 6) = 0

⇒ (n − 6)(n + 3) = 0

⇒ n = 6 (since the number of sides n must be positive, n ≠ −3)

Therefore, the polygon is a regular hexagon with 6 sides.

⇒ One exterior angle = 360° ÷ 6 = 60°

⇒ One interior angle = 180° − 60° = 120°

⇒ Difference = 120° − 60° = 60°

Why other options are incorrect:

Option (1) 55° is incorrect because if the difference is 55°, the interior angle would be 117.5° and the exterior angle would be 62.5°, which does not correspond to a regular polygon with integer sides.

Option (2) 70° is incorrect because if the difference is 70°, the interior angle would be 125° and the exterior angle would be 55°, which is incorrect.

Option (4) 48° is incorrect because if the difference is 48°, the interior angle would be 114° and the exterior angle would be 66°, which is incorrect.

∴ The correct answer is 60°.

Additional Information

Sum of Interior Angles

The sum of all interior angles of an n-sided polygon is given by (n − 2) × 180°.

Sum of Exterior Angles

The sum of all exterior angles of any polygon is always 360°.

Relation between Interior and Exterior Angle

At any vertex of a polygon, the interior angle and the exterior angle are supplementary, meaning their sum is 180°.

Shortcut Trick

Assume all 269 children are girls, then the total amount = 269 × 7 = ₹1883.

The difference between the actual amount and this assumed amount = 2239 − 1883 = ₹356.

This difference arises because boys get ₹2 more than girls (9 − 7 = ₹2).

Number of boys = Total Difference ÷ Extra share per boy = 356 ÷ 2 = 178.

∴ The correct answer is 178.

Alternate Method

Given:

Total children = 269

Total amount = ₹2,239

Amount per boy = ₹9 | Amount per girl = ₹7

Formula Used:

Total Amount = (Number of boys × Share per boy) + (Number of girls × Share per girl)

Let the number of boys be x.

Then, the number of girls = 269 − x.

⇒ 9 × x + 7 × (269 − x) = 2239

⇒ 9x + 1883 − 7x = 2239

⇒ 2x + 1883 = 2239

⇒ 2x = 2239 − 1883

⇒ 2x = 356

⇒ x = 356 ÷ 2

⇒ x = 178

∴ The correct answer is 178.

Additional Information

Alligation Rule

This problem can be solved using the alligation method where the mean value is 2239 ÷ 269. The ratio of boys to girls is (Mean − Girl's share) : (Boy's share − Mean).

Weighted Average

The total sum is the weighted average of individual shares: Total = (n₁w₁ + n₂w₂), where n is the count and w is the weight/share.

Linear Equations

For any two-variable problem (x + y = A and ax + by = B), substituting one variable in terms of the other is the most direct algebraic approach.

Shortcut Trick

Net Deviation Method: Assume the Average is 15.

Deviations: (6.5 − 15) + (10.7 − 15) + (20.2 − 15) + (a − 15) = 0

−8.5 − 4.3 + 5.2 + (a − 15) = 0

−7.6 + (a − 15) = 0 ⇒ a − 15 = 7.6

a = 15 + 7.6 = 22.6

∴ The correct answer is 22.6.

Alternate Method

Given:

Numbers = 6.5, 10.7, 20.2 and a

Total count of numbers (n) = 4

Average = 15

Formula Used:

Average = (Sum of all observations) ÷ (Total number of observations)

Calculations:

⇒ 15 = (6.5 + 10.7 + 20.2 + a) ÷ 4

⇒ 15 × 4 = 37.4 + a

⇒ 60 = 37.4 + a

⇒ a = 60 − 37.4

⇒ a = 22.6

∴ The correct answer is 22.6.

Additional Information

Sum of Observations

The total sum can always be calculated as Total Sum = Average × Number of terms.

Net Deviation Rule

The algebraic sum of deviations of all observations from their arithmetic mean is always zero.

Change in Average

If a constant k is added to or subtracted from every term, the new average also increases or decreases by k.

Shortcut Trick

Total amount to be deducted = 16 + 15 + 75 = ₹106.

Remaining amount = 5,398 − 106 = ₹5,292.

Ratio of remaining shares = 2 : 21 : 4 (Total units = 27).

Difference between Y and Z units = 21 − 4 = 17 units.

Difference between original shares = (Remaining difference) + (Difference in deductions) = (17/27 × 5,292) + (15 − 75) = 3,332 − 60 = ₹3,272.

∴ The correct answer is ₹3,272.

Alternate Method

Given: Total sum = ₹5,398. Deductions: X = ₹16, Y = ₹15, Z = ₹75. Ratio = 2 : 21 : 4.

⇒ Total deduction = 16 + 15 + 75 = ₹106.

⇒ Remaining sum = 5,398 − 106 = ₹5,292.

⇒ Total ratio parts = 2 + 21 + 4 = 27.

⇒ Value of 1 unit = 5,292 ÷ 27 = ₹196.

⇒ Y’s remaining share = 21 × 196 = ₹4,116.

⇒ Y’s original share = 4,116 + 15 = ₹4,131.

⇒ Z’s remaining share = 4 × 196 = ₹784.

⇒ Z’s original share = 784 + 75 = ₹859.

⇒ Required difference = 4,131 − 859 = ₹3,272.

∴ The correct answer is ₹3,272.

Additional Information

Ratio and Proportion

Ratio is a comparison of two or more quantities of the same kind. If a sum S is divided in ratio a:b:c, the shares are (a/Σratio)×S, (b/Σratio)×S, etc.

Handling Deductions

When specific amounts are deducted from shares before a ratio is applied, always subtract the total of these deductions from the total sum first.

Unitary Method

Find the value of a single 'ratio unit' by dividing the modified total amount by the sum of all ratio parts.

Given:

LEMA is coded as 5681

ALES is coded as 6513

So, the code for S = 3

Hence, the correct answer is Option 4.

The logic followed here is:

Given:

Fawad drives 13 km North

He turns right → 11 km East

He turns right → 14 km South

He turns right → 12 km West

He turns right → 1 km North

So, To reach Point A, he must go 1 km East.

Hence, the correct answer is Option 1.

Family Chart:

Decoding the Symbols:

Given: L × O # V + E @ R

It means: L is the wife of O, O is the brother of V, V is the sister of E, and E is the father of R.

So, L is R’s father’s brother’s wife.

Hence, the correct answer is "Option 4".

The logic followed here is:

thus, "132" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The logic followed here is:

Given:

Deepu drives 12 km East

He turns left → 6 km North

He turns right → 3 km East

He turns right → 6 km South

He turns right → 5 km West

So, To reach Point K, he must go 10 km West.

Hence, the correct answer is Option 4.

The logic followed here is:

thus, "112" will replace the question mark in the given series.

Hence, the correct option is "Option 4".

Given: J, K, L, M, N and O are sitting around a circular table facing the centre.

N is an immediate neighbour of both L and M.

J is sitting to the immediate left of L.

K is sitting third to the right of N.

Total people between J and M = 2

Hence, the correct answer is "Option 2".

The logic followed here is:

For, DUBW → PGNI

For, ZQXS → LCJE

Now, applying the same pattern to JAHC:

So, JAHC → VMTO

Hence, the correct answer is Option 1.

The logic followed here is:

So, 'HLO67' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

Given number: 5341256

Logic:

Odd digits → +3

Even digits → −2

Original number: 5 3 4 1 2 5 6

New number formed: 8 6 2 4 0 8 4 → 8624084

 

Hence, the correct answer is Option 2.

Given: (Left) C X Z A L P W T M D B R O J K F G V Q H E N (Right)

We are required to find the position of the letter “L” from the left end.

So, the letter L is at the 5th position from the left.

Hence, the correct answer is Option 2.

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

Now,

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

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

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

Total valid occurrences = 5.

Hence, the correct answer is 'Option 2'.

The logic followed here is:

thus, "211" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The logic followed here is:

Logic: Second Number = First Number ÷ 4 and Third Number = Second Number − 2.

For, (188, 47, 45)

⇒ 188 ÷ 4 = 47

⇒ 47 − 2 = 45

For, (224, 56, 54)

⇒ 224 ÷ 4 = 56

⇒ 56 − 2 = 54

Now, checking the options using the same pattern:

Option 1) (284, 71, 69)

⇒ 284 ÷ 4 = 71

⇒ 71 − 2 = 69

Option 2) (332, 83, 77)

⇒ 332 ÷ 4 = 83

⇒ 83 − 2 = 81 ≠ 77

Option 3) (152, 38, 32)

⇒ 152 ÷ 4 = 38

⇒ 38 − 2 = 36 ≠ 32

Option 4) (248, 68, 66)

⇒ 248 ÷ 4 = 62 ≠ 68

Hence, the correct answer is Option 1.

The logic followed here is:

Given numbers: 475, 326, 157, 761, 829

Logic: Arrange the given numbers in ascending order and identify the numbers whose positions remain unchanged after sorting.

Original sequence: 475, 326, 157, 761, 829

Arranging in ascending order: 157, 326, 475, 761, 829

Numbers whose positions remain unchanged: 326, 761, 829

Count = 3

Hence, the correct answer is Option 3.

Given:

Preeti’s rank from the top = 8th, rank from the bottom = 9th.

Total number of students = 8 + 9 – 1 = 16.

So, there are 16 students in the class.

Hence, the correct answer is "Option 1".

Given Statements:

Some grapes are oranges.

All oranges are apples.

The least possible Venn diagram for the given statements is:

 

Conclusions:

I. Some grapes are apples → Follows (Since some grapes are oranges and all oranges are apples, those grapes must also be apples)

II. All apples are oranges → Does not follow (This is incorrect because the correct relationship is All oranges are apples, not the reverse)

So, only conclusion I follows.

Hence, the correct answer is "Option 2".

BODMAS Table: 

Decoding the given information:

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

⇒ 170 × 2 + 150 × 2 − 254 ÷ 2 + 156 ÷ 3 + 10 = ?

⇒ 340 + 300 − 127 + 52 + 10 = ?

⇒ 640 − 127 + 52 + 10 = ?

⇒ 702 − 127 = ?

⇒ 575

Hence, the correct option is "Option 2".

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

Option 1: HMP

Option 2: VZC

Option 3: DHK

Option 4: YCF

Thus, HMP does not follow the uniform pattern of +4, +3.

Hence, the odd one out is Option 1.

Given: (Left) 2 5 6 & 8 & < $ < 7 4 ^ $ 6 5 9 2 & 7 2 % (Right)

Now,

We need to find symbols that are immediately preceded by a number and immediately followed by another symbol.

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

(Left) 2 5 6 & 8 & < $ < 7 4 ^ $ 6 5 9 2 & 7 2 % (Right)

Total valid symbols = 2.

Hence, the correct answer is 'Option 4'.

The logic followed here is:

For, BKQ → FOU

For, DJM → HNQ

Now, checking the options using the same pattern:

Option 1) BST → HIS

Option 2) ELO → IPS

Option 3) TYP → VHU

Option 4) VTO → FRS

Hence, the correct answer is Option 2.

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

Option 1: GLO

Option 2: VZC

Option 3: NSV

Option 4: KPS

Thus, VZC does not follow the uniform pattern of +5, +3.

Hence, the odd one out is Option 2.

Given:

Total people = 133

Mr. Ihg is 33rd from the left end,

and Mr. Lkj is 24th from the right end.

Number of people between them = 133 − (33 + 24) = 133 − 57 = 76.

So, there are 76 people between Mr. Ihg and Mr. Lkj.

Hence, the correct answer is "Option 3".