RRB Group D Official Paper (Held On: 26 Dec, 2025 Shift 3) (Previous Year Paper)

The correct answer is Refraction and dispersion, followed by internal reflection, and then finally refraction.

Key Points

• A rainbow is a natural spectrum appearing in the sky after rain, caused by the dispersion of sunlight by tiny water droplets present in the atmosphere.
• When sunlight enters a spherical water droplet, it first undergoes refraction because it moves from a rarer medium (air) to a denser medium (water). This process is accompanied by dispersion, where white light splits into its constituent colors (VIBGYOR).
• The dispersed light then strikes the inner back surface of the water droplet. If the angle of incidence is appropriate, the light undergoes internal reflection, bouncing back toward the front of the droplet.
• As the light leaves the droplet to reach the observer's eye, it undergoes a final refraction. This second bending further separates the colors, making the spectrum clearly visible.
• The combined effect of these three physical processes ensures that the VIBGYOR colors are spread out in a circular arc, usually at an angle of 40° to 42° relative to the observer's line of sight.

 Additional Information

• Primary and Secondary Rainbows:
• A primary rainbow involves a single internal reflection, resulting in red light on the outer arc and violet on the inner arc.
• A secondary rainbow is formed by two internal reflections within the droplet. It is fainter, and the color sequence is reversed, with violet on the outside.
• Condition for Visibility:
• The Sun must be shining in one part of the sky while it is raining in the opposite part.
• The observer must stand with their back towards the sun to view the rainbow arc.
• Atmospheric Refraction:
• Unlike rainbows, phenomena like mirages or the twinkling of stars are caused purely by atmospheric refraction due to varying air densities, rather than water droplet interaction.

The correct answer is Electrochemical method.

Key Points

• Refining is the final process in metallurgy used to obtain metals of high purity from the crude metal extracted through reduction.
• Electrochemical refining (or electrolytic refining) is the most widely used commercial method for purifying metals. Hence, the correct answer is Electrochemical method.
• In this process, the impure metal serves as the anode, and a strip of pure metal serves as the cathode.
• It is widely used for the commercial purification of Copper, Zinc, Tin, Silver, and Gold.
• During the electrolysis of Copper, impurities like Antimony, Selenium, and Tellurium settle down as anode mud.

Additional Information

• Physical Methods:
• Distillation: Used for metals with low boiling points such as Zinc, Mercury, and Cadmium. The impure metal is evaporated to obtain pure metal as distillate.
• Liquation: Used for metals with low melting points compared to their impurities, such as Tin (Sn) and Lead (Pb). The metal is melted on a sloping hearth to separate it from high-melting impurities.
• Chemical Methods:
• One major chemical refining technique is Vapour Phase Refining, which involves converting the metal into a volatile compound and then decomposing it to give pure metal. This includes the Mond Process and the Van Arkel Method.
• Zone Refining (Fractional Crystallization):
• This method is based on the principle that impurities are more soluble in the molten state than in the solid state of the metal.
• It is commercially essential for producing semiconductors of very high purity, such as Germanium, Silicon, Boron, Gallium, and Indium.

Important Points

• Chromatographic Methods: This chemical technique is based on the principle of differential adsorption. It is used when the impurities and the metal have similar chemical properties, allowing for purification in micro-quantities.
• Oxidative Refining: Processes like Cupellation (for Silver) and Bessemerization (for Iron/Steel) involve the oxidation of impurities to separate them from the metal.

The correct answer is 1 – 3 – 2 – 4.

Key Points

• Budding (मुकुलन) is a form of asexual reproduction in which a new organism develops from an outgrowth or bud due to cell division at one particular site.
• Bud formation (मुकुल निर्माण): The process begins when a small protuberance or bulb-like projection, called a bud, develops on the body of the parent organism. Hence, step 1 is the first stage.
• Nuclear division (केन्द्रक विभाजन): Once the bud is formed, the nucleus of the parent cell undergoes division (mitosis). One of the daughter nuclei then migrates into the developing bud. Hence, step 3 is the second stage.
• Cytoplasmic division (कोशिकाद्रव्य विभाजन): Following nuclear division, the cytoplasm starts to divide. The bud receives a portion of the parent's cytoplasm, and a constriction forms between the parent body and the bud. Hence, step 2 is the third stage.
• Separation of the bud (मुकुल का पृथक्करण): In the final stage, the bud grows to a certain size and eventually detaches from the parent body to become an independent individual. Hence, step 4 is the fourth stage.
• Therefore, the most suitable sequence for the process of budding in organisms is 1 (Bud formation) → 3 (Nuclear division) → 2 (Cytoplasmic division) → 4 (Separation).

Additional Information

• Organisms using Budding:
• Yeast (Saccharomyces cerevisiae): A unicellular fungus where budding is the primary mode of reproduction. In some cases, buds do not separate immediately and form a chain of buds.
• Hydra: A multicellular freshwater animal. In Hydra, a bud develops as an outgrowth due to repeated cell division at a specific site. These buds develop into tiny individuals and, when fully mature, detach from the parent body.
• Characteristics of Asexual Reproduction:
• It involves only a single parent.
• There is no fusion of gametes (sperm and egg).
• The offspring produced are genetically identical to the parent, often referred to as clones.
• This process is relatively rapid compared to sexual reproduction, allowing for quick population growth.
• Cellular Terms:
• Karyokinesis: The technical term for nuclear division. In budding, it ensures that the new individual receives the necessary genetic information.
• Cytokinesis: The technical term for cytoplasmic division, which physically separates the new cell or organism from the parent.
• Difference from Binary Fission: Unlike binary fission (seen in Amoeba), where the parent cell divides into two equal halves and the parent identity is lost, in budding, the parent organism remains intact after the smaller bud detaches.

Important Points

• Environmental Factors: Budding usually occurs when nutrients are abundant and environmental conditions are favorable for growth.
• Internal Budding: While most budding is external, some organisms like sponges undergo internal budding by forming gemmules to survive harsh conditions.
• Regenerative Cells: In multicellular organisms like Hydra, budding relies on the presence of regenerative cells that have the capacity to divide and differentiate into various cell types.

The correct answer is Spinal cord.

Key Points

• A reflex action is an automatic, rapid, and involuntary response to a stimulus that does not involve conscious thought.
• The Spinal cord acts as the main control center for most reflex actions in the human body. Hence, statement 2 is correct.
• This process is managed through a neural pathway known as the reflex arc, which allows for extremely fast physical reactions to occur before the brain even processes the sensation.
• The reflex arc typically involves five components: a receptor (to sense the stimulus), a sensory neuron (to carry the signal), the spinal cord (to process the signal), a motor neuron (to carry the response), and an effector (muscle or gland to execute the action).
• By bypassing the brain for the initial response, the spinal cord helps protect the body from immediate harm, such as pulling a hand away from a hot surface or a sharp object.

Additional Information

• Cranium (कपाल):
• The Cranium is the part of the skull that encloses and protects the brain.
• It is composed of 8 cranial bones fused together. While it protects the neural centers, it does not function as a center for reflex actions. Hence, statement 1 is incorrect.
• Hypothalamus (हाइपोथैलेमस):
• The Hypothalamus is a small but vital region located at the base of the brain.
• It plays a crucial role in maintaining homeostasis, regulating body temperature, hunger, thirst, and sleep cycles.
• It also acts as the link between the nervous system and the endocrine system via the pituitary gland. Hence, statement 3 is incorrect.
• Pituitary Gland (पीयूष ग्रंथि):
• Known as the "Master Gland," it is located in a bony cavity called the sella turcica below the hypothalamus.
• It secretes several essential hormones, such as Growth Hormone (GH), Prolactin, and TSH, which regulate other endocrine glands. Hence, statement 4 is incorrect.

Important Points

• The Spinal Cord is a long, thin, tubular bundle of nervous tissue that extends from the medulla oblongata of the brain down the vertebral column.
• In humans, there are 31 pairs of spinal nerves that emerge from the spinal cord to relay messages between the Central Nervous System (CNS) and the rest of the body.
• While the spinal cord handles "spinal reflexes" (like the knee-jerk reflex), "cerebral reflexes" (like blinking or salivation) are coordinated by the brain.
• The speed of a reflex action is remarkably high; for example, a signal can travel through the neurons at speeds exceeding 100 meters per second.

The correct answer is त्वरण तब ऋणात्मक होता है जब यह वेग की दिशा के विपरीत कार्य करता है।.

Key Points

• Acceleration is defined as the rate of change of velocity of an object with respect to time. It is a vector quantity, meaning it possesses both magnitude and direction.
• Statement 1: Acceleration is considered negative when it acts in the opposite direction of the velocity. This condition leads to a decrease in the speed of the object, a phenomenon commonly known as retardation or deceleration. Hence, statement 1 is correct.
• Statement 2: The sign of acceleration depends on the coordinate system and the change in velocity. It can be positive, negative, or zero. It is not always positive. Hence, statement 2 is incorrect.
• Statement 3: The SI unit of velocity is m/s (meters per second). However, acceleration is the change in velocity over time, making its SI unit m/s^2 (meters per second squared). Hence, statement 3 is incorrect.
• Statement 4: When acceleration is in the same direction as the velocity, it is positive, causing the object's speed to increase. If it is opposite to the velocity, it is negative. Hence, statement 4 is incorrect.

Additional Information

• Uniform and Non-Uniform Acceleration:
• If an object's velocity changes by an equal amount in equal intervals of time, it is said to have uniform acceleration. A common example is an object in free fall near the Earth's surface, where acceleration due to gravity is approximately 9.8 m/s^2.
• If the velocity changes by unequal amounts in equal intervals of time, the motion is described as non-uniform acceleration.
• Graphical Representation:
• On a Velocity-Time (v-t) graph, the slope of the line represents the acceleration of the object. A constant positive slope indicates uniform positive acceleration.
• On a Position-Time (s-t) graph, acceleration is represented by the curvature of the line. A parabola opening upwards indicates positive acceleration.
• Mathematical Formula:
• The average acceleration (a) can be calculated using the formula a = (v - u) / t, where v is the final velocity, u is the initial velocity, and t is the time taken for the change.

Important Points

• Direction of Acceleration: It is crucial to note that acceleration does not always point in the direction of motion. For instance, in uniform circular motion, the acceleration (centripetal) is always directed toward the center, which is perpendicular to the tangential velocity.
• Zero Acceleration: When an object moves with a constant velocity (constant speed in a straight line), the change in velocity is zero, and therefore, the acceleration is 0 m/s^2.
• Instantaneous Acceleration: This refers to the acceleration of an object at a specific moment in time, determined by the limit of the average acceleration as the time interval approaches zero.

The correct answer is वायुमंडलीय अपवर्तन के कारण.

Key Points

• Atmospheric Refraction is the phenomenon where Light Rays from the Sun bend as they pass through different layers of the Earth's Atmosphere.
• The Density of the atmosphere is not uniform; it is Denser near the surface and becomes Rarer with Altitude. This variation in density leads to a variation in the Refractive Index.
• When sunlight enters the Earth's atmosphere, it travels from a Vacuum (rarer medium) into the air (denser medium), causing the light to bend towards the Normal.
• Due to this continuous Refraction, the Sun appears to be slightly higher than its actual position when it is near the Horizon.
• As a result, we can see the Sun about 2 minutes before the Actual Sunrise (when the Sun is still below the horizon) and for about 2 minutes after the Actual Sunset. Hence, option 4 is correct.
• The idea that the Sun moves faster near the horizon is a common Optical Illusion but is physically incorrect as the Earth's Angular Velocity remains constant. Hence, option 1 is incorrect.
• The Rotation of the Earth is a uniform process at approximately 1,670 km/h at the equator and does not slow down during specific times of the day. Hence, option 2 is incorrect.
• The Gravitational Effect of the Moon on light (Gravitational Lensing) is negligible in the context of Earth's local atmosphere and does not contribute to the timing of sunrise or sunset. Hence, option 3 is incorrect.

Additional Information

• Refractive Index of Air: The refractive index of Vacuum is 1.00, while the refractive index of air at the surface is approximately 1.00029. This small difference is enough to bend light significantly over long atmospheric paths.
• Apparent Flattening of the Sun: During Sunrise and Sunset, the Sun appears Flattened or oval-shaped. This is also due to Atmospheric Refraction, as the light from the bottom edge of the Sun travels through thicker air and is refracted more than the light from the top edge.
• Total Day Length: Because of the 2-minute advance in sunrise and 2-minute delay in sunset, the total duration of Daylight is increased by approximately 4 minutes.
• Twinkling of Stars: This is another major application of Atmospheric Refraction. Since stars are point sources of light, the continuous change in the Atmosphere's Density causes the Apparent Position of the star to fluctuate, which our eyes perceive as Twinkling.
• Advanced Sunrise/Delayed Sunset Facts: These phenomena occur every day but are most noticeable in flat areas like Deserts or over the Ocean where the Horizon is clearly visible.

Important Points

• Scattering vs Refraction: It is important to distinguish between Refraction (which changes the position/timing) and Scattering (which changes the color). The Reddish Color of the Sun at dawn and dusk is due to Rayleigh Scattering, where shorter wavelengths (blue) are scattered away, leaving longer wavelengths (red).
• Snell's Law: The mathematical principle behind this bending is Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media.
• Mirage: On very hot days, Atmospheric Refraction can create a Mirage, where light from the sky is refracted upwards by the hot air near the ground, making it look like there is Water on the road or sand.

The correct answer is Vibration → Vibration in the particles of the medium → Propagation of sound wave → Sound is heard .

Key Points

• Sound production always begins with the vibration of an object. When an object vibrates, it releases energy that spreads into the surrounding environment.
• Once the object begins to vibrate, it creates a disturbance in the particles of the medium it comes into contact with . These particles begin to vibrate about their mean position.
• This disturbance is transferred from one particle to another, causing the propagation of a sound wave . In this case, the particles of the medium themselves do not move from one place to another, but only transfer energy. Therefore, the sequence of events given in option 2 is correct.
• When this transmitted sound wave reaches our ear, it creates vibrations in the eardrum, which are processed by the brain and we hear sound .
• Option 1 is incorrect because 'sound' is the result of the process, not its origin. Options 3 and 4 are also incorrect because electricity , light, or heat are not essential intermediate steps in normal sound production.

Additional Information

• Nature of Sound : Sound is a mechanical wave . It requires a physical medium to travel. It cannot travel in a vacuum because there are no particles to transmit vibrations.
• Effect of the medium : The speed of sound depends on the density and elasticity of the medium. The speed of sound is highest in solids , followed by liquids , and lowest in gases . For example, the speed of sound in air at 0°C is approximately 331 m/s .
• Longitudinal Waves : Sound waves are longitudinal, meaning that the particles of the medium vibrate parallel to the direction of propagation. This creates regions of compression and rarefaction .
• Frequency and Pitch : The number of vibrations per second is called frequency , measured in hertz (Hz) . Higher frequency means higher pitch (such as children's or women's voices).
• Audible Range : The human ear can normally hear frequencies between 20 Hz and 20,000 Hz . Sounds below 20 Hz are called infrasonic , and those above 20,000 Hz are called ultrasonic .

Important Points

• Amplitude of vibration : The maximum displacement of the vibration is called the amplitude . It determines the loudness of the sound. A higher amplitude means a louder sound.
• Decibel (dB) : The unit of measurement for sound intensity is the decibel . Sounds over 80 dB are generally considered noise that can be harmful to health.
• Effect of Temperature : As the temperature of the medium increases, the speed of sound also increases. This is why sound travels faster in warm air than in cold air.

The correct answer is Promoting afforestation.

Key Points

• Afforestation is the process of planting trees on land that has not recently been covered by forest, or was never a forest. It is a proactive method to increase green cover and ensure the conservation of natural ecosystems. Hence, statement 4 is correct.
• Deforestation refers to the permanent removal of trees to make room for something besides forest. This process leads to habitat loss, soil erosion, and a decrease in forest products. Hence, statement 1 is incorrect.
• Overgrazing by livestock in forest areas can destroy young saplings and seedlings, preventing the natural regeneration of the forest. It also leads to soil compaction, which hinders future plant growth. Hence, statement 2 is incorrect.
• Burning forests, whether through intentional clearing or uncontrolled forest fires, results in the immediate destruction of flora and fauna, loss of biodiversity, and the release of massive amounts of Carbon Dioxide into the atmosphere. Hence, statement 3 is incorrect.
• Promoting afforestation helps in maintaining the water cycle, preventing floods, and providing a sustainable source of timber and non-timber forest products (NTFP).

Additional Information

• Forest Conservation Act, 1980: This is a landmark act by the Indian Parliament aimed at protecting forests. It restricts the use of forest land for non-forest purposes without the prior approval of the Central Government.
• National Forest Policy, 1988: The main objective of this policy is to ensure environmental stability and maintain ecological balance. It set a national goal to have a minimum of one-third (33%) of the total land area of the country under forest or tree cover.
• Social Forestry: Launched in 1976, this program aims at the management and protection of forests and afforestation on barren lands with the purpose of helping in environmental, social, and rural development.
• Chipko Movement: A famous non-violent social and ecological movement by rural villagers, particularly women, in India in the 1970s, aimed at protecting trees and forests slated for government-backed logging. It originated in the Reni village of Chamoli district, Uttarakhand.
• Forest Products: Forests provide essential resources like timber, fuelwood, medicinal plants, resins, gums, and lac, which are vital for the livelihoods of millions of people, especially tribal communities.

Important Points

• Carbon Sink: Forests act as a major carbon sink by absorbing Carbon Dioxide during photosynthesis, which helps in mitigating the effects of Global Warming and Climate Change.
• Reforestation vs. Afforestation: While Afforestation is creating a new forest, Reforestation is the natural or intentional restocking of existing forests and woodlands that have been depleted, usually through deforestation.
• Sustainable Forest Management (SFM): This practice ensures that forest resources are used in a way that meets the needs of the present without compromising the ability of future generations to meet their own needs.
• Biodiversity Hotspots: Forests in India, such as the Western Ghats and the Eastern Himalayas, are recognized globally as biodiversity hotspots due to their high levels of endemic species.

The correct answer is 10 Ω.

Key Points

• The amount of heat produced in a conductor when an electric current passes through it is governed by Joule’s Law of Heating. According to this law, the heat generated (H) is directly proportional to the square of the current (I), the resistance (R) of the conductor, and the time (t) for which the current flows.
• The mathematical expression for this law is H = I²Rt. In this equation, H is measured in Joules (J), I in Amperes (A), R in Ohms (Ω), and t in seconds (s).
• In the given problem, the current (I) is 1 A, the time (t) is 10 seconds, and the heat produced (H) is 100 J.
• To find the resistance, we rearrange the formula to R = H / (I²t). Substituting the known values: R = 100 / (1² × 10).
• This simplifies to R = 100 / 10, which equals 10 Ω. Hence, the resistance of the geyser is 10 Ω, making option 1 the correct answer.

Additional Information

• Electric Geyser: It is an appliance that converts electrical energy into heat energy. It uses a heating element made of materials with high resistance and high melting point, such as Nichrome (an alloy of nickel and chromium).
• Resistance (R): It is the property of a conductor to oppose the flow of electric current. The SI unit of resistance is the Ohm, named after the German physicist Georg Simon Ohm. Resistance depends on the length, area of cross-section, nature of the material, and temperature.
• Current (I): It is defined as the rate of flow of electric charge through a cross-section of a conductor. Its SI unit is the Ampere (A), and it is measured using an instrument called an ammeter.
• Electrical Energy and Power: Power (P) is the rate at which electrical energy is consumed, given by P = VI or P = I²R. Heat (H) is simply the power multiplied by time (H = P × t).

Important Points

• Joule's Law Discovery: The heating effect of current was studied experimentally by James Prescott Joule in the year 1841. It is a fundamental principle used in domestic appliances like electric irons, toasters, ovens, and heaters.
• Units Consistency: When solving numerical problems related to Joule's Law, it is crucial to ensure that time is always in seconds. If time is given in minutes or hours, it must be converted (1 minute = 60 seconds).
• Practical Application: In a geyser, the resistance is designed such that for a standard voltage (usually 220V in India), the current flowing through it produces enough heat to raise the water temperature efficiently within a reasonable time.
• Safety Feature: Most heating appliances include a thermostat to break the circuit once a certain temperature is reached, preventing damage due to excessive heat production.

The correct answer is Amylase.

Key Points

• Amylase is the primary enzyme responsible for the chemical breakdown of complex carbohydrates (starch) into simple sugars such as maltose and glucose.
• In humans, this digestive process begins in the mouth, where salivary amylase (also known as ptyalin) is secreted by the salivary glands.
• The pancreas also produces pancreatic amylase, which is released into the small intestine to further digest any remaining starch into monosaccharides for absorption.
• Pepsin is an enzyme produced in the stomach specifically for the digestion of proteins into peptides. Hence, option 1 is incorrect.
• Bile Juice is produced by the liver and stored in the gallbladder; it does not contain enzymes but helps in the emulsification of fats. Hence, option 2 is incorrect.
• Lipase is an enzyme responsible for breaking down fats (lipids) into fatty acids and glycerol. Hence, option 3 is incorrect.

Additional Information

• Carbohydrate Digestion:
• It is a multi-step process that starts in the oral cavity. About 30% of starch is hydrolyzed in the mouth by salivary amylase at an optimum pH of 6.8.
• The final digestion occurs in the small intestine where enzymes like maltase, sucrase, and lactase convert disaccharides into glucose, fructose, and galactose.
• Pepsin and Protein Digestion:
• The stomach mucosa contains gastric glands that secrete proenzyme pepsinogen.
• On exposure to Hydrochloric Acid (HCl), pepsinogen is converted into the active enzyme Pepsin, which works best in an acidic pH of about 1.8.
• Role of Lipase:
• Lipases are secreted by the pancreas (steapsin) and in small amounts by the stomach (gastric lipase).
• They require the presence of bile salts to increase the surface area of fat droplets through emulsification.
• Bile Juice Functions:
• Bile contains bile pigments (bilirubin and biliverdin), bile salts, cholesterol, and phospholipids.
• It neutralizes the acidic chyme coming from the stomach and makes the medium alkaline for the action of pancreatic enzymes.

Important Points

• Location of Secretion: Salivary Amylase is secreted in the mouth, while Pancreatic Amylase is secreted in the duodenum.
• End Products: The ultimate goal of Amylase activity is to provide the body with Glucose, which is the primary energy source for cellular respiration.
• Enzyme Specificity: Enzymes are highly specific; Amylase only acts on alpha-1,4-glycosidic bonds in starch and cannot digest cellulose due to the lack of cellulase in humans.

The correct answer is धारा और तार से दूरी.

Key Points

• The intensity of the magnetic field (B) produced by a straight current-carrying wire is directly proportional to the magnitude of the electric current (I) flowing through the wire. If the current increases, the magnetic field strength also increases proportionately.
• The magnetic field strength is inversely proportional to the distance (r) from the wire. This implies that as one moves further away from the conductor, the intensity of the magnetic field weakens. Hence, statement 3 is correct.
• Mathematically, for an infinitely long straight wire, the relationship is expressed as B = (μ₀I) / (2πr), where μ₀ is the permeability of free space.
• The resistance of the wire (Option 1) affects the flow of current according to Ohm's Law, but it is not a direct variable in the formula determining the magnetic field at a specific point in space. Hence, statement 1 is incorrect.
• The length of the wire (Option 2) does not determine the field intensity at a point near the center of a very long or infinite wire; only the perpendicular distance and current matter in that context. Hence, statement 2 is incorrect.
• While applied voltage (Option 4) drives the current, the magnetic field is physically generated by the movement of charges (current) itself, making current and distance the fundamental dependent factors. Hence, statement 4 is incorrect.

Additional Information

• Right-Hand Thumb Rule: To find the direction of the magnetic field, imagine holding the wire in your right hand with the thumb pointing in the direction of the current. The direction in which the fingers curl gives the direction of the magnetic field lines.
• Magnetic Field Lines: Around a straight conductor, these lines form concentric circles. The circles are closer together near the wire, indicating a stronger field, and spread out as the distance increases.
• SI Unit: The Standard International (SI) unit of magnetic field intensity is the Tesla (T). Another common unit used for smaller fields is the Gauss (G), where 1 Tesla = 10,000 Gauss.
• Oersted's Experiment: In 1820, the Danish scientist Hans Christian Oersted accidentally discovered that a compass needle deflects when placed near a wire carrying an electric current, proving that electricity and magnetism are linked.
• Ampere's Circuital Law: This law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. It is a fundamental law used to calculate magnetic fields in highly symmetric situations.
• Permeability (μ₀): The constant μ₀ (permeability of free space) has a value of 4π × 10⁻⁷ T·m/A. It represents the measure of the ability of a vacuum to support the formation of a magnetic field.

The correct answer is निषेचन → युग्मनज → भ्रूण → गर्भ.

Key Points

• लैंगिक जनन (Sexual Reproduction) की प्रक्रिया में घटनाओं का एक निश्चित जैविक क्रम होता है जो नए जीव के निर्माण की ओर ले जाता है।
• निषेचन (Fertilization): यह जनन प्रक्रिया का प्रथम चरण है। इसमें पुरुष के शुक्राणु (Sperm) और स्त्री के अंडाणु (Egg/Ovum) का संलयन होता है। मानवों में यह प्रक्रिया आमतौर पर डिम्बवाहिनी नलिका (Fallopian Tube) में होती है। अतः, यह क्रम का प्रारंभिक हिस्सा है।
• युग्मनज (Zygote): निषेचन के परिणामस्वरूप एक एकल कोशिका का निर्माण होता है जिसे युग्मनज कहते हैं। यह नए जीव की पहली कोशिका होती है जिसमें माता और पिता दोनों के गुणसूत्र होते हैं। अतः, निषेचन के बाद युग्मनज बनता है।
• भ्रूण (Embryo): युग्मनज बार-बार विभाजित होकर कोशिकाओं के एक गोले में विकसित होता है। ये कोशिकाएँ धीरे-धीरे ऊतकों और अंगों में विकसित होने लगती हैं। विकास की इस प्रारंभिक अवस्था को भ्रूण कहा जाता है। यह गर्भाशय की दीवार में अंतःस्थापित (Implanted) होता है। अतः, युग्मनज के बाद भ्रूण का विकास होता है।
• गर्भ (Foetus): भ्रूण के विकास की वह अवस्था जिसमें शरीर के सभी अंगों (जैसे हाथ, पैर, सिर, आँखें आदि) को स्पष्ट रूप से पहचाना जा सकता है, गर्भ कहलाती है। यह जन्म से पहले की अंतिम विकासात्मक अवस्था है। अतः, भ्रूण के बाद गर्भ की अवस्था आती है।
• इसलिए, सही क्रम निषेचन → युग्मनज → भ्रूण → गर्भ है।

Additional Information

• Gametes (युग्मक): जनन के लिए आवश्यक विशेष कोशिकाएँ। पुरुषों में शुक्राणु और महिलाओं में अंडाणु को युग्मक कहा जाता है। ये अगुणित (Haploid) कोशिकाएँ होती हैं।
• Internal Fertilization (आंतरिक निषेचन): जब निषेचन की क्रिया मादा के शरीर के भीतर होती है, तो इसे आंतरिक निषेचन कहते हैं। यह मनुष्यों, गायों, कुत्तों और मुर्गियों जैसे स्तनधारियों और पक्षियों में पाया जाता है।
• External Fertilization (बाह्य निषेचन): जब निषेचन की क्रिया मादा के शरीर के बाहर (जैसे पानी में) होती है, तो इसे बाह्य निषेचन कहते हैं। यह मुख्य रूप से मेंढक और मछलियों जैसे जलीय जीवों में देखा जाता है।
• Implantation (रोपण): भ्रूण का गर्भाशय (Uterus) की दीवार से जुड़ना रोपण कहलाता है। यह निषेचन के लगभग 7 से 9 दिनों के बाद होता है।
• Gestation Period (गर्भावधि): गर्भधारण से लेकर शिशु के जन्म तक की अवधि। मनुष्य��ं में यह अवधि लगभग 9 महीने या 280 दिन की होती है।

Important Points

• Cell Division: युग्मनज से भ्रूण बनने की प्रक्रिया में समसूत्री विभाजन (Mitosis) होता है, जिससे कोशिकाओं की संख्या 1 से 2, 4, 8, 16 और इसी तरह बढ़ती जाती है।
• IVF (In Vitro Fertilization): इसे 'टेस्ट ट्यूब बेबी' तकनीक भी कहा जाता है। इसमें शरीर के बाहर कृत्रिम रूप से निषेचन कराया जाता है और फिर युग्मनज/भ्रूण को माता के गर्भाशय में स्थानांतरित कर दिया जाता है।
• Differentiation: भ्रूण अवस्था के दौरान ही कोशिकाओं का विभेदीकरण शुरू होता है, जहाँ अलग-अलग कोशिकाएँ विशिष्ट कार्य करने के लिए अलग-अलग अंगों का रूप लेती हैं।
• Placenta (अपरा): गर्भ और माता के बीच पोषक तत्वों, ऑक्सीजन और अपशिष्ट पदार्थों के आदान-प्रदान के लिए जिम्मेदार ऊतक को प्लेसेंटा कहा जाता है।

The correct answer is A is false, but R is true .

Key Points

• Assertion (A) states that precipitation reactions form soluble salts. This statement is false because a precipitation reaction is a chemical process in which two aqueous solutions react to form an insoluble solid called a precipitate . Soluble salts dissolve in water, while the precipitate separates. Therefore, Assertion (A) is false.
• Reason (R) states that precipitation reactions involve the exchange of ions in solution. This statement is true . Most precipitation reactions are examples of double displacement reactions , where ions are exchanged between the reactants . Therefore, Reason (R) is true.
• When aqueous solutions of two ionic compounds are mixed, their cations and anions change places. If one of the new compounds is insoluble in water , it settles to the bottom as a solid.
• As a well-known example, when solutions of sodium sulphate and barium chloride are mixed, a white precipitate of barium sulphate (BaSO4) is formed and sodium chloride (NaCl) remains in the solution.
• Therefore, the correct answer is A is false, but R is true.

Additional Information

• Precipitation Reaction: This is a reaction that results in the formation of an insoluble salt . It is often used in laboratories to identify the presence of a particular ion.
• Double Displacement Reaction: This is a process in which two compounds exchange ions to form two new compounds. The general formula is AB + CD → AD + CB .
• Solubility Rules: In chemistry, solubility charts are used to determine which substances will form a precipitate . For example, most nitrates are soluble, while silver chloride is insoluble.
• Examples in everyday life: Water purification plants use precipitation to remove unwanted minerals. Kidney stones are also a type of precipitation process where salts solidify.

Important Points

• Silver nitrate test: When silver nitrate (AgNO3) is added to sodium chloride (NaCl) , a curd-like white precipitate of silver chloride (AgCl) is obtained. This is an important test for identifying halide ions .
• Law of Conservation of Mass: Mass is conserved even during a precipitation reaction . The total weight of the solid precipitate and the solution is equal to the total weight of the reactants.
• Ionized state: These reactions occur primarily in the aqueous state because the ions are not free to move in the solid state. In 1887 , Svante Arrhenius better explained these processes through the ionic theory.

The correct answer is Their components can be separated by physical methods..

Key Points

• A mixture is a physical combination of two or more substances in which each component retains its own properties.
• The components of a mixture can be separated by physical methods such as:
• Filtration
• Evaporation
• Distillation
• Chromatography
• Magnetic separation
• In contrast, the components of a compound are chemically combined and can be separated only by chemical methods.
• Hence, the correct answer is Option 4 – Their components can be separated by physical methods.

Additional Information

• Option 1: Incorrect. Mixtures are formed by physical mixing; they are not necessarily formed by the absorption of heat.
• Option 2: Incorrect. In a mixture, the identity of the original substances is retained. The identity is lost only when substances form a compound.
• Option 3: Incorrect. Mixtures do not necessarily have high melting or boiling points. Their melting and boiling points depend on the nature and proportion of their components.
• Compounds have fixed composition, definite properties, and their constituents are chemically bonded.

Important Points

• Mixture: Components are physically combined and can be separated by physical methods.
• Compound: Components are chemically combined and require chemical methods for separation.
• Mixture: Variable composition; constituents retain their individual properties.
• Compound: Fixed composition; constituents lose their individual identities and form a new substance with different properties.

The correct answer is AgNO3 + NaCl → AgCl↓ + NaNO3.

Key Points

• A precipitation reaction is a type of chemical reaction in which two soluble salts in aqueous solution combine to form one or more insoluble products, called a precipitate.
• In the reaction AgNO3 + NaCl → AgCl↓ + NaNO3, aqueous Silver Nitrate reacts with aqueous Sodium Chloride to form Silver Chloride and Sodium Nitrate. The Silver Chloride (AgCl) is insoluble in water and settles down as a white precipitate. Hence, option 1 is correct.
• This reaction is also a classic example of a double displacement reaction, where the Silver (Ag+) and Sodium (Na+) cations exchange their respective Nitrate (NO3-) and Chloride (Cl-) anions.
• The downward arrow (↓) next to a chemical formula in an equation specifically denotes the formation of a precipitate, indicating that the substance has crashed out of the solution as a solid.
• Precipitation reactions are essential in qualitative inorganic analysis to identify various ions present in a solution based on the color and solubility of the precipitate formed.

Additional Information

• Decomposition Reaction:
• In the reaction CaCO3 → CaO + CO2↑, Calcium Carbonate (limestone) breaks down into Calcium Oxide (quicklime) and Carbon Dioxide gas upon heating.
• This is a thermal decomposition reaction. The upward arrow (↑) indicates the evolution of a gas. Hence, option 2 is incorrect.
• Single Displacement Reaction:
• The reaction Zn + H2SO4 → ZnSO4 + H2↑ involves Zinc metal reacting with Sulfuric Acid.
• Since Zinc is more reactive than Hydrogen, it displaces hydrogen from the acid to form Zinc Sulfate and Hydrogen gas. Hence, option 3 is incorrect.
• Neutralization Reaction:
• The reaction NaOH + HCl → NaCl + H2O is a neutralization reaction occurring between a strong base (Sodium Hydroxide) and a strong acid (Hydrochloric Acid).
• The products are Sodium Chloride (a soluble salt) and Water. No precipitate is formed in this specific reaction as all products remain in the aqueous phase or as liquid water. Hence, option 4 is incorrect.

Important Points

• Solubility Rules: To predict whether a precipitation reaction will occur, chemists use solubility rules. For example, most Nitrates (NO3-) are soluble, while most Silver salts (except nitrates and fluorides) are insoluble.
• Applications: Precipitation reactions are used in wastewater treatment to remove heavy metals or phosphates from water by turning them into solid precipitates that can be easily filtered out.
• Ionic Equation: The net ionic equation for the correct answer is Ag+(aq) + Cl-(aq) → AgCl(s), which focuses only on the species that actually change during the reaction.
• Identification: Silver Chloride is a white precipitate, Silver Bromide is pale yellow, and Silver Iodide is bright yellow. These distinct colors help in identifying halide ions.

The correct answer is displacement will be equal to 10 km .

Key Points

• Displacement is defined as the shortest straight distance between the initial position and the final position of an object .
• When an object moves in a straight line from point A to point B and does not change its direction, then the magnitude of distance covered and displacement is equal.
• Since the question states that the object travels a distance of 10 km in a straight line, the displacement between point A and point B will also be exactly 10 km . Hence, statement 1 is correct.
• Displacement is always less than 10 km only when the object moves along a curved or zigzag path. Here, the path is straight. Therefore, statement 3 is incorrect.
• The magnitude of displacement can never be greater than the distance traveled , as it is the shortest path between two points. Therefore, statement 4 is incorrect.
• Displacement is zero only when the object returns to the same starting point after starting its journey. Therefore, statement 2 is incorrect.

Additional Information

• Distance:
• It is the total path length of the actual path covered by a moving object .
• Distance is a scalar quantity , which has only magnitude and no definite direction.
• Distance is always positive and can never be zero or negative if the object has moved.
• Displacement:
• It is a vector quantity , which means it has both magnitude and direction .
• The value of displacement can be positive, negative or zero .
• Its SI unit is the metre (m), although for larger distances the kilometre (km) is used.
• Relation between distance and displacement:
• For any moving object, the distance is always equal to or greater than the magnitude of displacement (Distance ≥ |Displacement|).
• If an object moves on a circular path and completes one revolution, then the distance will be 2πr , but the displacement will be 0 .

Important Points

• Uniform Motion: If an object travels equal distances in equal intervals of time along a straight line, it is said to have uniform motion. In this case, velocity and speed remain the same.
• Example of zero displacement: If you go to school 5 km away from your home and come back home, your total distance will be 10 km , but your total displacement will be 0 km because your initial and final position are the same.
• Negative displacement: Displacement can be negative if the object moves in a direction opposite to the chosen reference direction.
• Year 1687: Sir Isaac Newton explained in detail the laws of motion and principles like displacement in his book 'Principia' .

The correct answer is प्रोपेनोन है, जो एक कीटोन है जिसके मध्य कार्बन पर कार्बोनिल होता है.

Key Points

• CH3COCH3 का रासायनिक नाम प्रोपेनोन (Propanone) है, जिसे सामान्यतः एसीटोन (Acetone) के रूप में जाना जाता है।
• यह कीटोन (Ketone) परिवार का सबसे सरल और छोटा सदस्य है। इसमें 3 कार्बन परमाणु होते हैं, जिसके कारण मूल शब्द 'प्रोपेन' का उपयोग किया जाता है।
• IUPAC नियमों के अनुसार, कीटोन के लिए प्रत्यय (suffix) '-ओन' (-one) जोड़ा जाता है। चूंकि कार्बोनिल समूह (C=O) मध्य कार्बन पर स्थित होता है, इसलिए इसे प्रोपेन-2-ओन या केवल प्रोपेनोन कहा जाता है।
• प्रोपीन एक एल्कीन है जिसमें कार्बन के बीच द्विआबंध होता है, यह विकल्प गलत है। अतः कथन 1 गलत है।
• प्रोपेनॉइक अम्ल में -COOH समूह होता है, जो CH3COCH3 की संरचना से भिन्न है। अतः कथन 2 गलत है।
• प्रोपेनाल एक एल्डिहाइड है जिसमें -CHO समूह होता है। अतः कथन 3 गलत है।
• प्रोपेनोन एक कीटोन है जिसमें कार्बोनिल समूह (>C=O) दो एल्किल समूहों के बीच स्थित होता है। अतः कथन 4 सही है।

Additional Information

• भौतिक गुण (Physical Properties):
• प्रोपेनोन एक रंगहीन, अत्यधिक वाष्पशील और ज्वलनशील तरल है।
• इसका क्वथनांक (Boiling Point) लगभग 56 डिग्री सेल्सियस (329.15 K) होता है।
• इसकी गंध विशिष्ट और तीखी होती है, जो अक्सर नेल पॉलिश रिमूवर में महसूस की जाती है।
• उपयोग (Uses):
• इसका व्यापक रूप से औद्योगिक विलायक (Solvent) के रूप में उपयोग किया जाता है, विशेष रूप से प्लास्टिक और सिंथेटिक फाइबर के उत्पादन में।
• यह प्रयोगशालाओं में कांच के बर्तनों को सुखाने और साफ करने के लिए एक सामान्य विलायक है।
• इसका उपयोग कार्बनिक रसायन विज्ञान में एसीटोन-बर्फ के स्नान के माध्यम से कम तापमान (-78 डिग्री सेल्सियस) बनाए रखने के लिए किया जाता है।
• समानधर्मी श्रेणियाँ (Homologous Series):
• प्रोपीन (C3H6): यह एक असंतृप्त हाइड्रोकार्बन है जिसमें एक दोहरा आबंध होता है।
• प्रोपेनाल (C3H6O): इसमें एल्डिहाइड कार्यात्मक समूह श्रृंखला के अंत में स्थित होता है।
• प्रोपेनॉइक अम्ल (C3H6O2): यह एक कार्बोक्जिलिक अम्ल है जिसका उपयोग परिरक्षक के रूप में किया जाता है।

Important Points

• संरचनात्मक सूत्र: प्रोपेनोन में कार्बोनिल कार्बन sp2 संकरित होता है, जिससे इसकी ज्यामिति त्रिकोणीय समतलीय (Trigonal Planar) होती है।
• घुलनशीलता: यह पानी, इथेनॉल और ईथर के साथ पूरी तरह से मिश्रणीय (miscible) है।
• द्रव्यमान: प्रोपेनोन का आणविक द्रव्यमान लगभग 58.08 g/mol होता है।
• नामकरण: IUPAC प्रणाली में, कार्यात्मक समूह की स्थिति को न्यूनतम अंक दिया जाता है, लेकिन 3 कार्बन वाली कीटोन श्रृंखला में कार्बोनिल हमेशा दूसरे कार्बन पर ही हो सकता है।

The correct answer is जिंक.

Key Points

• गैल्वनीकरण (Galvanization) एक रासायनिक-तकनीकी प्रक्रिया है जिसका मुख्य उद्देश्य लोहे (Iron) और स्टील (Steel) को संक्षारण (Corrosion) या जंग लगने से बचाना है।
• इस प्रक्रिया में, लोहे की वस्तुओं पर जिंक (Zinc), जिसे हिंदी में जस्ता भी कहा जाता है, की एक सुरक्षात्मक परत चढ़ाई जाती है। अतः, विकल्प 4 सही उत्तर है।
• जिंक का चयन इसलिए किया जाता है क्योंकि यह लोहे की तुलना में अधिक अभिक्रियाशील (Reactive) होता है। यदि जिंक की परत में कहीं खरोंच भी आ जाए, तो भी जिंक पहले ऑक्सीकृत होता है, जिससे नीचे मौजूद लोहा सुरक्षित रहता है। इसे कैथोडिक सुरक्षा (Cathodic Protection) कहा जाता है।
• गैल्वनीकरण की सबसे प्रचलित विधि हॉट-डिप गैल्वनाइजिंग (Hot-dip galvanizing) है। इसमें लोहे के घटकों को साफ करने के बाद लगभग 450°C (842°F) के तापमान पर पिघले हुए जिंक के घोल में डुबोया जाता है।
• यह प्रक्रिया न केवल धातु को वातावरण की नमी और ऑक्सीजन से बचाती है, बल्कि उसे एक चमकदार फिनिश भी प्रदान करती है, जिसका उपयोग ऑटोमोबाइल, निर्माण और बिजली के खंभों में व्यापक रूप से किया जाता है।

Additional Information

• जिंक (Zinc) के गुण:
• इसका परमाणु क्रमांक (Atomic Number) 30 है और इसका रासायनिक प्रतीक Zn है।
• यह आवर्त सारणी के ग्रुप 12 और डी-ब्लॉक (D-block) का तत्व है।
• जिंक का उपयोग पीतल (Brass) जैसी मिश्र धातुओं को बनाने में भी किया जाता है, जहाँ इसे तांबे (Copper) के साथ मिलाया जाता है।
• संक्षारण (Corrosion) और जंग:
• लोहे पर जंग तब लगती है जब वह ऑक्सीजन और नमी (Water/Moisture) के संपर्क में आता है।
• जंग का रासायनिक नाम हाइड्रेटेड आयरन (III) ऑक्साइड है, और इसका रासायनिक सूत्र Fe2O3·nH2O होता है।
• गैल्वनीकरण के अलावा, जंग रोकने के अन्य तरीकों में पेंटिंग, तेल या ग्रीस लगाना और इलेक्ट्रोप्लेटिंग शामिल हैं।
• अन्य विकल्पों का विश्लेषण:
• लोहा (Iron): यह वह आधार धातु है जिसे सुरक्षित किया जाना है; अतः लोहे पर लोहे की परत चढ़ाने से जंग से सुरक्षा नहीं मिलती।
• प्लेटिनम (Platinum) और चांदी (Silver): ये दोनों मृदा धातुएं (Noble Metals) हैं और अत्यधिक महंगी हैं। हालांकि ये संक्षारण प्रतिरोधी हैं, लेकिन औद्योगिक स्तर पर लोहे पर इनकी परत चढ़ाना आर्थिक रूप से व्यावहारिक नहीं है।

Important Points

• विद्युत लेपन (Electroplating): यह एक अन्य प्रक्रिया है जिसमें बिजली का उपयोग करके किसी धातु पर दूसरी धातु की परत चढ़ाई जाती है। गैल्वनीकरण इलेक्ट्रोप्लेटिंग के माध्यम से भी किया जा सकता है, जिसे इलेक्ट्रो-गैल्वनाइजिंग ��हते हैं।
• बलिदानी सुरक्षा (Sacrificial Protection): जिंक एक बलिदानी एनोड (Sacrificial Anode) के रूप में कार्य करता है। यह स्वयं को संक्षारित करके लोहे की आयु बढ़ाता है।
• शेरार्डाइजिंग (Sherardizing): यह गैल्वनीकरण का ही एक रूप है जिसमें धातु के पुर्जों को जिंक पाउडर के साथ एक बंद घूमने वाले ड्रम में गर्म किया जाता है, जिससे जिंक का प्रसार (Diffusion) लोहे की सतह में हो जाता है।
• भारत में, भारतीय मानक ब्यूरो (BIS) द्वारा गैल्वनीकरण के लिए विशिष्ट मानक (जैसे IS 2629) निर्धारित किए गए हैं ताकि गुणवत्ता सुनिश्चित की जा सके।

The correct answer is प्रजनन.

Key Points

• Meiosis is a specialized form of cell division that reduces the chromosome number by half, resulting in the production of four haploid daughter cells.
• The most specific and fundamental purpose of meiotic division is to facilitate reproduction (प्रजनन), specifically sexual reproduction, by creating gametes (sperm and egg cells).
• This process ensures that when fertilization occurs, the resulting zygote has the correct diploid number of chromosomes, maintaining chromosomal stability across generations.
• In contrast, options such as digestion (पाचन), respiration (श्वसन), and excretion ( उत्सर्जन) are physiological and metabolic processes handled by organ systems and do not involve this specific type of cell division.
• During Meiosis, genetic material is shuffled through crossing over, which creates genetic diversity among offspring, a key driver of evolution. Hence, the correct answer is Reproduction.

Additional Information

• Stages of Meiosis:
• Meiosis I: Known as reductional division, it involves the separation of homologous chromosomes. It includes phases like Prophase I, Metaphase I, Anaphase I, and Telophase I.
• Meiosis II: Known as equational division, it is similar to mitosis where sister chromatids are separated into four haploid cells.
• Comparison with Mitosis:
• While Meiosis is for reproduction and occurs in germ cells, Mitosis occurs in somatic cells for the purpose of growth, tissue repair, and asexual reproduction.
• Mitosis produces two genetically identical diploid daughter cells, whereas Meiosis produces four genetically different haploid cells.
• Significance of Crossing Over:
• Occurring during Pachytene of Prophase I, crossing over is the exchange of genetic material between non-sister chromatids, ensuring that no two gametes are exactly alike.

Important Points

• Discovery: Meiosis was first discovered and described in sea urchin eggs by the German biologist Oscar Hertwig in 1876.
• Location: In humans and other animals, this process takes place in the gonads—the testes in males and the ovaries in females.
• Numerical Value: In humans, meiosis reduces the 46 chromosomes (23 pairs) of a diploid cell to 23 chromosomes in a haploid gamete.
• Aneuploidy: Errors during meiosis, such as non-disjunction (failure of chromosomes to separate), can lead to chromosomal abnormalities like Down Syndrome (Trisomy 21).

The correct answer is एकपरमाणुक.

Key Points

• Atomicity is defined as the total number of atoms present in one molecule of an element or a compound. Based on this, molecules are classified as monoatomic, diatomic, triatomic, or polyatomic.
• An एकपरमाणुक (Monoatomic) molecule is one that consists of only one atom. Such elements are stable enough to exist independently without bonding to another atom of the same type.
• The most prominent examples of monoatomic elements are the Noble Gases found in Group 18 of the Periodic Table. These include Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), and Radon (Rn).
• These gases remain monoatomic because they possess a complete valence shell (octet or duet configuration), which makes them chemically inert and highly stable under standard conditions.
• Many metals, such as Sodium (Na), Iron (Fe), Copper (Cu), and Aluminium (Al), are also typically represented as monoatomic in chemical equations and formulas, although they exist in a metallic lattice structure in their solid state. Hence, the option for monoatomic is the correct answer.

Additional Information

• Diatomic Molecules (द्विपरमाणुक):
• These molecules are composed of exactly two atoms of the same or different chemical elements.
• Examples of diatomic elements include Hydrogen (H2), Nitrogen (N2), Oxygen (O2), Fluorine (F2), Chlorine (Cl2), Bromine (Br2), and Iodine (I2).
• Triatomic Molecules (त्रिपरमाणुक):
• These consist of three atoms bonded together.
• A common example of a triatomic elemental molecule is Ozone (O3), which is an allotrope of oxygen. Compounds like Carbon Dioxide (CO2) and Water (H2O) are also triatomic but are considered molecules of compounds rather than elements.
• Polyatomic Molecules (बहुपरमाणुक):
• These contain more than three atoms.
• Phosphorus usually exists as a tetraatomic molecule (P4), while Sulphur exists as an octatomic molecule (S8).
• Carbon in the form of Fullerene (C60) is another example of a complex polyatomic structure.
• Significance of Atomicity:
• Atomicity helps in determining the molecular mass of an element and is essential for balancing chemical equations.
• It reflects the chemical bonding behavior of the atoms, where non-metals typically form diatomic or polyatomic molecules to share valence electrons and reach a stable state.

Important Points

• The term Molecule of an Element specifically refers to molecules containing atoms of only one type of element, such as O2 or S8.
• The Noble Gases are the only elements that are naturally found in a stable, gaseous monoatomic state at room temperature and pressure.
• The Atomic Number of the element does not determine its atomicity; rather, it is the electron configuration and the tendency to form covalent bonds that dictates how many atoms will cluster together to form a molecule.

The correct answer is Kinetic energy.

Key Points

• Mechanical energy is defined as the energy possessed by an object due to its motion or its stored energy of position.
• It is the sum of two types of energy: Potential Energy and Kinetic Energy.
• Kinetic energy (गतिज ऊर्जा) is the energy an object has because of its motion. Any object that is moving, whether it is a rolling ball or a speeding car, possesses kinetic energy. Hence, option 2 is correct.
• Sound energy (ध्वनि ऊर्जा) is the form of energy generated by the vibrations of matter. While it involves movement of particles, it is categorized as a separate form of energy in classical mechanics. Hence, option 1 is incorrect.
• Chemical energy (रासायनिक ऊर्जा) is the energy stored in the bonds of chemical compounds, such as atoms and molecules. It is a form of potential energy but is usually classified under chemical processes rather than pure mechanical systems. Hence, option 3 is incorrect.
• Heat energy (ऊष्मा ऊर्जा) or Thermal energy is the internal energy of a system due to the random motion of its atoms and molecules. Hence, option 4 is incorrect.

Additional Information

• Kinetic Energy (KE):
• The formula for calculating kinetic energy is KE = 1/2 mv^2, where m represents the mass of the object and v represents its velocity.
• Since velocity is squared in the formula, doubling the speed of an object will quadruple its kinetic energy.
• The SI unit of kinetic energy is the Joule (J), named after the physicist James Prescott Joule.
• Potential Energy (PE):
• This is stored energy based on an object's position or configuration.
• Gravitational Potential Energy is calculated using the formula PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height.
• Examples include a stretched rubber band (Elastic Potential Energy) or water stored behind a dam.
• Law of Conservation of Energy:
• Energy can neither be created nor destroyed; it can only be transformed from one form to another.
• In a frictionless environment, the Total Mechanical Energy (KE + PE) of a system remains constant.

Important Points

• Scalar Quantity: Both mechanical energy and its components (KE and PE) are scalar quantities, meaning they have magnitude but no direction.
• Work-Energy Theorem: This theorem states that the net work done on an object is equal to the change in its kinetic energy.
• Applications: Mechanical energy is utilized in various technologies like wind turbines (converting kinetic energy of wind to electricity) and hydroelectric power plants (using the potential energy of water).
• Examples of Mechanical Energy: A flying airplane possesses both kinetic energy (due to its speed) and potential energy (due to its altitude). A hammer being swung to hit a nail possesses kinetic energy that does work on the nail.

The correct answer is Honey bee.

Key Points

• Pollination is the biological process of transferring pollen grains from the male part of a flower (anther) to the female part (stigma), enabling fertilization and the production of seeds.
• Honey bees (genus Apis) are the most prominent and effective biotic agents of pollination in the ecosystem.
• While foraging for nectar and pollen to feed their colony, bees inadvertently pick up pollen on their body hairs; this pollen is then deposited on the stigma of the next flower they visit.
• It is estimated that honey bees are responsible for approximately 80% of all insect-led pollination, making them vital for the production of commercial crops such as almonds, apples, and sunflowers.
• Bees exhibit floral fidelity, meaning they tend to visit the same species of flowers during a single trip, which significantly increases the efficiency of cross-pollination. Hence, the correct answer is Honey bee.

Additional Information

• Euglena:
• Euglena is a genus of single-celled flagellated microorganisms that possess characteristics of both plants (contain chloroplasts for photosynthesis) and animals (can ingest food).
• They are typically found in freshwater and saltwater environments and do not play any role in the reproduction or pollination of flowering plants.
• Plasmodium:
• Plasmodium is a genus of unicellular protozoan parasites.
• They are best known as the causative agents of Malaria in humans and are transmitted via the bite of an infected female Anopheles mosquito.
• They exist as obligate parasites and have no ecological function related to plant pollination.
• Amoeba:
• An Amoeba is a highly malleable unicellular organism belonging to the kingdom Protista.
• It moves and captures food using temporary cytoplasmic projections called pseudopodia (false feet).
• Like Euglena and Plasmodium, it is an aquatic or soil-dwelling microorganism with no involvement in floral biology.

Important Points

• Types of Pollination:
• Self-pollination: Occurs when pollen from the anther is deposited on the stigma of the same flower or another flower on the same plant.
• Cross-pollination: Occurs when pollen is transferred from the anther of one plant to the stigma of a different plant of the same species, promoting genetic diversity.
• Agents of Pollination:
• Biotic Agents: These include insects (bees, butterflies, beetles), birds (hummingbirds), and mammals (bats). Pollination by insects is specifically termed Entomophily.
• Abiotic Agents: These include wind (Anemophily) and water (Hydrophily). Wind-pollinated plants, like grasses and maize, produce large quantities of light, non-sticky pollen.
• Economic Impact: The Food and Agriculture Organization (FAO) highlights that pollinators like bees affect 35 percent of the world's crop production, increasing the outputs of 87 of the leading food crops worldwide.

The correct answer is अपघटन.

Key Points

• कैल्शियम कार्बोनेट (CaCO3) को गर्म करने पर इसका कैल्शियम ऑक्साइड (CaO) और कार्बन डाइऑक्साइड (CO2) में परिवर्तन अपघटन अभिक्रिया (Decomposition Reaction) का एक उत्कृष्ट उदाहरण है।
• अपघटन अभिक्रिया वह रासायनिक प्रक्रिया है जिसमें एक एकल अभिकारक ऊष्मा, प्रकाश या विद्युत जैसी ऊर्जा के प्रभाव में टूटकर दो या दो से अधिक सरल उत्पाद बनाता है।
• चूँकि इस विशिष्ट अभिक्रिया में कैल्शियम कार्बोनेट को तोड़ने के लिए ऊष्मा (Heat) का उपयोग किया जाता है, इसलिए इसे तापीय अपघटन (Thermal Decomposition) कहा जाता है।
• इस अभिक्रिया का रासायनिक समीकरण इस प्रकार है: CaCO3 (s) → CaO (s) + CO2 (g)। यहाँ CaCO3 चूना पत्थर (Limestone) है और CaO बिना बुझा हुआ चूना (Quicklime) है।
• यह अभिक्रिया औद्योगिक रूप से अत्यंत महत्वपूर्ण है क्योंकि उत्पादित कैल्शियम ऑक्साइड का उपयोग सीमेंट के निर्माण में बड़े पैमाने पर किया जाता है।

Additional Information

• संयोजन अभिक्रिया (Combination Reaction):
• यह अपघटन के विपरीत होती है। इसमें दो या दो से अधिक तत्व या यौगिक मिलकर एक एकल उत्पाद बनाते हैं।
• उदाहरण के लिए, जब कोयला (कार्बन) ऑक्सीजन में जलता है: C + O2 → CO2।
• विस्थापन अभिक्रिया (Displacement Reaction):
• इस अभिक्रिया में एक अधिक अभिक्रियाशील तत्व किसी कम अभिक्रियाशील तत्व को उसके जलीय विलयन से विस्थापित कर देता है।
• उदाहरण: जब लोहे की कील को कॉपर सल्फेट के घोल में डाला जाता है, तो लोहा कॉपर को हटा देता है: Fe + CuSO4 → FeSO4 + Cu।
• दोहरी विस्थापन अभिक्रिया (Double Displacement Reaction):
• इसमें दो अलग-अलग यौगिकों के बीच आयनों का आदान-प्रदान होता है, जिससे दो नए यौगिक बनते हैं।
• अक्सर इसमें एक अवक्षेप (Precipitate) बनता है। उदाहरण: Na2SO4 + BaCl2 → BaSO4 + 2NaCl।
• ऊष्माशोषी और ऊष्माक्षेपी अभिक्रियाएं:
• अपघटन अभिक्रियाएं आमतौर पर ऊष्माशोषी (Endothermic) होती हैं क्योंकि उन्हें बंधन तोड़ने के लिए ऊर्जा के अवशोषण की आवश्यकता होती है।
• इसके विपरीत, जिन अभिक्रियाओं में ऊर्जा बाहर निकलती है, उन्हें ऊष्माक्षेपी (Exothermic) कहा जाता है, जैसे श्वसन या प्राकृतिक गैस का जलना।

Important Points

• अपघटन के प्रकार: अपघटन केवल ऊष्मा से ही नहीं होता। यदि यह विद्युत द्वारा किया जाता है (जैसे पानी का इलेक्ट्रोलिसिस), तो इसे विद्युत अपघटन कहते हैं। यदि यह सूर्य के प्रकाश द्वारा किया जाता है (जैसे सिल्वर क्लोराइड का धूसर होना), तो इसे प्रकाशीय अपघटन कहा जाता है।
• कैल्शियम कार्बोनेट के स्रोत: प्रकृति में यह चूना पत्थर, खड़िया (Chalk) और संगमरमर (Marble) के रूप में पाया जाता है। इन सभी का रासायनिक सूत्र CaCO3 ही होता है।

The correct answer is Smooth muscle tissue.

Key Points

• Smooth muscle tissue is the type of muscle found in the walls of hollow visceral organs such as the stomach, intestines, urinary bladder, and blood vessels.
• These muscles are characterized as involuntary muscles because their movements cannot be consciously controlled by the individual; they are regulated by the Autonomic Nervous System (ANS).
• In the stomach, the smooth muscle layers are responsible for peristalsis and the mechanical churning of food, which aids in breaking down food particles and mixing them with gastric juices.
• The structure of smooth muscle cells is spindle-shaped (fusiform), with a single, centrally located nucleus, and they lack the striations (cross-bands) seen in skeletal or cardiac muscles. Hence, option 1 is correct.
• The stomach wall is unique as it typically contains three layers of smooth muscle: the inner oblique, middle circular, and outer longitudinal layers, which provide the multidirectional strength needed for digestion.

Additional Information

• Skeletal Muscle Tissue:
• These are voluntary muscles that are under the conscious control of the Somatic Nervous System.
• They are primarily attached to bones via tendons and are responsible for locomotion and body posture.
• Structurally, they are striated (striped) and contain multiple nuclei located at the periphery of the long, cylindrical cells. Hence, option 2 is incorrect.
• Cardiac Muscle Tissue:
• This specialized tissue is found exclusively in the heart (specifically the myocardium).
• Like smooth muscle, it is involuntary, but like skeletal muscle, it is striated.
• Cardiac muscle cells are branched and joined by intercalated discs, which allow for rapid transmission of electrical impulses for synchronized heart contractions. Hence, option 3 is incorrect.
• Fluid Connective Tissue:
• This is a category of connective tissue rather than muscular tissue.
• It includes blood and lymph, which circulate through the body to transport nutrients, oxygen, hormones, and waste products.
• It does not possess the contractile properties required to move the walls of the stomach. Hence, option 4 is incorrect.

Important Points

• Muscular System Overview: The human body contains over 600 muscles, categorized into three types based on their location, structure, and function.
• Functional Differences: While skeletal muscles fatigue quickly and require rest, smooth muscles (like those in the digestive tract) can maintain prolonged contractions without tiring easily, which is essential for the slow process of digestion.
• Microscopic Appearance: Smooth muscle is called "smooth" specifically because it lacks the sarcomere arrangement that creates the striated appearance in skeletal and cardiac tissues.
• Role in Homeostasis: Beyond the stomach, smooth muscles play a critical role in regulating blood pressure by altering the diameter of arteries and controlling the flow of air in the bronchioles of the lungs.

The correct answer is The pressure in a liquid depends on the shape of the container.

Key Points

• Statement 1 is Correct: Pressure is defined as the force acting normally per unit area.
  

P = F/A

• Statement 2 is Correct: Pressure exerted by a fluid at a given point acts in all directions. This is a consequence of the transmission of pressure in a fluid at rest.
• Statement 3 is Incorrect: The pressure at a particular depth in a liquid does not depend on the shape of the container. It depends on the depth, density of the liquid, and acceleration due to gravity.
  

P = ρgh

• Statement 4 is Correct: Since P = ρgh, pressure increases as the depth (h) increases, provided the liquid density and gravitational acceleration remain constant.
• Hence, the correct answer is Option 3.

Additional Information

• The pressure at a depth h in a liquid is given by:
  

P = P₀ + ρgh

where P₀ is the pressure at the liquid surface.

• For the same liquid and at the same depth, the pressure is the same regardless of the shape or size of the container.
• This principle is known as Pascal's law when referring to the transmission of pressure in an enclosed fluid.

Important Points

• Pressure = Force/Area.
• Fluid pressure acts in all directions.
• Liquid pressure does not depend on container shape.
• Liquid pressure increases with depth.

Shortcut Trick

Convert all into same root form

√8 = 2√2, √32 = 4√2, √128 = 8√2, √50 = 5√2

Expression = 2√2 + 2×4√2 − 8√2 + 2×5√2

= (2 + 8 − 8 + 10)√2 = 12√2

∴ Answer = 12√2

Alternate Method

Given:

√8 + 2√32 − √128 + 2√50

Concept Used:

Simplification of surds

Calculation:

⇒ √8 = √(4×2) = 2√2

⇒ √32 = √(16×2) = 4√2

⇒ √128 = √(64×2) = 8√2

⇒ √50 = √(25×2) = 5√2

⇒ Substitute values

⇒ = 2√2 + 2(4√2) − 8√2 + 2(5√2)

⇒ = 2√2 + 8√2 − 8√2 + 10√2

⇒ = (2 + 8 − 8 + 10)√2

⇒ = 12√2

∴ The correct answer is 12√2.

Additional Information

Surd Simplification

√(a×b) = √a × √b

Like Terms

Only same radicals can be added/subtracted

Perfect Squares

Extract perfect square factors for simplification

Shortcut Trick

Required percentage = (Value ÷ Base Value) × 100

Since both fractions have the same denominator (20), the percentage is simply (Numerator 1 ÷ Numerator 2) × 100.

Required % = (1 ÷ 11) × 100 ≈ 9.09%

∴ The correct answer is 9.09%.

Alternate Method

Given:

First value = 1/20

Second value (Base) = 11/20

Formula Used:

Percentage = (A/B) × 100

Calculations:

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

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

⇒ Required Percentage = (1/11) × 100

⇒ Required Percentage = 100 ÷ 11

⇒ Required Percentage = 9.090909...

⇒ Required Percentage ≈ 9.09%

∴ The correct answer is 9.09%.

Additional Information

Fraction to Percentage Conversion

To convert any fraction x/y into a percentage, multiply the fraction by 100 and add the % symbol.

Reciprocal Percentages

Knowing common reciprocals like 1/11 ≈ 9.09% and 1/9 ≈ 11.11% helps in solving Simplification and Percentage questions faster.

Percentage Change

Percentage change = [(New Value − Original Value) ÷ Original Value] × 100.

Shortcut Trick

0.2x + 60 = x

0.8x = 60 ⇒ x = 75

70% of x = 0.7 × 75

= 52.5

∴ Answer = 52.5

Alternate Method

Given:

20% of a number when added to 60 gives the number

Formula used:

Percentage = (value ÷ 100) × number

Calculation:

⇒ Let the number be x

⇒ 20% of x = (20/100) × x = 0.2x

⇒ According to question

⇒ 0.2x + 60 = x

⇒ x − 0.2x = 60

⇒ 0.8x = 60

⇒ x = 60 ÷ 0.8 = 75

⇒ Required percentage = 70% of 75

⇒ = (70/100) × 75

⇒ = 52.5

∴ The correct answer is 52.5.

Additional Information

Percentage Formula

x% of number = (x/100) × number

Equation Formation

Translate statement into linear equation

Decimal Conversion

20% = 0.2, 70% = 0.7

Shortcut Trick

Profit = SP − CP = 335 − 300 = 35.

Profit % = (Profit ÷ CP) × 100.

Profit % = (35 ÷ 300) × 100 = 35 ÷ 3 = 11²/₃%.

∴ The correct answer is 11(2)/(3)%.

Alternate Method

Given → Cost Price (CP) = ₹ 300, Selling Price (SP) = ₹ 335. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100

→ Profit = 335 − 300 = 35 → Profit % = (35 ÷ 300) × 100 → Profit % = 35 ÷ 3 = 11.66...% → In fraction form, 35/3 = 11²/₃%

∴ The correct answer is 11(2)/(3)%.

Additional Information

Profit and Loss Basics

Profit occurs when Selling Price (SP) is greater than Cost Price (CP). Loss occurs when CP > SP.

Percentage Calculation

Profit or Loss percentage is always calculated on the Cost Price (CP) unless stated otherwise.

Shortcut Trick

The area of a triangle sharing the same base and lying between the same parallel lines as a parallelogram is always half the area of that parallelogram.

Area(Δ APB) = 1/2 × Area(ABCD) (since they share base AB and lie between AB || CD).

Area(Δ BQC) = 1/2 × Area(ABCD) (since they share base BC and lie between BC || AD).

Since both triangles are equal to half of the same parallelogram, their areas must be equal.

∴ The correct answer is the area of Δ BQC.

Alternate Method

Given:ABCD is a parallelogram. P is a point on side DC and Q is a point on side AD.

Formula Used: Area of triangle = 1/2 × base × height; Area of parallelogram = base × height.

⇒ Area(Δ APB) = 1/2 × AB × (height of parallelogram with respect to base AB)

⇒ Area(ABCD) = AB × (height of parallelogram with respect to base AB)

⇒ Area(Δ APB) = 1/2 × Area(ABCD) --- (i)

⇒ Area(Δ BQC) = 1/2 × BC × (height of parallelogram with respect to base BC)

⇒ Area(ABCD) = BC × (height of parallelogram with respect to base BC)

⇒ Area(Δ BQC) = 1/2 × Area(ABCD) --- (ii)

⇒ From equations (i) and (ii), we get: Area(Δ APB) = Area(Δ BQC)

∴ The correct answer is the area of Δ BQC.

Additional Information

Area of Parallelogram

The area of a parallelogram is given by the product of its base and the corresponding altitude (height).

Triangle and Parallelogram Relationship

When a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is half the area of the parallelogram.

Parallelogram Properties

In a parallelogram, opposite sides are parallel and equal, and diagonals bisect each other, dividing the parallelogram into two triangles of equal area.

Shortcut Trick

Assume all 200 tickets sold were Youth tickets: Total = 200 × ₹150 = ₹30,000.

Extra revenue earned = Actual revenue − Assumed revenue = ₹38,000 − ₹30,000 = ₹8,000.

Difference between Adult and Youth ticket price = ₹250 − ₹150 = ₹100.

Number of Adult tickets = 8,000 ÷ 100 = 80 tickets.

Number of Youth tickets = Total − Adult = 200 − 80 = 120 tickets.

∴ The correct answer is 120 youth tickets and 80 adult tickets.

Alternate Method

Given: Youth ticket price = ₹150, Adult ticket price = ₹250, Total tickets = 200, Total Revenue = ₹38,000.

Method: We can use the Alligation Method by finding the Average Price per ticket.

⇒ Average price per ticket = Total Revenue ÷ Total Tickets

⇒ Average price = 38,000 ÷ 200 = ₹190.

⇒ Ratio of Youth tickets : Adult tickets = 60 : 40 = 3 : 2.

⇒ Total ratio parts = 3 + 2 = 5 units.

⇒ 5 units = 200 tickets.

⇒ 1 unit = 200 ÷ 5 = 40 tickets.

⇒ Youth tickets = 3 units = 3 × 40 = 120 tickets.

⇒ Adult tickets = 2 units = 2 × 40 = 80 tickets.

∴ The correct answer is 120 youth tickets and 80 adult tickets.

Additional Information

Linear Equations Method

This problem can also be solved using simultaneous equations: x + y = Total Quantity and (Price₁ × x) + (Price₂ × y) = Total Value.

Alligation Rule

Quantity of Cheaper / Quantity of Dearer = (Price of Dearer − Mean Price) / (Mean Price − Price of Cheaper).

Weighted Average

The overall average price of a mixture depends on the individual prices and the quantity (weight) of each component: A_avg = (n₁v₁ + n₂v₂) ÷ (n₁ + n₂).

Shortcut Trick For the equation X/75 = 12/X, the value of X is the geometric mean of the two denominators/numerators. X2 = 75 × 12 X = √(75 × 12) = √(900) = 30 ∴ The correct answer is 30. Alternate Method Given: Equation: X/75 = 12/X where X > 0 Formula Used: Cross-multiplication: a/b = c/d ⇒ a × d = b × c Calculations: ⇒ X/75 = 12/X ⇒ X × X = 75 × 12 ⇒ X2 = 900 ⇒ X = √900 ⇒ X = 30 (Since X > 0) ∴ The correct answer is 30. Additional Information Mean Proportional If a/x = x/b, then x is called the mean proportional between a and b, calculated as x = √(ab). Quadratic Roots A quadratic equation of the form x2 = k has two roots, √k and −√k. The condition X > 0 filters the positive root.

Shortcut Trick

Find factors of xy = 18 whose difference (x − y) is 3.

Possible pairs for 18 are (18, 1), (9, 2), and (6, 3).

Since 6 − 3 = 3, we have x = 6 and y = 3.

Substitute these in x² − y²: 6² − 3² = 36 − 9 = 27.

∴ The correct answer is 27.

Alternate Method

Given:

x − y = 3

xy = 18

Formula Used:

(x + y)² = (x − y)² + 4xy

x² − y² = (x − y)(x + y)

Calculations:

⇒ (x + y)² = 3² + 4 × 18

⇒ (x + y)² = 9 + 72

⇒ (x + y)² = 81

⇒ x + y = √81 = 9

Now, calculate x² − y²:

⇒ x² − y² = (x − y)(x + y)

⇒ x² − y² = 3 × 9

⇒ x² − y² = 27

∴ The correct answer is 27.

Additional Information

Difference of Squares

The algebraic identity for the difference of two squares is given by a² − b² = (a − b)(a + b).

Relationship between Sum and Difference

The square of the sum and the square of the difference are related by (a + b)² − (a − b)² = 4ab.

Square of a Binomial

Standard identities: (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Shortcut Trick

Identify the total number of days: Feb (24) + Mar (31) + Apr (18) = 73 days.

In competitive exams, 73 days is a standard value equal to exactly 1/5 of a year (73 ÷ 365 = 1/5).

Simple Interest = (Principal × Rate × Time) ÷ 100

Simple Interest = (2000 × 7 × 1/5) ÷ 100 = 400 × 7 ÷ 100 = ₹28.

∴ The correct answer is ₹28.

Alternate Method

Given:

Principal (P) = ₹2,000

Rate of Interest (R) = 7% per annum

Time Period = 4 February 2023 to 18 April 2023

Formula Used:

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

Calculations:

⇒ Number of days in February (non-leap year) = 28 − 4 = 24 days

⇒ Number of days in March = 31 days

⇒ Number of days in April = 18 days

⇒ Total Days = 24 + 31 + 18 = 73 days

⇒ Time (T) in years = 73 ÷ 365 = 1/5 years

⇒ SI = (2000 × 7 × 1/5) ÷ 100

⇒ SI = (400 × 7) ÷ 100

⇒ SI = 2800 ÷ 100 = 28

∴ The correct answer is ₹28.

Additional Information

Day Counting Rule

While calculating the number of days between two dates, usually the starting day is excluded and the last day is included.

Leap Year Consideration

Always check the year; if it is divisible by 4 (e.g., 2024), February has 29 days. Since 2023 is not divisible by 4, we used 28 days.

Standard Conversions

In interest problems, 73 days = 1/5 year and 146 days = 2/5 year are very common values used to simplify calculations.

Shortcut Trick

Combined efficiency of Arun + Manish + Tarun = (Total Work ÷ Days) / 2 = (4 + 5 + 6) ÷ 2 = 7.5 units/day.

Efficiency of Arun = Combined efficiency (A+M+T) − Efficiency of (M+T) = 7.5 − 5 = 2.5 units/day.

Time taken by Arun alone = Total Work ÷ Efficiency = 60 ÷ 2.5 = 24 days.

∴ The correct answer is 24 days.

Alternate Method

Given:

Arun and Manish (A + M) = 15 days

Manish and Tarun (M + T) = 12 days

Tarun and Arun (T + A) = 10 days

Formula Used:

Total Work = LCM of individual days

Efficiency = Total Work ÷ Time

Calculations:

⇒ 2 × (Arun + Manish + Tarun) = 4 + 5 + 6 = 15

⇒ Arun + Manish + Tarun = 15 ÷ 2 = 7.5

⇒ Arun's efficiency = (Arun + Manish + Tarun) − (Manish + Tarun)

⇒ Arun's efficiency = 7.5 − 5 = 2.5

⇒ Days taken by Arun = 60 ÷ 2.5

⇒ Days taken by Arun = 24

∴ The correct answer is 24 days.

Additional Information

Total Combined Efficiency

When pairs are given like (A+B), (B+C), and (C+A), the sum of their efficiencies is twice the efficiency of (A+B+C).

Work & Wages

Wages are always distributed in the ratio of the work done or the ratio of efficiencies when time taken is same.

Alternate Day Work

For alternate days, calculate work done in one cycle (sum of efficiencies) and then divide total work by cycle work.

Shortcut Trick

Distance from bottom (base) = 15 units.

Distance from top (hypotenuse) = 2 × 15 = 30 units.

Using the property of a 30-60-90 triangle where hypotenuse is double the base.

Height = Base × √3 = 15√3 units.

∴ The correct answer is 15√3 units.

Alternate Method

Given: Distance from bottom (BC) = 15 units. Distance from top (AC) = 2 × BC = 30 units.

Formula Used: Pythagoras Theorem: AB² + BC² = AC²

⇒ Let AB be the height of the building (h).

⇒ h² + 15² = 30²

⇒ h² + 225 = 900

⇒ h² = 900 − 225

⇒ h² = 675

⇒ h = √675 = √(225 × 3)

⇒ h = 15√3 units.

∴ The correct answer is 15√3 units.

Additional Information

Pythagoras Theorem

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².

30-60-90 Triangle Ratio

The sides of a 30-60-90 triangle are always in the ratio 1 : √3 : 2. If the shortest side (opposite 30°) is x, the hypotenuse is 2x and the height is x√3.

Trigonometric Ratios

cos θ = Base / Hypotenuse. In this case, cos θ = 15/30 = 1/2, which means the angle of elevation θ is 60°.

Shortcut Trick

Assume a base value (Assumed Mean) near the middle, say 50.

Calculate deviations from 50: −8, −21, −8, +8, −32, −11, −9, +29, +43.

Net deviation = −8 − 21 − 8 + 8 − 32 − 11 − 9 + 29 + 43 = −9.

Average deviation = −9 ÷ 9 = −1.

Actual Mean = Assumed Mean + Average Deviation = 50 + (−1) = 49.

∴ The correct answer is 49.

Alternate Method

Given Observations: 42, 29, 42, 58, 18, 39, 41, 79, 93

Total count (n): 9

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

⇒ Sum = 42 + 29 + 42 + 58 + 18 + 39 + 41 + 79 + 93

⇒ Sum = 441

⇒ Arithmetic Mean = 441 ÷ 9

⇒ Arithmetic Mean = 49

∴ The correct answer is 49.

Additional Information

Properties of Arithmetic Mean

The sum of deviations of items from their arithmetic mean is always zero (∑(x − x̄) = 0).

Effect of Changes

If each observation is increased, decreased, multiplied, or divided by a constant k, the mean also changes by that same constant k.

Combined Mean

If two groups have means x̄₁ and x̄₂ with sizes n₁ and n₂, the combined mean is (n₁x̄₁ + n₂x̄₂) ÷ (n₁ + n₂).

Shortcut Trick

Sum of reciprocals of two numbers = (Sum of numbers) ÷ (Product of numbers)

We know that Product of numbers = HCF × LCM

Sum of reciprocals = 60 ÷ (12 × 72)

Sum of reciprocals = 5 ÷ 72

∴ The correct answer is 5/72.

Alternate Method

Given:

Sum of two numbers (x + y) = 60

HCF = 12, LCM = 72

Formula Used:

Product of two numbers (x × y) = HCF × LCM

Sum of reciprocals = (1/x) + (1/y) = (x + y) / (xy)

Calculations:

⇒ Product (xy) = 12 × 72 = 864

⇒ Sum of reciprocals = 60 / 864

⇒ Dividing both numerator and denominator by 12:

⇒ 60 / 864 = 5 / 72

∴ The correct answer is 5/72.

Additional Information

HCF and LCM Relation

For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b.

Reciprocal Sum Property

The sum of the reciprocals of any two numbers is always equal to the sum of the numbers divided by their product.

Co-prime Numbers

If two numbers are co-prime, their HCF is 1 and their LCM is equal to their product.

Shortcut Trick

Total Surface Area (TSA) = Total Cost ÷ Rate = 100602 ÷ 23 = 4374 cm²

Side of the cube (a) = √(TSA ÷ 6) = √(4374 ÷ 6) = √729 = 27 cm

Volume of the cube = a³ = 27³ = 19,683 cm³

∴ The correct answer is 19,683 cm³.

Alternate Method

Given:

Total cost of painting = ₹1,006.02

Rate of painting = 23 paise per cm²

Formula Used:

Total Surface Area (TSA) of a cube = 6 × a²

Volume of a cube = a³ (where 'a' is the side of the cube)

Calculations:

⇒ Total Cost in paise = 1006.02 × 100 = 100,602 paise

⇒ Total Surface Area (TSA) = Total Cost ÷ Rate = 100,602 ÷ 23

⇒ TSA = 4,374 cm²

⇒ 6 × a² = 4,374

⇒ a² = 4,374 ÷ 6 = 729

⇒ a = √729 = 27 cm

⇒ Volume = a³ = 27 × 27 × 27

⇒ Volume = 19,683 cm³

∴ The correct answer is 19,683 cm³.

Additional Information

Lateral Surface Area (LSA)

The surface area of the four vertical faces of a cube is given by 4a².

Diagonal of a Cube

The length of the longest rod that can be placed inside a cube is its diagonal, calculated as d = a√3.

Unit Conversion

Always ensure the units of cost and rate are the same (either both in Rupees or both in Paise) before calculation.

Shortcut Trick

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

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

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

⇒ ∠AEB = 70° + 57° = 127°.

∴ The correct answer is 127°.

Alternate Method

Given: BD ⊥ AC, ∠DBC = 33°, ∠CAE = 70°.

In ΔBDC, ∠BDC = 90° (since BD ⊥ AC).

⇒ ∠BCD = 180° − (∠BDC + ∠DBC)

⇒ ∠BCD = 180° − (90° + 33°) = 57°.

Shortcut Trick

The Marked Price (MP) is always considered as 100%.

If Discount = 54%, then Selling Price (SP) = 100% − 54% = 46%.

According to the question, 46% → ₹ 29,946.

1% → 29,946 ÷ 46 = ₹ 651.

100% (MP) → 651 × 100 = ₹ 65,100.

∴ The correct answer is ₹ 65,100.

Alternate Method

Given: Selling Price (SP) = ₹ 29,946 and Discount% = 54%.

Formula: SP = MP × (100 − Discount%) ÷ 100

⇒ 29,946 = MP × (100 − 54) ÷ 100

⇒ 29,946 = MP × 46 ÷ 100

⇒ MP = (29,946 × 100) ÷ 46

⇒ MP = 651 × 100

⇒ MP = ₹ 65,100.

∴ The correct answer is ₹ 65,100.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on an item. Discount is always calculated on the Marked Price. Formula: SP = MP − Discount.

Discount Percentage

It is the ratio of discount to the marked price expressed as a percentage. Formula: Discount% = (Discount ÷ MP) × 100.

Shortcut Trick

Ratio of Teacher to Student age: Current = 4 : 1, Five years ago = 7 : 1.

Make the ratio difference equal: (4:1)×6 → 24:6 and (7:1)×3 → 21:3.

Difference in ratio units = 24 − 21 = 3 units, which corresponds to 5 years.

Current age of Teacher = 24 units → (5/3) × 24 = 40 years.

∴ The correct answer is 40 years.

Alternate Method

Given:

Let the current age of the Student be x.

Current age of the Teacher = 4x.

Calculations:

⇒ Age of Student 5 years ago = x − 5

⇒ Age of Teacher 5 years ago = 4x − 5

⇒ According to the problem: 4x − 5 = 7 × (x − 5)

⇒ 4x − 5 = 7x − 35

⇒ 3x = 30

⇒ x = 10

⇒ Current age of Teacher = 4 × 10 = 40 years.

∴ The correct answer is 40 years.

Additional Information

Age Ratio Constant Difference

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

Linear Equation Method

For age problems, always define the variable based on the current age to simplify calculations for past or future conditions.

Shortcut Trick

Combined efficiency (P+Q) = 60 ÷ 12 = 5 units/hr (Let Total Work = 60 units)

Efficiency of P = 60 ÷ 30 = 2 units/hr

Efficiency of Q = 5 − 2 = 3 units/hr

Time for Q to fill 1/4 of tank = (60 ÷ 4) ÷ 3 = 15 ÷ 3 = 5 hours

∴ The correct answer is 5 hours.

Alternate Method

Given:

Time taken by P and Q together = 12 hours

Time taken by P alone = 30 hours

Calculations:

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

⇒ Efficiency of Q = 5 − 2 = 3 units/hr

⇒ One-fourth of total tank capacity = 60 ÷ 4 = 15 units

⇒ Time taken by Q = Work ÷ Efficiency

⇒ Time = 15 ÷ 3 = 5 hours

∴ The correct answer is 5 hours.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to time. If a person takes 'n' days to complete a work, efficiency = 1/n units per day.

Pipes and Cisterns

Inlet pipes have positive efficiency, while outlet (leakage) pipes have negative efficiency. Net work = Sum of efficiencies.

Shortcut Trick

Combine ratios A : B = 3 : 1 and B : C = 7 : 12 to get A : B : C = 21 : 7 : 12.

Total units = 21 + 7 + 12 = 40 units.

Total profit ₹27,600 ÷ 40 units = ₹690 per unit.

C's share = 12 units × ₹690 = ₹8,280.

∴ The correct answer is ₹8,280.

Alternate Method

Given:

Ratio A : B = 18 : 6 = 3 : 1

Ratio B : C = 7 : 12

Total Profit = ₹27,600

Calculations:

⇒ To equalize B, multiply A : B by 7: (3 × 7) : (1 × 7) = 21 : 7

⇒ Combined Ratio A : B : C = 21 : 7 : 12

⇒ Sum of ratio terms = 21 + 7 + 12 = 40

⇒ C's share = (12 ÷ 40) × 27,600

⇒ C's share = 12 × 690

⇒ C's share = ₹8,280

∴ The correct answer is ₹8,280.

Additional Information

Partnership Profit Distribution

Profit is distributed in the ratio of (Capital × Time). If time is constant, profit ratio equals the capital ratio.

Combining Ratios

If A:B = a:b and B:C = c:d, then A:B:C = (a×c) : (b×c) : (b×d).

Ratio to Value Conversion

Value of a part = (Ratio of that part ÷ Sum of all ratios) × Total Value.

Shortcut Trick

Remaining Distance = 1/3 of 132 km = 44 km.

Remaining Time = 4/7 of 14 hours = 8 hours.

Required Speed = 44 ÷ 8 = 5.5 km/hr.

∴ The correct answer is 5.5 km/hr.

Alternate Method

Given: Total Distance = 132 km, Total Time = 14 hours.

Step 1: Calculate Remaining Distance

⇒ Distance covered = 2/3 × 132 = 88 km

⇒ Remaining Distance = 132 − 88 = 44 km

Step 2: Calculate Remaining Time

⇒ Time taken = 3/7 × 14 = 6 hours

⇒ Remaining Time = 14 − 6 = 8 hours

Step 3: Calculate Required Speed

⇒ Speed = Distance ÷ Time

⇒ Speed = 44 ÷ 8 = 5.5 km/hr

∴ The correct answer is 5.5 km/hr.

Additional Information

Average Speed Formula

Average Speed = Total Distance ÷ Total Time. In this case, 132 ÷ 14 ≈ 9.42 km/hr.

Uniform Speed Relationship

Distance = Speed × Time. To find any one parameter, the other two must be known or expressed in terms of a single variable.

Unit Conversion

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

Shortcut Trick

Increase in average = (New Score − Old Average) ÷ Total Innings after new score

Increase = (183 − 52) ÷ 13

Increase = 131 ÷ 13 = 10.0769...

Rounding to the nearest whole number ≈ 10.

∴ The correct answer is 10.

Alternate Method

Given:

Average score in 12 innings = 52 runs

Score in 13^th innings = 183 runs

Formula Used:

Average = Total runs ÷ Number of innings

Calculations:

⇒ Total runs in 12 innings = 12 × 52 = 624 runs

⇒ Total runs after 13 innings = 624 + 183 = 807 runs

⇒ New average = 807 ÷ 13

⇒ New average = 62.0769... runs

⇒ Increase in average = New average − Old average

⇒ Increase = 62.0769... − 52 = 10.0769... runs

⇒ Rounding to the nearest whole number, we get 10.

∴ The correct answer is 10.

Additional Information

Average Change Concept

When a new observation is added, the change in average is equal to the difference between the new value and the old average, divided by the new total count of observations.

Rounding Off Rules

If the decimal part is 0.5 or greater, round up to the next whole number; if it is less than 0.5, round down to the current whole number.

Total Sum Formula

Total Sum = Average × Number of items. This is used to find the new sum when an entry is added or removed.

Shortcut Trick

Total distance to cover = Sum of lengths of both trains = 968 + 968 = 1936 m.

Relative speed (opposite direction) = Sum of individual speeds = 2 × Speed (since speeds are same).

Relative Speed = Total Distance ÷ Time = 1936 ÷ 22 = 88 m/s.

Speed of each train = 88 ÷ 2 = 44 m/s.

∴ The correct answer is 44 m/s.

Alternate Method

Given:

Length of Train 1 (L₁) = 968 m

Length of Train 2 (L₂) = 968 m

Time taken to cross each other (t) = 22 seconds

Speed of each train = s (since speeds are the same)

Formula Used:

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

When two objects move in opposite directions, Relative Speed = s₁ + s₂

Calculations:

⇒ Total Distance = L₁ + L₂ = 968 + 968 = 1936 m

⇒ Relative Speed = s + s = 2s

⇒ 2s = 1936 ÷ 22

⇒ 2s = 88

⇒ s = 88 ÷ 2

⇒ s = 44 m/s

∴ The correct answer is 44 m/s.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference of their speeds (s₁ − s₂).

Unit Conversion

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

Crossing a Stationary Object

When a train crosses a pole or a person, the distance covered is equal to the length of the train.

Shortcut Trick

A number is divisible by 3 if the sum of its digits is divisible by 3.

Option (1): 7 + 8 + 1 = 16 (No)

Option (2): 1 + 2 + 3 = 6 (Yes, 6 is divisible by 3)

Option (3): 2 + 4 + 5 = 11 (No)

Option (4): 5 + 5 + 7 = 17 (No)

∴ The correct answer is 123.

Alternate Method

Given: Numbers 781, 123, 245, 557.

Rule: Divisibility by 3 depends on the sum of digits.

⇒ For 781: Sum = 7 + 8 + 1 = 16; 16 ÷ 3 = 5 Remainder 1.

⇒ For 123: Sum = 1 + 2 + 3 = 6; 6 ÷ 3 = 2 Remainder 0.

⇒ For 245: Sum = 2 + 4 + 5 = 11; 11 ÷ 3 = 3 Remainder 2.

⇒ For 557: Sum = 5 + 5 + 7 = 17; 17 ÷ 3 = 5 Remainder 2.

∴ The correct answer is 123.

Additional Information

Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Divisibility by 6

A number is divisible by 6 if it is even and the sum of its digits is divisible by 3.

Divisibility by 4

A number is divisible by 4 if the last two digits are divisible by 4.

Shortcut Trick

Ratio of Cost Price (CP) to Marked Price (MP) is given by (100 − D%) : (100 + P%).

Let CP = 100, then MP = 100 + 80 = 180.

Profit = 8%, so Selling Price (SP) = 100 + 8 = 108.

Discount = MP − SP = 180 − 108 = 72.

X = (Discount ÷ MP) × 100 = (72 ÷ 180) × 100 = 40%.

∴ The correct answer is 40.

Alternate Method

Given → Markup% = 80%, Profit% = 8%, Discount% = X%. Formulas: SP = CP × (100 + P%) ÷ 100 | SP = MP × (100 − D%) ÷ 100 | MP = CP × (100 + Markup%) ÷ 100.

⇒ Let Cost Price (CP) be 100. ⇒ Marked Price (MP) = 100 + 80% of 100 = 180. ⇒ Selling Price (SP) = 100 + 8% of 100 = 108. ⇒ Discount Amount = MP − SP = 180 − 108 = 72. ⇒ Discount Percentage (X) = (72 ÷ 180) × 100 = 40.

∴ The correct answer is 40.

Additional Information

Relation between CP, MP, Profit, and Discount

The formula CP × (1 + Markup%) × (1 − Discount%) = CP × (1 + Profit%) allows solving for any single unknown variable when others are provided.

Marked Price

It is the price displayed on the product label. Discounts are always calculated on the Marked Price (MP), while Profit or Loss is calculated on the Cost Price (CP).

Shortcut Trick

Use the Successive Multiplying Factor method.

Net Multiplier = 0.70 × 0.75 × 0.55 × 1.45

Net Multiplier = 0.525 × 0.7975 = 0.4186875

Decrease % = (1 − 0.4186875) × 100 = 58.13125%

∴ The correct answer is a decrease of 58.13%.

Alternate Method

Assume the original price of fuel is 100 units.

⇒ Price after 1st month = 100 × (100 − 30)/100 = 70

⇒ Price after 2nd month = 70 × (100 − 25)/100 = 70 × 0.75 = 52.5

⇒ Price after 3rd month = 52.5 × (100 − 45)/100 = 52.5 × 0.55 = 28.875

⇒ Price after 4th month = 28.875 × (100 + 45)/100 = 28.875 × 1.45 = 41.86875

⇒ Net decrease = 100 − 41.86875 = 58.13125

⇒ Percentage decrease = (58.13125 / 100) × 100 ≈ 58.13%

∴ The correct answer is a decrease of 58.13%.

Additional Information

Successive Percentage Change

For two successive changes a% and b%, the net change is given by [a + b + (ab/100)]%.

Multiplying Factor (MF)

For an x% increase, MF = (1 + x/100). For an x% decrease, MF = (1 − x/100). Final Value = Initial Value × MF₁ × MF₂ ...

Percentage Decrease Formula

Percentage Decrease = [(Initial Value − Final Value) / Initial Value] × 100%.

Here, the logic followed is as : In each pair, the second letter-group is obtained by subtracting 2 from the positional value of each letter in the first letter-group.

1. UW − SU

2. OQ − MO

3. DF − BD

4. IK − FK

It is observed that in all the other options, 2 is subtracted from each letter, whereas 'IK − FK' does not follow this pattern.

Therefore, 'IK − FK' does not belong to the group.

Hence, the correct answer is "Option 4".

Logic followed here is: (Positional value of each letter) + 6.

For

ACEH is related to GIKN →

KMOR is related to QSUX →

Similarly, let's find the related word for JLNQ:

Therefore, 'JLNQ' is related to PRTW.

Hence, the correct answer is "Option 2".

Given Number: 632517

Rule: Add 1 to each odd digit. Subtract 1 from each even digit.

Step 1:

Apply the rule to each digit:

Step 2:

New number formed: 541628

Step 3:

Largest digit = 8

Smallest digit = 1

Sum = 8 + 1 = 9

Therefore, the required sum is 9.

Hence, the correct answer is "Option 3".

Given Series:

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

We need to find the unique numbers greater than 7.

Numbers greater than 7 are: 8, 9

Total unique numbers greater than 7 = 2

Therefore, the answer is Two.

Hence, the correct answer is "Option 4".

Statements:

Some silver is gold.

Some silver is cash.

Some gold is fortune.

Venn Diagram Logic:

Conclusions:

(I) Some silver is fortune: **Does not follows (**Because there is no definite connection between silver and fortune.)

(II) Some gold is cash: **Does not follows (**Because there is no definite connection between gold and cash.)

Therefore, neither conclusion (I) nor (II) follows.

Hence, the correct answer is "Option 4".

Given:

Total students = 91

Mr. Akte is 33rd from the left.

Mr. Memi is 22nd to the right of Mr. Akte.

Step 1:

Find Mr. Memi's position from the left end.

Mr. Akte's position from the left = 33

Mr. Memi is 22 places to the right of Mr. Akte.

So,

33 + 22 = 55

Therefore, Mr. Memi is 55th from the left end.

Step 2:

Find Mr. Memi's position from the right end.

Formula:

Position from right = Total students − Position from left + 1

= 91 − 55 + 1

= 37

Therefore, Mr. Memi is 37th from the right end.

Hence, the correct answer is "Option 3".

Given:

Six neighbors — Amrita, Maria, Ruhi, Sunita, Ishaan and Vaibhav — are sitting around a round table facing the center.

Amrita sits second to the left of Maria.

Ruhi is the immediate neighbor of both Maria and Sunita.

Ishaan sits second to the right of Vaibhav.

From Amrita's right direction, the person between Amrita and Maria is Ishaan.

Therefore, Ishaan sits between Amrita and Maria.

Hence, the correct answer is "Option 3".

Given:

Seven people P, Q, R, S, T, U and V are sitting in a row facing north.

Q is sitting third from the right end.

V is sitting third to the left of S.

T is sitting to the right of Q and at one of the extreme ends of the row.

Only two people sit between U and T.

P is not sitting at any extreme end.

Find who is sitting second from the right end.

From the right end:

1st from right = T

2nd from right = S

Therefore, S is sitting second from the right end.

Hence, the correct answer is "Option 4".

Logic followed here is: (Sum of positional values of letters) × 2.

For

YISB is coded as 110 →

Sum of positional values = 25 + 9 + 19 + 2 = 55

Code = 55 × 2 = 110

PKJQ is coded as 108 →

Sum of positional values = 16 + 11 + 10 + 17 = 54

Code = 54 × 2 = 108

Similarly, let's find the code for CNXR:

Sum of positional values = 3 + 14 + 24 + 18 = 59

Code = 59 × 2 = 118

Therefore, the code for 'CNXR' is 118.

Hence, the correct answer is "Option 3".

Given Series:

(Left) 3 3 > + / \ ^ # + @ 7 9 3 6 $ \ + 9 > 6 & (Right)

We need to find the symbols which are:

→ Immediately preceded by a number

→ Immediately followed by a number

Required pattern: Number → Symbol → Number

Checking the series:

(Left) 3 3 > + / \ ^ # + @ 7 9 3 6 $ \ + 9 > 6 & (Right)

The symbols satisfying the condition are:

Therefore, the total number of such symbols is 1.

Hence, the correct answer is "Option 2".

Logic followed here is: The second letter-cluster in each pair is obtained by subtracting 1 from the positional value of each letter in the first letter-cluster.

1. AX - YY:

2. KH - JG:

3. XU - WT:

4. HE - GD:

The pattern followed by KH-JG, XU-WT, and HE-GD is a subtraction of 1 from each letter's positional value. AX-YY does not follow this pattern.

Therefore, the odd letter-group pair is AX - YY.

Hence, the correct answer is "Option 1".

Given Code Language:

Given Expression:

T # Q % C % N # P: T is the daughter of Q. Q is the father of C. C is the father of N. N is the daughter of P

Family Structure:

Q is father of C.

C is father of N.

N is daughter of P.

Therefore, P is wife of C.

Since T is daughter of Q and C is also child of Q, T is sister of C.

And P is wife of C.

So, T is the husband's sister of P.

Hence, the correct answer is "Option 2".

Given:

Tufail walks 100 m towards the north.

Then he turns right and walks 220 m.

Again, he turns right and walks 121 m.

So, from the starting point, Tufail is towards the Southeast direction.

Hence, the correct answer is "Option 2".