RRB Group D Official Paper (Held On: 30 Dec, 2025 Shift 1) (Previous Year Paper)

The correct answer is Mixed cropping.

Key Points

• Mixed cropping is an agricultural practice where two or more crops are grown simultaneously on the same piece of land.
• The primary objective of this method is to minimize the risk of total crop failure. If one crop fails due to adverse weather conditions, lack of rainfall, or pest infestation, the other crop ensures some insurance against complete loss.
• In mixed cropping, the seeds of the different crops are typically mixed together and sown in the field without any definite row arrangement or specific spatial pattern.
• Farmers generally choose crop combinations that have different nutrient requirements or different root depths to ensure that they do not compete intensely for the same resources.
• Common examples of mixed cropping in India include combinations such as Wheat + Gram, Wheat + Mustard, or Groundnut + Sunflower.

Additional Information

• Inter-cropping:
• Similar to mixed cropping, it involves growing two or more crops simultaneously, but in a definite row pattern.
• For example, a few rows of one crop may alternate with a few rows of another crop (e.g., Soybean + Maize).
• This method allows for better management of fertilizers and pesticides for individual crops compared to mixed cropping.
• Mono-cropping:
• This refers to the practice of growing only one type of crop on the same piece of land year after year.
• While it allows for specialization and mechanization, it often leads to the depletion of specific soil nutrients and increases the risk of pest outbreaks.
• Crop Rotation:
• It is the practice of growing different types of crops in the same area in sequential seasons.
• For instance, planting a leguminous crop (like pulses) after a cereal crop (like wheat) helps in nitrogen fixation and replenishes soil fertility naturally.
• Benefits of Diverse Cropping Systems:
• These systems improve soil health, increase biodiversity, and provide a varied diet and income source for farmers.
• They are essential components of sustainable agriculture and help in weed control and efficient utilization of solar energy.

The correct answer is Change in the kinetic energy of the body.

Key Points

• The Work-Energy Theorem states that the net work done by the sum of all forces acting on an object is equal to the change in the kinetic energy of that object.
• This principle is derived from Newton's Second Law of Motion and is applicable to both constant and variable forces. Hence, statement 3 is correct.
• Mathematically, the theorem can be expressed as W = ΔK, where W is the total work done and ΔK is the change in kinetic energy (Final KE - Initial KE).
• The formula for Kinetic Energy (KE) is 1/2 mv^2, where m represents the mass of the body and v represents its velocity.
• If the net work done on an object is positive, its kinetic energy increases, meaning the object speeds up. If the net work is negative, the kinetic energy decreases, and the object slows down.

Additional Information

• Work Done:
• In physics, work is done when a force acts upon an object to cause a displacement. It is a scalar quantity.
• The SI unit of work is the Joule (J), which is equivalent to 1 Newton-meter (N·m).
• The formula for work is W = Fd cosθ, where F is force, d is displacement, and θ is the angle between the force and displacement vectors.
• Potential Energy (PE):
• Potential Energy is the energy held by an object because of its position relative to other objects, stresses within itself, or its electric charge.
• The most common form is Gravitational Potential Energy, calculated as PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth) and h is the height.
• Kinetic Energy (KE):
• It is the energy that a body possesses by virtue of being in motion.
• Since it depends on the square of the velocity, kinetic energy is always a non-negative value.
• Law of Conservation of Energy:
• This law states that energy can neither be created nor destroyed; it can only be transformed from one form to another.
• In a closed system where only conservative forces act, the sum of Kinetic Energy and Potential Energy remains constant.

Important Points

• Scalar Nature: Both Work and Energy are scalar quantities, meaning they have magnitude but no direction.
• Power: The rate at which work is done or energy is transferred is called Power. Its SI unit is the Watt (W), where 1 Watt = 1 Joule per second.
• Static Energy: This usually refers to Electrostatic Energy (energy stored in an electric field) or potential energy in a stationary state, but it is not the primary component defined by the Work-Energy Theorem.
• Applications: The Work-Energy Theorem is widely used in engineering and mechanics to solve problems where force and displacement are known, avoiding the need to calculate acceleration via Newton's Second Law.

The correct answer is To pass genetic information to offspring.

Key Points

• DNA (Deoxyribonucleic Acid) replication is the fundamental process during reproduction that ensures the genetic blueprint is transferred from one generation to the next.
• In a dividing cell, the nucleus contains information for the inheritance of features from parents to offspring in the form of DNA molecules.
• The process of DNA copying creates two copies of the genetic material; these copies need to be separated from each other, with each going to a new daughter cell.
• Simply creating a DNA copy is not enough; it must be accompanied by the creation of an additional cellular apparatus (like mitochondria, ribosomes, etc.) so that the DNA copies have a functioning environment to survive. Hence, the primary purpose is to pass genetic information, making this statement the correct answer.
• The consistency of DNA copying during reproduction is important for maintaining the body design features that allow an organism to use a particular niche.

Additional Information

• Structure of DNA:
• DNA is a double-stranded helical structure first described by James Watson and Francis Crick in 1953.
• It is composed of nucleotides, which consist of a phosphate group, a deoxyribose sugar, and four types of nitrogenous bases: Adenine (A), Thymine (T), Guanine (G), and Cytosine (C).
• The Role of Variations:
• No biochemical process, including DNA copying, is 100% accurate. Small alterations occur during the process, leading to variations in the offspring.
• These variations are the source of evolution and allow species to survive in changing environments or ecological niches over long periods of time.
• While drastic changes in DNA can lead to the death of a cell, subtle variations provide a competitive advantage in the struggle for survival.
• Heredity and Genes:
• A gene is a specific segment of DNA that provides information for making a particular protein.
• If the information in the DNA changes, different proteins will be made, eventually leading to altered body designs or traits.
• Heredity is the process by which traits and characteristics are transmitted from parents to progeny through these genetic codes.
• Modes of Reproduction:
• In asexual reproduction, a single parent produces DNA copies that are almost identical, resulting in clones with very little variation.
• In sexual reproduction, DNA from two different individuals combines, leading to a greater degree of variation and genetic diversity.

Important Points

• Location: In eukaryotic cells, the majority of DNA is located in the cell nucleus, organized into structures called chromosomes. A small amount of DNA can also be found in mitochondria (mtDNA) and chloroplasts.
• Cell Division: Before mitosis or meiosis begins, the cell enters the S-phase (Synthesis phase) of the cell cycle, where DNA replication occurs.
• Biological Significance: Without DNA copying, the continuity of life would cease because new cells would lack the instructions necessary to perform metabolic functions or maintain biological structures.

The correct answer is Law of Segregation.

Key Points

• The Law of Segregation is Mendel's first law of inheritance, which he derived from his experiments with monohybrid crosses.
• A monohybrid cross is a genetic cross between two individuals that differ in only one specific trait, such as plant height (Tall vs. Dwarf).
• According to this law, every individual possesses two alleles for any particular trait, and these alleles segregate (separate) during the formation of gametes.
• During meiosis, each gamete receives only one of the two alleles, ensuring that the offspring receives one allele from each parent. Hence, the statement regarding the Law of Segregation is correct.
• Mendel observed that in the F2 generation of a monohybrid cross, the recessive trait reappeared in a phenotypic ratio of 3:1, proving that the alleles did not blend but remained distinct.

Additional Information

• Law of Independent Assortment:
• This is Mendel's second law, derived from dihybrid crosses (crosses involving two traits, such as seed color and seed shape).
• It states that the alleles of two (or more) different genes get sorted into gametes independently of one another.
• Law of Dominance:
• Also observed in monohybrid crosses, it states that in a heterozygous pair, the dominant allele will mask the expression of the recessive allele.
• The trait that appears in the F1 generation is the dominant trait.
• Gregor Johann Mendel:
• Known as the Father of Genetics, he performed his experiments on Pisum sativum (garden pea) between 1856 and 1863.
• He presented his findings in 1865 at the Natural History Society of Brunn, providing the foundation for modern genetics.
• Other Options:
• The Law of Constant Proportion is a law of Chemistry formulated by Joseph Proust, stating that a chemical compound always contains its component elements in a fixed ratio by mass.
• The Law of Evolution refers to the broader biological theory of natural selection and descent with modification, primarily associated with Charles Darwin.

Important Points

• Purity of Gametes: The Law of Segregation is also referred to as the Law of Purity of Gametes because a gamete is always pure for a particular trait, carrying only one allele.
• Ratios: In a standard Mendelian monohybrid cross:
• The Phenotypic ratio is 3:1 (3 dominant, 1 recessive).
• The Genotypic ratio is 1:2:1 (1 Homozygous Dominant, 2 Heterozygous, 1 Homozygous Recessive).
• Mechanism: The physical basis of segregation is the separation of homologous chromosomes during Anaphase I of meiosis.

The correct answer is –42,000 N.

Key Points

• The calculation of force is based on Newton's Second Law of Motion, which states that Force (F) = mass (m) × acceleration (a).
• First, we must convert the initial velocity (u) of the car from km/h to m/s to maintain SI unit consistency. Given the speed is 180 km/h, we multiply by 5/18. Therefore, u = 180 × (5/18) = 50 m/s.
• The car comes to a complete stop, which means the final velocity (v) is 0 m/s. The time (t) taken for this change is 5 seconds.
• We calculate the acceleration (a) using the first equation of motion: v = u + at. Rearranging for a, we get a = (v - u) / t. Plugging in the values: a = (0 - 50) / 5 = -10 m/s². Hence, the acceleration is –10 m/s².
• The total mass (m) of the system (car + passengers) is 4200 kg. Using the force formula: F = 4200 kg × (-10 m/s²) = -42,000 N.
• The negative sign in the result –42,000 N signifies that the force is acting in the opposite direction to the motion of the car, which is characteristic of a braking or retarding force. Hence, the correct answer is –42,000 N.

Additional Information

• Newton's Second Law of Motion: This law provides a quantitative measure of force. It establishes that the net force acting on an object is equal to the rate of change of its linear momentum. For an object with a constant mass, it simplifies to the product of mass and acceleration.
• Unit Conversion: In physics problems, it is crucial to use the International System of Units (SI). Velocity should be in meters per second (m/s), mass in kilograms (kg), and time in seconds (s). The conversion factor 5/18 is derived from 1000 meters / 3600 seconds.
• Concept of Retardation: When the velocity of an object decreases over time, the acceleration is negative. This is specifically referred to as retardation or deceleration. In this context, the brakes provide the necessary frictional force to cause this retardation.
• The Newton (N): The SI unit of force is the Newton, named after Sir Isaac Newton. 1 Newton is defined as the amount of force required to accelerate a 1 kg mass at a rate of 1 m/s².
• Applications: Understanding braking force is essential in automotive engineering and road safety. It helps in determining stopping distances and designing efficient braking systems like ABS (Anti-lock Braking System) to handle large inertial loads.

Important Points

• Momentum: The initial momentum of the car was 4200 kg × 50 m/s = 210,000 kg·m/s. The final momentum is 0. The impulse provided by the brakes is equal to this change in momentum.
• Force Direction: Since force is a vector quantity, the sign is vital. A positive force would imply the car is speeding up, while the negative force confirms the application of brakes to reduce speed.
• Mass Sensitivity: If the mass of the car were lower, the same braking force would stop the car in less time or a shorter distance, demonstrating the role of inertia in motion.

The correct answer is lower.

Key Points

• Pitch is a characteristic of sound that allows the brain to distinguish between a shrill sound and a grave (deep) sound; it is directly dependent on the frequency of the vibration.
• A man's voice is generally characterized by a lower pitch because his vocal cords are longer and thicker compared to those of a child or a woman.
• In adult men, the vocal cords are approximately 17 mm to 25 mm in length, whereas in children, the vocal cords are much shorter, leading to different vibrational properties.
• Because the vocal cords in men are larger, they vibrate at a lower frequency. A lower frequency of vibration results in a sound that is perceived as having a lower pitch.
• Conversely, a child's vocal cords are short and thin, which causes them to vibrate with a higher frequency, producing a higher pitch or a shriller voice. Hence, the correct answer is lower.

Additional Information

• The Larynx (Voice Box):
• The larynx is the organ in the throat of mammals that contains the vocal cords and produces sound.
• During puberty, the larynx in males grows significantly larger than in females, often becoming visible as the Adam's apple. This growth is driven by testosterone and results in the deepening of the voice.
• Frequency and Hertz:
• Frequency is defined as the number of vibrations per second and is measured in Hertz (Hz).
• The typical fundamental frequency for an adult male ranges from 85 to 155 Hz, while for an adult female, it ranges from 165 to 255 Hz. A child's frequency is even higher, often exceeding 250-300 Hz.
• Vocal Cord Composition:
• Vocal cords are composed of twin infoldings of mucous membrane stretched horizontally across the larynx.
• The tension, mass, and length of these cords determine the pitch of the sound produced. Higher tension and lower mass/length result in higher frequency.

Important Points

• Shrillness vs. Loudness:
• It is important to distinguish pitch from loudness. While pitch depends on frequency, loudness depends on the amplitude of the sound wave.
• A bird produces a high-pitched sound (high frequency), whereas a lion’s roar has a low pitch (low frequency) but high loudness (high amplitude).
• Gender Differences:
• Women's vocal cords are approximately 12.5 mm to 17.5 mm long, which is intermediate between men and children, explaining why their pitch is generally higher than men's but often lower than very young children's.

The correct answer is The endoplasmic reticulum stores genetic material in it.

Key Points

• The Endoplasmic Reticulum (ER) serves as a channel for the transport of materials, especially proteins, between various regions of the cytoplasm or between the cytoplasm and the nucleus. Hence, statement 1 is correct.
• Genetic material, specifically Deoxyribonucleic Acid (DNA), is stored within the Nucleus of the cell, not the Endoplasmic Reticulum. The ER is primarily involved in the synthesis and transport of molecules, while the nucleus acts as the control center containing hereditary information. Hence, statement 2 is incorrect.
• The Rough Endoplasmic Reticulum (RER) is characterized by the presence of ribosomes attached to its outer surface. These ribosomes are the primary sites for protein synthesis within the cell. Hence, statement 3 is correct.
• The Smooth Endoplasmic Reticulum (SER) lacks ribosomes and is responsible for the synthesis of lipids, including fats, steroids, and phospholipids. It also plays a role in carbohydrate metabolism. Hence, statement 4 is correct.
• Hence, the incorrect statement (and the correct answer) is that the endoplasmic reticulum stores genetic material.

Additional Information

• Structure of ER: The Endoplasmic Reticulum was first observed by Keith Porter, Albert Claude, and Ernest Fullam in 1945. It is a large network of membrane-bound tubules and sheets called cisternae.
• Detoxification: One of the crucial functions of the Smooth ER (SER) in the liver cells of vertebrates is detoxifying many poisons and drugs, making them water-soluble so they can be excreted from the body.
• Membrane Biogenesis: Some of the proteins and lipids synthesized by the ER help in building the cell membrane. This biological process is known as membrane biogenesis.
• Calcium Storage: In muscle cells, a specialized type of smooth ER called the sarcoplasmic reticulum stores calcium ions, which are essential for muscle contraction.
• Protein Folding: The Rough ER (RER) provides a surface where proteins are folded into their three-dimensional structures. Proteins that are improperly folded are usually retained or degraded.

Important Points

• The Endoplasmic Reticulum is absent in prokaryotic cells (like bacteria) and mature mammalian red blood cells (RBCs).
• It accounts for more than half of the total membrane in many eukaryotic cells.
• The lumen of the ER is the internal space enclosed by the ER membrane, which is distinct from the surrounding cytosol.

p data-end="57" data-start="0">The correct answer is It needs two parents.

 

Key Points

• Binary fission is a primary method of asexual reproduction where a single parent body divides into two nearly equal parts, each of which grows into an independent organism. Since it does not involve the fusion of gametes, it does not require two parents. Hence, statement 1 is incorrect (making it the correct answer).
• The process is remarkably fast and efficient, especially in prokaryotic organisms. Under ideal environmental conditions, some bacteria can undergo this process every 20 minutes, allowing for rapid colonization. Hence, statement 2 is correct.
• Because each division results in the doubling of the individuals, binary fission leads to an exponential population increase. This is a survival strategy that ensures the species can thrive quickly when resources are abundant. Hence, statement 3 is correct.
• Binary fission typically occurs in unicellular organisms belonging to the domains of Bacteria and Archaea, as well as some eukaryotic protists like Amoeba, Paramecium, and Euglena. Hence, statement 4 is correct.
• Hence, the correct answer is It needs two parents.

Additional Information

• The Process of Binary Fission:
• The process begins with DNA replication, where the genetic material of the single parent is copied. Following this, the cell undergoes elongation to separate the two copies of DNA.
• The final stage is cytokinesis, where the cytoplasm divides and a new cell wall or membrane forms down the middle, creating two daughter cells that are genetically identical clones of the parent.
• Types of Binary Fission:
• Irregular Binary Fission: Occurs in organisms like Amoeba where the plane of division can happen through any axis.
• Longitudinal Binary Fission: Observed in Euglena, where the division occurs along the longitudinal axis.
• Transverse Binary Fission: Seen in Paramecium and Planaria, where the division plane is perpendicular to the long axis of the organism.
• Advantages and Disadvantages:
• The main advantage is the speed of reproduction and the fact that no mate is required, which is energy-efficient for the organism.
• The primary disadvantage is the lack of genetic diversity. Since the offspring are clones, the entire population is equally susceptible to the same diseases or environmental changes.

Important Points

• Comparison with Mitosis:
• While binary fission in eukaryotes involves mitosis (division of the nucleus), prokaryotic binary fission is much simpler because bacteria lack a defined nucleus and spindle fibers.
• Biological Examples:
• Leishmania: This parasite causes Kala-azar and undergoes binary fission in a definite orientation in relation to its whip-like structures.
• Vibrio cholerae: The causative agent of cholera, which uses rapid fission to increase its bacterial load within the human gut.

The correct answer is Roasting or calcination → Reduction to metal → Purification.

Key Points

• The extraction of metals like Zinc from their concentrated ores is a multi-step metallurgical process that depends on the reactivity of the metal. Zinc is a metal of medium reactivity, usually found as sulphides or carbonates in nature.
• Roasting is the first step for sulphide ores (such as Zinc Blende, ZnS). The ore is heated strongly in the presence of excess air to convert it into Zinc Oxide (ZnO). Hence, the first part of the sequence is correct.
• Calcination is used for carbonate ores (such as Calamine, ZnCO3). The ore is heated strongly in limited air or the absence of air to convert it into Zinc Oxide (ZnO). Hence, this alternative first step is also correct.
• The Reduction of the metal oxide is the next step. It is easier to obtain a metal from its oxide than from its sulphides or carbonates. Zinc Oxide is reduced to metallic zinc by heating it with a reducing agent like Carbon (Coke). The reaction is ZnO + C -> Zn + CO. Hence, the second part of the sequence is correct.
• The metal obtained after reduction is often crude and contains impurities. The final step is Purification (or Refining), such as electrolytic refining or distillation, to obtain pure Zinc metal. Hence, the final part of the sequence is correct.
• Hence, the correct answer is Roasting or calcination → Reduction to metal → Purification.

Additional Information

• Roasting: This process is specifically used for sulphide ores. For example, 2ZnS + 3O2 -> 2ZnO + 2SO2. A significant byproduct of this process is Sulphur Dioxide, which is often used to manufacture Sulphuric Acid.
• Calcination: This process involves the thermal decomposition of carbonate ores. For example, ZnCO3 -> ZnO + CO2. This is typically performed in a reverberatory furnace where the air supply can be controlled.
• Reducing Agents: While Carbon (in the form of Coke) is the most common reducing agent for Zinc, other highly reactive metals like Sodium, Calcium, or Aluminium can also be used as reducing agents to displace metals of lower reactivity from their oxides.
• Electrolytic Refining: In this purification process, the impure metal is made the anode, and a thin strip of pure metal is made the cathode. A solution of the metal salt is used as an electrolyte. When current passes, pure metal from the anode deposits onto the cathode.
• Occurrence of Zinc: The major ores of Zinc include Zinc Blende (ZnS), Calamine (ZnCO3), and Zincite (ZnO). India has significant zinc resources, primarily located in Rajasthan (Zawar mines).

Important Points

• Reactivity Series: Zinc sits in the middle of the reactivity series. Metals at the top (like Potassium, Sodium) are extracted by electrolysis of their molten chlorides, while metals at the bottom (like Gold, Silver) often occur in a native state.
• Thermodynamics of Reduction: The reduction of ZnO with Carbon occurs at a temperature of approximately 1673 K. Since the boiling point of Zinc is 1180 K, the metal is collected as vapour and then condensed.
• Froth Flotation: Before roasting or calcination, sulphide ores like ZnS are usually concentrated using the Froth Flotation process to remove gangue (earthy impurities).

The correct answer is A train moving on a straight track.

Key Points

• Motion is defined as the change in the position of an object with respect to time and its surrounding environment. Depending on the path taken by the object, motion is classified into various types.
• Rectilinear Motion: This refers to the movement of an object along a straight line. In this type of motion, the direction of the object remains constant throughout its path.
• A fan blade rotating: This represents rotational motion or circular motion. The particles of the fan blades move in a circular path around a fixed axis. Hence, this option is incorrect.
• A child running around a park: Since a park usually involves a curved or circular boundary, the path is not a single straight line. This is typically an example of curvilinear motion or circular motion. Hence, this option is incorrect.
• A train moving on a straight track: When a train travels on tracks that do not curve, every part of the train moves the same distance in a straight path. This is a classic example of rectilinear motion. Hence, this option is correct.
• A pendulum swinging: This is an example of periodic motion or oscillatory motion. The bob of the pendulum moves to and fro about a central mean position at regular intervals of time. Hence, this option is incorrect.

Additional Information

• Translatory Motion:
• It occurs when all parts of an object move the same distance in the same interval of time.
• It is divided into two categories: Rectilinear motion (motion in a straight line, e.g., a falling stone) and Curvilinear motion (motion along a curved path, e.g., a thrown ball).
• Circular and Rotational Motion:
• Circular motion is when an object moves along the circumference of a circle (e.g., a satellite orbiting the Earth).
• Rotational motion occurs when an object turns around an internal axis (e.g., the spinning of the Earth or a spinning top).
• Periodic and Oscillatory Motion:
• Periodic motion repeats itself after a fixed period of time (e.g., hands of a clock).
• Oscillatory motion is a specific type of periodic motion where the object moves back and forth (e.g., vibrating strings of a guitar or a child on a swing).
• Random Motion:
• This occurs when an object moves in a disorderly manner with no fixed path or direction (e.g., the motion of a honeybee or gas molecules).

Important Points

• Distance vs. Displacement: In rectilinear motion, if an object moves in a single direction without turning back, the magnitude of distance is equal to the magnitude of displacement.
• Uniform Rectilinear Motion: When an object covers equal distances in equal intervals of time along a straight line, it is said to be in uniform motion, meaning its velocity is constant.
• Non-Uniform Rectilinear Motion: If the speed of the object changes while moving in a straight line, it is called accelerated motion or non-uniform linear motion (e.g., a car starting from rest on a straight road).
• Newton's First Law: It states that an object will remain in its state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.

The correct answer is ohm-meter.

Key Points

• Resistivity, often represented by the Greek letter rho (ρ), is a fundamental property of a material that measures how strongly it resists the flow of electric current.
• The relationship between resistance (R) and resistivity (ρ) is given by the formula: R = ρ (L / A), where L is the length of the conductor and A is the cross-sectional area.
• To find the unit of resistivity, we rearrange the formula to ρ = (R × A) / L.
• The SI unit of resistance is the ohm (Ω), the unit of area is square meters (m²), and the unit of length is meters (m).
• Substituting these into the formula: (ohm × m²) / m = ohm-meter (Ω·m). Hence, the correct unit is ohm-meter.
• The option ohm/meter represents resistance per unit length, which is not resistivity. Hence, statement 2 is incorrect.
• The option ohm is the SI unit for electrical resistance, which depends on the dimensions of the object, unlike resistivity. Hence, statement 4 is incorrect.

Additional Information

• Nature of Materials:
• Conductors: Materials like silver, copper, and aluminum have very low resistivity (in the range of 10⁻⁸ Ω·m), making them ideal for electrical wiring.
• Insulators: Materials like rubber, glass, and fused quartz have very high resistivity (ranging from 10¹² to 10¹⁷ Ω·m), preventing current flow.
• Semiconductors: Materials like silicon and germanium have resistivity levels between conductors and insulators.
• Temperature Dependence:
• For metallic conductors, resistivity increases as the temperature rises because atomic vibrations interfere with electron flow.
• For semiconductors, resistivity typically decreases with an increase in temperature as more charge carriers become available.
• Conductivity (σ): It is the reciprocal of resistivity (σ = 1/ρ). Its SI unit is siemens per meter (S/m) or mho/meter. It indicates how easily a material allows electricity to pass through.

Important Points

• Intrinsic vs. Extrinsic: While resistance is an extrinsic property (depends on size and shape), resistivity is an intrinsic property. This means the resistivity of copper is the same whether you have a one-meter wire or a ten-meter wire.
• Dimensional Formula: The dimensional formula for resistivity is [M¹ L³ T⁻³ A⁻²].
• Historical Context: Georg Simon Ohm, a German physicist, published his findings in 1827, which led to the definition of Ohm's Law and the subsequent naming of the unit for resistance after him.
• Specific Resistance: Resistivity is also frequently referred to as specific electrical resistance in many engineering and physics contexts.

The correct answer is 25 cm.

Key Points

• The minimum distance at which an object can be seen most distinctly without any strain on the eyes is known as the least distance of distinct vision (LDDV).
• For a normal human eye of a young adult, this distance is standardly measured to be 25 cm.
• This specific distance is also referred to as the near point of the eye, which represents the closest limit of clear focus.
• To see objects at this distance, the ciliary muscles of the eye contract to increase the curvature of the crystalline lens, making it thicker and decreasing its focal length.
• If an object is placed closer than 25 cm, the eye lens cannot become sufficiently curved to focus the light rays onto the retina, resulting in a blurred and uncomfortable image.

Additional Information

• Far Point of the Eye:
• The farthest distance up to which the eye can see objects clearly is called the far point. For a normal human eye, the far point is at infinity.
• The region between the near point (25 cm) and the far point (infinity) is known as the range of vision.
• Power of Accommodation:
• This is the ability of the eye lens to adjust its focal length to see objects at varying distances.
• When viewing distant objects, ciliary muscles are relaxed, the lens is thin, and the focal length is maximum.
• When viewing nearby objects, ciliary muscles contract, the lens becomes thick, and the focal length decreases.
• Defects of Vision:
• Myopia (Near-sightedness): A condition where a person can see nearby objects clearly but cannot see distant objects distinctly because the image forms in front of the retina.
• Hypermetropia (Far-sightedness): A condition where a person can see distant objects clearly but cannot see nearby objects distinctly because the near point is further than 25 cm.
• Presbyopia: A common condition associated with aging where the power of accommodation decreases, often requiring bifocal lenses.

Important Points

• Structure and Function: The human eye functions like a camera, where the cornea and lens system focus light onto the retina, which acts as a light-sensitive screen containing photoreceptors.
• Persistence of Vision: The impression of an image does not vanish immediately from the retina; it persists for about 1/16th of a second, allowing for the perception of continuous motion in films.
• Age Factors: The near point of the eye changes with age. In infants, it can be as close as 5 to 8 cm, but as a person grows older, the ciliary muscles weaken and the lens loses flexibility, pushing the near point further away.

The correct answer is CO2.

Key Points

• When Sodium Bicarbonate (NaHCO3), commonly known as baking soda, is mixed with dilute Hydrochloric Acid (HCl), a chemical reaction occurs that produces Sodium Chloride (NaCl), water (H2O), and Carbon Dioxide (CO2) gas.
• The balanced chemical equation for this reaction is: NaHCO3 + HCl → NaCl + H2O + CO2.
• The CO2 gas is released with brisk effervescence, which is a visible bubbling effect in the solution. Hence, the evolved gas is Carbon Dioxide.
• The identification of this gas is confirmed using the lime water test. When Carbon Dioxide is passed through lime water (an aqueous solution of Calcium Hydroxide), it turns the solution milky or turbid.
• The milkiness is caused by the formation of Calcium Carbonate (CaCO3), which is an insoluble white precipitate. The reaction is: Ca(OH)2 + CO2 → CaCO3 + H2O.

Additional Information

• Reaction of Acids with Metal Carbonates: In general, when acids react with metal carbonates or metal hydrogen carbonates (bicarbonates), the resulting products are always a salt, water, and carbon dioxide gas.
• Properties of Sodium Bicarbonate: It is a mild non-corrosive basic salt. It is widely used in the food industry as a leavening agent in baking and as an antacid to neutralize excess stomach acid.
• Excess CO2 Passage: If excess Carbon Dioxide is passed through the milky lime water, the milkiness eventually disappears. This is because the insoluble Calcium Carbonate converts into soluble Calcium Bicarbonate [Ca(HCO3)2].
• Uses of CO2: Apart from being a product in chemical tests, Carbon Dioxide is essential for photosynthesis in plants and is used in fire extinguishers because it does not support combustion and is denser than air.

Important Points

• Hydrogen Gas (H2): This gas is usually evolved when a reactive metal (like Zinc or Magnesium) reacts with a dilute acid. It is identified by the pop sound it makes when a burning splinter is brought near it.
• Chlorine Gas (Cl2): This is a greenish-yellow gas with a suffocating odor. It is typically produced during the electrolysis of brine (chlor-alkali process) or the reaction of metal oxides with concentrated HCl.
• Carbon Monoxide (CO): This is a colorless, odorless, and highly toxic gas produced during the incomplete combustion of carbon or hydrocarbons. It does not turn lime water milky.
• Lime Water Composition: Lime water is a clear, colorless solution of Calcium Hydroxide [Ca(OH)2]. It should not be confused with lime juice, which is citric acid.

The correct answer is By simple heating or chemical methods.

Key Points

• Metals that are low in the reactivity series, such as Gold (Au), Silver (Ag), Platinum (Pt), and Mercury (Hg), are very unreactive and often found in their native state or as easily reducible oxides.
• Because of their low affinity for oxygen, the oxides of these metals can be reduced to the metallic state by simple heating alone. Hence, option 1 is correct.
• For example, Mercury is extracted from its sulphide ore, Cinnabar (HgS). When heated in air, it is first converted into mercuric oxide (HgO), and upon further heating, it is reduced to mercury metal.
• Displacement reactions are typically used for metals of medium reactivity (like Iron or Zinc) where a more reactive metal is used to displace them from their ores. Hence, option 2 is incorrect.
• Electrolytic reduction is a method reserved for highly reactive metals like Sodium (Na), Magnesium (Mg), and Aluminium (Al), which cannot be reduced by carbon or heat. Hence, option 3 is incorrect.
• Reacting with acids is generally a method to study the properties of metals or to form salts, but it is not a standard industrial process for the extraction of low-reactivity metals from their ores. Hence, option 4 is incorrect.

Additional Information

• Reactivity Series:
• The reactivity series is a list of metals arranged in descending order of their chemical reactivity.
• Metals at the top (Potassium, Sodium) are so reactive that they are never found as free elements in nature.
• Metals at the bottom (Gold, Silver) are the least reactive and are often called noble metals because they do not easily react with air, water, or acids.
• Extraction of Silver and Gold:
• While they occur in a free state, they are also extracted through chemical methods such as leaching.
• In the MacArthur-Forrest process, the ore is treated with a dilute solution of Sodium Cyanide (NaCN) or Potassium Cyanide (KCN) in the presence of air to form a soluble complex.
• The metal is then recovered from the solution by displacement using a more reactive metal like Zinc (Zn).
• Refining of Metals:
• Even after extraction, metals like Gold and Silver contain impurities and must be purified using electrolytic refining.
• In this process, the impure metal is made the anode, and a thin strip of pure metal is made the cathode in a solution of the metal's salt.

Important Points

• Native State: Metals like Gold and Platinum are found in the Earth's crust in their pure form because they have very low electrode potential and do not oxidize easily.
• Cinnabar Ore: It is the primary ore of Mercury. The process of heating it in excess air is known as roasting, which is the first step in extracting the metal.
• Environmental Impact: Extraction processes for Gold involving cyanide are strictly regulated globally due to the high toxicity of cyanide compounds to the ecosystem.
• Industrial Use: Silver and Gold are highly valued not just for jewelry but also in electronics due to their excellent electrical conductivity and resistance to corrosion.

The correct answer is Decrease in inter-particle space.

Key Points

• According to the Kinetic Molecular Theory, the temperature of a substance is a direct measurement of the average kinetic energy of its particles. When the temperature increases, the particles absorb thermal energy, which significantly increases their kinetic energy. Hence, statement 4 is correct.
• As the kinetic energy of the particles rises, they begin to move more rapidly and vigorously. In solids, this manifests as stronger vibrations, while in liquids and gases, it results in faster random motion. Hence, statement 3 is correct.
• When temperature increases, the particles move faster and collide more forcefully, causing them to move further away from each other to overcome inter-molecular forces of attraction. This leads to an increase in inter-particle space, a phenomenon commonly known as thermal expansion. A decrease in space only occurs when temperature drops or pressure increases. Hence, statement 2 is incorrect (the correct answer).
• If the temperature continues to rise, the particles gain enough energy to completely overcome the attractive forces holding them in a specific state of matter. This results in a phase transition, such as melting (solid to liquid) or boiling (liquid to gas). Hence, statement 1 is correct.
• Therefore, among the given options, a decrease in inter-particle space is the only process that does not occur with an increase in temperature.

Additional Information

• Kinetic Energy and Temperature: The relationship is mathematically defined where Kinetic Energy is proportional to the Absolute Temperature (measured in Kelvin). At 0 Kelvin (Absolute Zero), particle motion is theoretically considered to be at its minimum.
• Inter-particle Forces: These are the forces of attraction or repulsion which act between neighboring particles (atoms, molecules, or ions). In solids, these forces are strongest, keeping inter-particle spaces minimal. In gases, these forces are weakest, resulting in maximum inter-particle spaces.
• States of Matter:
• Solid: Defined shape and volume; particles are closely packed with minimal inter-particle space.
• Liquid: Defined volume but no defined shape; particles have moderate inter-particle space.
• Gas: Neither defined shape nor volume; particles have maximum inter-particle space and move freely.
• Thermal Expansion: This is the tendency of matter to change its shape, area, and volume in response to a change in temperature. For example, railway tracks are laid with small gaps to allow for expansion during summer.

Important Points

• Anomalous Expansion of Water: While most substances expand on heating, water behaves differently between 0 degrees Celsius and 4 degrees Celsius. In this specific range, its density increases and volume decreases (inter-particle space effectively decreases) as it is heated. However, above 4 degrees Celsius, it follows the standard rule of expansion.
• Diffusion: The rate of diffusion (mixing of particles) also increases with an increase in temperature because particles move faster and occupy the inter-particle spaces of other substances more quickly.
• Evaporation: This is a surface phenomenon where particles gain enough energy to leave the liquid state and enter the vapor state. The rate of evaporation increases with temperature as more particles acquire the necessary kinetic energy to break free.

The correct answer is The occurrence of ocean tides.

Key Points

• The Universal Law of Gravitation, formulated by Sir Isaac Newton in 1687, states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Ocean tides are the periodic rise and fall of the sea level. This phenomenon is a direct consequence of the gravitational pull exerted by both the Moon and the Sun on the Earth. Hence, the occurrence of ocean tides is the correct answer.
• The Moon, being much closer to Earth than the Sun, exerts a stronger tidal force. This force is "differential" because the gravitational attraction is stronger on the side of the Earth facing the Moon than on the center or the far side, causing the water to bulge.
• The Sun also exerts gravitational attraction. When the Sun, Moon, and Earth are aligned (during New Moon and Full Moon), their combined forces create Spring Tides, which are exceptionally high.
• When the Sun and Moon are at right angles to each other relative to Earth, their gravitational forces partially counteract each other, resulting in Neap Tides, which have a lower tidal range.

Additional Information

• Variation of 'g' (Option 1):
• The acceleration due to gravity (g) is not constant everywhere on Earth. It is maximum at the poles and minimum at the equator.
• This variation occurs because the Earth is an oblate spheroid (bulged at the equator) and due to the centrifugal force generated by Earth's rotation. It does not rely on the Sun or Moon's combined attraction. Hence, statement 1 is incorrect.
• Motion of Planets (Option 2):
• The motion of planets around the Sun is explained by the gravitational force providing the necessary centripetal force for orbital motion.
• While this is a triumph of the universal law of gravitation, it describes the attraction between two bodies (Sun and a planet) rather than the combined differential attraction of two external bodies on a third. Hence, statement 2 is incorrect.
• Centripetal Force (Option 4):
• The centripetal force keeping a stone in a circular path when tied to a string is provided by tension in the string, not the gravitational attraction of the Sun or Moon.
• In a broader sense, gravity acts as a centripetal force for celestial bodies, but in the context of a "stone," it is a mechanical tension. Hence, statement 4 is incorrect.

Important Points

• Gravitational Constant (G): The value of the universal gravitational constant is 6.674 x 10^-11 Nm²/kg². It remains the same throughout the universe.
• Tidal Cycle: Most coastal areas experience two high tides and two low tides every 24 hours and 50 minutes. This is known as a lunar day.
• Barycenter: The Earth and Moon actually orbit around their common center of mass, called the barycenter, which is located inside the Earth but off-center. This orbital motion also contributes to the centrifugal force that creates the tide on the far side of the Earth.
• Mass vs. Distance: Although the Sun is about 27 million times more massive than the Moon, it is 400 times further away. Since the tidal force decreases with the cube of the distance, the Moon's effect on tides is about 2.2 times stronger than the Sun's.

The correct answer is Barium sulphate which is insoluble.

Key Points

• When an aqueous solution of Barium chloride (BaCl2) is mixed with an aqueous solution of Sodium sulphate (Na2SO4), a chemical reaction occurs that results in the formation of Barium sulphate (BaSO4) and Sodium chloride (NaCl).
• The Barium sulphate formed in this reaction is a white solid that does not dissolve in water. This solid is known as a precipitate. Hence, the statement regarding Barium sulphate being insoluble is correct.
• This specific type of chemical reaction is classified as a Double Displacement Reaction. In such reactions, the cations and anions of two different compounds switch places to form two entirely new compounds.
• The chemical equation for this process is: BaCl2 (aq) + Na2SO4 (aq) → BaSO4 (s) + 2NaCl (aq). Here, the (s) denotes the solid state of the precipitate, while (aq) denotes the aqueous state of the other substances.
• The formation of the white precipitate is a primary observation in this experiment, serving as a qualitative test for the presence of sulphate ions in a solution.

Additional Information

• Precipitation Reaction: This is a sub-category of chemical reactions where two soluble salts in aqueous solution combine to form one or more insoluble products (precipitates). These reactions are vital in analytical chemistry for identifying various ions.
• Barium Sulphate (BaSO4):
• It is a naturally occurring mineral known as barite.
• Due to its high density and insolubility in water and acids, it is widely used in the medical field as a radiopaque contrast medium (often called a Barium meal) for X-ray imaging of the digestive system.
• It is also used as a pigment in paints and as a filler in plastics and rubber products.
• Sodium Chloride (NaCl): Common salt remains in the aqueous phase during this reaction because it is highly soluble in water. It does not contribute to the visible precipitate.
• Solubility Rules: In chemistry, solubility rules help predict which compounds will form a precipitate. Generally, most sulphates are soluble, but those of Barium, Lead, Calcium, and Strontium are notable exceptions as they are insoluble or sparingly soluble.

Important Points

• Safety Considerations: While Barium sulphate is non-toxic because it is insoluble and cannot be absorbed by the body, Barium chloride is highly toxic and water-soluble. Careful handling is required in laboratory environments.
• Ion Exchange: During the reaction, the Barium ions (Ba2+) from the barium chloride solution react with the Sulphate ions (SO4 2-) from the sodium sulphate solution to form the ionic lattice of the solid precipitate.
• Reaction Observation: The white color is characteristic of the barium sulphate solid. If the reaction resulted in Sodium chloride crystallizing (as mentioned in option 4), it would only happen if the water was evaporated, not upon the immediate mixing of the two aqueous solutions.

The correct answer is Anode – Cl₂, Cathode – H₂, Solution – NaOH.

Key Points

• The process of electrolysis of an aqueous solution of sodium chloride (commonly known as brine) is industrially termed the Chlor-alkali process.
• When electricity is passed through brine, it decomposes to form sodium hydroxide, chlorine, and hydrogen. The name "Chlor-alkali" is derived from the products: "chlor" for chlorine and "alkali" for sodium hydroxide.
• At the Anode (the positive electrode), chlorine gas (Cl₂) is produced as chloride ions lose electrons (oxidation).
• At the Cathode (the negative electrode), hydrogen gas (H₂) is produced as hydrogen ions from the water gain electrons (reduction).
• The Sodium hydroxide (NaOH) solution is formed in the remaining liquid, typically near the cathode compartment.
• The overall chemical reaction representing this process is: 2NaCl(aq) + 2H₂O(l) → 2NaOH(aq) + Cl₂(g) + H₂(g).

Additional Information

• Chlorine (Cl₂): It is a versatile gas used primarily for water treatment, disinfecting swimming pools, and the manufacture of PVC (Polyvinyl Chloride), disinfectants, CFCs, and pesticides.
• Hydrogen (H₂): This byproduct is highly valuable as a fuel, for the hydrogenation of oils to produce margarine, and in the synthesis of ammonia for agricultural fertilizers.
• Sodium Hydroxide (NaOH): Commonly known as caustic soda, it is used for de-greasing metals, manufacturing soaps and detergents, in paper making, and for creating artificial fibers like rayon.
• Brine: It refers to a saturated or highly concentrated solution of salt (NaCl) in water. In a typical industrial setup, the concentration of salt is approximately 26%.

Important Points

• In the electrolytic cell, the migration of ions is specific: the negatively charged chloride ions (Cl^-) migrate toward the positive anode, and the hydrogen ions (H⁺) (from water) migrate toward the negative cathode.
• The membrane cell and diaphragm cell are the modern technologies used to ensure that the chlorine gas produced does not react with the sodium hydroxide, as they would otherwise form sodium hypochlorite (bleach).
• The Chlor-alkali industry is one of the largest segments of the chemical industry, providing raw materials for thousands of downstream products including medicines and plastics.

The correct answer is Movement in our body.

Key Points

• Skeletal muscles are a specialized type of muscle tissue that is primarily attached to the bones of the skeleton, and their primary function is to facilitate locomotion and movement of various body parts. Hence, statement 4 is correct.
• These muscles are under voluntary control, meaning an individual can consciously decide when to contract or relax them through signals sent by the somatic nervous system.
• Physically, skeletal muscles appear striated (striped) under a microscope due to the highly organized arrangement of actin and myosin filaments within the muscle cells.
• They are connected to the bones via tough, fibrous connective tissues known as tendons, which act as levers to pull the bones during muscle contraction.
• While Circulation is primarily managed by the cardiac muscle of the heart and Excretion involves smooth muscles in the urinary system, skeletal muscles are uniquely designed for physical mobility and force generation. Hence, statements 1, 2, and 3 are incorrect.

Additional Information

• Types of Muscle Tissues:
• Smooth Muscle: These are non-striated and involuntary muscles found in the walls of internal organs like the stomach, intestines, and blood vessels. They assist in functions like peristalsis and regulating blood pressure.
• Cardiac Muscle: Found exclusively in the heart, these muscles are striated but involuntary. They are responsible for the rhythmic pumping of blood throughout the circulatory system.
• Functional Unit: The basic functional unit of a muscle fiber is the sarcomere. It contains the proteins necessary for contraction, allowing the muscle to shorten and exert force.
• Thermoregulation: Skeletal muscles play a vital role in maintaining body temperature. When they contract, they release heat as a byproduct, which is why the body shivers in cold conditions to generate warmth.
• Posture and Stability: Beyond active movement, these muscles provide postural support by resisting the pull of gravity, allowing humans to stand upright and maintain joint stability.

Important Points

• Antagonistic Pairs: Skeletal muscles typically work in pairs. For example, to flex the arm, the biceps contract (agonist) while the triceps relax (antagonist). Since muscles can only pull and not push, this pairing is essential for back-and-forth movement.
• Energy Source: Muscle contraction requires a significant amount of Adenosine Triphosphate (ATP). This energy is derived from glucose and fatty acids through aerobic respiration or anaerobic glycolysis during intense exercise.
• Muscle Mass: In an average healthy adult male, skeletal muscle accounts for approximately 40% to 50% of the total body weight, whereas in females, it accounts for about 30% to 40%.
• Hypertrophy vs. Atrophy: Regular physical exercise leads to hypertrophy (increase in muscle size and strength), while lack of use or aging can lead to atrophy (wasting away of muscle tissue).

The correct answer is Mixtures can be separated by physical methods, while compounds require chemical methods.

Key Points

• Mixtures consist of two or more substances that are physically combined but not chemically bonded. Because there are no chemical bonds between the components, they can be separated using physical methods such as filtration, distillation, crystallization, or magnetization. In contrast, compounds are substances formed by the chemical combination of elements in a fixed proportion. To separate a compound into its constituent elements, chemical methods or electrochemical reactions like electrolysis are required. Hence, statement 2 is correct.
• A mixture does not have a fixed melting or boiling point. Instead, it typically exhibits a range of temperatures during phase changes because the composition can vary. Conversely, compounds are pure substances and possess sharp, fixed boiling and melting points. Hence, statement 1 is incorrect.
• In a mixture, each constituent substance retains its original properties. For example, in a mixture of iron filings and sulfur, the iron can still be attracted by a magnet. However, when a compound is formed (like Iron Sulfide), the individual properties of the elements are lost, and the new substance has entirely different chemical and physical characteristics. Hence, statement 3 is incorrect.
• Compounds are always homogeneous in nature, meaning they have a uniform composition and appearance throughout. Mixtures can be homogeneous (like solutions) or heterogeneous (like suspensions or soil), where the different components are visible to the naked eye or under a microscope. Hence, statement 4 is incorrect.

Additional Information

• Homogeneous vs Heterogeneous Mixtures:
• Homogeneous mixtures have a uniform composition throughout their mass. Examples include air, alloys (like brass), and salt dissolved in water.
• Heterogeneous mixtures do not have a uniform composition. Examples include a mixture of sand and sugar, chalk powder in water, or oil and water.
• Characteristics of Compounds:
• Compounds follow the Law of Definite Proportions, which states that a chemical compound always contains exactly the same proportion of elements by mass. For example, Water (H2O) always contains hydrogen and oxygen in a 1:8 mass ratio.
• The formation of a compound involves a chemical change accompanied by the absorption or evolution of energy in the form of heat, light, or electricity.
• Separation Techniques:
• Physical methods: Used for mixtures. Chromatography is used to separate colors, and centrifugation is used to separate cream from milk.
• Chemical methods: Used for compounds. Thermal decomposition uses heat to break down a compound into simpler substances (e.g., Calcium Carbonate breaking into Calcium Oxide and Carbon Dioxide).

Important Points

• Energy Changes: During the preparation of a mixture, energy (heat, light, etc.) is usually neither given out nor absorbed. However, the preparation of a compound is always accompanied by a significant energy change.
• Composition: The components of a mixture can be present in any ratio, whereas the elements in a compound are always present in a fixed, definite ratio by weight.
• Purity: Compounds are considered pure substances because they consist of only one type of molecule, while mixtures are considered impure substances.

The correct answer is Axon.

Key Points

• The Axon is a long, slender projection of a nerve cell or neuron that typically conducts electrical impulses known as action potentials away from the cell body (also known as the soma). Hence, option 2 is correct.
• It serves as the primary transmission line of the nervous system, and as a bundle, axons help make up nerves.
• The axon originates from a specialized region of the cell body called the axon hillock, which acts as a junction where signals are integrated before being sent down the axon.
• Most large axons are wrapped in a fatty insulating layer called the myelin sheath, which is formed by glial cells. This sheath allows the nerve impulse to travel rapidly through a process called saltatory conduction.
• At its far end, the axon divides into several branches called axon terminals. these terminals are responsible for releasing neurotransmitters into the synapse to communicate with other neurons, muscles, or glands.

Additional Information

• Nucleus:
• The nucleus is located within the cell body (soma) of the neuron.
• It contains the genetic material (DNA) and controls the biosynthetic activities of the cell, such as growth and repair. It does not play a direct role in carrying the electrical impulse. Hence, option 1 is incorrect.
• Dendrites:
• Dendrites are branch-like structures that extend from the cell body.
• Their primary function is to receive incoming signals from other neurons and transmit those impulses toward the cell body. Hence, option 3 is incorrect.
• Synapse:
• A synapse is a microscopic junction or gap between the axon terminal of one neuron and the dendrite or cell body of another neuron.
• It is the site where chemical or electrical signals are passed between cells via neurotransmitters. Hence, option 4 is incorrect.

Important Points

• Direction of Impulse: In a healthy neuron, the flow of information is unidirectional. It is received by the dendrites, processed in the cell body, and then transmitted away via the axon.
• Nodes of Ranvier: These are the periodic gaps in the myelin sheath where the axonal membrane is exposed to the extracellular space. These nodes are essential for the rapid regeneration of the action potential.
• Length of Axons: Axons vary greatly in length. In the human body, the longest axon is part of the sciatic nerve, which can extend over one meter from the spinal cord to the big toe.
• Myelination Cells: In the Central Nervous System (CNS), myelin is produced by oligodendrocytes, while in the Peripheral Nervous System (PNS), it is produced by Schwann cells.

The correct answer is Particles to come closer.

Key Points

• Applying pressure to a gas results in the reduction of the space between its constituent particles. Because gases have large intermolecular spaces, increasing external pressure forces these particles into a smaller total volume, which effectively makes the particles come closer to each other. Hence, statement 3 is correct.
• According to Boyle's Law, at a constant temperature, the pressure of a given mass of an ideal gas is inversely proportional to its volume. This means that when pressure is increased, the volume must decrease, not increase. Hence, statement 1 is incorrect.
• The speed at which particles move is a function of their kinetic energy, which is directly proportional to the absolute temperature of the gas. While increasing pressure through compression can sometimes increase temperature (and thus speed) in an adiabatic process, pressure itself is a measure of force per unit area and does not fundamentally define the speed of particles in the same way temperature does. Hence, statement 2 is incorrect.
• When a gas is compressed (pressure is increased), work is done on the system. In most real-world scenarios, such as adiabatic compression, this causes the temperature to increase rather than decrease. A decrease in temperature usually requires the gas to expand or for heat to be removed from the system. Hence, statement 4 is incorrect.
• The high compressibility of gases is one of their most significant physical properties, distinguishing them from liquids and solids, where particles are already very close together.

Additional Information

• Boyle's Law: Discovered by Robert Boyle in 1662, it states that P1V1 = P2V2. This principle is fundamental in understanding how pneumatic systems and respiratory mechanisms function.
• Kinetic Molecular Theory: This theory explains that gas consists of a large number of submicroscopic particles (atoms or molecules), all of which are in constant, random motion. The distance between these particles is much larger than the size of the particles themselves.
• Liquefaction of Gases: By applying high pressure and reducing temperature, gases can be converted into liquids. This is the principle used in the production of LPG (Liquefied Petroleum Gas) and Liquid Oxygen used in hospitals.
• Compressibility Factor: In thermodynamics, the deviation of a real gas from ideal gas behavior is measured by the compressibility factor (Z). For an ideal gas, Z = 1, but for real gases, this value changes depending on the pressure and temperature.
• Diffusion and Effusion: Because particles in a gas are far apart and move rapidly, they can easily mix with other gases (diffusion) or escape through tiny openings (effusion). Increasing pressure can influence the rate at which these processes occur.

Important Points

• Industrial Applications: Compressed gases like CNG (Compressed Natural Gas) are used as fuel in vehicles because large volumes of gas can be squeezed into small cylinders by applying high pressure.
• Ideal Gas Equation: The relationship between pressure, volume, and temperature is summarized by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
• Mean Free Path: When pressure increases and particles come closer, the mean free path (the average distance a particle travels between collisions) decreases. This leads to an increase in the frequency of collisions against the walls of the container.

The correct answer is virtual and erect.

Key Points

• Magnification (m) produced by a spherical mirror or lens is defined as the ratio of the height of the image (h') to the height of the object (h).
• A positive sign in the value of magnification indicates that the image is virtual and erect. This is because both the object and the image are situated above the principal axis, and according to the Cartesian sign convention, heights measured upwards are taken as positive. Hence, the correct answer is virtual and erect.
• If the magnification has a negative sign, it implies that the image is real and inverted. In this case, the image is formed below the principal axis, and heights measured downwards are taken as negative. Hence, statement 1 and statement 4 are incorrect.
• A virtual image cannot be obtained on a screen as the light rays do not actually meet but only appear to diverge from a point. Only real images can be caught on a screen. Hence, statement 3 is incorrect.
• The numerical value of magnification represents the size of the image relative to the object. If m = 1, the image is the same size as the object; if m > 1, the image is magnified; and if m < 1, the image is diminished.

Additional Information

• Magnification for Mirrors:
• In the case of spherical mirrors, magnification is also related to the object distance (u) and image distance (v). It is expressed as m = -v/u.
• For a plane mirror, the magnification is always +1, indicating the image is virtual, erect, and of the same size as the object.
• Convex mirrors always produce a magnification that is positive and less than 1 because they always form virtual, erect, and diminished images.
• Magnification for Lenses:
• For lenses, the magnification is given by the ratio m = v/u.
• A concave lens always gives a positive magnification less than 1, as it always forms a virtual, erect, and diminished image regardless of the object position.
• A convex lens can produce both positive and negative magnification depending on where the object is placed relative to the focus (F) and optical center (O).

Important Points

• Sign Convention: According to the New Cartesian Sign Convention, the object is always placed to the left of the mirror/lens. All distances measured to the right of the origin (pole/optical center) are positive, and those to the left are negative.
• Real Image: Formed when light rays actually intersect after reflection or refraction. These are always inverted and have a negative magnification.
• Virtual Image: Formed when light rays appear to meet when produced backwards. These are always erect and have a positive magnification.
• Applications: Understanding magnification is crucial in designing microscopes, telescopes, and corrective eyeglasses where specific image sizes and orientations are required.

The correct answer is both magnitude and direction.

Key Points

• A magnetic field is defined as a vector quantity, which by definition means it possesses both magnitude (strength) and direction.
• The magnitude of a magnetic field refers to the intensity of the magnetic force at a specific point. In the International System of Units (SI), the magnitude is measured in Tesla (T). Another common unit used is the Gauss (G), where 1 Tesla is equal to 10,000 Gauss.
• The direction of the magnetic field at any point is the direction in which the north pole of a compass needle points when placed at that location. Outside a magnet, the field lines emerge from the North Pole and enter the South Pole.
• It can be visualized using magnetic field lines. The density of these lines indicates the magnitude (stronger where lines are closer), and the tangent to the line at any point indicates the direction. Hence, the statement that it has both magnitude and direction is correct.

Additional Information

• Vector vs. Scalar Quantities:
• Vectors: Quantities like force, velocity, acceleration, and magnetic field require both a numerical value and a spatial orientation to be fully described.
• Scalars: Quantities like mass, time, temperature, and electric potential only have magnitude and no direction.
• Magnetic Flux Density: The magnetic field is often referred to as magnetic flux density (represented by the symbol B). It represents the amount of magnetic flux through a unit area taken perpendicular to the direction of the magnetic field.
• Sources of Magnetic Fields: Magnetic fields are produced by moving electric charges (electric currents) and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property known as spin.
• Lorentz Force: When a charge q moves with a velocity v in a magnetic field B, it experiences a force F = q(v × B). This cross-product mathematical relationship confirms that the magnetic field must have a direction to determine the resulting force.

Important Points

• Properties of Magnetic Field Lines:
• Field lines never intersect each other because, at a single point, the field cannot have two different directions.
• They form continuous closed loops, unlike electric field lines which begin on positive charges and end on negative charges.
• The strength of the field is proportional to the closeness of the lines; they are crowded near the poles where the magnetic field is strongest.
• Right-Hand Thumb Rule: To find the direction of a magnetic field produced by a straight current-carrying wire, point the thumb of the right hand in the direction of the current; the curled fingers then give the direction of the magnetic field lines.
• Historical Context: Hans Christian Ørsted discovered the relationship between electricity and magnetism in 1820, proving that an electric current creates a circular magnetic field around the wire.

The correct answer is Amrita Devi Bishnoi.

Key Points

• The historic sacrifice for environmental conservation took place in September 1731 in the village of Khejarli, located in the Jodhpur district of Rajasthan.
• Amrita Devi Bishnoi, along with her three daughters, stood against the soldiers of Maharaja Abhai Singh of Marwar, who were sent to cut Khejri trees to fuel lime kilns for the construction of a new palace.
• During this protest, Amrita Devi famously declared that if a tree could be saved at the cost of one's head, it was still a cheap price to pay. She was the first to be martyred while hugging a tree to protect it.
• Following her example, a total of 363 members of the Bishnoi community from 84 villages sacrificed their lives to save the sacred trees. Hence, the statement regarding Amrita Devi Bishnoi is correct.
• This event is recognized as a pioneering movement in environmentalism and served as a major inspiration for the modern Chipko Movement led by Sunderlal Bahuguna in the 1970s.

Additional Information

• Medha Patkar:
• She is a prominent Indian social activist known for her leading role in the Narmada Bachao Andolan (NBA).
• The movement was started in 1985 to protest against the construction of large dams across the Narmada River, particularly the Sardar Sarovar Dam, due to the displacement of local tribal communities and environmental damage.
• Vandana Shiva:
• She is an world-renowned environmentalist and eco-feminist based in Delhi.
• She founded Navdanya in 1987, an organization dedicated to biodiversity conservation, organic farming, and the rights of farmers to save and share seeds.
• Sunita Narain:
• She is a distinguished Indian environmentalist who serves as the Director General of the Centre for Science and Environment (CSE).
• She has been a vocal advocate for sustainable development and was named in Time Magazine’s list of 100 Most Influential People in 2016.

Important Points

• The Khejri Tree (Prosopis cineraria):
• It was declared the State Tree of Rajasthan in 1983.
• Known as the "Golden Tree of the Desert" or "Ghaf," it plays a vital role in the ecosystem of the Thar Desert by preventing soil erosion and providing fodder (Loom) and food (Sangri).
• Bishnoi Community:
• The sect was founded by Guru Jambheshwar (also known as Jambhoji) in 1485.
• The community follows 29 tenets (Bish-noi), which include a strict prohibition against cutting green trees and killing animals, making them some of the world's first organized environmentalists.
• Amrita Devi Bishnoi Wildlife Protection Award:
• The Government of India and the Rajasthan Government instituted this national award to honor individuals and communities for their extraordinary courage and dedication to protecting wildlife and forests.
• A commemorative fair (Mela) is held every year on Bhadrapad Shukla Dashmi at Khejarli village to pay tribute to the martyrs.

Shortcut Trick

In a 45°−45°−90° triangle, the ratio of sides is 1 : 1 : √2.

Base (distance) = 1 unit = 25 m.

Height of standing part = 1 unit = 25 m.

Hypotenuse (broken part) = √2 units = 25√2 m.

Total height of pole = Standing part + Broken part = 25 + 25√2 = 25(√2 + 1) m.

∴ The correct answer is 25(√2 + 1) m.

Alternate Method

Given:

Distance from foot to top (BC) = 25 m.

Angle of elevation (θ) = 45°.

Formula Used:

tan θ = Perpendicular / Base

cos θ = Base / Hypotenuse

Calculations:

⇒ In ΔABC, tan 45° = AB / BC

⇒ 1 = AB / 25

⇒ Standing part (AB) = 25 m

⇒ cos 45° = BC / AC

⇒ 1 / √2 = 25 / AC

⇒ Broken part (AC) = 25√2 m

⇒ Total length of pole = AB + AC

⇒ Total length = 25 + 25√2 = 25(√2 + 1) m

∴ The correct answer is 25(√2 + 1) m.

Additional Information

Trigonometric Ratios for 45°

For a 45° angle, sin 45° = 1/√2, cos 45° = 1/√2, and tan 45° = 1.

Pythagoras Theorem

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

Height and Distance Logic

The total height of a broken object is always the sum of the vertical part still standing and the hypotenuse formed by the broken part.

Shortcut Trick

Net percentage change formula = a + b + (a × b)/100

Here, a = −25 (decrease) and b = +12 (increase)

Net change = −25 + 12 + (−25 × 12)/100

Net change = −13 − 3 = −16%

∴ The correct answer is Decreases by 16%.

Alternate Method

Given:

First decrease = 25%

Second increase = 12%

Calculations:

⇒ Let the initial salary of Sonali be 100 units.

⇒ Salary after 25% decrease = 100 − (25% of 100) = 75 units.

⇒ Salary after 12% increase = 75 + (12% of 75)

⇒ 75 + (12 × 75)/100 = 75 + 9 = 84 units.

⇒ Net change = Final salary − Initial salary = 84 − 100 = −16 units.

⇒ Net percentage effect = (−16 / 100) × 100 = −16%.

∴ The correct answer is Decreases by 16%.

Additional Information

Successive Percentage Change

When a value is changed by x% and then by y%, the net effective change is given by [x + y + (xy/100)]%.

Base Value Concept

Percentage change is always calculated on the preceding value in a series of successive changes, not the original base unless specified.

Ratio Method

For 25% decrease, ratio is 4:3. For 12% increase, ratio is 25:28. Multiplying ratios (4×25):(3×28) = 100:84, which shows a 16% decrease.

Shortcut Trick

If each number in a data set is decreased by a constant value k, the average of the set is also decreased by k.

Given: Old Average = 25 and Decrease (k) = 3.

New Average = Old Average − k

New Average = 25 − 3 = 22.

∴ The correct answer is 22.

Alternate Method

Given:

Total numbers (n) = 7

Initial Average = 25

Decrease in each number = 3

Formula Used:

Average = Sum of observations ÷ Total number of observations

Calculations:

⇒ Total Sum of 7 numbers = 7 × 25 = 175

⇒ Total decrease across all numbers = 7 × 3 = 21

⇒ New Total Sum = 175 − 21 = 154

⇒ New Average = 154 ÷ 7

⇒ New Average = 22

∴ The correct answer is 22.

Additional Information

Properties of Averages

If every term in a set is increased by k, the average increases by k. If every term is multiplied or divided by k, the average is also multiplied or divided by k respectively.

Sum of Observations

Total Sum = Average × Total number of observations. This is the fundamental relation used for most average-based problems.

Average of Consecutive Numbers

For a set of consecutive numbers (AP), the average is always the middle term or (First term + Last term) ÷ 2.

Shortcut Trick

In right-angled triangle BDC, ∠C = 90° − ∠DBC = 90° − 33° = 57°.

In triangle AEC, ∠AEB is the exterior angle at vertex E.

By the Exterior Angle Theorem, ∠AEB = ∠CAE + ∠C.

⇒ ∠AEB = 45° + 57° = 102°.

∴ The correct answer is 102°.

Alternate Method

Given:

In triangle ABC, BD ⊥ AC at D, ∠DBC = 33°, and ∠CAE = 45° where E is on BC.

Formula Used:

1. Angle Sum Property of a triangle: Sum of angles = 180°.
2. Linear Pair: Sum of angles on a straight line = 180°.

Calculations:

⇒ In right-angled triangle BDC, ∠BDC = 90°.

⇒ ∠BCD + ∠DBC + ∠BDC = 180°

⇒ ∠BCD + 33° + 90° = 180°

⇒ ∠BCD = 180° − 123° = 57°

⇒ Now, consider triangle AEC. The sum of interior angles is 180°.

⇒ ∠CAE + ∠ACE + ∠AEC = 180°

⇒ 45° + 57° + ∠AEC = 180°

⇒ 102° + ∠AEC = 180°

⇒ ∠AEC = 180° − 102° = 78°

⇒ Since B, E, and C are collinear, ∠AEB and ∠AEC form a linear pair.

⇒ ∠AEB + ∠AEC = 180°

⇒ ∠AEB + 78° = 180°

⇒ ∠AEB = 180° − 78° = 102°

∴ The correct answer is 102°.

Additional Information

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

Angle Sum Property

The sum of the interior angles of any triangle is always 180°.

Linear Pair Postulate

If two angles form a linear pair, then the measures of the angles add up to 180°.

Shortcut Trick

Use the direct algebraic identity: 2ab = (a + b)² − (a² + b²)

Substitute the given values: 2ab = 50² − 1300

2ab = 2500 − 1300 = 1200

ab = 1200 ÷ 2 = 600

∴ The correct answer is 600.

Alternate Method

Given:

Total number of widgets produced (a + b) = 50

Sum of squares of widgets produced (a² + b²) = 1300

Formula Used:

(a + b)² = a² + b² + 2ab

Calculations:

⇒ (50)² = 1300 + 2ab ⇒ 2500 = 1300 + 2ab ⇒ 2ab = 2500 − 1300 ⇒ 2ab = 1200 ⇒ ab = 1200 ÷ 2 ⇒ ab = 600

∴ The correct answer is 600.

Additional Information

Square of Difference Identity

(a − b)² = a² + b² − 2ab. This can be used to find the difference between two quantities when their sum of squares and product are known.

Sum and Product Relation

The relationship (a + b)² − (a − b)² = 4ab is frequently used in quantitative aptitude to solve problems involving two variables without finding individual values.

Alternate Expression for Sum of Squares

a² + b² = (a + b)² − 2ab or a² + b² = (a − b)² + 2ab. These are fundamental algebraic identities for competitive exams.

Shortcut Trick

Let Total Capacity of the tank be LCM of 4, 6, and 8 = 24 units.

Net efficiency of (A + B − C) = 6 + 4 − 3 = 7 units/hr.

Work done in first 3 hours = 7 × 3 = 21 units.

Remaining work = 24 − 21 = 3 units, to be filled by (A + B) with efficiency 10.

Additional time = 3/10 hours = 18 minutes.

Total time = 3 hours + 18 minutes = 3 hr 18 min.

∴ The correct answer is 3 hr 18 min.

Alternate Method

Given: Filling time for Pipe A = 4 hr, Pipe B = 6 hr, and Emptying time for Pipe C = 8 hr.

Step-by-step Calculations:

⇒ Total efficiency when all pipes are open = (6 + 4 − 3) = 7 units/hr

⇒ Tank filled in first 3 hours = 7 × 3 = 21 units

⇒ Remaining tank capacity to be filled = 24 − 21 = 3 units

⇒ Efficiency of (A + B) only = 6 + 4 = 10 units/hr

⇒ Time taken by A and B to fill remaining part = 3 ÷ 10 = 0.3 hr

⇒ Converting to minutes: 0.3 × 60 = 18 min

⇒ Total time required = 3 hr + 18 min = 3 hr 18 min

∴ The correct answer is 3 hr 18 min.

Additional Information

Net Efficiency Concept

In pipes and cisterns, efficiency of an inlet pipe is positive (+) and efficiency of an outlet/leak pipe is negative (−).

Time and Work Relation

Total Work = Time taken × Efficiency. To find total time, add the durations of different operational stages separately.

Unit Conversion

To convert hours into minutes, multiply the fractional or decimal part of the hour by 60.

Shortcut Trick

Average Speed = (2 × s₁ × s₂) ÷ (s₁ + s₂) = (2 × 5 × 4) ÷ (5 + 4) = 40 ÷ 9 km/hr.

Total Time = 4 hours 30 minutes = 4.5 hours = 9/2 hours.

Total Distance (both ways) = Average Speed × Total Time = (40 ÷ 9) × (9 ÷ 2) = 20 km.

One-way Distance = 20 ÷ 2 = 10 km.

∴ The correct answer is 10 km.

Alternate Method

Given: Speed while going (s₁) = 5 km/hr, Speed while returning (s₂) = 4 km/hr, Total time (T) = 4.5 hours.

Formula Used: Distance (D) = [ (s₁ × s₂) ÷ (s₁ + s₂) ] × Total Time

⇒ Total Time (T) = 4 + 30/60 = 4.5 = 9/2 hours

⇒ D = [ (5 × 4) ÷ (5 + 4) ] × (9 ÷ 2)

⇒ D = (20 ÷ 9) × (9 ÷ 2)

⇒ D = 10 km

∴ The correct answer is 10 km.

Additional Information

Average Speed Formula

When a person travels equal distances at speeds x and y, the average speed for the whole journey is (2xy) ÷ (x + y).

Time, Speed, and Distance Relationship

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

Conversion of Time

To convert minutes to hours, divide the value by 60 (e.g., 30 mins = 30/60 = 0.5 hours).

Shortcut Trick

Convert Volume: 21.560 litres × 1000 = 21560 cm³.

Let Radius (r) = 2x and Height (h) = 5x ⇒ Volume = (22/7) × (2x)² × 5x = 21560.

Solving: (22/7) × 4x² × 5x = 21560 ⇒ 110/7 × 4x³ = 21560 ⇒ x³ = 343 ⇒ x = 7.

Dimensions: r = 14 cm, h = 35 cm ⇒ Total Surface Area = 2πr(r + h) = 88 × 49 = 4312 cm².

∴ The correct answer is 4312 cm².

Alternate Method

Given:

Volume (V) = 21.560 litres

Radius (r) = 2/5 × Height (h)

Formula Used:

1 litre = 1000 cm³

Volume of Cylinder = πr²h

Total Surface Area (TSA) = 2πr(r + h)

Calculations:

⇒ Volume = 21.560 × 1000 = 21560 cm³

⇒ r = (2/5)h → h = (5/2)r

⇒ 21560 = (22/7) × r² × (5/2)r

⇒ 21560 = (110/14) × r³

⇒ r³ = (21560 × 14) ÷ 110

⇒ r³ = 196 × 14 = 2744

⇒ r = √³2744 = 14 cm

⇒ h = (5 × 14) ÷ 2 = 35 cm

⇒ TSA = 2 × (22/7) × 14 × (14 + 35)

⇒ TSA = 2 × 22 × 2 × 49

⇒ TSA = 88 × 49 = 4312 cm²

∴ The correct answer is 4312 cm².

Additional Information

Cylinder Surface Areas

The Curved Surface Area (CSA) of a cylinder is 2πrh. The Total Surface Area (TSA) includes the area of two circular bases: TSA = 2πrh + 2πr² = 2πr(r + h).

Unit Conversions

Capacity and Volume relationship: 1 Litre = 1000 cm³ = 1 dm³; 1 m³ = 1000 Litres.

Volume of Cylinder

The amount of space occupied by a 3D cylinder is given by the base area times the height: V = πr²h.

Shortcut Trick

List the first 17 prime numbers and sum them manually as there is no arithmetic progression formula for primes.

Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59.

Sum = (2+3+5+7) + (11+13+17+19) + (23+29+31+37) + (41+43+47) + (53+59)

Sum = 17 + 60 + 120 + 131 + 112 = 440.

∴ The correct answer is 440.

Alternate Method

Given: The first 17 prime numbers.

Formula: Sum = p₁ + p₂ + ... + p₁₇

⇒ Prime numbers are natural numbers greater than 1 with exactly two factors: 1 and itself.

⇒ Sequence: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59.

⇒ Sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59

⇒ Sum = (2+3+5+7+11+13+17+19+23+29) + (31+37+41+43+47+53+59)

⇒ Sum = 129 + 311

⇒ Sum = 440

∴ The correct answer is 440.

Additional Information

Definition of Prime Numbers

A prime number is a whole number greater than 1 whose only factors are 1 and itself. 2 is the only even prime number.

Sum of Primes Property

There is no general algebraic formula to find the sum of the first n prime numbers; it requires direct addition of the specific terms.

Composite Numbers

Numbers that have more than two factors are composite numbers. Note that 1 is neither prime nor composite.

Shortcut Trick

Total Effective Cost Price (CP) = 20,000 + 2,000 + 3,000 = ₹25,000.

Selling Price (SP) = ₹30,000.

Ratio of CP : SP = 25,000 : 30,000 = 5 : 6.

Profit = 6 − 5 = 1 unit.

Profit % = (1 ÷ 5) × 100 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given: Purchase Price = ₹20,000, Repair = ₹2,000, Transportation = ₹3,000, Selling Price (SP) = ₹30,000. Formulas: Total CP = Purchase Price + Overheads | Profit = SP − CP | Profit % = (Profit ÷ CP) × 100

⇒ Total Cost Price (CP) = 20,000 + 2,000 + 3,000 = ₹25,000. ⇒ Profit = SP − CP = 30,000 − 25,000 = ₹5,000. ⇒ Profit % = (5,000 ÷ 25,000) × 100 ⇒ Profit % = (1 ÷ 5) × 100 = 20%.

∴ The correct answer is 20%.

Additional Information

Effective Cost Price

Any overhead expenses like repairs, labor, or freight are always added to the original purchase price to calculate the actual CP.

Profit and Loss Calculation

Both Profit Percentage and Loss Percentage are always calculated on the Cost Price (CP) unless otherwise stated.

Shortcut Trick

Apply BODMAS: First solve the innermost product, then the brackets, and finally the subtraction.

Inner curly bracket: 3/4 − (1/2 × 8/3) = 3/4 − 4/3 = −7/12.

Outer square bracket: 7/3 ÷ (−7/12) = 7/3 × (−12/7) = −4.

Final calculation: 11/2 − (−4) = 11/2 + 4 = 19/2.

∴ The correct answer is 19/2.

Alternate Method

Given: 5 1/2 − [ 2 1/3 ÷ { 3/4 − 1/2 × 8/3 } ]

Method: BODMAS Rule (Brackets, Of, Division, Multiplication, Addition, Subtraction)

⇒ Convert mixed fractions: 5 1/2 = 11/2 and 2 1/3 = 7/3

⇒ 11/2 − [ 7/3 ÷ { 3/4 − (1/2 × 8/3) } ]

⇒ 11/2 − [ 7/3 ÷ { 3/4 − 4/3 } ]

⇒ 11/2 − [ 7/3 ÷ { (9 − 16) / 12 } ]

⇒ 11/2 − [ 7/3 ÷ { −7/12 } ]

⇒ 11/2 − [ 7/3 × (−12/7) ]

⇒ 11/2 − [ −4 ]

⇒ 11/2 + 4

⇒ (11 + 8) / 2 = 19/2

∴ The correct answer is 19/2.

Additional Information

BODMAS / VBODMAS Rule

Operations must be performed in the order: Vinculum, Brackets ( (), {}, [] ), Of, Division, Multiplication, Addition, and Subtraction.

Mixed Fraction Conversion

A mixed fraction A b/c is converted to an improper fraction using the formula: (A × c + b) / c.

Division of Fractions

To divide one fraction by another, multiply the first fraction by the reciprocal of the second: (a/b) ÷ (c/d) = (a/b) × (d/c).

Shortcut Trick

Convert all numbers to base 2.

16 = 2⁴, 8 = 2³, and (1/2)³ = 2⁻³.

For multiplication add powers, and for division subtract powers.

Resulting power = 4 + 5 + 3 − (−3) = 15.

∴ The correct answer is 2¹⁵.

Alternate Method

Given:

Expression: 16 × 2⁵ × 8 ÷ (1/2)³

Formula Used:

a^m × aⁿ = a^m+n

a^m ÷ aⁿ = a^m−n

(1/a)ⁿ = a⁻ⁿ

Calculation:

⇒ First, express each term as a power of 2.

⇒ 16 = 2⁴

⇒ 8 = 2³

⇒ (1/2)³ = 2⁻³

⇒ Substitute these values into the given expression:

⇒ 2⁴ × 2⁵ × 2³ ÷ 2⁻³

⇒ Using the multiplication rule (add exponents):

⇒ 2^{(4 + 5 + 3)} ÷ 2⁻³

⇒ 2¹² ÷ 2⁻³

⇒ Using the division rule (subtract exponents):

⇒ 2^{12 − (−3)}

⇒ 2^{12 + 3} = 2¹⁵

∴ The correct answer is 2¹⁵.

Additional Information

BODMAS Rule

Simplification follows the BODMAS order: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction.

Laws of Exponents (Multiplication & Division)

When multiplying terms with the same base, add their exponents: a^m × aⁿ = a^m+n. When dividing, subtract their exponents: a^m ÷ aⁿ = a^m−n.

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent: a⁻ⁿ = 1 ÷ aⁿ.

Shortcut Trick

Expenditure Ratio = (Price Ratio) × (Quantity Ratio)

Expenditure on Jowar : Gram = (1 × 5) : (3 × 11)

Expenditure ratio = 5 : 33

∴ The correct answer is 5 : 33.

Alternate Method

Given:

Ratio of Market Price (Jowar : Gram) = 1 : 3

Ratio of Quantity Consumed (Jowar : Gram) = 5 : 11

Formula Used:

Expenditure = Price per unit × Quantity

Calculations:

⇒ Let the prices be 1x and 3x respectively.

⇒ Let the quantities consumed be 5y and 11y respectively.

⇒ Expenditure on Jowar = 1x × 5y = 5xy

⇒ Expenditure on Gram = 3x × 11y = 33xy

⇒ Ratio of Expenditure = 5xy : 33xy

⇒ Ratio = 5 : 33

∴ The correct answer is 5 : 33.

Additional Information

Product of Ratios

When a value depends on the product of two independent variables, its ratio is the product of the individual ratios of those variables.

Compound Ratio

The compound ratio of (a : b) and (c : d) is (ac : bd). This is used in calculating total Expenditure, Revenue, or Work.

Inverse Relation

If Expenditure is constant, the Price is inversely proportional to the Quantity (P₁/P₂ = Q₂/Q₁).

Shortcut Trick

Assume Savings = 100 units.

Expenditure = 100 + 150% of 100 = 250 units.

Net change in Income = (Change in Expenditure + Change in Savings) ÷ Initial Income.

Net change = (−12% × 250 + 37% × 100) ÷ 350 = (−30 + 37) ÷ 350 = 7 ÷ 350 = 1/50 = 2%.

∴ The correct answer is 2%.

Alternate Method

Given:

Expenditure = 150% more than Savings.

Decrease in Expenditure = 12%.

Increase in Savings = 37%.

Formula Used:

Income = Expenditure + Savings

Let Savings = 100

⇒ Expenditure = 100 + (150/100) × 100 = 250

⇒ Initial Income = 250 + 100 = 350

⇒ New Expenditure = 250 − 12% of 250 = 250 − 30 = 220

⇒ New Savings = 100 + 37% of 100 = 100 + 37 = 137

⇒ New Income = 220 + 137 = 357

⇒ Increase in Income = 357 − 350 = 7

⇒ Percentage Increase = (7 ÷ 350) × 100 = 2%

∴ The correct answer is 2%.

Additional Information

Income and Expenditure Relationship

The fundamental equation is Income = Expenditure + Savings. Any percentage change in components affects the total income proportionally.

Percentage Change

Percentage Increase/Decrease = (Final Value − Initial Value) ÷ Initial Value × 100.

Weighted Average in Income

Income change % = (E % × E_ratio + S % × S_ratio) ÷ (Total ratio). Here (250 × −12 + 100 × 37) ÷ 350 = 2%.

Shortcut Trick

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

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

Amount = 121% of ₹6,500 = 1.21 × 6,500.

Amount = ₹7,865.

∴ The correct answer is ₹7,865.

Alternate Method

Given:

Principal (P) = ₹6,500

Rate (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P × (1 + R/100)ⁿ

Calculations:

⇒ A = 6,500 × (1 + 10/100)²

⇒ A = 6,500 × (1 + 0.1)²

⇒ A = 6,500 × (1.1)²

⇒ A = 6,500 × 1.21

⇒ A = 65 × 121

⇒ A = ₹7,865

∴ The correct answer is ₹7,865.

Additional Information

CI vs SI Difference for 2 Years

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

Half-Yearly Compounding

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

Compound Interest Formula

Compound Interest (CI) alone can be calculated as CI = A − P = P[(1 + R/100)ⁿ − 1].

Shortcut Trick

Age ratio of Father : Son = 5 : 1

Difference in ratio parts = 5 − 1 = 4 units

Given age difference = 30 years

4 units = 30 years → 1 unit = 30 ÷ 4 = 7.5 years

∴ The correct answer is 7.5 years.

Alternate Method

Let the current age of the son be x years.

The father's age is 5× that of the son ⇒ 5x years.

Given that the father is 30 years older than the son.

⇒ 5x − x = 30

⇒ 4x = 30

⇒ x = 30 ÷ 4

⇒ x = 7.5

∴ The correct answer is 7.5 years.

Additional Information

Age Difference Constant

The difference between the ages of two persons remains constant at any point in time.

Ratio Method

If the ratio of ages is a:b and the difference is D, then 1 unit = D ÷ (a−b).

Linear Equations in Ages

Problems involving 'n' years ago or 'n' years hence require adding or subtracting 'n' from the current age variables.

Shortcut Trick

20% of number + 60 = number

⇒ 80% of number = 60

⇒ Number = 60 ÷ 0.8 = 75

75% of number = 0.75 × 75 = 56.25

∴ The correct answer = 56.25

Alternate Method

Given:

20% of a number + 60 = number

Formula Used:

Percentage = (Value ÷ 100) × Number

Calculations:

⇒ 0.2x + 60 = x

⇒ x − 0.2x = 60

⇒ 0.8x = 60

⇒ x = 75

⇒ 75% of x = 0.75 × 75 = 56.25

∴ The correct answer is 56.25.

Additional Information

Percentage Basics

20% = 1/5 and 75% = 3/4

Equation Formation

Translate statements into algebraic equations

Shortcut Logic

If x − 20% of x = constant, then remaining % = constant

Shortcut Trick

The Surface Area of a sphere is 4 × π × (radius)².

Given Radius = 35 cm.

Surface Area = 4 × π × (35)² = 4 × π × 1225 = 4900π cm².

∴ The correct answer is 4900π cm².

Alternate Method

Given:

Radius (r) of the Sphere = 35 cm.

Formula Used:

Surface Area (A) of a sphere = 4πr²

Calculations:

⇒ Surface Area = 4 × π × (35)²

⇒ Surface Area = 4 × π × (35 × 35)

⇒ Surface Area = 4 × π × 1225

⇒ Surface Area = 4900π cm²

∴ The correct answer is 4900π cm².

Additional Information

Volume of a Sphere

The amount of space inside a sphere is given by the formula V = (4/3)πr³.

Curved Surface Area of Hemisphere

For a hemisphere (half-sphere), the curved surface area is exactly half of a full sphere: CSA = 2πr².

Total Surface Area of Hemisphere

A solid hemisphere includes the base circle (πr²), making the total area: TSA = 2πr² + πr² = 3πr².

Shortcut Trick

Simplified ratio: 1/5 : 1/2 : 11/16

Multiply by LCM (80): 16 : 40 : 55

Difference (Greatest − Smallest): 55 − 16 = 39 units

39 units = 78 ⇒ 1 unit = 2

Largest number (55 units) = 55 × 2 = 110

∴ The correct answer is 110.

Alternate Method

Given: Ratio of three numbers = 1/5 : 9/18 : 11/16

Formula: To convert fractional ratios to integers, multiply each term by the LCM of denominators.

⇒ First, simplify 9/18 = 1/2

⇒ Ratio = 1/5 : 1/2 : 11/16

⇒ LCM of 5, 2, 16 = 80

⇒ Simplified Ratio = (1/5 × 80) : (1/2 × 80) : (11/16 × 80) = 16 : 40 : 55

⇒ Let numbers be 16x, 40x, and 55x

⇒ Difference = 55x − 16x = 39x

⇒ Given 39x = 78 ⇒ x = 2

⇒ Largest number = 55x = 55 × 2 = 110

∴ The correct answer is 110.

Additional Information

Ratio Simplification

To simplify a ratio of fractions a/b : c/d, multiply both terms by the LCM of b and d to obtain a ratio of whole numbers.

Proportional Constant

The 'x' in ratios like ax : bx represents the highest common factor (HCF) of the original numbers being compared.

Compound Ratio

The compound ratio of a:b and c:d is (a × c) : (b × d). This is useful when combining multiple relationships.

Shortcut Trick

Net Selling Price (SP) = Marked Price (MP) × (100 − d₁)% × (100 − d₂)%

SP = 7500 × (100 − 14)% × (100 − 28)%

SP = 7500 × 86% × 72%

SP = 7500 × (86 ÷ 100) × (72 ÷ 100) = 75 × 0.86 × 72

SP = 5400 × 0.86 = 4644

∴ The correct answer is ₹4,644.

Alternate Method

Given: Marked Price (MP) = ₹7,500, First Discount (d₁) = 14%, Second Discount (d₂) = 28%.

Formulas: Successive Discount = a + b − (a × b ÷ 100) | SP = MP × (100 − Total Discount%) ÷ 100

⇒ Price after first discount = 7500 × (100 − 14) ÷ 100 = 7500 × 0.86 = ₹6,450

⇒ Final Selling Price (SP) = 6450 × (100 − 28) ÷ 100 = 6450 × 0.72

⇒ SP = ₹4,644

∴ The correct answer is ₹4,644.

Additional Information

Marked Price & Discount

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

Successive Discount Calculation

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

Shortcut Trick

New person age = New Average + (Previous Total Members × Increase in Average)

Here, Previous Members = 32, New Average = 22, Increase = 22 − 21 = 1

⇒ Teacher age = 22 + (32 × 1)

⇒ 22 + 32 = 54 years

∴ The correct answer is 54 years.

Alternate Method

Given:

Number of students = 32

Average age of students = 21 years

Total members after teacher is included = 32 + 1 = 33

New average age = 22 years

Formula Used:

Sum of observations = Average × Number of observations

Calculations:

⇒ Total age of 32 students = 32 × 21 = 672 years

⇒ Total age of 33 persons (including teacher) = 33 × 22 = 726 years

⇒ Age of the teacher = Total age (33 persons) − Total age (32 students)

⇒ Age of the teacher = 726 − 672

⇒ Age of the teacher = 54 years

∴ The correct answer is 54 years.

Additional Information

Weighted Average Formula

Used to find the average of combined groups: Avg_combined = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Net Deviation Method

The sum of deviations from the average is always zero. Addition of a person with age higher than average increases the overall average.

Arithmetic Mean Properties

If every value in a set is increased by a constant 'k', the average also increases by 'k'.

Shortcut Trick

Net change percentage = a + b + (a × b) ÷ 100

Here, markup percentage (a) = +5% and discount percentage (b) = −40%.

Net change = 5 − 40 + (5 × −40) ÷ 100 = −35 − 2 = −37%.

Negative sign indicates a loss of 37%.

∴ The correct answer is 37%.

Alternate Method

Given: Markup = 5%, Discount = 40%.

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

⇒ Let the Cost Price (CP) be 100.

⇒ Marked Price (MP) = 100 + 5% of 100 = 105.

⇒ Selling Price (SP) = 105 − 40% of 105 = 105 − 42 = 63.

⇒ Loss = CP − SP = 100 − 63 = 37.

⇒ Loss percentage = (37 ÷ 100) × 100 = 37%.

∴ The correct answer is 37%.

Additional Information

Marked Price & Discount

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

Successive Percentage Change

When a value is increased by x% and then decreased by y%, the net effect is [x − y − (xy ÷ 100)]%.

Shortcut Trick

Net filling efficiency = (1/7 − 1/14) of tank per minute.

Net efficiency = (2 − 1)/14 = 1/14 of tank per minute.

Time to fill full tank = 14 minutes.

Time to fill one-half of the tank = 14 ÷ 2 = 7 minutes.

∴ The correct answer is 7 minutes.

Alternate Method

Given: Filling Pipe (A) = 7 minutes, Emptying Pipe (B) = 14 minutes.

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

⇒ Combined Efficiency (A + B) = +2 − 1 = 1 unit/min.

⇒ Target Work = 1/2 × Total Capacity = 1/2 × 14 = 7 units.

⇒ Time required = Target Work ÷ Combined Efficiency = 7 ÷ 1 = 7 minutes.

∴ The correct answer is 7 minutes.

Additional Information

Pipes and Cisterns Rule

If an inlet pipe fills in x hours and an outlet pipe empties in y hours, net work done in 1 hour = (1/x − 1/y) when both are open.

Efficiency Concept

Filling efficiency is taken as positive (+), while emptying efficiency is always taken as negative (−).

Shortcut Trick

Ratio of Person to Sibling = 3 : 1

Sum of ratio parts = 3 + 1 = 4 units

4 units = 40 years → 1 unit = 10 years

Age of the person = 3 units = 3 × 10 = 30 years

∴ The correct answer is 30 years.

Alternate Method

Given:

Sum of ages = 40 years

Person age = 3 × Sibling age

Calculations:

⇒ Let the age of the sibling be x years.

⇒ Age of the person = 3x years.

⇒ x + 3x = 40

⇒ 4x = 40

⇒ x = 40 ÷ 4 = 10 years

⇒ Person age = 3 × 10 = 30 years.

∴ The correct answer is 30 years.

Additional Information

Ratio and Proportion in Ages

When ages are given in a ratio a:b and their sum is S, the ages are [a/(a+b)] × S and [b/(a+b)] × S.

Age Difference Constant

The difference between the ages of two people remains constant throughout their lives, regardless of how many years pass.

Future and Past Ages

If current age is x, then age 'n' years ago was (x − n) and age 'n' years later will be (x + n).

Shortcut Trick

Relative Speed (opposite direction) = 40 + 60 = 100 km/h.

Convert Speed to m/s: 100 × (5/18) = 250/9 m/s.

Total Distance to cover = Length of Train 1 + Length of Train 2 = 125 + 125 = 250 m.

Time = Distance ÷ Speed = 250 ÷ (250/9) = 9 seconds.

∴ The correct answer is 9 sec.

Alternate Method

Given: Speed of Train A (S₁) = 40 km/h, Speed of Train B (S₂) = 60 km/h, Length of each train (L) = 125 m.

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

⇒ Total Distance = 125 + 125 = 250 m

⇒ Relative Speed = 40 + 60 = 100 km/h

⇒ Relative Speed in m/s = 100 × (5/18) = 500/18 = 250/9 m/s

⇒ Time taken = 250 ÷ (250/9)

⇒ Time taken = 250 × (9/250) = 9 seconds

∴ The correct answer is 9 sec.

Additional Information

Relative Speed Concept

When two objects move in opposite directions, relative speed is the sum of individual speeds (S₁ + S₂). If moving in the same direction, it is the difference (S₁ − S₂).

Unit Conversion

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

Crossing Distance

When a train crosses another train, platform, or bridge, the total distance is always the sum of their lengths.

Shortcut Trick

Condition to check: Odd Number → Even Number → Even Number

Instead of checking every single number, directly scan the series for two consecutive even numbers.

The only consecutive even numbers in the entire series are 4 and 6 near the end.

Check the number before 4: It is 3 (an Odd number).

Thus, the triplet 3, 4, 6 is the only one that perfectly satisfies the required condition.

∴ The correct answer is 1.

Alternate Method

Given Series:

9 6 9 4 7 8 9 9 1 6 7 3 6 5 9 7 4 7 1 7 7 8 3 4 6 9 3

Condition to be fulfilled:

⇒ Odd Number → Even Number → Even Number

Let us identify all the even numbers in the series from left to right and check their adjacent numbers:

⇒ 9, 6, 9 → Preceded by Odd, Followed by Odd ×

⇒ 9, 4, 7 → Preceded by Odd, Followed by Odd ×

⇒ 7, 8, 9 → Preceded by Odd, Followed by Odd ×

⇒ 1, 6, 7 → Preceded by Odd, Followed by Odd ×

⇒ 3, 6, 5 → Preceded by Odd, Followed by Odd ×

⇒ 7, 4, 7 → Preceded by Odd, Followed by Odd ×

⇒ 7, 8, 3 → Preceded by Odd, Followed by Odd ×

⇒ 3, 4, 6 → Preceded by Odd, Followed by Even ✔

⇒ 4, 6, 9 → Preceded by Even, Followed by Odd ×

⇒ Clearly, there is only one such even number (4) which is immediately preceded by an odd number and immediately followed by an even number.

∴ The correct answer is 1.

Additional Information

Preceded By

In any reasoning sequence, if an element X is 'preceded by' Y, it means Y comes immediately before X in the series (i.e., Y → X).

Followed By

If an element X is 'followed by' Z, it means Z comes immediately after X in the sequence (i.e., X → Z).

Odd and Even Numbers

An even number is an integer perfectly divisible by 2 (e.g., 2, 4, 6, 8), while an odd number leaves a remainder of 1 when divided by 2 (e.g., 1, 3, 5, 7, 9).

Given Statements:

All wheels are cars.

All cars are trucks.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some trucks are cars - Follows  (Since all cars are inside trucks, at least some trucks are cars).

II. All wheels are trucks - Follows  (All wheels are cars and all cars are trucks, therefore all wheels are trucks).

So, both conclusions I and II follow.

Hence, the correct answer is Option 1.

The logic followed here is:

For, GIMJ is related to LNRO

For, QSWT is related to VXBY

Now, applying the same logic for TVZW

So, TVZW → YAEB

Hence, the correct answer is "Option 4".

Given: Mr. Memi is 34th from the left and Mr. Zzz is 9th from the right.

Total number of persons = 104

Convert Mr. Zzz’s position from right into left:

<br>

Position from left = (Total + 1) − Position from right

<br>

= (104 + 1) − 9

<br>

= 96th

Now, positions:

<br>

Mr. Memi = 34th from left

<br>

Mr. Zzz = 96th from left

Number of persons between them = (96 − 34) − 1

<br>

= 62 − 1

<br>

= 61

Hence, the correct answer is Option 1.

The logic followed here is:

So, the next term = HVO

Hence, the correct answer is Option 3.

The logic followed here is:

For, PLI − MIF

For, VRO − SOL

Now, applying the same logic for FBY − CYV

So, FBY − CYV follows the same pattern correctly.

Hence, the correct answer is "Option 4".

The logic followed here is:

thus, "6" will replace the question mark in the given series.

Hence, the correct option is "Option 2"

The logic followed here is:

Given:

‘pig peak salad’ is coded as ‘aq ym lq’

‘lemon salad grape’ is coded as ‘wq cv ym’

<br>

So, salad → ym

Hence, the correct answer is Option 1.

Given: Z is 61st from the right end, and total number of students is 97.

Z’s position from left = (97 − 61) + 1 = 37th

G is 28th to the left of Z, so:

<br>

G’s position from left = 37 − 28 = 9th

Therefore, G’s position from the left end is 9th.

Hence, the correct answer is Option 1.

Given:

Kavya walks 100 metres North.

She turns right → 40 metres East.

She turns right → 30 metres South.

She turns right → 40 metres West.

So, she is 70 metres away from her original position.

Hence, the correct answer is Option 4.