RRB Technician Grade III Official Paper (Held On: 29 Dec, 2024 Shift 3) (Previous Year Paper)

The correct answer is Position of the metals in the reactivity series.

Key Points

• In a displacement reaction, the reactivity of the metals involved plays a crucial role.
• The reactivity series is an arrangement of metals in order of their reactivity, from most reactive to least reactive.
• A more reactive metal can displace a less reactive metal from its compound.
• This is because the more reactive metal has a greater tendency to lose electrons and form positive ions.
• For example, zinc can displace copper from copper sulfate solution because zinc is higher in the reactivity series than copper.

 Additional Information

• Temperature of the reaction
• While temperature can affect the rate of reaction, it does not determine whether one metal will displace another.
• Displacement reactions are more influenced by the reactivity of the metals involved.
• Size of the metal atoms
• The size of metal atoms does not play a significant role in displacement reactions.
• It is the reactivity and ability to lose electrons that matter more in these reactions.
• Concentration of the compound
• While the concentration of the compound can affect the rate of a reaction, it does not determine the displacement of metals.
• The ability to displace another metal is primarily dependent on the relative reactivity of the metals.

The Correct answer is All metals are equally reactive.

Key Points

• Not all metals have the same level of reactivity. Metals differ in their ability to react with other substances.
• The reactivity series is a list of metals arranged in order of their reactivity, from highest to lowest. For instance, potassium and sodium are highly reactive, while gold and silver are much less reactive.
• Potassium is known to be more reactive than gold, which is why it is never found in its free state in nature.
• Silver is less reactive than sodium, meaning it does not react as easily or vigorously with other elements or compounds.
• The differences in reactivity among metals are due to their varying atomic structures and the energy required to remove an electron to form a positive ion.

 Additional Information

• Potassium
• Potassium is an extremely reactive metal and is placed high in the reactivity series.
• It reacts vigorously with water and even with moisture in the air, often producing a flame.
• Because of its high reactivity, potassium is stored under mineral oil to prevent it from reacting with atmospheric moisture and oxygen.
• Gold
• Gold is a noble metal, meaning it is highly resistant to corrosion and oxidation.
• This low reactivity makes gold ideal for use in jewelry and electronics.
• Gold does not react with most chemicals, and it is only attacked by a mixture of nitric acid and hydrochloric acid, known as aqua regia.
• Silver
• Silver is less reactive than metals like sodium and potassium but more reactive than gold.
• It tarnishes when exposed to air due to the formation of silver sulfide from the reaction with sulfur compounds.
• Silver is widely used in jewelry, cutlery, and electrical contacts due to its relative reactivity and high conductivity.

The Correct answer is The solute is present in a smaller amount than the solvent.

Key Points

• A solution is a homogeneous mixture of two or more substances.
• In a solution, the substance in the smaller amount is called the solute and the substance in the larger amount is called the solvent.
• The solute dissolves in the solvent to form a solution.
• For example, in a saltwater solution, salt is the solute and water is the solvent.
• It is possible to have solutions where the solute is present in a very small amount compared to the solvent, such as in dilute solutions.

 Additional Information

• Simple Filtration
• Simple filtration is a method used to separate an insoluble solid from a liquid.
• Solutions cannot be separated by simple filtration because the solute is completely dissolved in the solvent.
• Concentration of a Solution
• The concentration of a solution can be expressed in various ways, such as mass per cent, molarity, molality, and normality.
• Heterogeneous Mixture
• A heterogeneous mixture consists of substances that are not evenly distributed and have distinct phases.
• A solution is a homogeneous mixture, meaning the solute is uniformly distributed within the solvent.

Given: Seven people, A, B, E, F, P, Q and R, are sitting in a row, facing north. 

1) Only P sits to the right of Q.

2) Only one person sits between E and Q.

3) Only two people sit between A and E.

4) R sits at some place to the right of B but at some place to the left of F.

Thus, according to the final arrangement, F sits third from the right end of the row.

Hence, "Option 1" is the correct answer.

The correct answer is Only (ii) and (iii).

Key Points

• UV radiation is indeed damaging to organisms as it can cause skin cancer and cataracts in humans, and can also harm marine ecosystems, including phytoplankton.
• Ozone at the higher levels of the atmosphere (the stratosphere) is indeed a product of UV radiation acting on oxygen molecules (O₂), resulting in the formation of ozone (O₃).
• The amount of ozone in the atmosphere began to drop sharply in the 1980s due to the release of chlorofluorocarbons (CFCs) and other ozone-depleting substances.

 Additional Information

• UV radiation
• UV radiation is a form of electromagnetic radiation that comes from the sun and artificial sources like tanning beds.
• It has both beneficial and harmful effects. For instance, it helps in the production of vitamin D in humans but excessive exposure can cause skin cancer.
• Ozone Layer
• The ozone layer is a region of Earth's stratosphere that absorbs most of the Sun's ultraviolet radiation.
• It contains high concentrations of ozone (O₃) molecules.
• The ozone layer was significantly depleted by human-made chemicals, primarily CFCs, leading to global environmental issues such as the ozone hole.
• Chlorofluorocarbons (CFCs)
• CFCs are compounds that were commonly used in air conditioning, refrigeration, and as propellants in aerosol sprays.
• They are harmful to the ozone layer because they release chlorine atoms upon exposure to UV radiation, which then deplete ozone molecules.
• The use of CFCs has been largely phased out under the Montreal Protocol, an international treaty agreed upon in 1987 to protect the ozone layer.

The correct answer is greater in water than in glass.

Key Points

• The speed of light varies in different media.
• In a vacuum, the speed of light is approximately 299,792 kilometers per second (km/s).
• When light travels from one medium to another, its speed changes due to the refractive index of the media.
• The refractive index of water is about 1.33, while the refractive index of glass is typically around 1.5.
• A higher refractive index indicates that light travels more slowly in that medium. Therefore, light travels faster in water than in glass.
• This is because the refractive index of water is lower than that of glass, meaning there is less optical density to slow down the light.

 Additional Information

• greater in water than in air
• Light travels slower in water than in air because the refractive index of air is approximately 1.0003, which is lower than that of water.
• same in air, glass and water
• This option is incorrect because the speed of light changes as it moves between different media with different refractive indices.
• greater in glass than in water
• This is incorrect as the refractive index of glass is higher than that of water, meaning light travels slower in glass.

Shortcut Trick

Direct Application of Speed Formula:

Speed = Distance ÷ Time

Speed = 150 ÷ 3 = 50 km/h

∴ The correct answer is 50 km/h.

Alternate Method

Given:

Total Distance = 150 km

Total Time = 3 hrs

Formula Used:

Speed = Distance / Time

Calculations:

⇒ Speed = 150 km / 3 hrs

⇒ Speed = 50 km/h

∴ The correct answer is 50 km/h.

Additional Information

Unit Conversion

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

Average Speed

Average Speed = (Total Distance) ÷ (Total Time). If distances are equal, Average Speed = 2xy/(x+y) where x and y are individual speeds.

Relative Speed

For objects moving in the same direction, subtract speeds (S₁ − S₂). For opposite directions, add speeds (S₁ + S₂).

The correct answer is Plasmodium.

Key Points

• Plasmodium is a genus of parasitic protozoa, many of which cause malaria in humans and other animals.
• Multiple fission is a form of asexual reproduction where a single organism divides into many new organisms simultaneously.
• In Plasmodium, multiple fission occurs during the schizogony stage of its life cycle.
• During schizogony, the nucleus of the parasite divides multiple times before the cell splits into several daughter cells called merozoites.
• This process allows Plasmodium to rapidly increase its population within the host, contributing to the spread of malaria.
• The life cycle of Plasmodium involves both a human host and a mosquito vector (usually of the genus Anopheles).

 Additional Information

• Hydra
• Hydra is a simple freshwater animal of the phylum Cnidaria.
• It reproduces asexually through a process called budding, not multiple fission.
• In budding, a new organism grows out of the body of the parent organism.
• Leishmania
• Leishmania is a genus of trypanosomes that cause the disease leishmaniasis.
• It reproduces asexually by binary fission rather than multiple fission.
• Leishmania is transmitted by the bite of infected sandflies.
• Yeast
• Yeast is a type of fungus that reproduces asexually primarily through a process called budding.
• In budding, a new cell grows out from the surface of the parent cell.
• Yeast is widely used in the baking and brewing industries due to its ability to ferment sugars.

Shortcut Trick

To double a sum, the Interest must be equal to 100% of the Principal.

Time (T) = 100 ÷ Rate %

Time (T) = 100 ÷ 5 = 20 years.

∴ The correct answer is 20 years.

Alternate Method

Given:

Let the Principal (P) be ₹100.

Since the sum doubles itself, the Amount (A) = 2 × 100 = ₹200.

Simple Interest (SI) = Amount − Principal = 200 − 100 = ₹100.

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ 100 = (100 × 5 × T) ÷ 100

⇒ 100 = 5 × T

⇒ T = 100 ÷ 5

⇒ T = 20 years

∴ The correct answer is 20 years.

Additional Information

Simple Interest Multiplier Rule

If a sum becomes 'n' times in 'T' years, then (n − 1) = (R × T) ÷ 100. For doubling, n = 2.

Rate and Time Relation

Rate and Time are inversely proportional for a fixed interest amount. R = 100(n − 1) ÷ T.

Rule of 72 (CI Approximation)

In Compound Interest, a sum doubles in approximately 72 ÷ R years. For SI, it is exactly 100 ÷ R years.

Shortcut Trick

For any regular polygon, the sum of all exterior angles is always 360°.

A decagon has n = 10 sides.

Each exterior angle = 360° ÷ n = 360° ÷ 10 = 36°.

∴ The correct answer is 36°.

Alternate Method

Given: Shape = Regular Decagon.

Formula Used: Each Exterior Angle of a regular polygon = 360° ÷ n, where n is the number of sides.

⇒ Number of sides in a decagon (n) = 10.

⇒ Sum of all exterior angles of any convex polygon = 360°.

⇒ Since the polygon is regular, all exterior angles are equal.

⇒ Each exterior angle = 360° ÷ 10.

⇒ Each exterior angle = 36°.

∴ The correct answer is 36°.

Additional Information

Interior Angle of a Regular Polygon

Each interior angle is given by [(n − 2) × 180°] ÷ n. For a decagon, it is [(10 − 2) × 180°] ÷ 10 = 144°.

Relation between Interior and Exterior Angles

The sum of an interior angle and its corresponding exterior angle is always 180° (linear pair).

Sum of Interior Angles

The sum of all interior angles of an n-sided polygon is (n − 2) × 180°.

The Correct answer is Nucleus.

Key Points

• The gold foil experiment was conducted by Ernest Rutherford in 1909.
• This experiment involved the bombardment of gold foil with alpha particles.
• Rutherford observed that most of the alpha particles passed through the foil, but some were deflected at large angles.
• He concluded that atoms have a small, dense, positively charged center which he called the nucleus.
• Rutherford's findings significantly changed the atomic model from J.J. Thomson's plum pudding model to the nuclear model.
• The discovery of the nucleus led to a better understanding of the structure of the atom and the nature of atomic interactions.

 Additional Information

• Neutron
• The neutron was discovered by James Chadwick in 1932.
• It is a neutral particle found in the nucleus of an atom.
• Neutrons play a crucial role in the stability of the nucleus.
• Electron
• The electron was discovered by J.J. Thomson in 1897.
• Electrons are negatively charged particles that orbit the nucleus of an atom.
• They are essential in chemical bonding and electricity.
• Proton
• The proton was discovered by Ernest Rutherford in 1917.
• Protons are positively charged particles found in the nucleus of an atom.
• The number of protons in the nucleus determines the atomic number and identity of an element.

The correct answer is CnH2n+2.

Key Points

• Alkanes are a class of hydrocarbons that consist of only single bonds between carbon atoms.
• The general formula for alkanes is CnH2n+2, where n represents the number of carbon atoms.
• Alkanes are also known as paraffins and are saturated hydrocarbons.
• They are the simplest type of hydrocarbon and are typically found in natural gas and petroleum.
• Examples of alkanes include methane (CH4), ethane (C2H6), and propane (C3H8).
• Alkanes are used as fuels and lubricants due to their properties.

 Additional Information

• C2nH2n
• This formula does not correspond to any common class of hydrocarbons.
• CnHn
• This formula does not align with any known hydrocarbons.
• CnH2n
• This formula represents the general formula for alkenes, which are unsaturated hydrocarbons containing at least one carbon-carbon double bond.

The correct answer is Homogeneous mixture.

Key Points

• A homogeneous mixture is a mixture that has the same composition throughout.
• In a homogeneous mixture, the different components are uniformly distributed at the molecular level.
• Air is a mixture of different gases such as nitrogen (78%), oxygen (21%), and small amounts of other gases like argon and carbon dioxide.
• These gases are thoroughly mixed, resulting in a uniform composition throughout the sample.
• Because the composition is uniform, air is considered a homogeneous mixture.

 Additional Information

• Suspension
• A suspension is a heterogeneous mixture in which solid particles are dispersed in a liquid or gas but are not dissolved.
• In a suspension, the particles are large enough to eventually settle out due to gravity.
• An example of a suspension is muddy water, where soil particles are dispersed in water.
• Heterogeneous mixture
• A heterogeneous mixture is a mixture where the components are not uniformly distributed, and different parts of the mixture have different compositions.
• An example of a heterogeneous mixture is a salad, where different ingredients like lettuce, tomatoes, and cucumbers can be seen and separated physically.
• Colloids
• A colloid is a mixture where very small particles of one substance are evenly distributed throughout another substance.
• The particles in a colloid are larger than those in a solution but smaller than those in a suspension.
• An example of a colloid is milk, which contains fat droplets dispersed in water.

The correct answer is Tartaric acid.

Key Points

• Tartaric acid is an organic acid that is naturally present in many plants, particularly in grapes, bananas, and tamarinds.
• It is commonly used in combination with baking soda to form baking powder, which acts as a leavening agent in baking.
• When combined with baking soda, tartaric acid reacts to produce carbon dioxide gas, which helps dough and batter rise during the baking process.
• This reaction occurs because tartaric acid is a strong acid that can effectively neutralize the alkaline nature of baking soda.
• Baking powder, which contains tartaric acid, is essential in making fluffy and light baked goods such as cakes, muffins, and bread.

 Additional Information

• Lactic acid
• Lactic acid is found in sour milk products like yogurt and some cottage cheeses.
• It is produced by the fermentation of lactose by bacteria.
• Lactic acid is not typically used in baking powder.
• Vinegar
• Vinegar is an acidic liquid produced from the fermentation of ethanol by acetic acid bacteria.
• It is often used in cooking and pickling but not usually in baking powder.
• Sodium chloride
• Sodium chloride, commonly known as table salt, is used to enhance flavor in foods.
• It does not have the leavening properties needed for baking powder.

The Correct answer is Neutralisation reaction

Key Points

• A neutralisation reaction occurs when an acid and a base react to form salt and water.
• The general chemical equation for a neutralisation reaction is:
  

Acid + Base → Salt + Water.

• For example, the reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH) forms sodium chloride (NaCl) and water (H₂O):
  

HCl + NaOH → NaCl + H₂O.

• This reaction helps to maintain the pH balance in various chemical and biological processes.
• Antacids, which are used to treat acidity in the stomach, work on the principle of neutralisation.
• It is an example of a double displacement reaction, where ions are exchanged between the reactants.
• Neutralisation reactions play a crucial role in agriculture, medicine, and environmental science by neutralising acidic or basic substances.

 Additional Information

• Photosynthesis reaction
• Photosynthesis is a process by which plants, algae, and some bacteria convert sunlight into chemical energy.
• The reaction involves the conversion of carbon dioxide (CO₂) and water (H₂O) into glucose (C₆H₁₂O₆) and oxygen (O₂) using sunlight.
• The overall equation for photosynthesis is:
  

6CO₂ + 6H₂O + Light → C₆H₁₂O₆ + 6O₂.

• This process occurs in the chloroplasts of plant cells and is essential for producing oxygen and sustaining life on Earth.
• Hydrolysis reaction
• A hydrolysis reaction is a chemical reaction where a molecule reacts with water to form two or more new substances.
• It is commonly seen in the breakdown of carbohydrates, proteins, and lipids in biological systems.
• For example, the breakdown of sucrose (table sugar) into glucose

The Correct answer is black.

Key Points

• In the absence of an atmosphere, the sky would appear black instead of its usual blue color.
• This is because there would be no air molecules to scatter the sunlight, a phenomenon known as Rayleigh scattering.
• Rayleigh scattering is responsible for scattering shorter wavelengths of light, such as blue, more than longer wavelengths.
• The scattered blue light is what makes the sky appear blue to our eyes when the sun is up.
• Without an atmosphere, sunlight would travel directly to the surface without scattering, leaving the sky dark and black, similar to how it appears from space.

 Additional Information

• Blue
• The sky appears blue because of the scattering of sunlight by the Earth's atmosphere.
• The shorter blue wavelengths are scattered in all directions by the air molecules, making the sky look blue from the ground.
• Yellow
• The sky can appear yellow during sunrise or sunset due to the scattering of longer wavelengths of light, such as red and yellow.
• This occurs when the sun is low on the horizon and the light has to travel through more of the Earth's atmosphere.
• Red
• The sky can appear red during sunrise or sunset, similar to yellow, but with even more scattering of shorter wavelengths.
• This is often seen when there are particles or pollutants in the air that enhance the scattering effect.

Given:

(2/3 + 1/3) × 23 − 13 + 9

Formula used:

BODMAS Rule (Bracket, Of, Division, Multiplication, Addition, Subtraction)

Calculations:

(2/3 + 1/3) × 23 − 13 + 9

⇒ (3/3) × 23 − 13 + 9

⇒ 1 × 23 − 13 + 9

⇒ 23 − 13 + 9

⇒ 10 + 9

⇒ 19

∴ The correct answer is option (4).

Given series: (Left) 3 Ω 9 # 1 7 3 @ 1 ^ 9 # * £ 5 8 8 5 7 & * £ 5 (Right)

According to the question, such symbols which are immediately preceded by an even number and is immediately followed by a symbol:

Required condition: Even number - Symbol - Symbol

(Left) 3 Ω 9 # 1 7 3 @ 1 ^ 9 # * £ 5 8 8 5 7 & * £ 5 (Right)

Thus, there are no such symbols which are immediately preceded by an even number and is immediately followed by a symbol.

Hence, "Option 2" is the correct answer.

The correct answer is Culture of Integrity for Nation's Prosperity.

Key Points

• The theme "Culture of Integrity for Nation's Prosperity" underscores the importance of fostering a culture of integrity to achieve overall prosperity and development for the nation.
• This theme highlights the role of moral values, ethics, and integrity in combating corruption and promoting transparent governance.
• It aims to encourage individuals and organizations to commit to ethical practices and uphold the highest standards of honesty and integrity.
• The Central Vigilance Commission (CVC) organizes the Vigilance Awareness Week annually to promote vigilance and integrity among public servants and citizens.
• By emphasizing a culture of integrity, the theme seeks to create a society where corruption is not tolerated, and every individual plays a role in eradicating it.
• Promoting integrity helps in building trust in public institutions and contributes to nation-building efforts.

 Additional Information

• Satark Bharat, Samriddh Bharat
• This theme translates to "Vigilant India, Prosperous India."
• It was used in the past for Vigilance Awareness Week to emphasize the need for vigilance to achieve prosperity.
• Say No to Corruption; Commit to the Nation
• This theme focuses on encouraging individuals to reject corruption and pledge their commitment to the nation.
• It aims to raise awareness about the adverse effects of corruption on national development.
• Corruption Free India for a Developed Nation
• This theme underscores the need to eliminate corruption to achieve the goal of a developed nation.
• It highlights the correlation between a corruption-free environment and national progress.

The Correct answer is Justice DY Chandrachud.

Key Points

• Justice DY Chandrachud served as the 50th Chief Justice of India (CJI).
• He succeeded Justice Uday Umesh Lalit as the Chief Justice of India.
• Justice Chandrachud is known for his significant judgments on constitutional law, human rights, and gender justice.
• He has a strong educational background with degrees from Harvard University.
• Justice Chandrachud has also served as the Chief Justice of the Allahabad High Court before being elevated to the Supreme Court of India.

 Additional Information

• Justice Abhay S Oka
• Justice Abhay S Oka is a judge of the Supreme Court of India.
• He previously served as the Chief Justice of the Karnataka High Court.
• Justice Oka is known for his judicial pronouncements on public interest litigations (PILs) and human rights.
• Justice Surya Kant
• Justice Surya Kant is a sitting judge of the Supreme Court of India.
• He has previously served as the Chief Justice of the Himachal Pradesh High Court.
• Justice Surya Kant is known for his work in the field of environmental law and administrative law.
• Justice Sanjeev Khanna
• Justice Sanjeev Khanna is a judge of the Supreme Court of India.
• He was elevated from the Delhi High Court.
• Justice Khanna has delivered important judgments on corporate law and commercial disputes.

The logic followed here is:

Given: 

PL-QN-ST

And,

JF-KH-MN  

So, checking each option one by one:

Option 1) MI-NK-PQ

Option 2) QM-RO-TV

Option 3) TP-UR-WY 

Option 4) SO-TQ-VX

Thus, out of all the options 'MI-NK-PQ' follows the same logic as given.

Hence, "Option 1" is the correct answer.

Given:

Expression: x^1/2 × Y⁻¹ × z^2/3

Value of x = 9

Value of Y = 3

Value of z = 8

Formula used:

a^m/n = (ⁿ√a)^m

a⁻ⁿ = 1 / aⁿ

Calculations:

Substitute the values in the expression:

⇒ 9^1/2 × 3⁻¹ × 8^2/3

⇒ √9 × (1 / 3) × (³√8)²

⇒ 3 × (1 / 3) × (2)²

⇒ 1 × 4

⇒ 4

∴ The correct answer is option (4).

The Correct answer is Bacterial infections : Gonorrhoea and syphilis.

Key Points

• Gonorrhoea is a sexually transmitted infection caused by the bacterium Neisseria gonorrhoeae.
• Syphilis is another sexually transmitted infection caused by the bacterium Treponema pallidum.
• Warts are caused by the human papillomavirus (HPV), which is a viral infection.
• HIV-AIDS is caused by the Human Immunodeficiency Virus (HIV), which is also a viral infection.

 Additional Information

• Warts and HIV-AIDS
• Warts are typically harmless growths on the skin caused by the human papillomavirus (HPV).
• HIV-AIDS affects the immune system, specifically targeting CD4 cells (T cells), and can lead to acquired immunodeficiency syndrome (AIDS).
• Bacterial infections
• Bacterial infections are caused by harmful bacteria and can often be treated with antibiotics.
• Examples include Gonorrhoea and Syphilis.

The logic followed here is:

Hence, "Option 2" is the correct answer.

Given statement: School X has received a notice from the Commissioner of Police on the many complaints that have been received regarding the traffic jam caused outside the school gates every morning between 8 a.m. and 9 a.m. due to illegal parking of cars.

Given courses of Action:

(I) School X should deploy security personnel to monitor the illegal car parking outside school gates and clear any jams being caused. → Follow

Deploying security personnel to monitor illegal parking and manage traffic congestion is a practical step. Since the school is directly affected by the issue, taking measures to regulate parking can help prevent jams and ensure smooth traffic flow.

(II) School X should ban parents from dropping their children by car to the school. → Does not follow

Completely banning parents from dropping their children by car is an extreme measure. Many parents rely on private vehicles for transportation, and a sudden ban may cause inconvenience. Instead, implementing proper parking regulations or staggered drop-off timings would be more feasible.

Thus, Only I follows.

Hence, "Option 1" is the correct answer.

Shortcut Trick

Total sum of 7 numbers = 30 × 7 = 210

Sum of constant terms = 22.5 + 56 + 42.5 + 1 − 2 + 36 = 156

Sum of variables = 2x + x + 3x = 6x

6x + 156 = 210 ⇒ 6x = 54 ⇒ x = 9

∴ The correct answer is 9.

Alternate Method

Given: Observations = {22.5, 56, 42.5, 2x + 1, x − 2, 3x, 36}, Count (n) = 7, Mean = 30

Formula Used: Sum of observations = Mean × Total number of observations

⇒ (22.5 + 56 + 42.5 + 2x + 1 + x − 2 + 3x + 36) = 30 × 7

⇒ (22.5 + 56 + 42.5 + 1 − 2 + 36) + (2x + x + 3x) = 210

⇒ 156 + 6x = 210

⇒ 6x = 210 − 156

⇒ 6x = 54

⇒ x = 54 ÷ 6

⇒ x = 9

∴ The correct answer is 9.

Additional Information

Arithmetic Mean Properties

If each observation is increased by a constant 'k', the new mean also increases by 'k'. If multiplied by 'k', the mean is multiplied by 'k'.

Sum of Deviations

The sum of deviations of all observations from their arithmetic mean is always zero. ∑(x_i − mean) = 0.

Weighted Average

When observations have different weights, the mean is calculated as (∑w_ix_i) ÷ ∑w_i.

The correct answer is Adani.

Key Points

• The Adani Group was named the principal sponsor for Team India at the Paris Olympics 2024.
• The Adani Group is an Indian multinational conglomerate headquartered in Ahmedabad, Gujarat.
• It was founded by Gautam Adani in 1988.
• The group has diverse business interests, including energy, resources, logistics, agribusiness, real estate, financial services, and defense.
• The Adani Group has a significant presence in the ports and logistics sector through its subsidiary, Adani Ports and SEZ Limited.
• This sponsorship aligns with the Adani Group's commitment to supporting sports and athletes in India.

 Additional Information

• Puma
• Puma is a leading German multinational corporation that designs and manufactures athletic and casual footwear, apparel and accessories.
• The company was founded in 1948 by Rudolf Dassler.
• Puma is known for its sponsorship deals with various sports teams and athletes globally.
• Reliance
• Reliance Industries Limited (RIL) is an Indian multinational conglomerate company headquartered in Mumbai, Maharashtra.
• It was founded by Dhirubhai Ambani in 1960.
• Reliance's businesses include energy, petrochemicals, textiles, natural resources, retail, and telecommunications.
• Aditya Birla
• Aditya Birla Group is an Indian multinational conglomerate headquartered in Worli, Mumbai, Maharashtra.
• The group was founded by Seth Shiv Narayan Birla in 1857.
• Its businesses include viscose staple fiber, metals, cement, textiles, carbon black, telecom, and financial services.

Given series: (Left) 9 @ 8 $ 7 & 3 Ω 9 # 1 * £ 5 & % 4 6 (Right)

According to the question, such symbols which are immediately preceded by an odd number and is immediately followed by a symbol:

Required condition: Odd number - Symbol - Symbol

(Left) 9 @ 8 $ 7 & 3 Ω 9 # 1 * £ 5 & % 4 6 (Right)

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

Hence, "Option 4" is the correct answer.

The correct answer is Bhabha Atomic Research Centre (BARC), Mumbai.

Key Points

• Dr. Avesh Kumar Tyagi is associated with the Bhabha Atomic Research Centre (BARC), Mumbai.
• Bhabha Atomic Research Centre (BARC) is India's premier nuclear research facility, headquartered in Mumbai, Maharashtra.
• Bhabha Atomic Research Centre was established in 1954 by Dr. Homi Jehangir Bhabha, the father of India's nuclear program.
• BARC conducts research and development in nuclear science, engineering, and related areas.
• It plays a pivotal role in the development of nuclear energy and technology in India, including the design and construction of nuclear reactors.

 Additional Information

• Raja Ramanna Centre for Advanced Technology (RRCAT), Indore
• The Raja Ramanna Centre for Advanced Technology (RRCAT) is located in Indore, Madhya Pradesh.
• RRCAT is involved in research and development in the areas of accelerator technologies and laser technologies.
• Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam
• The Indira Gandhi Centre for Atomic Research (IGCAR) is situated in Kalpakkam, Tamil Nadu.
• IGCAR specializes in the development of fast breeder reactor technology.
• Variable Energy Cyclotron Centre (VECC), Kolkata
• The Variable Energy Cyclotron Centre (VECC) is based in Kolkata, West Bengal.
• VECC is primarily focused on research in the field of accelerator-based science and nuclear physics.

The correct answer is displacement.

Key Points

• Displacement is a vector quantity, which means it has both magnitude and direction.
• It measures the shortest distance from the initial to the final position of an object.
• Displacement is different from distance, which is a scalar quantity and measures the total path length traveled by an object without considering direction.
• It is important in physics because it provides information about the change in position of an object in a specified direction.
• Displacement can be positive, negative, or zero, depending on the direction of movement.
• In mathematical terms, displacement is often represented as a change in position, denoted as Δx in one-dimensional motion.

 Additional Information

• Acceleration
• Acceleration is the rate at which an object's velocity changes over time.
• It is a vector quantity, having both magnitude and direction.
• Acceleration can be caused by changes in speed, direction, or both.
• Speed
• Speed is a scalar quantity that refers to how fast an object is moving.
• It is the rate at which an object covers distance, measured in units such as meters per second (m/s).
• Unlike velocity, speed does not consider the direction of movement.
• Velocity
• Velocity is a vector quantity that describes the speed of an object in a particular direction.
• It can be represented as the displacement divided by the time taken.
• Velocity is important in understanding the motion of objects in physics.

The correct answer is i - d, ii - a, iii - b, iv - c.

Key Points

• Ovary (i) - makes the female gametes (d): The primary function of the ovary is to produce the female gametes, also known as ova or eggs. It also secretes hormones such as estrogen and progesterone.
• Oviduct (ii) - fertilisation (a): The oviduct, also known as the fallopian tube, is the site where fertilisation occurs. The sperm meets the egg in the oviduct to form a zygote.
• Uterus (iii) - implantation (b): The uterus is the organ where the fertilised egg implants and develops into a fetus. It provides a nurturing environment for the developing embryo.
• Placenta (iv) - nourishes the growing embryo (c): The placenta is an organ that develops in the uterus during pregnancy. It provides oxygen and nutrients to the growing baby and removes waste products from the baby's blood.

 Additional Information

• Ovary
• The ovaries are part of the female reproductive system and are located on each side of the uterus.
• They are about the size and shape of an almond.
• The ovaries also play a key role in the menstrual cycle and fertility.
• Oviduct
• The oviducts are also known as fallopian tubes.
• Each woman has two oviducts, one on each side of the uterus.
• The oviducts are approximately 10-12 cm in length.
• Uterus
• The uterus is also known as the womb.
• It is a hollow, muscular organ located in the female pelvis between the bladder and rectum.
• The uterus is about the size and shape of an upside-down pear.
• Placenta
• The placenta is a temporary organ that develops during pregnancy.
• It attaches to the wall of the uterus and connects to the baby via the umbilical cord.
• The placenta is typically 9 inches in diameter and 1 inch thick.

The correct answer is uniform circular motion.

Key Points

• When an object moves in a circular path with a uniform speed, it is said to be in uniform circular motion.
• In uniform circular motion, the speed of the object remains constant, but the direction of the velocity changes continuously.
• This continuous change in direction means that the object is always undergoing acceleration, even though the speed is constant.
• The acceleration in uniform circular motion is called centripetal acceleration, and it is directed towards the centre of the circular path.
• Examples of uniform circular motion include the motion of a satellite orbiting the Earth, the rotation of a ceiling fan, and the motion of a car turning in a roundabout.

 Additional Information

• Motion along a hemisphere
• This refers to the motion of an object along the surface of a hemisphere. It is not related to uniform circular motion.
• Examples might include the motion of a ball on a dome-shaped surface, but it is not uniform circular motion.
• Motion along a straight line
• This is also known as linear motion or rectilinear motion.
• In this type of motion, an object moves in a straight path without changing its direction.
• Examples include a car driving on a straight road or a train moving on straight tracks.
• Linear motion
• This type of motion refers to the movement of an object in a straight line.
• Linear motion can be uniform (constant speed) or non-uniform (changing speed).
• Examples include the motion of a sprinter running on a straight track or an elevator moving up and down.

The Correct answer is Pituitary gland.

Key Points

• The pituitary gland is often referred to as the "master gland" of the endocrine system.
• It is located at the base of the brain, beneath the hypothalamus.
• The pituitary gland has two parts: the anterior pituitary and the posterior pituitary, each releasing different hormones.
• The anterior pituitary produces and releases growth hormone (GH), which stimulates growth, cell reproduction, and regeneration in humans.
• The secretion of growth hormone is regulated by the hypothalamus through releasing and inhibiting hormones.
• Growth hormone plays a crucial role in physical development in children and adolescents and also helps maintain tissues and organs throughout life.

 Additional Information

• Thyroid gland
• The thyroid gland is located in the neck and produces hormones like thyroxine (T4) and triiodothyronine (T3).
• These hormones regulate the body's metabolism, energy levels, and growth and development.
• Adrenal gland
• The adrenal glands are located on top of each kidney.
• They produce hormones such as adrenaline (epinephrine), cortisol, and aldosterone.
• These hormones help regulate metabolism, immune response, and stress responses.
• Testes
• The testes are male reproductive glands located in the scrotum.
• They produce testosterone, which is essential for the development of male secondary sexual characteristics and reproductive functions.

The Correct answer is CH4.

Key Points

• CH4 stands for methane, which is a simple covalent compound.
• It consists of one carbon atom bonded to four hydrogen atoms through covalent bonds.
• Covalent bonds are formed when atoms share electrons.
• Methane is a major component of natural gas and is used as a fuel.
• It is also a significant greenhouse gas contributing to global warming.
• Methane is produced naturally by processes such as decomposition of organic matter.

 Additional Information

• MgO
• Magnesium oxide (MgO) is an ionic compound.
• It consists of magnesium and oxygen ions held together by strong electrostatic forces.
• It is used in various applications like refractory materials, electrical insulation, and as a dietary supplement.
• MgCl2
• Magnesium chloride (MgCl2) is another example of an ionic compound.
• It consists of magnesium and chlorine ions.
• MgCl2 is often used for de-icing roads and as a coagulant in water treatment.
• NaCl
• Sodium chloride (NaCl) is commonly known as table salt.
• It is an ionic compound made up of sodium and chloride ions.
• NaCl is widely used in food for seasoning and preservation.

The correct answer is Unidirectional.

Key Points

• In a food web, the energy transfer follows a unidirectional pattern.
• This means that energy flows in one direction—from the producers (such as plants) to various levels of consumers (herbivores, carnivores, omnivores).
• Producers capture energy from the sun through the process of photosynthesis.
• This captured energy is then transferred to herbivores that consume the plants.
• From herbivores, the energy is passed on to carnivores and omnivores that eat the herbivores.
• At each transfer, a portion of the energy is lost as heat, making the transfer inefficient and ensuring that it does not revert back to the previous stage.
• The laws of thermodynamics support this unidirectional flow, particularly the second law which states that energy transformations are not 100% efficient.
• This unidirectional flow helps maintain the structure and function of ecosystems.

 Additional Information

• Circular
• The term circular is not applicable to energy transfer in a food web because energy is not recycled in the same manner as nutrients in an ecosystem.
• Multidimensional
• Multidimensional suggests multiple directions or dimensions, which is not accurate for the one-way flow of energy in food webs.
• Bidirectional
• Bidirectional would imply energy flows in two directions, which is not true for food webs as energy moves from producers to consumers in a one-way direction.

The correct answer is equal to 2f.

Key Points

• For a concave mirror, when the object is placed at a distance equal to the radius of curvature (2f), the image formed is of the same size as that of the object.
• The image formed in this case is real, inverted, and of the same size as the object.
• This is derived from the mirror formula and the magnification equation for concave mirrors.
• According to the mirror equation: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
• For an image to be the same size as the object, the object distance u must be equal to 2f.
• This scenario is a classic case of image formation by concave mirrors used in optics problems.

 Additional Information

• Concave Mirror
• A concave mirror is a spherical mirror that curves inward like a portion of the interior of a sphere.
• It can form real and virtual images, depending on the position of the object.
• It is often used in applications like reflecting telescopes, makeup mirrors, and headlights of vehicles.
• Focal Length
• The focal length (f) is the distance between the mirror's surface and the focal point.
• It is half of the radius of curvature (R), i.e., f = R/2.
• Focal length is a crucial parameter in determining the image formation properties of the mirror.

The correct answer is It stimulates growth in all organs.

Key Points

• The growth hormone, also known as somatotropin, is secreted by the anterior pituitary gland.
• Its primary function is to stimulate growth in all organs and tissues of the body, including bones and muscles.
• It plays a crucial role in the regulation of body composition, body fluids, muscle and bone growth, sugar and fat metabolism, and possibly heart function.
• Growth hormone stimulates the liver to produce an insulin-like growth factor (IGF-1), which is a key player in muscle growth and repair.
• The hormone is most active during childhood and adolescence, which are critical periods for growth and development.

 Additional Information

• It regulates the blood sugar level
• The regulation of blood sugar levels is primarily controlled by hormones such as insulin and glucagon, which are secreted by the pancreas.
• While growth hormone does have some influence on metabolism, its direct role in blood sugar regulation is limited compared to insulin.
• It regulates the menstrual cycle
• The menstrual cycle is regulated by a complex interaction of hormones including estrogen, progesterone, luteinizing hormone (LH), and follicle-stimulating hormone (FSH).
• These hormones are primarily produced by the ovaries and the pituitary gland, but the growth hormone does not play a direct role in this process.
• It regulates metabolism for body growth
• While growth hormone does influence metabolism, its primary function is to stimulate growth in all organs rather than solely regulating metabolism.
• Other hormones like thyroid hormones, insulin, and adrenal hormones also play significant roles in regulating metabolism.

Shortcut Trick

Identify the numbers as (10000 − 7) and (10000 + 7).

Apply the algebraic identity (a − b)(a + b) = a² − b².

⇒ (10000)² − (7)² = 100000000 − 49 = 99999951.

∴ The correct answer is 99999951.

Alternate Method

Given: Expression 9993 × 10007

Formula Used: Algebraic identity (a − b)(a + b) = a² − b²

⇒ 9993 = 10000 − 7

⇒ 10007 = 10000 + 7

⇒ 9993 × 10007 = (10000 − 7) × (10000 + 7)

⇒ Result = (10000)² − (7)²

⇒ Result = 100,000,000 − 49

⇒ Result = 99,999,951

∴ The correct answer is 99999951.

Additional Information

Algebraic Identities

Standard identities like (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b² are often used to simplify large multiplications.

BODMAS Rule

Always follow the order: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction for complex expressions.

Unit Digit Check

In multiplication, the unit digit of the product is the product of the unit digits: 3 × 7 = 21, so the answer must end in 1.

Shortcut Trick

Use the direct formula for expenditure constant: % Increase in consumption = [r ÷ (100 − r)] × 100

Here, r = 20% (decrease in price).

% Increase = [20 ÷ (100 − 20)] × 100 = (20 ÷ 80) × 100 = (1/4) × 100 = 25%.

∴ The correct answer is 25%.

Alternate Method

Given: Decrease in price of sugar = 20%. Expenditure remains unchanged.

Formula: Expenditure = Price × Consumption

⇒ Let original Price = 100 and original Consumption = 100.

⇒ Original Expenditure = 100 × 100 = 10,000.

⇒ New Price = 100 − 20% of 100 = 80.

⇒ Since Expenditure is unchanged, New Consumption = 10,000 ÷ 80 = 125.

⇒ Increase in Consumption = 125 − 100 = 25.

⇒ % Increase = (25 ÷ 100) × 100 = 25%.

∴ The correct answer is 25%.

Additional Information

Inverse Variation Rule

When the product of two variables is constant (Price × Consumption = Expenditure), an x% decrease in one requires a [x ÷ (100 − x)] × 100% increase in the other.

Percentage Change in Expenditure

If both price and consumption change, the net % change in expenditure is given by the successive percentage formula: a + b + (ab/100).

Fractional Conversion

A 20% decrease is a factor of 1/5. To keep the product same, consumption must increase by 1/(5−1) = 1/4, which is 25%.

The correct answer is Approval of seven Project 17B stealth frigates for the Indian Navy.

Key Points

• The Project 17B is a class of stealth frigates being constructed for the Indian Navy.
• These frigates are equipped with advanced stealth features that minimize their detection by enemy radar and sonar.
• They come with enhanced combat capabilities and are designed to carry out a variety of missions including anti-surface, anti-submarine, and anti-air operations.
• The approval of these seven Project 17B frigates significantly boosts India's naval defense capabilities.
• This project involves the use of advanced technologies and indigenous resources, contributing to India's self-reliance in defense production.

 Additional Information

• Advanced naval radar systems
• These systems are crucial for surveillance and target detection in maritime operations.
• They provide the navy with the ability to detect and track both surface and aerial threats.
• Aircraft carriers
• Aircraft carriers serve as a floating airbase and are pivotal in power projection and force multiplication in naval warfare.
• India already has INS Vikramaditya and the indigenous INS Vikrant in its fleet.
• Multi-role submarines
• These submarines are capable of performing a variety of roles including surveillance, reconnaissance, and combat operations.
• They are equipped with advanced sonar systems and torpedoes.

Shortcut Trick

Ratio of A : B : C : D = 4 : 7 : 9 : 3

Difference between C and D in units = 9 − 3 = 6 units

Given, 6 units = ₹720 → 1 unit = ₹120

Difference between C and B in units = 9 − 7 = 2 units

Value of 2 units = 2 × 120 = ₹240

∴ The correct answer is ₹240.

Alternate Method

Given:

Ratio of shares A : B : C : D = 4 : 7 : 9 : 3

Let the shares be 4x, 7x, 9x, and 3x respectively.

Calculations:

⇒ Share of C − Share of D = 720

⇒ 9x − 3x = 720

⇒ 6x = 720

⇒ x = 720 ÷ 6 = 120

⇒ Required difference = Share of C − Share of B

⇒ Difference = 9x − 7x = 2x

⇒ Difference = 2 × 120 = 240

∴ The correct answer is ₹240.

Additional Information

Ratio and Proportion

A ratio compares two quantities. If a : b = c : d, then a × d = b × c (Product of extremes = Product of means).

Unitary Method in Ratios

Find the value of 1 unit by dividing the given total or difference by its corresponding ratio parts, then multiply to find the unknown.

Compound Ratio

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

Shortcut Trick

Let the Cost Price (CP) be 100 units.

Marked Price (MP) = 100 + 22% of 100 = 122 units.

Selling Price (SP) = 122 × (100 − 15) ÷ 100 = 122 × 0.85 = 103.7 units.

Given SP = Rs. 5,185 ⇒ 103.7 units = 5185.

CP (100 units) = (5185 ÷ 103.7) × 100 = 50 × 100 = Rs. 5000.

∴ The correct answer is Rs. 5000.

Alternate Method

Given: Markup% = 22%, Discount% = 15%, Selling Price (SP) = Rs. 5,185.

Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100

⇒ Let CP be x.

⇒ MP = x × (122 ÷ 100) = 1.22x.

⇒ SP = 1.22x × (85 ÷ 100) = 5185.

⇒ 1.037x = 5185.

⇒ x = 5185 ÷ 1.037 = 5000.

∴ The correct answer is Rs. 5000.

Additional Information

Markup and Discount Relation

Profit% = Markup% − Discount% − (Markup × Discount ÷ 100). This helps find net profit quickly.

Marked Price Formula

CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%). This ratio links CP and MP directly.

The logic followed here is:

‘REPS’ is coded as '9631'

‘EARS’ is coded as ‘6914’

Thus, code for ‘A’ is '4'.

Hence, "Option 1" is the correct answer.

The correct answer is Pradhan Mantri MUDRA Yojana (PMMY).

Key Points

• The Pradhan Mantri MUDRA Yojana (PMMY) was launched in April 2015 by the Government of India.
• The scheme aims to provide loans up to Rs. 10 lakhs to non-corporate, non-farm small/micro enterprises.
• The loans are categorized into three products based on the loan amount: Shishu (up to Rs. 50,000), Kishore (Rs. 50,000 to Rs. 5 lakhs), and Tarun (Rs. 5 lakhs to Rs. 10 lakhs).
• The objective of the scheme is to promote entrepreneurship and generate employment opportunities.
• Under the Union Budget 2024-25, the loan limit under PMMY has been increased to Rs. 20 lakhs.
• The scheme is implemented through Commercial Banks, RRBs, Small Finance Banks, MFIs, and NBFCs.

 Additional Information

• Credit Guarantee Fund Trust for Micro and Small Enterprises (CGTMSE)
• The CGTMSE scheme was launched by the Government of India and the SIDBI to provide credit guarantees for loans extended to Micro and Small Enterprises (MSEs).
• The scheme aims to provide collateral-free credit to the MSE sector.
• Prime Minister's Employment Generation Programme (PMEGP)
• The PMEGP is a credit-linked subsidy program launched in 2008 to generate employment opportunities through the establishment of micro-enterprises in rural and urban areas.
• It is implemented by the Khadi and Village Industries Commission (KVIC).
• Stand-Up India Scheme
• The Stand-Up India Scheme was launched in April 2016 to promote entrepreneurship among Scheduled Castes/Scheduled Tribes and women.
• It provides bank loans between Rs. 10 lakhs and Rs. 1 crore for setting up greenfield enterprises.

Shortcut Trick

Investment ratio of Lakhan and Ram = 48,000 : 72,000 = 2 : 3.

Total ratio parts = 2 + 3 = 5 units.

Total annual profit = Rs. 6,530.

Value of 1 unit = 6,530 ÷ 5 = Rs. 1,306.

Ram's share (3 units) = 3 × 1,306 = Rs. 3,918.

∴ The correct answer is Rs. 3,918.

Alternate Method

Given: Investment of Lakhan = Rs. 48,000, Investment of Ram = Rs. 72,000, Total Profit = Rs. 6,530.

Formula: Profit Share Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂)

⇒ Ratio of profit = 48,000 : 72,000 = 2 : 3 (Since time is constant for both).

⇒ Sum of ratios = 2 + 3 = 5.

⇒ Ram's share = (Ram's Ratio ÷ Total Ratio) × Total Profit.

⇒ Ram's share = (3 ÷ 5) × 6,530.

⇒ Ram's share = 3 × 1,306 = Rs. 3,918.

∴ The correct answer is Rs. 3,918.

Additional Information

Partnership Basics

In a simple partnership, profits are distributed in the direct ratio of the capitals invested when the time period is the same for all partners.

Compound Partnership

If investments are for different time periods, the profit is divided in the ratio of the product of (Investment × Time).

Shortcut Trick

Let the number of students in Class A be A and Class B be B.

From the second condition: If 1 student goes from B to A, they become equal ⇒ B − 1 = A + 1 ⇒ B − A = 2.

Check options for B: If B = 19, then A = 17.

Verify first condition: If 5 shift from A to B, A becomes 17 − 5 = 12, and B becomes 19 + 5 = 24.

Since 24 is twice of 12, the condition is satisfied.

∴ The correct answer is 19 students.

Alternate Method

Let Class A have x students and Class B have y students.

Case 1: 5 students shifted from A to B.

⇒ 2(x − 5) = y + 5

⇒ 2x − 10 = y + 5 ⇒ 2x − y = 15 --- (Eq. 1)

Case 2: 1 student sent from B to A.

⇒ x + 1 = y − 1

⇒ y − x = 2 ⇒ x = y − 2 --- (Eq. 2)

Substitute x in Eq. 1:

⇒ 2(y − 2) − y = 15

⇒ 2y − 4 − y = 15

⇒ y = 19

∴ The correct answer is 19 students.

Additional Information

Linear Equations in Two Variables

These problems are solved by translating word conditions into algebraic equations of the form ax + by = c.

Substitution Method

Expressing one variable in terms of the other from the simpler equation and substituting it into the more complex one to find the value.

Elimination Method

Multiplying equations by suitable constants so that adding or subtracting them eliminates one variable.

The correct answer is Sajid Wajid Sheikh.

Key Points

• Sajid Wajid Sheikh won the first 'MTArt Agency x India Art Fair Artist Prize' during the 15th India Art Fair held in February 2024.
• The India Art Fair is a prestigious event that showcases a wide range of artworks from contemporary artists.
• The MTArt Agency is known for supporting and promoting talented artists globally.
• This prize recognizes the significant contributions of emerging artists in the field of contemporary art.
• Sajid Wajid Sheikh's work is celebrated for its unique style and cultural relevance.

 Additional Information

• Devika Rani
• Devika Rani was an early Indian film actress who is remembered as the first lady of Indian cinema.
• She was the recipient of the Dadasaheb Phalke Award, India's highest award in cinema, for her lifetime contribution to Indian cinema.
• Birendranath Sircar
• Birendranath Sircar was a pioneering Indian film producer and founder of New Theatres Calcutta.
• He was also awarded the Dadasaheb Phalke Award for his contributions to Indian cinema.
• Asha Parekh
• Asha Parekh is a renowned Indian film actress, director, and producer who was active in the Hindi film industry during the 1960s and 1970s.
• She has received numerous awards for her performances, including the Padma Shri, one of India's highest civilian honors.

The Correct answer is Adipocyte.

Key Points

• Adipocytes are also known as fat cells.
• They are the cells that primarily compose adipose tissue, specialized in storing energy as fat.
• Adipocytes do not contain neurons; their main function is to store fat for energy and provide cushioning to the body.
• Neurons are specialized cells that transmit nerve impulses, and they are not present in adipose tissue.

 Additional Information

• Nerves
• Nerves are bundles of neurons that transmit signals between different parts of the body.
• They are essential for coordinating various functions such as movement and sensation.
• Brain
• The brain is the central organ of the nervous system and is composed of billions of neurons.
• It controls most of the activities in the body by processing and transmitting information through neural networks.
• Spinal cord
• The spinal cord is a long, thin, tubular structure composed of nervous tissue, which contains numerous neurons.
• It connects the brain to the peripheral nervous system and facilitates the transmission of neural signals to and from the brain.

Shortcut Trick

Days for B alone = (A × Combined) ÷ (A − Combined) = (4 × 2) ÷ (4 − 2) = 4 days.

For 19-times the work, B takes = 19 × 4 = 76 days.

∴ The correct answer is 76 days.

Alternate Method

Given: (A + B) can do work in 2 days, A can do work in 4 days.

Formula: Total Work = LCM of days; Efficiency = Total Work ÷ Days.

⇒ Efficiency of B = Efficiency of (A + B) − Efficiency of A

⇒ Efficiency of B = 2 − 1 = 1 unit/day

⇒ Time for B to do 1-time work = 4 ÷ 1 = 4 days

⇒ Time for B to do 19-times work = 19 × 4 = 76 days

∴ The correct answer is 76 days.

Additional Information

Work and Efficiency Relation

Time is inversely proportional to efficiency. If work increases by n-times, the time required at the same efficiency also increases by n-times.

Combined Work Formula

If A takes 'x' days and B takes 'y' days, together they take (x × y) ÷ (x + y) days to complete the work.

Pipes and Cisterns

This logic applies to inlet pipes. If an outlet pipe is present, its efficiency is taken as negative.

The Correct answer is 5 A

Key Points

• The power of the electric geyser is given as 100 J/s, which is equivalent to 100 W since 1 watt = 1 joule per second.
• According to Ohm’s Law, the relationship between voltage, current, and resistance is given by V = IR, where V is the voltage, I is the current, and R is the resistance.
• The power formula in electrical circuits is P = I²R, where P is the power, I is the current, and R is the resistance.
• Rearranging the formula to find the current, I = √(P/R).
• Substituting the values: I = √(100/4) = √25 = 5 A.
• Thus, the current flowing through the electric geyser is 5 A, which makes this the correct answer.

 Additional Information

• Ohm's Law states that the current passing through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant.
• The unit of power in the SI system is the watt (W), where 1 W = 1 J/s.
• The relationship between power, resistance, and current is crucial for calculating electrical parameters in circuits.
• Electrical appliances like geysers, heaters, and irons operate based on the principle of Joule heating, which states that the heat produced in a resistor is proportional to the square of the current.

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

According to the question, such odd digits which are immediately preceded by an odd digit and is immediately followed by an odd digit:

Required condition: Odd digit - Odd digit - Odd digit

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

Thus, there are three such odd digits which are immediately preceded by an odd digit and is immediately followed by an odd digit.

Hence, "Option 1" is the correct answer.

The correct answer is unicellular.

Key Points

• Unicellular organisms are those that consist of a single cell.
• They are the simplest form of life and can perform all necessary functions for survival.
• Examples of unicellular organisms include bacteria, archaea, and many protists.
• These organisms are often microscopic and can be found in almost every environment on Earth.
• Unicellular organisms reproduce through various methods such as binary fission, budding, and sporulation.
• They play a crucial role in ecosystems, including decomposition, nutrient cycling, and as part of the food chain.

 Additional Information

• Multicellular
• Multicellular organisms are composed of multiple cells that work together.
• Examples include humans, animals, and plants.
• They have specialized cells that perform different functions, allowing for greater complexity.
• Unisexual
• Unisexual organisms have either male or female reproductive organs but not both.
• Examples include certain plants and animals where individuals are distinctly male or female.

The correct answer is 1/2 mv²

Key Points

• Kinetic Energy is the energy possessed by an object due to its motion.
• The formula for kinetic energy is derived from the work-energy principle.
• According to this principle, the work done on an object is equal to the change in its kinetic energy.
• The work done to accelerate an object from rest to a velocity is given by the formula (1)/(2)mv^2.
• Here, m is the mass of the object and v is its velocity.
• This formula shows that the kinetic energy is directly proportional to the mass of the object and the square of its velocity.
• Thus, any increase in velocity will result in a significant increase in kinetic energy.

 Additional Information

• Option 2
• The formula (1)/(3)mv^2 is incorrect because it does not accurately represent the work-energy principle for kinetic energy.
• Option 3
• The expression mv-2 does not align with the physical principles defining kinetic energy.
• Option 4
• The term mv2 is not a valid representation of kinetic energy as it misses the constant factor of (1)/(2).
• Option 5
• The option is incomplete and does not provide a valid formula for kinetic energy.

Given: Seven boxes A, B, E, F, L, M and Pare kept one over.

1) Only A is kept above E.

2) Only F is kept between E and B.

3) Only P is kept below M.

After positioning P and M only one position is left which will be occupied by the only person left i.e. L.

Thus, according to the final arrangement one boxe are kept between L and P.

Hence, "Option 4" is the correct answer.

Shortcut Trick

By the fundamental definition of number systems, a prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

This implies that it is divisible only by 1 and the number itself.

Therefore, the set of factors for any prime number p is strictly {1, p}.

The total count of these factors is always exactly 2.

∴ The correct answer is 2.

Alternate Method

Given: A prime number.

Definition: A prime number is a positive integer that has no positive divisors other than 1 and itself.

⇒ Let us verify with examples:

⇒ For 2 (smallest prime): Factors are 1 and 2. Count = 2.

⇒ For 3: Factors are 1 and 3. Count = 2.

⇒ For 11: Factors are 1 and 11. Count = 2.

⇒ For 19: Factors are 1 and 19. Count = 2.

∴ The correct answer is 2.

Additional Information

Composite Numbers

Natural numbers that have more than two factors (e.g., 4 has factors 1, 2, and 4).

Special Case of 1

The number 1 has only one factor (itself), so it is neither prime nor composite.

Even Prime Number

The number 2 is the only even prime number; all other prime numbers are odd.

Co-prime Numbers

Two numbers are said to be co-prime if their Highest Common Factor (HCF) is 1.

Given: 35 × 7 + 2 ÷ 6 - 13 = ?

According to the question, after ‘+’ and ‘-’ are interchanged and ‘×’ and ‘÷’ are interchanged:

35 × 7 + 2 ÷ 6 - 13 = ? ⇒ 35 ÷ 7 - 2 × 6 + 13 = ?

⇒ 35 ÷ 7 - 2 × 6 + 13 = ?

⇒ 5 - 2 × 6 + 13 = ?

⇒ 5 + 13 - 12 = ?

⇒ 18 - 12 = ?

⇒ 6 = ?

Hence, "Option 1" is the correct answer.

Shortcut Trick

Total Work = LCM(15, 10, 30) = 30 units.

Efficiencies: A = 2, B = 3, C = 1.

Work in a 3-day cycle: (A) + (A) + (A+B+C) = 2 + 2 + (2+3+1) = 10 units.

Total days for 30 units = (30 ÷ 10) × 3 = 9 days.

∴ The correct answer is 9 days.

Alternate Method

Given: A works alone on the 1st and 2nd days. A, B, and C work together on the 3rd day.

⇒ Work on Day 1 (A) = 2 units

⇒ Work on Day 2 (A) = 2 units

⇒ Work on Day 3 (A + B + C) = 2 + 3 + 1 = 6 units

⇒ Total work in 1 cycle (3 days) = 2 + 2 + 6 = 10 units

⇒ Number of cycles required = Total Work ÷ Work per cycle = 30 ÷ 10 = 3 cycles

⇒ Total time = 3 cycles × 3 days/cycle = 9 days

∴ The correct answer is 9 days.

Additional Information

Alternate Day Work

In problems involving alternate days or specific assistance patterns, calculate the total work done in one complete cycle and then divide the total work by this value.

Efficiency Relation

Efficiency is inversely proportional to the time taken. Efficiency = Total Work ÷ Time.

The logic followed here is:

Given:

(3, 12, 36)

3 × 4 = 12

12 × 3 = 36

And,

(8, 32, 96) 

8 × 4 = 32

32 × 3 = 96

So, checking each option one by one:

Option 1) (14, 48, 144) 

14 × 4 = 56 ≠ 48

48 × 4 = 144

Option 2) (12, 48, 124)

12 × 4 = 48

48 × 4 = 144 ≠ 124

Option 3) (12, 42, 144)

12 × 4 = 48 ≠ 42

42 × 4 = 168 ≠ 144

Option 4) (12, 48, 144)

12 × 4 = 48

48 × 3 = 144

Thus, out of all the options, '(12, 48, 144)' follows the same logic as given.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Ratio of present ages of Amit and Amita = 7 : 5.

Ratio (Amit − 5) : (Amita + 5) = 1 : 1 ⇒ Amit − 5 = Amita + 5 ⇒ Amit − Amita = 10 years.

Difference in ratio parts (7 − 5) = 2 units. So, 2 units = 10 years ⇒ 1 unit = 5 years.

Present sum of ages = (7 + 5) × 5 = 60 years. Target sum = 72 years.

Total years to add = 72 − 60 = 12 years. Since there are 2 people, each grows by 12 ÷ 2 = 6 years.

∴ The correct answer is 6 years.

Alternate Method

Given: Present age ratio = 7 : 5. Condition: (Amit − 5)/(Amita + 5) = 1/1.

Formula Used: Age after n years = Present Age + n.

⇒ Let Amit present age = 7x and Amita present age = 5x.

⇒ According to the question: (7x − 5) / (5x + 5) = 1 / 1

⇒ 7x − 5 = 5x + 5

⇒ 2x = 10 ⇒ x = 5.

⇒ Amit present age = 7 × 5 = 35 years; Amita present age = 5 × 5 = 25 years.

⇒ Total present age = 35 + 25 = 60 years.

⇒ Let after 'n' years their total age be 72.

⇒ (35 + n) + (25 + n) = 72

⇒ 60 + 2n = 72 ⇒ 2n = 12 ⇒ n = 6.

∴ The correct answer is 6 years.

Additional Information

Concept of Constant Difference

The difference between the ages of two people always remains constant, regardless of the number of years passed or subtracted.

Ratio and Proportions in Ages

When a ratio a:b is given for present ages, we use a common variable 'x' to represent actual values as ax and bx. For 'n' years later, we use (ax+n) and (bx+n).

Total Sum of Ages

If the sum of ages of 'k' people is 'S' now, then after 'n' years, the total sum will be S + (k × n).

Given:

The bar graph represents the number of people who like different cuisines:

Indian: 6000

Italian: 4500

Chinese: 5500

Thai: 3500

Japanese: 4000

Miscellaneous: 6500

Calculation:

The number of people who like the cuisines are:

Indian: 6000

Chinese: 5500

Thai: 3500

Miscellaneous: 6500

The sum of these values is:

6000 + 5500 + 3500 + 6500 = 21,500

The average number of people is:

Average = 21,500 / 4 = 5375

∴ The average number of people who like Indian, Chinese, Thai, and miscellaneous cuisines is 5375.

The logic followed here is:

Given: 

WILD - IWLD - WLDI

And,

TALK - ATLK - TLKA 

So, checking each option one by one:

Option 1) BOSE - OBSE - OSEB

Option 2) RICE - RCIE - ECIR 

Option 3) FAIL - AFIL - LAIF 

Option 4) VICE - IVCE - VCEI

Thus, out of all the options 'VICE - IVCE - VCEI' follows the same logic as given.

Hence, "Option 4" is the correct answer.

Decoding letters:

Given: 16 C 24 A 3 B 8 D 5 = ?

After interchanging the letters,

16 C 24 A 3 B 8 D 5 = ? ⇒ 16 + 24 ÷ 3 × 8 - 5 = ?

⇒ 16 + 24 ÷ 3 × 8 - 5 = ?

⇒ 16 + 8 × 8 - 5 = ?

⇒ 16 + 64 - 5 = ?

⇒ 80 - 5 = ?

⇒ 75 = ?

Hence, "Option 3" is the correct answer.

Given:

Devansh starts from point A and drives 10 km towards the North.

He takes two simultaneous right turns and drives 3 km and 6 km, respectively.

He takes a final right turn and drives 3 km to reach point B. 

Thus, Devansh should drive (10 km + 6 km) 4 km in the south direction in order to reach Point A again.

Hence, "Option 3" is the correct answer.

Shortcut Trick

Mode is the value that appears most frequently in a data set.

Count the frequency of each number:

66 → 3 times | 69 → 4 times | 71 → 3 times | 73 → 1 time | 74 → 3 times | 83 → 5 times | 84 → 3 times | 90 → 2 times

The value 83 occurs most frequently (5 times).

∴ The correct answer is 83.

Alternate Method

Given Data: 66, 69, 83, 69, 84, 74, 71, 83, 69, 84, 73, 83, 69, 71, 84, 74, 83, 66, 74, 71, 83, 66, 90, 90

Formula Used: Mode = Value with the maximum frequency.

⇒ Frequency of 66 = 3

⇒ Frequency of 69 = 4

⇒ Frequency of 71 = 3

⇒ Frequency of 73 = 1

⇒ Frequency of 74 = 3

⇒ Frequency of 83 = 5

⇒ Frequency of 84 = 3

⇒ Frequency of 90 = 2

⇒ Maximum Frequency = 5

⇒ Value corresponding to maximum frequency = 83

∴ The correct answer is 83.

Additional Information

Empirical Relationship

The relationship between Mean, Median, and Mode is: Mode = 3 × Median − 2 × Mean.

Bimodal and Multimodal

If two or more values have the same maximum frequency, the data set is called bimodal or multimodal.

Mean and Median

Mean is the average (Sum ÷ Count), while Median is the middle value when the data is arranged in ascending or descending order.

The correct answer is Ministry of Culture.

Key Points

• The Ministry of Culture is responsible for the preservation and promotion of art and culture in India.
• The special festival series titled 'Amrit Parampara' was presented to celebrate and promote India's rich cultural heritage.
• This initiative is part of the larger celebrations of India's 75th year of independence, known as 'Azadi Ka Amrit Mahotsav'.
• The festival series aims to showcase various traditional and contemporary art forms, including music, dance, theatre, and visual arts.
• The Ministry of Culture collaborates with various cultural organizations, artists, and institutions to organize such events.

 Additional Information

• Ministry of Tourism
• The Ministry of Tourism is responsible for the promotion of tourism in India.
• It works on policies and strategies to attract tourists and develop tourism infrastructure.
• The ministry also promotes India as a destination for foreign tourists and domestic travelers.
• Ministry of External Affairs
• The Ministry of External Affairs handles India's foreign relations and international diplomacy.
• It oversees bilateral and multilateral relations with other countries and international organizations.
• This ministry is also responsible for the welfare of Indian citizens abroad.
• Ministry of Textiles
• The Ministry of Textiles is responsible for the development and promotion of the textile industry in India.
• It formulates policies and programs to enhance the competitiveness of the textile sector.
• The ministry also supports the growth of handlooms, handicrafts, and sericulture.

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

Conclusions:

(I) Some jackets are not coats → Not Follow (As all coats are jackets, but we don't have the information related to the rest part of jacket, it can only be possible but not define, there, it is false)

(II) Some jackets are sweaters → Follow (As all coats are jackets and some coats are sweaters. As some part of sweaters is common with coats which whole comes in jackets, therefore it is true.)

∴ Here, Only conclusion II follows .​

Hence, the correct answer is "Option 1"

The logic followed here is:

​

Hence, "Option 3" is the correct answer.

The Correct answer is Both a and b.

Key Points

• The separation of H+ ions from HCl molecules indeed cannot occur in the absence of water. Water is necessary to facilitate the dissociation process.
• Hydrogen ions in an aqueous solution are always shown as H+ (aq) or H3O+ (hydronium ion). This is because hydrogen ions cannot exist freely in water; they combine with water molecules to form hydronium ions.
• When an acid like HCl is dissolved in water, it dissociates into H+ (aq) and Cl- (aq), demonstrating the necessity of water for this process.
• The correct representation of hydrogen ions in water as H+ (aq) or H3O+ ensures a more accurate depiction of their behavior in solution.
• Both statements are correct and together they provide a comprehensive understanding of the behavior of acids in water.

 Additional Information

• Hydronium Ion (H3O+)
• The hydronium ion is formed when a water molecule accepts a hydrogen ion (proton).
• It plays a key role in the chemistry of acids and bases in aqueous solutions.
• Hydronium ions are responsible for the acidic properties of solutions.
• Dissociation in Water
• Dissociation is the process by which molecules split into smaller particles such as ions.
• This process is crucial in understanding the behavior of acids, bases, and salts in water.
• Water acts as a solvent and facilitates the dissociation of ionic compounds.

The Correct answer is Tides.

Key Points

• Tides are caused by the gravitational interaction between the Earth and the Moon.
• The Moon's gravity pulls on Earth, creating a bulge of water on the side of Earth facing the Moon.
• Another bulge occurs on the opposite side of Earth due to the inertia of the water.
• This results in high tides at these bulges and low tides in the areas in between.
• The Sun's gravity also affects tides, but its effect is smaller than that of the Moon.

 Additional Information

• Blue color of the sky
• The blue color of the sky is due to Rayleigh scattering.
• This phenomenon occurs because shorter wavelengths of light (blue and violet) are scattered in all directions by the gases and particles in the atmosphere.
• Blue light is scattered more than other colors because it travels as shorter, smaller waves.
• Thunderstorms
• Thunderstorms are caused by the rapid upward movement of warm, moist air into colder air in the upper atmosphere.
• This can result in the formation of cumulonimbus clouds and produce lightning, thunder, heavy rain, and sometimes hail.
• Rainbow
• A rainbow is caused by the refraction, dispersion, and reflection of sunlight in water droplets.
• This results in a spectrum of light appearing in the sky, taking the form of a circular arc of colors.

The logic followed here is:

Option 1) NJ-MP

Option 2) LH-KN 

Option 3) JF-IL 

Option 4) QM-PR

Thus, out of all the options 'QM-PR' is the odd one out.

Hence, "Option 4" is the correct answer.

The logic followed here is:

Hence, "Option 3" is the correct answer.

Shortcut Trick

When two items are sold at the same Selling Price (SP), one at a gain of x% and another at a loss of x%, there is always a net loss.

Shortcut: Net Loss% = x² ÷ 100.

Given x = 5.

Net Loss% = 5² ÷ 100 = 25 ÷ 100 = 0.25%.

∴ The correct answer is 0.25% loss.

Alternate Method

Given: SP of each house = Rs. 1.995 lakhs, Gain = 5%, Loss = 5%.

Formulas: CP = SP × 100 ÷ (100 ± Profit/Loss%), Net Loss% = (x² ÷ 100)%.

⇒ House 1 CP = 1.995 × 100 ÷ 105 = 1.9 lakhs.

⇒ House 2 CP = 1.995 × 100 ÷ 95 = 2.1 lakhs.

⇒ Total CP = 1.9 + 2.1 = 4.0 lakhs.

⇒ Total SP = 1.995 × 2 = 3.99 lakhs.

⇒ Net Loss = 4.0 − 3.99 = 0.01 lakh.

⇒ Net Loss% = (0.01 ÷ 4.0) × 100 = 0.25%.

∴ The correct answer is 0.25% loss.

Additional Information

Two same-SP articles

If two articles are sold at the same price, one at x% profit and another at x% loss, the transaction always results in a loss of (x/10)²%.

Successive Percentage Change

The net change can also be calculated using the formula a + b + (ab/100), where a is +5 and b is −5.

The correct answer is +1 J.

Key Points

• Work Done is defined as the product of the force applied and the displacement in the direction of the force.
• The formula for work done is W = F × d, where W is the work done, F is the force, and d is the displacement.
• In this case, the force (F) is 1 N and the displacement (d) is 1 m.
• Therefore, the work done (W) is 1 N × 1 m = 1 J.
• The positive sign indicates that the force and the displacement are in the same direction.

 Additional Information

• Negative Work Done
• Negative work occurs when the force and the displacement are in opposite directions.
• In such cases, the work done is calculated as -F × d.
• This situation typically occurs in scenarios involving friction or opposing forces.
• Zero Work Done
• Zero work is done when either the force is zero, or the displacement is zero, or the force is perpendicular to the direction of displacement.
• In mathematical terms, this can be expressed as W = 0.

Shortcut Trick

For a 3-year period at 10%, the Effective Percentage Rate of Compound Interest is 33.1%.

Compound Interest = Principal × 33.1%

⇒ 12,000 × 0.331 = 3,972

∴ The correct answer is Rs. 3972.

Alternate Method

Given: Principal (P) = Rs. 12,000, Time (n) = 3 years, Rate (R) = 10% p.a.

Formula Used: Amount (A) = P(1 + R/100)ⁿ and Compound Interest (CI) = A − P

⇒ A = 12000 × (1 + 10/100)³

⇒ A = 12000 × (11/10) × (11/10) × (11/10)

⇒ A = 12 × 11 × 11 × 11

⇒ A = 12 × 1331 = 15,972

⇒ CI = 15,972 − 12,000

⇒ CI = 3,972

∴ The correct answer is Rs. 3972.

Additional Information

Effective Rate of Interest

For 2 years, effective rate = x + y + (xy/100). For 3 years at 10%, it is 33.1%.

Difference between CI and SI

For 3 years, Difference = P(R/100)² × (3 + R/100).

Compound Interest Formula

CI = P[(1 + R/100)ⁿ − 1] where P is principal, R is rate, and n is time.

The Correct answer is 0.

Key Points

• The work done by a force is defined as the product of the force and the displacement of the object in the direction of the force.
• The formula for work done is: Work = Force × Displacement × cos(θ), where θ is the angle between the force and the direction of displacement.
• If the displacement of the body is zero, then the work done by any force, regardless of its magnitude, will be zero.
• In this scenario, the force applied is 2 Newtons, but the displacement in the direction of the applied force is zero.
• Therefore, the work done by the force is 0 joules.
• This concept is important in understanding the relationship between force, displacement, and work in the context of physics.

 Additional Information

• Force
• A force is a push or pull upon an object resulting from the object's interaction with another object.
• Forces can cause an object to accelerate, slow down, remain in place, or change shape.
• Forces are measured in Newtons (N) in the International System of Units (SI).
• Displacement
• Displacement is a vector quantity that refers to an object's change in position.
• It is the shortest distance from the initial to the final position of a point.
• Displacement has both magnitude and direction.
• Work
• Work is done when a force causes a displacement of an object.
• Work is a scalar quantity and is measured in Joules (J).
• Positive work is done when the force and displacement are in the same direction, while negative work is done when they are in opposite directions.

The Correct answer is The cell body of a neuron has many nuclei.

Key Points

• The cell body of a neuron, also known as the soma, typically contains a single nucleus, not multiple nuclei.
• Neurons are specialized cells responsible for transmitting information throughout the nervous system.
• Neurons have unique structures, including a long axon and multiple short, branching dendrites.
• The axon is responsible for carrying impulses away from the cell body to other neurons or effector cells.
• Dendrites receive signals from other neurons and convey this information to the cell body.

 Additional Information

• Neurons
• Neurons are the basic working units of the brain and are designed to transmit information to other nerve cells, muscle, or gland cells.
• The structure of a neuron allows it to rapidly transmit signals over long distances.
• Axon
• The axon is a singular, long projection that conducts electrical impulses away from the neuron's cell body.
• The length of the axon can vary, with some reaching up to a meter in length.
• Dendrites
• Dendrites are tree-like structures that receive messages from other nerve cells and transmit these messages to the cell body.
• They play a critical role in integrating synaptic inputs and determining the extent to which action potentials are produced by the neuron.

The Correct answer is A Sharath Kamal.

Key Points

• A Sharath Kamal is a prominent Indian table tennis player.
• He has been a significant contributor to Indian table tennis for many years.
• Sharath Kamal has won multiple Commonwealth Games medals, including gold medals in both singles and team events.
• He has also represented India in several Asian Games and Olympic Games.
• Sharath Kamal's dedication and success have made him a leading figure in Indian sports.

 Additional Information

• Vinesh Phogat
• Vinesh Phogat is an Indian wrestler who has won medals in various international wrestling competitions.
• She has secured gold medals in the Commonwealth Games and the Asian Games.
• Vinesh is part of the famous Phogat family, known for producing several successful Indian wrestlers.
• MC Mary Kom
• MC Mary Kom is a celebrated Indian boxer who has won multiple world championships.
• She has also secured a bronze medal at the 2012 London Olympics.
• Mary Kom is widely regarded as one of the greatest female boxers in history.
• Neeraj Chopra
• Neeraj Chopra is an Indian javelin thrower who won the gold medal at the 2020 Tokyo Olympics.
• He is the first Indian athlete to win an Olympic gold in track and field events.
• Neeraj Chopra has set several national records in javelin throw.

Shortcut Trick

Ratio of Volumes (V₁ : V₂) = 729 : 1331

Ratio of Sides (s₁ : s₂) = √³729 : √³1331 = 9 : 11

Ratio of Surface Areas (A₁ : A₂) = (s₁)² : (s₂)² = 9² : 11² = 81 : 121

∴ The correct answer is 81 : 121.

Alternate Method

Given: Ratio of volumes of two cubes = 729 : 1331

Formula Used: Volume of cube = (side)³; Total Surface Area = 6 × (side)²

⇒ Let sides of cubes be a₁ and a₂.

⇒ (a₁)³ / (a₂)³ = 729 / 1331

⇒ a₁ / a₂ = √³(729 / 1331) = 9 / 11

⇒ Ratio of Total Surface Areas = (6 × a₁²) / (6 × a₂²)

⇒ Ratio = (a₁ / a₂)² = (9 / 11)²

⇒ Ratio = 81 / 121

∴ The correct answer is 81 : 121.

Additional Information

Cube Properties

For a cube of side 'a', the Diagonal is a√3 and the Lateral Surface Area is 4a².

Scaling Rules

If the ratio of sides of two similar figures is x : y, then the ratio of their areas is x² : y² and the ratio of their volumes is x³ : y³.

Given:

Decimal number = 0.333...

Formula used:

To convert a recurring decimal to a fraction, the numerator is the repeating digit and the denominator consists of as many 9s as the number of repeating digits.

Calculations:

Let x = 0.333...

⇒ x = 0.$\overline{3}$

Since one digit (3) is repeating:

⇒ x = 3/9

⇒ x = 1/3

∴ The correct answer is option (1).

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

1) B sits third from the right end.

2) Only one person sits to the left of D.

3) E is an immediate neighbour of C and D.

4) F sits to the right of B but left of G.

After positioning F and G only one position is left which will be occupied by the only person left i.e. A.

Thus, according to the final arrangement, five people sit between A and G.

Hence, "Option 3" is the correct answer.

The correct answer is Lactic acid — 4 carbon molecules.

Key Points

• Lactic acid is an organic acid with the chemical formula C3H6O3.
• It contains 3 carbon atoms, not 4.
• Lactic acid is produced in muscles during intense activity where oxygen levels are low, leading to anaerobic respiration.
• It is also found in sour milk products, such as yogurt and kefir, due to the fermentation process by lactic acid bacteria.
• Lactic acid plays a significant role in various biochemical processes and is used in the food, pharmaceutical, and cosmetic industries.

 Additional Information

• Pyruvate — 3 carbon molecules
• Pyruvate is a key intermediate in several metabolic pathways throughout the cell.
• It is a 3-carbon molecule with the chemical formula C3H4O3.
• Pyruvate is formed during glycolysis and can be further processed to either lactic acid or enter the mitochondria for aerobic respiration.
• Ethanol — 2 carbon molecules
• Ethanol, commonly known as alcohol, has the chemical formula C2H5OH.
• It contains 2 carbon atoms.
• Ethanol is widely used as a recreational substance and is also used in the medical and industrial fields as a disinfectant and solvent.
• Glucose — 6 carbon molecules
• Glucose is a simple sugar with the chemical formula C6H12O6.
• It contains 6 carbon atoms.
• Glucose is a primary source of energy for living organisms and is a crucial component of cellular respiration.
• It is found naturally in fruits and other parts of plants and is the main product of photosynthesis.