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​Ringworm: A common fungal skin infection that often looks like a circular rash.

• Approximately 40 different species of fungi can cause ringworm; the scientific names for the types of fungi that cause ringworm are Trichophyton, Microsporum, and Epidermophyton.

Key Points

• Trichophyton is a genus of fungi, which includes the parasitic varieties that cause tinea, including athlete's foot, ringworm, jock itch, and similar infections of the nail, beard, skin and scalp. Trichophyton fungi are molds characterized by the development of both smooth-walled macro- and microconidia.

Hence we can conclude that Tricophyton is responsible for ringworm.

Additional Information

• Candida infections of the mouth, throat, and esophagus: Caused by the yeast Candida, also called “thrush.
• The fungal disease, called Fusarium Wilt, is popularly known as the Panama Disease’ and afflicts banana plants.
• Aspergillus (mold fungus) is responsible for causing Aspergillosis. It affects the respiratory tract and causes illness by its spore.

The correct answer is CaCO₃.

Explanation:

• The chemical name of marble is calcium carbonate.
• It has the chemical formula CaCO₃ and is an inorganic chemical compound.

Ca(OH)₂ (aq) + CO₂ (g) → CaCO₃ (s) + H₂O (l)

• Calcium hydroxide slowly reacts with the carbon dioxide (CO₂) in the air to form a thin layer of calcium carbonate on the walls.
• Calcium carbonate is formed after two to three days of whitewashing and gives a shiny finish to the walls.
• Calcium carbonate is a non-toxic, odourless chemical compound that occurs naturally as a white mineral in marbles, limestones, and chalks.
• It is one of the most abundant minerals found in the crust of the earth.

Thus, chemical formula of marble is CaCO3.

The correct answer is [ML²T^-2].

Key Points

• The dimensional formula of energy is [ML²T^-2].
• Energy is defined as the capacity to do work, and its SI unit is the joule (J).
• The dimensional formula can be derived from the work done (force x distance), where force is [MLT^-2] and distance is [L].
• Therefore, combining these gives [ML²T^-2].

Additional Information

• Work:
• Work is defined as the product of the force applied and the distance moved by the force in the direction of the force.
• The SI unit of work is the joule (J).
• Dimensional formula of work is [ML²T^-2].
• Power:
• Power is the rate at which work is done or energy is transferred.
• The SI unit of power is the watt (W).
• Dimensional formula of power is [ML²T^-3].
• Force:
• Force is any interaction that, when unopposed, will change the motion of an object.
• The SI unit of force is the newton (N).
• Dimensional formula of force is [MLT^-2].
• Kinetic Energy:
• Kinetic energy is the energy possessed by an object due to its motion.
• The formula for kinetic energy is 1/2 mv², where m is mass and v is velocity.
• Dimensional formula of kinetic energy is [ML²T^-2].

The correct answer is Germanium

Key Points

• Germanium is a metalloid in the carbon group (Group 14) of the periodic table.
• It shares similar chemical properties with its group neighbours, tin and silicon.
• Germanium has a similar electron configuration to tin and silicon, leading to comparable chemical behavior.
• It is used in semiconductors and various electronic applications, similar to silicon.
• Germanium forms compounds like germanium dioxide (GeO₂) and germanium tetrachloride (GeCl₄), which are analogous to silicon and tin compounds.

Additional Information

• Germanium was discovered by Clemens Winkler in 1886.
• It is a lustrous, hard, grayish-white metalloid in the carbon group, chemically similar to its group neighbours tin and silicon.
• Germanium is less abundant in the Earth's crust compared to silicon but more abundant than tin.
• It is primarily obtained from sphalerite (zinc ore) and from the by-products of coal combustion.
• In addition to its use in electronics, germanium is also used in fiber optics, infrared optics, and as a catalyst in polymerization processes.

The correct answer is Vitamin C.

Key Points

• Scurvy is a disease resulting from a deficiency of vitamin C, known scientifically as ascorbic acid.
• Vitamin C is essential for the synthesis of collagen, which helps in maintaining the integrity of connective tissues.
• Symptoms of scurvy include weakness, anemia, gum disease, and skin problems due to the breakdown of collagen.
• Humans cannot synthesize vitamin C endogenously, so it must be obtained through diet, particularly from fruits and vegetables.

Additional Information

• Vitamin C
• Vitamin C, also known as ascorbic acid, is a water-soluble vitamin found in various foods and sold as a dietary supplement.
• It is essential for the biosynthesis of collagen, L-carnitine, and certain neurotransmitters; it is also involved in protein metabolism.
• Vitamin C is also an important physiological antioxidant and has been shown to regenerate other antioxidants within the body, including alpha-tocopherol (vitamin E).
• It improves the absorption of non-heme iron, the form of iron present in plant-based foods.
• Severe vitamin C deficiency leads to scurvy, which is characterized by bleeding gums, bruising, joint pain, and poor wound healing.
• Vitamin D
• Vitamin D is a fat-soluble vitamin that is naturally present in very few foods, added to others, and available as a dietary supplement.
• It is also produced endogenously when ultraviolet rays from sunlight strike the skin and trigger vitamin D synthesis.
• Vitamin D promotes calcium absorption in the gut and maintains adequate serum calcium and phosphate concentrations to enable normal mineralization of bone and to prevent hypocalcemic tetany.
• It is also needed for bone growth and bone remodeling by osteoblasts and osteoclasts.
• Vitamin A
• Vitamin A is a fat-soluble vitamin that is important for normal vision, the immune system, and reproduction.
• It also helps the heart, lungs, kidneys, and other organs work properly.
• Vitamin A is found in foods such as spinach, dairy products, and liver.
• It is available as a dietary supplement.
• Vitamin K
• Vitamin K refers to a group of structurally similar, fat-soluble vitamins that the human body needs for the complete synthesis of certain proteins that are prerequisites for blood coagulation (K from Koagulation, German for "coagulation") and which the body also needs for controlling binding of calcium in bones and other tissues.
• The vitamin K-related modification of proteins allows them to bind calcium ions, which they cannot do otherwise.
• Without vitamin K, blood coagulation is seriously impaired, and uncontrolled bleeding occurs.

The correct answer is Bark.

Key Points

Quinine:

• ​Quinine remains an important anti-malarial drug almost 400 years after its effectiveness was first documented.
• The discovery of quinine is considered the most serendipitous medical discovery of the 17^th century.
• Quinine, as a component of the bark of the cinchona (Quina Quina) tree, was used to treat malaria.
• Quinine is a cinchona alkaloid that belongs to the aryl amino alcohol group of drugs.
• It is an extremely basic compound and is, therefore, always presented as a salt.
• Quinine is rapidly absorbed both orally and parenterally, reaching peak concentrations within 1-3 hours.

Additional Information

• Malaria is a disease caused by Plasmodium parasites that are transmitted to humans through the bites of infected female Anopheles mosquitoes. High fever with a shiver, headache, vomiting, and nausea are common symptoms of malaria.
• Quinine medicine was made from the bark of the cinchona tree.
• Quinine is a medication used to treat malaria and babesiosis. Quinine was first isolated in 1820 from the bark of a cinchona tree. It is an antimalarial drug that is made from Cinchona bark.
• Cinchona is used in eye lotions to numb pain, kill germs, and as an astringent.

The correct answer is CO₂.

Key Points

• Carbon dioxide (CO₂) is the primary gas used in the production of soft drinks to create carbonation.
• Carbonation occurs when CO₂ is dissolved in water under high pressure, forming carbonic acid, which gives the soft drink its fizzy texture and tangy taste.
• The release of CO₂ from a soft drink upon opening the bottle or can creates the characteristic bubbles and effervescence.
• CO₂ is non-toxic, colorless, and odorless, making it safe for use in beverages.
• It also acts as a mild preservative by inhibiting the growth of spoilage-causing microorganisms in soft drinks.

Additional Information

• Carbonation Process
• Carbonation is the process of dissolving CO₂ into water under high pressure.
• When the pressure is released (e.g., opening a bottle), CO₂ escapes, creating bubbles.
• History of Carbonated Beverages
• The concept of carbonated water was first introduced by Joseph Priestley in 1767.
• Soft drinks gained popularity in the 19^th century as flavored carbonated beverages became commercially available.
• Other Gases and Their Uses
• NH₃ (Ammonia): Used in refrigeration systems and fertilizers, not in beverages.
• PH₃ (Phosphine): A toxic gas used in pest control, not related to food or drinks.
• COCl₂ (Phosgene): A highly toxic gas used in chemical manufacturing, not safe for consumption.
• Health Considerations
• Excessive consumption of carbonated drinks can lead to health issues like dental erosion and obesity.
• Moderation is key to enjoying soft drinks without adverse health effects.

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of motion or state of rest is called force.
• Force is denoted by F and the SI unit is Newton (N).
• Force (F) = Mass (m) × acceleration (a)
• Dimensional Formula: It depicts the way to relate any unit to fundamental Units.
• If we have to find The dimensional formula of any quantity, At first, we find its units in terms of these fundamental units, and then replace units with these dimensions.

EXPLANATION:

• Force can be written mathematically as

⇒ F = m × a

As we know, the dimension of mass (m) = [M]

The dimension of acceleration (a) = [LT^-2]

∴ The dimension of force (F) is

⇒ F = [M] ×  [LT-2] = [MLT-2]

Additional Information

Given:

S.P of transistor = Rs. 450

Loss = 10%

Formula used:

C.P = S.P × [100/(100 – loss%)]

Calculation:

C.P = Rs. 450 × (100/90)

⇒ Rs. 500

∴ The cost price of the transistor is Rs. 500

Shortcut Trick

If x − 1/x = k, then x³ − 1/x³ = k³ + 3k.

Given k = 4.

∴ x³ − 1/x³ = 4³ + 3 × 4 = 64 + 12 = 76.

∴ The correct answer is 76.

Alternate Method

Given: x − 1/x = 4

Formula Used: (a − b)³ = a³ − b³ − 3ab(a − b)

⇒ Cubing both sides of the equation: (x − 1/x)³ = 4³

⇒ x³ − 1/x³ − 3 × x × (1/x) × (x − 1/x) = 64

⇒ x³ − 1/x³ − 3 × (x − 1/x) = 64

⇒ Substitute the value x − 1/x = 4 into the equation:

⇒ x³ − 1/x³ − 3 × 4 = 64

⇒ x³ − 1/x³ − 12 = 64

⇒ x³ − 1/x³ = 64 + 12

⇒ x³ − 1/x³ = 76

∴ The correct answer is 76.

Additional Information

Standard Algebraic Identities for Reciprocals

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k.

Square Relations

If x + 1/x = k, then x² + 1/x² = k² − 2 and if x − 1/x = k, then x² + 1/x² = k² + 2.

Power 4 Relation

If x + 1/x = k, then x⁴ + 1/x⁴ = (k² − 2)² − 2.