RRB Group D Official Paper (Held On: 10 Dec, 2025 Shift 1) (Previous Year Paper)

The correct answer is Pollination → Fertilisation → Embryo → Seedling.

Key Points

• Pollination: The process begins with pollination, where the pollen grains are transferred from the anther (male part) of a flower to the stigma (female part). This process can occur through various agents such as wind, water, insects, or animals. This step is vital for sexual reproduction in flowering plants.
• Fertilisation: After successful pollination, fertilisation occurs. The pollen grain germinates on the stigma, and the pollen tube grows down the style into the ovary. The male gamete fuses with the female gamete (egg) to form a zygote.
• Embryo Formation: The fertilised zygote develops into an embryo. This stage marks the beginning of the formation of a new plant. The embryo consists of the plumule, radicle, and cotyledons, which later give rise to the shoot, root, and seed storage tissue, respectively.
• Seedling Development: Once the embryo matures within the seed, it germinates under favourable conditions (water, temperature, oxygen) to form a seedling, which develops into a new plant. This marks the completion of the reproduction cycle in flowering plants.

Additional Information

• Pollination Types:
• Self-pollination: Pollen from the anther is transferred to the stigma of the same flower or another flower on the same plant.
• Cross-pollination: Pollen is transferred from the anther of one flower to the stigma of a flower on a different plant of the same species. Agents include insects, wind, and water.
• Fertilisation Process:
• Fertilisation is the fusion of male and female gametes to form a zygote.
• This process occurs within the ovule, which is housed in the ovary of the flower.
• Double fertilisation is unique to flowering plants, where one sperm fertilises the egg, forming the zygote, and the other sperm combines with polar nuclei to form the endosperm.
• Seed and Embryo Development:
• After fertilisation, the ovule develops into a seed, and the ovary becomes the fruit.
• The seed contains the embryo and stored food, surrounded by a protective seed coat.
• Seed Germination:
• Germination is the process where a seed develops into a seedling under favourable conditions.
• Essential factors include water, oxygen, and an appropriate temperature.
• During germination, the radicle (embryonic root) emerges first, followed by the plumule (embryonic shoot).

Important Points

• Sequence of Events: The correct sequence in the reproduction of flowering plants is Pollination → Fertilisation → Embryo → Seedling. Any deviation from this sequence will disrupt the reproductive cycle.
• Role of Pollination: Pollination is a pre-requisite for fertilisation. Without it, the male gametes cannot reach the female gametes.
• Double Fertilisation: Unique to angiosperms, where two fertilisation events occur: one forming the embryo and the other forming the endosperm, which nourishes the developing embryo.
• Importance of Seed Germination: Germination ensures the continuation of the species by giving rise to new plants under suitable conditions.

The correct answer is It blocks the vas deferens to prevent sperm release..

Key Points

• Vasectomy is a surgical procedure performed on males as a method of permanent contraception. It involves cutting or blocking the vas deferens, which are the tubes that carry sperm from the testicles to the urethra.
• By blocking the vas deferens, sperm cannot mix with the semen that is ejaculated. This prevents the sperm from being released during ejaculation, making fertilization impossible.
• Unlike common misconceptions, vasectomy does not affect the production of the hormone testosterone. The testicles continue to produce testosterone, so male characteristics and sexual function remain unaffected.
• The procedure is typically performed under local anesthesia and is considered a safe, effective, and minimally invasive procedure. Recovery time is usually short, and complications are rare.
• It is important to note that vasectomy does not offer immediate contraception. Residual sperm may still be present in the vas deferens for a few weeks or months after the procedure. Therefore, alternative contraception methods are recommended until follow-up tests confirm the absence of sperm.

Additional Information

• Testosterone Production:
• The claim that vasectomy stops testosterone production is false. The testicles continue to produce testosterone after vasectomy, maintaining secondary sexual characteristics like facial hair, voice depth, and libido.
• Seminal Vesicles:
• Vasectomy does not involve the removal of seminal vesicles. These glands continue to function normally and produce seminal fluid, which constitutes the majority of the ejaculate.
• Sperm and the Uterus:
• The statement that vasectomy kills sperm cells reaching the uterus is incorrect. Vasectomy ensures that sperm do not even leave the male reproductive system, so they cannot reach the female uterus.
• The body naturally absorbs sperm that are produced after vasectomy since they are no longer transported via the vas deferens.
• Effectiveness of Vasectomy:
• Vasectomy is one of the most effective methods of birth control, with a success rate of over 99%. It is considered a permanent solution for those who do not wish to have more children.
• It does not protect against sexually transmitted infections (STIs), so additional protection like condoms may still be necessary in certain situations.
• Reversal of Vasectomy:
• Although vasectomy is considered a permanent method of contraception, it can sometimes be reversed through a procedure called vasovasostomy. However, the success of reversal depends on factors such as the time elapsed since the vasectomy.

Important Points

• Procedure and Recovery:
• Vasectomy is a relatively simple outpatient procedure that typically takes about 15–30 minutes.
• Post-procedure care includes avoiding heavy physical activity for a few days and using an ice pack to reduce swelling or discomfort.
• Prevalence:
• Vasectomy is widely used as a method of contraception in several countries, including the United States, Canada, and New Zealand.
• According to the World Health Organization (WHO), vasectomy accounts for approximately 5–10% of contraceptive use worldwide.
• Counseling and Consent:
• Before undergoing a vasectomy, individuals should receive proper counseling regarding its permanency and the need for follow-up testing to confirm its effectiveness.

The correct answer is Current.

Key Points

• Resistors in Series: When resistors are connected in series, the same current flows through all resistors. This is because there is only one path for the current to travel. Hence, the correct answer is Current.
• Voltage Distribution: The voltage across each resistor in a series connection is different and depends on the resistance of each resistor. The sum of these voltages equals the total voltage across the series circuit.
• Resistance in Series: The total resistance of resistors in series is the sum of their individual resistances. This is mathematically expressed as R_total = R₁ + R₂ + R₃...
• Power Consumption: The power consumed by each resistor in a series circuit is different and depends on the voltage drop across it and its resistance. Total power consumption is the sum of individual power consumptions.
• Application: Series circuits are commonly used in applications like string lights, where the same current flows through all the bulbs, ensuring they light up uniformly.

Additional Information

• Ohm's Law: Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It is expressed as I = V/R, where I is the current, V is the voltage, and R is the resistance.
• Voltage Divider Rule: In a series circuit, the voltage is divided among the resistors in proportion to their resistances. This is represented as V₁ = (R₁ / R_total) × V_total, where V₁ is the voltage across resistor R₁.
• Applications of Series Circuits: Series circuits are used in applications where uniform current flow is necessary. Examples include Christmas tree lights, water heaters, and simple electronic testing setups.
• Characteristics of Series Circuits:
• The total resistance increases as more resistors are added.
• If one resistor fails, the entire circuit stops functioning since current flow is interrupted.
• Comparison with Parallel Circuits: Unlike series circuits, parallel circuits allow current to flow through multiple paths, resulting in different currents through each path but the same voltage across all paths.

Important Points

• Mathematical Representation: In series circuits, the current is constant across all components, and voltage is distributed based on individual resistances.
• Practical Implications: Series circuits are less commonly used in household applications due to their dependency on all components functioning correctly. If one component fails, the circuit becomes open.
• Safety Considerations: Series circuits are safer for low-current applications but may not be ideal for high-power systems due to increased resistance and potential overheating.
• Historical Context: The concept of series and parallel circuits stems from the study of electrical circuits in the 19th century, with contributions from scientists like Georg Simon Ohm, who formulated Ohm's Law in 1827.

The correct answer is Because their atomic numbers and electronic configurations differ.

Key Points

• Isobars are atoms of different elements that have the same mass number (sum of protons and neutrons) but different atomic numbers.
• The chemical properties of an element are primarily determined by its atomic number, which defines the number of protons in the nucleus and the electronic configuration of the atom.
• Since isobars have different atomic numbers, they belong to different elements, leading to different electronic configurations and, consequently, different chemical behaviors.
• For example, Carbon-14 (atomic number 6) and Nitrogen-14 (atomic number 7) are isobars. While Carbon-14 exhibits chemical properties of carbon, Nitrogen-14 behaves chemically as nitrogen. This difference is due to their distinct electronic arrangements.
• While they have the same mass number, the difference in proton and neutron distribution leads to variation in their nuclear properties as well, but it is the atomic number that dictates chemical behavior.

Additional Information

• Definition of Isobars:
• Isobars are atoms of different elements that have the same mass number but different atomic numbers.
• Example: Argon-40 (Atomic number 18) and Calcium-40 (Atomic number 20) are isobars.
• Determination of Chemical Properties:
• Chemical properties depend on the number and arrangement of electrons in an atom, which is governed by its atomic number.
• Isobars, having different atomic numbers, have different chemical properties.
• Examples of Isobars:
• Carbon-14 and Nitrogen-14 – Both have a mass number of 14, but their chemical properties differ due to different atomic numbers (6 and 7, respectively).
• Potassium-40 and Calcium-40 – Both have a mass number of 40 but different atomic numbers (19 and 20, respectively).
• Difference Between Isobars and Isotopes:
• Isobars: Atoms with the same mass number but different atomic numbers (e.g., Argon-40 and Calcium-40).
• Isotopes: Atoms of the same element with the same atomic number but different mass numbers (e.g., Carbon-12, Carbon-13, and Carbon-14).
• Nuclear Properties of Isobars:
• While their chemical properties differ, isobars may have similar or different nuclear stability and radioactive behavior depending on their neutron-to-proton ratio.

Important Points

• The mass number is the sum of protons and neutrons in the nucleus.
• The atomic number is the number of protons, which also equals the number of electrons in a neutral atom, determining its chemical nature.
• Isobars are useful in nuclear physics and studies of radioactivity, as they help in understanding nuclear processes like beta decay.
• Isobars are often used in dating techniques such as radiocarbon dating using isotopes like Carbon-14.

"

The correct answer is Ionic bond.

Key Points

• An ionic bond is formed when a metal reacts with a non-metal. This bond occurs due to the transfer of electrons from the metal to the non-metal.
• Metals have a tendency to lose electrons and form positively charged ions (cations), while non-metals tend to gain electrons to form negatively charged ions (anions).
• The resulting electrostatic attraction between the oppositely charged ions leads to the formation of an ionic bond.
• For example, in the case of sodium chloride (NaCl), sodium (a metal) donates one electron to chlorine (a non-metal), resulting in the formation of Na⁺ and Cl⁻ ions.
• Ionic bonds are typically strong and result in the formation of crystalline structures, such as salt crystals, which have high melting and boiling points.

Additional Information

• Covalent bond:
• A covalent bond is formed when two non-metals share electrons to achieve stability. This type of bond does not involve the transfer of electrons.
• For example, in a water molecule (H₂O), oxygen and hydrogen share electrons to form covalent bonds.
• Covalent bonds generally result in the formation of molecules with lower melting and boiling points compared to ionic compounds.
• Hydrogen bond:
• A hydrogen bond is a weak bond that occurs between a hydrogen atom bonded to a highly electronegative atom (e.g., oxygen, nitrogen, or fluorine) and another electronegative atom.
• Hydrogen bonding is responsible for many properties of water, such as its high boiling point and surface tension.
• This bond is not a type of ionic or covalent bond but a secondary interaction.
• Metallic bond:
• A metallic bond is formed between metal atoms. It involves a "sea of electrons" that are free to move around, providing metals with their characteristic properties, such as conductivity, malleability, and ductility.
• This bond is unique to metals and does not involve non-metals.
• Examples of ionic compounds:
• Sodium chloride (NaCl): Common table salt formed by the ionic bond between sodium and chlorine.
• Magnesium oxide (MgO): Formed by the ionic bond between magnesium and oxygen.
• Calcium fluoride (CaF₂): Formed by the ionic bond between calcium and fluorine.

The correct answer is 5.5.

Key Points

• Tooth enamel, the hardest substance in the human body, starts to corrode when the pH in the mouth drops below 5.5. This is commonly referred to as the "critical pH" for enamel demineralization.
• At a pH below 5.5, the acidic environment in the mouth begins to dissolve the calcium phosphate minerals present in the enamel, leading to dental erosion.
• Bacteria, especially Streptococcus mutans and Lactobacillus, produce acids as they metabolize sugars, which reduces the pH in the oral cavity. This is a major cause of enamel corrosion.
• The saliva in the mouth acts as a natural buffer to neutralize acids. However, when the acid production exceeds the buffering capacity of saliva, the pH falls below 5.5, initiating enamel demineralization.
• Consuming acidic foods and beverages like citrus fruits, carbonated drinks, or sugary snacks can accelerate the drop in pH, increasing the risk of enamel erosion.

Additional Information

• Role of Tooth Enamel:
• Tooth enamel is composed primarily of hydroxyapatite crystals, a form of calcium phosphate.
• It serves as a protective barrier for the underlying dentin and pulp, shielding the tooth from physical damage, temperature changes, and bacterial invasion.
• Enamel does not regenerate once damaged, making its protection crucial for maintaining oral health.
• pH and Oral Health:
• The pH scale ranges from 0 to 14, where 7 is neutral, below 7 is acidic, and above 7 is alkaline.
• A healthy oral pH is typically around 6.8 to 7.4, which supports remineralization and inhibits bacterial growth.
• When the pH drops below 5.5, the conditions favor demineralization, leading to dental caries and enamel erosion.
• Preventive Measures:
• Reduce consumption of sugary and acidic foods/beverages to maintain a healthy oral pH.
• Practice good oral hygiene, such as brushing twice daily with fluoride toothpaste and flossing to remove food particles and plaque.
• Use fluoride-based products, as fluoride strengthens enamel and enhances resistance to acid attacks.
• Chewing sugar-free gum can stimulate saliva production, which helps neutralize acids and restore pH balance.
• Saliva’s Role:
• Saliva contains minerals like calcium and phosphate, which aid in the remineralization of enamel.
• It has enzymes like amylase that help break down food particles and maintain oral health.
• Saliva also acts as a natural buffer to counteract acidic environments in the mouth.

Important Points

• Demineralization vs. Remineralization:
• Demineralization occurs when acids dissolve the minerals in enamel, leading to erosion and cavities.
• Remineralization is the natural repair process where minerals like calcium and phosphate are redeposited into enamel.
• Fluoride plays a vital role in enhancing remineralization and preventing further decay.
• Risk Factors for Enamel Erosion:
• Frequent consumption of acidic foods and drinks, poor oral hygiene, and dry mouth conditions.
• Conditions like GERD (Gastroesophageal Reflux Disease) can expose teeth to stomach acids, increasing the risk of erosion.
• Excessive brushing with abrasive toothpaste can also wear down enamel over time.
• Fluoride’s Role:
• Fluoride integrates into the enamel structure, forming fluoroapatite, which is more resistant to acids.
• Regular use of fluoride toothpaste and mouthwash significantly reduces the risk of cavities and enamel erosion.
• pH Testing in Dentistry:
• Modern dental practices use pH strips or advanced devices to monitor oral pH levels and assess enamel health.
• Patients with consistently low pH levels may be advised on dietary changes and oral care routines to prevent enamel damage.

"

The correct answer is 16 m/s.

Key Points

• Force and Mass: The body has a mass of 5 kg, and a constant force of 20 N acts on it. Using Newton's Second Law, Force = Mass × Acceleration, the acceleration can be calculated.
• Acceleration = Force / Mass = 20 / 5 = 4 m/s².
• This calculation is correct based on the given values.
• Initial velocity: The body is initially at rest, meaning the initial velocity is 0 m/s. This is explicitly mentioned in the question, and the statement is correct.
• Time: The force acts on the body for 4 seconds. This duration is crucial for calculating the final velocity using the formula for uniformly accelerated motion. The statement is correct.
• Final velocity calculation: Using the formula Final Velocity = Initial Velocity + (Acceleration × Time):
• Final Velocity = 0 + (4 × 4) = 16 m/s.
• The correct option is 16 m/s.
• Correct Answer: The calculated final velocity matches the given option 16 m/s, making it the correct choice.

Additional Information

• Newton's Second Law of Motion:
• It states that the force acting on an object is equal to the rate of change of its momentum, or Force = Mass × Acceleration.
• This principle is widely used in physics to calculate motion parameters like acceleration and velocity.
• Equations of Motion:
• These equations describe the relationship between velocity, acceleration, time, and displacement.
• The formula used here, Final Velocity = Initial Velocity + Acceleration × Time, is one of the fundamental equations of uniformly accelerated motion.
• Units and Dimensions:
• Force is measured in Newtons (N), mass in kilograms (kg), acceleration in meters per second squared (m/s²), and velocity in meters per second (m/s).
• Understanding units and their conversions is essential for solving physics problems accurately.
• Applications:
• Such calculations are essential in understanding the motion of objects in various fields, including engineering, space exploration, vehicle dynamics, and sports science.
• For example, calculating the velocity of vehicles after a certain time helps in designing better braking systems.

Important Points

• Constant Force: When a constant force acts on a body, the acceleration remains constant throughout the motion.
• Uniform Acceleration: The equations of motion are applicable only under uniform acceleration conditions.
• Initial Conditions: The initial velocity is critical in determining the final velocity, especially when the object starts from rest.
• Practical Uses: Understanding force and motion is foundational for designing systems like rockets, vehicles, and machinery.

The correct answer is The white blood cell (WBC) has a round and fixed shape..

Key Points

• The white blood cell (WBC) has a round and fixed shape: This statement is incorrect. Unlike red blood cells (RBCs), WBCs do not have a fixed shape. They are highly flexible and capable of changing their shape to move through blood vessel walls and reach sites of infection or injury. This property, called amoeboid movement, allows them to perform their immune function effectively.
• The muscle cell is spindle-shaped: This statement is correct. Muscle cells, especially smooth muscle cells, are elongated and spindle-shaped to facilitate contraction and relaxation during various body functions, such as digestion and blood flow regulation.
• The nerve cell is long and branched in shape: This statement is correct. Nerve cells (neurons) are specialized for transmitting signals and are characterized by their long, branched structure, including dendrites (short branches) and axons (long branches). This shape ensures efficient communication across the nervous system.
• The red blood cell (RBC) is disc-shaped with a central depression: This statement is correct. RBCs have a biconcave disc shape with a central depression, which maximizes their surface area for oxygen and carbon dioxide exchange and enables them to squeeze through narrow capillaries.

Additional Information

• White Blood Cells (WBCs):
• WBCs are part of the immune system and help the body fight infections.
• They exhibit amoeboid movement and can change shape to engulf pathogens through a process called phagocytosis.
• Types of WBCs include neutrophils, lymphocytes, monocytes, eosinophils, and basophils, each with specific immune functions.
• Muscle Cells:
• Muscle cells are specialized for contraction and movement.
• Smooth muscle cells, found in organs like the stomach and intestines, are spindle-shaped, while skeletal muscle cells are cylindrical and striated.
• Cardiac muscle cells are branched and connected by intercalated discs for synchronized contraction.
• Nerve Cells (Neurons):
• Neurons are the basic units of the nervous system, transmitting signals through electrical impulses.
• They have specialized structures, such as dendrites for receiving signals and axons for transmitting them.
• The synapse is the junction where neurons communicate with other neurons or target cells.
• Red Blood Cells (RBCs):
• RBCs contain hemoglobin, a protein responsible for oxygen transport.
• Their biconcave shape increases surface area and facilitates gas exchange.
• They lack a nucleus in mammals, allowing more space for hemoglobin but limiting their lifespan to about 120 days.

Important Points

• Cell Shape and Function:
• The shape of a cell is closely related to its function. For example, the biconcave shape of RBCs aids in oxygen transport, while the flexible shape of WBCs facilitates immune responses.
• Other Examples of Cell Shapes:
• Platelets: Small, irregularly shaped cell fragments involved in blood clotting.
• Plant Cells: Have a fixed rectangular shape due to a rigid cell wall, aiding in structural support.
• Guard Cells: Kidney-shaped cells in plants that regulate the opening and closing of stomata for gas exchange.
• Diseases Related to Cell Shapes:
• Sickle Cell Anemia: A genetic disorder where RBCs become crescent-shaped, reducing their oxygen-carrying capacity and causing blockages in blood vessels.
• Leukemia: A type of cancer involving abnormal proliferation of WBCs.

The correct answer is One long and one short line parallel to each other.

Key Points

• The symbol for a cell in a circuit diagram is represented by one long and one short line parallel to each other. The long line represents the positive terminal, and the short line represents the negative terminal.
• This standard symbol is used universally in electrical and electronic circuit diagrams to represent a single electrochemical cell.
• The long line (+) indicates the higher electric potential, while the short line (-) indicates the lower electric potential. This helps in understanding the flow of current in the circuit.
• A single cell symbol can also be combined to represent a battery, where multiple cells are connected in series or parallel.
• In contrast, other options like a “circle with a cross inside,” “two equal lines parallel to each other,” or “a rectangle with a diagonal line” do not represent a cell in circuit diagrams. These symbols represent different components like bulbs, resistors, or other devices.

Additional Information

• Electrochemical Cell:
• An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause chemical reactions.
• It consists of two electrodes (anode and cathode) and an electrolyte. The anode is the negative terminal, while the cathode is the positive terminal.
• Battery Symbol:
• A battery symbol in a circuit diagram is represented by multiple cells connected together, where the number of long and short lines indicates the number of cells in the battery.
• Batteries are used in various devices, from small electronic gadgets to large-scale power storage systems.
• Electric Circuit Components:
• Bulb: Represented by a circle with a cross inside in circuit diagrams. It shows the presence of a light-emitting component in the circuit.
• Resistor: Represented by a rectangle or zigzag line, indicating a component that resists the flow of current.
• Switch: Denoted by a break in the line with a lever, it indicates a controlling device that can open or close the circuit.
• Direction of Current:
• The conventional direction of current flow is from the positive terminal (long line) to the negative terminal (short line) of the cell.
• This aligns with the movement of positive charges, even though electrons actually flow in the opposite direction.

Important Points

• Standards in Circuit Diagrams: The symbols used in circuit diagrams follow international conventions set by organizations like IEC (International Electrotechnical Commission) to ensure uniformity and understanding.
• Applications of Cells: Electrochemical cells are used in batteries, portable devices, vehicles, and energy storage systems for renewable energy applications.
• Types of Cells: Cells can be classified as primary cells (non-rechargeable) and secondary cells (rechargeable), based on their ability to be reused.
• Real-World Example: A common example of a cell is an AA battery, widely used in household devices like remote controls and clocks.

The correct answer is Amplitude.

Key Points

• Loudness of a sound is primarily determined by its amplitude, which refers to the height of the sound wave. The greater the amplitude, the louder the sound is perceived.
• Amplitude is a measure of the energy of the sound wave. When the amplitude increases, the energy carried by the wave also increases, resulting in higher sound intensity.
• Loudness is a subjective measure and depends on the sensitivity of the human ear. However, higher amplitude generally corresponds to higher loudness.
• For instance, in a graphical representation of sound waves, a wave with a larger peak-to-trough distance (amplitude) represents a louder sound compared to a wave with smaller amplitude.
• Amplitude is measured in decibels (dB), which quantifies the intensity of the sound.

Additional Information

• Pitch:
• The pitch of a sound is determined by its frequency, which is the number of vibrations per second. Higher frequency results in a higher-pitched sound, while lower frequency results in a lower-pitched sound.
• Pitch is measured in hertz (Hz), and it does not directly affect the loudness of a sound.
• Wavelength:
• Wavelength refers to the distance between two consecutive crests or troughs in a sound wave. It is inversely proportional to the frequency of the wave.
• While it influences the type of sound, wavelength does not determine the loudness of a sound.
• Frequency:
• Frequency is the number of oscillations or cycles per second of a sound wave. It determines the pitch of the sound, not its loudness.
• A sound with a high frequency is perceived as a high-pitched sound, whereas a low-frequency sound is perceived as low-pitched.
• Decibels (dB):
• Decibels are the unit of measurement for sound intensity. A small increase in decibel level represents a significant increase in sound intensity.
• For example, normal conversation occurs at around 60 dB, while a rock concert can reach levels of 120 dB or more.

Important Points

• Sound Waves: Sound waves are mechanical waves that require a medium (like air, water, or solids) to travel. They are longitudinal waves, where the particles of the medium vibrate parallel to the direction of the wave's propagation.
• Human Hearing Range: The average human ear can detect sounds in the frequency range of 20 Hz to 20,000 Hz. Sounds outside this range are inaudible to humans.
• Resonance: When an object vibrates at its natural frequency due to an external sound wave, it amplifies the sound. This phenomenon is called resonance and plays a role in enhancing sound loudness.
• Threshold of Pain: Loudness levels above 120 dB can cause pain or even damage to the human ear. Prolonged exposure to high decibel levels can lead to hearing loss.

The correct answer is He has myopia and needs a concave lens.

Key Points

• Myopia (Nearsightedness): It is a common refractive error in which a person can see nearby objects clearly but has difficulty seeing distant objects. This is due to the light rays focusing in front of the retina instead of directly on it.
• Symptoms of Myopia: The student’s inability to read the blackboard clearly while sitting at the back of the class is a typical symptom of myopia. However, the ability to read a book clearly at a close distance (25 cm) confirms that near vision is unaffected.
• Cause of Myopia: It occurs due to either an elongated eyeball or an excessively curved cornea, leading to improper focusing of light rays on the retina.
• Correction: Myopia is corrected using a concave lens (diverging lens), which helps to diverge the light rays before they enter the eye, ensuring they focus directly on the retina instead of in front of it.
• Age Factor: Myopia is commonly detected in childhood or adolescence. It may stabilize or progress with age.

Additional Information

• Hypermetropia (Farsightedness):
• In hypermetropia, a person can see distant objects clearly but has difficulty focusing on nearby objects. This condition is corrected using a convex lens (converging lens).
• It occurs when the eyeball is too short or the cornea has insufficient curvature, causing light rays to focus behind the retina.
• This condition is not applicable in the given scenario as the student can see nearby objects clearly.
• Presbyopia:
• This is an age-related condition typically occurring in individuals aged 40 and above. It leads to difficulty in focusing on nearby objects due to the loss of elasticity in the eye’s lens.
• It is corrected using bifocal lenses or progressive lenses, which aid both near and distant vision.
• The student in the question does not exhibit age-related symptoms, ruling out presbyopia.
• Cataract:
• A cataract is a condition where the eye’s lens becomes cloudy, leading to blurred vision. It is most common in older adults.
• Surgery is the only effective treatment for cataract, involving the replacement of the clouded lens with an artificial intraocular lens.
• The symptoms described in the question do not align with cataract-related vision issues.
• Important Characteristics of a Concave Lens:
• It is thinner at the center and thicker at the edges.
• It diverges light rays, making it suitable for correcting myopia by enabling light to focus correctly on the retina.
• Concave lenses are denoted with a negative power (e.g., -2.0 D).
• Global Prevalence of Myopia:
• Studies indicate that myopia is rapidly increasing worldwide, especially among children and adolescents. It is estimated that by 2050, half of the global population may be myopic.
• Factors contributing to this rise include increased screen time, reduced outdoor activities, and genetic predisposition.

Important Points

• Prevention of Myopia Progression:
• Encourage children to spend more time outdoors as natural light may reduce the progression of myopia.
• Limit screen time and ensure proper lighting while reading or studying to reduce eye strain.
• Regular eye check-ups are crucial for early detection and management of refractive errors.
• Advanced Treatments:
• Orthokeratology (Ortho-K) involves wearing specialized contact lenses to reshape the cornea temporarily.
• Refractive surgery, such as LASIK, can permanently correct myopia for eligible candidates.

The correct answer is Cytoplasm.

Key Points

• Cytoplasm is not classified as a cell organelle. It is a gel-like substance that fills the cell and acts as a medium in which cell organelles are suspended.
• The cytoplasm is a part of the cell but does not perform specific functions like organelles such as the mitochondria, endoplasmic reticulum, or Golgi apparatus.
• It serves as the site for numerous biochemical reactions and provides structural support to the cell. However, it is not considered an "organelle" since it does not have a membrane-bound structure.
• Endoplasmic Reticulum (ER), Mitochondria, and Golgi Apparatus are true organelles, as they are membrane-bound and perform specialized functions within the cell.
• The cytoplasm includes the cytosol (fluid portion), organelles, and other cellular components but is not categorized as a discrete organelle itself.

Additional Information

• Endoplasmic Reticulum (ER):
• The ER is a membrane-bound organelle found in eukaryotic cells.
• It is classified into two types: Rough ER (with ribosomes) and Smooth ER (without ribosomes).
• Functions include protein synthesis (Rough ER), lipid synthesis (Smooth ER), and detoxification of harmful substances.
• Mitochondria:
• Known as the powerhouse of the cell, mitochondria are membrane-bound organelles responsible for energy production through the process of cellular respiration.
• They generate ATP (adenosine triphosphate), which is the primary energy currency of the cell.
• Mitochondria have their own DNA and ribosomes, allowing them to produce some of their own proteins.
• Golgi Apparatus:
• The Golgi apparatus is a membrane-bound organelle involved in the processing, packaging, and transport of proteins and lipids.
• It modifies proteins produced in the ER and sorts them for transport to various destinations within or outside the cell.
• It plays a crucial role in the secretion of substances like enzymes and hormones.
• Cytoplasm:
• The cytoplasm is the jelly-like material that occupies the space between the cell membrane and the nucleus.
• It contains water, salts, and organic molecules, providing the medium for intracellular processes.
• While it plays an essential role in cell structure and function, it is not classified as an organelle because it lacks a membrane-bound structure.

Important Points

• Cell Organelles:
• Organelles are specialized structures within a cell that perform specific functions necessary for the cell's survival and function.
• Examples include the nucleus (control center), lysosomes (waste disposal), chloroplasts (photosynthesis in plant cells), and ribosomes (protein synthesis).
• Most organelles are membrane-bound, providing a distinct environment for their functions.
• Cytoplasm vs. Cytosol:
• The cytoplasm includes the cytosol (fluid), organelles, and other cellular components.
• The cytosol is specifically the fluid portion of the cytoplasm, excluding organelles.
• Both play critical roles in maintaining cellular structure and facilitating biochemical reactions.
• Prokaryotic vs. Eukaryotic Cells:
• Prokaryotic cells lack membrane-bound organelles and a defined nucleus. Examples include bacteria and archaea.
• Eukaryotic cells contain membrane-bound organelles and a nucleus. Examples include plant, animal, and fungal cells.
• The cytoplasm is present in both cell types, but organelles like mitochondria and the Golgi apparatus are exclusive to eukaryotic cells.

The correct answer is Zinc.

Key Points

• Zinc can displace iron from iron sulfate solution because zinc is more reactive than iron according to the reactivity series of metals. This series ranks metals based on their ability to lose electrons and form positive ions.
• The reactivity series places zinc above iron, indicating that zinc has a greater tendency to form ions and can replace iron in a compound.
• When zinc is introduced into an iron sulfate solution, a single displacement reaction occurs, forming zinc sulfate and displacing iron. The chemical equation is:
  

Zn + FeSO₄ → ZnSO₄ + Fe.

• Silver, Copper, and Chromium cannot displace iron from iron sulfate solution because they are less reactive than iron. Their positions in the reactivity series are lower than that of iron, indicating their inability to replace iron in a compound.
• Such displacement reactions are governed by the principles of chemical reactivity and are commonly used in applications such as metal extraction and purification.

Additional Information

• Reactivity Series:
• The reactivity series is a list of metals ranked in order of their reactivity with water, acids, and other substances. More reactive metals can displace less reactive metals from their compounds.
• In the series, potassium and sodium are the most reactive, while gold and platinum are the least reactive.
• Zinc is placed above iron in the reactivity series, enabling it to displace iron from compounds like iron sulfate.
• Displacement Reaction:
• A displacement reaction occurs when a more reactive metal displaces a less reactive metal from its compound.
• Example: In the reaction between zinc and iron sulfate, zinc replaces iron because it is more reactive.
• Displacement reactions are used in processes like metal extraction, corrosion prevention, and laboratory experiments.
• Applications of Zinc:
• Zinc is used in galvanization to prevent rusting of iron and steel.
• It plays a vital role in battery production, especially in zinc-carbon and alkaline batteries.
• Zinc compounds, such as zinc oxide, are used in cosmetics, pharmaceuticals, and rubber manufacturing.
• Iron Sulfate:
• Iron sulfate (FeSO₄) is commonly used in agriculture as a fertilizer to correct iron deficiencies in soil.
• It is also used in water treatment to remove impurities and as a precursor in the manufacture of other iron compounds.

Important Points

• Silver: Silver is a precious metal known for its low reactivity. It does not displace iron from iron sulfate solution because it is less reactive.
• Copper: Copper is also less reactive than iron and is used for electrical wiring and coinage due to its excellent conductivity and malleability.
• Chromium: Although chromium is used in stainless steel for its corrosion resistance, it cannot displace iron due to its lower position in the reactivity series.

The correct answer is Isobutane.

Key Points

• Branched-chain hydrocarbons are hydrocarbons in which carbon atoms are arranged in a non-linear structure with branches or side chains attached to the main chain.
• Isobutane is a branched-chain hydrocarbon. Its chemical structure is CH(CH3)3, where one carbon atom branches off from the main chain, forming a tertiary structure.
• Butane, on the other hand, is a straight-chain hydrocarbon with no branches. Its molecular formula is C4H10, and the carbon atoms are connected linearly.
• Propane and Ethane are also straight-chain hydrocarbons. Propane (C3H8) has three carbon atoms in a single chain, while ethane (C2H6) has two carbon atoms in a straight configuration.
• Isobutane, as a branched-chain hydrocarbon, is used widely in industries such as refrigeration and as a precursor for making other chemicals.

Additional Information

• Characteristics of branched-chain hydrocarbons:
• They generally have lower boiling points compared to their straight-chain counterparts due to decreased surface area for intermolecular forces.
• They are less prone to forming crystals, making them more suitable for use as fuels.
• Branched hydrocarbons are important in the petrochemical industry for producing high-octane fuels.
• Isobutane:
• Its molecular formula is C4H10, and it is an isomer of n-butane.
• It is widely used as a refrigerant, aerosol propellant, and in the production of isooctane, a high-octane fuel additive.
• Isobutane is produced through the refining of petroleum and natural gas.
• Applications of straight-chain hydrocarbons:
• Butane: Used in portable stoves, lighters, and as a propellant in aerosol sprays.
• Propane: Commonly used as a fuel for heating, cooking, and in engines.
• Ethane: Primarily used as a feedstock for ethylene production in the petrochemical industry.
• Hydrocarbon classification:
• Hydrocarbons are classified into alkanes, alkenes, and alkynes based on the type of bonds between carbon atoms.
• Alkanes like methane, ethane, propane, and butane consist only of single bonds and can be straight-chain or branched-chain.

Important Points

• Isomerism:
• Isomers are compounds with the same molecular formula but different structural arrangements.
• Isobutane is a structural isomer of n-butane, highlighting the importance of branching in hydrocarbons.
• Environmental impact:
• Hydrocarbons like isobutane are used as clean refrigerants because they have low ozone depletion potential (ODP).
• However, they are classified as greenhouse gases, contributing to global warming.
• Industrial relevance:
• Branched-chain hydrocarbons like isobutane enhance fuel quality by increasing the octane number, making them essential for the production of gasoline.
• Proper utilization of hydrocarbons supports energy efficiency and industrial development.

The correct answer is A compound has a fixed composition and definite properties, unlike a solution..

Key Points

• A compound is a substance formed when two or more elements chemically combine in a fixed ratio. This fixed composition gives it unique and definite physical and chemical properties.
• A solution is a homogeneous mixture of two or more substances where the composition can vary. For example, you can have different concentrations of sugar dissolved in water.
• Unlike compounds, solutions do not have fixed properties. Their properties depend on the ratio of the solute to the solvent.
• The components of a compound are bonded chemically and cannot be separated by physical methods such as filtration or evaporation. Solutions, on the other hand, can be separated using physical methods, like distillation or evaporation.
• For example, water (H₂O) is a compound with a fixed composition of hydrogen and oxygen in a 2:1 ratio, whereas saltwater is a solution where the salt concentration can vary.

Additional Information

• Characteristics of a Compound:
• Compounds have a fixed composition. For example, water always contains two hydrogen atoms and one oxygen atom.
• The properties of a compound are different from the properties of its constituent elements. For example, sodium (a reactive metal) and chlorine (a poisonous gas) combine to form sodium chloride (common table salt).
• They are formed through chemical bonds, such as ionic or covalent bonds, and require chemical reactions to separate.
• Examples include carbon dioxide (CO₂), sodium chloride (NaCl), and methane (CH₄).
• Characteristics of a Solution:
• Solutions are mixtures where the solute (e.g., salt) is completely dissolved in the solvent (e.g., water).
• They are homogeneous, meaning their composition is uniform throughout.
• Properties of solutions, such as boiling and freezing points, depend on the concentration of the solute.
• Examples include sugar water, saltwater, and alcohol mixed with water.
• Differences Between Compounds and Solutions:
• Bonding: Compounds involve chemical bonding, while solutions involve physical mixing without chemical bonding.
• Separation: Compounds require chemical methods for separation, while solutions can be separated by physical methods.
• Properties: Compounds have fixed properties, whereas solutions have variable properties depending on their composition.
• Examples: Compounds include water (H₂O) and ammonia (NH₃), while solutions include seawater and vinegar.
• Applications:
• Compounds are essential in chemical reactions, pharmaceuticals, and materials science.
• Solutions are widely used in industrial processes, medicine (e.g., saline solution), and food preparation.

Important Points

• Misconceptions Clarified:
• Statement 1: "A compound can be separated by physical methods, while a solution cannot." This is incorrect because compounds require chemical methods, not physical methods, for separation.
• Statement 3: "Compounds are always liquid, but solutions can be in any state." This is incorrect as compounds can exist in solid, liquid, or gaseous states.
• Statement 4: "Compounds are mixtures of two or more elements, while solutions are mixtures of compounds only." This is incorrect because compounds are not mixtures; they are chemically bonded substances.
• Examples for Better Understanding:
• Compound: Carbon dioxide (CO₂) used in soft drinks and fire extinguishers.
• Solution: Saltwater used in cooking and experiments.

The correct answer is Butterflies – herbivores, Squirrels – herbivores.

Key Points

• Butterflies are classified as herbivores because they primarily feed on nectar from flowers, which is a plant-based food source. Nectar provides them with energy to sustain their activities and reproduction.
• Squirrels are also classified as herbivores because their diet mainly consists of nuts, seeds, fruits, and plant-based materials. These foods provide essential nutrients and energy for their survival.
• Both butterflies and squirrels play important roles in their respective ecosystems. Butterflies help in pollination by transferring pollen from one flower to another, facilitating plant reproduction.
• Squirrels contribute to the environment by aiding in seed dispersal. As they bury nuts and seeds for later consumption, some of these remain uneaten and grow into new plants.
• The classification of organisms as herbivores, omnivores, or carnivores depends on their dietary habits and the type of food they consume regularly.

Additional Information

• Butterflies:
• Lifecycle: Butterflies undergo complete metamorphosis, including the stages of egg, larva (caterpillar), pupa (chrysalis), and adult butterfly.
• Pollination Role: Butterflies contribute to pollination, although they are less effective than bees due to their feeding behavior. They prefer bright, fragrant flowers.
• Diet: While adult butterflies feed on nectar, some caterpillars consume plant leaves, making them herbivorous during the larval stage as well.
• Habitat: Butterflies are found in diverse habitats, such as gardens, forests, grasslands, and wetlands, depending on the availability of host plants and flowers.
• Example Species: Common butterflies include the Monarch, Swallowtail, and Painted Lady.
• Squirrels:
• Diet: Squirrels primarily eat nuts, seeds, fruits, buds, and sometimes fungi. Occasionally, they may consume small insects or bird eggs, but they are predominantly herbivorous.
• Habitat: Squirrels are found in forests, urban parks, and gardens. They adapt well to human environments where food sources are abundant.
• Seed Dispersal Role: Squirrels bury seeds and nuts, many of which remain uneaten and grow into new plants, aiding forest regeneration.
• Types: Common species include the Eastern Gray Squirrel, Red Squirrel, and Flying Squirrel.
• Behavior: Squirrels are agile climbers and spend significant time in trees, building nests and foraging for food.

Important Points

• Herbivores:
• Organisms classified as herbivores rely solely on plant-based food sources like leaves, nectar, fruits, nuts, and seeds.
• Examples include deer, rabbits, elephants, butterflies, and squirrels.
• Pollination:
• Pollination is the transfer of pollen from the male part (anther) of a flower to the female part (stigma), enabling fertilization and the production of seeds.
• Butterflies, bees, birds, and other pollinators are essential for maintaining biodiversity and supporting agricultural production.
• Seed Dispersal:
• Seed dispersal mechanisms include animal activity, wind, and water. Animals like squirrels play a key role in spreading seeds across large areas.
• This process ensures plant reproduction and helps maintain ecological balance.

The correct answer is The fruits fall down due to inertia..

Key Points

• Inertia: When the tree branches are shaken vigorously, the branches experience motion due to external force, but the fruits resist this motion because of their inertia. Inertia is the property of an object to resist changes in its state of motion or rest.
• The shaking causes the branches to move rapidly back and forth, but the fruits attached to the branches remain in their initial position due to their inertia.
• Detachment of fruits: The rapid motion of the branches creates a force that weakens the attachment of the fruits to the branches. When the force exceeds the strength of the attachment, the fruits detach and fall.
• Newton's First Law: This phenomenon is explained by Newton's First Law of Motion, which states that an object will remain at rest or in uniform motion unless acted upon by an external force. The fruits initially remain at rest due to this principle.
• Direction of motion: Once detached, the fruits are influenced by gravity and fall vertically downward to the ground.

Additional Information

• Inertia of Rest: Inertia can be categorized into three types. In this case, the inertia of rest is relevant because the fruits initially remain at rest when the branches are shaken.
• Newton's Laws: The concept of inertia is a fundamental aspect of Newton's First Law of Motion, which is also known as the Law of Inertia. It explains why objects resist changes in their state of motion.
• Example: Similar examples of inertia include a passenger moving forward when a car suddenly stops or dust being removed from a carpet by vigorous shaking.
• Gravity's Role: Once the fruits detach from the branches, gravity acts upon them, causing them to accelerate downward at a rate of 9.8 m/s².
• Applications: Understanding inertia helps in various applications, such as designing safety features in vehicles (e.g., seat belts), understanding motion in sports, and analyzing forces in mechanical systems.

Important Points

• Option Analysis:
• Option 1: "The fruits fall down due to change in momentum" is incorrect because momentum involves mass and velocity, but here, the fruits are initially at rest.
• Option 3: "The fruits fall down due to action-reaction forces" is incorrect because while forces are involved, the primary reason is inertia, not action-reaction forces.
• Option 4: "The fruits fall down due to frictional force" is incorrect because friction opposes motion, and in this case, it does not play a significant role in the detachment of fruits.
• Scientific Principle: The phenomenon of fruits falling due to inertia is an excellent demonstration of Newtonian mechanics and the fundamental laws of motion.
• Educational Context: This concept is widely taught in physics to illustrate the principles of motion and forces.

The correct answer is Plants respond using hormonal and electrical-chemical signals.

Key Points

• Plants do not have a nervous system like animals. However, they can still respond to stimuli such as light, touch, gravity, and chemicals through alternative mechanisms.
• Plants primarily use hormonal signals (e.g., auxins, gibberellins, cytokinins, ethylene, and abscisic acid) to coordinate their responses to environmental changes and internal cues.
• In addition to hormones, plants also utilize electrical and chemical signaling pathways for rapid communication across cells. For example, the closure of the Venus flytrap involves electrical signals known as action potentials.
• Specific examples of plant responses include phototropism (growth towards light), thigmotropism (response to touch), and gravitropism (response to gravity), all of which are regulated by these non-nervous mechanisms.
• Although plants lack a brain or nerves, their ability to adapt and respond to their environment demonstrates a highly evolved and efficient system of communication and response. Hence, the student's statement that plants cannot respond to anything is incorrect.

Additional Information

• Plant Hormones:
• Auxins: Control cell elongation, phototropism, and gravitropism. Example: bending of plants towards light.
• Gibberellins: Promote stem elongation, seed germination, and flowering.
• Cytokinins: Stimulate cell division and delay leaf aging.
• Ethylene: Regulates fruit ripening and response to mechanical stress.
• Abscisic Acid (ABA): Facilitates stomatal closure and induces dormancy during water stress.
• Electrical Signaling in Plants:
• Plants generate action potentials and electrical signals to transmit information across cells.
• For example, Mimosa pudica (touch-me-not plant) folds its leaves when touched, a reaction triggered by electrical signaling.
• Phototropism:
• Plants grow towards a light source due to the uneven distribution of auxins.
• Auxins accumulate on the shaded side of the plant, causing cells to elongate more on that side, bending the plant towards light.
• Thigmotropism:
• It is the response of plants to touch or physical contact. For example, climbing plants like pea plants curl around support structures.
• This response is mediated by differential cell growth and signaling mechanisms.
• Gravitropism:
• Roots grow downward (positive gravitropism), and shoots grow upward (negative gravitropism) due to the redistribution of auxins.
• Gravity-sensing cells in the root cap help direct this growth pattern.

Important Points

• Comparison with Animal Nervous Systems:
• Unlike animals, plants lack specialized organs like the brain or nerves for processing and transmitting information.
• However, plants rely on hormonal and signal transduction pathways to achieve similar adaptive responses to their environment.
• Misconceptions:
• The idea that plants are incapable of response arises from the absence of visible structures like nerves or muscles. However, scientific research has shown they possess sophisticated systems for perception and reaction.
• Applications of Plant Responses:
• Understanding plant responses aids in agriculture, allowing for improved crop management and stress resistance.
• For example, the knowledge of phototropism and gravitropism is applied in optimizing plant growth in controlled environments.

The correct answer is the total energy before and after the transformation remains the same.

Key Points

• During the transformation of energy from one form to another, such as gravitational potential energy converting into kinetic energy during free fall, the total energy in the system remains conserved.
• This principle is governed by the Law of Conservation of Energy, which states that energy cannot be created or destroyed, only transformed from one form to another.
• In the case of free fall, the gravitational potential energy decreases as the object falls, while the kinetic energy increases equivalently, keeping the total mechanical energy constant in the absence of external forces like air resistance.
• The total mechanical energy (sum of kinetic energy and potential energy) remains constant throughout the motion, provided there is no energy loss to external factors like friction or air drag. Hence, this statement is correct.
• Options suggesting energy loss, increase in total energy, or creation of new energy violate the fundamental laws of physics and are incorrect.

Additional Information

• Law of Conservation of Energy:
• According to this law, the total energy in an isolated system remains constant over time.
• Energy can change forms, such as potential energy transforming into kinetic energy or heat energy, but the total quantity remains unchanged.
• Gravitational Potential Energy (GPE):
• GPE is the energy possessed by an object due to its position relative to a reference point, such as height above the ground.
• It is calculated using the formula: GPE = mgh, where m is mass, g is the gravitational acceleration (approximately 9.8 m/s²), and h is the height.
• Kinetic Energy (KE):
• KE is the energy possessed by an object due to its motion and is calculated using the formula: KE = 1/2 mv², where m is mass and v is velocity.
• As an object falls, its velocity increases, causing an increase in kinetic energy.
• Applications of Energy Conservation:
• The principle of energy conservation is fundamental in various fields, including mechanics, thermodynamics, and electrical engineering.
• Examples include the functioning of pendulums, roller coasters, and hydroelectric power plants where potential energy converts to kinetic energy or electrical energy.
• Role of Friction and Air Resistance:
• In real-world scenarios, some energy is lost as heat or sound due to friction or air resistance, making the system non-conservative.
• However, in idealized cases (e.g., vacuum environments), the total mechanical energy remains completely conserved.

The correct answer is Nature of the Functional Group.

Key Points

• Prefixes and suffixes are essential components in chemical nomenclature, particularly in organic chemistry. They indicate specific modifications based on the functional group present in the compound.
• The functional group is a specific group of atoms within a molecule that is responsible for the characteristic chemical reactions of that molecule. Examples include alcohol (-OH), aldehyde (-CHO), carboxylic acid (-COOH), etc.
• In the International Union of Pure and Applied Chemistry (IUPAC) system of nomenclature, a prefix is used to indicate substituents or side chains attached to the parent chain, while a suffix denotes the main functional group.
• The naming convention is hierarchical, where the primary functional group determines the suffix, and other substituents or groups are represented as prefixes.
• For example:
  
• Methanol (CH₃OH): The suffix "-ol" indicates the presence of an alcohol functional group.
  
• Ethanoic acid (CH₃COOH): The suffix "-oic acid" indicates the presence of a carboxylic acid functional group.

Additional Information

• Nomenclature Rules in Organic Chemistry:
• The longest continuous carbon chain is identified as the parent chain, and its name is used as the base name of the compound.
• The functional group with the highest priority (as per IUPAC hierarchy) dictates the suffix, while other substituents are named as prefixes.
• If multiple substituents are present, their positions are indicated with numbers, and the substituents are listed in alphabetical order.
• For example, 2-bromo-3-chloropentane has bromine and chlorine substituents at positions 2 and 3, respectively.
• Common Functional Groups and Their Suffixes:
• Alcohol: Suffix "-ol" (e.g., ethanol, methanol).
• Aldehyde: Suffix "-al" (e.g., formaldehyde, acetaldehyde).
• Ketone: Suffix "-one" (e.g., propanone, butanone).
• Carboxylic Acid: Suffix "-oic acid" (e.g., ethanoic acid).
• Ester: Suffix "-oate" (e.g., methyl ethanoate).
• Importance of Functional Groups:
• Functional groups determine the chemical reactivity and physical properties of compounds, such as solubility and boiling point.
• They are critical in biochemistry for understanding the structure and function of biomolecules like proteins, carbohydrates, and nucleic acids.
• For example, the hydroxyl group (-OH) in alcohols makes them polar and increases their solubility in water.
• Applications of Functional Group Identification:
• Widely used in medicinal chemistry to design drugs with specific biological activities.
• Helps in predicting the behavior of compounds in chemical reactions.
• Essential for analytical techniques like spectroscopy (e.g., IR, NMR) to identify substances based on their functional groups.

Important Points

• Hierarchy of Functional Groups in IUPAC Nomenclature:
• Functional groups are prioritized based on their reactivity and importance in the compound's structure.
• For example, carboxylic acids have higher priority over alcohols, ketones, and aldehydes.
• This hierarchy determines whether a group is named as a suffix or a prefix in the chemical name.
• Examples of Prefixes:
• Halogens like fluorine, chlorine, and bromine are named as prefixes (e.g., chloroform).
• Other groups like nitro (-NO₂) and alkyl groups (e.g., methyl, ethyl) are also used as prefixes.

The correct answer is Skeletal muscles.

Key Points

• Skeletal muscles are also known as striated muscles because they exhibit alternate light and dark bands when stained appropriately under a microscope.
• These muscles are attached to bones and play a vital role in voluntary movements of the body.
• The striated appearance is due to the organized arrangement of actin and myosin filaments within the muscle fibers, which form repeating units called sarcomeres.
• Each sarcomere is bordered by Z-lines, and the alternating light (I-bands) and dark (A-bands) regions contribute to the characteristic striations.
• Unlike other muscle types, skeletal muscles are under voluntary control, meaning their movements are consciously regulated by the nervous system.

Additional Information

• Visceral muscles:
• These are also known as smooth muscles and are found in the walls of internal organs such as the stomach, intestines, and blood vessels.
• They do not exhibit striations and are under involuntary control.
• Muscles of the alimentary canal:
• These are primarily smooth muscles that aid in the movement of food through peristalsis.
• They lack striations and function involuntarily.
• Involuntary muscles:
• This category includes both smooth muscles and cardiac muscles.
• Cardiac muscles are striated but function involuntarily, making them distinct from skeletal muscles.
• Structure of skeletal muscles:
• Skeletal muscles are composed of long, cylindrical fibers that are multinucleated.
• Each muscle fiber is surrounded by a plasma membrane known as the sarcolemma.
• These muscles are responsible for movements such as walking, running, and lifting objects.

Important Points

• Skeletal muscle examples:
• Examples include biceps, triceps, deltoids, and quadriceps.
• These muscles are attached to the skeleton via tendons, allowing movement at the joints.
• Cardiac muscles:
• Cardiac muscles are striated like skeletal muscles but are involuntary in function.
• They are found exclusively in the heart and are responsible for pumping blood throughout the body.
• Muscle contraction mechanism:
• The sliding filament theory explains how muscles contract, with actin and myosin filaments sliding over each other to shorten the sarcomere.
• This process requires energy in the form of ATP and is regulated by calcium ions and the protein troponin.

The correct answer is is always smaller than the object.

Key Points

• A convex mirror, also known as a diverging mirror, always forms a virtual, erect, and smaller image of the object irrespective of its position in front of the mirror.
• This is because convex mirrors have a curved reflecting surface that bulges outward, causing the reflected rays to diverge.
• The image is formed behind the mirror, and the size of the image is always reduced compared to the object's size.
• The nature of the image formed by a convex mirror is described using the mirror formula: 1/f = 1/v + 1/u, where:
• f = focal length (positive for convex mirrors)
• v = image distance
• u = object distance
• Convex mirrors are widely used as rear-view mirrors in vehicles because they provide a wider field of view and always produce smaller, upright images of objects, enabling drivers to see more area.

Additional Information

• Characteristics of Convex Mirrors:
• Convex mirrors always produce a virtual image (an image that cannot be projected onto a screen).
• The image is always erect (upright) and smaller in size compared to the object.
• The focal length (f) of a convex mirror is positive because the focus lies on the same side as the reflected rays.
• Applications of Convex Mirrors:
• Rear-view mirrors: Used in vehicles to provide a wider field of view, helping drivers observe traffic conditions behind them.
• Surveillance mirrors: Installed in shops, warehouses, and parking lots to monitor activities in a large area.
• Road safety: Used at blind turns on roads to help drivers see oncoming traffic.
• Comparison with Concave Mirrors:
• Concave mirrors can produce real and inverted images or virtual and erect images depending on the object's position relative to the focal point.
• In contrast, convex mirrors always produce virtual, erect, and smaller images regardless of the object's position.
• Mirror Formula and Magnification:
• The mirror formula is given as: 1/f = 1/v + 1/u.
• The magnification (m) is calculated as: m = h'/h = -v/u, where:
• h' = height of the image
• h = height of the object
• v = image distance
• u = object distance

Important Points

• Convex Mirrors in Optics:
• Convex mirrors are part of the spherical mirror family, which includes concave mirrors.
• Their reflective surface bulges outward, making them ideal for producing reduced, virtual images.
• Usage in Daily Life:
• Convex mirrors are commonly seen in public spaces such as stores and parking lots to enhance visibility.
• They are crucial for road safety at blind spots and intersections.

The correct answer is Regenerative cells.

Key Points

• Hydra, a small freshwater organism, reproduces asexually through a process called budding. In this process, a new individual grows out of the body of the parent organism.
• The type of cells responsible for reproduction in Hydra during budding are regenerative cells, which have the ability to divide and differentiate into various cell types required for forming a new organism.
• Regenerative cells in Hydra are located in the body column and play a crucial role in regenerating missing tissues or developing new buds.
• These cells ensure that the new Hydra inherits a complete and functional body structure, including tentacles and the gastrovascular cavity.
• Unlike gametic cells, which are used in sexual reproduction, regenerative cells are involved in asexual reproduction, making budding a quick and efficient mode of reproduction for Hydra.

Additional Information

• Budding Process in Hydra:
• In budding, a small outgrowth or bud forms on the parent organism due to localized cell division at a particular spot.
• This bud grows gradually, developing structures like tentacles and a mouth, and eventually detaches from the parent to live as an independent organism.
• Regenerative Cells in Other Organisms:
• Regenerative cells are also found in other organisms like planarians, starfish, and some amphibians, where they contribute to tissue repair and regeneration.
• In humans, stem cells act as regenerative cells, aiding in tissue repair and development.
• Comparison of Cell Types:
• Stomatal cells: Found in plants, responsible for gas exchange and water regulation, unrelated to reproduction in Hydra.
• Gametic cells: Involved in sexual reproduction, such as sperm and eggs, not used in asexual reproduction like budding.
• Photosynthetic cells: Specialized cells in plants and algae that carry out photosynthesis, not present in Hydra.
• Advantages of Asexual Reproduction in Hydra:
• It allows for rapid population growth as new individuals are produced quickly without the need for a mate.
• Since the offspring are genetically identical to the parent, successful traits are preserved across generations.

Important Points

• Why Hydra is a Model Organism:
• Hydra is widely used in scientific research due to its simple body structure and remarkable regenerative abilities.
• It has been extensively studied to understand the mechanisms of regeneration and stem cell biology.
• Other Modes of Reproduction in Hydra:
• Besides budding, Hydra can reproduce sexually under unfavorable conditions by producing gametes.
• This ensures genetic diversity and survival in challenging environments.
• Applications of Regenerative Biology:
• Research on regenerative cells in organisms like Hydra provides insights into potential medical applications, such as tissue engineering and regenerative medicine.
• Understanding regenerative mechanisms may lead to breakthroughs in treating injuries and degenerative diseases in humans.

The correct answer is Because the density of ice is less than that of water.

Key Points

• Ice floats on water due to its lower density: When water freezes, it expands and forms a crystalline structure that has more space between molecules. This increases the volume of ice, reducing its density compared to liquid water.
• Density of water vs. ice: The density of liquid water is approximately 1 g/cm³, while the density of ice is about 0.92 g/cm³. This lower density allows ice to float.
• Hydrogen bonding: Water molecules form hydrogen bonds in ice, creating a lattice structure. This structure is less compact than in liquid water, making ice less dense.
• Buoyancy principle: Ice displaces an amount of water equal to its weight, and since it is less dense, it floats on the surface of the water.
• Thermal insulation effect: Floating ice forms a layer on water bodies, preventing the water below from freezing completely. This is crucial for aquatic life survival during winters.

Additional Information

• Density: Density is defined as mass per unit volume. For water, the maximum density occurs at 4°C, and as it cools further, the density decreases as it transitions to ice.
• Hydrogen Bonding in Water: Water molecules are polar, and hydrogen bonding is responsible for the unique properties of water, including its lower density in the solid state (ice).
• Role of Ice in the Environment: Ice floating on water bodies acts as an insulator, protecting aquatic ecosystems by maintaining stable temperatures beneath the ice.
• Applications: This property of ice is vital for biological and environmental processes, such as the survival of aquatic organisms during freezing temperatures.
• Other Substances: Unlike water, most substances are denser in their solid state than in their liquid state. Water's behavior is an exception due to its molecular structure.

Important Points

• Option 2 (Ice is at a lower temperature): This is incorrect. While ice is colder than liquid water, its floating property is attributed to its lower density, not temperature.
• Option 3 (Displaces water equal to its weight): This is partially true but not the primary reason. The lower density of ice compared to water is the main factor enabling it to float.
• Option 4 (Weight of ice is very small): Incorrect. The weight of ice is not the determining factor; its density relative to water is what matters.

The correct answer is Pascal.

Key Points

• SI Unit of Pressure: The SI unit of pressure is the Pascal (Pa), named after the French mathematician, physicist, and philosopher Blaise Pascal.
• One Pascal is defined as the pressure exerted when a force of 1 Newton (N) is applied uniformly over an area of 1 square meter (m²).
• Pressure is mathematically expressed as P = F/A, where P is pressure, F is force, and A is the area over which the force is applied.
• Pascal Conversion: 1 Pascal is equal to 1 N/m². In other units, 1 atmosphere (atm) is approximately 101,325 Pascals, and 1 mmHg is approximately 133.322 Pascals.
• Pascal is widely used in various fields, including physics, engineering, meteorology, and fluid mechanics, for measuring pressure in gases, liquids, and solids.

Additional Information

• Other Units of Pressure:
• mmHg (millimeters of Mercury): Commonly used in medical fields, especially in measuring blood pressure. 1 mmHg = 133.322 Pascals.
• Atmosphere (atm): Used in meteorology and scuba diving. 1 atm = 101,325 Pascals.
• Torr: Equivalent to 1 mmHg. It is often used in vacuum measurements. 1 Torr = 133.322 Pascals.
• Bar: Another unit of pressure used in meteorology and engineering. 1 bar = 100,000 Pascals.
• Applications of Pressure Measurement:
• In meteorology, pressure is used to measure atmospheric conditions, with instruments like barometers.
• In medical science, blood pressure is measured using units like mmHg.
• In engineering, pressure is crucial for designing hydraulic systems, aerodynamics, and structural integrity tests.
• In fluid mechanics, pressure is a key parameter in studying fluid behavior and dynamics.
• Historical Context: Blaise Pascal's work in fluid mechanics and the study of pressure laid the groundwork for adopting the Pascal as the SI unit of pressure in the 20th century.
• Important Conversion Factors:
• 1 atm = 760 mmHg = 101,325 Pascals.
• 1 bar = 100,000 Pascals.
• 1 psi (pound per square inch) = 6,894.76 Pascals.

Important Points

• SI Units: The International System of Units (SI) is the globally accepted system for measuring physical quantities, ensuring uniformity and standardization worldwide.
• Derived Units: Pressure is a derived quantity in the SI system, expressed in terms of base SI units (kg·m⁻¹·s⁻²).
• Relevance of Standard Units: Standardized units like the Pascal ensure consistency in scientific research, industrial applications, and education.
• Real-World Example: The air pressure in car tires is often expressed in units like psi or bar, but it can be converted to Pascals for precise scientific calculations.

Shortcut Trick

Find LCM of 56, 80, 16 and 60.

LCM (56, 80, 16, 60) = 1680.

The number must be of form (1680 × k) + 2.

For k = 3, target number = 5040 + 2 = 5042.

Smallest natural number to add = 5042 − 4478 = 564.

∴ The correct answer is 564.

Alternate Method

Given: Numbers = 56, 80, 16, 60; Remainder = 2; Initial number = 4478.

Formula: Target Number = [LCM(divisors) × k] + Remainder.

⇒ Prime Factorization:

⇒ 56 = 2³ × 7

⇒ 80 = 2⁴ × 5

⇒ 16 = 2⁴

⇒ 60 = 2² × 3 × 5

⇒ LCM = 2⁴ × 3 × 5 × 7 = 16 × 105 = 1680.

⇒ Multiple of 1680 just greater than 4478:

⇒ 1680 × 2 = 3360 (Smaller than 4478)

⇒ 1680 × 3 = 5040.

⇒ Resulting Number = 5040 + 2 = 5042.

⇒ Number to be added = 5042 − 4478 = 564.

∴ The correct answer is 564.

Additional Information

LCM and Remainder Concept

The smallest number which when divided by a, b, and c leaves a remainder r in each case is LCM(a, b, c) + r.

Multiple LCM Application

For problems requiring a number close to a specific value, find the general form [LCM × k + r] and solve for the integer k.

Shortcut Trick

Total Work = 20 × 18 = 360 units.

Let 9 men leave after x days. Remaining men = 11.

Total Work = (20 × x) + (11 × (30 − x)) = 360.

20x + 330 − 11x = 360 ⇒ 9x = 30 ⇒ x = 30/9 = 10/3 days.

∴ The correct answer is 10/3 days.

Alternate Method

Given: Initial men (M₁) = 20, Days (D₁) = 18. Target Days = 30.

Formula Used: Total Work = Men × Days

⇒ Total Work = 20 × 18 = 360 man-days

⇒ Let 9 men stop working after x days.

⇒ For the first x days, 20 men worked: Work done = 20 × x

⇒ After 9 men left, remaining men = 20 − 9 = 11 men.

⇒ These 11 men worked for the remaining (30 − x) days.

⇒ Work done by 11 men = 11 × (30 − x)

⇒ 20x + 11(30 − x) = 360

⇒ 20x + 330 − 11x = 360

⇒ 9x = 360 − 330

⇒ 9x = 30

⇒ x = 30/9 = 10/3 days

∴ The correct answer is 10/3 days.

Additional Information

Chain Rule Formula

The relationship between men, days, and work is given by (M₁×D₁×H₁)/W₁ = (M₂×D₂×H₂)/W₂.

Inverse Proportion

For a constant amount of work, the number of men is inversely proportional to the time taken (M ∝ 1/D).

Total Work Concept

Total work is always considered as the product of efficiency and time. Here, efficiency of 1 man is assumed as 1 unit/day.

Shortcut Trick

Relative Speed (opposite direction) = 16 + 29 = 45 km/hr.

Time taken = Distance ÷ Relative Speed = 60 ÷ 45 hours.

Time in minutes = (60 ÷ 45) × 60 = 4 × 20 = 80 min.

∴ The correct answer is 80 min.

Alternate Method

Given:

Initial Distance between engines = 60 km

Speed of first engine (S₁) = 16 km/hr

Speed of second engine (S₂) = 29 km/hr

Formula Used:

Relative Speed (opposite) = S₁ + S₂

Time = Distance ÷ Relative Speed

Calculations:

⇒ Relative Speed = 16 + 29 = 45 km/hr

⇒ Time (in hours) = 60 ÷ 45

⇒ Time (in hours) = 4/3 hours

⇒ Time (in minutes) = (4/3) × 60

⇒ Time = 4 × 20 = 80 min

∴ The correct answer is 80 min.

Additional Information

Relative Speed Concept

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

Time-Speed-Distance Relation

Distance = Speed × Time. To convert km/hr to m/s, multiply by 5/18. To convert hours to minutes, multiply by 60.

Meeting Point Distance

The distance from the starting point of engine A to the meeting point = Speed of A × Meeting Time.

Shortcut Trick

Cutting a sphere into 4 equal parts through the center creates 4 new circular faces in total.

Total Surface Area (TSA) = Original Surface Area + 4 × Area of Circle = 4πr² + 4πr² = 8πr².

Given diameter = 14 cm ⇒ radius (r) = 7 cm.

TSA = 8 × (22/7) × 7 × 7 = 8 × 154 = 1232 cm².

∴ The correct answer is 1232 cm².

Alternate Method

Given:

Diameter of the sphere (D) = 14 cm

Radius of the sphere (r) = D/2 = 14/2 = 7 cm

Formula Used:

Total Surface Area of 4 equal parts = Original Curved Surface Area + Area of all flat faces created by cuts.

Calculations:

⇒ When a sphere is cut into 4 equal parts by two perpendicular planes, each part is a quarter sphere.

⇒ Surface Area of one quarter part = (1/4) × 4πr² + 2 × (1/2)πr² = 2πr²

⇒ Total Surface Area of 4 such parts = 4 × 2πr² = 8πr²

⇒ TSA = 8 × (22/7) × 7 × 7

⇒ TSA = 8 × 22 × 7

⇒ TSA = 1232 cm²

∴ The correct answer is 1232 cm².

Additional Information

Surface Area of Sphere

The total surface area of a complete sphere with radius r is given by 4πr².

Total Surface Area of Hemisphere

For a hemisphere, the TSA includes the curved surface (2πr²) and the flat base area (πr²), totaling 3πr².

Volume of Sphere

The volume or capacity of a sphere is calculated using the formula V = (4/3)πr³.

Shortcut Trick

Income ratio = 5 : 8, Expenditure ratio = 1 : 4

Difference in income parts (8 − 5 = 3) and expenditure parts (4 − 1 = 3) is same.

Income − Expenditure = Savings ⇒ 5 − 1 = 4 units or 8 − 4 = 4 units.

4 units = ₹78,000 → 1 unit = ₹19,500.

Gopal's income (5 units) = 5 × 19,500 = ₹97,500.

∴ The correct answer is ₹97500.

Alternate Method

Given: Ratio of incomes = 5 : 8, Ratio of expenditures = 1 : 4, Savings = ₹78,000 each.

Formula: Income − Savings = Expenditure

⇒ Let incomes be 5x and 8x.

⇒ (5x − 78,000) / (8x − 78,000) = 1 / 4

⇒ 4(5x − 78,000) = 1(8x − 78,000)

⇒ 20x − 3,12,000 = 8x − 78,000

⇒ 12x = 2,34,000

⇒ x = 19,500

⇒ Gopal's income = 5x = 5 × 19,500 = 97,500

∴ The correct answer is ₹97500.

Additional Information

Income, Expenditure, and Savings Relationship

The fundamental equation is Income = Expenditure + Savings. For two people with same savings, the difference between their incomes equals the difference between their expenditures.

Cross Multiplication Method

When two ratios and a constant change (savings) are given: (Ratio1_a × Ratio2_b) − (Ratio1_b × Ratio2_a) units = Savings × (Ratio2_b − Ratio2_a).

Ratio Balancing

To make differences equal, multiply one ratio by the difference of the other ratio's terms: New Ratio = Old Ratio × (Difference of other ratio terms).

Shortcut Trick

Selling Price (SP) = CP × (100 − Discount%) ÷ 100

SP = 2,400 × (100 − 41) ÷ 100

SP = 2,400 × 59 ÷ 100

SP = 24 × 59 = 1,416

∴ The correct answer is ₹1,416.

Alternate Method

Given: Cost Price (CP) = ₹2,400, Discount Rate = 41% on CP. Formulas: Discount Amount = (Discount% ÷ 100) × CP | SP = CP − Discount Amount.

⇒ Discount Amount = (41 ÷ 100) × 2,400 ⇒ Discount Amount = 41 × 24 = ₹984 ⇒ Selling Price (SP) = 2,400 − 984 ⇒ SP = 1,416

∴ The correct answer is ₹1,416.

Additional Information

Discount Calculation

A discount is a reduction in price. Usually, it is calculated on the Marked Price (MP), but if the problem specifies the Cost Price (CP), we apply the percentage directly to the CP.

Selling Price Formula

When a discount is offered on CP, SP = CP × (100 − D%) / 100. This is similar to a Loss Percentage calculation.

Shortcut Trick

Present ratio of Mr. Gupta and Daughter = 3 : 1

Ratio after 6 years = 5 : 2

To make the gap between ratio parts equal: (3:1) × 1 and (5:2) is not balanced. Check cross-product: (3×2 − 5×1) units = 6 years × (5 − 2)

⇒ (6 − 5) units = 6 × 3 ⇒ 1 unit = 18 years

Daughter's present age = 1 unit = 18 years.

∴ The correct answer is 18 years.

Alternate Method

Let the present age of the daughter be x years.

Then, the present age of Mr. Gupta = 3x years.

According to the question, after 6 years:

⇒ (3x + 6) / (x + 6) = 5 / 2

⇒ 2 × (3x + 6) = 5 × (x + 6)

⇒ 6x + 12 = 5x + 30

⇒ 6x − 5x = 30 − 12

⇒ x = 18

∴ The correct answer is 18 years.

Additional Information

Ratio and Proportion in Ages

The difference between the ages of two persons remains constant throughout their lives. This property is often used to balance ratios by multiplying with appropriate constants.

Linear Equation Method

For age problems involving multiple time frames (past/future), setting up a linear equation in one variable (x) based on the given ratio is the most reliable approach.

Shortcut Trick

Total Valid Votes = 9000

NOTA = 1% of 9000 = 90

Remaining for P + Q = 9000 − 90 − 5830 = 3080

P receives 4 parts of 3080 (since Q = 1/4 of P ⇒ P:Q = 4:1) = 4/5 × 3080 = 2464

R (highest in R:S = 3:2) = 3/5 × 5830 = 3498

Comparing P(2464), Q(616), R(3498), S(2332), the maximum is 3498.

∴ The correct answer is 3498 votes.

Alternate Method

Given: Total Valid Votes = 9000, NOTA = 1%, R + S = 5830, Ratio R : S = 3 : 2, Q = 25% of P.

⇒ NOTA Votes = 1% × 9000 = 90

⇒ Votes for R = 5830 × (3 / 5) = 1166 × 3 = 3498

⇒ Votes for S = 5830 × (2 / 5) = 1166 × 2 = 2332

⇒ Remaining Votes (P + Q) = 9000 − (5830 + 90) = 9000 − 5920 = 3080

⇒ Ratio P : Q = 100 : 25 = 4 : 1

⇒ Votes for P = 3080 × (4 / 5) = 616 × 4 = 2464

⇒ Votes for Q = 3080 × (1 / 5) = 616

⇒ Comparing all candidates: P = 2464, Q = 616, R = 3498, S = 2332.

⇒ Winning Candidate = R = 3498

∴ The correct answer is 3498 votes.

Additional Information

Ratio and Proportion

To divide a quantity X into a ratio a:b, the parts are [a/(a+b)] × X and [b/(a+b)] × X.

Percentage to Ratio Conversion

25% is equivalent to 1/4. If Q is 25% of P, then Q = P/4 or P:Q = 4:1.

Winning Margin

The winning margin is the difference between the votes of the winner and the immediate runner-up.

Shortcut Trick

In right-angled ΔBDC, ∠C = 90° − ∠DBC = 90° − 71° = 19°.

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

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

∠AEB = 57° + 19° = 76°.

∴ The correct answer is 76°.

Alternate Method

Given: BD ⊥ AC, ∠DBC = 71°, and ∠CAE = 57°.

Formula Used: Angle sum property of a triangle and the Exterior Angle Theorem.

⇒ In ΔBDC, ∠BDC = 90° (since BD ⊥ AC).

⇒ ∠BCD = 180° − (∠BDC + ∠DBC)

⇒ ∠BCD = 180° − (90° + 71°) = 180° − 161° = 19°.

⇒ In ΔAEC, the angle ∠ACE is the same as ∠BCD, so ∠ACE = 19°.

⇒ Point E lies on BC, making ∠AEB the exterior angle to ΔAEC at vertex E.

⇒ ∠AEB = ∠CAE + ∠ACE

⇒ ∠AEB = 57° + 19° = 76°.

∴ The correct answer is 76°.

Additional Information

Exterior Angle Theorem

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

Angle Sum Property

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

Complementary Angles in Right Triangles

In a right-angled triangle, the two acute angles are always complementary, meaning their sum is 90°.

Shortcut Trick

Combined efficiency of A, B and C working together can be found using the LCM method.

LCM of 3, 24, and 8 is 24, which is the Total Work.

Combined efficiency = 8 + 1 + 3 = 12 units/day.

Time taken for twice the work = (2 × 24) ÷ 12 = 4 days.

∴ The correct answer is 4 days.

Alternate Method

Given:

Time taken by A = 3 days

Time taken by B = 24 days

Time taken by C = 8 days

Formula Used:

Total Work = LCM of individual times

Efficiency = Total Work ÷ Individual Time

Time = Total Work ÷ Total Efficiency

Calculations:

⇒ Total Efficiency of A + B + C = 8 + 1 + 3 = 12 units/day

⇒ Total Work to be done = 2 × 24 = 48 units

⇒ Time taken = 48 ÷ 12 = 4 days

∴ The correct answer is 4 days.

Additional Information

Time and Work Relation

Time and efficiency are inversely proportional to each other. If efficiency is doubled, the time taken to complete the same work is halved.

Work and Wages

Wages are always distributed in the direct ratio of the work done by individuals, which is equal to the ratio of their efficiencies when they work for the same duration of time.

Shortcut Trick

Teacher age = New Average + (Previous Count × Increase in Average)

Increase in average = 20 − 19 = 1 year

Teacher age = 20 + (57 × 1)

Teacher age = 20 + 57 = 77 years

∴ The correct answer is 77 years.

Alternate Method

Given:

Number of students = 57

Average age of students = 19 years

New average age (including teacher) = 20 years

Formula Used:

Total Age = Average × Number of persons

Calculations:

⇒ Total age of 57 students = 57 × 19

⇒ Total age of 57 students = 1083 years

⇒ Total number of persons = 57 + 1 = 58

⇒ Total age of 58 persons = 58 × 20

⇒ Total age of 58 persons = 1160 years

⇒ Age of teacher = Total age of 58 persons − Total age of 57 students

⇒ Age of teacher = 1160 − 1083

⇒ Age of teacher = 77 years

∴ The correct answer is 77 years.

Additional Information

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Net Deviation Method

In any distribution, the sum of deviations taken from the actual mean is always zero.

Properties of Average

If each number in a dataset is increased by a constant 'k', the average of the dataset also increases by 'k'.

Shortcut Trick

Time taken for 2 pages = 40 minutes.

Time taken for 1 page = 40 ÷ 2 = 20 minutes.

Time taken for 96 pages = 96 × 20 = 1920 minutes.

∴ The correct answer is 1920 minutes.

Alternate Method

Given:

Number of pages (W₁) = 2 pages

Time taken (T₁) = 40 minutes

Number of pages (W₂) = 96 pages

Formula Used:

Since the rate of work is constant, we use the Unitary Method or the work-time ratio: (W₁ / T₁) = (W₂ / T₂)

Calculations:

⇒ 2 / 40 = 96 / T₂

⇒ 1 / 20 = 96 / T₂

⇒ T₂ = 96 × 20

⇒ T₂ = 1920 minutes

∴ The correct answer is 1920 minutes.

Additional Information

Unitary Method

It is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Direct Proportion

In this case, Work is directly proportional to Time. If the number of pages increases, the time taken will also increase proportionally (W₁/T₁ = W₂/T₂).

Time and Work Relation

The basic formula used in time and work is Work = Efficiency × Time. Here, efficiency of the typist remains constant.

Shortcut Trick

Total Marked Price (MP) = 600 × 91 = ₹54,600.

Using the multiplier method: Final Price = MP × (1 − d₁/100) × (1 − d₂/100) × (1 − d₃/100).

Successive multipliers are 0.75, 0.75, and 0.72.

Final Cash Payment = 54,600 × 3/4 × 3/4 × 18/25 = 54,600 × 162/400.

Final Cash Payment = 136.5 × 162 = ₹22,113.

∴ The correct answer is ₹22,113.

Alternate Method

Given → Quantity = 600 pairs, Price per pair = ₹91, Discounts = 25%, 25%, and 28%. Formulas: Total MP = Quantity × Price | Net SP = MP × (100 − D₁)% × (100 − D₂)% × (100 − D₃)%

⇒ Total MP = 600 × 91 = ₹54,600. ⇒ After 1^st discount of 25%: 54,600 × 0.75 = ₹40,950. ⇒ After 2^nd discount of 25%: 40,950 × 0.75 = ₹30,712.5. ⇒ After 3^rd discount of 28% (Cash): 30,712.5 × 0.72 = ₹22,113.

∴ The correct answer is ₹22,113.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the net discount is not the simple sum. Two discounts a% and b% result in a net discount of (a + b − ab/100)%.

Marked Price (MP)

The price listed on the product or invoice before any discounts are applied. Selling Price = MP × (100 − Discount%)/100.

Shortcut Trick

Convert fractions to a common denominator: 1/20 = 5/100.

Required percentage = (First value ÷ Second value) × 100

Calculation: (5/100 ÷ 11/100) × 100 = 5/11 × 100 ≈ 45.45%

∴ The correct answer is 45.45%.

Alternate Method

Given: First value = 1/20, Second value = 11/100

Formula Used: Percentage = (Part ÷ Whole) × 100

⇒ Required % = [(1/20) / (11/100)] × 100

⇒ Required % = (1/20) × (100/11) × 100

⇒ Required % = (5/11) × 100

⇒ Required % = 500 ÷ 11

⇒ Required % = 45.4545...

∴ The correct answer is 45.45%.

Additional Information

Fraction to Percentage

To convert any fraction a/b to a percentage, multiply it by 100 and add the % symbol.

Percentage Comparison

When comparing two fractions, it is often easier to equate their denominators or convert both to decimals first.

Reciprocal values

Knowing that 1/11 ≈ 9.09% helps in calculating 5/11 as 5 × 9.09% = 45.45% quickly.

Shortcut Trick

Factorize the expression: x⁴ − 1 = (x² − 1)(x² + 1) and x³ − 1 = (x − 1)(x² + x + 1).

Substitute these into the expression: [(x² − 1)(x² + 1)(x² + x + 1)] ÷ [(x − 1)(x² + x + 1)(x² + 1)].

Cancel common factors (x² + 1) and (x² + x + 1) to get (x² − 1) ÷ (x − 1).

Simplify further: (x − 1)(x + 1) ÷ (x − 1) = x + 1.

∴ The correct answer is x + 1.

Alternate Method

Given:

Expression = ((x⁴ − 1)(x² + x + 1)) ÷ ((x³ − 1)(x² + 1))

Formula Used:

1. a² − b² = (a − b)(a + b)
2. a³ − b³ = (a − b)(a² + ab + b²)

Calculations:

⇒ Simplify x⁴ − 1: (x²)² − (1)² = (x² − 1)(x² + 1) = (x − 1)(x + 1)(x² + 1)

⇒ Simplify x³ − 1: (x − 1)(x² + x × 1 + 1²) = (x − 1)(x² + x + 1)

⇒ Substitute these back into the original expression:

⇒ [((x − 1)(x + 1)(x² + 1)) × (x² + x + 1)] ÷ [((x − 1)(x² + x + 1)) × (x² + 1)]

⇒ Cancel the common terms from the numerator and denominator:

⇒ Terms to cancel: (x − 1), (x² + 1), and (x² + x + 1)

⇒ Remaining term = x + 1

∴ The correct answer is x + 1.

Additional Information

Algebraic Identities

Difference of Squares: a² − b² = (a − b)(a + b). This is used for simplifying even powers like x⁴ − 1.

Cubic Identities

Difference of Cubes: a³ − b³ = (a − b)(a² + ab + b²). Sum of Cubes: a³ + b³ = (a + b)(a² − ab + b²).

Simplification Tip

Always factorize completely before canceling. For complex fractions, identify common algebraic factors in the numerator and denominator to reduce the expression.

Shortcut Trick

Using the identity 1 − sin² B = cos² B.

The equation becomes cos² B = K × sin² B.

Dividing both sides by sin² B gives K = cos² B ÷ sin² B.

Since cos B ÷ sin B = cot B, then K = cot² B.

∴ The correct answer is cot² B.

Alternate Method

Given: 1 − sin² B = K × sin² B

Formula used: sin² θ + cos² θ = 1 and cot θ = cos θ ÷ sin θ

⇒ 1 − sin² B = K × sin² B

⇒ cos² B = K × sin² B

⇒ K = cos² B / sin² B

⇒ K = (cos B / sin B)²

⇒ K = cot² B

∴ The correct answer is cot² B.

Additional Information

Pythagorean Identities

Fundamental relations: sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Reciprocal Ratios

Relationship between ratios: tan θ = sin θ ÷ cos θ and cot θ = cos θ ÷ sin θ = 1 ÷ tan θ.

Shortcut Trick

For two numbers, if Sum (S) and Difference (D) are given:

Larger Number = (Sum + Difference) ÷ 2

Larger Number = (40 + 14) ÷ 2 = 54 ÷ 2 = 27

∴ The correct answer is 27.

Alternate Method

Given:

Sum of two integers = 40

Difference of two integers = 14

Let the two integers be x and y, where x is the larger integer.

⇒ x + y = 40 --- (Equation 1)

⇒ x − y = 14 --- (Equation 2)

Adding Equation 1 and Equation 2:

⇒ (x + y) + (x − y) = 40 + 14

⇒ 2x = 54

⇒ x = 54 ÷ 2

⇒ x = 27

∴ The correct answer is 27.

Additional Information

Finding the Smaller Integer

The smaller integer can be found using the formula: (Sum − Difference) ÷ 2. In this case, (40 − 14) ÷ 2 = 13.

Linear Equations in Two Variables

When solving equations of form x+y=a and x−y=b, the values are always x = (a+b)/2 and y = (a−b)/2.

Product of the Numbers

The product of these two integers can be calculated as x × y = 27 × 13 = 351.

Shortcut Trick

For two numbers x and y, the mean proportional is √(x × y).

Given 28 = √(A × 112)

Square both sides: 28 × 28 = A × 112

A = (28 × 28) ÷ 112 = 784 ÷ 112 = 7

∴ The correct answer is 7.

Alternate Method

Given:

First number = A

Second number = 112

Mean Proportional = 28

Formula Used:

Mean Proportional (M) = √(First number × Second number)

Calculations:

⇒ 28 = √(A × 112)

⇒ 28² = A × 112

⇒ 784 = A × 112

⇒ A = 784 ÷ 112

⇒ A = 7

∴ The correct answer is 7.

Additional Information

Third Proportional

The third proportional of two numbers a and b is given by c = b² ÷ a.

Fourth Proportional

For three numbers a, b, and c, the fourth proportional d is calculated as d = (b × c) ÷ a.

Continued Proportion

Three quantities a, b, c are in continued proportion if a/b = b/c, where b is the mean proportional.

Shortcut Trick Use the Empirical Formula: Mode = 3 × Median − 2 × Mean. Given Mean × Mode = 24 and Median × Mean = 32. Let Mean = x. Substitute 24/x = 3(32/x) − 2x ⇒ 24/x = 96/x − 2x ⇒ 2x = 72/x ⇒ x2 = 36 ⇒ Mean = 6. Then Mode = 4 and 3 × Median = 3 × (32/6) = 16. Expression = √(62 + 162 + 42) = √308 = 2√(7 × 11). Here a = 2, b = 7. ∴ The correct answer is 3. Alternate Method Given: Mean (A) × Mode (Mo) = 24 Median (Me) × Mean (A) = 32 Formula Used: Mode = 3 × Median − 2 × Mean

Calculations: ⇒ Mo = 24/A and Me = 32/A ⇒ 24/A = 3 × (32/A) − 2A ⇒ 24/A = 96/A − 2A ⇒ 2A = 96/A − 24/A = 72/A ⇒ 2A2 = 72 ⇒ A2 = 36 ⇒ Mean (A) = 6 ⇒ Mode (Mo) = 24/6 = 4 ⇒ 3 × Median (3Me) = 3 × (32/6) = 16 ⇒ √[A2 + (3Me)2 + Mo2] = √[62 + 162 + 42] ⇒ √[36 + 256 + 16] = √308 ⇒ √308 = √(4 × 77) = 2 × √(7 × 11) ⇒ Comparing with a × √(b × 11): a = 2, b = 7 ⇒ √(a + b) = √(2 + 7) = √9 = 3 ∴ The correct answer is 3. Additional Information Empirical Relationship For a moderately skewed distribution, the relationship is Mode = 3 × Median − 2 × Mean. Symmetrical Distribution In a perfectly symmetrical distribution, the Mean, Median, and Mode are all equal (Mean = Median = Mode). Skewness Property In a positively skewed distribution, Mean > Median > Mode. In a negatively skewed distribution, Mode > Median > Mean.

Shortcut Trick

Average Speed = (Total Distance) ÷ (Total Time)

Total Distance = (20 × 80) + (50 × 70) = 1600 + 3500 = 5100 m

Total Time = 80 + 70 = 150 min

Average Speed = 5100 ÷ 150 = 34 m/min

∴ The correct answer is 34 m/min.

Alternate Method

Given:

Speed₁ = 20 m/min, Time₁ = 80 min

Speed₂ = 50 m/min, Time₂ = 70 min

Formula Used:

Distance = Speed × Time

Average Speed = (Total Distance) ÷ (Total Time)

⇒ Distance₁ = 20 × 80 = 1600 m

⇒ Distance₂ = 50 × 70 = 3500 m

⇒ Total Distance = 1600 + 3500 = 5100 m

⇒ Total Time = 80 + 70 = 150 min

⇒ Average Speed = 5100 ÷ 150

⇒ Average Speed = 34 m/min

∴ The correct answer is 34 m/min.

Additional Information

Weighted Average of Speeds

When the time durations t₁ and t₂ are known, Average Speed = (s₁t₁ + s₂t₂) ÷ (t₁ + t₂).

Harmonic Mean for Equal Distances

If distances are equal, the average speed is the harmonic mean of the speeds: 2s₁s₂ ÷ (s₁ + s₂).

Relative Speed

In the same direction, speed = s₁ − s₂. In opposite directions, speed = s₁ + s₂.

Shortcut Trick

Initial product ratio (Volume) = 1 × 2 × 3 = 6

New dimensions ratio = (1 × 200%) : (2 × 150%) : (3 × 180%) = 2 : 3 : 5.4

New product ratio (Volume) = 2 × 3 × 5.4 = 32.4

Percentage increase = [(32.4 − 6) ÷ 6] × 100 = (26.4 ÷ 6) × 100 = 440%

∴ The correct answer is 440%.

Alternate Method

Given: Ratio of Length (L), Breadth (B), and Height (H) = 1 : 2 : 3. Percentage increases are 100%, 50%, and 80% respectively.

Formula Used: Volume of Cuboid = L × B × H

⇒ Let L = 1x, B = 2x, H = 3x

⇒ Initial Volume (V₁) = 1x × 2x × 3x = 6x³

⇒ New Length (L') = 1x + 100% of 1x = 2x

⇒ New Breadth (B') = 2x + 50% of 2x = 3x

⇒ New Height (H') = 3x + 80% of 3x = 3x + 2.4x = 5.4x

⇒ New Volume (V₂) = 2x × 3x × 5.4x = 32.4x³

⇒ Increase in Volume = 32.4x³ − 6x³ = 26.4x³

⇒ Percentage Increase = (Increase ÷ V₁) × 100

⇒ Percentage Increase = (26.4x³ ÷ 6x³) × 100 = 4.4 × 100 = 440%

∴ The correct answer is 440%.

Additional Information

Total Surface Area of Cuboid

The total area of all six faces of the cuboid is given by TSA = 2(LB + BH + HL).

Diagonal of a Cuboid

The longest rod that can be placed inside a cuboid is its diagonal, calculated as D = √(L² + B² + H²).

Successive Percentage Change

If dimensions change by a%, b%, and c%, the final volume becomes (1 + a/100)(1 + b/100)(1 + c/100) times the original.

Shortcut Trick

Initial Ratio (Acid : Water) = 4 : 3

Final Ratio (Acid : Water) = 8 : 4 = 2 : 1

Make Water parts equal: Initial (4 : 3) and Final (6 : 3)

Total initial parts = 4 + 3 = 7 units → 532 litres. So, 1 unit = 76 litres.

Acid added = 6 − 4 = 2 units ⇒ 2 × 76 = 152 litres.

∴ The correct answer is 152 litres.

Alternate Method

Initial Quantity = 532 litres

Initial Ratio (Acid : Water) = 4 : 3

⇒ Quantity of Acid = (4/7) × 532 = 304 litres

⇒ Quantity of Water = (3/7) × 532 = 228 litres

Let 'x' litres of Acid be added.

⇒ (304 + x) / 228 = 8 / 4

⇒ (304 + x) / 228 = 2 / 1

⇒ 304 + x = 456

⇒ x = 456 − 304 = 152 litres

∴ The correct answer is 152 litres.

Additional Information

Constant Quantity Rule

When one component is added to a mixture, the quantity of the other component remains constant. Always equate the parts of the constant component in both ratios.

Ratio Balancing

To balance ratios, multiply the entire ratio by a factor such that the value of the unchanged substance becomes the same in both the initial and final states.

Mixture Replacement

If a part of the mixture is replaced by a component, the quantity of the other component decreases proportionally before the addition.

Given:

90 − [36 ÷ 3 + 2 × (P² − 21)] ÷ 3 = 70 ÷ 3

Formula Used:

BODMAS rule

Calculation:

⇒ 90 − [12 + 2 × (P² − 21)] ÷ 3 = 70 ÷ 3

⇒ 90 − [12 + 2P² − 42] ÷ 3 = 70 ÷ 3

⇒ 90 − [2P² − 30] ÷ 3 = 70 ÷ 3

⇒ 90 − (2P² − 30) ÷ 3 = 70 ÷ 3

⇒ Multiply both sides by 3

⇒ 270 − (2P² − 30) = 70

⇒ 270 − 2P² + 30 = 70

⇒ 300 − 2P² = 70

⇒ 2P² = 300 − 70

⇒ 2P² = 230

⇒ P² = 115

⇒ P = √115

∴ The correct answer is √115.

Shortcut Trick

Net difference in interest rates per annum = 7% − 3.5% = 3.5%

Total difference for 3 years = 3.5% × 3 = 10.5%

Required Interest Difference = 10.5% of ₹4,60,000

Value = 0.105 × 4,60,000 = ₹48,300

∴ The correct answer is ₹48,300.

Alternate Method

Given:

Principal (P) = ₹4,60,000 | Time (T) = 3 years | Rate A (R₁) = 3.5% | Rate B (R₂) = 7%

Formula Used:

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

Calculations:

⇒ SI from Bank A = (4,60,000 × 3.5 × 3) ÷ 100

⇒ SI from Bank A = 4,600 × 10.5 = ₹48,300

⇒ SI from Bank B = (4,60,000 × 7 × 3) ÷ 100

⇒ SI from Bank B = 4,600 × 21 = ₹96,600

⇒ Positive Difference = SI from Bank B − SI from Bank A

⇒ Positive Difference = ₹96,600 − ₹48,300 = ₹48,300

∴ The correct answer is ₹48,300.

Additional Information

Simple Interest Amount Formula

The total amount (A) after T years is given by A = P + SI = P[1 + (R × T) ÷ 100].

Interest Difference Shortcut

When the principal and time are the same, the difference in SI is directly proportional to the difference in rates: Difference = P × T × (R₂ − R₁) ÷ 100.

SI vs CI for Same Rate

For the first year, Simple Interest and Compound Interest are equal (if compounded annually). From the second year onwards, CI > SI.

Shortcut Trick

Ratio of Cost Price (CP) to Selling Price (SP) = 2500 : 3250 = 10 : 13.

Profit units = 13 − 10 = 3 units.

Profit % = (Profit units ÷ CP units) × 100 = (3 ÷ 10) × 100 = 30%.

∴ The correct answer is 30%.

Alternate Method

Given: Cost Price (CP) = ₹2,500, Selling Price (SP) = ₹3,250. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

⇒ Profit = 3250 − 2500 = ₹750.

⇒ Profit % = (750 ÷ 2500) × 100.

⇒ Profit % = 750 ÷ 25 = 30%.

∴ The correct answer is 30%.

Additional Information

Profit and Loss Basics

Profit occurs when SP > CP. Loss occurs when CP > SP. Both Profit% and Loss% are always calculated on the Cost Price (CP) unless stated otherwise.

Selling Price Formula

SP = CP × (100 + Profit%) ÷ 100 or SP = CP × (100 − Loss%) ÷ 100.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some herbs are bushes → Follow (As all bushes are herbs. As whole bushes comes in herbs, therefore it is true.)

II. All trees are herbs → Follow (As all trees are bushes and all bushes are herbs. As whole trees comes in bushes which whole comes in herbs, therefore it is true.)

∴ Here, Both conclusions (I) and (II) follow.​

Hence, the correct answer is "Option 3".

The logic followed here is:

IJ 8 is related to KE −1

And,

TP 3 is related to VK −6

Similarly,

PQ 12 is related to

Hence, "Option 4" is the correct answer.

The logic followed here is:

Total students → 37

Nisha's rank from the left end → 13

Manasa's rank from the right end → 15

Total people stand between Nisha and Manasa → Total students - Nisha's rank from the left end - Manasa's rank from the right end

→ 37 - 13 - 15 = 9

Hence, the correct answer is "Option 1".

The logic followed here is:

Hence, "Option 2" is the correct answer.

The logic followed here is:

Total students → 30

Arun's rank from the right end → 7

Harish's rank from the left end → 8

Total people stand between Nisha and Manasa → Total students - Arun's rank from the right end - Harish's rank from the left end

→ 30 - 7 - 8 = 15

Hence, the correct answer is "Option 3".

Given: Six students, S1, S2, S3, S4, S5 and S6, are sitting around a circular table, facing the centre.

1. S1 is second to the right of S4.

2) S1 and S3 are sitting next to each other.

3) S4 is the common neighbour of S2 and S3. 

4) The student S6 is sitting next to both S5 and S2.

Thus, S4 is sitting fourth to the right of S1.

Hence, the correct answer is "Option 3".

According to the question:

Thus, 'fix' is coded as 'pd'.

Hence, "Option 4" is the correct answer.

Given: 

Devesh starts from Point Y and drives 21 km towards the east.

He then takes a left turn, drives 25 km, turns left and drives 67 km.

He then takes a right turn and drives 29 km.

He takes a right turn, drives 46 km, turns left, drives 41 km to stop at Point Z.

Thus, Devesh should drive 95 km in the south direction in order to reach Point Y again.

Hence, the correct answer is "Option 2".

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

According to the question:

Required condition: Odd number - Even number - Odd number

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

Thus, there are five such even numbers which are immediately preceded by an odd number and also immediately followed by an odd number.

Hence, "Option 3" is the correct answer.

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

According to the question:

Required condition: Perfect cube

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

Thus, there are six perfect cubes.

Hence, "Option 3" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some roads are cars → Does not follow (As some roads are fans and no fan is a car. So it is possible but not definite.)

II. Some fans are roads → Follow (As some roads are fans. As some part of roads is common with fans, therefore it is true.)

∴ Here, Only conclusion (II) follows.​

Hence, the correct answer is "Option 2".

According to the question:

Thus, 'learning' is coded as 'mn'.

Hence, "Option 1" is the correct answer.

The logic followed here is:

​

Hence, the correct answer is "Option 2".

Given Expression: G & H % I & T # S

G & H → G is the sister of H. 

H % I → H is the father of I.

I & T → I is the sister of T. 

T # S → T is the brother of S. 

Thus, G is S's wife’s father's sister.

Hence, "Option 1" is the correct answer.

The logic followed here is:

Option 1) IM-PK

Option 2) CG-JD

Option 3) GK-NH

Option 4) EI-LF

Thus, out of all 'IM-PK' is the odd one out.

Hence, "Option 1" is the correct answer.

Given series: 2134567

According to the question.

So, the sum of the digits which are second from the left and second from the right in the new number thus formed → 2+ 6 = 8

Hence, "Option 4" is the correct answer.

The logic followed here is:

JHK−IGJ

And,

LJM−KIL

Similarly,

DBE−CAD

Hence, "Option 1" is the correct answer.

Given number: 4635923

According to the question, 

So, the sum of the digits which are second from the left and second from the right in the new number thus formed → 7 + 3 = 10

Hence, "Option 2" is the correct answer.

Given series: 2175684

According to the question.

So, the number of position digit that remains unchanged → 5 and 6 → Two

Hence, "Option 4" is the correct answer.

The logic followed here is:

​

Hence, the correct answer is "Option 3".

Given series: (Left) 2 8 + 7 5 > 9 2 @ 3 = 4 6 % 3 & 8 4 % 9 1 8 3 # 7 6 9 (Right)

According to the question:

Required condition: Odd number - Symbols - Odd number

(Left) 2 8 + 7 5 > 9 2 @ 3 = 4 6 % 3 & 8 4 % 9 1 8 3 # 7 6 9 (Right)

Thus, there are two such symbols which are immediately preceded by an odd number and also immediately followed by an odd number.

Hence, "Option 1" is the correct answer.

The logic followed here is:

​(9, 31, 26)

→ 9 × 3 + 4 ⇒ 27 + 4 = 31

→ 31 - 5 = 26

And,

(13, 43, 38)

→ 13 × 3 + 4 ⇒ 39 + 4 = 43

→ 43 - 5 = 38

Similarly,

(15 ,49 ,44)

→ 15 × 3 + 4 ⇒ 45 + 4 = 49

→ 49 - 5 = 44

Hence, the correct answer is "Option 2".

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

1. E sits third to the right of B.