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The correct answer is Atomic mass of Ca + (2 times atomic mass of Cl) = 40 + 71 = 111 u.

Key Points

• The formula unit mass of a substance is defined as the sum of the atomic masses of all atoms present in the formula unit of an ionic compound. It is numerically equivalent to molecular mass but used specifically for compounds composed of ions.
• In the chemical formula for Calcium Chloride (CaCl₂), there is one atom of Calcium (Ca) and two atoms of Chlorine (Cl).
• The atomic mass of Calcium (Ca) is approximately 40 u. Calcium is a group 2 alkaline earth metal with an atomic number of 20.
• The atomic mass of Chlorine (Cl) is approximately 35.5 u. This fractional value is the weighted average of its naturally occurring isotopes, Chlorine-35 and Chlorine-37.
• To calculate the formula unit mass, the mass of Ca is added to twice the mass of Cl: 40 + (2 × 35.5).
• Multiplying the mass of Chlorine by two gives 71 u. Adding this to the 40 u of Calcium results in a total of 111 u.

 Additional Information

• Calcium (Ca):
• It is an essential alkaline earth metal used in construction, cement production, and biological functions like bone mineralization.
• In CaCl₂, it exists as a Ca²⁺ cation.
• Chlorine (Cl):
• It is a highly reactive halogen found in Group 17 of the periodic table.
• In CaCl₂, it exists as two Cl⁻ anions to balance the charge of the calcium ion.
• Unified Atomic Mass Unit (u):
• The unit u represents the unified atomic mass unit, where 1 u is exactly 1/12^th the mass of an atom of Carbon-12.
• It is approximately equal to 1.66 × 10⁻²⁷ kg.
• Stoichiometry and Bonding:
• Calcium Chloride is an ionic compound formed by the electrostatic attraction between oppositely charged ions.
• The formula CaCl₂ represents the simplest whole-number ratio of ions in the crystal lattice.

The correct answer is Zero.

Key Points

• In the field of physics, work done is defined as the product of the component of the force acting on an object and the displacement caused by that force in its own direction.
• The mathematical expression for work is W = F × s × cos(θ), where W represents work, F denotes the magnitude of the applied force, s is the magnitude of the displacement, and θ is the angle between the force and displacement vectors.
• When an object remains stationary (s = 0) despite the application of an external force, the total mechanical work performed on the object is calculated as W = F × 0 × cos(θ) = 0.
• This scenario occurs frequently in real-world situations, such as a person pushing against a load-bearing wall or a student holding a heavy textbook at a constant height; although biological energy is consumed, no physical work is done on the objects because they do not move.
• Since work measures the transfer of energy, a lack of displacement implies that no energy has been transferred to the object to change its kinetic or potential energy state through that specific force.

 Additional Information

• Variations of Work Done:
• Positive Work: Occurs when the force and displacement are in the same direction (0° ≤ θ < 90°), such as an object in free fall where gravity does positive work.
• Negative Work: Occurs when the force acts opposite to the direction of motion (90° < θ ≤ 180°), commonly seen with frictional forces or air resistance.
• Zero Work (Angular): Work is also zero when the force is applied perpendicularly to the direction of motion (θ = 90°), such as centripetal force in circular motion.
• Standard Units:
• The SI unit of work is the Joule (J), named after the English physicist James Prescott Joule.
• One Joule is defined as the work done by a force of one Newton causing a displacement of one meter.

The correct answer is Heating elements (e.g., nichrome).

Key Points

• An alloy is a metallic substance composed of two or more elements, generally exhibiting physical properties that differ from its constituent pure metals.
• The electrical resistivity (ρ) of an alloy is significantly higher than that of the pure metals from which it is made, which directly increases the electrical resistance (R = ρl/A) of the component.
• According to Joule's Law of Heating (H = I²Rt), a higher resistance leads to the generation of more thermal energy when an electric current passes through the material.
• Alloys such as Nichrome (a blend of nickel, chromium, manganese, and iron) do not readily undergo oxidation or burn at high temperatures, even when they become red-hot.
• These properties make alloys the preferred choice for constructing heating elements in household appliances such as electric irons, toasters, and room heaters.

 Additional Information

• Filaments of electric bulbs:
• Primarily made of Tungsten because of its exceptionally high melting point (3422°C), allowing it to emit light without melting.
• Connecting wires:
• Materials like Copper (Cu) and Aluminum (Al) are used because they have extremely low resistivity, ensuring minimal energy loss as heat during power transmission.
• Circuit fuses:
• These use alloys of Lead (Pb) and Tin (Sn) specifically for their low melting point, designed to melt and break the circuit during an overcurrent or short circuit.

The correct answer is Using quality seeds, irrigation, fertilisers, crop protection.

Key Points

• Quality seeds, particularly High Yielding Varieties (HYV), are developed to have a higher germination rate and better genetic potential, which directly correlates to a significant increase in the total biomass and grain weight produced per hectare.
• Irrigation provides a controlled and consistent water supply to the soil, which is essential for the process of transpiration and nutrient uptake; it mitigates the risks associated with erratic rainfall and drought conditions.
• Fertilisers supplement the soil with vital macronutrients such as Nitrogen (N), Phosphorus (P), and Potassium (K), which are often depleted during intensive farming, ensuring optimal plant growth and metabolic functions.
• Crop protection involves the strategic use of pesticides, herbicides, and fungicides to shield crops from biotic stresses like insects, weeds, and pathogens that can otherwise destroy up to 30−40% of the potential yield.

 Additional Information

• The Green Revolution:
• Initiated in India during the mid-1960s, this movement focused on the modern agricultural package of HYV seeds, chemical inputs, and improved irrigation infrastructure.
• M.S. Swaminathan is widely recognized as the Father of the Green Revolution in India for his role in introducing high-yielding wheat and rice varieties.
• The use of chemical fertilisers helped India transition from a ship-to-mouth economy to a self-sufficient, food-surplus nation.
• Impact of Neglecting Factors:
• Rainfed agriculture is highly susceptible to climate change, making it less reliable for high-density food production compared to irrigated farming.
• Poor seed quality results in uneven plant stands and low resistance to environmental stressors, drastically reducing the efficiency of other inputs like water and fertilisers.

The correct answer is To reflect sound evenly.

Key Points

• The use of curved ceilings in concert halls and auditoriums is based on the principle of the reflection of sound. Sound waves behave similarly to light waves when they encounter a surface.
• A curved surface (specifically concave) acts as a reflector that directs sound waves downward. This ensures that the sound is evenly distributed across the entire seating area, including the corners and the far back of the hall.
• When sound waves from the stage hit the concave ceiling, they are reflected back at specific angles (where the angle of incidence equals the angle of reflection) toward the audience.
• This architectural design prevents the sound from being lost in the upper reaches of the building and eliminates acoustic shadows, which are dead zones where sound is faint or inaudible.
• By creating multiple reflections that are directed toward the listeners, the sound intensity and clarity are significantly enhanced for everyone in the venue.

 Additional Information

• Soundboards:
• A soundboard is a curved wooden or metal board placed behind the speaker or performer. The source of sound is placed at the principal focus of the board, which reflects the sound as a parallel beam toward the audience.
• Reverberation Control:
• While reflection is necessary, excessive reflection can cause reverberation, where sound persists too long and becomes blurred. Architects use sound-absorbent materials like compressed fiberboard, plaster, or heavy draperies to balance reflection and absorption.
• Acoustic Design Elements:
• In addition to curved ceilings, modern halls use diffusers to scatter sound randomly and bass traps to manage low-frequency energy, ensuring high-fidelity audio reproduction.

The correct answer is Both statements are true, but Statement 2 does not explain Statement 1.

Key Points

• A suspension is a heterogeneous mixture in which the solute particles do not dissolve but remain suspended throughout the bulk of the medium. These particles are large enough (typically greater than 1000 nm) to be seen by the naked eye and are capable of scattering a beam of light passing through them, which makes the path of light visible. Hence, statement 1 is correct.
• The scattering of light by particles in a mixture is known as the Tyndall Effect. In a suspension, this effect is prominent as long as the particles remain distributed in the solvent. Hence, statement 1 is correct.
• Suspensions are inherently unstable systems. When left undisturbed for a period, the relatively large and heavy particles settle down at the bottom of the container due to the force of gravity, a process known as sedimentation. Once the particles have settled, the mixture loses its turbidity and its ability to scatter light effectively because the large particles are no longer in the path of the beam. Hence, statement 2 is correct.
• While both statements are scientifically accurate, the fact that particles stop scattering light after settling (Statement 2) is a result of the mixture's instability and does not provide the causal mechanism for why suspensions scatter light in their active state (Statement 1). The scattering is fundamentally caused by particle size and optical interference. Hence, statement 2 does not explain statement 1.

 Additional Information

• Types of Mixtures based on Particle Size:
• True Solutions: These are homogeneous mixtures with a particle size less than 1 nm. They do not scatter light, and the path of the beam is not visible.
• Colloids: These mixtures have particle sizes between 1 nm and 1000 nm. They are stable and do not settle, yet they are large enough to exhibit the Tyndall Effect.
• Suspensions: These have the largest particles (over 1000 nm). They scatter light but are unstable and can be separated by filtration.
• Physical Separation:
• Unlike solutions and colloids, the particles of a suspension can be separated from the mixture using filter paper because of their large dimensions.

The correct answer is ureters; urinary bladder.

Key Points

• The Urinary System consists of the kidneys, ureters, urinary bladder, and urethra, working together to filter blood and eliminate liquid waste.
• Urine is continuously produced in the Kidneys through the filtration of blood and then travels to the Renal Pelvis, a funnel-shaped structure.
• The Ureters are two muscular tubes, typically 25 to 30 cm (10-12 inches) long, that connect each kidney to the urinary bladder.
• Urine does not flow simply by gravity; the Smooth Muscles in the walls of the ureters create waves of Peristalsis to force urine downward into the bladder.
• The Urinary Bladder is a hollow, distensible muscular organ located in the Pelvic Cavity that serves as a reservoir for storing urine until it is excreted.
• In a healthy adult, the bladder can hold approximately 400 to 600 mL of urine before the pressure triggers the urge to urinate.

 Additional Information

• Urethra:
• This is the final canal through which urine is discharged from the body during Micturition.
• In biological females, the urethra is short (about 4 cm), while in biological males, it is longer (about 20 cm) and also serves as a passage for semen.
• Nephrons:
• These are the microscopic structural and functional units of the kidney, with each kidney containing approximately 1 million nephrons.
• They perform three primary processes: Glomerular Filtration, Tubular Reabsorption, and Tubular Secretion to maintain blood Homeostasis.
• Internal and External Sphincters:
• The Internal Urethral Sphincter is involuntary, whereas the External Urethral Sphincter is under voluntary control, allowing humans to decide when to release urine.

The correct answer is Statement 1 is true but Statement 2 is false.

Key Points

• A homologous series is defined as a sequence of organic compounds that possess the same functional group and similar chemical properties, where each successive member differs from the previous one by a methylene unit, which is the -CH2- group. Hence, statement 1 is correct.
• The molecular mass of any member in a series is determined by the sum of the atomic masses of its constituent atoms. Since successive members differ by a -CH2- group, the difference in their molecular masses is calculated as the mass of one Carbon atom (12 u) plus two Hydrogen atoms (2 × 1 u), totaling 14 u. Hence, statement 2 is incorrect.

 Additional Information

• Characteristics of Homologous Series:
• General Formula: All members of a specific series can be represented by a single general molecular formula. For instance, Alkanes follow C_nH_2n+2, Alkenes follow C_nH_2n, and Alkynes follow C_nH_2n−2.
• Chemical Properties: Because they share the same functional group, all members exhibit almost identical chemical reactions.
• Physical Properties: There is a gradual gradation in physical properties such as melting point, boiling point, and solubility as the molecular mass increases. For example, the boiling point increases with the increase in the number of carbon atoms due to stronger Van der Waals forces.
• Example Calculation: In the Alkane series, Methane (CH₄) has a mass of 16 u, while Ethane (C₂H₆) has a mass of 30 u. The difference is 30 − 16 = 14 u, which corresponds to the -CH2- unit.

The correct answer is Boron.

Key Points

• The chemical symbol B represents Boron, which is a chemical element with the atomic number 5.
• It is classified as a metalloid, meaning it exhibits properties intermediate between those of typical metals and non-metals.
• Boron is located in Group 13 and Period 2 of the Periodic Table, serving as the head of the boron group.
• The electronic configuration of Boron is 1s² 2s² 2p¹, indicating it has three electrons in its outermost shell.
• It is a rare element in the Solar System and Earth's crust, primarily produced by cosmic ray spallation and not by stellar nucleosynthesis.
• Boron is never found as a free element on Earth; it occurs naturally in water-soluble compounds such as borates, borax, and boric acid.
• The element was first isolated in 1808 by the French chemists Joseph Louis Gay-Lussac and Louis Jacques Thénard, and independently by the British chemist Sir Humphry Davy.

 Additional Information

• Beryllium (Be):
• Identified by the symbol Be with atomic number 4.
• It is a steel-gray, strong, and lightweight alkaline earth metal used in high-speed aircraft and satellite components.
• Barium (Ba):
• Represented by the symbol Ba with atomic number 56.
• A soft, silvery-white metal belonging to the alkaline earth metal group, frequently used in drilling fluids for oil wells and as a contrast agent in medical imaging.
• Bromine (Br):
• Represented by the symbol Br with atomic number 35.
• It is a member of the Halogen group and is the only non-metallic element that is a liquid at room temperature.
• Significance of Boron:
• Boron is essential for the cell walls of plants and is used in the manufacture of borosilicate glass, which is highly resistant to thermal shock.
• In nuclear technology, Boron-10 is used as a neutron absorber in the control rods of nuclear reactors due to its high neutron capture cross-section.

The correct answer is Bright flame and rapid reaction.

Key Points

• Potassium (K) is an Alkali Metal located in Group 1 of the periodic table, characterized by its extreme chemical reactivity due to a single valence electron.
• When potassium comes into contact with water, a highly exothermic reaction occurs, represented by the chemical equation: 2K + 2H₂O → 2KOH + H₂.
• The reaction produces Potassium Hydroxide and releases Hydrogen gas. The heat generated is so intense that it causes the evolved hydrogen gas to ignite almost instantly.
• This combustion results in a distinctive lilac-colored flame (light purple), which is a signature identification for the presence of potassium ions.
• During the process, the metal reacts so rapidly that it melts into a small silvery ball and skims across the surface of the water before eventually disappearing.

 Additional Information

• Reactivity of Group 1 Metals:
• Lithium: Reacts slowly with water, causing steady effervescence (bubbling) as hydrogen is released, but it does not usually catch fire.
• Sodium: Reacts vigorously and melts into a ball, producing a yellow flame if the hydrogen ignites.
• Rubidium and Caesium: These are even more reactive than potassium and react explosively even with cold water.
• Storage Protocols: Because potassium reacts violently with atmospheric moisture and oxygen, it must be stored submerged in kerosene or paraffin oil to maintain its metallic state.
• Density: Potassium is less dense than water, which is why it floats and moves on the surface during the chemical reaction.