RRB Group D Official Paper (Held On: 21 Dec, 2025 Shift 3) (Previous Year Paper)

The correct answer is convex mirrors.

Key Points

• Convex mirrors, also known as diverging mirrors, are the standard choice for rear-view mirrors (both side-view and interior mirrors) in automobiles.
• The primary reason for using a convex mirror is that it provides a much wider field of view compared to a plane mirror or a concave mirror because it is curved outwards.
• A convex mirror always forms a virtual, erect, and diminished image of the objects behind the vehicle, regardless of the distance of the object from the mirror.
• Because the images are diminished (smaller in size), it allows the driver to see a large area of the traffic behind them within a relatively small mirror surface.
• The focal point and the center of curvature of a convex mirror are imaginary points located behind the mirror, which cannot be reached.

Additional Information

• Plane Mirrors:
• In a plane mirror, the image is virtual, erect, and exactly the same size as the object.
• While it provides an accurate representation of distance, its field of view is quite narrow, making it less effective for monitoring multiple lanes of traffic.
• Concave Mirrors:
• A concave mirror is curved inwards (like a spoon). It can form both real and virtual images depending on the position of the object.
• If used as a rear-view mirror, the image would appear inverted (upside down) once the following vehicle moves beyond the focal length, which would be dangerous for a driver.
• Common uses of concave mirrors include shaving mirrors, dentist mirrors, and solar furnaces.
• Parabolic Mirrors:
• These are specialized spherical mirrors used to focus light into a single point or to produce a parallel beam of light.
• They are typically used in car headlights, torches, and telescopes rather than as rear-view monitors.

Important Points

• Magnification: For a convex mirror, the magnification (m) is always positive and less than 1. This indicates that the image is erect and smaller than the object.
• Mirror Formula: The relationship between object distance (u), image distance (v), and focal length (f) is expressed as 1/v + 1/u = 1/f.
• Sign Convention: According to the Cartesian sign convention, the focal length of a convex mirror is always positive, while that of a concave mirror is negative.
• Safety Warning: Many passenger-side convex mirrors carry the warning "Objects in the mirror are closer than they appear" because the diminished size of the image can trick the driver's perception of distance.
• Uses: Apart from vehicles, convex mirrors are used in ATM security, hallways of hospitals, and stores to prevent theft by providing a broad view of the surroundings.

The correct answer is Action and reaction are equal and opposite but act on two different bodies.

Key Points

• Newton’s Third Law of Motion states that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.
• According to the law, action and reaction are equal in magnitude but opposite in direction. They must act on two different bodies rather than a single body. Hence, statement 2 is correct.
• If the action and reaction acted on the same body, the net force would always be zero, and acceleration would be impossible. Hence, statement 1 is incorrect.
• The law emphasizes that forces always occur in pairs; there is no such thing as an isolated single force in nature. These forces act simultaneously and do not result in a time lag. Hence, statement 3 is incorrect.
• Since action and reaction act on different objects, they do not cancel each other out. A force can only be canceled by another force acting on the same object. Hence, statement 4 is incorrect.

Additional Information

• Historical Context: Sir Isaac Newton formulated the laws of motion and published them in his monumental work, "Philosophiæ Naturalis Principia Mathematica," in the year 1687.
• Examples of the Third Law:
• Recoil of a Gun: When a bullet is fired from a gun, it exerts a forward force (action) on the bullet, and the bullet exerts an equal and opposite force (reaction) on the gun, causing it to recoil.
• Walking: When a person walks, they push the ground backward with their feet (action), and the ground pushes the person forward with an equal force (reaction).
• Rocket Propulsion: A rocket accelerates forward by expelling exhaust gases backward at high velocity; the gases exert a reaction force (thrust) on the rocket.
• Law of Conservation of Momentum: Newton’s Third Law is the fundamental basis for the Law of Conservation of Momentum, which states that the total linear momentum of a closed system remains constant if no external force acts on it.
• Force Definition: In physics, a force is an interaction that, when unopposed, will change the motion of an object. It is a vector quantity measured in Newtons (N).

Important Points

• Internal vs. External Forces: While action-reaction pairs are equal and opposite, they are internal to the system of two interacting bodies. To change the acceleration of the system as a whole, an external force is required.
• Mass and Acceleration: Although the magnitude of the force is the same on both bodies, the resulting acceleration may differ significantly if the bodies have different masses, as per Newton’s Second Law (F = ma). For example, the Earth exerts the same gravitational force on a falling apple as the apple exerts on the Earth, but the Earth's massive size makes its acceleration negligible.

The correct answer is Ductility and malleability.

Key Points

• Ductility is the physical property of a material, specifically metals, that allows it to be stretched or drawn into thin wires without breaking or snapping. This property is essential for making electrical wiring.
• Malleability is the ability of a material to be deformed under compressive stress, which allows it to be beaten into thin sheets or foils using a hammer or by rolling, without cracking.
• Among all known elements, Gold is considered the most malleable and ductile metal. For instance, a wire of about 2 km length can be drawn from just 1 gram of Gold. Hence, the combination of these two properties is the correct answer.
• These properties arise because the atoms in a metallic lattice are arranged in layers that can slide over one another when force is applied, while the metallic bonds hold the structure together.

Additional Information

• Lustre and Hardness:
• Metallic Lustre refers to the shining surface of metals in their pure state. This is due to the reflection of light by free electrons.
• Hardness varies from metal to metal. While Iron and Copper are hard, alkali metals like Sodium and Potassium are so soft that they can be cut with a knife.
• Sonorous and Conductivity:
• Sonorous metals produce a ringing sound when they strike a hard object. This property is used in the manufacturing of school bells and musical instruments.
• Conductivity refers to the ability to transmit heat and electricity. Silver is the best conductor of electricity, followed by Copper and Aluminium.
• Melting Point and State:
• Most metals are solids at room temperature, with the notable exception of Mercury, which is a liquid.
• Metals generally have high melting points. Tungsten has the highest melting point (about 3422°C), making it ideal for bulb filaments. In contrast, Gallium and Cesium have very low melting points and can melt on a human palm.
• Chemical Nature:
• Metals are electropositive elements because they lose electrons to form positive ions. When metals burn in oxygen, they produce basic oxides (like Magnesium oxide), whereas non-metals produce acidic or neutral oxides.

The correct answer is Reflex action.

Key Points

• A reflex action is an automatic, spontaneous, and involuntary response of the body to a specific stimulus without the involvement of conscious thought.
• When a person touches a hot object, the heat acts as a stimulus that is detected by thermoreceptors (heat receptors) in the skin.
• The neural pathway that controls a reflex action is called a reflex arc. It involves sensory neurons carrying the signal to the spinal cord, and motor neurons carrying the response back to the effector muscles.
• In this process, the spinal cord processes the signal instead of the brain to ensure an extremely rapid response, which helps in protecting the body from immediate physical harm or injury. Hence, pulling a hand back on touching a hot object is a reflex action.
• Common examples of reflex actions include the knee-jerk reflex, blinking of eyes when an object approaches quickly, and pupil constriction in bright light.

Additional Information

• Thinking Action (Voluntary Action):
• These actions are performed consciously and are controlled by the forebrain (specifically the cerebrum).
• They involve deliberation, memory, and decision-making. Examples include writing a letter, riding a bicycle, or solving a mathematical problem.
• Unlike reflex actions, thinking actions are slower because the signal must travel to the brain for processing.
• Conditioned Action (Acquired Reflex):
• A conditioned reflex is a response that is learned through experience or repetitive training rather than being inborn.
• The most famous example is Ivan Pavlov’s experiment with dogs, where the dogs began to salivate at the sound of a bell.
• Other examples include typing on a keyboard or playing a musical instrument, where the body responds automatically due to long-term habituation.
• Hormonal Action:
• This refers to the chemical coordination in the body mediated by hormones secreted by endocrine glands.
• Hormonal responses are generally slower than nervous responses but have long-lasting effects.
• Examples include the release of Adrenaline during a "fight or flight" situation, or the regulation of blood sugar levels by Insulin.

Important Points

• Components of a Reflex Arc:
• Receptor: Organ like skin that receives the stimulus.
• Sensory Neuron: Conducts the nerve impulse from the receptor to the Central Nervous System (CNS).
• Relay Neuron (Interneuron): Located in the spinal cord, it connects the sensory neuron to the motor neuron.
• Motor Neuron: Conducts the response signal from the spinal cord to the effector.
• Effector: The muscle or gland that executes the final action, such as muscle contraction.
• Significance: Reflex actions are essential for survival as they allow the body to react to dangerous stimuli in milliseconds, often before the brain even perceives pain.

The correct answer is W = F x S.

Key Points

• Work Done (W) is defined in physics as the product of the Force (F) applied to an object and the Displacement (S) caused by that force in the direction of the force.
• The general mathematical expression for work is W = F S cos(theta), where theta represents the angle between the Force vector and the Displacement vector.
• In this specific case, the body moves in the same direction as the force, which means the angle theta is 0 degrees. Since the value of cos(0) is 1, the formula simplifies directly to W = F x S. Hence, the relation W = F x S is correct.
• The relation W = F/S suggests that work is inversely proportional to displacement for a constant force, which contradicts the physical definition of work. Hence, statement 1 is incorrect.
• The relations W = F + S and W = F - S are physically inconsistent because Force (measured in Newtons) and Displacement (measured in meters) have different dimensions and cannot be added or subtracted. Hence, statements 2 and 3 are incorrect.

Additional Information

• Nature of Work: Work is a scalar quantity, meaning it has only magnitude and no direction, even though it is derived from two vector quantities (Force and Displacement).
• SI Unit: The Standard International (SI) unit of work is the Joule (J). 1 Joule is defined as the work performed by a force of 1 Newton acting over a distance of 1 meter (1 J = 1 N-m).
• Types of Work:
• Positive Work: Occurs when the force and displacement are in the same direction (angle between 0 and 90 degrees), such as an object falling under gravity.
• Negative Work: Occurs when the force acts opposite to the direction of motion (angle between 90 and 180 degrees), such as the frictional force acting on a sliding box.
• Zero Work: Occurs when the force is perpendicular to the displacement (angle is 90 degrees), such as a person carrying a box horizontally, where gravity acts downwards.
• CGS Unit: In the Centimetre-Gram-Second system, the unit of work is the erg. One Joule is equal to 10^7 ergs.

Important Points

• Dimensional Formula: The dimensions of work are represented as [ML^2T^-2]. This is identical to the dimensions of Energy and Torque.
• Work-Energy Theorem: This principle states that the net work done by all forces acting on a particle is equal to the change in the Kinetic Energy of that particle.
• Prerequisites for Work: For work to be non-zero, two conditions must be met: a Force must be exerted, and there must be a Displacement of the object. If a person pushes against a stationary wall, the displacement is zero; therefore, the work done is zero.
• Power Correlation: Power is defined as the rate of doing work. It is calculated by dividing the Work Done by the Time (t) taken, expressed as P = W / t. The SI unit for power is the Watt (W).

The correct answer is Carbon dioxide gas.

Key Points

• When Ethanoic acid (commonly known as Acetic acid) reacts with Sodium carbonate (also known as Washing soda), a chemical reaction occurs that releases Carbon dioxide gas.
• The chemical equation for this reaction is 2CH3COOH + Na2CO3 → 2CH3COONa + H2O + CO2. In this process, Ethanoic acid reacts with the metal carbonate to produce Sodium ethanoate (a salt), Water, and Carbon dioxide.
• The evolution of Carbon dioxide gas is observed as brisk effervescence, which refers to the rapid formation of bubbles in the liquid as the gas escapes.
• This reaction is a characteristic property of carboxylic acids, where they react with carbonates and bicarbonates to evolve CO2, serving as a common laboratory test to identify the presence of a carboxyl group.
• The gas evolved can be identified by passing it through lime water (calcium hydroxide), which will turn milky due to the formation of Calcium carbonate.

Additional Information

• Ethanoic Acid (CH3COOH):
• It is a weak organic acid and the second simplest carboxylic acid after formic acid.
• In its concentrated form, it is called Glacial Acetic Acid because it freezes at 16.6 degrees Celsius, forming ice-like crystals.
• It is widely used in the food industry as Vinegar, which typically contains 5% to 8% ethanoic acid by volume.
• Sodium Carbonate (Na2CO3):
• Commonly known as Washing Soda, it is a basic salt derived from a strong base and a weak acid.
• It is used in glass manufacturing, water softening, and as a laboratory reagent.
• When it reacts with acids, it consistently produces Carbon dioxide, making it useful in fire extinguishers and effervescent salts.
• Hydrogen Gas (H2):
• Unlike carbonates, when metals like Zinc or Magnesium react with acids, they typically release Hydrogen gas.
• Hydrogen is a colorless, odorless gas that burns with a pop sound when a burning splinter is brought near it.
• Oxygen Gas (O2):
• Oxygen is not typically released in simple acid-base neutralization or acid-carbonate reactions.
• It is usually produced during the decomposition of certain oxides or electrolysis of water.

Important Points

• Reaction with Sodium Bicarbonate: Ethanoic acid also reacts with Sodium bicarbonate (NaHCO3, or baking soda) to produce the same gas, Carbon dioxide. The equation is CH3COOH + NaHCO3 → CH3COONa + H2O + CO2.
• Test for Carbon Dioxide: To confirm the identity of the gas, it is passed through Lime Water [Ca(OH)2]. The lime water turns milky because of the formation of insoluble Calcium Carbonate (CaCO3). If the gas is passed in excess, the milkiness disappears due to the formation of soluble Calcium Hydrogen Carbonate [Ca(HCO3)2].
• Functional Group Identification: The reaction with Sodium Carbonate is a standard analytical test to distinguish carboxylic acids from phenols and alcohols, as the latter do not typically release CO2 with carbonates.
• Salt Formation: The salt formed in this specific reaction, Sodium ethanoate (CH3COONa), is used in the textile industry and as a buffering agent in various chemical applications.

The correct answer is Antoine Laurent Lavoisier.

Key Points

• Antoine Laurent Lavoisier (1743–1794) was a prominent French chemist who is widely regarded as the "Father of Modern Chemistry" for his revolutionary contributions to the field.
• He was the first scientist to establish a strictly functional and modern definition of a chemical element.
• Lavoisier defined an element as a basic form of matter that cannot be broken down into simpler substances by any known chemical reaction. Hence, option 1 is correct.
• His findings and this specific definition were published in his landmark book, Traité Élémentaire de Chimie (Elementary Treatise on Chemistry), in the year 1789.
• In this work, he listed 33 substances that he considered elements based on this definition, including oxygen, nitrogen, hydrogen, phosphorus, mercury, zinc, and sulfur.

Additional Information

• Robert Boyle:
• Robert Boyle was an Anglo-Irish natural philosopher and chemist.
• In 1661, in his book The Sceptical Chymist, he was the first to use the term "element" in a scientific context to challenge the ancient Greek idea of four elements (earth, air, fire, water).
• While he laid the conceptual groundwork, he did not provide the experimental definition that Lavoisier later perfected.
• Robert Hooke:
• Robert Hooke (often misspelled as Hookie) was an English polymath and architect.
• He is most famous for discovering the law of elasticity, known as Hooke's Law, and for his work in microscopy.
• In 1665, he published Micrographia, where he used a microscope to observe cork and coined the biological term "cell."
• Charles Darwin:
• Charles Darwin was an English naturalist, geologist, and biologist.
• He is best known for his contributions to the science of evolution.
• His theory of natural selection was detailed in his 1859 book, On the Origin of Species, which transformed the biological sciences.

Important Points

• Law of Conservation of Mass: Lavoisier formulated this fundamental law, which states that in a chemical reaction, the mass of the products is always equal to the mass of the reactants; matter is neither created nor destroyed.
• Oxygen and Combustion: He played a vital role in naming oxygen in 1778 and hydrogen in 1783. He effectively debunked the phlogiston theory by proving that oxygen is necessary for combustion to occur.
• Chemical Nomenclature: Along with other colleagues, Lavoisier helped devise the first systematic method of chemical nomenclature, ensuring that the name of a chemical compound reflects its elemental composition.
• Metric System: As a member of various French academies, he was instrumental in the development of the metric system to standardize weights and measures across France.

The correct answer is 10.0 m/s2.

Key Points

• The relationship between the applied force, the mass of an object, and the resulting acceleration is defined by Newton’s Second Law of Motion.
• According to this law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The mathematical formula is expressed as F = m × a, or a = F / m.
• In the given problem, the Force (F) acting on the object is 60 N and the Mass (m) of the object is 6 kg.
• By substituting these values into the acceleration formula: a = 60 N / 6 kg.
• The calculation results in an acceleration (a) of 10.0 m/s2. Hence, the calculated value matches the correct option.

Additional Information

• Newton (N): It is the SI unit of force. One Newton is defined as the amount of force required to give a mass of 1 kilogram an acceleration of 1 meter per second squared (1 kg·m/s2).
• Mass (m): This is a fundamental property of matter that represents an object's resistance to acceleration when a force is applied. It is a scalar quantity and is measured in kilograms (kg) in the SI system.
• Acceleration (a): This is a vector quantity that describes the rate at which an object changes its velocity. Its standard unit is meters per second squared (m/s2).
• Newton's Second Law: This law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Important Points

• Vector Nature: Since Force is a vector, the acceleration produced will always occur in the same direction as the applied net force.
• Inertia: Mass is a measure of inertia; therefore, a larger mass requires a greater force to achieve the same acceleration as a smaller mass.
• Dimensional Consistency: When performing physics calculations, it is vital to ensure units are consistent. If the force is in Newtons and mass is in kilograms, the acceleration will naturally result in m/s2.
• Zero Acceleration: If the net force acting on a mass is zero, the acceleration will also be zero, meaning the object will either remain at rest or continue to move at a constant velocity, as per Newton's First Law.

The correct answer is One atom of the element only.

Key Points

• The symbol of an element is a shorthand notation or abbreviation used in chemistry to represent a specific chemical element. Primarily, it represents one atom of that element in a chemical reaction or formula. Hence, statement 4 is correct.
• A chemical symbol provides a qualitative and quantitative representation. Qualitatively, it identifies the name of the element; quantitatively, it represents one atom or a definite mass (atomic mass) of that element.
• While the symbol is derived from the name, it is not the full name itself but a standardized abbreviation consisting of one or two letters. Hence, statement 1 is incorrect.
• The concept of one mole of an element refers to 6.022 x 10²³ atoms (Avogadro's number). While a symbol in a balanced chemical equation can represent a molar ratio, fundamentally, the symbol itself stands for a single atomic unit. Hence, statement 2 is incorrect.
• The atomic number (number of protons) and mass number (protons plus neutrons) are numerical properties of an atom. Although they are often written alongside a symbol (as subscript and superscript), the symbol itself does not inherently "represent" these numbers; it represents the identity of the element. Hence, statement 3 is incorrect.
• For example, the symbol "C" represents one atom of Carbon. Similarly, "He" represents one atom of Helium.

Additional Information

• Origin of Chemical Symbols: The modern system of using letters to represent elements was proposed by the Swedish chemist J.J. Berzelius in the early 19th century (specifically around 1813). Before this, alchemists used complex pictorial symbols.
• Naming Conventions: The first letter of a symbol is always capitalized, while the second letter (if present) is always lowercase. For instance, Co represents Cobalt, whereas CO represents Carbon Monoxide (a compound).
• Latin and Greek Roots: Many symbols are derived from the Latin or Greek names of elements. For example, Fe comes from Ferrum (Iron), Au from Aurum (Gold), Cu from Cuprum (Copper), and Na from Natrium (Sodium).
• IUPAC Standardization: The International Union of Pure and Applied Chemistry (IUPAC) is the global authority that approves the official names and symbols for newly discovered elements to ensure consistency in scientific communication across all countries.
• Significance in Formulas: When a subscript is added to a symbol, it indicates the number of atoms in a molecule. For example, H represents one atom of Hydrogen, but H₂ represents one molecule of Hydrogen consisting of two atoms.

Important Points

• Atomic Mass Unit (amu): The symbol of an element also represents a mass equal to its atomic mass expressed in atomic mass units. For example, the symbol O represents 16 amu of Oxygen.
• Gram Atomic Mass: In laboratory calculations, the symbol can represent the gram atomic mass of an element, which is the mass of one mole of atoms in grams.
• Valency: The symbol is used to determine the valency or combining capacity of an element when writing chemical formulas using the criss-cross method.
• Isotopes: Symbols are also used to distinguish between isotopes of the same element by adding the mass number, such as ¹²C and ¹⁴C, though the base symbol remains the same as the number of protons (atomic number) does not change.

The correct answer is starch.

Key Points

• During the process of photosynthesis, plants utilize sunlight, water, and carbon dioxide to produce glucose, which serves as their primary source of energy.
• Glucose is a simple sugar (monosaccharide) that is highly soluble in water; if stored directly, it would increase the osmotic pressure within the plant cells, potentially causing them to burst or lose water balance.
• To prevent this, plants convert the surplus glucose into starch, a complex polysaccharide. Starch is insoluble in water and chemically inert, making it the most efficient form for long-term energy storage.
• This starch is stored in various parts of the plant, including the chloroplasts of leaves and specialized organelles called amyloplasts located in roots, seeds, and tubers.
• When the plant requires energy during periods without sunlight, such as at night or during dormancy, it breaks down the stored starch back into glucose to fuel its metabolic activities.

Additional Information

• Glucose: It is the immediate product of photosynthesis. It provides the energy needed for cellular respiration and acts as a building block for other organic molecules. However, it is not the primary storage molecule.
• Cellulose: While also a polymer of glucose, cellulose is a structural carbohydrate. It is the main component of the plant cell wall, providing rigidity and mechanical strength. Unlike starch, it is not used as a reserve food source.
• Proteins: These are macromolecules made of amino acids. Plants synthesize proteins by combining the carbohydrates produced in photosynthesis with nitrogen, phosphorus, and sulfur absorbed from the soil. They are essential for growth and enzymatic functions.
• Sucrose: This is a disaccharide (composed of glucose and fructose). Sucrose is the form in which carbohydrates are transported or translocated through the phloem from the leaves to other parts of the plant like the roots and fruits.

Important Points

• Composition of Starch: Starch is composed of two types of glucose polymers: amylose (a linear chain) and amylopectin (a highly branched chain).
• Iodine Test: The presence of starch in a plant leaf can be confirmed using the Iodine Test. When iodine solution is added to a leaf containing starch, it turns blue-black in color.
• Animal Storage: It is important to note that while plants store carbohydrates as starch, animals (including humans) store their excess glucose as glycogen in the liver and muscles.
• Economic Importance: Many staple foods consumed by humans, such as potatoes, rice, wheat, and maize, are rich in starch because these plants store significant reserves in their tubers or grains.
• Conversion Process: The conversion of glucose to starch involves a series of enzymatic reactions, specifically during the Calvin cycle and subsequent metabolic pathways in the stroma of the chloroplast.

The correct answer is near the conductor.

Key Points

• The magnetic field strength (magnetic flux density) produced by a straight current-carrying conductor is directly proportional to the magnitude of the current and inversely proportional to the distance from the conductor.
• According to Ampere’s Circuital Law and the Biot-Savart Law, the magnetic field (B) at a point is given by the relation B ∝ 1/r, where r is the radial distance from the wire.
• Near the conductor: As the distance r decreases, the value of the magnetic field B increases significantly. Therefore, the field is at its maximum intensity in the immediate proximity of the wire. Hence, statement 2 is correct.
• Far from the conductor: As the distance r increases, the magnetic field strength weakens rapidly. At very large distances, the field becomes negligible. Hence, statement 1 is incorrect.
• Outside a solenoid: In an ideal solenoid, the magnetic field lines are nearly parallel and very close together inside, but they spread out extensively in the exterior space. The magnetic field outside a solenoid is considered to be zero or extremely weak. Hence, statement 3 is incorrect.
• Equidistant from the conductor: Points that are equidistant from the conductor lie on a concentric circle. While the magnetic field strength is uniform (the same) at all these points, this phrase does not describe where the field is "strongest" relative to other locations. Hence, statement 4 is incorrect.

Additional Information

• Right-Hand Thumb Rule:
• This rule is used to determine the direction of the magnetic field around a straight conductor.
• If you hold the conductor in your right hand such that the thumb points in the direction of the electric current, then your fingers will curl around the conductor in the direction of the magnetic field lines.
• Characteristics of Magnetic Field Lines:
• For a straight wire, the field lines form concentric circles centered on the wire.
• The density of these field lines indicates the strength; they are crowded near the conductor and become spaced out as we move away.
• Magnetic field lines never intersect each other.
• Magnetic Field in a Solenoid:
• A solenoid is a long coil containing a large number of close turns of insulated copper wire.
• The magnetic field inside a solenoid is uniform and strong, represented by parallel straight lines. This property is used to magnetize materials like soft iron to create electromagnets.
• Units and Discovery:
• The SI unit of magnetic field strength is the Tesla (T), named after the physicist Nikola Tesla.
• In 1820, Hans Christian Oersted discovered that an electric current creates a magnetic field, marking the birth of electromagnetism.

Important Points

• Factors affecting the Magnetic Field:
• Current (I): Increasing the current increases the magnetic field strength (B ∝ I).
• Number of Turns (N): In a coil or solenoid, the field is proportional to the number of turns (B ∝ N).
• Medium: The presence of a ferromagnetic core (like soft iron) inside a coil increases the magnetic field intensity by thousands of times due to high magnetic permeability.
• Mathematical Representation: For an infinitely long straight wire, the formula is B = (μ₀I) / (2πr), where μ₀ is the permeability of free space (approximately 4π × 10⁻⁷ T·m/A).

The correct answer is the star is near the horizon.

Key Points

• The twinkling of stars, scientifically known as stellar scintillation, is caused by the atmospheric refraction of starlight as it passes through the Earth's atmosphere.
• When a star is near the horizon, the light coming from it has to travel through a much thicker layer of the atmosphere compared to when it is directly overhead (at the zenith).
• Because the light travels through more atmospheric layers with varying densities and temperatures, it undergoes multiple refractions. These layers are constantly moving due to thermal turbulence and wind, causing the light to bend in different directions rapidly.
• This continuous change in the refractive index of the air causes the apparent position and brightness of the star to fluctuate, making the twinkling effect more visible and pronounced. Hence, the correct answer is the star is near the horizon.
• In contrast, when a star is at the zenith, the starlight enters the atmosphere perpendicularly and travels the shortest distance, resulting in minimal refraction and less twinkling. Hence, statement 2 is incorrect.

Additional Information

• Atmospheric Refraction: This phenomenon occurs because the Earth's atmosphere is not uniform. It consists of several layers with different optical densities. As starlight enters the atmosphere, it gradually bends towards the normal because the air becomes denser closer to the Earth's surface.
• Planets do not twinkle: Unlike stars, which act as point sources of light due to their immense distance, planets are much closer to Earth and are seen as extended sources (a collection of many point sources). While the individual points of light from a planet may twinkle, the average brightness remains constant as the fluctuations cancel each other out.
• Apparent Position: Due to refraction, a star appears slightly higher in the sky than its actual position. This effect is most significant when the star is near the horizon.
• Sky conditions: While a cloudy sky might block starlight entirely or scatter it, it does not specifically make the "twinkling" more pronounced in a scientific sense; rather, it often obscures the star. Hence, statement 1 is incorrect.
• Moonlight: A bright moon increases the background luminance of the sky, which can actually make it harder to observe the subtle intensity changes of twinkling stars. Hence, statement 3 is incorrect.

Important Points

• Refractive Index: The refractive index of air depends on its temperature. Hot air is less dense and has a lower refractive index than cold air. The mixing of these air masses creates turbulent cells that act like tiny moving lenses.
• Vacuum: If there were no atmosphere (such as on the Moon or in outer space), stars would appear as steady, non-twinkling points of light because there would be no medium to refract the light.
• Color Flashing: Very bright stars near the horizon (like Sirius) often appear to flash different colors. This is because the atmosphere acts as a prism, dispersing the white starlight into its component colors through chromatic refraction.
• Observation: Astronomers often place telescopes on high mountains or in space (like the Hubble Space Telescope) to avoid the "blurring" and "twinkling" caused by the Earth's turbulent atmosphere, allowing for clearer images.

The correct answer is To filter nitrogenous waste materials from the blood.

Key Points

• The kidneys are the primary organs of the human excretory system, responsible for maintaining the chemical balance of the body by processing blood.
• Their most critical function is to filter out metabolic waste products, specifically nitrogenous wastes such as urea, uric acid, and creatinine, from the bloodstream. Hence, option 1 is correct.
• Each kidney contains approximately 1 million structural and functional units called nephrons, which perform the actual filtration process.
• The filtration process in the nephron involves glomerular filtration (ultrafiltration), tubular reabsorption, and tubular secretion to ensure essential nutrients are retained while wastes are removed.
• The waste product formed after this filtration process is urine, which is then excreted from the body through the ureters, urinary bladder, and urethra.

Additional Information

• Homeostasis and Osmoregulation: The kidneys play a vital role in maintaining homeostasis by regulating the osmolarity of body fluids. They control the levels of water and electrolytes like sodium, potassium, and calcium.
• Regulation of Blood Pressure: Through the Renin-Angiotensin-Aldosterone System (RAAS), the kidneys help regulate long-term blood pressure by adjusting blood volume and vascular resistance.
• Endocrine Functions: The kidneys act as endocrine organs by secreting hormones such as Erythropoietin, which stimulates the production of red blood cells in the bone marrow, and Renin.
• Vitamin D Activation: They are responsible for converting calcifediol into calcitriol, the active form of Vitamin D, which is essential for calcium absorption in the intestines.
• pH Balance: The kidneys help maintain the acid-base balance (pH) of the blood by excreting hydrogen ions and reabsorbing bicarbonate from the urine.

Important Points

• Anatomy: In a healthy adult, each kidney is about 10-12 cm long, 5-7 cm wide, and weighs approximately 120-170 grams. They are located in the retroperitoneal space at the level of T12 to L3 vertebrae.
• Filtration Rate: The kidneys filter about 180 liters of fluid daily; however, nearly 99% of this is reabsorbed into the blood, resulting in only about 1.5 liters of urine production per day.
• Comparison with Other Functions:
• Digestion and nutrient absorption (Option 2) are primarily the functions of the stomach and small intestine.
• Oxygen absorption and carbon dioxide release (Option 3) are the primary functions of the lungs in the respiratory system.
• Transport of glucose and hormones (Option 4) is handled by the circulatory system (heart and blood vessels).
• Renal Failure: When kidneys lose their ability to filter, it leads to a condition called uremia, which may require medical interventions like dialysis or a kidney transplant.

The correct answer is Copper-T.

Key Points

• Copper-T (CuT) is a type of Intrauterine Device (IUD) that is inserted by medical professionals or expert nurses into the uterus through the vagina.
• It is a non-hormonal contraceptive device made of plastic and copper. It is T-shaped to fit the anatomy of the uterine cavity.
• The primary mechanism of action involves the release of copper ions, which increase the phagocytosis of sperm within the uterus.
• The released copper ions also suppress sperm motility and reduce the fertilizing capacity of the sperm, thereby preventing the sperm from reaching and fertilizing the egg.
• It is considered one of the most effective long-term reversible contraceptive methods, with specific models like CuT-380A providing protection for up to 10 years.
• In India, IUDs like Copper-T are widely accepted as a primary method of contraception for women who wish to space children or delay pregnancy.

Additional Information

• Condom:
• It is a barrier method of contraception made of thin rubber or latex sheath.
• It is used to cover the penis in the male or the vagina and cervix in the female just before coitus.
• Unlike IUDs, condoms prevent the physical meeting of the sperm and the ovum and offer the added benefit of protecting against Sexually Transmitted Infections (STIs) and AIDS.
• Oral Pills:
• These are hormonal contraceptives taken in the form of tablets. They contain small doses of either progestogens or a progestogen-estrogen combination.
• They work by inhibiting ovulation and implantation, as well as altering the quality of cervical mucus to prevent/retard the entry of sperm.
• Saheli is a well-known non-steroidal oral pill developed by the Central Drug Research Institute (CDRI) in Lucknow, India.
• Hormonal Patch:
• This is a transdermal patch applied to the skin that releases synthetic estrogen and progestogen hormones into the bloodstream.
• Similar to oral pills, the patch prevents ovulation (the release of an egg from the ovary) and thickens the cervical mucus.
• Categories of IUDs:
• Non-medicated IUDs: Example includes the Lippes Loop.
• Copper releasing IUDs: Examples include CuT, Cu7, and Multiload 375.
• Hormone releasing IUDs: Examples include Progestasert and LNG-20, which make the uterus unsuitable for implantation and the cervix hostile to sperm.

Important Points

• The effectiveness of Copper-T starts immediately upon insertion by a healthcare provider.
• While Copper-T is highly effective at preventing pregnancy, it does not provide any protection against HIV/AIDS or other sexually transmitted diseases.
• It is a reversible method; fertility returns to normal as soon as the device is removed from the uterus.
• Common side effects may include heavier menstrual bleeding or cramping, especially in the first few months after insertion.

The correct answer is Ionic bond.

Key Points

• An Ionic bond is a type of chemical linkage formed through the electrostatic attraction between two oppositely charged ions. This bond typically forms when a metal reacts with a non-metal.
• During the formation of an ionic bond, the metal atom loses one or more valence electrons to become a positively charged ion, known as a cation.
• The non-metal atom accepts these electrons to complete its outer shell, becoming a negatively charged ion, known as an anion.
• This complete transfer of electrons happens because metals generally have low ionization energy (they lose electrons easily), while non-metals have high electron affinity (they gain electrons easily).
• A common example is Sodium Chloride (NaCl), where a Sodium (Na) atom (metal) transfers its single valence electron to a Chlorine (Cl) atom (non-metal). Hence, the correct answer is Ionic bond.

Additional Information

• Covalent Bond:
• This bond involves the sharing of electron pairs between atoms. It typically occurs between two non-metals.
• Examples include Water (H₂O), Methane (CH₄), and Carbon Dioxide (CO₂).
• Unlike ionic bonds, there is no complete transfer of electrons; instead, the atoms reach stability by sharing.
• Metallic Bond:
• This bond occurs specifically between metal atoms. It is characterized by a "sea of delocalized electrons" that move freely around a lattice of positive metal nuclei.
• This structure accounts for properties like electrical conductivity, malleability, and ductility in metals like Copper (Cu) and Iron (Fe).
• Hydrogen Bond:
• This is a relatively weak intermolecular force rather than a primary chemical bond.
• It occurs when a hydrogen atom is covalently bonded to a highly electronegative atom (such as Nitrogen, Oxygen, or Fluorine) and experiences attraction to another electronegative atom nearby.

Important Points

• Electronegativity Difference: The nature of a bond is often determined by the electronegativity difference between the two elements. If the difference is greater than 1.7 on the Pauling scale, the bond is usually Ionic; if it is lower, it is Covalent.
• Physical State: Ionic compounds are typically crystalline solids at room temperature and have very high melting and boiling points due to the strong attraction between ions.
• Conductivity: Ionic compounds do not conduct electricity in solid form because the ions are fixed in place. However, they are excellent conductors when molten or dissolved in water (aqueous state) because the ions are free to move.
• Lattice Energy: The stability of an ionic compound is derived from its lattice energy, which is the energy released when gaseous ions combine to form a solid ionic crystal.
• Octet Rule: The primary driving force for forming ionic bonds is the Octet Rule, where atoms lose or gain electrons to achieve a stable electronic configuration similar to Noble Gases (usually 8 electrons in the outermost shell).

The correct answer is Taste.

Key Points

• Gustatory receptors are specialized sensory cells responsible for the perception of taste. These receptors are primarily located on the tongue, though they are also found on the soft palate, epiglottis, and pharynx.
• These receptors are clustered into structures known as taste buds, which are embedded within papillae (small bumps on the tongue surface). Each taste bud contains 50 to 100 taste receptor cells.
• The primary function of gustatory receptors is to detect chemical substances dissolved in saliva. These chemicals (tastants) bind to the receptors, triggering nerve impulses that are sent to the brain for processing.
• Human gustatory receptors can distinguish between five primary tastes: Sweet, Sour, Salty, Bitter, and Umami (savory).
• While gustatory receptors detect taste, the overall perception of flavor is a combination of signals from both taste buds and olfactory (smell) receptors. Hence, the correct answer is Taste.

Additional Information

• Smell (Olfaction):
• The detection of smell is performed by olfactory receptors located in the olfactory epithelium at the top of the nasal cavity.
• These are chemoreceptors that detect volatile chemical molecules in the air. Hence, statement 1 is incorrect regarding gustatory receptors.
• Light (Vision):
• Light is detected by photoreceptors located in the retina of the eye.
• There are two main types of photoreceptors: Rods (responsible for vision in low light) and Cones (responsible for color vision and detail). Hence, statement 2 is incorrect.
• Sound (Hearing):
• Sound waves are detected by phonoreceptors (also called auditory receptors), which are a type of mechanoreceptor.
• These are found in the Organ of Corti within the cochlea of the inner ear. They convert mechanical vibrations into electrical signals. Hence, statement 4 is incorrect.
• Touch (Somatosensation):
• The skin contains various receptors such as mechanoreceptors (for pressure and texture), thermoreceptors (for temperature), and nociceptors (for pain).

Important Points

• Cranial Nerves: Taste information from the gustatory receptors is carried to the brainstem (specifically the medulla oblongata) by three main cranial nerves: the Facial Nerve (VII) for the front two-thirds of the tongue, the Glossopharyngeal Nerve (IX) for the back one-third, and the Vagus Nerve (X) for the throat area.
• The Umami Taste: This was officially recognized as the fifth basic taste in the year 1985, though it was first identified by Japanese chemist Kikunae Ikeda in 1908. It detects the presence of glutamate, often found in protein-rich foods.
• Adaptation: Gustatory receptors exhibit rapid adaptation, meaning the sensitivity to a constant taste stimulus decreases quickly over time (e.g., the first bite of food often tastes more intense than the last).
• Age and Taste: The number of taste buds typically decreases with age, often starting after age 50, which can lead to a reduced ability to detect flavors.

The correct answer is Concentration → Reduction → Refining.

Key Points

• The extraction of metals from their ores involves several physical and chemical processes collectively known as Metallurgy. The standard sequence followed is Concentration, followed by Reduction, and finally Refining.
• Concentration of Ore: Also known as ore-dressing or beneficiation, this is the initial step where impurities such as sand, clay, and rocks (collectively called gangue) are removed from the mined ore. Methods used include hydraulic washing, magnetic separation, or froth flotation. Hence, the first stage in the sequence is Concentration.
• Reduction: Once the ore is concentrated and usually converted into a metal oxide (via roasting or calcination), it undergoes reduction. In this stage, the metal oxide is reduced to the crude metal by removing oxygen. This is often done using reducing agents like carbon (coke), carbon monoxide, or through electrolysis for highly reactive metals. Hence, the second stage in the sequence is Reduction.
• Refining: The metal obtained after reduction is usually impure and contains other metals or non-metals. Refining is the final treatment to obtain pure metal of high grade. Common techniques include distillation, liquation, and electrolytic refining. Hence, the third stage in the sequence is Refining.
• Therefore, the correct operational sequence in metallurgical extraction is Concentration → Reduction → Refining. Hence, option 1 is correct.

Additional Information

• Gangue and Flux: Gangue refers to the earthy impurities associated with the ore. A substance called Flux is added during the extraction process to remove gangue by forming a fusible material known as Slag.
• Roasting and Calcination:
• Roasting: The process of heating sulphide ores strongly in the presence of excess air to convert them into oxides.
• Calcination: The process of heating carbonate or hydrated ores strongly in the absence or limited supply of air to remove volatile impurities and convert them into oxides.
• Reactivity Series and Extraction:
• High Reactivity Metals (e.g., Sodium, Magnesium, Aluminium): These are extracted by electrolytic reduction of their molten chlorides or oxides because they cannot be reduced by carbon.
• Medium Reactivity Metals (e.g., Zinc, Iron, Lead): Usually found as sulphides or carbonates, converted to oxides, and then reduced using carbon.
• Low Reactivity Metals (e.g., Mercury, Copper): These can often be reduced to metal by simply heating their ores in air.
• Electrolytic Refining: This is the most widely used method for refining metals like Copper (Cu), Zinc (Zn), and Nickel (Ni). In this process, the impure metal acts as the anode, and a thin strip of pure metal acts as the cathode. On passing electricity, pure metal from the anode dissolves into the electrolyte and deposits onto the cathode.

Important Points

• Froth Flotation: This specific concentration method is primarily used for sulphide ores. It relies on the principle that ore particles are wetted by oil while gangue particles are wetted by water.
• Thermite Process: A reduction method where a highly reactive metal like Aluminium is used as a reducing agent to displace a metal from its oxide, often used for joining railway tracks (Iron oxide reduction).
• Purity Levels: While concentration increases the percentage of the metal in the ore, and reduction yields the metal, only Refining ensures a purity level often exceeding 99.9%.

The correct answer is Sound is the fastest in solids, slower in liquids and the slowest in gases..

Key Points

• Sound is a mechanical wave that requires a material medium (solid, liquid, or gas) to travel. It cannot travel through a vacuum.
• The speed of sound depends on the elasticity and density of the medium. In solids, the molecules are tightly packed and held together by strong intermolecular forces, allowing vibrations to transfer very rapidly. Hence, statement 2 is correct.
• In liquids, the molecules are less tightly packed than in solids but more so than in gases. Consequently, sound travels slower in liquids than in solids but faster than in gases. For example, the speed of sound in water is approximately 1480 m/s.
• In gases, molecules are far apart, meaning the collisions between them occur less frequently, which results in the slowest speed of propagation. For instance, in air at 20°C, sound travels at approximately 343 m/s. Hence, statement 1 is incorrect.
• Sound cannot travel through a vacuum because there are no particles to carry the vibrations. Hence, statement 3 is incorrect.
• The speed of sound is not the same in all mediums; it varies significantly based on the physical state and temperature of the substance. Hence, statement 4 is incorrect.

Additional Information

• Nature of Sound Waves:
• Sound waves are longitudinal waves, meaning the particles of the medium vibrate parallel to the direction of the wave's propagation.
• In solids, sound can also travel as transverse waves, but in fluids (liquids and gases), they are primarily longitudinal.
• Effect of Temperature:
• The speed of sound increases with an increase in temperature. For example, in air, the speed increases by approximately 0.6 meters per second for every 1 degree Celsius rise in temperature.
• This happens because higher temperatures increase the kinetic energy of the molecules, leading to more frequent collisions.
• Elasticity vs. Density:
• While higher density usually tends to slow down sound, the significantly higher elasticity (bulk modulus) of solids more than compensates for their density, resulting in the highest speeds in materials like steel (approx 5960 m/s) or aluminum (approx 6420 m/s).
• Historical Context and Applications:
• The Bell Jar Experiment is a classic scientific demonstration used to prove that sound cannot travel in a vacuum.
• Understanding sound propagation is essential in fields like SONAR (Sound Navigation and Ranging) used by submarines, medical ultrasonography, and seismology to study Earth's interior.

Important Points

• Human Hearing Range: The human ear can typically hear frequencies between 20 Hz and 20,000 Hz (20 kHz).
• Infrasonic and Ultrasonic: Sounds with frequencies below 20 Hz are called infrasonic (often produced by elephants or whales), while frequencies above 20,000 Hz are ultrasonic (used by bats for navigation).
• Mach Number: This is the ratio of the speed of an object to the speed of sound in the surrounding medium. If an aircraft travels faster than sound, it is called supersonic, which produces a sonic boom.

The correct answer is Salivary Amylase.

Key Points

• Salivary amylase, also referred to as ptyalin, is the primary enzyme present in the saliva of humans and several other mammals.
• It is synthesized and secreted by the salivary glands, which include the parotid, submandibular, and sublingual glands.
• The main function of this enzyme is to initiate the chemical digestion of carbohydrates (specifically starch) in the buccal cavity (mouth).
• Salivary amylase works by breaking down the long chains of starch (polysaccharides) into simpler disaccharides like maltose and smaller polymers called dextrins.
• The enzyme operates most efficiently at an optimum pH of 6.8, which is slightly acidic, and requires chloride ions (Cl-) for its activation.
• It is estimated that nearly 30 percent of the total dietary starch is hydrolyzed in the oral cavity before the food reaches the stomach. Hence, the correct answer is Salivary Amylase.

Additional Information

• Composition of Saliva:
• Saliva is a watery fluid containing 99.5% water and 0.5% solutes, including electrolytes like Sodium (Na+), Potassium (K+), Chloride (Cl-), and Bicarbonate (HCO3-).
• Apart from amylase, it contains Lysozyme, an antibacterial agent that prevents infections by attacking the cell walls of certain bacteria.
• Other Digestive Enzymes:
• Proteases: These are enzymes that digest proteins. While Salivary Protease is not a standard component of human saliva, protein digestion mainly begins in the stomach with pepsin.
• Lipases: While a very small amount of lingual lipase is secreted by glands on the tongue, its activity is minimal in the mouth and becomes more significant in the acidic environment of the stomach.
• Pancreatic Amylase: Once food reaches the small intestine, the digestion of remaining starch is completed by amylase secreted by the pancreas.
• The Salivary Glands:
• Parotid Glands: Located near the ears; these are the largest salivary glands.
• Submandibular Glands: Located along the inner side of the lower jaw.
• Sublingual Glands: Located beneath the tongue.

Important Points

• Bolus Formation: The mechanical action of teeth (mastication) combined with the lubricating effect of mucus in saliva turns food into a soft mass called a bolus, which is then swallowed (deglutition).
• Inactivation in Stomach: When the bolus reaches the stomach, the highly acidic gastric juice (pH 1.5 to 2.5) denatures and inactivates the salivary amylase, halting carbohydrate digestion until it reaches the duodenum.
• Taste Perception: Saliva acts as a solvent, dissolving food chemicals so they can be detected by taste buds located on the papillae of the tongue.
• Dental Health: The Bicarbonate ions in saliva act as a buffer, neutralizing acids produced by bacteria, thereby protecting the tooth enamel from decay.

The correct answer is 4F N.

Key Points

• According to Newton’s Law of Universal Gravitation, every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• The mathematical expression for this force is F = G (M × m) / r², where G is the Gravitational Constant, M is the mass of the Earth, m is the mass of the body, and r is the distance between them.
• In the initial scenario, the force is given as F. If the mass of the body m is increased to 4m while keeping the mass of the Earth M and the distance r constant, the new force F' is calculated as: F' = G (M × 4m) / r².
• By rearranging the equation, we get F' = 4 × [G (M × m) / r²]. Since the term in the bracket is the original force F, the new force becomes 4F. Hence, the gravitational force increases by four times.

Additional Information

• Universal Gravitational Constant (G): It is a scalar quantity and its value is 6.674 × 10⁻¹¹ N·m²/kg². This value was first experimentally determined by Henry Cavendish in 1798 and remains constant everywhere in the universe.
• Mass vs. Weight: While mass is the amount of matter in a body and remains constant (m), weight is the gravitational force exerted by the Earth on that body (W = mg). If the mass of an object increases, its weight increases proportionally.
• Inverse Square Law: The gravitational force is highly sensitive to distance. If the distance between the Earth and the body were doubled, the force would decrease to one-fourth (F/4) of its original value.
• Acceleration due to Gravity (g): On the surface of the Earth, the value of g is approximately 9.8 m/s². It is derived from the formula g = GM / r², showing that the acceleration of a falling object does not depend on the mass of the object itself, but the force acting on it does.
• Earth's Characteristics: The Earth has a mass of approximately 5.97 × 10²⁴ kg and a mean radius of about 6,371 km. These parameters define the strength of the gravitational field we experience daily.

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

Key Points

• Statement A: Heating Sodium Hydrogen Carbonate (commonly known as Baking Soda) results in its thermal decomposition to produce Sodium Carbonate, water, and carbon dioxide. While Sodium Carbonate is the base of washing soda, Washing Soda specifically refers to the crystalline form, Sodium Carbonate Decahydrate (Na2CO3.10H2O). To obtain washing soda, recrystallization of the anhydrous sodium carbonate with ten molecules of water is necessary. Simple heating alone produces soda ash (anhydrous sodium carbonate), not the hydrated washing soda. Hence, statement A is incorrect.
• Statement B: Sodium carbonate (washing soda) is a highly versatile chemical used in various industrial processes. It is a primary raw material in the Glass industry for manufacturing bottles and window glass. It is also a key ingredient in the Soap and detergent industry due to its ability to act as a builder and surfactant booster. Furthermore, it is used in the Paper industry for the pulping and bleaching processes. Hence, statement B is correct.
• The chemical formula for Baking Soda is NaHCO3, and the reaction for its decomposition upon heating is: 2NaHCO3 → Na2CO3 + H2O + CO2.
• The transition from Sodium Carbonate to Washing Soda involves the addition of 10 molecules of water of crystallization, represented by the formula Na2CO3 + 10H2O → Na2CO3.10H2O.
• Hence, the correct answer is Statement A is incorrect but B is correct.

Additional Information

• Washing Soda (Sodium Carbonate Decahydrate):
• It is a basic salt that turns red litmus solution to blue, indicating its alkaline nature.
• One of its most important functions is the removal of permanent hardness of water by precipitating magnesium and calcium ions as carbonates.
• It is manufactured commercially using the Solvay Process (also known as the ammonia-soda process) which uses Brine, Ammonia, and Limestone as raw materials.
• Apart from glass and soap, it is used in the production of sodium compounds like Borax and as a cleaning agent for domestic purposes.
• Baking Soda (Sodium Hydrogen Carbonate):
• It is produced using the Solvay process where Carbon dioxide is passed through a concentrated solution of Sodium Chloride and Ammonia.
• It is used as an Antacid in medicine to neutralize excess Hydrochloric acid in the stomach, providing relief from acidity.
• In the culinary world, it is used to make Baking Powder, which is a mixture of baking soda and a mild edible acid like Tartaric acid. When heated, it releases CO2 gas, which makes bread or cakes rise and become soft and spongy.
• It is also a key component in Soda-acid fire extinguishers because it releases carbon dioxide when reacting with acids, which helps smother flames.

Important Points

• Water of Crystallization: This refers to the fixed number of water molecules present in one formula unit of a salt. For washing soda, this number is 10, making it a decahydrate.
• Efflorescence: When Washing Soda crystals are exposed to air, they lose nine molecules of water to form a monohydrate (Na2CO3.H2O), a process known as efflorescence.
• Chemical Nature: Both baking soda and washing soda are sodium salts of carbonic acid, but they differ in their pH levels and solubility, with washing soda being more strongly alkaline.

The correct answer is Producing male germ cells.

Key Points

• The stigma is the uppermost part of the carpel (female reproductive organ) of a flower like Hibiscus, and its primary role is receiving pollen grains during the process of pollination. Hence, statement 1 is a correct function of the stigma.
• To effectively capture pollen from various pollinators or the wind, the stigma provides a sticky surface. This stickiness ensures that the pollen grains adhere firmly to the flower. Hence, statement 3 is a correct function of the stigma.
• Once the pollen grain lands, the stigma plays a vital role in facilitating pollen tube growth by providing the necessary chemical signals and nutrients for the pollen to germinate. Hence, statement 4 is a correct function of the stigma.
• The production of male germ cells (male gametes) does not happen in the stigma. Instead, these cells are produced within the pollen grains, which are generated in the anther (the male part of the flower). Hence, statement 2 is NOT a function of the stigma.
• In a Hibiscus flower, the stigma is typically pentafid, meaning it is divided into five distinct lobes, each corresponding to a locule in the ovary.

Additional Information

• Structure of the Hibiscus Flower:
• The Hibiscus rosa-sinensis is a bisexual or hermaphrodite flower, meaning it contains both male (androecium) and female (gynoecium) reproductive parts.
• The stamen (male part) consists of the anther and filament. In Hibiscus, the filaments are fused to form a staminal tube, a condition known as monadelphous.
• The pistil or carpel (female part) consists of the stigma, style, and ovary. The style passes through the staminal tube.
• The Process of Fertilization:
• After pollination, the pollen tube grows down through the style to reach the ovary.
• The ovary contains ovules, which house the female gamete (egg cell).
• The male germ cells travel through the pollen tube to fuse with the egg cell, a process called syngamy or fertilization, resulting in a zygote.

Important Points

• Hibiscus is often used as a model organism in botany to study floral morphology because its reproductive parts are large and easily identifiable.
• The anthers of the Hibiscus are reniform (kidney-shaped) and monothecous (having one lobe).
• The stigma acts as a gatekeeper, often performing pollen rejection to prevent self-pollination or the growth of pollen from different species, thereby ensuring genetic diversity.
• The male germ cells are specifically formed when the generative cell inside the pollen grain divides by mitosis.

The correct answer is A circle with a ‘V’ inside, connected in parallel.

Key Points

• In a schematic electric circuit diagram, a voltmeter is represented by a circle with the letter ‘V’ inscribed inside it. This device is specifically designed to measure the electric potential difference between two points in a circuit.
• A voltmeter must always be connected in parallel with the component or part of the circuit across which the voltage is to be measured. This is because the potential difference remains the same across all branches in a parallel connection. Hence, statement 1 is correct.
• The standard symbol for a voltmeter is a circle; using a square with a ‘V’ is not a standard practice in conventional electrical schematics. Hence, statement 2 is incorrect.
• A circle with an ‘A’ inside represents an ammeter, which is used to measure electric current. Unlike a voltmeter, an ammeter is connected in series because current remains constant in a series circuit. Hence, statement 3 is incorrect.
• A rectangle with an ‘R’ (or more commonly a zig-zag line) represents a resistor, which is a passive component that provides resistance to the flow of current, rather than a measuring instrument. Hence, statement 4 is incorrect.
• An ideal voltmeter is considered to have infinite resistance. This characteristic ensures that it does not draw any significant current from the main circuit, thereby providing an accurate reading of the potential difference without altering the circuit's behavior.

Additional Information

• Potential Difference (Voltage):
• It is defined as the work done to move a unit positive charge from one point to another in an electric field. The SI unit of potential difference is the Volt (V), named after the physicist Alessandro Volta.
• Mathematically, Voltage (V) = Work Done (W) / Charge (Q).
• Ammeter vs. Voltmeter:
• An ammeter measures current in Amperes (A) and has very low resistance to minimize its impact on the total circuit resistance. It is always placed in series.
• A voltmeter measures voltage in Volts (V) and has very high resistance. It is always placed in parallel.
• Ohm's Law:
• Proposed by Georg Simon Ohm in 1827, it states that the current passing through a conductor between two points is directly proportional to the voltage across the two points, provided physical conditions like temperature remain constant (V = IR).
• Galvanometer:
• A galvanometer is an instrument used for detecting and measuring small electric currents. It can be converted into a voltmeter by connecting a high resistance (multiplier) in series with it.

Important Points

• Circuit Safety: Connecting a voltmeter in series can stop the flow of current in a circuit due to its exceptionally high resistance, rendering the circuit non-functional. Conversely, connecting an ammeter in parallel can lead to a short circuit and damage the meter because of its low resistance.
• Measurement Units:
• 1 Volt is the potential difference between two points when 1 Joule of work is done to move a charge of 1 Coulomb.
• Instruments like the Multimeter are versatile tools that can function as a voltmeter, ammeter, or ohmmeter depending on the setting chosen by the user.
• Schematic Symbols: Standard symbols facilitate global communication among engineers. A battery is shown as a series of long and short parallel lines, while a switch is shown as a break in the line that can be "opened" or "closed."

The correct answer is Milk.

Key Points

• Milk is considered a colloidal solution because it consists of liquid fat globules dispersed throughout an aqueous (water-based) solution.
• A colloid is a heterogeneous mixture in which the particle size of the substance is intermediate between a true solution and a suspension. The diameter of the particles typically ranges from 1 nanometer to 1000 nanometers.
• In milk, the dispersed phase is fat (lipids) and the dispersion medium is water. Because both the dispersed phase and the medium are liquids, it is specifically categorized as an emulsion.
• Colloids like milk exhibit the Tyndall effect, which is the scattering of a beam of light as it passes through the mixture, making the path of light visible.
• Unlike suspensions, the particles in a colloidal solution do not settle down at the bottom when left undisturbed for a long period, showing that milk is relatively stable.

Additional Information

• Salt Water:
• It is a True Solution. In this mixture, the sodium chloride (NaCl) particles are completely dissolved in water.
• The particle size is less than 1 nanometer, making it impossible to see them even with a powerful microscope. It does not scatter light.
• Sugar Solution:
• Like salt water, a sugar solution is also a True Solution. It is a homogeneous mixture where the solute (sugar) is uniformly distributed in the solvent (water).
• The particles are molecular in size and do not settle over time, nor can they be separated by filtration.
• Sand in Water:
• This is a Suspension. It is a heterogeneous mixture containing large solid particles (greater than 1000 nanometers) that are visible to the naked eye.
• If left undisturbed, the sand particles will settle at the bottom due to gravity. This mixture can be easily separated using a filter paper.

Important Points

• Types of Colloids: Colloids are classified based on the state of the dispersed phase and dispersion medium. Common examples include Fog (Aerosol), Whipped Cream (Foam), Jelly (Gel), and Muddy Water (Sol).
• Separation Techniques: While true solutions cannot be separated by physical means like filtration, colloids like milk can be separated into their components (like cream/fat) using centrifugation.
• Brownian Motion: The particles in a colloidal solution move in a zig-zag path, known as Brownian motion, which helps in keeping the particles in suspension and prevents them from settling.

The correct answer is Scrotum.

Key Points

• The scrotum is a pouch-like anatomical structure located outside the abdominal cavity in male mammals, specifically situated behind the penis.
• Its primary function is to house and protect the testes (testicles), which are the primary male reproductive organs. Hence, the statement regarding the location of testes is correct.
• The location of the scrotum outside the body is vital for thermoregulation. The process of spermatogenesis (production of sperm) requires a temperature that is 2 to 2.5°C lower than the standard internal body temperature (which is approximately 37°C or 98.6°F).
• The testes descend from the abdominal cavity into the scrotum through the inguinal canal during the seventh month of fetal development.
• The scrotum contains the dartos muscle and the cremaster muscle, which contract or relax to move the testes closer to or further from the body to maintain the optimal temperature for sperm survival.

Additional Information

• Penis:
• This is the male external genitalia and serves as the copulatory organ.
• It is composed of specialized erectile tissue that facilitates erection to assist in insemination.
• The tip of the penis, known as the glans penis, is covered by a retractable fold of skin called the prepuce or foreskin.
• Urinary Bladder:
• The bladder is a muscular, hollow organ located in the pelvic cavity.
• Its primary function is the storage of urine before it is expelled from the body via the urethra.
• In males, the bladder sits above the prostate gland and in front of the rectum.
• Ureter:
• These are narrow, muscular tubes (typically two) that measure about 25 to 30 cm in length.
• Their function is to transport urine from the kidneys to the urinary bladder using peristaltic movements.
• They are part of the urinary system and do not play a direct role in the reproductive system.

Important Points

• Testicular Lobules: Each testis is divided into approximately 250 compartments called testicular lobules, each containing seminiferous tubules where sperm is produced.
• Hormonal Function: The Leydig cells (interstitial cells) found in the testes secrete androgens, mainly testosterone, which is responsible for male secondary sexual characteristics and the regulation of spermatogenesis.
• Cryptorchidism: This is a medical condition where one or both of the testes fail to descend into the scrotum before birth. If left untreated, it can lead to infertility due to the high internal body temperature affecting sperm production.
• Sperm Pathway: Once produced in the seminiferous tubules, sperm travels through the rete testis, vasa efferentia, and the epididymis (where it matures) before entering the vas deferens.

Shortcut Trick

Ratio of Expenditure to Savings = 225 : 100 = 9 : 4.

Net change in Income = (9 × −14% + 4 × 38%) ÷ (9 + 4)

Net change = (−126 + 152) ÷ 13 = 26 ÷ 13 = 2%.

∴ The correct answer is 2%.

Alternate Method

Given: Expenditure is 125% more than Savings.

⇒ Let Savings = 100

⇒ Expenditure = 100 + 125% of 100 = 225

⇒ Income = Expenditure + Savings = 225 + 100 = 325

⇒ New Expenditure = 225 × (100 − 14)/100 = 225 × 0.86 = 193.5

⇒ New Savings = 100 × (100 + 38)/100 = 138

⇒ New Income = 193.5 + 138 = 331.5

⇒ Increase in Income = 331.5 − 325 = 6.5

⇒ Percentage Increase = (6.5 ÷ 325) × 100 = 2%

∴ The correct answer is 2%.

Additional Information

Income-Expenditure Relationship

The fundamental accounting equation used in these problems is Income = Expenditure + Savings.

Weighted Average Application

Percentage change in Income is the weighted average of percentage changes in Expenditure and Savings based on their initial values.

Successive Percentage Change

For two successive changes a% and b%, the net effect is given by [a + b + (a×b)/100]%, though not directly applicable to additions like Income.

Shortcut Trick

Given: tanθ + cotθ = 4

Convert to sin and cos: (sinθ/cosθ) + (cosθ/sinθ) = 4 ⇒ (sin²θ + cos²θ) / (sinθ cosθ) = 4

Using identity sin²θ + cos²θ = 1: 1 / (sinθ cosθ) = 4

Squaring both sides: 1 / (sin²θ cos²θ) = 16

Since sec²θ = 1/cos²θ and csc²θ = 1/sin²θ, the expression is equal to 16.

∴ The correct answer is 16.

Alternate Method

Given: tanθ + cotθ = 4

Formula Used: tanθ + cotθ = secθ × cscθ

⇒ (sinθ/cosθ) + (cosθ/sinθ) = 4

⇒ (sin²θ + cos²θ) / (sinθ cosθ) = 4

⇒ 1 / (sinθ cosθ) = 4

⇒ secθ × cscθ = 4

⇒ (secθ × cscθ)² = 4²

⇒ sec²θ × csc²θ = 16

∴ The correct answer is 16.

Additional Information

Trigonometric Identity Relation

The expression tanθ + cotθ is always equal to secθ × cscθ or 1/(sinθcosθ).

Pythagorean Identities

sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = csc²θ.

Sum of Squares Identity

sec²θ + csc²θ = sec²θ × csc²θ. This unique property allows switching between sum and product.

Shortcut Trick

The Empirical Relationship between averages is: (Mode − Mean) = 3 × (Median − Mean).

From this, the ratio of differences is: (Mode − Median) : (Mode − Mean) = 2 : 3.

Given: (Mode − Mean) = 77.7, which corresponds to 3 units.

Value of 1 unit = 77.7 ÷ 3 = 25.9.

Required: (Mode − Median) = 2 units = 2 × 25.9 = 51.8.

∴ The correct answer is 51.8.

Alternate Method

Given:

Difference between Mode and Mean (Mode − Mean) = 77.7

Formula Used:

Empirical Formula: Mode = 3 × Median − 2 × Mean

Calculations:

⇒ Mode = 3 × Median − 2 × Mean

⇒ Mode + 2 × Mean = 3 × Median

⇒ To find the difference between Mode and Median, subtract 3 × Mode from both sides:

⇒ Mode + 2 × Mean − 3 × Mode = 3 × Median − 3 × Mode

⇒ 2 × Mean − 2 × Mode = 3 × (Median − Mode)

⇒ −2 × (Mode − Mean) = −3 × (Mode − Median)

⇒ 2 × 77.7 = 3 × (Mode − Median)

⇒ Mode − Median = (2 × 77.7) ÷ 3

⇒ Mode − Median = 155.4 ÷ 3

⇒ Mode − Median = 51.8

∴ The correct answer is 51.8.

Additional Information

Empirical Relationship

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

Symmetric Distribution

In a perfectly symmetrical distribution, the Mean, Median, and Mode are all equal (Mean = Median = Mode).

Positively Skewed Distribution

In a positively skewed (right-skewed) distribution, the relation is usually Mean > Median > Mode.

Negatively Skewed Distribution

In a negatively skewed (left-skewed) distribution, the relation is usually Mode > Median > Mean.

Shortcut Trick

Convert percentages and fractions into a single multiplying factor.

Number = 303 ÷ (0.30 × 0.50 × 4/7)

Number = 303 × (100/30) × (100/50) × (7/4)

Number = 303 × (10/3) × 2 × (7/4) = 101 × 10 × 3.5 = 3535.

∴ The correct answer is 3535.

Alternate Method

Given: 30% of 50% of 4/7 of x = 303

Formula Used: Percentage = Value/100

⇒ (30/100) × (50/100) × (4/7) × x = 303

⇒ (3/10) × (1/2) × (4/7) × x = 303

⇒ (3 × 1 × 4) / (10 × 2 × 7) × x = 303

⇒ (12 / 140) × x = 303

⇒ (3 / 35) × x = 303

⇒ x = (303 × 35) / 3

⇒ x = 101 × 35 = 3535

∴ The correct answer is 3535.

Additional Information

Percentage to Fraction Conversion

To simplify calculations, convert common percentages: 50% = 1/2, 25% = 1/4, 20% = 1/5, and 10% = 1/10.

Successive Percentage Rule

A% of B% of C is equivalent to (A × B / 100)% of C. This is useful for multi-step discount or growth problems.

Reciprocal Property

When solving for a number, multiply the result by the reciprocal of the total fraction: x = Result × (Denominator / Numerator).

Shortcut Trick

Calculate the semi-perimeter (s): (105 + 137 + 88) ÷ 2 = 165 cm.

Note that s = 165 (multiple of 11) and (s − c) = 165 − 88 = 77 (multiple of 7 and 11).

By Heron's Formula, the Area must be a multiple of 11 and 7.

Checking options for divisibility by 11 and 7: Only 4620 satisfies both conditions.

∴ The correct answer is 4620 cm².

Alternate Method

Given: Sides of the triangle are a = 105 cm, b = 137 cm, and c = 88 cm.

Formula Used: Area of a triangle = √[s(s − a)(s − b)(s − c)], where s is the semi-perimeter.

⇒ s = (a + b + c) ÷ 2

⇒ s = (105 + 137 + 88) ÷ 2 = 330 ÷ 2 = 165 cm

⇒ Area = √[165 × (165 − 105) × (165 − 137) × (165 − 88)]

⇒ Area = √[165 × 60 × 28 × 77]

⇒ Area = √[(11 × 15) × (4 × 15) × (4 × 7) × (11 × 7)]

⇒ Area = √[11² × 15² × 4² × 7²]

⇒ Area = 11 × 15 × 4 × 7 = 165 × 28

⇒ Area = 4620 cm²

∴ The correct answer is 4620 cm².

Additional Information

Heron's Formula

Used for finding the area of any triangle when all three sides are known: Area = √[s(s − a)(s − b)(s − c)].

Equilateral Triangle Area

If all sides are equal to 'a', the area is given by (√3 ÷ 4) × a².

Right-Angled Triangle Area

The area of a triangle with base 'b' and height 'h' is 1/2 × b × h.

Inradius of a Triangle

The radius of the incircle (r) is related to the area (A) and semi-perimeter (s) by the formula: r = A ÷ s.

Shortcut Trick

If CP of x articles = SP of y articles, then Profit% = [(x − y) ÷ y] × 100.

Given: x = 60 and y = 45.

Profit% = [(60 − 45) ÷ 45] × 100 = [15 ÷ 45] × 100.

Profit% = (1 ÷ 3) × 100 = 33.33%.

∴ The correct answer is 33.33%.

Alternate Method

Given → CP of 60 guavas = SP of 45 guavas. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100

⇒ 60 × CP = 45 × SP ⇒ SP ÷ CP = 60 ÷ 45 = 4 ÷ 3 ⇒ Let CP = 3 units and SP = 4 units. ⇒ Profit = 4 − 3 = 1 unit. ⇒ Profit% = (1 ÷ 3) × 100 = 33.333...% ⇒ Rounded to 2 decimal places = 33.33%.

∴ The correct answer is 33.33%.

Additional Information

Profit and Loss on Article Quantity

When the cost price of a certain number of items equals the selling price of another number, the base for percentage calculation is always the number of items sold (SP quantity).

Rounding Off Rules

To round to 2 decimal places, look at the third decimal digit; if it is 5 or greater, round up the second digit, otherwise keep it as is.

Shortcut Trick

Total Successive Discount for 16%, 29% and 4% can be calculated using the Effective Discount formula.

Step 1: Discount for 16% and 29% ⇒ 16 + 29 − (16 × 29) ÷ 100 = 45 − 4.64 = 40.36%.

Step 2: Discount for 40.36% and 4% ⇒ 40.36 + 4 − (40.36 × 4) ÷ 100 = 44.36 − 1.6144 = 42.7456%.

Rounding off to two decimal places, we get 42.75%.

∴ The correct answer is 42.75%.

Alternate Method

Given → Successive Discounts: d₁ = 16%, d₂ = 29%, d₃ = 4%. Formulas: Equivalent Discount = [1 − (1 − d₁/100) × (1 − d₂/100) × (1 − d₃/100)] × 100.

⇒ Let Marked Price (MP) = 100. ⇒ Price after 16% discount = 100 × (84/100) = 84. ⇒ Price after 29% discount = 84 × (71/100) = 59.64. ⇒ Price after 4% discount = 59.64 × (96/100) = 57.2544. ⇒ Total Discount = MP − Final SP = 100 − 57.2544 = 42.7456%. ⇒ Rounding to two decimal places = 42.75%.

∴ The correct answer is 42.75%.

Additional Information

Successive Discount Concept

When multiple discounts are applied one after another, the base for the subsequent discount is the reduced price from the previous step. Formula for two discounts: a + b − (ab/100).

Marked Price & Discount

Discount is always calculated on the Marked Price. SP = MP × (100 − D%)/100.

Shortcut Trick

Combine the profit sharing ratios: P : Q : R = (2 × 11) : (1 × 11) : (1 × 7) = 22 : 11 : 7.

Total units = 22 + 11 + 7 = 40 units.

Given 40 units = ₹25,000 → 1 unit = ₹625.

Share of R = 7 units = 7 × 625 = ₹4,375.

∴ The correct answer is ₹4375.

Alternate Method

Given:

Total profit = ₹25,000

Ratio P : Q = 2 : 1 and Q : R = 11 : 7

Calculations:

⇒ To equalize Q, multiply P : Q by 11: P : Q = 22 : 11

⇒ Combined Ratio P : Q : R = 22 : 11 : 7

⇒ Sum of ratio parts = 22 + 11 + 7 = 40

⇒ Share of R = (R's part / Total parts) × Total Profit

⇒ Share of R = (7 / 40) × 25000

⇒ Share of R = 7 × 625

⇒ Share of R = 4375

∴ The correct answer is ₹4375.

Additional Information

Compound Ratio

When two or more ratios are multiplied together, the result is a compound ratio. For P:Q and Q:R, the combined P:Q:R is found by making the common term (Q) equal.

Partnership Profit Distribution

Profit is distributed in the ratio of (Capital × Time). If time is constant, profit is shared directly in the ratio of investment/shares.

Ratio Proportion Property

If a : b = c : d, then product of extremes (a × d) equals product of means (b × c).

Shortcut Trick

Simplify the surds directly by extracting perfect square factors:

⇒ (√98 + √200 − 2√8)²

⇒ (7√2 + 10√2 − 4√2)²

⇒ (13√2)²

⇒ 169 × 2 = 338

∴ The correct answer is 338.

Alternate Method

Given:

(√98 + √200 − 2√8)²

Calculations:

Break down each radical into its simplest form by factoring out perfect squares:

⇒ √98 = √(49 × 2) = 7√2

⇒ √200 = √(100 × 2) = 10√2

⇒ 2√8 = 2 × √(4 × 2) = 2 × 2√2 = 4√2

Substitute the simplified values back into the given expression:

⇒ (7√2 + 10√2 − 4√2)²

Combine the like terms:

⇒ (17√2 − 4√2)²

⇒ (13√2)²

Square the combined term:

⇒ 13² × (√2)²

⇒ 169 × 2 = 338

∴ The correct answer is 338.

Additional Information

Simplification of Surds

A surd is simplified by identifying and extracting the largest perfect square factor from under the root: √(a² × b) = a√b.

Addition and Subtraction of Surds

Only like surds (surds having the exact same irrational part) can be added or subtracted directly: a√x + b√x = (a + b)√x.

BODMAS Rule

Always simplify the expressions inside the Brackets first before applying higher order operations like exponentiation (Order).

Shortcut Trick

When distance is constant, Speed is inversely proportional to Time.

Speed Ratio (Usual : New) = 4 : 3 → Time Ratio (Usual : New) = 3 : 4.

Difference in time units = 4 − 3 = 1 unit.

Given, 1 unit = 20 minutes.

Usual time = 3 units = 3 × 20 = 60 minutes.

∴ The correct answer is 60 min.

Alternate Method

Given: New speed = 3/4 of Usual speed. Delay = 20 minutes.

Formula Used: Usual Time = [Numerator / (Denominator − Numerator)] × Delay (when speed is reduced to n/d of usual speed).

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

⇒ Distance (D) = S × T

⇒ New speed = 3/4 S, New time = T + 20

⇒ D = (3/4 S) × (T + 20)

⇒ S × T = 3/4 S × (T + 20)

⇒ T = 3/4(T + 20)

⇒ 4T = 3T + 60

⇒ T = 60 minutes

∴ The correct answer is 60 min.

Additional Information

Inverse Relation of Speed and Time

For a fixed distance, if speed becomes a/b of its original value, time becomes b/a of its original value. The change in time is |b/a − 1| × original time.

Average Speed Formula

If a person covers equal distances at speeds x and y, the average speed for the whole journey is (2xy) / (x + y).

Relative Speed

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

Shortcut Trick

Combined efficiency (P+Q) = 1/10 per hour

Efficiency of P = 1/20 per hour

Efficiency of Q = 1/10 − 1/20 = 1/20 per hour

Time for Q to fill 1/4th cistern = (1/4) ÷ (1/20) = 5 hours

∴ The correct answer is 5 hours.

Alternate Method

Given:

Time taken by P and Q = 10 hours

Time taken by P alone = 20 hours

Calculations:

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

⇒ Efficiency of Q = 2 − 1 = 1 unit/hour

⇒ One-fourth of the total work = 20 ÷ 4 = 5 units

⇒ Time taken by Q alone = 5 ÷ 1 = 5 hours

∴ The correct answer is 5 hours.

Additional Information

Pipes and Cisterns Efficiency

The efficiency of a pipe is inversely proportional to the time taken to fill the tank. Total Work = Time taken × Efficiency.

Combined Work Formula

If two pipes A and B fill a tank in x and y hours respectively, they together fill it in (xy) ÷ (x + y) hours.

Negative Work (Inlet/Outlet)

Inlet pipes perform positive work (+), while outlet pipes (leaks) perform negative work (−) on the cistern capacity.

Shortcut Trick

Required number = LCM(20, 98, 35, 21) × k + Remainder

LCM(20, 98, 35, 21) = 1470 × 4 = 5880

Desired number must be of form 5880k + 5

For k = 1, Number = 5880 + 5 = 5885

Number to be added = 5885 − 5023 = 862

∴ The correct answer is 862.

Alternate Method

Given: Divisors are 20, 98, 35, 21 and remainder is 5.

Formula: Required Number = LCM(Divisors) × k + Remainder

⇒ Prime factorization of divisors:

⇒ 20 = 2² × 5

⇒ 98 = 2 × 7²

⇒ 35 = 5 × 7

⇒ 21 = 3 × 7

⇒ LCM = 2² × 5 × 7² × 3 = 4 × 5 × 49 × 3 = 2940

⇒ Note: Rechecking LCM(20, 98, 35, 21): 20=4×5, 98=2×49, 35=5×7, 21=3×7. LCM = 4 × 5 × 49 × 3 = 2940.

⇒ Next number after 5023 in the form 2940k + 5:

⇒ For k = 2: 2940 × 2 + 5 = 5880 + 5 = 5885

⇒ Number to be added = 5885 − 5023 = 862

∴ The correct answer is 862.

Additional Information

LCM Method for Remainders

When the remainder is the same for all divisors, the general form is (LCM × k) + Remainder.

LCM Calculation

LCM is the product of the highest powers of all prime factors present in the given numbers.

Natural Numbers

Natural numbers are positive integers starting from 1 {1, 2, 3, ...}.

Shortcut Trick

Total Distance = Sum of lengths = 297 + 243 = 540 m.

Relative Speed (Opposite) = 42 + 66 = 108 km/hr.

Convert to m/sec: 108 × (5/18) = 30 m/sec.

Time = 540 ÷ 30 = 18 sec.

∴ The correct answer is 18 sec.

Alternate Method

Given: Length of Train 1 (L₁) = 297 m, Length of Train 2 (L₂) = 243 m, Speed 1 (S₁) = 42 km/hr, Speed 2 (S₂) = 66 km/hr.

Formula Used: Time = (L₁ + L₂) ÷ (S₁ + S₂)

⇒ Total Length = 297 + 243 = 540 m

⇒ Relative Speed = 42 + 66 = 108 km/hr

⇒ Speed in m/sec = 108 × (5/18) = 6 × 5 = 30 m/sec

⇒ Time taken = 540 ÷ 30

⇒ Time taken = 18 sec

∴ The correct answer is 18 sec.

Additional Information

Relative Speed in Opposite Direction

When two objects move in opposite directions, their relative speed is the sum of their individual speeds: V_rel = V₁ + V₂.

Unit Conversion

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

Crossing Distance

When two trains cross each other completely, the total distance covered is always the sum of the lengths of both trains (L₁ + L₂).

"

• Wait, I'm repeating myself. I'll just generate the output now.

Shortcut Trick

In any quadrilateral ABCD, the angle formed by the bisectors of two adjacent angles (say ∠C and ∠D) is equal to half the sum of the other two angles (∠A and ∠B).

∠DOC = (∠A + ∠B) ÷ 2

∠DOC = (88° + 81°) ÷ 2

∠DOC = 169° ÷ 2 = 84.5°

∴ The correct answer is 84.5°.

Alternate Method

Given: ∠A = 88°, ∠B = 81° in quadrilateral ABCD. CO and DO are angle bisectors of ∠C and ∠D respectively.

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

Calculations:

⇒ In quadrilateral ABCD, &ang

Shortcut Trick

Ratio change: (7 : 6) → (8 : 7). Both parts increase by 1 unit.

This 1 unit increase corresponds to the 8-year time gap.

⇒ 1 unit = 8 years.

Present age of B = 6 units = 6 × 8 = 48 years.

∴ The correct answer is 48 years.

Alternate Method

Given: Ratio of present ages of A and B is 7 : 6. After 8 years, the ratio becomes 8 : 7.

Let the present ages of A and B be 7x and 6x.

⇒ (7x + 8) ÷ (6x + 8) = 8 ÷ 7

⇒ 7 × (7x + 8) = 8 × (6x + 8)

⇒ 49x + 56 = 48x + 64

⇒ 49x − 48x = 64 − 56

⇒ x = 8

⇒ Present age of B = 6x = 6 × 8 = 48 years.

∴ The correct answer is 48 years.

Additional Information

Age Difference Property

The difference between the ages of two persons remains constant regardless of how many years pass.

Ratio Balancing

If the differences between ratio parts are not equal, multiply the ratios by the difference of the other ratio to balance the units.

Future and Past Ages

If current age is x, age 'n' years hence is (x + n) and age 'n' years ago was (x − n).

Shortcut Trick

Rahul's share = (Total − Difference) ÷ 2

Rahul's share = (50 − 16) ÷ 2

Rahul's share = 34 ÷ 2 = 17

∴ The correct answer is ₹17.

Alternate Method

Given:

Total amount (Amit + Rahul) = ₹50

Difference (Amit − Rahul) = ₹16

Let the amount with Rahul be ₹x.

Amount with Amit = ₹(x + 16).

⇒ x + (x + 16) = 50

⇒ 2x + 16 = 50

⇒ 2x = 50 − 16

⇒ 2x = 34

⇒ x = 34 ÷ 2

⇒ x = 17

∴ The correct answer is ₹17.

Additional Information

Linear Equations in One Variable

An equation which can be written in the form ax + b = 0, where a and b are real numbers and a ≠ 0.

Sum and Difference Method

If (A + B) = S and (A − B) = D, then the larger value A = (S + D) ÷ 2 and the smaller value B = (S − D) ÷ 2.

Verification

Rahul has ₹17, Amit has 17 + 16 = ₹33. Total = 17 + 33 = ₹50. The condition is satisfied.

Shortcut Trick

For third proportional, use the relation: b² = a × c

Here, a = 64, b = Z, and c = 4.

⇒ Z² = 64 × 4 = 256

⇒ Z = √256 = 16

∴ The correct answer is 16.

Alternate Method

Given: First number (a) = 64, Second number (b) = Z, Third proportional (c) = 4.

Formula Used: If a, b, and c are in continued proportion, then a : b = b : c.

⇒ 64 ÷ Z = Z ÷ 4

⇒ Z × Z = 64 × 4

⇒ Z² = 256

⇒ Z = √256

⇒ Z = 16

∴ The correct answer is 16.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(a × b).

Fourth Proportional

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

Duplicate Ratio

The duplicate ratio of a : b is a² : b².

Shortcut Trick

Successive percentage formula: Net Change = a + b + (a × b) ÷ 100.

Here, a = +85% (Mark-up) and b = −20% (Discount).

Profit% = 85 − 20 + (85 × (−20)) ÷ 100.

Profit% = 65 − (1700 ÷ 100) = 65 − 17 = 48%.

∴ The correct answer is 48%.

Alternate Method

Given: Marked Price (MP) = 85% above Cost Price (CP), Discount = 20%. Formulas: MP = CP × (100 + Mark-up%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100 | Profit% = (SP − CP) ÷ CP × 100.

⇒ Let the Cost Price (CP) be 100 units.

⇒ Marked Price (MP) = 100 + 85% of 100 = 185 units.

⇒ Selling Price (SP) = 185 − 20% of 185 = 185 − 37 = 148 units.

⇒ Profit = SP − CP = 148 − 100 = 48 units.

⇒ Profit Percentage = (48 ÷ 100) × 100 = 48%.

∴ The correct answer is 48%.

Additional Information

Mark-up and Discount Relationship

Profit% is the net result of the Mark-up percentage and the Discount percentage applied sequentially on the CP.

Selling Price Formula

SP can be directly calculated as: SP = CP × (1 + Mark-up%) × (1 − Discount%).

Shortcut Trick Total Volume = 33 + 43 + 53 = 27 + 64 + 125 = 216 cm3 New Edge = √3216 = 6 cm Initial Area = 6 × (32 + 42 + 52) = 6 × 50 = 300 cm2 New Area = 6 × 62 = 6 × 36 = 216 cm2 Percentage Decrease = [(300 − 216) ÷ 300] × 100 = 28% ∴ The correct answer is 28% decrease. Alternate Method Given: Edges of three cubes = 3 cm, 4 cm, 5 cm Formula Used: Volume of cube = a3 Total Surface Area (TSA) of cube = 6a2 Percentage change = [(Initial Value − Final Value) ÷ Initial Value] × 100

⇒ Total Volume of three cubes = 33 + 43 + 53 ⇒ Total Volume = 27 + 64 + 125 = 216 cm3 ⇒ Volume of the new single cube = 216 cm3 ⇒ Edge of new cube (A) = √3216 = 6 cm ⇒ Initial Total Surface Area = 6 × (32 + 42 + 52) ⇒ Initial TSA = 6 × (9 + 16 + 25) = 6 × 50 = 300 cm2 ⇒ New Total Surface Area = 6 × 62 = 6 × 36 = 216 cm2 ⇒ Change in Area = 300 − 216 = 84 cm2 ⇒ Percentage change = (84 ÷ 300) × 100 ⇒ Percentage change = 28% ∴ The correct answer is 28% decrease. Additional Information Melting and Recasting Rule When multiple solid objects are melted and formed into a single object, the total volume remains constant, although the surface area usually changes. Cube Properties For a cube with side 'a', Lateral Surface Area (LSA) = 4a2 and the longest diagonal = a√3. Percentage Change Logic If the final value is less than the initial value, the change is always a percentage decrease. In this problem, 216 < 300, hence a decrease.

Shortcut Trick

Total Capacity (LCM of 12, 24) = 24 units.

Efficiency: A = +2, B = −1. Net efficiency (A+B) = +1.

Work done by A in 4 mins = 4 × 2 = 8 units.

Remaining work = 24 − 8 = 16 units.

Time for remaining part = 16 ÷ 1 = 16 minutes.

∴ The correct answer is 16 minutes.

Alternate Method

Given: Pipe A fills for 4 minutes, then B is opened.

⇒ Work done by Pipe A in first 4 minutes = Efficiency × Time

⇒ 2 × 4 = 8 units

⇒ Remaining capacity to be filled = Total Work − Work Done

⇒ 24 − 8 = 16 units

⇒ When both pipes are open, Combined Efficiency = 2 + (−1) = 1 unit/min

⇒ Time taken to fill remaining tank = Remaining capacity ÷ Combined Efficiency

⇒ 16 ÷ 1 = 16 minutes

∴ The correct answer is 16 minutes.

Additional Information

Inlet and Outlet Pipes

An inlet pipe fills the tank (positive work), while an outlet pipe empties it (negative work).

Net Efficiency

If Pipe A fills in x hours and Pipe B empties in y hours, the net work per hour is (1/x − 1/y).

Remaining Work Concept

Always subtract the initial work done by the first pipe(s) from the total capacity before calculating time for the second phase.

Shortcut Trick

Numbers divisible by both 4 and 3 must be divisible by their LCM.

LCM of (4, 3) = 12.

Number of terms = Greatest Integer of (Upper Limit ÷ LCM).

Number of terms = [200 ÷ 12] = 16.66...

Taking the integer part, we get 16.

∴ The correct answer is 16.

Alternate Method

Given: Upper limit = 200, Divisors = 4 and 3.

Formula: Numbers divisible by both a and b are divisible by LCM(a, b).

⇒ LCM(4, 3) = 12

⇒ The sequence is an Arithmetic Progression (AP): 12, 24, 36, ..., 192

⇒ Here, First term (a) = 12, Common difference (d) = 12, Last term (l) = 192

⇒ l = a + (n − 1)d

⇒ 192 = 12 + (n − 1) × 12

⇒ 180 = (n − 1) × 12

⇒ 15 = n − 1

⇒ n = 16

∴ The correct answer is 16.

Additional Information

LCM Concept

To find numbers divisible by multiple divisors, always use their Least Common Multiple (LCM) as the effective divisor.

Arithmetic Progression (AP)

The number of terms n in an AP can be found using n = [(Last Term − First Term) ÷ Difference] + 1.

Divisibility of Range

If finding numbers between x and y, use [ (y−1) ÷ d ] − [ x ÷ d ] for exclusive boundaries.

Shortcut Trick

Assume an Assumed Mean as 50.

Find deviations from 50: +14, −39, +16, +48, −25, −33, 0, +25, +12.

Sum of deviations = 115 − 97 = +18.

Average deviation = 18 ÷ 9 = +2.

Arithmetic Mean = Assumed Mean + Average Deviation = 50 + 2 = 52.

∴ The correct answer is 52.

Alternate Method

Given: Observations = 64, 11, 66, 98, 25, 17, 50, 75, 62 and Total number of observations (n) = 9.

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

⇒ Sum = 64 + 11 + 66 + 98 + 25 + 17 + 50 + 75 + 62

⇒ Sum = 468

⇒ Arithmetic Mean = 468 ÷ 9

⇒ Arithmetic Mean = 52

∴ The correct answer is 52.

Additional Information

Properties of Arithmetic Mean

The algebraic sum of deviations of a set of observations from their arithmetic mean is always zero (Σ(x − Mean) = 0).

Combined Mean Formula

If two groups have sizes n₁, n₂ and means x₁, x₂, the Combined Mean = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Effect of Change in Origin and Scale

If every observation is increased by a constant k, the mean increases by k. If multiplied by k, the mean is multiplied by k.

Shortcut Trick

Use the algebraic identity: (2A + B)² = (4A² + B²) + 4AB.

Substitute the given values directly: (2A + B)² = 24 + 4(4).

⇒ (2A + B)² = 24 + 16 = 40.

⇒ 2A + B = ±√40 = ±2√10.

∴ The correct answer is ±2√10.

Alternate Method

Given:

4A² + B² = 24

AB = 4

Formula Used:

The standard expansion of the square of a sum: (x + y)² = x² + y² + 2xy

Calculations:

⇒ We need to find the value of 2A + B. Let us square this expression.

⇒ (2A + B)² = (2A)² + B² + 2 × (2A) × (B)

⇒ (2A + B)² = 4A² + B² + 4AB

⇒ Now, substitute the values 4A² + B² = 24 and AB = 4 into the equation:

⇒ (2A + B)² = 24 + 4 × 4

⇒ (2A + B)² = 24 + 16

⇒ (2A + B)² = 40

⇒ Taking the square root on both sides:

⇒ 2A + B = ±√40

⇒ 2A + B = ±√(4 × 10)

⇒ 2A + B = ±2√10

∴ The correct answer is ±2√10.

Additional Information

Algebraic Identity (a + b)²

The identity (a + b)² = a² + 2ab + b² is used to expand the square of a binomial or to find the sum of terms when their squares and product are known.

Algebraic Identity (a − b)²

The identity (a − b)² = a² − 2ab + b² helps in finding the difference between terms using similar logic.

Nature of Square Roots

In algebra, if x² = k (where k > 0), then x has two possible values: +√k and −√k, often written as ±√k.

Shortcut Trick

Salary is always 100%.

Savings = 35% ⇒ Expenditure = 100% − 35% = 65%.

Monthly Expenditure = 65% of ₹7,420.

Monthly Expenditure = 0.65 × 7420 = ₹4,823.

∴ The correct answer is ₹4,823.

Alternate Method

Given: Monthly Salary = ₹7,420 and Savings Percentage = 35%.

Formula Used: Expenditure = Total Salary − Savings

⇒ Monthly Savings = 35% of 7,420

⇒ Monthly Savings = (35 ÷ 100) × 7420

⇒ Monthly Savings = 0.35 × 7420 = ₹2,597

⇒ Monthly Expenditure = 7,420 − 2,597

⇒ Monthly Expenditure = ₹4,823

∴ The correct answer is ₹4,823.

Additional Information

Percentage Change

To find the percentage change, use the formula: (Change ÷ Original Value) × 100.

Successive Percentage

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

Base Change Rule

If A is x% more than B, then B is [x ÷ (100 + x)] × 100% less than A.

Shortcut Trick

The effective rate of compound interest for 2 years at 10% per annum = 10 + 10 + (10 × 10 / 100) = 21%.

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

Amount = 121% of ₹1,000 = 1.21 × 1000 = ₹1,210.

∴ The correct answer is ₹1,210.

Alternate Method

Given:

Principal (P) = ₹1,000

Rate (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 1000 × (1 + 10/100)²

⇒ A = 1000 × (110/100)²

⇒ A = 1000 × (11/10) × (11/10)

⇒ A = 1000 × (121 / 100)

⇒ A = 10 × 121

⇒ A = ₹1,210

∴ The correct answer is ₹1,210.

Additional Information

Effective Interest Rate

For two successive years with rate R%, the effective Compound Interest rate is R + R + (R×R/100)%.

CI and SI Difference

The difference between Compound Interest and Simple Interest for 2 years is given by P(R/100)².

Compounding Period

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

Logic followed here is: The pattern followed within each triad depends on the addition and subtraction of positional values between the consecutive elements.

For Triad 1: JS-LU-OQ

For Triad 2: LU-NW-QS

The common pattern observed is: Element1 (+2, +2) → Element2 (+3, -4) → Element3.

Similarly, let's find the triad from the options that follows this pattern:

Checking NW-PY-SU:

Therefore, the triad that follows the pattern is NW-PY-SU.

Hence, the correct answer is "Option 1".

Logic followed here is substituting the letters with their respective mathematical operations and then applying the BODMAS rule to solve the expression.

Symbol Mapping:

Given equation:

72 A 4 C 6 B 9 D 20 A 2 C 88 A 8 D 15 = ?

Replacing the letters with their respective signs, we get:

72 ÷ 4 + 6 × 9 - 20 ÷ 2 + 88 ÷ 8 - 15 = ?

⇒ 18 + 54 - 10 + 11 - 15 = ?

⇒ 83 - 25 = ?

⇒ 58 = ?

Therefore, the value that will come in place of the question mark is 58.

Hence. the correct answer is "Option 2".

Given:

“what you have” → “nq jl mk”

“have you been” → “rs nq jl”

Therefore, ‘been’ is coded as ‘rs’.

Hence, the correct answer is "Option 2".

Logic followed here is: Identify the highest and lowest numbers from the given series, then extract the required digits to find their sum.

Given numbers:

 

1. Second digit of the highest number:

From the given set, the highest number is 657.

The second digit of the highest number is 5.

 

2. Third digit of the lowest number:

From the given set, the lowest number is 249.

The third digit of the lowest number is 9.

Calculation of the resultant:

Pattern observed: (Second digit of highest number) + (Third digit of lowest number)

Resultant = 5 + 9 = 14

Hence, the cirrect answer is "Option 3".

Given series:

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

Logic followed:

We need to find odd numbers which are:

Immediately preceded by an odd number

Immediately followed by an even number

Required pattern: Odd Number → Odd Number → Even Number

Checking the series:

2 4 2 7 4 8 9 1 2 4 5 7 5 2 3 1 3 9 5 4 4 7 9 3

The odd numbers satisfying the condition are:

• 1 (in 9 1 2)

• 5 (in 9 5 4)

• 9 (in 7 9 3)

Therefore, there are 3 such odd numbers.

Hence, the correct answer is "Option 1".

Given pairs:

17 → 33

13 → 25

Observe the pattern:

17 × 2 − 1 = 33

13 × 2 − 1 = 25

So, the logic is:

Second number = (First number × 2) − 1

Check the options:

Option 1:

23 × 2 − 1 = 45 ≠ 35

Option 2:

54 × 2 − 1 = 107 ≠ 108

Option 3:

74 × 2 − 1 = 147 ≠ 146

Option 4:

31 × 2 − 1 = 61 

Hence, the correct answer is "Option 4".

Given Series: ASE QIU GYK WOA ?

The pattern followed here is:

Folloing this pattern MEQ will replace the (?) mark.

Hence, the correct answer is "Option 2".

Given series:

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

Logic followed:

We need to find perfect squares which are:

Immediately preceded by an odd number

Immediately followed by an even number

Perfect squares among single-digit numbers are: 1, 4, 9

Required pattern:

Odd Number → Perfect Square → Even Number

Checking the series:

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

Perfect squares satisfying the condition are:

→ 9 in (7 9 4)

→ 4 (in 9 4 8)

→ 1 (in 5 1 2)

→ 9 (in 9 9 6)

Thus, the number of such perfect squares is 4.

Therefore, the answer is More than three.

Hence, the correct answer is "Option 4".

Given:

Six people A, B, C, D, E and F are sitting in a row facing north.

F sits to the immediate left of A.

C sits third to the left of D.

C is an immediate neighbour of A.

B sits to the immediate left of E.

Now find the number of people between E and C:

Therefore, 1 people sit between E and C.

Hence, the correct answer is "Option 2".

Given:

Six teachers — Judith, Anil, Myriam, Bina, Teresa and Jason — are sitting around a circular table facing the centre.

Judith is sitting second to the right of Anil.

Anil is an immediate neighbour of both Myriam and Bina.

Teresa is sitting second to the left of Myriam.

Jason is sitting second to the left of Anil.

Now find who is sitting between Jason and Judith, when counted from the left of Jason:

From Jason, move towards left (anticlockwise):

Jason → Teresa → Judith

Therefore, Teresa is sitting between Jason and Judith.

Hence, the correct answer is "Option 1".

Logic followed here is: The series follows a pattern of constant subtraction where each subsequent term is obtained by subtracting 10 from the preceding term.

Pattern analysis:

For the first missing number (?)

Term before the first question mark is 769.

First missing number = 769 - 10 = 759

For the second missing number (?)

Term before the second question mark is 749.

Second missing number = 749 - 10 = 739

The completed series is: 789, 779, 769, 759, 749, 739, 729.

Therefore, the numbers that should come in place of the question marks are 759 and 739, respectively.

Hence, the correct answer is "Option 4".

Given Statements:

All atoms are protons.

Some protons are neutrons.

Venn Diagram Representation:

Conclusions:

(I) All atoms are neutrons: Does not follows (Because only some protons are neutrons. There is no definite relation given between atoms and neutrons.)

(II) No neutron is a proton: Does not follows (Because the statement says “Some protons are neutrons”, which means some neutrons are protons.)

∴ Neither conclusion I nor II follows.

Hence, the correct answer is "Option 2".