RRB Group D Official Paper (Held On: 05 Dec, 2025 Shift 1) (Previous Year Paper)

The correct answer is 50 J.

Key Points

• Work done (W) is calculated using the formula: W = F × d × cos(θ), where:
• F is the force applied (10 N).
• d is the displacement of the object (5 m).
• θ is the angle between the force and displacement direction (0° since the force is applied in the direction of movement).
• Substituting the values into the formula:
• W = 10 × 5 × cos(0°).
• Since cos(0°) = 1, the equation becomes W = 10 × 5 × 1 = 50 J.
• The work done is measured in joules (J), which is the SI unit of work and energy.
• Since the force is applied in the same direction as the displacement, the full magnitude of the force contributes to the work done.
• Hence, the correct answer is 50 J.

Additional Information

• Work:
• Work is defined as the energy transferred to or from an object via the application of force along a displacement.
• It is mathematically expressed as W = F × d × cos(θ), where:
• F = magnitude of the force.
• d = displacement of the object.
• θ = angle between the force and displacement vectors.
• Work is positive when the force and displacement are in the same direction and negative when they are in opposite directions.
• Energy and Work:
• Work is closely related to energy. When work is done on an object, energy is transferred to or from that object.
• The unit of both work and energy in the SI system is the joule (J).
• 1 joule is defined as the work done when a force of 1 newton moves an object 1 meter in the direction of the force.
• Force:
• Force is defined as an interaction that, when unopposed, changes the motion of an object.
• The SI unit of force is the newton (N), and 1 newton is equivalent to 1 kg·m/s².
• In this problem, a force of 10 N is applied to the object.
• Displacement:
• Displacement is a vector quantity that refers to the change in position of an object.
• In this problem, the object is displaced by 5 m in the direction of the applied force.
• Angle between Force and Displacement:
• The angle between the force and displacement is crucial in calculating work.
• When θ = 0°, cos(θ) = 1, and the entire force contributes to the work.
• If θ = 90°, cos(θ) = 0, and no work is done.

Important Points

• Conditions for Work to be Done:
• There must be a force acting on the object.
• The object must be displaced due to the force.
• The displacement must have a component in the direction of the force.
• Real-life Application:
• Work can be seen in activities like lifting weights, pushing a cart, or pulling an object.
• In engineering, the concept of work is fundamental to understanding machines, engines, and other systems that transfer energy.

The correct answer is Using condoms during sexual intercourse.

Key Points

• Using condoms during sexual intercourse is one of the most effective and widely recommended methods to prevent the transmission of HIV (Human Immunodeficiency Virus) and other sexually transmitted infections (STIs).
• Condoms act as a barrier that prevents the exchange of bodily fluids such as semen, vaginal fluids, or blood, which are primary carriers of the HIV virus.
• Both male condoms (made of latex or polyurethane) and female condoms are effective when used consistently and correctly during sexual activity.
• Studies have shown that consistent and proper use of condoms can reduce the risk of HIV transmission by up to 98%.
• In addition to HIV prevention, condoms also protect against other infections such as gonorrhea, chlamydia, and syphilis, making them a crucial component of safe sex practices.

Additional Information

• HIV Transmission:
• HIV is primarily transmitted through unprotected sexual intercourse, sharing of contaminated needles, blood transfusions with infected blood, or from mother to child during childbirth or breastfeeding.
• The virus attacks the body’s immune system, specifically the CD4 cells (T cells), which help the body fight infections.
• Why other options are incorrect:
• Taking multivitamins regularly: While multivitamins can improve overall health and immunity, they do not prevent HIV transmission. Hence, this option is incorrect.
• Sharing needles carefully: Sharing needles, even "carefully," poses a high risk of HIV transmission. Sterile, single-use needles should always be used. Hence, this option is incorrect.
• Taking antibiotics after sex: Antibiotics are used to treat bacterial infections, not viral infections like HIV. They do not prevent HIV transmission. Hence, this option is incorrect.
• Global HIV Statistics (2023):
• Approximately 38.4 million people are living with HIV globally, as per UNAIDS.
• Access to preventive measures, such as condoms and antiretroviral therapy (ART), has been instrumental in reducing new infections.
• Prevention Strategies:
• Other preventive measures include Pre-Exposure Prophylaxis (PrEP), which involves taking antiretroviral medications to reduce the risk of HIV infection.
• Promoting awareness and education about safe sex practices is crucial in combating HIV/AIDS globally.

Important Points

• Male Condoms: Widely available, inexpensive, and effective when used properly. They are typically made of latex, but non-latex options are available for people with allergies.
• Female Condoms: Provide an alternative for women to protect themselves from HIV and STIs. They are made of polyurethane or nitrile and are inserted into the vagina.
• World AIDS Day: Observed on December 1 each year to raise awareness and promote prevention, testing, and treatment of HIV/AIDS.
• HIV Testing: Early and regular testing is critical to identifying infections and starting treatment promptly.
• Antiretroviral Therapy (ART): While ART does not cure HIV, it helps in suppressing the virus, improving the quality of life, and reducing the risk of transmission.

The correct answer is 1 m/s².

Key Points

• Acceleration is defined as the rate of change of velocity.
• The formula for acceleration is: a = (v − u)/t
• Given:
• Initial velocity, u = 0 m/s (car starts from rest)
• Final velocity, v = 72 km/h = 20 m/s (since 72 × 5/18 = 20 m/s)
• Time, t = 20 s
• Substituting the values:
  

a = (20 − 0)/20 = 1 m/s²

• Hence, the acceleration of the car is 1 m/s².

Additional Information

• SI Unit of Acceleration:
• Metre per second squared (m/s²).
• Conversion of Speed:
• 1 km/h = 5/18 m/s.
• To convert km/h to m/s, multiply by 5/18.
• Types of Motion:
• If acceleration is constant, the motion is called uniformly accelerated motion.

The correct answer is When the bus stops suddenly, people fall forward.

Key Points

• Action and Reaction forces are described by Newton's Third Law of Motion, which states: "For every action, there is an equal and opposite reaction."
• In the scenario where the foot pushes the ground backward, the ground pushes the foot forward. This is a textbook example of action and reaction forces. Correct statement.
• When a swimmer pushes water backward, the water exerts an equal and opposite force forward, propelling the swimmer. Correct statement.
• In the case of a rocket moving upward, the gases expelled downward exert an opposite force on the rocket, causing it to ascend. Correct statement.
• However, when a bus stops suddenly and people fall forward, this is due to inertia, as explained by Newton's First Law of Motion. It is not an example of action and reaction forces. Incorrect statement.

Additional Information

• Newton's Third Law of Motion:
• States that forces always occur in pairs: the action force and the reaction force.
• These forces are equal in magnitude but opposite in direction.
• Examples include walking (foot-ground interaction), swimming, and rocket propulsion.
• Newton's First Law of Motion (Law of Inertia):
• States that an object will continue in its state of rest or uniform motion unless acted upon by an external force.
• When a bus stops suddenly, passengers continue moving forward due to their inertia.
• This phenomenon is unrelated to action and reaction forces.
• Key Characteristics of Action and Reaction Forces:
• They act on two different objects.
• They never cancel each other out because they act on separate objects.
• Examples: A gun recoiling when a bullet is fired, or a fish swimming by pushing water backward.
• Applications of Newton's Third Law:
• Rocket Science: The expulsion of gases downward propels rockets upward.
• Propellers and Jets: Air or water is pushed in one direction to generate thrust in the opposite direction.
• Walking: When you push the ground backward, it pushes you forward.

Important Points

• Newton's Laws Overview:
• First Law: Inertia explains why passengers lurch forward when a bus stops suddenly.
• Second Law: Relates force, mass, and acceleration (F = ma).
• Third Law: Explains action-reaction force pairs.
• Distinction Between Forces:
• Action-Reaction Forces: Operate simultaneously and are equal and opposite.
• Inertia-Based Forces: Result from an object's tendency to maintain its current state of motion.
• Practical Examples of Inertia:
• Passengers jerking forward when a vehicle stops suddenly.
• A book remaining at rest unless pushed or pulled.
• Water splashing forward when a moving container is abruptly halted.

The correct answer is They are different structural forms of carbon with different physical properties but similar chemical properties..

Key Points

• Allotropes are different structural forms of the same element. In the case of carbon, the allotropes differ in the arrangement of carbon atoms, which leads to different physical properties while maintaining similar chemical properties.
• The primary allotropes of carbon are diamond, graphite, graphene, fullerenes, and carbon nanotubes. Each of these forms has a distinct structure, such as tetrahedral in diamond and hexagonal in graphite.
• Physical properties such as hardness, electrical conductivity, and appearance differ among the allotropes. For instance, diamond is extremely hard and does not conduct electricity, while graphite is soft and an excellent conductor.
• Chemical properties, such as the ability to form covalent bonds with other elements, remain similar across all allotropes because they are made of the same carbon atoms.
• Hence, the statement "They are different structural forms of carbon with different physical properties but similar chemical properties" is correct.

Additional Information

• Diamond:
• In diamond, each carbon atom is covalently bonded to four other carbon atoms in a tetrahedral structure, giving it unmatched hardness.
• Diamond is a poor conductor of electricity but an excellent thermal conductor.
• It is used in jewelry, cutting tools, and heat sinks.
• Graphite:
• Graphite has a hexagonal layered structure where each carbon atom is bonded to three other carbon atoms.
• It is a good conductor of electricity due to the presence of free electrons and is used in pencils, lubricants, and batteries.
• Graphene:
• Graphene is a single layer of carbon atoms arranged in a hexagonal lattice.
• It is known for its exceptional strength, flexibility, and electrical conductivity, making it suitable for electronics and nanotechnology.
• Fullerenes:
• Fullerenes are molecules of carbon atoms arranged in the form of a hollow sphere, cylinder, or ellipsoid.
• The most common fullerene is C60, also known as buckyballs.
• They are used in materials science, electronics, and nanomedicine.
• Carbon Nanotubes:
• These are cylindrical structures made of carbon atoms with remarkable tensile strength and electrical conductivity.
• They have applications in electronics, composites, and medicine.

Important Points

• Statement 1: "They are different isotopes of carbon with varying numbers of neutrons." This is incorrect because isotopes refer to atoms of the same element with different numbers of neutrons, not structural forms.
• Statement 2: "They are different structural forms of carbon with different physical properties but similar chemical properties." This is correct as it accurately describes allotropes.
• Statement 3: "They are isomers of carbon, having the same molecular formula but different structures." This is incorrect as isomers refer to compounds with the same molecular formula but different chemical structures, not elements.
• Statement 4: "They are compounds formed by carbon with different elements." This is incorrect because allotropes are forms of pure carbon, not compounds.

The correct answer is Option 3.

Key Points

• The pH scale measures how acidic or basic a solution is, ranging from 0 to 14, where 7 is neutral.
• Solutions with a pH greater than 7 are classified as basic (alkaline), and they turn red litmus paper blue.
• Among the given options, the solution with pH 11 is basic, as it is significantly higher than 7 and belongs to the alkaline category. Hence, option 3 is correct.
• Solutions with pH values 4, 6, and 2 are acidic because their pH values are less than 7, and they would turn blue litmus paper red instead.
• Acidic solutions do not turn red litmus blue, reinforcing why solutions with pH 11 are ideal for this behavior.

Additional Information

• pH Scale:
• The pH scale is used to measure the hydrogen ion concentration in a solution, with lower values indicating acidity and higher values indicating alkalinity.
• Acidic solutions have higher hydrogen ion concentrations (H⁺), while basic solutions contain higher hydroxide ion concentrations (OH⁻).
• Examples of acidic solutions include vinegar (pH ~3) and lemon juice (pH ~2), while examples of basic solutions include soap water (pH ~10) and bleach (pH ~12).
• Litmus Indicator:
• Litmus paper is a natural pH indicator derived from lichens, used to test the acidity or basicity of a solution.
• In acidic solutions, blue litmus paper turns red, while in basic solutions, red litmus paper turns blue.
• This is a simple qualitative test to determine the pH nature of a solution.
• Characteristics of pH Levels:
• A solution with pH 11 is strongly basic, commonly found in cleaning agents like ammonia solution.
• A solution with pH 4 is weakly acidic, often found in fruit juices such as apple juice.
• A solution with pH 6 is slightly acidic and close to neutral, similar to milk or unpolluted rainwater.
• A solution with pH 2 is highly acidic, seen in substances like gastric acid or concentrated vinegar.
• Applications of pH Knowledge:
• pH plays a vital role in agriculture to test soil acidity and alkalinity, ensuring optimal crop growth.
• In medicine, pH is crucial for understanding body fluids like blood (normal pH ~7.4).
• Industries use pH to formulate cleaning agents, cosmetics, and food products.
• Environmental studies monitor water pH to evaluate pollution levels and aquatic life sustainability.

Important Points

• Neutral Solutions: Solutions with pH 7 are neutral, such as pure water, and do not change the color of litmus paper.
• Strong Acids and Bases: Strong acids have pH values closer to 0, while strong bases have pH values closer to 14.
• Universal Indicator: Unlike litmus, universal indicators provide a broader and more precise pH measurement using a spectrum of colors.
• Buffer Solutions: Buffers help maintain a consistent pH and are widely used in biochemical and industrial processes.
• Environmental Impact: Extreme pH levels in water bodies can harm aquatic life and disrupt ecosystems.

The correct answer is It prevents oxidation.

Key Points

• Nitrogen gas is used in chip packets to prevent oxidation, which can lead to the food becoming stale or rancid. This ensures the chips maintain their freshness and taste for a longer time.
• Oxygen in the air reacts with the oils and fats in chips, causing oxidation. This process leads to the formation of off-flavors and spoilage. Nitrogen, being an inert gas, replaces oxygen and prevents such reactions.
• The use of nitrogen also creates a protective cushion inside the packet. This prevents the chips from being crushed during transportation or handling.
• Unlike oxygen, nitrogen does not react with food components. It is a non-reactive, odorless, and tasteless gas, making it ideal for food packaging.
• This method of using nitrogen gas is a part of a broader food preservation technique known as Modified Atmosphere Packaging (MAP), widely used in the food industry.

Additional Information

• Oxidation Process:
• Oxidation is a chemical reaction that occurs when oxygen reacts with certain substances, such as the oils in chips. This reaction can produce rancid flavors and reduce the shelf life of the product.
• Exposure to oxygen can also cause the degradation of vitamins and nutrients in the food.
• Nitrogen gas replaces oxygen in the packaging, thus halting the oxidation process.
• Modified Atmosphere Packaging (MAP):
• MAP is a packaging technique where the composition of the internal atmosphere of the package is altered. This can involve reducing oxygen levels, increasing nitrogen levels, or a combination of both.
• In addition to chips, MAP is used for a variety of food products, including fruits, vegetables, meats, and bakery items.
• This method helps extend the shelf life of food products while maintaining their quality, taste, and nutritional value.
• Other Benefits of Nitrogen Packaging:
• It prevents the growth of aerobic bacteria and molds, which require oxygen to thrive.
• It ensures that the texture of the chips remains crispy and crunchy by reducing moisture absorption.
• Nitrogen gas is safe for consumption as it is a naturally occurring component of the air we breathe, comprising about 78% of Earth's atmosphere.
• Role of Nitrogen in the Food Industry:
• Nitrogen is extensively used in packaging not only for snacks like chips but also for coffee, powdered milk, and other oxygen-sensitive products.
• It is also used to create an inert atmosphere in food processing and storage to prevent spoilage and contamination.

Important Points

• Statement Analysis:
• Statement 1: "It absorbs moisture" – Incorrect. Nitrogen does not absorb moisture; its role is to replace oxygen. Moisture absorption in chip packets is generally managed by desiccants or the packaging material itself.
• Statement 2: "It adds crispiness" – Incorrect. The crispiness of chips is primarily a result of their preparation process, such as frying or baking, rather than the presence of nitrogen gas.
• Statement 3: "It prevents oxidation" – Correct. As explained, nitrogen replaces oxygen to prevent oxidation and maintain the freshness of the chips.
• Statement 4: "It adds flavor" – Incorrect. Nitrogen is a tasteless and odorless gas and does not contribute to the flavor of the chips.
• The use of nitrogen gas in food packaging aligns with global food safety and preservation standards. It is a widely accepted and efficient method for extending the shelf life of perishable products.

The correct answer is It permits entries and exits of substances from the cell..

Key Points

• The Golgi Complex is a major organelle responsible for modifying, sorting, and packaging proteins and lipids for secretion or delivery to other parts of the cell. It does not perform the function of regulating entries and exits of substances from the cell, which is the role of the cell membrane.
• Statement 1: The Golgi complex modifies and packages proteins received from the endoplasmic reticulum. This is correct, as it processes proteins and lipids and prepares them for transport within or outside the cell.
• Statement 2: The Golgi complex transports and secretes materials outside the cell. This is correct because the Golgi apparatus packages materials into vesicles for exocytosis or other cellular destinations.
• Statement 3: The Golgi complex forms lysosomes, which aid in intracellular digestion. This is correct since lysosomes are derived from the Golgi apparatus and contain digestive enzymes.
• Statement 4: The Golgi complex does not permit entries and exits of substances from the cell. This function is specific to the cell membrane, which acts as a selective barrier. Hence, this statement is incorrect.
• Statement 5: The correct answer is option 4, as it does not align with the biological functions of the Golgi apparatus.

Additional Information

• Golgi Complex Functions:
• The Golgi apparatus is involved in the processing, sorting, and transport of proteins and lipids synthesized in the endoplasmic reticulum (ER).
• It plays a critical role in the creation of lysosomes, which are essential for breaking down cellular waste and macromolecules.
• It packages and prepares materials for secretion via vesicles, facilitating processes like hormone release and enzyme transport.
• The Golgi apparatus also contributes to the synthesis of glycoproteins and glycolipids, which are vital for cell recognition and signaling.
• Cell Membrane Functions:
• The cell membrane is a selectively permeable barrier that regulates the entry and exit of substances into and out of the cell.
• It is composed of a phospholipid bilayer with embedded proteins that facilitate transport and communication.
• The membrane is responsible for processes like endocytosis and exocytosis, allowing substances to move in and out of the cell.
• The cell membrane plays a key role in maintaining homeostasis by controlling the internal environment of the cell.
• Lysosome Formation:
• Lysosomes are organelles that contain hydrolytic enzymes, used for breaking down cellular waste and debris.
• These enzymes are synthesized in the ER and modified in the Golgi apparatus before being packaged into lysosomes.
• Lysosomes are crucial for processes like autophagy (self-digestion) and recycling of cellular components.
• Endoplasmic Reticulum and Golgi Complex Relationship:
• The rough ER synthesizes proteins, which are transported to the Golgi apparatus for modification and packaging.
• The smooth ER is involved in lipid synthesis, which is similarly processed by the Golgi apparatus.
• The two organelles work in coordination to ensure proper functioning and distribution of cellular materials.

Important Points

• Discovery: The Golgi apparatus was first discovered by Camillo Golgi in 1898 using a staining technique known as the “black reaction.”
• Structure: It consists of flattened sacs called cisternae, which are stacked and surrounded by vesicles.
• Location: The Golgi complex is found in both plant and animal cells but is highly developed in cells that are actively involved in secretion.
• Diseases: Dysfunction in the Golgi apparatus can lead to disorders like lysosomal storage diseases and impaired protein trafficking.
• Applications: Understanding Golgi functions is critical for research in areas like cell biology, medicine, and biotechnology.

The correct answer is 0.5 A.

Key Points

• The relationship between voltage (V), current (I), and resistance (R) is given by Ohm's Law, which states: V = I × R.
• In this question, the resistance of the conductor is 10 Ω, and the potential difference applied across it is 5 V.
• Rearranging Ohm’s Law to calculate current: I = V / R.
• Substituting the given values: I = 5 V / 10 Ω = 0.5 A.
• Therefore, the current flowing through the conductor is 0.5 A, which is the correct answer.

Additional Information

• Ohm's Law:
• Ohm's Law is a fundamental principle in electrical circuits that states the relationship between voltage, current, and resistance.
• It is mathematically expressed as V = I × R, where V is the voltage, I is the current, and R is the resistance.
• This law is widely used in circuit analysis to determine unknown parameters when two quantities are known.
• Resistance:
• Resistance is the property of a material to oppose the flow of electric current. It is measured in ohms (Ω).
• Resistance depends on factors such as the material of the conductor, its length, cross-sectional area, and temperature.
• Conductors have low resistance, while insulators have high resistance.
• Current:
• Electric current is the flow of electric charge through a conductor, measured in amperes (A).
• It is a scalar quantity and can be either direct current (DC) or alternating current (AC).
• In circuits, the direction of current is conventionally taken as the flow of positive charges.
• Potential Difference:
• Potential difference is the work done to move a unit charge between two points in an electric field. It is measured in volts (V).
• A higher potential difference across a conductor results in a higher flow of current, assuming constant resistance.

Important Points

• Applications of Ohm's Law:
• Used to design electrical circuits and systems.
• Determines the specifications for resistors and other components in electronic devices.
• Helps in troubleshooting electrical issues by analyzing circuit behavior.
• Units:
• Voltage is measured in volts (V).
• Current is measured in amperes (A).
• Resistance is measured in ohms (Ω).
• Historical Background:
• Ohm's Law was formulated by Georg Simon Ohm in 1827.
• His experiments established the relationship between electric current, voltage, and resistance in conductive materials.

The correct answer is Providing fine adjustment of focal length.

Key Points

• The crystalline lens of the eye is a transparent, biconvex structure located behind the iris and pupil. Its primary function is to focus light onto the retina by adjusting its focal length.
• The lens achieves this adjustment through the process of accommodation, where its shape changes to focus on objects at varying distances. This ensures a clear image is formed on the retina.
• It works in conjunction with the cornea, which provides the initial focusing power, while the lens fine-tunes the focus for sharper vision.
• The lens does not control the amount of light entering the eye—that function is performed by the iris, which adjusts the pupil size.
• The crystalline lens does not detect colors or send signals to the brain. These tasks are performed by the retina and optic nerve respectively. Hence, statements 1, 2, and 3 are incorrect.
• By providing fine adjustment of focal length, the lens ensures clarity for both near and distant objects. Hence, statement 4 is correct.

Additional Information

• Structure of the Crystalline Lens:
• The lens is composed of layers of specialized cells that lack blood vessels, ensuring transparency for light passage.
• It is encapsulated by a thin, elastic membrane called the lens capsule, which helps maintain its shape.
• The lens is held in place by zonular fibers, which connect it to the ciliary body.
• Process of Accommodation:
• Accommodation is the ability of the eye to adjust the lens shape for focusing.
• When viewing near objects, the ciliary muscles contract, causing the lens to become more rounded and increase its refractive power.
• For distant objects, the ciliary muscles relax, and the lens becomes flatter, reducing its refractive power.
• Common Conditions Affecting the Lens:
• Cataracts: A condition where the lens becomes cloudy, leading to impaired vision. It is common in older adults and may require surgical replacement of the lens.
• Presbyopia: A condition associated with aging where the lens loses its flexibility, making it difficult to focus on nearby objects.
• Myopia and Hyperopia: Refractive errors caused by improper focusing of light due to changes in the eye's shape or lens function.
• Functions of Other Eye Structures:
• Cornea: Provides most of the eye's focusing power by bending light onto the lens.
• Iris: Regulates the amount of light entering the eye by controlling the size of the pupil.
• Retina: Detects light and color, converting visual information into neural signals sent to the brain.
• Optic Nerve: Transmits signals from the retina to the brain for processing visual information.

Important Points

• Age-Related Changes:
• The lens becomes less flexible with age, leading to conditions like presbyopia.
• Cataracts are more prevalent in individuals over the age of 60, affecting vision clarity.
• Interesting Fact:
• The lens has the ability to focus light without any external energy source, relying entirely on its elasticity and interaction with the ciliary muscles.
• The refractive power of the lens is approximately 15-20 diopters, depending on its shape during accommodation.

The correct answer is nervous system.

Key Points

• The nervous system is the primary control center for sensitivity or responsiveness in animals. It governs the detection, transmission, and processing of external and internal stimuli.
• It consists of the central nervous system (CNS), which includes the brain and spinal cord, and the peripheral nervous system (PNS), which connects the CNS to the rest of the body.
• Specialized structures like sensory organs (e.g., eyes, ears, skin) are part of the nervous system, enabling animals to respond to environmental changes effectively.
• The nervous system uses electrical impulses and chemical signals (neurotransmitters) to coordinate responses, ensuring survival and adaptation.
• Functions controlled by the nervous system include reflex actions, voluntary movements, and involuntary processes like heartbeat regulation.

Additional Information

• Central Nervous System (CNS):
• The CNS includes the brain and spinal cord. It processes information and coordinates responses.
• The brain is divided into regions like the cerebrum, cerebellum, and brainstem, each performing specialized functions such as decision-making, balance, and basic life functions.
• The spinal cord acts as a communication highway between the brain and peripheral nerves.
• Peripheral Nervous System (PNS):
• The PNS includes sensory nerves that detect stimuli and motor nerves that initiate responses.
• It is divided into the somatic nervous system (controls voluntary movements) and the autonomic nervous system (regulates involuntary functions).
• The autonomic nervous system is further divided into the sympathetic and parasympathetic systems, which manage "fight or flight" and "rest and digest" responses, respectively.
• Sensory Organs:
• Sensory organs like the eyes, ears, skin, tongue, and nose are integral to the nervous system. They detect external stimuli such as light, sound, temperature, and chemicals.
• For example, the retina in the eyes detects light, and the cochlea in the ears processes sound waves.
• Comparison with Other Systems:
• The circulatory system is responsible for transporting nutrients, oxygen, and waste products but does not directly control sensitivity or responsiveness.
• The digestive system focuses on nutrient absorption and energy production, which indirectly supports the nervous system's functioning.
• The respiratory system facilitates oxygen intake and carbon dioxide removal, essential for cellular activities but not directly involved in sensory or response mechanisms.

Important Points

• Reflex Actions: Reflex actions are automatic responses to stimuli, controlled by the spinal cord. Example: Pulling your hand away from a hot object.
• Neurotransmitters: Chemicals like dopamine, serotonin, and acetylcholine transmit signals between neurons.
• Adaptation: The nervous system allows animals to adapt to their environment through learning and memory.
• Examples: Octopuses are known for their highly developed nervous systems, enabling advanced problem-solving and camouflage abilities.
• Diseases: Disorders like Parkinson's disease and Alzheimer's disease affect the nervous system's functioning, leading to motor and cognitive impairments.

The correct answer is Electrons are embedded in a positively charged sphere.

Key Points

• Thomson's Model of the Atom: In 1904, J.J. Thomson proposed a model of the atom often referred to as the "plum pudding model." According to this model, the atom is composed of a positively charged sphere with negatively charged electrons embedded in it, similar to raisins in a pudding.
• Charge Neutrality: Thomson stated that the positive charge of the sphere is equal in magnitude to the total negative charge of the embedded electrons, making the atom electrically neutral.
• Structure Description: The correct statement that aligns with Thomson’s model is that “Electrons are embedded in a positively charged sphere”. This was his attempt to explain the stability and neutrality of atoms.
• Incorrect Statements: Other statements in the question, such as "The atom contains only neutrons and electrons" or "Electrons revolve around a central nucleus in fixed orbits," are incorrect as they describe later models of the atom, such as Rutherford's or Bohr's models.
• Limitations: Thomson's model could not explain experimental results like the gold foil experiment by Rutherford, which later led to the discovery of the nucleus.

Additional Information

• J.J. Thomson:
• He was a British physicist who discovered the electron in 1897 through his experiments with cathode rays.
• Thomson was awarded the Nobel Prize in Physics in 1906 for his work on the conduction of electricity in gases and his discovery of the electron.
• Rutherford’s Model:
• In 1911, Ernest Rutherford conducted the famous gold foil experiment, which showed that atoms have a dense, positively charged nucleus.
• He proposed that electrons revolve around the nucleus in orbits, contradicting Thomson's model.
• Bohr’s Model:
• In 1913, Niels Bohr refined Rutherford's model by introducing the concept of fixed energy levels for electrons orbiting the nucleus.
• This model explained the stability of atoms and the emission spectrum of hydrogen.
• Modern Quantum Model:
• The current understanding of atomic structure is based on quantum mechanics, where electrons are described as existing in probabilistic regions called orbitals.
• This model incorporates principles such as the Heisenberg Uncertainty Principle and Schrodinger's wave equation.

Important Points

• Key Characteristics of Thomson’s Model:
• Proposed the concept of a positively charged sphere with embedded electrons.
• Explained the overall neutrality of atoms but failed to account for atomic structure complexity.
• Did not address the arrangement of electrons or the presence of a nucleus.
• Historical Context: Thomson’s model was significant as it was the first attempt to describe the internal structure of atoms, paving the way for more advanced theories.
• Experimental Evidence: The gold foil experiment conducted by Rutherford invalidated Thomson's model by proving the existence of a nucleus.

The correct answer is Food Web.

Key Points

• A food web represents the complex and interlinked feeding relationships between various organisms in an ecosystem. It is a network of multiple food chains.
• Unlike a simple linear food chain, a food web shows a series of branching lines that depict how energy and nutrients are passed through multiple interconnected organisms.
• Food webs highlight the fact that most organisms consume multiple types of food and are part of several food chains simultaneously.
• For example, in a forest ecosystem, plants are eaten by herbivores like deer, which are then eaten by carnivores like tigers. The same plants may also be consumed by insects, which are further eaten by birds or small mammals. This interconnection forms a food web.
• The study of food webs is essential in understanding the stability and health of an ecosystem, as it helps identify key species and their roles in maintaining ecological balance.

Additional Information

• Trophic Levels:
• Organisms in a food web are classified into trophic levels, such as primary producers (plants), primary consumers (herbivores), secondary consumers (carnivores), and tertiary consumers (top predators).
• Energy transfer between trophic levels follows the 10% rule, where only about 10% of energy is transferred from one level to the next, with the rest lost as heat.
• Differences Between Food Chain and Food Web:
• A food chain is a simple, linear sequence showing who eats whom, while a food web is a complex network of interconnected food chains.
• Food webs more accurately represent the diverse feeding relationships in an ecosystem compared to food chains.
• Importance of Food Webs:
• Food webs help in understanding the energy flow and nutrient cycling in an ecosystem.
• They reveal the impact of disturbances (e.g., extinction of a species or climate change) on the overall ecosystem.
• Types of Food Webs:
• Grazing food web: It starts with autotrophs (like plants) and involves herbivores and predators.
• Detrital food web: It begins with decomposers like fungi and bacteria, which consume dead organic matter.

Important Points

• Option 1 - Trophic Level: Refers to each step in a food chain or web but does not represent the interconnection of multiple chains.
• Option 2 - Worldwide Web: Incorrect, as it refers to the internet and not ecological relationships.
• Option 3 - Spider Web: Incorrect, as it pertains to the structure created by spiders for trapping prey.
• Option 4 - Food Web: Correct, as it represents a complex network of feeding relationships in an ecosystem.

The correct answer is Sound requires a medium to travel and is longitudinal..

Key Points

• Sound requires a medium to travel: Sound is a mechanical wave, meaning it needs a material medium (solid, liquid, or gas) to propagate. It cannot travel through a vacuum because there are no particles to vibrate. Hence, statement 2 is correct.
• Sound waves are longitudinal: Sound propagates as longitudinal waves where particles of the medium vibrate parallel to the direction of wave propagation. This is distinct from transverse waves, like light, where particles oscillate perpendicular to the wave direction. Hence, statement 2 is correct.
• Sound does not travel faster in vacuum: Since sound requires a medium, it cannot exist or travel in a vacuum. This invalidates statements suggesting sound travels faster in a vacuum. Statement 1 is incorrect.
• Sound waves are not transverse: Sound waves are longitudinal by nature, not transverse. Statements suggesting otherwise are scientifically inaccurate. Statement 4 is incorrect.
• Vacuum and sound: The absence of particles in a vacuum makes it impossible for sound to propagate. Hence, any statement asserting sound can travel in a vacuum is incorrect. Statement 3 is incorrect.

Additional Information

• Speed of sound: Sound travels at different speeds depending on the medium:
• In air, the speed of sound is approximately 343 m/s at standard temperature and pressure.
• In water, sound travels faster at about 1500 m/s.
• In solids, the speed of sound is even higher, varying depending on the material. For instance, in steel, it can reach up to 5000 m/s.
• Types of waves: Waves are categorized as mechanical or electromagnetic:
• Mechanical waves require a medium to propagate (e.g., sound waves).
• Electromagnetic waves do not require a medium and can travel through a vacuum (e.g., light waves).
• Longitudinal vs. Transverse Waves:
• Longitudinal waves: Particles vibrate parallel to the direction of wave propagation (e.g., sound waves).
• Transverse waves: Particles vibrate perpendicular to the direction of wave propagation (e.g., water waves, light waves).
• Propagation of sound: The propagation of sound is due to successive compressions and rarefactions in the medium. These are regions of high and low pressure caused by the vibration of particles.
• Human hearing range: Humans can hear sound waves within the frequency range of 20 Hz to 20 kHz. Sounds below 20 Hz are called infrasound, while sounds above 20 kHz are termed ultrasound.

Important Points

• Vacuum and sound: A vacuum lacks particles, so sound waves cannot propagate through it.
• Medium dependency: The speed of sound is directly proportional to the density and elasticity of the medium. Denser and more elastic mediums allow faster sound propagation.
• Applications of sound: Sound is widely used in technologies such as ultrasound imaging in medicine, sonar for underwater navigation, and acoustic engineering for noise control.
• Shock waves: When an object travels faster than the speed of sound, it generates shock waves, which are characterized by a sudden change in pressure. This phenomenon is known as breaking the sound barrier.

The correct answer is Angle of deviation.

Key Points

• Angle of deviation is defined as the angle between the incident ray and the emergent ray after passing through the prism. It measures the bending of light due to the prism.
• When light enters the prism, it undergoes refraction, bending towards the normal at the first surface, and again bending away from the normal at the second surface. This results in the deviation of light from its original path.
• The angle of deviation depends on the angle of incidence, the material of the prism (refractive index), and the angle of the prism. A larger refractive index or angle of the prism results in a larger deviation.
• The minimum angle of deviation (δ_min) occurs when the light ray passes symmetrically through the prism, i.e., when the angle of incidence equals the angle of emergence.
• The formula for the angle of deviation is: δ = i + e - A Where: i = Angle of incidence e = Angle of emergence A = Angle of the prism

Additional Information

• Angle of incidence:
• The angle between the incident ray and the normal to the surface at the point of incidence.
• It plays a crucial role in determining how much the light ray bends within the prism.
• For smaller angles of incidence, the deviation is less, but as the angle of incidence increases, the deviation increases.
• Angle of refraction:
• It is the angle between the refracted ray and the normal to the surface at the point of refraction.
• It depends on the refractive index of the material and follows Snell’s Law: n₁sin(i) = n₂sin(r)
• Snell’s Law governs how light bends when transitioning between two media with different refractive indices.
• Angle of emergence:
• The angle between the emergent ray and the normal to the surface where the ray exits the prism.
• It is related to the angle of incidence and the geometry of the prism.
• Angle of the prism:
• The angle between the two refracting surfaces of the prism.
• It is a fixed property of the prism and influences the deviation experienced by the light ray.
• Prisms with larger angles produce greater deviation.
• Examples of practical applications:
• Dispersion of light: Prisms are used to split white light into its constituent colors due to varying angles of deviation for different wavelengths.
• Optical instruments: Prisms are widely used in telescopes, binoculars, and cameras for light manipulation.
• Spectroscopy: Prisms are essential in spectrometers for studying the properties of light and materials.

Important Points

• Refractive Index:
• The refractive index of a material governs how much light bends when entering or exiting the prism.
• Higher refractive index materials produce greater deviation and dispersion.
• Critical Angle:
• If the angle of incidence exceeds the critical angle, total internal reflection occurs instead of refraction.
• Critical angle depends on the refractive indices of the two media.
• Applications in Physics:
• Prisms are used in experiments studying refraction, dispersion, and the properties of light.
• They form an essential component of optical systems and scientific instruments.
• Historical Significance:
• Isaac Newton used a prism to demonstrate the dispersion of light, providing insights into the nature of white light.
• This experiment laid the foundation for modern optics and spectroscopy.

The correct answer is v = u - gt.

Key Points

• When a ball is thrown vertically upward with an initial velocity u, it moves against the force of gravity (g), which acts downward.
• The velocity of the ball decreases over time due to the acceleration caused by gravity (g), which has a constant value of approximately 9.8 m/s² near the Earth's surface.
• The relation between the velocity v of the ball at any time t, initial velocity u, and acceleration due to gravity g is given by the equation v = u - gt.
• This equation indicates that the velocity v decreases linearly with time t, as gravity continuously slows down the upward motion of the ball.
• Hence, the equation v = u - gt correctly represents the velocity of the ball at time t during its upward motion.

Additional Information

• Upward Motion:
• When an object is thrown upward, it moves against gravity, which causes its velocity to decrease over time.
• The maximum height is reached when the velocity becomes 0, at which point the object momentarily stops before beginning its downward motion.
• Equation of Motion:
• The equation v = u - gt is derived from one of the equations of motion: v = u + at, where a = -g for upward motion.
• Here, u is the initial velocity, v is the velocity at time t, g is the acceleration due to gravity, and t is the time elapsed.
• Gravity:
• Acceleration due to gravity (g) near the Earth's surface is approximately 9.8 m/s².
• It acts downward, irrespective of the object's initial motion direction.
• Incorrect Options:
• v = u + gt: This equation implies acceleration adds to the velocity, which is incorrect for upward motion as gravity acts to reduce velocity.
• v = u ⋅ gtv: This is mathematically incorrect and does not represent any physical principle in this scenario.
• v = gt - uv: This equation does not match the relationship governing upward motion under gravity.
• Applications:
• Understanding the motion of objects under gravity is crucial in fields like physics, engineering, and sports science.
• Examples include projectile motion, space exploration, and designing equipment for sports involving vertical jumps.

Important Points

• Free Fall: If the ball were dropped instead of being thrown, the initial velocity u would be 0, and the velocity would increase due to gravity as v = gt.
• Time to Reach Maximum Height: The time to reach maximum height can be calculated using the formula t = u/g, where u is the initial velocity.
• Symmetry of Motion: The time taken to ascend to the highest point is equal to the time taken to descend back to the ground, assuming no air resistance.
• Energy Considerations: At the maximum height, the object's kinetic energy is converted entirely into potential energy.
• These principles are essential for solving problems related to vertical motion in competitive exams and academic studies.

The correct answer is Oviduct.

Key Points

• Fertilisation in humans typically occurs in the oviduct (also known as the fallopian tube), which is a part of the female reproductive system.
• The oviduct is a narrow, muscular tube that connects the ovaries to the uterus and serves as the site where the male sperm meets the female egg (ovum).
• When an egg is released from the ovary during ovulation, it is captured by the fimbriae (finger-like projections) at the end of the oviduct and transported into the tube where fertilisation takes place.
• The fertilised egg (zygote) begins cell division as it travels through the oviduct and eventually implants in the uterus for further development.
• Other parts of the reproductive system, such as the vagina, uterus, or cervix, do not typically facilitate fertilisation but play significant roles in reproduction.

Additional Information

• Oviduct (Fallopian Tube):
• The oviduct is divided into four parts: infundibulum (closest to the ovary), ampulla (the widest section where fertilisation usually occurs), isthmus (a narrow portion), and interstitial portion (where it connects to the uterus).
• The ampulla region provides an ideal environment for fertilisation due to the presence of cilia and secretions that aid in sperm mobility and survival.
• It is critical for the transport of both the egg and sperm, ensuring they meet for fertilisation to occur.
• Other parts of the female reproductive system:
• Vagina: The vagina serves as the passageway through which sperm enters the female reproductive tract. It is not involved in the process of fertilisation.
• Uterus: The uterus is the organ where the fertilised egg implants and grows into a fetus. It does not facilitate fertilisation.
• Cervix: The cervix is the lower part of the uterus that opens into the vagina. It acts as a gateway for sperm to enter the uterus but does not play a direct role in fertilisation.
• Fertilisation Process:
• Fertilisation occurs when a sperm cell penetrates the egg and combines its genetic material with the egg's genetic material, forming a zygote.
• The process involves three main steps: sperm capacitation, penetration of the egg's outer layers, and fusion of the sperm and egg nuclei.
• The zygote undergoes mitotic divisions (cleavage) as it travels down the oviduct toward the uterus.
• Important Points about Human Reproduction:
• Human reproduction is a complex process that involves the coordinated functioning of several organs and hormones.
• The process begins with ovulation, followed by fertilisation in the oviduct, and ends with implantation in the uterus.
• Hormones such as estrogen, progesterone, and luteinizing hormone play crucial roles in regulating the reproductive cycle.

The correct answer is Paper Industry.

Key Points

• Sodium hydroxide (NaOH), also known as caustic soda, is extensively used in the Paper Industry to process wood pulp. It helps in breaking down lignin, a complex organic polymer found in wood.
• The process of converting wood into pulp involves the Kraft pulping or chemical pulping method, where sodium hydroxide is used along with sodium sulfide to remove lignin and separate cellulose fibers.
• This method ensures the production of high-quality paper by providing the necessary conditions for efficient delignification and maintaining the strength of cellulose fibers.
• Other industries such as the Food Industry, Soap Industry, and Textile Industry also use sodium hydroxide, but its primary and most significant application in terms of wood pulp processing is in the Paper Industry.
• Hence, the correct answer is the Paper Industry.

Additional Information

• Sodium Hydroxide in the Paper Industry:
• In the Kraft process, sodium hydroxide plays a crucial role in breaking down lignin, which binds cellulose fibers in wood. This results in the separation of fibers, producing pulp.
• The chemical also helps in adjusting the pH during the bleaching process of pulp, ensuring the removal of residual lignin.
• Sodium hydroxide is used to regenerate chemicals in the recovery cycle of the Kraft process, making it a sustainable and cost-effective choice.
• The Paper Industry is one of the largest consumers of sodium hydroxide globally due to its pivotal role in the pulping and bleaching stages.
• Applications of Sodium Hydroxide in Other Industries:
• Food Industry: Sodium hydroxide is used in food processing to peel fruits and vegetables, process cocoa and chocolate, and thicken ice cream.
• Soap Industry: It is used in the saponification process, where fats and oils react with sodium hydroxide to produce soap and glycerin.
• Textile Industry: Sodium hydroxide is utilized in mercerization, which improves the strength, luster, and dyeing properties of cotton fabrics.
• Important Facts about Sodium Hydroxide:
• It is a highly corrosive alkali with the chemical formula NaOH.
• It is manufactured through the chlor-alkali process, which also produces chlorine and hydrogen as by-products.
• Sodium hydroxide is widely used in industries due to its ability to react with acids, dissolve fats, and break down organic material.
• Environmental Concerns:
• The use of sodium hydroxide in industrial processes must be managed carefully to prevent environmental damage.
• Effluents containing sodium hydroxide should be neutralized before being released into water bodies to avoid harm to aquatic ecosystems.

The correct answer is Sieve tubes.

Key Points

• Phloem is a complex permanent tissue in vascular plants that transports organic nutrients (mainly sucrose) from the leaves to other parts of the plant.
• Sieve tubes are the primary conducting elements of phloem. They are long, tubular structures formed by a series of sieve tube elements arranged end-to-end.
• The end walls of sieve tube elements have perforations called sieve plates, which facilitate the flow of nutrients and other substances between cells.
• Unlike xylem, which primarily transports water, phloem transports both nutrients and signaling molecules to various parts of the plant.
• Other components of phloem tissue include companion cells, phloem parenchyma, and phloem fibers, but sieve tubes are the primary conducting structures.

Additional Information

• Tracheids:
• Tracheids are elongated cells present in the xylem tissue, not phloem.
• They are responsible for the conduction of water and minerals and provide mechanical support to the plant.
• Tracheids are dead at maturity and have thick, lignified walls.
• Vessels:
• Vessels are another component of the xylem tissue and are not found in phloem.
• They are more specialized than tracheids for water conduction and consist of a series of hollow, cylindrical cells placed end-to-end.
• Vessels are also lignified and dead at maturity.
• Xylem fibers:
• Xylem fibers are supportive, elongated cells present in the xylem tissue.
• They contribute to the mechanical strength of the plant by providing structural support.
• They are not involved in nutrient transport and are unrelated to phloem functions.
• Phloem components and their roles:
• Sieve tubes: Conduct sugars and other nutrients.
• Companion cells: Assist sieve tubes in nutrient transport by providing energy and maintaining metabolic activities.
• Phloem parenchyma: Stores food and other substances.
• Phloem fibers: Provide mechanical support to the phloem tissue.

Important Points

• The phloem is part of the plant's vascular system and works alongside xylem to ensure proper nutrient and water distribution.
• Phloem transport is often described as bidirectional, meaning nutrients can move both upwards and downwards, unlike xylem, which only conducts water and minerals upwards.
• The process of nutrient transport in the phloem is termed translocation, which is driven by pressure-flow mechanisms.
• Phloem is found in all vascular plants, including gymnosperms and angiosperms.
• The proper functioning of the phloem is vital for plant growth, reproduction, and survival as it delivers energy-rich compounds to growing and storage tissues.

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

Key Points

• The relative strength of the magnetic field: The closeness of magnetic field lines represents the relative strength of the magnetic field. The closer the lines, the stronger the magnetic field in that region. This is a fundamental property of magnetic field lines. Hence, statement (i) is correct.
• Intersection of magnetic field lines: Magnetic field lines never intersect each other. If they did, it would mean that at the point of intersection, the magnetic field has two different directions, which is physically impossible. Hence, statement (ii) is correct.
• Magnetic field around a bar magnet: The magnetic field lines emerge from the north pole of the bar magnet and enter the south pole, forming closed loops. This pattern demonstrates the continuous nature of magnetic field lines.
• Representation of field strength: The density of field lines (lines per unit area) around a bar magnet visually indicates the intensity of the magnetic field in a particular region.
• Applications: Understanding magnetic field lines is crucial in various applications such as designing magnets, electric motors, and magnetic resonance imaging (MRI).

Additional Information

• Magnetic field lines:
• Magnetic field lines are imaginary lines that represent the direction and strength of a magnetic field.
• They are denser near the poles of a magnet, indicating stronger magnetic fields in these areas.
• The field lines are continuous loops that extend from the north pole to the south pole outside the magnet and from the south pole to the north pole inside the magnet.
• Magnetic field properties:
• The magnetic field is a vector quantity, having both magnitude and direction.
• The strength of the magnetic field decreases as the distance from the magnet increases.
• Applications of magnetic fields:
• Magnetic fields are used in various devices such as electric motors, generators, transformers, and magnetic storage devices.
• They are also used in medical imaging techniques such as MRI.
• Earth's magnetic field:
• The Earth behaves like a giant bar magnet with its magnetic field lines extending from the magnetic south pole to the magnetic north pole.
• It protects the Earth from harmful solar radiation by deflecting charged particles.
• Magnetic field visualization:
• Iron filings can be used to visualize magnetic field lines. When placed near a magnet, the filings align themselves along the field lines.
• This experiment helps in understanding the pattern and distribution of magnetic fields around a magnet.

Important Points

• Magnetic monopoles: Unlike electric charges, magnetic monopoles do not exist. Every magnet has both a north and a south pole.
• Magnetism in materials: Materials can be classified as diamagnetic, paramagnetic, or ferromagnetic based on their response to magnetic fields.
• Historical significance: The study of magnets dates back to ancient Greece, where naturally occurring magnets were first discovered in the region of Magnesia.
• Modern advancements: Magnetic materials are used in advanced technologies such as maglev trains, data storage devices, and magnetic levitation systems.

The correct answer is A drop of ink spreads evenly in water without stirring.

Key Points

• The observation where a drop of ink spreads evenly in water without stirring demonstrates the concept of the existence of particles in matter.
• This phenomenon is caused by the random motion of particles in both the ink and water, known as Brownian motion.
• It provides evidence that matter is made up of tiny particles that are in constant motion.
• When ink is added to water, the particles of ink mix with the water particles due to their random motion, leading to uniform spreading. This proves that the particles of matter are continuously moving and interacting.
• This is the strongest evidence compared to other options, as it directly demonstrates the particle nature of matter and their movement without the need for external force or heating.

Additional Information

• Ice melts into water when heated:
• This demonstrates the change of state of matter due to heat energy.
• When ice is heated, the molecules gain kinetic energy and transition from a solid (fixed structure) to a liquid (free-moving particles).
• While this shows that particles in matter can change states, it does not directly prove their existence.
• Water boils and produces steam:
• This is an example of the phase transition of matter from liquid to gas upon heating.
• Boiling increases the kinetic energy of water molecules, allowing them to overcome intermolecular forces and escape as steam.
• It supports the idea of particle interaction but does not directly provide evidence for the existence of particles.
• Salt dissolves faster in warm water than in cold water:
• When salt dissolves in water, the particles of salt mix with water particles due to the interaction between them.
• Warmer water provides more kinetic energy to the water molecules, speeding up the dissolution process.
• While this indicates particle interaction, the evidence is indirect compared to the ink diffusion example.
• Key Characteristics of Particles of Matter:
• Small size: Particles of matter are extremely small and cannot be seen with the naked eye.
• Constant motion: Particles are always moving, as evidenced by Brownian motion.
• Interparticle spaces: Matter has spaces between its particles, allowing diffusion or dissolution.
• Attraction: Particles of matter attract each other with varying strength depending on the state (solid, liquid, gas).

Important Points

• Brownian Motion:
• Discovered by Robert Brown in 1827, it refers to the random motion of particles suspended in a fluid.
• This motion is caused by the collision of fluid particles with the suspended particles.
• It provides strong evidence for the particle nature of matter.
• Diffusion:
• It is the process by which particles spread out from a region of higher concentration to a region of lower concentration.
• Diffusion occurs in gases, liquids, and even solids, demonstrating the movement and interaction of particles.
• Examples include the spreading of perfume in air or ink in water.

The correct answer is 23.

Key Points

• The mass number of an atom is the sum of the number of protons and neutrons in its nucleus. The formula is:
  

Mass Number = Number of Protons + Number of Neutrons.

• In the given case, the atom has 11 protons and 12 neutrons. Thus, the mass number can be calculated as: Mass Number = 11 + 12 = 23.
• The atom is described as neutral. This means the number of protons (positively charged) equals the number of electrons (negatively charged). Hence, the atom has 11 electrons as it has 11 protons.
• The mass number does not include electrons since their mass is negligible compared to protons and neutrons.
• Therefore, the correct mass number of this neutral atom is 23.

Additional Information

• Atomic Number:
• The atomic number is the number of protons in the nucleus of an atom. It defines the chemical element. For example, an atom with 11 protons has an atomic number of 11, which corresponds to the element sodium (Na).
• The number of electrons in a neutral atom equals its atomic number. In this case, the atom has 11 electrons.
• Isotopes:
• Atoms of the same element can have different numbers of neutrons, leading to different mass numbers. These are called isotopes.
• For instance, the isotopes of hydrogen include protium (1 proton, 0 neutrons, mass number = 1), deuterium (1 proton, 1 neutron, mass number = 2), and tritium (1 proton, 2 neutrons, mass number = 3).
• Subatomic Particles:
• Atoms are composed of three main subatomic particles: Protons (positively charged, located in the nucleus), Neutrons (neutral, located in the nucleus), and Electrons (negatively charged, orbiting the nucleus).
• Protons and neutrons have approximately the same mass, which is significantly larger than the mass of electrons. Hence, they contribute most to the atom's mass.
• Mass Number vs Atomic Mass:
• The mass number is a whole number representing the total number of protons and neutrons in an atom's nucleus.
• The atomic mass is a weighted average of all the isotopes of an element, expressed in atomic mass units (amu).
• For example, the atomic mass of sodium is approximately 22.99 amu, while its most common isotope has a mass number of 23.

The correct answer is It can bond ionically.

Key Points

• Statement 1: It is tetravalent – Carbon has a valency of 4, meaning it can form four covalent bonds with other atoms, including carbon atoms. This allows it to create stable and complex molecules. Hence, this statement is correct.
• Statement 2: It can bond ionically – Carbon primarily forms covalent bonds, not ionic bonds, due to its small size and the requirement of a very high amount of energy to lose or gain four electrons to achieve a stable electronic configuration. Hence, this statement is incorrect.
• Statement 3: It has catenation – Catenation is the ability of carbon to form long chains and rings with other carbon atoms. This property makes carbon versatile in forming various organic compounds. Hence, this statement is correct.
• Statement 4: It can have single, double, and triple bonds – Carbon can form all three types of bonds (single, double, and triple) with itself or other elements, enabling diverse molecular structures. Hence, this statement is correct.
• Statement 5: No specific statement provided – Not applicable to the question.

Additional Information

• Versatility of Carbon:
• The versatility of carbon is primarily due to its tetravalency and its ability to form strong covalent bonds with other elements.
• Carbon can form chains, branched structures, and rings due to catenation.
• It can bond with a wide variety of elements, such as hydrogen, oxygen, nitrogen, and halogens, to form numerous compounds.
• Carbon’s ability to form multiple bonds (single, double, and triple) allows for the formation of diverse organic and inorganic compounds.
• Covalent Bonding:
• Carbon forms covalent bonds by sharing electrons with other atoms to attain a stable electronic configuration.
• The strength and stability of covalent bonds contribute to the diversity of organic molecules.
• Ionic Bonding:
• Carbon does not typically form ionic bonds because it would require either losing or gaining four electrons, which is highly energy-intensive and not feasible under normal conditions.
• Instead, carbon prefers to share electrons, forming covalent bonds.
• Catenation:
• Catenation is the ability of carbon to form long chains, branched structures, and rings by bonding with itself.
• This property is unique and significant in forming complex organic molecules, such as hydrocarbons and biomolecules.
• Applications of Carbon's Versatility:
• Carbon's versatility is the foundation of organic chemistry, which studies carbon-based compounds.
• It is the basis for the formation of essential biomolecules such as proteins, carbohydrates, lipids, and nucleic acids.
• Carbon compounds are also used in industrial applications, including fuels, polymers, and pharmaceuticals.

The correct answer is To combine long lactation with disease resistance.

Key Points

• Cross-breeding between exotic and local cattle breeds aims to combine the beneficial traits of both breeds, ensuring better productivity and adaptability.
• Exotic breeds, such as Jersey and Holstein Friesian, are known for their high milk yield and long lactation periods.
• Local breeds, such as Gir, Sahiwal, and Red Sindhi, are better adapted to local environmental conditions and are highly disease-resistant.
• The goal of cross-breeding is to produce offspring that exhibit both higher milk production (a trait of exotic breeds) and resilience to diseases (a trait of local breeds).
• This approach enhances the overall economic viability of cattle farming by reducing costs associated with healthcare and improving milk productivity.

Additional Information

• Exotic Breeds:
• Jersey: Originating from the British Channel Island of Jersey, this breed is known for its high milk fat content and adaptability to varying climates.
• Holstein Friesian: Originating from the Netherlands, this breed is globally recognized for its high milk yield and is often used in commercial dairy farming.
• Indigenous Breeds:
• Gir: A native Indian breed, known for its heat tolerance, disease resistance, and milk production.
• Sahiwal: Originating from Punjab, this breed is renowned for its high milk yield and adaptability to tropical climates.
• Red Sindhi: Known for its hardiness and suitability for both milk production and draught work.
• Advantages of Cross-Breeding:
• Improved milk production due to traits inherited from exotic breeds.
• Enhanced disease resistance and heat tolerance due to traits from indigenous breeds.
• Better economic returns for farmers by reducing veterinary costs and increasing productivity.
• Challenges of Cross-Breeding:
• Cross-bred animals may require specialized feeding and care.
• Potential for loss of genetic diversity in indigenous breeds if not managed properly.
• Breeding programs need to be monitored to ensure the sustainability of the resulting population.
• Relevant Programs in India:
• Rashtriya Gokul Mission: Aims to preserve and develop indigenous breeds through scientific breeding techniques.
• National Dairy Plan (NDP): Focuses on increasing milk production and improving the productivity of milch animals through genetic improvements.

Important Points

• Long Lactation Period: Exotic breeds like Holstein Friesian can produce milk for extended durations, making them ideal for commercial dairy farming.
• Disease Resistance: Indigenous breeds have a natural immunity to local diseases, reducing dependency on veterinary interventions.
• Economic Impact: Cross-breeding helps farmers achieve higher profitability by combining productivity and resilience traits.
• Breeding Techniques: Programs like artificial insemination ensure controlled cross-breeding to achieve desirable traits without compromising genetic diversity.

The correct answer is prevents overcrowding and competition.

Key Points

• Seed dispersal is a mechanism by which plants spread their seeds to different locations to ensure the survival of their species.
• It helps prevent overcrowding and competition among plants. If seeds fall directly beneath the parent plant, they may face competition for sunlight, water, and nutrients. Hence, option 2 is correct.
• Seed dispersal enhances genetic diversity by allowing seeds to grow in varied environments, reducing the risk of localized extinction due to pests, diseases, or unfavorable conditions.
• It aids in colonizing new areas, ensuring the spread and growth of plants in diverse ecosystems.
• Different methods of seed dispersal include wind, water, animals, and mechanical forces, each adapted to specific plant types and environments.

Additional Information

• Statement Analysis:
• 1) Ensures seed death after fertilization: This statement is incorrect. Seed dispersal does not lead to seed death; rather, it ensures survival by spreading seeds to favorable locations.
• 2) Prevents overcrowding and competition: This is the correct statement. Dispersal ensures that seedlings grow in areas where they do not compete with the parent plant or other seedlings for resources.
• 3) Increases the size of seeds: This statement is incorrect. Seed dispersal does not influence the size of seeds; seed size is determined by genetic and environmental factors during development.
• 4) Prevents pollination: This statement is incorrect. Seed dispersal occurs after pollination and fertilization; it does not prevent pollination.
• Methods of Seed Dispersal:
• Wind dispersal: Seeds are lightweight or winged, allowing them to be carried away by wind. Examples include dandelions and maples.
• Water dispersal: Seeds adapted for floating are dispersed by water. Examples include coconut and lotus.
• Animal dispersal: Seeds with hooks or sticky surfaces attach to animals, or fruits are eaten and seeds excreted. Examples include burdock and cherries.
• Mechanical dispersal: Some plants have explosive mechanisms to shoot seeds away. Examples include touch-me-not (Impatiens).
• Importance of Seed Dispersal:
• Ensures the survival and spread of plant species across diverse ecosystems.
• Promotes biodiversity by allowing plants to colonize new areas.
• Reduces the likelihood of competition between parent plants and offspring.
• Helps plants adapt to changing environmental conditions, ensuring long-term survival.

Important Points

• Environmental Adaptations:
• Plants have evolved diverse seed dispersal mechanisms based on their ecosystems. For instance, coastal plants rely on water dispersal while desert plants utilize wind dispersal.
• Seed dispersal strategies are critical to maintaining balance in ecosystems and ensuring the regeneration of forests and grasslands.
• Ecological Role:
• Seed dispersal directly supports pollinators and animals that depend on plants for food, ensuring ecosystem stability.
• It aids in the reforestation of degraded areas and contributes to climate change mitigation by promoting vegetation growth.

Shortcut Trick

Total time = 50 minutes. Remaining time = 50 − (11 + 25) = 14 minutes.

Total Distance = Σ(Speed × Time). Use speed in km/hr and time in hours.

30 = (x × 11/60) + (2x × 25/60) + (x × 14/60)

30 = (11x + 50x + 14x) / 60 ⇒ 30 = 75x / 60 ⇒ 30 = 1.25x

x = 30 / 1.25 = 24

∴ The correct answer is 24 km/hr.

Alternate Method

Given: Total Distance = 30 km, Total Time = 50 min.

Formula Used: Distance = Speed × Time

⇒ Time₁ = 11 min, Time₂ = 25 min, Time₃ = 50 − (11 + 25) = 14 min.

⇒ Total Distance = (Speed₁ × Time₁) + (Speed₂ × Time₂) + (Speed₃ × Time₃)

⇒ 30 = [x × (11/60)] + [2x × (25/60)] + [x × (14/60)]

⇒ 30 = (11x/60) + (50x/60) + (14x/60)

⇒ 30 = (11x + 50x + 14x) / 60

⇒ 30 = 75x / 60

⇒ 1800 = 75x

⇒ x = 1800 / 75 = 24

∴ The correct answer is 24 km/hr.

Additional Information

Unit Conversion

To convert minutes to hours, divide by 60. To convert km/hr to m/s, multiply by 5/18.

Average Speed

Average Speed = Total Distance ÷ Total Time. For equal distances at speeds u and v, Average Speed = 2uv/(u+v).

Relative Speed

In the same direction, relative speed is (u − v). In the opposite direction, it is (u + v).

Shortcut Trick To find the largest number below 5000 divisible by 42, divide 5000 by 42. 5000 ÷ 42 ⇒ Quotient = 119, Remainder = 2. Largest number = 5000 − Remainder = 5000 − 2 = 4998. Check: 4998 is between 4000 and 5000 and is exactly divisible by 42. ∴ The correct answer is 4998.

Alternate Method Given: Range is 4000 to 5000 and divisor is 42. Formula Used: Dividend = (Divisor × Quotient) + Remainder

⇒ Divide 5000 by 42 to find the nearest multiple. ⇒ 5000 = 42 × 119 + 2 ⇒ The largest multiple less than or equal to 5000 = 42 × 119 ⇒ 42 × 119 = 4998 ⇒ Since 4000 < 4998 < 5000, it satisfies the condition. ∴ The correct answer is 4998.

Additional Information Divisibility Rule of 42 A number is divisible by 42 if it is simultaneously divisible by its prime factors 2, 3, and 7. Finding Multiples in a Range To find the smallest number in a range (a, b) divisible by n, calculate: a + (n − (a mod n)). To find the largest, calculate: b − (b mod n). Remainder Theorem Subtracting the remainder from the dividend always results in a number perfectly divisible by the divisor.

Shortcut Trick

Total age after 3 years = 35 years.

Total present age = 35 − (3 × 2) = 29 years.

Let Rahul age be R. Then sister age = R + 5.

2R + 5 = 29 ⇒ 2R = 24 ⇒ R = 12 years.

∴ The correct answer is 12 years.

Alternate Method

Given: Difference between ages = 5 years; Sum after 3 years = 35 years.

Let Rahul present age = x years

Then Sister present age = x + 5 years

After 3 years:

⇒ (x + 3) + (x + 5 + 3) = 35

⇒ 2x + 11 = 35

⇒ 2x = 35 − 11

⇒ 2x = 24

⇒ x = 12

∴ The correct answer is 12 years.

Additional Information

Age Difference Property

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

Sum of Ages Calculation

To find the sum of ages 'n' years ago or 'n' years hence, subtract or add (n × number of persons) to the present sum.

Ratio of Ages

If the ratio of ages is given, use the multiplier method (kx and ky) to set up linear equations based on the conditions provided.

Shortcut Trick

Area of metal sheet used = Base area + Area of 4 walls

Area = (60 × 40) + 2 × 30 × (60 + 40) = 2400 + 6000 = 8400 cm²

Convert to m²: 8400 ÷ 10,000 = 0.84 m²

Total Cost = 0.84 × 50 = ₹42

∴ The correct answer is ₹42.

Alternate Method

Given:

Length (L) = 60 cm, Breadth (B) = 40 cm, Height (H) = 30 cm

Cost rate = ₹50 per m²

Formula Used:

Area of box without a lid = LB + 2H(L + B)

Calculations:

⇒ Total Area = (60 × 40) + 2 × 30 × (60 + 40)

⇒ Total Area = 2400 + 60 × 100

⇒ Total Area = 2400 + 6000 = 8400 cm²

⇒ Area in m² = 8400 ÷ 10000 = 0.84 m²

⇒ Total Cost = Area × Rate

⇒ Total Cost = 0.84 × 50 = ₹42

∴ The correct answer is ₹42.

Additional Information

Total Surface Area of Cuboid

The surface area including the top lid is given by TSA = 2(LB + BH + HL).

Lateral Surface Area

The area of the four vertical walls only is LSA = 2H(L + B).

Unit Conversion

Since 1 m = 100 cm, it follows that 1 m² = 100 × 100 = 10,000 cm².

Given:

20% of number + 96 = number

Formula Used:

Percentage = value ÷ 100

Calculation:

⇒ Let number = x

⇒ (20 ÷ 100)x + 96 = x

⇒ 0.2x + 96 = x

⇒ x − 0.2x = 96

⇒ 0.8x = 96

⇒ x = 96 ÷ 0.8

⇒ x = 120

⇒ 60% of number = (60 ÷ 100) × 120

⇒ 60% = 72

∴ The correct answer is 72.

Given:

$-5 \times [-4 \times {-3 - (2 \times (-3) \times (-4) + 5 \times 6) - 3} \div (-20 \times 3)] \times \frac{0.5}{2 \times 5}$

Concept Used:

$\text{BODMAS rule}$

Calculation:

$\Rightarrow -5 \times [-4 \times {-3 - (2 \times 12 + 30) - 3} \div (-60)] \times \frac{0.5}{10}$

$\Rightarrow -5 \times [-4 \times {-3 - (24 + 30) - 3} \div (-60)] \times \frac{0.5}{10}$

$\Rightarrow -5 \times [-4 \times {-3 - 54 - 3} \div (-60)] \times \frac{0.5}{10}$

$\Rightarrow -5 \times [-4 \times (-60) \div (-60)] \times \frac{0.5}{10}$

$\Rightarrow -5 \times [240 \div (-60)] \times \frac{0.5}{10}$

$\Rightarrow -5 \times (-4) \times \frac{0.5}{10}$

$\Rightarrow 20 \times \frac{0.5}{10}$

$\Rightarrow 20 \times \frac{1}{20}$

$\Rightarrow 1$

∴ The correct answer is $1$

Shortcut Trick

Use the standard algebraic identity: If x + y + z = 0, then x³ + y³ + z³ = 3xyz.

Here, let x = 2a, y = b, and z = c. Given that 2a + b + c = 0.

Applying the identity: (2a)³ + b³ + c³ = 3 × (2a) × b × c ⇒ 8a³ + b³ + c³ = 6abc.

Comparing with kabc, we get k = 6.

Calculation: k² = 6² = 36.

∴ The correct answer is 36.

Alternate Method

Given: 2a + b + c = 0 and 8a³ + b³ + c³ = kabc.

Formula Used: x³ + y³ + z³ − 3xyz = (x + y + z)(x² + y² + z² − xy − yz − zx)

⇒ Let x = 2a, y = b, z = c.

⇒ Since x + y + z = 0, x³ + y³ + z³ = 3xyz.

⇒ (2a)³ + b³ + c³ = 3 × 2a × b × c

⇒ 8a³ + b³ + c³ = 6abc

⇒ Given: 8a³ + b³ + c³ = kabc

⇒ kabc = 6abc

⇒ k = 6

⇒ k² = 6² = 36

∴ The correct answer is 36.

Additional Information

Special Identity Condition

For any three variables, the relation a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) holds true.

Sum of Cubes when Sum is Zero

If the sum of three terms is zero, their cubes sum to exactly three times their product. Example: (−5) + 2 + 3 = 0 ⇒ (−5)³ + 2³ + 3³ = 3(−5)(2)(3) = −90.

General Expansion

The expression a² + b² + c² − ab − bc − ca can be rewritten as ½[(a−b)² + (b−c)² + (c−a)²].

Shortcut Trick

Relation: Since 3πr_h² = 4πr_s², the Radius ratio is r_s = r_h × (√3/2).

Calculation: r_s = 3.5 × (√3/2) = 7√3/4 cm.

Volume = (4/3) × (22/7) × (7√3/4)³ = 539√3/8 cm³.

∴ The correct answer is 539√3/8 cm³.

Alternate Method

Given:

Radius of Hemisphere (r_h) = 3.5 cm = 7/2 cm.

Total Surface Area of Hemisphere = Surface Area of Sphere.

Formula Used:

Total Surface Area of Hemisphere = 3πr²

Surface Area of Sphere = 4πr²

Volume of Sphere = (4/3)πr³

Calculations:

⇒ 3 × π × (3.5)² = 4 × π × r_s²

⇒ 3 × (7/2)² = 4 × r_s²

⇒ 3 × (49/4) = 4 × r_s²

⇒ r_s² = (3 × 49) / (4 × 4) = 147/16

⇒ r_s = √(147/16) = (7√3)/4 cm

⇒ Volume of Sphere = (4/3) × (22/7) × ((7√3)/4)³

⇒ Volume = (4/3) × (22/7) × (343 × 3√3 / 64)

⇒ Volume = (22 × 49 × √3) / 16 × 2 (after simplification)

⇒ Volume = 539√3/8 cm³

∴ The correct answer is 539√3/8 cm³.

Additional Information

Total Surface Area of a Sphere

The total surface area of a sphere is equal to its curved surface area, given by 4πr².

Curved Surface Area of a Hemisphere

The curved surface area includes only the dome part and is given by 2πr².

Volume of a Hemisphere

The volume of a hemisphere is exactly half that of a sphere: V = (2/3)πr³.

Shortcut Trick

List the frequency of each observation in the given data set.

Observation 14 occurs 2 times and observation 16 occurs 2 times.

Since 2 is the maximum frequency, the possible modes are 14 and 16.

Product of modes = 14 × 16 = 224.

∴ The correct answer is 224.

Alternate Method

Given: Marks of 15 students = {14, 12, 17, 16, 19, 13, 14, 15, 11, 23, 16, 22, 21, 18, 25}

Formula Used: Mode is the value that appears most frequently in a data set. A set with two modes is bimodal.

⇒ Count the frequency of each score:

11 → 1 | 12 → 1 | 13 → 1 | 14 → 2 | 15 → 1 | 16 → 2 | 17 → 1 | 18 → 1 | 19 → 1 | 21 → 1 | 22 → 1 | 23 → 1 | 25 → 1

⇒ The maximum frequency is 2, which occurs for marks 14 and 16.

⇒ Possible modes = 14 and 16.

⇒ Product = 14 × 16

⇒ Product = 224.

∴ The correct answer is 224.

Additional Information

Mode

The value in a data set that occurs with the highest frequency. It is a measure of central tendency.

Bimodal and Multimodal

If two values share the same maximum frequency, the data is bimodal. If more than two, it is multimodal.

Empirical Formula

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

Shortcut Trick

To combine p : q : r and r : s, make the value of r common in both ratios.

In the first ratio, r = 14. In the second ratio, r = 42.

Multiply the first ratio by 3 to make r = 42: (13 × 3) : (5 × 3) : (14 × 3) = 39 : 15 : 42.

Now combine with r : s = 42 : 3 → 39 : 15 : 42 : 3.

∴ The correct answer is 39:15:42:3.

Alternate Method

Given: p : q : r = 13 : 5 : 14 and r : s = 42 : 3

Formula Used: Ratio equalization method.

⇒ p : q : r = 13 : 5 : 14

⇒ r : s = 42 : 3

⇒ To equalize r, LCM(14, 42) = 42.

⇒ Multiply (p : q : r) by 3 → (13 × 3) : (5 × 3) : (14 × 3) = 39 : 15 : 42

⇒ Resulting p : q : r : s = 39 : 15 : 42 : 3

∴ The correct answer is 39:15:42:3.

Additional Information

Compound Ratio

The compound ratio of (a : b) and (c : d) is (ac : bd).

Ratio Balancing

When combining multiple ratios (A:B and B:C), ensure the common term (B) has the same numerical value by multiplying by appropriate factors.

Simplification of Ratio

A ratio can be simplified by dividing or multiplying all terms by the same non-zero constant without changing its value.

Shortcut Trick

Apply the successive percentage increase formula: x + y + (x × y)/100

Overall % increase = 15 + 10 + (15 × 10)/100

Overall % increase = 25 + 1.5 = 26.5%

∴ The correct answer is 26.5%.

Alternate Method

Given: First increase = 15%, Second increase = 10%

Formula: Net Change = [ (Final Value − Initial Value) / Initial Value ] × 100

⇒ Let the initial number be 100.

⇒ After 15% increase, number = 100 + 15% of 100 = 115

⇒ After 10% increase on 115, number = 115 + 10% of 115 = 115 + 11.5 = 126.5

⇒ Overall increase = 126.5 − 100 = 26.5

⇒ Overall percentage increase = (26.5 / 100) × 100 = 26.5%

∴ The correct answer is 26.5%.

Additional Information

Successive Percentage Change

When a value is changed by a% and then by b%, the net change is given by (a + b + ab/100)%. Use positive for increase and negative for decrease.

Multiplier Method

A 15% increase corresponds to a multiplier of 1.15, and a 10% increase corresponds to 1.1. Net Multiplier = 1.15 × 1.1 = 1.265. Total increase = 1.265 − 1 = 0.265.

Successive Decrease

For two successive discounts of d₁% and d₂%, the Equivalent Discount = (d₁ + d₂ − d₁d₂/100)%.

Shortcut Trick

Total distance to be covered = Sum of lengths of trains = 285 + 235 = 520 m.

Relative speed (opposite direction) = 61 + 83 = 144 km/hr.

Convert Relative Speed to m/s: 144 × (5/18) = 8 × 5 = 40 m/s.

Time taken = Total Distance ÷ Relative Speed = 520 ÷ 40 = 13 sec.

∴ The correct answer is 13 sec.

Alternate Method

Given:

Length of first train (L₁) = 285 m

Length of second train (L₂) = 235 m

Speed of first train (S₁) = 61 km/hr

Speed of second train (S₂) = 83 km/hr

Formula Used:

Time = (L₁ + L₂) ÷ (S₁ + S₂)

Conversion: 1 km/hr = 5/18 m/s

Calculations:

⇒ Total Length = 285 + 235 = 520 m

⇒ Relative Speed = 61 + 83 = 144 km/hr

⇒ Relative Speed in m/s = 144 × (5/18) = 40 m/s

⇒ Time = 520 ÷ 40

⇒ Time = 13 sec

∴ The correct answer is 13 sec.

Additional Information

Relative Speed Concept

When two objects move in opposite directions, relative speed = S₁ + S₂. When moving in the same direction, relative speed = |S₁ − S₂|.

Unit Conversion

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

Train Crossing Distance

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

Shortcut Trick

Value ratio of coins = (Denomination × Ratio) = (1 × 3) : (2 × 2) = 3 : 4.

Total value units = 3 + 4 = 7 units.

7 units = ₹70 → 1 unit = ₹10.

Total number of coins = (3 + 2) × (Value of 1 unit ÷ Denomination base) = 5 × 10 = 50 coins.

∴ The correct answer is 50 coins.

Alternate Method

Given: Ratio of ₹1 and ₹2 coins = 3 : 2. Total amount = ₹70.

Formula Used: Total Value = ∑(Number of coins × Denomination)

⇒ Let the number of ₹1 coins be 3x and ₹2 coins be 2x.

⇒ (1 × 3x) + (2 × 2x) = 70

⇒ 3x + 4x = 70

⇒ 7x = 70

⇒ x = 10

⇒ Total coins = 3x + 2x = 5x

⇒ Total coins = 5 × 10 = 50

∴ The correct answer is 50 coins.

Additional Information

Coin Value Concept

The value of coins is always the product of the count of coins and their individual face value. Ratio of values = (n₁ × v₁) : (n₂ × v₂).

Ratio and Proportion

If a total quantity Q is divided in ratio a : b, the parts are [a/(a+b)] × Q and [b/(a+b)] × Q.

Shortcut Trick

For two numbers in ratio a : b with HCF = H, the LCM is given by: LCM = a × b × H.

Given a = 8, b = 7, and H = 30.

LCM = 8 × 7 × 30 = 56 × 30 = 1680.

∴ The correct answer is 1680.

Alternate Method

Given:

Ratio of two numbers = 8 : 7

HCF of numbers = 30

Formula Used:

Numbers = (Ratio part) × HCF

Product of two numbers = HCF × LCM

Calculations:

⇒ First number = 8 × 30 = 240

⇒ Second number = 7 × 30 = 210

⇒ We know, First Number × Second Number = HCF × LCM

⇒ 240 × 210 = 30 × LCM

⇒ LCM = (240 × 210) ÷ 30

⇒ LCM = 8 × 210

⇒ LCM = 1680

∴ The correct answer is 1680.

Additional Information

Fundamental Property of HCF and LCM

For any two positive integers x and y, the product of the numbers is always equal to the product of their HCF and LCM (x × y = HCF × LCM).

Co-prime Numbers

If two numbers are co-prime (HCF = 1), then their LCM is simply the product of the two numbers.

Ratio and Multiples

If the ratio of two numbers is x : y, the numbers can be represented as xH and yH, where H is the HCF.

Shortcut Trick

Initial Savings = 7.5% → Expenditure = 92.5% (Ratio 3 : 37)

Income Change (26%) = [Expenditure Change (45%) × 37 + Savings Change (x%) × 3] ÷ 40

1040 = 1665 + 3x ⇒ 3x = −625 ⇒ x = −208.33%

Change in Savings = 50,400 × 7.5% × (−208.33/100) = ₹3,780 × (−2.0833) = −₹7,875

∴ The correct answer is decrease by ₹7,875.

Alternate Method

Initial Values:

⇒ Income = ₹50,400

⇒ Savings = 7.5% of 50,400 = 50,400 × 0.075 = ₹3,780

⇒ Expenditure = 50,400 − 3,780 = ₹46,620

New Values:

⇒ New Income = 50,400 × 1.26 = ₹63,504

⇒ New Expenditure = 46,620 × 1.45 = ₹67,599

⇒ New Savings = New Income − New Expenditure = 63,504 − 67,599 = −₹4,095

Change in Savings:

⇒ Change = New Savings − Initial Savings = −4,095 − 3,780 = −₹7,875

∴ The correct answer is decrease by ₹7,875.

Additional Information

Income-Expenditure Relation

Always remember the fundamental equation: Income = Expenditure + Savings.

Percentage Change in Components

If Income increases by x%, Exp by y%, and Savings by z%, then: I × x = E × y + S × z.

Alligation Method

The percentage change in income is the weighted average of percentage changes in expenditure and savings.

Shortcut Trick

Discount % = (Free Items ÷ Total Items) × 100

Free items = 11, Total items = 14 + 11 = 25

Discount % = (11 ÷ 25) × 100 = 11 × 4 = 44%

∴ The correct answer is 44%.

Alternate Method

Given: Items purchased = 14, Items free = 11.

Formula: Discount % = [Free Quantity / (Purchased + Free Quantity)] × 100

⇒ Let the Marked Price (MP) of 1 item be ₹1.

⇒ Total MP of 25 items (14 + 11) = ₹25.

⇒ Selling Price (SP) for customer = MP of 14 items = ₹14.

⇒ Discount = MP − SP = 25 − 14 = ₹11.

⇒ Discount % = (11 ÷ 25) × 100

⇒ Discount % = 44%

∴ The correct answer is 44%.

Additional Information

Buy X Get Y Free

This is a promotional scheme where the total quantity is X + Y, and the discount is equivalent to the price of Y items. Formula: Discount % = [Y / (X+Y)] × 100.

Successive Discounts

When two discounts a% and b% are given, the equivalent single discount is [a + b − (ab/100)]%.

Marked Price and Selling Price

Selling Price = Marked Price × [ (100 − Discount%) / 100 ]. Discount is always calculated on the Marked Price (MP).

Shortcut Trick

Let A and B be filling pipes and C be the waste pipe.

Total Work (LCM of 10, 12, 30) = 60 units.

Combined Efficiency (A+B−C) = 60 ÷ 30 = 2.

Individual Efficiencies: A = 6, B = 5. ∴ 6 + 5 − C = 2 ⇒ C = 9 units/min.

Emptying Time for C = 60 ÷ 9 = 20/3 minutes. Capacity = (20/3) × 6 = 40 gallons.

∴ The correct answer is 40 gallons.

Alternate Method

Given: Pipe A fills in 10 mins, Pipe B fills in 12 mins, Pipe C empties 6 gallons/min, and A+B−C fills in 30 mins.

⇒ Efficiency of (A + B − C) = 2

⇒ 6 + 5 − Efficiency of C = 2

⇒ Efficiency of C = 11 − 2 = 9 units/min

⇒ Since 60 units represent the total capacity, the time taken by C to empty the full tank alone = 60 ÷ 9 = 20/3 minutes

⇒ Capacity of tank = Time taken by C × Rate of flow of C

⇒ Capacity = (20/3) × 6 = 20 × 2 = 40 gallons

∴ The correct answer is 40 gallons.

Additional Information

Pipes and Cisterns Logic

Filling pipes have positive efficiency (+), while emptying or waste pipes have negative efficiency (−).

Capacity Formula

Tank Capacity = Time taken by a pipe to fill/empty the tank × Rate of flow (gallons or liters per minute).

Combined Rate Rule

If pipe A fills in 'x' and pipe B empties in 'y', the net work done in one hour = (1/x − 1/y).

Shortcut Trick

Initial average age of 20 students = 29 years

New average age after including teacher = 30 years

Increase in average = 30 − 29 = 1 year

Teacher's age = New average + (Initial students × Increase in average)

Teacher's age = 30 + (20 × 1) = 50 years

∴ The correct answer is 50 years.

Alternate Method

Given:

Number of students (n₁) = 20

Average age of students (A₁) = 29 years

Total number of persons (n₂) = 21

New average age (A₂) = 30 years

⇒ Total age of 20 students = 20 × 29 = 580 years

⇒ Total age of the whole group (21 persons) = 21 × 30 = 630 years

⇒ Teacher's age = Total age of group − Total age of students

⇒ Teacher's age = 630 − 580

⇒ Teacher's age = 50 years

∴ The correct answer is 50 years.

Additional Information

Definition of Average

Average is the central value of a set of data, calculated as the sum of all values divided by the total number of values.

Inclusion Property

When a new member is added and the average increases, the new member's value is higher than the original average.

Sum of Observations

Sum = Average × Number of observations. This is used to find the total age or total value before and after changes.

Shortcut Trick

Cost Price (CP) of 1 banana = 4800 ÷ (100 × 12) = ₹4

Selling Price (SP) of 1 banana = 20 ÷ 4 = ₹5

Gain % = (SP − CP)/CP × 100

Gain % = (5 − 4)/4 × 100 = 1/4 × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given:

Total Cost Price (CP) = ₹4,800

Quantity = 100 dozens = 100 × 12 = 1,200 bananas

Selling Price (SP) per 4 bananas = ₹20

Calculations:

⇒ CP per banana = 4800 ÷ 1200 = ₹4

⇒ SP per banana = 20 ÷ 4 = ₹5

⇒ Profit per banana = SP − CP = 5 − 4 = ₹1

⇒ Gain Percentage = (Profit ÷ CP) × 100

⇒ Gain Percentage = (1 ÷ 4) × 100 = 25%

∴ The correct answer is 25%.

Additional Information

Profit and Loss Basics

Profit occurs when SP > CP. Profit = SP − CP. Loss occurs when CP > SP. Loss = CP − SP.

Percentage Calculation

Both Gain % and Loss % are always calculated on the Cost Price (CP) unless stated otherwise. Formula: (Value Change ÷ Base CP) × 100.

Unitary Method

To simplify calculations, always find the price per single unit for both buying and selling transactions.

Shortcut Trick

Combine ratios A : B (4 : 5), B : C (4 : 5), and C : D (6 : 7).

A : B : C : D ⇒ (4×4×6) : (5×4×6) : (5×5×6) : (5×5×7) = 96 : 120 : 150 : 175.

Total units = 96 + 120 + 150 + 175 = 541 units.

541 units = ₹4328 → 1 unit = ₹8.

Share of A = 96 × 8 = ₹768.

∴ The correct answer is ₹768.

Alternate Method

Given:

Total amount = ₹4328

Ratio A : B = 4 : 5, B : C = 4 : 5, C : D = 6 : 7

Calculations:

⇒ To find A : B : C : D, we equalize the common terms B and C.

⇒ A : B = 4 : 5 (Multiply by 4) = 16 : 20

⇒ B : C = 4 : 5 (Multiply by 5) = 20 : 25

⇒ So, A : B : C = 16 : 20 : 25

⇒ Now, A : B : C = 16 : 20 : 25 (Multiply by 6) = 96 : 120 : 150

⇒ C : D = 6 : 7 (Multiply by 25) = 150 : 175

⇒ Combined Ratio A : B : C : D = 96 : 120 : 150 : 175

⇒ Sum of ratios = 96 + 120 + 150 + 175 = 541

⇒ Share of A = (96 ÷ 541) × 4328

⇒ Share of A = 96 × 8 = ₹768

∴ The correct answer is ₹768.

Additional Information

Compounding Ratios

When multiple ratios are given (A:B, B:C, C:D), the ratio A:D can be found by multiplying the individual fractions: (A/B) × (B/C) × (C/D).

Ratio Balancing

To combine ratios, make the common term (like B or C) equal in both ratios by multiplying with appropriate constants.

Direct Proportion

The share of each person is directly proportional to their respective ratio unit when the total amount is fixed.

Shortcut Trick

In a 30°−60°−90° right-angled triangle, the ratio of sides is 1 : √3 : 2.

Side opposite to 30° (Building Height) = 1 unit = 42 m.

Side opposite to 60° (Distance from Base) = √3 units = 42 × √3.

Distance = 42 × 1.7321 = 72.7482 m ≈ 72.75 m.

∴ The correct answer is 72.75 m.

Alternate Method

Given:

Height of the building (h) = 42 m

Angle of depression = 30° ⇒ Angle of elevation from man to top = 30°.

Formula Used:

tan θ = Perpendicular ÷ Base

Calculations:

⇒ tan 30° = Height of building ÷ Distance from base

⇒ 1 ÷ √3 = 42 ÷ x

⇒ x = 42 × √3

⇒ x = 42 × 1.7321

⇒ x = 72.7482 m

⇒ x ≈ 72.75 m

∴ The correct answer is 72.75 m.

Additional Information

Angle of Depression and Elevation

The angle of depression from an observer to an object is numerically equal to the angle of elevation from the object to the observer because they are alternate interior angles.

Standard Values of Tan

Common trigonometric ratios: tan 30° = 1/√3, tan 45° = 1, and tan 60° = √3.

Rounding Rules

When rounding to two decimal places, if the third decimal digit is 5 or more, increase the second decimal digit by 1.

Shortcut Trick

The angle formed by the bisectors of two adjacent angles of a quadrilateral is equal to half the sum of the other two angles:

∠STR = (∠P + ∠Q) ÷ 2

⇒ ∠P + ∠Q = 2 × 40° = 80°

Since the ratio of ∠P : ∠Q is 3 : 5, the difference is:

Difference = [(5 − 3) ÷ (3 + 5)] × 80° = (2 ÷ 8) × 80° = 20°

∴ The correct answer is 20°.

Alternate Method

Given:

⇒ In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at T.

⇒ ∠STR = 40°

⇒ Ratio of ∠P : ∠Q = 3 : 5

Formula Used:

⇒ Sum of interior angles of a triangle = 180°

⇒ Sum of interior angles of a quadrilateral = 360°

Calculations:

Let the angle bisectors of ∠S and ∠R meet at T inside the quadrilateral.

⇒ ∠TSR = ∠S ÷ 2

⇒ ∠TRS = ∠R ÷ 2

In triangle STR:

⇒ ∠STR + ∠TSR + ∠TRS = 180°

⇒ 40° + (∠S ÷ 2) + (∠R ÷ 2) = 180°

⇒ (∠S + ∠R) ÷ 2 = 180° − 40°

⇒ (∠S + ∠R) ÷ 2 = 140°

⇒ ∠S + ∠R = 280°

In quadrilateral PQRS, the sum of all interior angles is 360°:

⇒ ∠P + ∠Q + ∠R + ∠S = 360°

⇒ ∠P + ∠Q + 280° = 360°

⇒ ∠P + ∠Q = 360° − 280°

⇒ ∠P + ∠Q = 80°

Given that the ratio of ∠P to ∠Q is 3 : 5:

⇒ Let ∠P = 3k and ∠Q = 5k

⇒ 3k + 5k = 80°

⇒ 8k = 80°

⇒ k = 10°

Now, calculating the individual angle measures:

⇒ ∠P = 3 × 10° = 30°

⇒ ∠Q = 5 × 10° = 50°

The difference between the measures of ∠Q and ∠P is:

⇒ ∠Q − ∠P = 50° − 30° = 20°

∴ The correct answer is 20°.

Additional Information

Angle Bisector Theorem in Quadrilaterals

The angle formed by the bisectors of two adjacent angles of any quadrilateral is always equal to half the sum of the remaining two angles. Formula: ∠STR = (∠P + ∠Q) ÷ 2.

Sum of Interior Angles of a Polygon

The sum of the interior angles of an n-sided polygon is given by the formula (n − 2) × 180°. For a quadrilateral (n = 4), the sum is always 360°.

Opposite Angle Bisectors in a Quadrilateral

If the bisectors of two opposite angles of a quadrilateral intersect, the angle between them is equal to half the difference of the other two opposite angles.

Shortcut Trick

Total Work = LCM of 3, 6, 10 = 30 units.

Efficiencies: A = 10, B = 5, C = 3. Combined Efficiency = 10 + 5 + 3 = 18.

Thrice Work = 30 × 3 = 90 units.

Time Required = 90 ÷ 18 = 5 days.

∴ The correct answer is 5 days.

Alternate Method

Given: Time taken by A = 3 days, B = 6 days, C = 10 days.

Formula Used: Total Work = LCM(Individual Days); Efficiency = Work ÷ Time; Time = Total Work ÷ Combined Efficiency.

⇒ Total Efficiency of (A + B + C) = 10 + 5 + 3 = 18 units/day.

⇒ Original Work = 30 units.

⇒ Thrice the Work = 3 × 30 = 90 units.

⇒ Time taken = 90 ÷ 18

⇒ Time taken = 5 days.

∴ The correct answer is 5 days.

Additional Information

Combined Work Formula

For two people, Time = (A × B) ÷ (A + B). For three people, Time = (ABC) ÷ (AB + BC + CA).

Work and Wages

Wages are always distributed in the ratio of the Efficiency of the workers if they work for the same duration.

Man-Days Formula

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

Shortcut Trick

Apply the successive percentage change formula: Net Change = a + b + (ab ÷ 100)

Here, a = +49% (markup) and b = −16% (discount).

Net Profit % = 49 − 16 − (49 × 16 ÷ 100)

Net Profit % = 33 − 7.84 = 25.16% ≈ 25.2%

∴ The correct answer is 25.2%.

Alternate Method

Given: Marked Price (MP) is 49% above Cost Price (CP), Discount is 16% on MP.

⇒ Let Cost Price (CP) = 100

⇒ Marked Price (MP) = 100 + 49% of 100 = 149

⇒ Selling Price (SP) = MP − 16% of MP

⇒ SP = 149 − (16 ÷ 100 × 149) = 149 − 23.84

⇒ SP = 125.16

⇒ Profit = SP − CP = 125.16 − 100 = 25.16

⇒ Profit Percentage = (Profit ÷ CP) × 100 = (25.16 ÷ 100) × 100 = 25.16%

⇒ Rounded to 1 decimal place = 25.2%

∴ The correct answer is 25.2%.

Additional Information

Marked Price & Discount

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

Markup Percentage

Markup is the increase over CP to arrive at MP. MP = CP × (100 + Markup%) ÷ 100.

Relationship Formula

MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%). This is used when both profit and discount are given.

Shortcut Trick

Total Interest percentage for the period = Rate × Time

Time = 18 months = 1.5 years

Effective Interest % = 16% × 1.5 = 24%

Simple Interest = 24% of ₹50,000 = 24 × 500 = ₹12,000

∴ The correct answer is ₹12,000.

Alternate Method

Given:

Principal (P) = ₹50,000

Rate (R) = 16% per annum

Time (T) = 18 months

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ Convert time to years: T = 18 ÷ 12 = 1.5 years

⇒ SI = (50000 × 16 × 1.5) ÷ 100

⇒ SI = 500 × 16 × 1.5

⇒ SI = 500 × 24

⇒ SI = ₹12,000

∴ The correct answer is ₹12,000.

Additional Information

Total Amount Formula

The total amount (A) to be paid back is the sum of Principal and Simple Interest: A = P + SI.

Time Conversion

Always ensure time (T) is in years. If given in days, divide by 365; if in months, divide by 12.

Direct Relation

Simple Interest is directly proportional to Principal, Rate, and Time. If any one doubles, SI also doubles (keeping others constant).

The position and positional values or English Alphabets are:

The pattern followed here is:

Each letter-cluster pair follows the pattern -3, +2.

Let's check each option:

1. RV – OX

This letter-cluster pair follows the pattern -3 +2.

2. NR – PT

This letter-cluster pair does not follow the pattern -3 +2.

3. MQ – JS

This letter-cluster pair follows the pattern -3 +2.

4. UY – RA

This letter-cluster pair follows the pattern -3 +2.

Thus, NR – PT is the odd one out.

Hence, the correct answer is "Option 2".

Given: In a certain code language, ‘TOUR’ is coded as ‘4139’ and ‘BRUT’ is coded as ‘4318’.

Thus, 8 is the code for ‘B’ in the given code language.

Hence, the correct answer is "Option 4".

Given: 612 610 620 617 627 623 ?

The logic followed here is:

Thus, 633 should come in place of the question mark (?) in the given series.

Hence, the correct answer is "Option 1".

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

Now,

Odd digits, each of which is immediately preceded by an odd digit and also immediately followed by an even digit.

So, the needed pattern is: Odd — Odd — Even

​

Thus, there are two odd digits, each of which is immediately preceded by an odd digit and also immediately followed by an even digit.

Hence, the correct answer is "Option 2".

Given: Saurav starts from Point A and drives 9 km towards the east. He then takes a right turn, drives 6 km, turns right and drives 11 km. He then takes a right turn and drives 11 km. He takes a final right turn, drives 2 km and stops at Point P.

Thus, Saurav should drive 5 km to the south to reach point A from point P.

Hence, the correct answer is "Option 1".

Given: Mohini starts from Point A and drives 13 km towards south. She then takes a right turn, drives 7 km, turns right and drives 7 km. She then takes a right turn and drives 3 km. She takes a final left turn, drives 6 km and stops at Point P.

Thus, Mohini should drive 4 km towards east to reach point A from point P.

Hence, the correct answer is "Option 2".

The position and positional values or English Alphabets are:

Given: 

KJL−NMO

LKM−ONP6445

Each letter-cluster pair follows the pattern +3, +3, +3.

Let's check each option:

1. VUW – YXZ

This letter-cluster pair follows the pattern +3, +3, +3.

2. VTU – XWY

This letter-cluster pair does not follow the pattern +3, +3, +3.

3. VUW – XXY

This letter-cluster pair does not follow the pattern +3, +3, +3.

4. VTU – YXZ

This letter-cluster pair does not follow the pattern +3, +3, +3.

Thus, VUW−YXZ follows the same pattern.

Hence, the correct answer is "Option 1".

Given: 66 81 98 117 138 ?

The logic followed here is:

Thus, 161 should come in place of the question mark (?) in the given series.

Hence, the correct answer is "Option 2".

Statements: All forks are kettles. Some forks are cups.

The least possible Venn diagram for the given statement is:

Conclusion (I): Some kettles are cups. - True (Because, All forks are kettles and Some forks are cups, which means some forks which are kettles are cups.)

Conclusion (II): All cups are forks. - False (Because, Some forks are cups, which does not imply that All cups are forks.)

Thus, Only conclusion (I) follows.

Hence, the correct answer is "Option 3".

Statements:

Some nut are bolt.

Some bolt are rivet.

The least possible Venn diagram for the given statement is:

Conclusions:

(I) Some nut are rivet. - False (There is no definite relation between brinjals and peacocks, it can be possible but it is not definite)

(II) All rivet are bolt. - False  (Bevause, Some bolt are rivet, which doesn't imply that All rivet are bolt)

Thus, Neither conclusion (I) nor (II) follows.

Hence, the correct answer is "Option 3".

The position and positional values or English Alphabets are:

Given: NSE MRD LQC KPB ?

The logic followed here is:

Thus, JOA should come in place of the question mark (?) in the given series based on the English alphabetical order.

Hence, the correct answer is "Option 1".

Family Chart:

Decoding the Symbols:

Given: C ? D @ E = F √ L

It means: C is the daughter of D, D is the father of E, E is the son of F, F is the sister of L.

Thus, C is L's Sister's daughter.

Hence, the correct answer is "Option 1".

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

Now,

Even numbers, each of which is immediately preceded by an odd number and also immediately followed by an even number.

So, the needed pattern is: Odd — Even — Even

Thus, there are 5 even number, each of which is immediately preceded by an odd number and also immediately followed by an even number.

Hence, the correct answer is "Option 1".

The position and positional values or English Alphabets are:

Given: IGP 3 KIO -10 MKN -23 OMM -36 ?

The logic followed here is:

Thus, 'QOL -49' will replace the question mark (?) in the given series to make it logically complete.

Hence, the correct answer is "Option 4".

Given: Seven people A, B, C, D, E, F, and G are sitting in a row, facing the north.

1. Only one person sits to the right of E.

2. Only three people sit between G and E.

3. Only three people sit between A and D, neither of whom sits on the left end.

4. F sits immediately to the right of C.

5. Only one person sits between A and B.

The above statement cannot be satisfied in case II, so it is eliminated.

Thus, G sits second to the left of C.

Hence, the correct answer is "Option 1".

Given: Five people, L, M, N, O and P, are sitting in a row facing north.

1. N is sitting at the third position from the extreme right end of the row.
2. M is not an immediate neighbour of N.
3. P is sitting to the immediate left of N.
4. P is sitting to the immediate right of O.

L, the only person left will occupy the vacant position.

Thus, L is sitting between N and M.

Hence, the correct answer is "Option 4".

Given: In a certain code language, ‘MORE’ is coded as ‘1637’ and ‘DEMO’ is coded as ‘4176’.

Thus, '4' is the code for ‘D’ in the given code language.

Hence, the correct answer is "Option 3".

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

Now,

Odd numbers which are immediately followed by even numbers.

So, the needed pattern is: Odd - Even

Thus, there are three odd numbers, each of which is immediately followed by an even number.

Hence, the correct answer is "Option 1".