RRB Group D Official Paper (Held On: 06 Feb, 2026 Shift 1) (Previous Year Paper)

The correct answer is The action and reaction forces act on the same object..

Key Points

• Newton’s Third Law of Motion states that for every action, there is always an equal and opposite reaction. This means that forces always exist in pairs.
• A fundamental requirement of this law is that the action and reaction forces act on two different objects. If they acted on the same object, the net force would always be zero, making it impossible for any individual object to accelerate or change its state of motion. Hence, statement 1 is incorrect.
• The forces involved in the interaction act simultaneously. There is no time delay or "cause and effect" lag between the action and the reaction; they happen at the exact same moment. Hence, statement 2 is correct.
• When one object (Object A) exerts a force on another (Object B), the second object (Object B) instantaneously exerts a force back on the first (Object A). Hence, statement 3 is correct.
• These two forces are equal in magnitude but opposite in direction. This is why the law is often expressed mathematically using vectors as Fab = -Fba. Hence, statement 4 is correct.
• Hence, the correct answer is that the statement "The action and reaction forces act on the same object" is the incorrect one.

Additional Information

• Sir Isaac Newton: He formulated the three laws of motion and published them in his monumental work, "Philosophiae Naturalis Principia Mathematica", in the year 1687. These laws form the basis of Classical Mechanics.
• Newton's First Law (Law of Inertia): It states that an object will remain at rest or continue to move at a constant velocity unless acted upon by an external unbalanced force.
• Newton's Second Law: It establishes that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a), commonly expressed as F = ma. It also defines force as the rate of change of momentum.
• Practical Examples of the Third Law:
• Recoil of a Gun: When a bullet is fired (action), the gun pushes back on the shoulder of the shooter (reaction).
• Walking: To walk forward, a person pushes the ground backward with their foot (action), and the ground pushes the person forward (reaction).
• Propulsion of a Rocket: The rocket engine expels hot exhaust gases downward (action), and the gases exert an upward thrust on the rocket (reaction), allowing it to lift off.
• Swimming: A swimmer pushes the water backward (action), and the water pushes the swimmer forward (reaction).
• Force Measurement: The SI unit of force is the Newton (N). One Newton is defined as the force required to accelerate a mass of 1 kilogram at a rate of 1 meter per second squared (1 kg·m/s²).

Important Points

• Cancellation of Forces: A common misconception is that because the forces are equal and opposite, they should cancel each other out. However, cancellation only occurs when multiple forces act on the same single body. Since action-reaction pairs act on different bodies, they do not cancel each other.
• Mass and Acceleration: While the forces are equal in magnitude, the resulting accelerations of the two objects may be very different depending on their masses (as per the Second Law). For example, the Earth pulls on a falling apple with the same force the apple pulls on the Earth, but the Earth's massive inertia means its acceleration is negligible.

The correct answer is R = ρL/A.

Key Points

• The electrical resistance (R) of a conductor is defined as the opposition offered by the conductor to the flow of electric current through it.
• It has been experimentally observed that the resistance of a uniform metallic conductor is directly proportional to its length (L). This means that as the length of the wire increases, the resistance increases proportionally. Hence, the numerator must contain L.
• The resistance is also inversely proportional to the area of cross-section (A) of the conductor. A larger cross-sectional area allows more electrons to flow, thereby reducing the resistance. Hence, the denominator must contain A.
• The resistivity (ρ), also known as specific resistance, is a constant of proportionality that depends on the nature of the material and the temperature. It is a fundamental property of a material that quantifies how strongly it resists or conducts electric current.
• By combining these dependencies, we arrive at the mathematical relation: R = ρ (L / A). This formula is used to calculate the resistance of any linear conductor when its physical dimensions and material properties are known. Hence, the correct relation is R = ρL/A.

Additional Information

• SI Units:
• The SI unit of resistance (R) is the Ohm, represented by the Greek symbol Ω.
• The SI unit of resistivity (ρ) is the Ohm-meter (Ω·m).
• Length (L) is measured in meters (m), and Area (A) is measured in square meters (m²).
• Nature of Materials:
• Conductors, such as Silver, Copper, and Aluminium, have very low resistivity, typically in the range of 10^-8 Ω·m to 10^-6 Ω·m.
• Insulators like Rubber, Glass, and Ebonite have very high resistivity, often ranging from 10^12 Ω·m to 10^17 Ω·m.
• Alloys like Constantan and Manganin have higher resistivity than their constituent metals and are often used to make standard resistors because their resistance does not change significantly with temperature.
• Conductance and Conductivity:
• The reciprocal of resistance is called Conductance (G), measured in Siemens (S) or mho.
• The reciprocal of resistivity is called Electrical Conductivity (σ), which measures the ability of a material to conduct electricity.

Important Points

• Effect of Temperature: For most metallic conductors, the resistance and resistivity increase with an increase in temperature. However, for semiconductors (like Silicon and Germanium), the resistance decreases as the temperature rises.
• Stretching a Wire: If a wire of resistance R is stretched to n times its original length, its new resistance becomes n²R. This is because while the length (L) increases, the area of cross-section (A) decreases simultaneously to keep the volume constant.
• Resistivity vs Resistance: It is important to note that while resistance depends on the shape and size (length and area) of the conductor, resistivity is independent of dimensions and depends only on the material and temperature.
• Ohm's Law: This relation is often used in conjunction with Ohm's Law (V = IR), where V is the potential difference and I is the current flowing through the conductor.

The correct answer is Galvanisation.

Key Points

• Galvanisation is a widely used method to protect Iron and Steel from corrosion or rusting by applying a thin protective layer of Zinc.
• The process typically involves Hot-Dip Galvanizing, where the metal component is submerged in a bath of molten Zinc at a temperature of approximately 450°C (842°F).
• The Zinc coating acts as a physical barrier, preventing Oxygen and moisture (water) from reaching the Iron surface, which are the two primary requirements for rust formation.
• Even if the coating is damaged or scratched, the Zinc provides cathodic protection by acting as a sacrificial anode; it corrodes in preference to the Iron because Zinc is more chemically active.
• Common applications of this method include G.I. pipes (Galvanised Iron), roofing sheets, nails, screws, fencing wire, and structural steel used in construction. Hence, the correct answer is Galvanisation.

Additional Information

• The Chemistry of Rusting:
• Rusting is an oxidation reaction where Iron reacts with Oxygen in the presence of water to form Hydrated Iron (III) Oxide (Fe2O3·nH2O).
• Unlike the oxide layer on Aluminum, rust is porous and flaky; it does not protect the underlying metal but instead promotes further corrosion.
• Alloying:
• This involves mixing Iron with other elements like Chromium and Nickel to produce Stainless Steel.
• The Chromium (usually at least 10.5%) reacts with Oxygen to form a very thin, invisible, and self-healing layer of Chromium Oxide that prevents rust.
• Other Protective Methods:
• Painting: Provides a simple barrier; commonly used for bridges, ships, and cars.
• Greasing and Oiling: Used for moving machine parts and tools where paint cannot be applied; it displaces moisture.
• Electroplating: Using electricity to deposit a layer of metals like Tin, Chromium, or Nickel on the surface of Iron objects.
• Incorrect Options:
• Magnetising: This is the process of making a substance magnetic and has no effect on the chemical process of rusting.
• Melting: This is a physical change from solid to liquid and does not offer any long-term protection against oxidation.
• Heating: Exposure to high heat in the presence of air can actually accelerate the formation of metal oxides rather than preventing them.

Important Points

• The rate of rusting is significantly higher in coastal areas because the saltwater (saline water) contains ions that increase the electrical conductivity of the water film on the metal, speeding up the electrochemical reaction.
• Zinc has an atomic number of 30 and is placed higher than Iron (atomic number 26) in the Reactivity Series of metals.
• Anodizing is a similar electrochemical process but is specifically used to thicken the natural oxide layer on Aluminum surfaces to increase durability.
• The Iron Pillar of Delhi, built in the 4th century CE, is a world-famous example of corrosion resistance achieved through specific metallurgical compositions (high phosphorus content) rather than modern Galvanisation.

The correct answer is 6.3 x 10^-7 Ωm.

Key Points

• The relationship between the resistance (R) of a wire, its length (L), and its area of cross-section (A) is given by the formula R = ρ (L / A), where ρ (rho) represents the resistivity of the material.
• In this problem, the given values are: Resistance (R) = 10 Ω, Length (L) = 2 m, and Diameter (d) = 0.4 mm. The temperature is constant at 25°C, ensuring that the resistivity remains stable during the measurement.
• First, the diameter must be converted to meters (m) to maintain SI unit consistency. Since 1 mm = 10^-3 m, the diameter (d) is 0.4 x 10^-3 m or 4 x 10^-4 m.
• The area of cross-section (A) of the wire is calculated using the formula for the area of a circle, A = (πd²) / 4. Substituting π = 3.14 and d = 4 x 10^-4 m, we get A = (3.14 x (4 x 10^-4)²) / 4, which simplifies to 12.56 x 10^-8 m².
• To find the resistivity (ρ), we rearrange the formula to ρ = (R x A) / L. Substituting the values: ρ = (10 Ω x 12.56 x 10^-8 m²) / 2 m. This calculation yields ρ = 6.28 x 10^-7 Ωm, which is approximately 6.3 x 10^-7 Ωm.

Additional Information

• Resistivity (ρ): It is an intrinsic property of a material that quantifies how strongly it resists the flow of electric current. Unlike resistance, it does not depend on the shape or size of the object but only on the nature of the material and its temperature.
• SI Unit: The standard unit of resistivity is the Ohm-meter (Ωm). Materials with low resistivity, such as Copper (1.68 x 10^-8 Ωm) and Silver, are excellent conductors, while those with high resistivity, like Glass or Rubber, act as insulators.
• Temperature Dependence: For most metals, resistivity increases linearly with an increase in temperature. This is because increased thermal vibrations of atoms impede the flow of electrons. The specific temperature of 25°C mentioned in the question is a standard reference point for such physical constants.
• Resistance vs. Resistivity: While resistance (R) changes if you stretch or cut a wire (changing its length or area), the resistivity (ρ) remains the same as long as the material and temperature are unchanged. This makes resistivity a vital parameter in material science and electrical engineering for selecting appropriate wires for circuits.

Important Points

• Mathematical Steps Summary:
• Radius (r) = d / 2 = 0.2 mm = 2 x 10^-4 m.
• Area (A) = πr² = 3.14 x (2 x 10^-4)² = 3.14 x 4 x 10^-8 = 1.256 x 10^-7 m².
• Resistivity (ρ) = (10 x 1.256 x 10^-7) / 2 = 6.28 x 10^-7 Ωm.
• Significance of Diameter: Small changes in diameter have a squared effect on the area, significantly impacting the total resistance of the wire. A thinner wire (smaller diameter) will have a much higher resistance for the same length and material.
• Applications: Knowing the resistivity helps in designing heating elements (like Nichrome) where high resistivity is desired to generate heat, or transmission lines (like Aluminum) where low resistivity is essential to minimize energy loss.

The correct answer is Presence of contractile proteins.

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Key Points

 

• Muscular tissue consists of elongated cells, also known as muscle fibers. This tissue is responsible for all types of movement within the body of an animal.
• Muscles contain special proteins called contractile proteins, which contract and relax to cause movement. The two primary types of these proteins are actin and myosin.
• When these proteins slide over one another, the muscle cell shortens, leading to contraction. When they return to their original position, it leads to relaxation. This coordinated cycle is the fundamental mechanism of locomotion and internal physical functions.
• Regarding the other options provided in the question:
• Storage of fat droplets: This is a primary function of adipose tissue, which acts as an energy reservoir and insulator. Hence, statement 1 is incorrect.
• Presence of contractile proteins: These are the mechanical engines of the muscle cell that facilitate physical displacement and force. Hence, statement 2 is correct.
• Ability to transmit nerve impulses: While muscles respond to electrical signals, the actual transmission of impulses over long distances is the specialized function of nervous tissue (neurons). Hence, statement 3 is incorrect.
• Secretion of digestive enzymes: This is a function performed by epithelial tissue, specifically glandular epithelium found in the stomach, pancreas, and intestines. Hence, statement 4 is incorrect.

Additional Information

• Types of Muscular Tissue:
• Striated Muscle (Skeletal Muscle): These are voluntary muscles mostly attached to bones. Under a microscope, they show alternate light and dark bands or striations. They are long, cylindrical, unbranched, and multinucleated.
• Smooth Muscle (Unstriated Muscle): These are involuntary muscles found in the walls of hollow internal organs such as the alimentary canal, blood vessels, and the iris of the eye. They are spindle-shaped (tapering at ends) and have a single nucleus.
• Cardiac Muscle: These are found exclusively in the heart. They are involuntary, cylindrical, branched, and uninucleated. They show rhythmic contraction and relaxation throughout the lifespan of the animal without getting fatigued.
• Mechanism of Movement:
• The Sliding Filament Theory is the most widely accepted explanation for muscle contraction. It states that the thick (myosin) and thin (actin) filaments slide past each other, decreasing the length of the sarcomere (the functional unit of contraction).
• Muscle contraction is often triggered by Calcium ions (Ca2+) released from the sarcoplasmic reticulum following a stimulus from the nervous system.

Important Points

• Sarcomere: It is defined as the segment between two neighboring Z-lines and is considered the basic unit of a muscle's cross-striated myofibril.
• Excitability: This is the ability of muscle tissue to receive and respond to stimuli, which distinguishes it from other connective tissues.
• Energy Requirement: Muscle contraction is an active process that requires a significant amount of Adenosine Triphosphate (ATP), which is why muscle cells contain a high number of mitochondria.
• Locomotion vs. Movement: While movement refers to the change in position of any part of the body, locomotion specifically refers to the movement of the entire animal from one location to another.

The correct answer is The graph is a straight line.

Key Points

• For an object moving with uniform speed, the distance traveled is directly proportional to the time taken. This linear relationship ensures that as time increases, the distance increases at a constant rate.
• In a distance-time graph, time is typically plotted on the X-axis (independent variable) and distance is plotted on the Y-axis (dependent variable).
• The slope of a distance-time graph represents the speed of the object. Since the speed is uniform (constant), the slope remains the same at every point on the graph, which mathematically results in a straight line.
• A straight line passing through the origin (0,0) indicates that the object was at the reference starting point at time zero and moved with a constant velocity thereafter. Hence, statement 4 is correct.
• A sine wave graph represents oscillatory or periodic motion, such as a pendulum, where the position varies harmonically over time. Hence, statement 1 is incorrect.
• A zig-zag line represents non-uniform motion where the speed and direction change abruptly and inconsistently. Hence, statement 3 is incorrect.

Additional Information

• Uniform Motion:
• An object is said to be in uniform motion if it covers equal distances in equal intervals of time, no matter how small these time intervals may be.
• In this state, the acceleration of the object is zero because the velocity does not change in magnitude or direction.
• Non-Uniform Motion:
• If an object covers unequal distances in equal intervals of time, it is in non-uniform motion.
• The distance-time graph for non-uniform motion is a curved line, indicating that the speed is changing (accelerating or decelerating).
• Object at Rest:
• When an object is stationary, its distance from the reference point does not change as time passes.
• The distance-time graph for an object at rest is a horizontal straight line parallel to the time-axis (X-axis), where the slope is zero.
• Speed Calculation from Graph:
• To find the speed from a distance-time graph, one can pick any two points (x1, y1) and (x2, y2) on the line and calculate the gradient.
• The formula used is Speed = (Distance2 - Distance1) / (Time2 - Time1). For a straight line, this value will always be constant.

Important Points

• Steepness of the Graph: The steepness or gradient of the straight line indicates the magnitude of speed. A steeper line represents a higher speed, while a flatter line represents a lower speed.
• Physical Constraints: A distance-time graph can never be a vertical line parallel to the Y-axis. This would imply the object is covering distance in zero time, which means it has infinite speed—a physical impossibility in classical mechanics.
• Comparison: By plotting distance-time lines for two different objects on the same graph, one can easily compare their relative speeds by looking at which line is closer to the Y-axis (steeper).
• Units: Standard SI units used in these graphs are meters (m) for distance and seconds (s) for time, making the unit of the slope (speed) m/s.

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

Key Points

• A concave lens is an optical device that is thinner at the center than at the edges. It is fundamentally known as a diverging lens because it causes parallel rays of light to spread out or diverge after passing through it. Hence, statement (i) is correct.
• The divergence of light rays means they never meet on the opposite side of the lens; instead, they appear to originate from a single point called the principal focus on the same side as the object.
• A concave lens always produces a virtual, erect, and diminished image, regardless of where the object is placed. It cannot form a real and inverted image because the refracted rays do not actually intersect. Hence, statement (ii) is incorrect.
• Because the image is always formed by the apparent intersection of light rays, it is categorized as virtual. Since the image is oriented in the same direction as the object, it is described as erect. Hence, statement (iii) is correct.
• Therefore, the correct answer is Both (i) and (iii).

Additional Information

• Optical Characteristics:
• The focal length of a concave lens is considered negative according to the Cartesian sign convention.
• The power of a concave lens is also negative, expressed in Dioptres (D). For example, a prescription of -2.0 D indicates a concave lens.
• Image Positions:
• If an object is placed at infinity, the image is formed at the focus (F1), being highly diminished and point-sized.
• If the object is between infinity and the optical center (O), the image is formed between the focus and the optical center on the same side as the object.
• Common Applications:
• Spectacles: These lenses are the primary tool used to correct Myopia (nearsightedness), helping the eye focus light correctly on the retina.
• Flashlights: They are used to diverge the light beam to cover a larger area.
• Peepholes: Installed in doors to provide a diminished but wide-angle view of the area outside.
• Telescopes: Often used in the eyepieces of Galilean telescopes to provide an upright image.

Important Points

• Lens Formula: The mathematical relationship between object distance (u), image distance (v), and focal length (f) is given by the formula 1/f = 1/v - 1/u.
• Magnification (m): It is the ratio of the height of the image to the height of the object, or m = v/u. For a concave lens, the magnification is always positive and less than 1, indicating the image is virtual and smaller than the object.
• Refractive Index: The degree of divergence depends on the refractive index of the material (like glass or plastic) and the curvature of the lens surfaces.
• Comparison: Unlike a convex lens (converging lens), which can form real, inverted, magnified, or virtual images based on the object's position, the concave lens is much more limited and consistent in its image properties.

The correct answer is Filtration, because the solid particles in mud are not dissolved in water.

Key Points

• Filtration is a physical separation method used to remove insoluble solid particles from a liquid or gas by passing the mixture through a porous medium (like filter paper).
• A mixture of mud and water is a heterogeneous mixture (specifically a suspension), meaning the components are not uniformly distributed and the solid mud particles do not dissolve in the water. Hence, the statement provided in option 4 is correct.
• During this process, the clear liquid that passes through the filter is called the filtrate, while the solid particles trapped on the filter medium are referred to as the residue.
• This method is highly effective for pond water because the particle size of mud is significantly larger than the pore size of standard filtration media, ensuring a clear separation without needing heat or chemical additives.
• Unlike methods that involve phase changes, filtration preserves both the solid and the liquid components in their original states, making it efficient for large volumes of muddy water.

Additional Information

• Evaporation:
• This method involves heating the mixture until the solvent (water) turns into vapor, leaving the solute (mud) behind.
• While it separates the mud, it is less "effective" for general separation because the water is lost to the atmosphere unless a condenser is used. It is typically used for homogeneous mixtures like salt and water.
• Distillation:
• Distillation is a process that separates components based on differences in their boiling points.
• It is primarily used to separate miscible liquids (like alcohol and water) or to obtain pure water from a salt solution. Using it for mud and water is unnecessarily complex and energy-intensive compared to filtration.
• Chromatography:
• This technique is used to separate components of a mixture based on their different rates of movement through a stationary phase under the influence of a mobile phase.
• It is used for separating dyes, pigments, or chemicals in a solution, rather than separating bulk solids like mud from water.
• Heterogeneous vs. Homogeneous Mixtures:
• Heterogeneous mixtures (e.g., mud in water, oil in water) have visible boundaries of separation.
• Homogeneous mixtures (e.g., sugar in water, air) have a uniform composition throughout and cannot be separated by simple filtration.

Important Points

• Sedimentation and Decantation: Before filtration, a mixture of mud and water can be left undisturbed to allow the heavier mud particles to settle at the bottom due to gravity; this is sedimentation. The clear water can then be poured out, which is decantation. Filtration is often the final step after these to ensure total clarity.
• Loading: Sometimes, very fine mud particles stay suspended. To speed up sedimentation, Alum (potash alum) is added. This process is called loading, where the alum particles attach to the fine dirt, making them heavy enough to sink.
• Applications: Filtration is a critical step in municipal water treatment plants, where large-scale sand filters are used to provide potable water to cities. In daily life, it is used in tea strainers and HEPA filters in vacuum cleaners to trap dust.

The correct answer is 10√10 m/s.

Key Points

• The problem describes a case of vertical motion under gravity, which is a form of uniformly accelerated motion where the acceleration is constant.
• When an object is thrown vertically upward, its velocity decreases until it reaches the highest point. At this maximum height, the final velocity (v) of the object becomes 0 m/s.
• To find the initial velocity (x), we use the third equation of motion: v² = u² + 2as. In this context, u is the initial velocity (x), v is the final velocity (0 m/s), a is the acceleration due to gravity (-g), and s is the maximum height (H).
• Given values are maximum height (H) = 50 m and acceleration due to gravity (g) = 10 m/s². Because the ball is moving upward against the pull of gravity, the acceleration is taken as -10 m/s².
• Substituting the values into the equation: 0² = x² + 2(-10)(50). This simplifies to 0 = x² - 1000.
• Solving for x, we get x² = 1000, which means x = √1000. This can be simplified to x = √(100 × 10), resulting in x = 10√10 m/s. Hence, the calculated value of initial velocity is correct.

Additional Information

• Newton's Equations of Motion:
• These equations describe the relationship between velocity, acceleration, time, and displacement for an object moving with constant acceleration.
• The first equation is v = u + at, used to find velocity or time.
• The second equation is s = ut + (1/2)at², used to determine the displacement of an object over a period of time.
• The third equation is v² = u² + 2as, which is independent of time and relates velocity directly to displacement.
• Acceleration due to Gravity (g):
• This is the acceleration gained by an object due to the gravitational force of the Earth.
• Its standard value is approximately 9.8 m/s² at sea level, but for competitive exams and simplified calculations, it is often taken as 10 m/s².
• The value of g varies slightly depending on altitude and latitude, being higher at the poles and lower at the equator.
• Maximum Height (H):
• The maximum height attained by a projectile or a vertically thrown object occurs when its kinetic energy is fully converted into potential energy (neglecting air resistance).
• The formula derived from the equations of motion for maximum height is H = u² / (2g).
• If the initial velocity is doubled, the maximum height will increase by four times, following the square relationship.

Important Points

• Sign Convention: In physics problems involving vertical motion, it is crucial to maintain a consistent sign convention. Usually, upward direction is taken as positive and downward direction as negative. Since gravity always acts downward, g is treated as negative when an object is thrown upward.
• Mass Independence: In a vacuum (where air resistance is zero), the maximum height reached by an object depends only on its initial velocity and gravity, not on its mass. A heavy ball and a light ball thrown with the same velocity will reach the same height.
• Time of Ascent and Descent: For an object thrown vertically upward, the time taken to reach the maximum height (time of ascent) is equal to the time taken to return to the original level (time of descent), provided air resistance is ignored. This is calculated as t = u / g.
• Kinetic and Potential Energy: At the point of projection, the object has maximum kinetic energy. At the maximum height of 50 m, its kinetic energy is zero, and its potential energy is at its maximum value.

The correct answer is Butane.

Key Points

• Butane is a saturated hydrocarbon belonging to the alkane family with the molecular formula C4H10.
• A saturated hydrocarbon is one where all the carbon-carbon bonds are single covalent bonds, allowing the maximum number of hydrogen atoms to be bonded to the carbon skeleton.
• The term straight-chain refers to an acyclic structure where the carbon atoms are linked in a continuous, unbranched sequence. Butane (specifically n-butane) consists of 4 carbon atoms arranged in a line. Hence, statement 1 is correct.
• In Butane, each of the two inner carbon atoms is bonded to 2 hydrogen atoms, and the two terminal carbon atoms are bonded to 3 hydrogen atoms, following the general formula for alkanes, which is CnH2n+2.
• It is a colorless, highly flammable gas at room temperature and atmospheric pressure, commonly used as fuel in LPG (Liquefied Petroleum Gas) and lighters.

Additional Information

• Propene:
• It is an unsaturated hydrocarbon with the chemical formula C3H6.
• It belongs to the alkene group because it contains at least one double bond between carbon atoms.
• Since it contains a double bond, it does not meet the criteria of being "saturated." Hence, statement 3 is incorrect.
• Cyclohexane:
• It is a saturated hydrocarbon because it contains only single bonds, but it is cyclic rather than straight-chain.
• Its molecular formula is C6H12, and the carbon atoms form a hexagonal ring structure.
• While it is saturated, its ring structure excludes it from being a "straight-chain" hydrocarbon. Hence, statement 2 is incorrect.
• Benzene:
• It is an aromatic hydrocarbon with the chemical formula C6H6.
• It is cyclic and highly unsaturated, containing three alternating double bonds within a 6-carbon ring.
• Because it is both cyclic and unsaturated, it does not fit the category of straight-chain saturated hydrocarbons. Hence, statement 4 is incorrect.

Important Points

• Alkanes (Saturated): These hydrocarbons follow the general formula CnH2n+2. Examples include Methane (CH4), Ethane (C2H6), and Propane (C3H8). They are generally less reactive than unsaturated hydrocarbons.
• Alkenes and Alkynes (Unsaturated): These contain double (CnH2n) or triple bonds (CnH2n-2), respectively. They are called unsaturated because they can undergo addition reactions to bond with more hydrogen atoms.
• Isomerism: While n-butane is a straight chain, it has an isomer called isobutane (or 2-methylpropane), which is a branched-chain saturated hydrocarbon. Both share the same formula C4H10 but have different structural arrangements.
• Homologous Series: Alkanes form a homologous series where each successive member differs from the previous one by a CH2 group and has a mass difference of 14 units.

The correct answer is The forebrain.

Key Points

• The forebrain, also known as the prosencephalon, is the most developed and largest part of the human brain, primarily responsible for higher-order cognitive functions.
• It consists of the cerebrum, thalamus, and hypothalamus. The cerebrum forms the bulk of the brain and is the seat of intelligence, memory, and consciousness.
• The cerebral cortex, the outer layer of the cerebrum, is highly folded into gyri and sulci to increase surface area, allowing for complex interpretation of sensory information such as vision, hearing, and touch. Hence, the statement regarding higher-level thought processes is correct.
• It is the site where voluntary motor actions are initiated and where abstract reasoning, problem-solving, and language processing occur.
• The thalamus within the forebrain acts as a major relay station, filtering and directing sensory impulses to the appropriate regions of the cerebral cortex for processing.

Additional Information

• Structure of the Cerebrum:
• The cerebrum is divided into two cerebral hemispheres connected by a thick band of nerve fibers called the corpus callosum.
• Each hemisphere is divided into four lobes: the Frontal lobe (decision making and motor control), Parietal lobe (sensory perception), Temporal lobe (auditory processing and memory), and Occipital lobe (visual processing).
• The Hypothalamus:
• Located at the base of the forebrain, it plays a critical role in maintaining homeostasis.
• It regulates body temperature, hunger, thirst, and circadian rhythms, and controls the pituitary gland, linking the nervous system to the endocrine system.
• The Cerebellum:
• Located in the hindbrain, it is known as the "little brain." Its primary function is the coordination of voluntary movements, maintenance of posture, and balance.
• It does not initiate movement but fine-tunes it for accuracy and timing.
• The Brainstem:
• Comprising the midbrain, pons, and medulla oblongata, it connects the brain to the spinal cord.
• It controls autonomic functions essential for survival, such as breathing, heart rate, and blood pressure.

Important Points

• The Spinal Cord: This is a long, thin bundle of nervous tissue that extends from the brainstem. It primarily functions as a conduction pathway for messages between the brain and the rest of the body and coordinates spinal reflexes.
• Limbic System: Often referred to as the "emotional brain," it is located within the forebrain and includes the amygdala (emotion) and hippocampus (long-term memory formation).
• Gray Matter vs. White Matter: The cerebral cortex is composed of gray matter (cell bodies), while the inner part of the forebrain contains white matter (myelinated axons) that facilitates communication between different brain regions.
• Evolutionary Context: The forebrain has undergone the most significant expansion in mammals, particularly in humans, which accounts for our advanced cognitive capabilities compared to other species.

The correct answer is CH4.

Key Points

• Methane is a chemical compound with the chemical formula CH4. It is the simplest member of the alkane series, which consists of saturated hydrocarbons.
• A single molecule of methane consists of one carbon atom located at the center, which is bonded to four hydrogen atoms.
• The bonding in methane is characterized by four single covalent bonds. The carbon atom shares its four valence electrons with four individual hydrogen atoms, allowing all atoms to achieve a stable electronic configuration.
• The molecular geometry of methane is tetrahedral. This means the four hydrogen atoms are positioned at the corners of a tetrahedron with the carbon atom at the center, resulting in bond angles of approximately 109.5 degrees.
• Methane is the primary component of natural gas, often comprising 70% to 90% of the mixture depending on the source.

Additional Information

• Physical Properties:
• At standard temperature and pressure, methane is a colorless, odorless, and tasteless gas. Because it is odorless, gas companies often add a chemical called mercaptan (which smells like rotten eggs) to natural gas to make leaks detectable.
• It has a very low boiling point of approximately -161.5 degrees Celsius and a melting point of -182.5 degrees Celsius.
• Industrial and Domestic Uses:
• Methane is a vital fuel source used globally for heating, cooking, and generating electricity in power plants.
• In the chemical industry, it serves as a primary raw material for the production of hydrogen gas, methanol, acetic acid, and acetylene through processes like steam reforming.
• Environmental and Biological Significance:
• Methane is a potent greenhouse gas. Although it persists in the atmosphere for a shorter time than carbon dioxide, its Global Warming Potential (GWP) is estimated to be 25 to 28 times greater than that of CO2 over a 100-year period.
• Natural sources include wetlands, termites, and oceans. Human-related sources include landfills, rice agriculture, and livestock farming (through enteric fermentation in ruminants like cattle).

Important Points

• Chemical Reaction (Combustion): When methane burns in the presence of sufficient oxygen, it undergo complete combustion to produce carbon dioxide and water vapor, releasing 891 kJ/mol of energy. The balanced equation is: CH4 + 2O2 -> CO2 + 2H2O.
• Molar Mass: The molar mass of methane is approximately 16.04 grams per mole, calculated from the atomic mass of Carbon (12.01) and Hydrogen (1.008 x 4).
• Historical Context: Methane was first scientifically identified by Alessandro Volta between 1776 and 1778 while he was studying marsh gas from Lake Maggiore in Italy.
• Alternative Names: Methane is frequently referred to as marsh gas, swamp gas, or firedamp (specifically when found in coal mines).

The correct answer is Capture fishing.

Key Points

• Capture fishing is the process of obtaining fish directly from natural resources such as rivers, lakes, oceans, and seas.
• In this method, the fish population is not manually bred or reared; instead, it relies on the natural reproduction and growth of fish in their wild habitats. Hence, the statement aligns with the definition of capture fishing.
• Capture fishing can be classified into two main types: Marine fishery (conducted in salt water) and Inland fishery (conducted in fresh water).
• Common techniques used in Capture fishing include the use of fishing nets, traditional boats, and mechanized trawlers to harvest fish from the wild.
• Popular marine fish varieties caught through this method include Mackerel, Tuna, Sardines, and Pomphret, which are of high economic value.

Additional Information

• Culture Fishing (Aquaculture):
• This involves the controlled cultivation and rearing of aquatic organisms, including fish, mollusks, and crustaceans.
• Unlike capture fishing, Culture fishing requires human intervention in the breeding process to increase production.
• Mariculture:
• This is a specialized branch of aquaculture involving the cultivation of marine organisms for food in the open ocean or enclosed sections of the sea.
• Commonly cultured organisms include Prawns, Oysters, and Seaweeds.
• Composite Fish Culture:
• This is a highly productive system where five or six fish species are grown together in a single fishpond.
• Species are selected such that they have different feeding habits and do not compete for food. For example, Catla are surface feeders, Rohu feed in the middle zone, and Mrigal and Common Carp are bottom feeders.
• This method ensures that the food available in all parts of the pond is utilized efficiently, leading to a high yield.
• Blue Revolution:
• The Blue Revolution refers to the time of intense growth in the worldwide aquaculture industry from the mid-1960s to the present day.
• In India, it was launched during the 7th Five-Year Plan (1985-1990) to double the income of fish farmers and increase fish production through modern technology.

Important Points

• Inland Fisheries: These include freshwater resources like canals, ponds, reservoirs, and rivers, as well as brackish water resources like estuaries and lagoons.
• Economic Significance: Fish is a cheap source of animal protein and fishing provides a livelihood to millions of people, especially in coastal states of India such as Kerala, West Bengal, and Andhra Pradesh.
• Sustainable Fishing: Due to over-exploitation, many natural fish stocks are depleting, making the balance between capture fishing and culture fishing essential for environmental sustainability.

The correct answer is Refraction.

Key Points

• Refraction is the fundamental optical principle where light rays bend when they pass from one transparent medium to another of different optical density, such as from air into a glass or plastic lens.
• Spectacle lenses are designed with specific curvatures to utilize refraction to redirect light. This ensures that the light rays entering the eye are properly focused directly onto the retina, rather than in front of or behind it.
• The degree of bending depends on the refractive index of the lens material and the angle of incidence. Corrective lenses use materials with a higher refractive index than air to achieve the desired vision correction.
• This principle is governed by Snell’s Law, which describes the relationship between the angles of incidence and refraction. Hence, the correct answer is Refraction.

Additional Information

• Myopia (Nearsightedness):
• In this condition, the eyeball is too long or the cornea is too curved, causing light to focus in front of the retina.
• It is corrected using a Concave Lens (diverging lens), which spreads the light rays before they reach the eye, moving the focal point back onto the retina.
• Hypermetropia (Farsightedness):
• In this case, light focuses behind the retina because the eyeball is too short or the lens lacks sufficient converging power.
• A Convex Lens (converging lens) is used to bend the light rays inward earlier, allowing them to converge exactly on the retinal surface.
• Other Optical Principles (Incorrect Options):
• Reflection: This is the bouncing back of light when it hits a surface. While mirrors work on reflection, lenses do not rely on this to correct vision. Statement 3 is incorrect.
• Polarization: This process involves filtering light waves to vibrate in a single plane. It is used in sunglasses to reduce glare from reflective surfaces like water or roads, but it does not correct refractive errors. Statement 1 is incorrect.
• Diffraction: This is the slight bending of light as it passes around the edge of an object or through an opening. It is not the principle used for standard vision correction in spectacles. Statement 2 is incorrect.
• Astigmatism: This occurs when the cornea or lens has an irregular shape, leading to blurred vision at all distances. It is corrected using Cylindrical Lenses that refract light differently in horizontal and vertical planes.

Important Points

• Lens Power: The ability of a lens to refract light is measured in Dioptres (D). The power (P) is the reciprocal of the focal length (f) in metres (P = 1/f).
• Lens Formula: The relationship between the object distance (u), image distance (v), and focal length (f) is given by 1/v - 1/u = 1/f.
• Presbyopia: A condition associated with age (typically appearing after 40 years), where the eye's natural lens loses elasticity, making it difficult to focus on close objects. It is often corrected with Bifocal or Progressive lenses.
• Contact Lenses: These work on the same principle of refraction but are placed directly on the tear film of the cornea.

The correct answer is is zero.

Key Points

• In physics, Work Done is defined as the product of the component of the Force in the direction of the Displacement and the magnitude of that displacement.
• The mathematical formula used to calculate work is W = F s cos θ, where W is the work done, F is the magnitude of the force applied, s is the displacement of the object, and θ (theta) is the angle between the force vector and the displacement vector.
• When a force is applied at an angle of 90 degrees to the direction of displacement, it is considered perpendicular. In trigonometry, the value of cos 90 degrees is exactly 0.
• Substituting this into the formula (W = F x s x 0), the resulting Work Done becomes zero. This indicates that the force does not contribute to the movement of the object in that specific direction. Hence, the statement that work done is zero is correct.
• A practical example is a person walking on a flat road while carrying a load on their head. The force of gravity acts vertically downwards, while the displacement is horizontal (at a 90-degree angle). Therefore, the work done by gravity on the load is zero.

Additional Information

• Positive Work: This occurs when the force and the displacement are in the same direction, meaning the angle θ is 0 degrees (or generally between 0 and 90). In this scenario, cos θ is positive, and the work done adds kinetic energy to the object.
• Negative Work: This happens when the force acts in the opposite direction to the displacement, such as when the angle θ is 180 degrees. A common example is the force of friction, which opposes motion, resulting in a negative value because cos 180 degrees is -1.
• SI Unit: The standard International System of Units (SI) unit for work is the Joule (J). One Joule is defined as the work done by a force of one Newton (N) causing a displacement of one meter (m).
• Scalar Nature: Although both force and displacement are vector quantities, work done is a scalar quantity. This means it only has magnitude and no specific direction in space.

Important Points

• Centripetal Force: In the case of uniform circular motion, the centripetal force is always directed towards the center of the circle, while the displacement is tangential. Because the angle between them is always 90 degrees, the work done by the centripetal force is always zero.
• Zero Displacement: Even if a massive amount of force is applied, the work done is zero if the object does not move. For example, pushing against a rigid stone wall that does not budge results in no work being performed in the scientific sense.
• Energy Transformation: Work is a method of energy transfer. When zero work is done at a 90-degree angle, it signifies that no energy is being transferred into or out of the system by that particular force component.
• Dimensions: The dimensional formula for work is [M1 L2 T-2], which is the same as the dimensional formula for energy and torque.

The correct answer is it loses oxygen or gains hydrogen.

Key Points

• Reduction is a fundamental chemical process that can be defined in multiple ways. Classically, it refers to the removal of oxygen from a chemical species or the addition of hydrogen to it. Hence, statement 1 is correct.
• While gaining hydrogen is a form of reduction, the definition is broader than just hydrogen alone. Focusing only on hydrogen neglects the oxygen-loss aspect of the process. Hence, statement 2 is incorrect.
• Similarly, while losing oxygen is a hallmark of reduction, the definition also encompasses the gain of hydrogen. Relying only on oxygen loss makes the definition incomplete in classical chemistry. Hence, statement 3 is incorrect.
• The process of losing hydrogen or gaining oxygen is actually the definition of Oxidation, which is the chemical opposite of reduction. Hence, statement 4 is incorrect.
• In modern electronic theory, reduction is more accurately described as a process where an atom, ion, or molecule gains one or more electrons. This gain of electrons leads to a decrease in the oxidation state of the substance.

Additional Information

• Oxidation and Reduction (Redox): These two processes never occur in isolation. If one substance is reduced, another must be oxidized. These coupled reactions are known as Redox reactions. For example, in the reaction between Magnesium and Oxygen to form Magnesium Oxide, magnesium is oxidized while oxygen is reduced.
• Reducing Agents: A substance that provides electrons or hydrogen, or removes oxygen, is called a Reducing Agent. Paradoxically, the reducing agent itself undergoes oxidation during the reaction. Common reducing agents include Carbon (C), Carbon Monoxide (CO), and Hydrogen gas (H2).
• Industrial Applications: Reduction is vital in Metallurgy. Most metals exist in nature as oxides. To obtain pure metal, the ore must be reduced. For instance, in a Blast Furnace, Iron(III) Oxide is reduced by carbon monoxide to produce molten iron.
• Biological Significance: Reduction processes are essential for life. In Photosynthesis, Carbon Dioxide (CO2) is reduced to form Glucose (C6H12O6). In cellular respiration, electron carriers like NAD+ are reduced to NADH to transport energy within the cell.
• Mnemonics for Memory: Students often use the phrase "OIL RIG" to remember the electronic definitions: Oxidation Is Loss (of electrons), Reduction Is Gain (of electrons). Another popular one is "LEO says GER": Lose Electrons Oxidation, Gain Electrons Reduction.

Important Points

• Oxidation Number: A clear indicator of reduction is a numerical decrease in the oxidation number. For example, if an ion goes from a +3 charge to a +2 charge, it has been reduced.
• Electropositive/Electronegative Elements: Beyond oxygen and hydrogen, reduction can be defined as the addition of an electropositive element or the removal of an electronegative element from a compound.
• Corrosion: While oxidation causes the corrosion of metals (like the rusting of iron), reduction is used in electroplating and cathodic protection to prevent such damage by supplying electrons to the metal surface.

The correct answer is Carbon dioxide.

Key Points

• When hydrochloric acid (HCl) is added to calcium carbonate (CaCO3), a chemical reaction occurs that produces calcium chloride (CaCl2), water (H2O), and carbon dioxide (CO2).
• The balanced chemical equation for this reaction is: CaCO3 + 2HCl → CaCl2 + H2O + CO2.
• The release of carbon dioxide gas is observed as brisk effervescence, which is the rapid formation of bubbles in the liquid.
• This reaction is a classic example of an acid-carbonate reaction, where an acid reacts with a metal carbonate to yield a salt, water, and carbon dioxide gas.
• The carbon dioxide released in this process is a colorless and odorless gas that is heavier than air.

Additional Information

• Calcium Carbonate (CaCO3):
• It is a chemical compound found naturally in rocks as limestone, chalk, and marble.
• It is the primary component of eggshells, shells of marine organisms (like corals and mollusks), and pearls.
• In the pharmaceutical industry, it is used as an antacid to relieve heartburn and indigestion or as a calcium supplement.
• Hydrochloric Acid (HCl):
• It is a strong acid and a major component of gastric acid found in the human stomach, where it aids in digestion.
• In industrial applications, it is used for pickling of steel, production of organic compounds, and pH regulation.
• Testing for Carbon Dioxide:
• The standard laboratory test for CO2 involves passing the gas through lime water (an aqueous solution of calcium hydroxide).
• The lime water turns milky or turbid due to the formation of insoluble calcium carbonate (CaCO3).
• If the gas continues to be passed through the milky solution, the milkiness disappears because soluble calcium bicarbonate (Ca(HCO3)2) is formed.

Important Points

• Properties of CO2: Carbon dioxide is essential for photosynthesis in plants. However, in high concentrations, it acts as a greenhouse gas, contributing to global warming.
• Reaction with other acids: Similar reactions occur with other acids. For example, sulfuric acid (H2SO4) reacting with calcium carbonate produces calcium sulfate, water, and carbon dioxide.
• Fire Extinguishers: The principle of producing CO2 through the reaction of an acid and a carbonate (like sodium bicarbonate) was historically used in soda-acid fire extinguishers to smother fires by displacing oxygen.
• Daily Life Examples: The "fizz" felt when vinegar (acetic acid) is poured onto baking soda (sodium bicarbonate) is also due to the release of carbon dioxide gas.

The correct answer is Statement A is correct, but B is incorrect.

Key Points

• Ethanol, also known as ethyl alcohol, with the chemical formula C2H5OH, is the active ingredient in all alcoholic drinks. It is a colorless liquid at room temperature and is highly inflammable.
• Statement A: Consumption of even small quantities of dilute ethanol leads to drunkenness or intoxication. This occurs because ethanol acts as a depressant on the central nervous system, affecting motor skills and judgement. Hence, statement A is correct.
• Statement B: Intake of pure ethanol (also known as absolute alcohol) is not safe. Consuming even a very small amount of 100% pure ethanol can be lethal to the human body and cause severe damage to the internal organs. Hence, statement B is incorrect.
• While ethanol is used widely in industrial processes and medicines like tincture iodine, cough syrups, and many tonics due to its properties as a good solvent, its consumption as a beverage is strictly regulated due to its addictive nature and health risks.
• When a person consumes alcohol, it reaches the brain through the bloodstream and slows down metabolic processes, leading to a lack of coordination, mental confusion, and drowsiness.

Additional Information

• Absolute Alcohol: This refers to ethanol that contains no more than 1% water. It is primarily used in laboratories and for industrial applications. It is extremely toxic if ingested directly.
• Denatured Alcohol: To prevent the misuse of industrial ethanol for drinking, it is often made unfit for consumption by adding poisonous substances like methanol. Dyes like copper sulphate are also added to give it a blue color so that it can be identified easily.
• Methanol Toxicity: Unlike ethanol, methanol (CH3OH) is highly poisonous even in very tiny quantities. In the liver, methanol is oxidized to methanal (formaldehyde), which reacts rapidly with the components of cells, causing protoplasm coagulation. It can also affect the optic nerve, leading to permanent blindness.
• Physical Properties of Ethanol: It has a melting point of 156 K and a boiling point of 351 K. It is soluble in water in all proportions.

Important Points

• Health Hazards: Long-term consumption of alcohol (ethanol) leads to various health issues, including cirrhosis of the liver, cardiovascular diseases, and damage to the nervous system.
• Social Impact: Alcohol acts by lowering inhibitions, which can lead to social problems and accidents, particularly drunk driving.
• Uses in Industry: Ethanol is used as a fuel (often blended with petrol to create gasohol) and in the manufacture of paints, varnishes, and perfumes.
• Chemical Reactions: Ethanol reacts with sodium to form sodium ethoxide and hydrogen gas. This reaction is often used as a test for the presence of an alcohol group.

The correct answer is Plasma.

Key Points

• Blood is a specialized connective tissue consisting of a fluid matrix, plasma, and formed elements.
• Plasma is the straw-colored, viscous fluid that constitutes nearly 55 per cent of the total blood volume. It serves as the fluid matrix in which all the cellular components of blood are suspended. Hence, the correct option is Plasma.
• Chemically, plasma is composed of about 90-92 per cent water, while proteins contribute approximately 6-8 per cent of its composition.
• The major proteins found in the plasma matrix include Fibrinogens, Globulins, and Albumins. Fibrinogens are essential for the clotting or coagulation of blood; Globulins are primarily involved in the defense mechanisms of the body; and Albumins help in maintaining osmotic balance.
• In addition to proteins, plasma contains small amounts of minerals like Na+, Ca++, Mg++, HCO3-, and Cl-. Glucose, amino acids, and lipids are also present as they are always in transit in the body.

Additional Information

• Red Blood Cells (RBCs):
• Also known as Erythrocytes, these are the most abundant cells in the blood. A healthy adult man has an average of 5 million to 5.5 million RBCs per cubic millimeter of blood.
• They contain a red-colored, iron-carrying complex protein called hemoglobin, which plays a significant role in the transport of respiratory gases.
• RBCs have an average lifespan of 120 days, after which they are destroyed in the spleen (often called the graveyard of RBCs).
• White Blood Cells (WBCs):
• Also known as Leukocytes, they are part of the body's immune system and help fight infections. They are nucleated and are relatively lesser in number, averaging 6000-8000 per cubic millimeter of blood.
• They are divided into two main categories: Granulocytes (Neutrophils, Eosinophils, and Basophils) and Agranulocytes (Lymphocytes and Monocytes).
• Platelets:
• Also known as Thrombocytes, these are cell fragments produced from megakaryocytes (special cells in the bone marrow).
• Blood normally contains 1,50,000-3,50,000 platelets per cubic millimeter. Their primary function is to release substances that aid in the coagulation or clotting of blood to prevent excessive blood loss.
• Serum:
• When plasma is separated from the clotting factors (like fibrinogen), the remaining fluid is called Serum.

Important Points

• The pH of human blood is slightly basic, typically maintained at approximately 7.4.
• The process of formation of blood cells is known as Haemopoiesis, which primarily occurs in the red bone marrow in adults.
• The formed elements (RBCs, WBCs, and Platelets) together constitute about 45 per cent of the blood, while the plasma matrix accounts for the other 55 per cent.

The correct answer is Cytoplasm.

Key Points

• Cytoplasm is a thick, jelly-like substance that fills each cell and is enclosed by the cell membrane.
• It is mainly composed of water, salts, and proteins. In eukaryotic cells, the cytoplasm includes all of the material inside the cell and outside of the nucleus.
• All the cellular organelles, such as the mitochondria, ribosomes, endoplasmic reticulum, and Golgi apparatus, are suspended within it.
• It plays a crucial role in maintaining the shape of the cell and providing a medium for chemical reactions and metabolic activities like glycolysis.
• The fluid portion of the cytoplasm that does not contain organelles is specifically referred to as the cytosol.

Additional Information

• Stroma:
• The Stroma refers to the colorless fluid surrounding the grana within the chloroplast in plant cells.
• It contains the chloroplast DNA, ribosomes, and various enzymes required for the Calvin cycle (light-independent reactions of photosynthesis).
• Lumen:
• In biology, a Lumen is the inside space of a tubular structure, such as an artery or intestine.
• In cellular biology, it can refer to the internal space of organelles like the Endoplasmic Reticulum (ER) or the thylakoids in chloroplasts.
• Nucleoplasm:
• Nucleoplasm is a type of protoplasm that is found within the nucleus of a cell, surrounded by the nuclear envelope.
• It serves as a suspension medium for the nucleolus and chromatin (DNA and proteins), facilitating gene expression and DNA replication.

Important Points

• The term protoplasm is often used to describe the entire content of a live cell, including the cytoplasm and the nucleus.
• In prokaryotic cells (like bacteria), which lack a defined nucleus, the cytoplasm contains the primary genetic material (the nucleoid).
• The cytoskeleton, a network of protein fibers (microtubules and microfilaments), is located within the cytoplasm to provide structural support and aid in intracellular transport.
• The cytoplasm acts as a physical buffer, protecting the genetic material and organelles from damage caused by movement or collision with other cells.

The correct answer is Seed.

Key Points

• In the life cycle of flowering plants (Angiosperms), the process of fertilisation triggers significant developmental changes in the floral organs.
• The ovule, which contains the female gametophyte, undergoes a series of transformations following the fusion of gametes and eventually develops into a seed. Hence, option 1 is correct.
• During this transition, the integuments (the protective outer layers of the ovule) harden and dry out to form the seed coat or testa, which protects the internal embryo.
• The zygote, formed by the fusion of one male gamete with the egg cell, divides and differentiates to become the embryo, which is the "baby plant" contained within the seed.
• While the ovules turn into seeds, the surrounding ovary grows in size and ripens to become the fruit, acting as a vessel for seed protection and dispersal.

Additional Information

• Double Fertilisation: This is a characteristic feature of Angiosperms. It involves two fusions: one male gamete fuses with the egg (Syngamy) to form a diploid zygote, and the other fuses with two polar nuclei (Triple Fusion) to form a triploid endosperm.
• Endosperm: This tissue serves as a highly nutritious food store for the developing embryo. In some seeds, like Castor, the endosperm persists, while in others, like Pea and Bean, it is consumed during development.
• Fruit vs. Seed:
• The fruit is the ripened ovary.
• The seed is the ripened ovule.
• Fruit Types:
• True Fruits: Fruits that develop only from the ovary after fertilisation, such as Mango and Grapes.
• False Fruits: Fruits where other floral parts, like the thalamus, contribute to fruit formation, such as Apple, Cashew, and Strawberry.
• Parthenocarpic Fruits: Fruits that develop without fertilisation and are usually seedless, like Banana.

Important Points

• The micropyle, a small opening in the ovule, remains as a tiny pore in the seed coat. This is essential for the entry of water and oxygen during the process of germination.
• As the seed reaches maturity, its water content is significantly reduced, reaching about 10 to 15 percent moisture by mass.
• The embryo may enter a state of dormancy, which is a period of suspended growth that allows the seed to survive unfavorable environmental conditions until germination is possible.
• In Gymnosperms, seeds are produced but they are "naked" because they do not develop inside an ovary, and therefore, gymnosperms do not produce fruits.

The correct answer is The particles are closely packed in a fixed arrangement.

Key Points

• In a solid, the constituent particles (atoms, molecules, or ions) are held together by very strong intermolecular forces of attraction, which keeps them in a fixed arrangement.
• Because the particles are closely packed, there is negligible intermolecular space between them, making solids rigid and giving them a definite shape and volume. Hence, statement 1 is correct.
• The particles are randomly arranged in liquids and gases (and to some extent in amorphous solids), which prevents them from maintaining a permanent, rigid structure. Hence, statement 2 is incorrect.
• Solids do not have large spaces between particles; instead, they have the highest density compared to other states of matter because the particles are packed so tightly. Hence, statement 3 is incorrect.
• The particles in a solid cannot move freely past each other; they only vibrate about their fixed mean positions. The ability to flow or move freely is a property of fluids (liquids and gases). Hence, statement 4 is incorrect.

Additional Information

• Characteristics of Solids:
• They possess rigidity and are incompressible because the particles are already at minimum distance from each other.
• Solids can be classified into Crystalline (regular long-range order, e.g., Quartz, Sodium Chloride) and Amorphous (irregular short-range order, e.g., Glass, Rubber).
• The Kinetic Energy of particles in a solid is the lowest among the three primary states of matter.
• Comparison with Liquids:
• Liquids have a definite volume but no definite shape. They take the shape of the container because their particles have enough energy to slide over one another.
• The intermolecular forces in liquids are weaker than in solids but stronger than in gases.
• Comparison with Gases:
• Gases have neither a definite shape nor a definite volume. They expand to fill whatever container they are in.
• Gases have maximum intermolecular spaces and maximum kinetic energy, allowing particles to move at high speeds in all directions.

Important Points

• Thermal Energy vs. Intermolecular Forces: The state of matter is a result of the competition between Intermolecular Forces (which try to keep particles together) and Thermal Energy (which tries to keep them apart by increasing movement).
• In solids, at low temperatures, the thermal energy is low enough that intermolecular forces dominate, locking the particles into a fixed position.
• Diffusion: Solids show a very slow rate of diffusion compared to liquids and gases because the particle movement is restricted to vibration.
• Density: Most substances are densest in their solid state, with Ice being a notable exception (it is less dense than liquid water due to its open cage-like structure).

The correct answer is To detect birth defects and monitor the baby’s growth.

Key Points

• Ultrasonography (USG), often called an ultrasound, is a primary diagnostic tool used during pregnancy to visualize the fetus and the mother's reproductive organs.
• Its main function is to monitor the baby’s growth and development, ensuring that the fetus is hitting appropriate gestational milestones based on the date of conception.
• A critical application of this technology is to detect birth defects or congenital anomalies. Structural issues related to the heart, spine, brain, and limbs can often be identified through detailed scans like the Anomaly Scan (usually performed between 18 to 22 weeks).
• It is used to check the position of the placenta, the amount of amniotic fluid, and the heartbeat of the fetus, providing a comprehensive assessment of the pregnancy's health.
• Regarding the other options: It cannot determine the blood group of the baby (which requires invasive procedures like amniocentesis or cordocentesis), it is not used to measure mother's weight (done via a weighing scale), and while it can see the mother's organs, its primary routine use in pregnancy is not to check the mother’s heartbeat (which is monitored via pulse or ECG).

Additional Information

• Mechanism of Action: Ultrasonography works by emitting high-frequency sound waves (ultrasound) through a transducer. These waves bounce off internal structures and return as echoes, which a computer translates into real-time images.
• Types of Ultrasounds:
• 2D Ultrasound: The standard scan providing flat, cross-sectional images of the baby.
• 3D/4D Ultrasound: Used to see facial features and movements in more detail; often used to detect specific cleft lips or spinal defects.
• Doppler Ultrasound: Used to measure the blood flow through the baby's umbilical cord and heart.
• Safety: Unlike X-rays, ultrasonography does not use ionizing radiation, making it safe for both the mother and the developing fetus when used by trained professionals.
• Timelines:
• First Trimester (6-9 weeks): Used for dating the pregnancy and confirming the number of fetuses.
• Second Trimester (18-22 weeks): The Anomaly Scan (Level II) is performed to check for physical abnormalities.
• Third Trimester: Used to check fetal presentation (position like breech or cephalic) before delivery.

Important Points

• Legal Regulations in India: The use of ultrasound is strictly governed by the Pre-Conception and Pre-Natal Diagnostic Techniques (PCPNDT) Act, 1994.
• The PCPNDT Act prohibits the use of ultrasonography for sex determination to prevent female foeticide.
• It is mandatory for all ultrasound clinics and genetic laboratories to be registered under this Act, and disclosing the gender of the fetus is a criminal offense punishable by imprisonment and fines.
• Diagnostic Limitations: While highly effective, ultrasound cannot detect 100% of birth defects; some genetic disorders may require additional biochemical screening or DNA testing.

The correct answer is Localized repeated cell division at a specific site.

Key Points

• Budding is a form of asexual reproduction in which a new individual develops from a generative anatomical point of the parent organism.
• In organisms like Hydra, a bud develops as an outgrowth due to localized repeated cell division at one specific site. This ensures that the new individual is genetically identical to the parent.
• These buds grow into tiny individuals and, when fully mature, detach from the parent body to become new independent individuals.
• This process is characteristic of certain multicellular organisms (like Hydra) and unicellular organisms (like Yeast).
• Unlike sexual reproduction, this process does not involve the fusion of gametes or the production of seeds. Hence, statement 4 is correct.

Additional Information

• Asexual Reproduction:
• It is a mode of reproduction by which offspring arise from a single organism, and inherit the genes of that parent only.
• The offspring produced are clones, meaning they are morphologically and genetically identical to each other and to their parent.
• Common methods include binary fission (Amoeba), fragmentation (Spirogyra), spore formation (Rhizopus), and vegetative propagation (Rose, Potato).
• Reproduction in Yeast:
• Yeast is a unicellular fungus that reproduces asexually by budding.
• A small bulb-like projection, called a bud, comes out from the yeast cell. The nucleus of the parent cell divides into two, and one of the nuclei moves into the bud.
• The bud grows and eventually gets detached from the parent cell to form a new yeast cell.
• Comparison with Other Options:
• Development of seeds from flowers: This is a result of sexual reproduction involving pollination and fertilization. Hence, statement 1 is incorrect.
• Fusion of gametes: This defines syngamy in sexual reproduction, leading to genetic variation. Hence, statement 2 is incorrect.
• Random cell death: Also known as apoptosis, it is a programmed process for tissue maintenance or development (like losing a tail in tadpoles) but does not initiate new individuals in budding. Hence, statement 3 is incorrect.

Important Points

• Regenerative Cells: Organisms like Hydra use regenerative cells for reproduction in the process of budding. These cells undergo mitotic division rapidly.
• Conditions for Budding: This process usually occurs when environmental conditions are favorable, and there is an abundant supply of nutrients.
• Vegetative Propagation: In higher plants, reproduction through parts like roots, stems, or leaves is termed vegetative propagation. For example, Bryophyllum produces buds along its leaf margins which can grow into new plants.
• Binary Fission vs. Budding: In binary fission, the parent body divides into two nearly equal halves (e.g., Amoeba), whereas in budding, the parent remains intact while a smaller outgrowth is formed.

The correct answer is Hidden (recessive) alleles in sweet peas may offer resistance against future environmental stress.

Key Points

• Sexual reproduction in sweet pea plants (Pisum sativum) is a fundamental process that facilitates genetic recombination. This process involves meiosis, where crossing over and independent assortment create unique combinations of alleles in offspring.
• In a large population, recessive alleles can remain "hidden" in heterozygous individuals (carriers). While these traits might not be beneficial in current stable conditions, they provide a genetic reservoir that may contain traits essential for survival if the environment changes, such as resistance to a new pathogen or drought. Hence, statement 3 is correct.
• Maintaining "purity" through self-pollination or avoiding cross-pollination (Option 1) actually reduces genetic diversity and can lead to inbreeding depression, which weakens the long-term survival of the species. Hence, statement 1 is incorrect.
• Genetic variation inherently promotes diversity and phenotypic differences, such as variations in flower color, seed shape, and plant height. It does not aim for uniformity (Option 2), which is more characteristic of asexual reproduction or cloning. Hence, statement 2 is incorrect.
• While sexual reproduction is vital for evolution, it is generally slower and more energy-intensive than asexual reproduction. Biomass production (Option 4) is usually maximized through rapid vegetative growth rather than the complex process of gamete formation and fertilization. Hence, statement 4 is incorrect.

Additional Information

• Mendelian Genetics: Gregor Mendel conducted his historic experiments on sweet peas in the 1850s and 1860s. He identified that traits are inherited as discrete units (now known as genes) and established the Law of Segregation and the Law of Independent Assortment.
• Gene Pool: The total collection of genes and alleles in a population is called the gene pool. A large, diverse gene pool is a buffer against extinction, as it increases the likelihood that some individuals will possess the traits necessary to survive environmental shifts.
• Heterozygote Advantage: This occurs when an individual with a heterozygous genotype has higher fitness than those with homozygous dominant or recessive genotypes. This mechanism helps maintain recessive alleles within a population over generations.
• Environmental Stressors: These include biotic factors like fungal infections (e.g., powdery mildew) and abiotic factors like soil salinity or temperature fluctuations. Genetic variation ensures that the sweet pea population is not wiped out by a single adverse event.

Important Points

• Role of Meiosis: During Prophase I of meiosis, homologous chromosomes exchange segments (crossing over), ensuring that no two gametes are identical. This is the primary engine of variation in sexually reproducing organisms.
• Long-term Survival vs. Short-term Efficiency: Sexual reproduction may seem "wasteful" because it requires finding a pollinator or mate, but the evolutionary benefit of adaptation far outweighs the metabolic costs in dynamic ecosystems.
• Population Size: In large populations, the impact of genetic drift (random changes in allele frequencies) is minimized, allowing natural selection to act more effectively on the variation produced by sexual reproduction.

Shortcut Trick

For 2 years, the effective compound interest rate is calculated using the formula: x + y + (xy/100)%

Effective Rate = 15 + 15 + (15 × 15)/100 = 30 + 2.25 = 32.25%

Total Amount = 100% (Principal) + 32.25% (Interest) = 132.25%

Required Amount = 8400 × 132.25% = 84 × 132.25 = 11109

∴ The correct answer is ₹11,109.

Alternate Method

Given: Principal (P) = ₹8,400, Rate (R) = 15% per annum, Time (n) = 2 years.

Formula Used: Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 8400 × (1 + 15/100)²

⇒ A = 8400 × (1 + 3/20)²

⇒ A = 8400 × (23/20) × (23/20)

⇒ A = 8400 × 529 / 400

⇒ A = 21 × 529

⇒ A = 11109

∴ The correct answer is ₹11,109.

Additional Information

Compound Interest vs Simple Interest for 2 Years

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

Effective Rate of Interest

For a rate of R% compounded annually for 2 years, the net effective rate is 2R + R²/100 %.

Compounding Frequency

If interest is compounded half-yearly, the rate becomes R/2 and the time period becomes 2n.

Shortcut Trick

Total New Price = 6 × [(860 × 1.05) + (2900 × 1.10)]

New Price of 1 Faucet = 860 + 43 = ₹903

New Price of 1 Wash Basin = 2900 + 290 = ₹3190

Total for 6 sets = 6 × (903 + 3190) = 6 × 4093 = ₹24,558

∴ The correct answer is ₹24,558.

Alternate Method

Given:

Price of faucet = ₹860

Price of wash basin = ₹2900

Increase in faucet price = 5%

Increase in wash basin price = 10%

Calculations:

⇒ New price of 1 faucet = 860 + (5/100 × 860) = 860 + 43 = ₹903

⇒ New price of 1 wash basin = 2900 + (10/100 × 2900) = 2900 + 290 = ₹3190

⇒ New price of 6 faucets = 6 × 903 = ₹5418

⇒ New price of 6 wash basins = 6 × 3190 = ₹19140

⇒ Total price = 5418 + 19140 = ₹24558

∴ The correct answer is ₹24,558.

Additional Information

Percentage Increase

New Value = Original Value × (1 + Rate/100). For a 5% increase, multiply by 1.05.

Distributive Property

To find the cost of multiple sets, use n × (Price A + Price B) which is equal to (n × Price A) + (n × Price B).

Successive Changes

If a price increases by x% and then y%, the effective increase is [x + y + (xy/100)]%.

Shortcut Trick

Assume all 363 children are girls, total amount = 363 × 6 = ₹2,178.

Difference from actual amount = 2,443 − 2,178 = ₹265.

Difference between a boy's share and a girl's share = 7 − 6 = ₹1.

Number of boys = Total Difference ÷ Share Difference = 265 ÷ 1 = 265.

∴ The correct answer is 265 boys.

Alternate Method

Given: Total children = 363, Total amount = ₹2,443, Girl's share = ₹6, Boy's share = ₹7.

⇒ Let the number of boys be x and the number of girls be (363 − x).

⇒ Total Amount = (Number of girls × 6) + (Number of boys × 7)

⇒ 2,443 = 6(363 − x) + 7x

⇒ 2,443 = 2,178 − 6x + 7x

⇒ 2,443 − 2,178 = x

⇒ x = 265

∴ The correct answer is 265 boys.

Additional Information

Alligation Method

This problem can also be solved using alligation by finding the average share per child (2,443 ÷ 363) and placing it in the center of the cross diagram.

Linear Equations in Two Variables

Standard algebraic approach: B + G = 363 and 7B + 6G = 2443. Multiply the first by 6 and subtract from the second to find B.

Unitary Method Logic

The surplus amount beyond the minimum guaranteed share (₹6 per child) is entirely attributed to the extra ₹1 given to each boy.

Shortcut Trick

Net discount % = a + b − (a × b) ÷ 100

Net discount = 20 + 30 − (20 × 30) ÷ 100 = 50 − 6 = 44%

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

SP = 7750 × (100 − 44) ÷ 100 = 7750 × 0.56 = 4340

∴ The correct answer is ₹4,340.

Alternate Method

Given → Marked Price (MP) = ₹7,750, Discount₁ (d₁) = 20%, Discount₂ (d₂) = 30%. Formulas: SP = MP × (100 − d₁)% × (100 − d₂)%

⇒ Price after 1st discount = 7750 × (80 ÷ 100) = 6200 ⇒ Final Selling Price = 6200 × (70 ÷ 100) ⇒ SP = 62 × 70 = 4340

∴ The correct answer is ₹4,340.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on an item. Discount is always calculated on the Marked Price to arrive at the Selling Price.

Successive Discount

When a series of discounts are applied, the second discount is calculated on the value remaining after the first discount. Formula: SP = MP × (1 − d₁/100) × (1 − d₂/100).

Shortcut Trick

Total Provision = Men × Days = 1200 × 13

New Men = 1200 + 360 = 1560

New Days = (1200 × 13) ÷ 1560

New Days = 15600 ÷ 1560 = 10

∴ The correct answer is 10 days.

Alternate Method

Given:

Initial Men (M₁) = 1200

Initial Days (D₁) = 13

Increase in Men = 360

Final Men (M₂) = 1200 + 360 = 1560

Formula Used:

M₁D₁ = M₂D₂

Calculations:

⇒ 1200 × 13 = 1560 × D₂

⇒ D₂ = (1200 × 13) ÷ 1560

⇒ D₂ = 15600 ÷ 1560

⇒ D₂ = 10

∴ The correct answer is 10 days.

Additional Information

Inverse Proportion

When the number of men increases, the number of days provisions last decreases proportionally: M₁ × D₁ = M₂ × D₂.

Chain Rule

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

Ratio Method

Ratio of Men = 1200 : 1560 = 10 : 13. Therefore, ratio of Days = 13 : 10. Since 13 units = 13 days, 10 units = 10 days.

Shortcut Trick A 45° sector represents exactly 1/8 of the circle's total circumference. Circumference = 2 × (22/7) × 21 = 132 m. Arc Length = 132 ÷ 8 = 16.5 m. Total Perimeter = Arc Length + (2 × Radius) = 16.5 + 42 = 58.5 m. ∴ The correct answer is 58.5 m. Alternate Method Given: Radius (r) = 21 m Central Angle (θ) = 45° π = 22/7 Formula Used: Perimeter of Sector = Arc Length (l) + 2 × Radius (r) Arc Length (l) = (θ ÷ 360) × 2 × π × r

Calculations: ⇒ Arc length (l) = (45 ÷ 360) × 2 × (22 ÷ 7) × 21 ⇒ l = (1 ÷ 8) × 2 × 22 × 3 ⇒ l = (1 ÷ 8) × 132 = 16.5 m ⇒ Perimeter = 16.5 + (2 × 21) ⇒ Perimeter = 16.5 + 42 ⇒ Perimeter = 58.5 m ∴ The correct answer is 58.5 m. Additional Information Area of a Sector The region bounded by two radii and an arc, calculated as Area = (θ/360) × πr2 or (1/2) × l × r. Length of an Arc The distance along the curved edge of a sector, given by the formula l = (θ/360) × 2πr. Major and Minor Sectors A minor sector has an angle θ < 180°, while a major sector has an angle of (360 − θ).

Shortcut Trick

Total amount to be deducted = 33 + 70 + 19 = ₹122

Remaining amount = 12,986 − 122 = ₹12,864

Ratio of remaining shares A : B : C = 14 : 8 : 2 (Total parts = 24)

Difference between B and C parts = 8 − 2 = 6 parts

Difference in shares = (12,864 ÷ 24) × 6 + (70 − 19) = 3216 + 51 = ₹3,267

∴ The correct answer is ₹3,267.

Alternate Method

Given: Total sum = ₹12,986. Deductions from A, B, and C are ₹33, ₹70, and ₹19 respectively. Ratio after deduction = 14 : 8 : 2.

⇒ Sum of remaining shares = 12,986 − (33 + 70 + 19)

⇒ Sum of remaining shares = 12,986 − 122 = ₹12,864

⇒ Total ratio parts = 14 + 8 + 2 = 24 units

⇒ 24 units = 12,864

⇒ 1 unit = 12,864 ÷ 24 = ₹536

⇒ B's original share = (8 × 536) + 70 = 4288 + 70 = ₹4,358

⇒ C's original share = (2 × 536) + 19 = 1072 + 19 = ₹1,091

⇒ Difference = 4,358 − 1,091 = ₹3,267

∴ The correct answer is ₹3,267.

Additional Information

Ratio and Proportion

Ratio is the comparison of two quantities of the same kind. If a : b = c : d, then ad = bc (Product of extremes = Product of means).

Deduction Rule

When values are deducted from a total sum to maintain a ratio, subtract the total deduction from the principal amount before applying the ratio division.

Shortcut Trick

Convert all to same base

4 = 2², 16 = 2⁴, 3⁴ and 9 = 3²

Compare powers of 2 and 3 separately

⇒ a = 1, b = 2

∴ Answer = (1, 2)

Alternate Method

Given:

(4²)^a × (16²)^2a × (3⁴)^b × (9²)^2b = 2²⁰ × (9²)⁶

Concept Used:

Laws of exponents

Calculation:

⇒ (4²)^a = (2⁴)^a = 2^4a

⇒ (16²)^2a = (2⁸)^2a = 2^16a

⇒ Total power of 2 = 2^20a

⇒ RHS = 2²⁰ ⇒ 20a = 20 ⇒ a = 1

⇒ (3⁴)^b = 3^4b

⇒ (9²)^2b = (3⁴)^2b = 3^8b

⇒ Total power of 3 = 3^12b

⇒ RHS = (9²)⁶ = (3⁴)⁶ = 3²⁴

⇒ 12b = 24 ⇒ b = 2

∴ The correct answer is (1, 2).

Additional Information

Exponent Rule

(a^m)ⁿ = a^mn

Same Base Rule

a^x = a^y ⇒ x = y

Conversion Trick

Convert numbers into prime base form

Separation Method

Compare powers of different bases separately

Shortcut Trick

Product of two numbers = HCF × LCM

216 × 120 = HCF × 1080

HCF = (216 × 120) ÷ 1080 = 216 ÷ 9 = 24

∴ The correct answer is 24.

Alternate Method

Given:

First Number (A) = 216

Second Number (B) = 120

LCM = 1080

Formula Used:

A × B = HCF(A, B) × LCM(A, B)

Calculations:

⇒ 216 × 120 = HCF × 1080

⇒ 25920 = HCF × 1080

⇒ HCF = 25920 ÷ 1080

⇒ HCF = 24

∴ The correct answer is 24.

Additional Information

HCF and LCM Relation

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

Co-prime Numbers

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

Fractional LCM/HCF

LCM of fractions = (LCM of Numerators) ÷ (HCF of Denominators). HCF of fractions = (HCF of Numerators) ÷ (LCM of Denominators).

Shortcut Trick

Total Expenditure % = 25% + 15% + 10% = 50%

Savings % = 100% − 50% = 50%

Monthly Savings = 50% of ₹40,000 = ₹20,000

∴ The correct answer is ₹20,000.

Alternate Method

Given:

Total Income = ₹40,000

Rent = 25% | Food = 15% | Transportation = 10%

Calculations:

⇒ Total spending = 25% + 15% + 10% = 50%

⇒ Remaining savings percentage = 100% − 50% = 50%

⇒ Savings amount = (50 ÷ 100) × 40,000

⇒ Savings amount = 0.5 × 40,000 = 20,000

∴ The correct answer is ₹20,000.

Additional Information

Percentage Change

To find the percentage of a value, use (Percentage/100) × Base Value.

Successive Percentage

If expenses are calculated on the remaining balance, use the formula: Final = Initial × (1 − r₁/100) × (1 − r₂/100).

Income-Expenditure Relation

Income = Expenditure + Savings. This base formula is used to solve most budget-related problems.

Shortcut Trick

Total Surface Area of a cylinder = 2πr(r + h), where π = 22/7.

The final result must be a multiple of 11 as it contains the factor 22.

Check divisibility by 11 (Difference of sum of digits at odd and even places):

Option (1) 2244: (2+4) − (2+4) = 0 (Divisible by 11).

Other options are not divisible by 11, so 2244 is the answer.

∴ The correct answer is 2244 cm².

Alternate Method

Given: Volume (V) = 6776 cm³, Height (h) = 44 cm

Formula Used: Volume = πr²h, Total Surface Area (TSA) = 2πr(r + h)

⇒ Volume = πr²h

⇒ 6776 = (22/7) × r² × 44

⇒ r² = (6776 × 7) / (22 × 44)

⇒ r² = 154 × 7 / 22 = 7 × 7

⇒ r = 7 cm

⇒ TSA = 2πr(r + h)

⇒ TSA = 2 × (22/7) × 7 × (7 + 44)

⇒ TSA = 44 × 51

⇒ TSA = 2244 cm²

∴ The correct answer is 2244 cm².

Additional Information

Curved Surface Area of a Cylinder

It is the area of the curved surface only, excluding the top and bottom circles. Formula: CSA = 2πrh.

Volume of a Cylinder

It is the total space occupied by the cylinder. Formula: Volume = πr²h.

Total Surface Area of a Cylinder

It is the sum of the curved surface area and the areas of the two circular bases. Formula: TSA = 2πr(r + h).

Radius and Diameter Relation

The diameter (d) of the circular base is always twice the radius (r). Formula: d = 2r.

Shortcut Trick

Distance is constant ∴ Speed ratio is the inverse of Time ratio.

Time ratio (Forward : Return) = 6 : 9 = 2 : 3

Speed ratio (Forward : Return) = 3 : 2

Speed difference = 3 − 2 = 1 unit → 2 km/h

Return speed = 2 units = 2 × 2 = 4 km/h

∴ The correct answer is 4 km/h.

Alternate Method

Given:

Time taken while walking forward (T₁) = 6 h

Time taken while returning (T₂) = 9 h

Decrease in speed = 2 km/h

Formula Used:

Distance = Speed × Time

⇒ Let the initial speed while walking forward be S km/h.

⇒ Distance covered = Speed × Time = S × 6 = 6S

⇒ Returning speed = (S − 2) km/h

⇒ Distance covered while returning = (S − 2) × 9 = 9(S − 2)

⇒ Since the distance is the same for both journeys:

⇒ 6S = 9(S − 2)

⇒ 6S = 9S − 18

⇒ 18 = 9S − 6S

⇒ 18 = 3S

⇒ S = 18 ÷ 3 = 6 km/h

⇒ Returning speed = S − 2 = 6 − 2 = 4 km/h

∴ The correct answer is 4 km/h.

Additional Information

Speed-Time Relationship

When distance is constant, speed is inversely proportional to time (S₁ × T₁ = S₂ × T₂).

Average Speed for Equal Distances

If an object covers equal distances at speeds x and y, the average speed is 2xy ÷ (x + y).

Unit Conversion

To convert speed from km/h to m/s, multiply the value by 5 ÷ 18.

Shortcut Trick

In an equilateral triangle ABC of side 'a', if a point D divides side BC such that BD = a/n,

The relation is given by the formula: n²AD² = (n² − n + 1)AB².

Here, 3BD = BC ⇒ BD = BC/3, so n = 3.

Substituting n = 3: 3²AD² = (3² − 3 + 1)AB²

9AD² = (9 − 3 + 1)AB² ⇒ 9AD² = 7AB².

∴ The correct answer is 9AD²=7AB².

Alternate Method

Given: ΔABC is equilateral, so AB = BC = CA. Point D is on BC such that BD = BC/3.

Formula Used: Pythagoras Theorem: Hypotenuse² = Base² + Perpendicular².

Let the side of the equilateral triangle AB = BC = CA = a.

Draw altitude AM ⊥ BC. In an equilateral triangle, altitude bisects the base.

⇒ BM = MC = BC/2 = a/2.

⇒ AM = √(AB² − BM²) = √(a² − (a/2)²) = √(3a²/4) = (√3/2)a.

Given BD = BC/3 = a/3.

⇒ DM = BM − BD = a/2 − a/3 = (3a − 2a)/6 = a/6.

In right-angled ΔADM, apply Pythagoras theorem:

⇒ AD² = AM² + DM²

⇒ AD² = [(√3/2)a]² + (a/6)²

⇒ AD² = 3a²/4 + a²/36

⇒ AD² = (27a² + a²) / 36

⇒ AD² = 28a² / 36 = 7a² / 9

⇒ 9AD² = 7a²

Since a = AB:

⇒ 9AD² = 7AB².

∴ The correct answer is 9AD²=7AB².

Additional Information

Height of Equilateral Triangle

The altitude or height (h) of an equilateral triangle with side 'a' is always (√3/2)×a.

Area of Equilateral Triangle

The area is given by (√3/4)×a², where 'a' is the length of the side.

Inradius and Circumradius

For side 'a', the Inradius (r) is a/(2√3) and the Circumradius (R) is a/√3. Note that R = 2r.

Apollonius Theorem

For any triangle with side AB, AC and median AD on BC: AB² + AC² = 2(AD² + BD²).

Shortcut Trick

LCM of 9 and 12 = 36 units (Total Capacity of the tank).

Efficiency of Filling pipe = 36 ÷ 9 = +4 units/min.

Efficiency of Emptying pipe = 36 ÷ 12 = −3 units/min.

Combined Efficiency = 4 − 3 = 1 unit/min.

Time to fill one-half (36 ÷ 2 = 18 units) = 18 ÷ 1 = 18 minutes.

∴ The correct answer is 18.

Alternate Method

Given:

Time taken by filling pipe = 9 minutes

Time taken by emptying pipe = 12 minutes

Formula used: Efficiency = Total Work ÷ Time

Calculations:

⇒ Total Capacity of tank = LCM(9, 12) = 36 units

⇒ Net efficiency of both pipes = 4 − 3 = 1 unit/min

⇒ Required capacity to fill = 1/2 × Total Capacity

⇒ Required capacity = 36 ÷ 2 = 18 units

⇒ Time required = Required capacity ÷ Net efficiency

⇒ Time = 18 ÷ 1 = 18 minutes

∴ The correct answer is 18.

Additional Information

Inflow and Outflow Concept

Efficiency of an inlet pipe is always taken as positive, while the efficiency of an outlet or emptying pipe is taken as negative.

Net Rate of Filling

If pipe A fills in x hours and pipe B empties in y hours (where y > x), the net part filled in 1 hour is (1/x − 1/y).

Time and Work Relation

Total Capacity = Time × Efficiency. For fractional work, Time = (Fraction × Total Capacity) ÷ Efficiency.

Shortcut Trick

Let assumed mean be 70.

Deviations from 70: −3, +6, +27, −36, −32, −7, +25, +25, +4

Sum of deviations = −3 + 6 + 27 − 36 − 32 − 7 + 25 + 25 + 4 = +9

Adjustment = Sum ÷ Count = 9 ÷ 9 = +1

Correct Mean = 70 + 1 = 71.

∴ The correct answer is 71.

Alternate Method

Given: Observations = 67, 76, 97, 34, 38, 63, 95, 95, 74

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

⇒ Total number of observations (n) = 9

⇒ Sum of observations = 67 + 76 + 97 + 34 + 38 + 63 + 95 + 95 + 74

⇒ Sum = 639

⇒ Arithmetic Mean = 639 ÷ 9

⇒ Arithmetic Mean = 71

∴ The correct answer is 71.

Additional Information

Properties of Arithmetic Mean

The sum of the deviations of a set of items from their arithmetic mean is always zero: Σ(x_i − mean) = 0.

Median and Mode

Median is the middle value of sorted data. Mode is the value that appears most frequently (here, 95).

Weighted Arithmetic Mean

Used when observations have different levels of importance: Mean = Σ(w_i × x_i) ÷ Σw_i.

Shortcut Trick

Net percentage increase for two successive years at 10% each = 10 + 10 + (10 × 10)/100 = 21%.

Total multiplying factor = 121% or 1.21.

Income in 2021 = 22,200 × 1.21 = 26,862.

∴ The correct answer is 26,862.

Alternate Method

Given:

Income in 2019 (P) = ₹22,200

Rate of increment (R) = 10% per annum

Time (n) = 2021 − 2019 = 2 years

Formula used: Final Income = P × (1 + R/100)ⁿ

⇒ Income in 2021 = 22200 × (1 + 10/100)²

⇒ Income in 2021 = 22200 × (110/100) × (110/100)

⇒ Income in 2021 = 22200 × 1.1 × 1.1

⇒ Income in 2021 = 22200 × 1.21

⇒ Income in 2021 = 26862

∴ The correct answer is 26,862.

Additional Information

Successive Percentage Change

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

Compound Growth Formula

The formula for population or income growth is A = P(1 + r/100)ⁿ, where P is the initial value and n is the number of years.

Multiplying Factor Method

For a 10% increase, the multiplying factor is (1 + 0.1) = 1.1. For n years, it becomes (1.1)ⁿ.

Shortcut Trick

The average of the first n odd natural numbers is always equal to n.

Here, the number of terms n = 10.

∴ Average = 10.

∴ The correct answer is 10.

Alternate Method

Given:

First 10 odd natural numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.

Formula Used:

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

Sum of an Arithmetic Progression (AP) = (n/2) × [First term + Last term]

Calculations:

⇒ Total terms (n) = 10

⇒ Sum = (10/2) × [1 + 19]

⇒ Sum = 5 × 20 = 100

⇒ Average = 100 ÷ 10

⇒ Average = 10

∴ The correct answer is 10.

Additional Information

Sum of first n odd numbers

The sum of the first n odd natural numbers is given by the formula n².

Average of first n even numbers

The average of the first n even natural numbers is always (n + 1).

Average of first n natural numbers

The average of the first n natural numbers is calculated as (n + 1) ÷ 2.

Shortcut Trick

When distance is constant, Speed is inversely proportional to Time (S ∝ 1/T).

Ratio of Time (T₁ : T₂) = 8 : 5

Ratio of Speed (S₁ : S₂) = 5 : 8

Given: 5 units = 17 km/h ⇒ 1 unit = 3.4 km/h

Required Speed (8 units) = 8 × 3.4 = 27.2 km/h

∴ The correct answer is 27.2 km/h.

Alternate Method

Given:

Initial Speed (S₁) = 17 km/h

Initial Time (T₁) = 8 min = 8/60 hours

New Time (T₂) = 5 min = 5/60 hours

Formula Used:

Distance = Speed × Time

⇒ Distance = S₁ × T₁

⇒ Distance = 17 × (8/60) km

⇒ New Speed (S₂) = Distance ÷ New Time (T₂)

⇒ S₂ = [17 × (8/60)] ÷ (5/60)

⇒ S₂ = 17 × 8 ÷ 5

⇒ S₂ = 136 ÷ 5

⇒ S₂ = 27.2 km/h

∴ The correct answer is 27.2 km/h.

Additional Information

Constant Distance Relation

When the same distance is covered at different speeds, S₁ × T₁ = S₂ × T₂. This allows for direct substitution without calculating distance.

Average Speed

If a person covers two equal distances at speeds x and y, then the average speed is (2xy) ÷ (x + y).

Unit Conversion

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

Shortcut Trick

Use the formula: Emptying time = (a × b) ÷ (b − a)

where a = filling time without leak and b = filling time with leak.

⇒ Emptying time = (6 × 8) ÷ (8 − 6)

⇒ Emptying time = 48 ÷ 2 = 24 hours.

∴ The correct answer is 24 hours.

Alternate Method

Given: Filling pipe (A) time = 6 hours | Filling pipe with leak (A + L) time = 8 hours.

Total capacity of cistern = LCM of (6, 8) = 24 units.

⇒ Efficiency of Leak (L) = Efficiency of (A + L) − Efficiency of A

⇒ Efficiency of L = 3 − 4 = −1 units/hour (Negative sign indicates emptying)

⇒ Time taken by leak to empty cistern = Total Capacity ÷ |Efficiency of L|

⇒ Time taken = 24 ÷ 1 = 24 hours.

∴ The correct answer is 24 hours.

Additional Information

Leakage Principle

A leak acts as an emptying pipe. Net efficiency = (Efficiency of filling pipe) − (Efficiency of leak).

Combined Rate Formula

If two pipes fill at rates x and y, combined rate = (x × y) ÷ (x + y). If one is a leak, the rate becomes (x × y) ÷ (y − x).

Pipes and Cisterns Basics

This topic follows the same logic as Time and Work, where work done is equivalent to cistern capacity.

Shortcut Trick

SP (excluding GST) = 1680 ÷ 1.2 = 1400

CP = 1400 ÷ 1.12 = 1250

∴ The correct answer is 1,250.

Alternate Method

Given:

Selling Price (including GST) = ₹1,680

GST Rate = 20%

Profit = 12%

Formula Used:

SP (excluding tax) = Total SP ÷ (1 + Tax%/100)

CP = SP (excluding tax) ÷ (1 + Profit%/100)

Calculations:

⇒ SP (without GST) = 1680 ÷ (1 + 20/100)

⇒ SP (without GST) = 1680 ÷ 1.2 = 1400

⇒ CP × (1 + 12/100) = 1400

⇒ CP × 1.12 = 1400

⇒ CP = 1400 ÷ 1.12

⇒ CP = 1250

∴ The correct answer is 1,250.

Additional Information

Profit and Loss Relationship

Profit % is always calculated on the Cost Price (CP) unless stated otherwise. SP = CP × (100 + Profit%)/100.

GST and Sales Tax

Taxes are applied to the net selling price. Total SP = Base SP × (100 + Tax%)/100.

Successive Percentage Change

If a value changes by a% then b%, the net multiplier is (1 + a/100) × (1 + b/100).

Shortcut Trick

Scheme A: 19 + 19 − 3.61 = 34.39%

Scheme B: Buy 2 get 10 → Discount = (8/10) × 100 = 80%

Scheme C: 11%

Scheme D: 25 + 17 − 4.25 = 37.75%

Comparing discounts: 80% > 37.75% > 34.39% > 11%

∴ The correct answer is B.

Alternate Method

Given:

Scheme A: Successive discounts 19% and 19%

Scheme B: Buy 2, get 10 items total

Scheme C: Single discount 11%

Scheme D: Successive discounts 25% and 17%

Formula Used:

Net Discount for successive a% and b% = [a + b − (ab/100)]%

Discount % for Buy X Get Y = [(Y − X) / Y] × 100

Calculations:

⇒ Net Discount A = 19 + 19 − (19 × 19)/100

⇒ Net Discount A = 38 − 3.61 = 34.39%

⇒ Net Discount B = [(10 − 2) / 10] × 100

⇒ Net Discount B = (8 / 10) × 100 = 80%

⇒ Net Discount C = 11%

⇒ Net Discount D = 25 + 17 − (25 × 17)/100

⇒ Net Discount D = 42 − 4.25 = 37.75%

⇒ Highest Discount = 80%

∴ The correct answer is B.

Additional Information

Successive Discounts

When two discounts a% and b% are given, the total discount is always less than the sum (a+b) because the second discount is applied to the already reduced price.

Buy X Get Y Free

The effective discount percentage is calculated as [Free items ÷ Total items (Paid + Free)] × 100.

Marked Price and Selling Price

Selling Price = Marked Price × (100 − D%)/100. For multiple discounts, SP = MP × (100 − d₁)/100 × (100 − d₂)/100.

Shortcut Trick

To find the quantity of the larger value when the sum and difference are known:

Quantity of Mangoes = (Sum of fruits + Difference) ÷ 2

Quantity of Mangoes = (96 + 42) ÷ 2

Quantity of Mangoes = 138 ÷ 2 = 69

∴ The correct answer is 69.

Alternate Method

Given:

Total fruits (Mangoes + Oranges) = 96

Difference (Mangoes − Oranges) = 42

Method: Linear Equation in One Variable

Let the number of Oranges be x.

Then, the number of Mangoes = x + 42

According to the question:

⇒ x + (x + 42) = 96

⇒ 2x + 42 = 96

⇒ 2x = 96 − 42

⇒ 2x = 54

⇒ x = 54 ÷ 2

⇒ x = 27 (Number of Oranges)

⇒ Number of Mangoes = 27 + 42 = 69

∴ The correct answer is 69.

Additional Information

Sum and Difference Formula

If the sum (S) and difference (D) of two numbers are known, the larger number is (S+D)÷2 and the smaller number is (S−D)÷2.

Linear Equations

Equations in the form ax + b = c are solved by isolating the variable x through inverse operations on both sides.

Ratio from Sum and Difference

The ratio of the two numbers can be calculated directly as (S+D) : (S−D). Here, Ratio = (96+42) : (96−42) = 138 : 54 = 23 : 9.

Shortcut Trick

Apply the identity (a − b)(a + b) = a² − b² successively to the terms.

(x − 1/x)(x + 1/x) = x² − 1/x²

(x² − 1/x²)(x² + 1/x²) = x⁴ − 1/x⁴

(x⁴ − 1/x⁴)(x⁴ + 1/x⁴) = x⁸ − 1/x⁸

∴ The correct answer is (x⁸ − 1/x⁸).

Alternate Method

Given: (x − 1/x)(x + 1/x)(x² + 1/x²)(x⁴ + 1/x⁴)

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

⇒ Simplifying the first two brackets:

⇒ (x − 1/x) × (x + 1/x) = x² − (1/x)² = x² − 1/x²

⇒ Multiplying the result with the third bracket:

⇒ (x² − 1/x²) × (x² + 1/x²) = (x²)² − (1/x²)² = x⁴ − 1/x⁴

⇒ Multiplying the result with the fourth bracket:

⇒ (x⁴ − 1/x⁴) × (x⁴ + 1/x⁴) = (x⁴)² − (1/x⁴)² = x⁸ − 1/x⁸

∴ The correct answer is (x⁸ − 1/x⁸).

Additional Information

Difference of Two Squares

The identity (a − b)(a + b) = a² − b² is used to simplify products of binomials containing the same terms with opposite signs.

Power of a Power Rule

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

Algebraic Identities

Other common identities include (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Shortcut Trick

The trigonometric ratio sin θ = 3/5 corresponds to Perpendicular / Hypotenuse.

Recognize the fundamental Pythagorean triplet: (3, 4, 5).

In this triplet, if Perpendicular = 3 and Hypotenuse = 5, then Base must be 4.

Using the ratio cos θ = Base / Hypotenuse, we get cos θ = 4/5.

∴ The correct answer is 4/5.

Alternate Method

Given: sin θ = 3/5

Formula: sin²θ + cos²θ = 1

⇒ cos²θ = 1 − sin²θ

⇒ cos θ = √(1 − (3/5)²)

⇒ cos θ = √(1 − 9/25)

⇒ cos θ = √((25 − 9) / 25)

⇒ cos θ = √(16/25)

⇒ cos θ = 4/5

∴ The correct answer is 4/5.

Additional Information

Trigonometric Identities

The primary identity is sin²θ + cos²θ = 1, from which we derive cos θ = √(1 − sin²θ).

Pythagorean Theorem

In a right-angled triangle, Base² + Perpendicular² = Hypotenuse².

Pythagorean Triplets

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

Ratio Definitions

sin θ = P/H, cos θ = B/H, tan θ = P/B, cot θ = B/P, sec θ = H/B, cosec θ = H/P.

Shortcut Trick

Ratio of Anil (A) to Bhavya (B) present ages = 5 : 4

Let present ages be 5x and 4x.

According to question: (4x + 6) = 2 × (5x) − 6

⇒ 4x + 6 = 10x − 6

⇒ 6x = 12 ⇒ x = 2

Difference between their ages = 5x − 4x = x = 2 years.

∴ The correct answer is 2.

Alternate Method

Given:

4 × Anil = 5 × Bhavya

After 6 years, Bhavya = 2 × Anil (Present) − 6

Let Anil's age = A and Bhavya's age = B

⇒ 4A = 5B ⇒ B = 4A/5

⇒ (B + 6) = 2A − 6

⇒ (4A/5) + 6 = 2A − 6

⇒ 4A/5 + 12 = 2A

⇒ 12 = 2A − 0.8A

⇒ 1.2A = 12

⇒ A = 10 years

⇒ B = (4 × 10)/5 = 8 years

⇒ Difference = 10 − 8 = 2 years

∴ The correct answer is 2.

Additional Information

Constant Age Difference

The difference between the ages of two people remains the same regardless of how many years pass.

Ratio to Value Conversion

If two quantities are in the ratio x : y, they can be represented as kx and ky, where k is the common multiplier.

Future and Past Ages

If current age is X, age after n years is (X + n) and age n years ago was (X − n).

The logic followed here is:

Option 1) TG – XK

Option 2) DW – HA

Option 3) BN – GS

Option 4) VR – ZV

Here, BN – GS is odd from the given options.

Hence, the correct answer is "Option 3".

The logic followed here is:

Given:

TEAR → 5731

POST → 2148

So, the code for T = 1.

Hence, the correct answer is Option 2.

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

Now,

Even numbers, which are immediately preceded by an odd number and also immediately followed by an odd number.

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

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

So, total valid even numbers = 4

Hence, the correct answer is Option 1.

Given:

Priya is 9th from the left end and Neeraj is 27th from the right end in a row of 36 students.

Here,

Neeraj’s position from the left end = (36 − 27) + 1 = 10th

Now, Number of people between Priya and Neeraj = (10 − 9) − 1

= 1 − 1

= 0

So, there are no people standing between Priya and Neeraj.

Hence, the correct answer is "Option 2".

The logic followed here is:

For LMUG → RHYD

Now, for JNSF → PIWC

Now, applying the same logic for HIVT:

So, HIVT → NDZQ

Hence, the correct answer is "Option 4".

The logic followed here is:

So, the missing term = XNG 62

Hence, the correct answer is Option 1.

The logic followed here is:

For ANTY → CKOZ

Now, for UIQL → WFLM

Now, applying the same logic for DSNB:

So, DSNB → FPIC

Hence, the correct answer is "Option 4".

The logic followed here is:

thus, "110" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

BODMAS Table: 

Decoding the given information:

 

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

⇒ 42 ÷ 7 × 8 + 16 − 9 = ?

⇒ 6 × 8 + 16 − 9 = ?

⇒ 48 + 16 − 9 = ?

⇒ 64 − 9 = ?

⇒ 55

Hence, the correct option is "Option 4".

The logic followed here is:

So, the missing term = KR25

Hence, the correct answer is Option 2.

The logic followed here is:

Option 1) EIM

Option 2) WBF

Option 3) MRV

Option 4) TYC

Here, EIM is odd from the given options.

Hence, the correct answer is "Option 1".

Given Statements:

Some bats are nets.

All cubs are nets.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some bats are cubs – Does not follow (No direct relation is given between bats and cubs).

II. All nets are cubs – Does not follow (Only all cubs are nets is given, not the reverse).

So, neither conclusion I nor conclusion II follows.

Hence, the correct answer is "Option 3".

The logic followed here is:

For JITD → EEQB

Now, for QHSB → LDPZ

Now, applying the same logic for TNYT:

So, TNYT → OJVR

Hence, the correct answer is "Option 3".

Given: 629, 125, 534, 756, 438

Now, Arrange the numbers in ascending order and compare their positions with the original sequence.

Original sequence: 629 125 534 756 438

Ascending order: 125 438 534 629 756

Only one number, 534, remains in the same position.

So, total unchanged positions = 1

Hence, the correct answer is Option 2.

The logic followed here is:

Given:

Anand starts from Point A and drives 43 km towards the south.

He then takes a left turn, drives 40 km, turns left and drives 45 km.

He then takes a left turn and drives 51 km.

He takes a final left turn, drives 2 km and stops at Point P.

 

So, To reach Point A, he must go 11 km towards the East

Hence, the correct answer is Option 2.

Given Statements:

All pencils are erasers.

All pencils are rulers.

All rulers are boxes.

The least possible Venn diagram for the given statement is:

Conclusions:

I. All pencils are boxes – Follows (All pencils are rulers and all rulers are boxes, so all pencils are boxes).

II. Some rulers are erasers –  Follows (Pencils are common to both rulers and erasers, so some rulers are erasers).

So, both conclusion I and conclusion II follow.

Hence, the correct answer is "Option 1".

Given:

Raman is 10th from the top and 5th from the bottom.

Here, Total students = 10 + 5 − 1 = 14

So, there are 14 students in the class.

Hence, the correct answer is "Option 2".

Family Chart:

Decoding the Symbols:

Given: N ÷ O × P − Q + S

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

Hence, N is the grandmother of S from the father’s side, i.e., father’s mother.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: Third Number = First Number + Second Number + 16.

For, (5, 14, 35) →

⇒ 5 + 14 = 19

⇒ 19 + 16 = 35

For, (4, 13, 33) →

⇒ 4 + 13 = 17

⇒ 17 + 16 = 33

Now, checking the options:

Option 1) (7, 16, 40)

⇒ 7 + 16 = 23

⇒ 23 + 16 = 39 ≠ 40

Option 2) (8, 17, 27)

⇒ 8 + 17 = 25

⇒ 25 + 16 = 41 ≠ 27

Option 3) (16, 7, 21)

⇒ 16 + 7 = 23

⇒ 23 + 16 = 39 ≠ 21

Option 4) (10, 19, 45)

⇒ 10 + 19 = 29

⇒ 29 + 16 = 45

Hence, the correct answer is Option 4.

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

Now,

Odd digits, which are immediately preceded by an odd digit and also immediately followed by an odd digit.

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

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

So, total valid odd digits = 9

Hence, the correct answer is Option 1.

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

Only two people sit to the left of U.

Only three people sit between U and R.

Only one person sits between R and S.

E sits to the immediate left of A.

D is not an immediate neighbor of R.

Now, People to the right of Q  →  1

Hence, the correct answer is "Option 2".

The logic followed here is:

Given:

Ravi drove 20 km from his office towards the north.

He then took a right turn and drove 5 km.

He took another right turn and drove 10 km,

and then turned right, drove 5 km,

and stopped at point A.

 

​

Hence, the shortest distance from the starting point is 10 km

Hence, the correct answer is Option 4.

The logic followed here is:

Given:

YARN → 5731

ROSE → 2148

So, the code for R = 1.

Hence, the correct answer is Option 3.

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

B sits second to the right of A.

E sits to the immediate left of A.

C is the immediate neighbour of F and G.

D sits second to the left of F.

 

So, No person sits between E and G.

Hence, the correct answer is "Option 3".

The logic followed here is:

Given number: 5431786

Logic:

Add 1 to each odd digit

Subtract 2 from each even digit

Original number: 5 4 3 1 7 8 6

New number: 6 2 4 2 8 6 4

Now, Highest digit = 8

Lowest digit = 2

Difference = 8 − 2 = 6

Hence, the correct answer is Option 4.

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

Only three people are seated to the left of H.

Only Q is seated to the right of S.

Only three people are seated between Q and I.

G is seated at some place to the right of R.

Now, People between R and S → 3

Hence, the correct answer is "Option 4".

The logic followed here is:

thus, "323" will replace the question mark in the given series.

Hence, the correct option is "Option 2".

The logic followed here is:

thus, "228" will replace the question mark in the given series.

Hence, the correct option is "Option 4".

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

Now,

Even numbers, which are immediately preceded by an odd number and also immediately followed by an even number.

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

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

So, total valid even numbers = 1

Hence, the correct answer is Option 1.

BODMAS Table: 

Decoding the given information:

<br>

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

⇒ 59 × 4 ÷ 2 + 150 × 2 − 102 ÷ 2 − 15 ÷ 5 − 10

⇒ 59 × 2 + 150 × 2 − 51 − 3 − 10

⇒ 118 + 300 − 51 − 3 − 10

⇒ 418 − 51 − 3 − 10

⇒ 367 − 3 − 10

⇒ 364 − 10

⇒ 354

Hence, the correct option is "Option 2".