RRB Technician Grade III Official Paper (Held On: 30 Dec, 2024 Shift 3) (Previous Year Paper)

Shortcut Trick

Net Interest Percentage = Rate × Time = 11% × 2 = 22%.

Simple Interest = 22% of ₹2,00,000.

⇒ 22 × 2000 = ₹44,000.

∴ The correct answer is ₹44,000.

Alternate Method

Given:

Principal (P) = ₹2,00,000

Rate of Interest (R) = 11% per annum

Time Period (T) = 2 years

Formula Used:

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

Calculations:

⇒ SI = (2,00,000 × 11 × 2) ÷ 100

⇒ SI = 2,000 × 11 × 2

⇒ SI = 2,000 × 22

⇒ SI = ₹44,000

∴ The correct answer is ₹44,000.

Additional Information

Total Amount Formula

The total amount (A) to be paid back is the sum of Principal and Simple Interest: A = P + SI.

Nature of Simple Interest

Simple Interest remains constant for every year if the Principal and Rate are unchanged, unlike Compound Interest which increases annually.

SI vs CI Difference for 2 Years

The difference between Compound Interest and Simple Interest for 2 years is given by the formula: Difference = P × (R/100)².

The Correct answer is Water is the solvent.

Key Points

• A homogeneous mixture is a mixture in which the composition is uniform throughout, and the components cannot be easily separated.
• In the case of a mixture of sugar in water, water acts as the solvent, which means it is the substance that dissolves the solute (sugar).
• The component present in the larger amount in a solution is typically considered the solvent, and water is present in a larger quantity than sugar in this mixture.
• Sugar, being the substance that is dissolved, is the solute.
• Water is known as the universal solvent because it can dissolve a vast number of substances, including sugar, salt, and many other compounds.
• The resulting solution of sugar and water is transparent, and the sugar molecules are evenly distributed throughout the water.
• Homogeneous mixtures like this one do not separate into distinct phases upon standing.
• This principle is utilized in various industries, such as the food and beverage industry, where sugar solutions are commonly used.

 Additional Information

• Both water and sugar are solvents
• This is incorrect because in a solution, only one component acts as a solvent, and the other as a solute.
• Water is the solvent in this case, and sugar is the solute. They cannot both be solvents simultaneously.
• Sugar is the solvent
• This is incorrect because sugar is the solute, which means it is the substance being dissolved in the solvent (water).
• Sugar does not have the properties of a universal solvent like water.
• Water is the solute
• This is incorrect because water is the solvent, not the solute, as it dissolves the sugar to form a homogeneous mixture.
• Solutes are present in smaller amounts, whereas solvents are present in larger amounts. In this case, water is present in a larger quantity.

Shortcut Trick

If the sum of three terms is zero, i.e., x + y + z = 0, then x³ + y³ + z³ = 3xyz.

Let x = (a − b), y = (b − c), and z = (c − a).

Check sum: (a − b) + (b − c) + (c − a) = 0.

∴ (a − b)³ + (b − c)³ + (c − a)³ = 3(a − b)(b − c)(c − a).

∴ The correct answer is 3(a - b) (b - c) (c - a).

Alternate Method

Given: Expression (a − b)³ + (b − c)³ + (c − a)³

Formula Used: Algebraic Identity: a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

Calculations:

⇒ Let X = (a − b), Y = (b − c), and Z = (c − a).

⇒ First, calculate the sum X + Y + Z:

⇒ (a − b) + (b − c) + (c − a) = a − a + b − b + c − c = 0.

⇒ According to the identity, if X + Y + Z = 0, then the term (X + Y + Z)(X² + Y² + Z² − XY − YZ − ZX) becomes 0.

⇒ X³ + Y³ + Z³ − 3XYZ = 0

⇒ X³ + Y³ + Z³ = 3XYZ

⇒ Substituting the values back: (a − b)³ + (b − c)³ + (c − a)³ = 3(a − b)(b − c)(c − a).

∴ The correct answer is 3(a - b) (b - c) (c - a).

Additional Information

Standard Algebraic Identity

The expansion of a³ + b³ + c³ − 3abc is always (a + b + c)(a² + b² + c² − ab − bc − ca).

Conditional Identity

If a² + b² + c² − ab − bc − ca = 0, then it implies a = b = c, which also leads to a³ + b³ + c³ = 3abc.

Square Transformation

The term (a² + b² + c² − ab − bc − ca) can be rewritten as ½[(a − b)² + (b − c)² + (c − a)²].

Shortcut Trick

Age ratio (Now : Marriage) = 1(1/5) : 1 = 6 : 5

Difference in ratio units = 6 − 5 = 1 unit

Given time difference = 10 years ⇒ 1 unit = 10 years

Lavanya's present age = 6 units = 60 years

Son's age = 1/10 × 60 = 6 years

∴ The correct answer is 6 years.

Alternate Method

Given: Marriage happened 10 years ago. Present age = 6/5 of marriage age. Son's age = 1/10 of present age.

Let marriage age be x years.

⇒ Present age = x + 10

⇒ x + 10 = (6/5) × x

⇒ 5(x + 10) = 6x

⇒ 5x + 50 = 6x

⇒ x = 50 years (Age at marriage)

⇒ Lavanya's present age = 50 + 10 = 60 years

⇒ Son's present age = 60 ÷ 10 = 6 years

∴ The correct answer is 6 years.

Additional Information

Ratio Method for Age

If the ratio of ages is given at two different times, the difference between the ratio parts must correspond to the actual years passed.

Age Difference Property

The numerical difference between the ages of two persons remains constant throughout their lives, regardless of the years passed.

The Correct answer is Na₂SO₄ (aq) + BaCl₂ (aq) → BaSO₄ (s) + 2NaCl (aq).

Key Points

• This reaction is an example of a double displacement reaction, where two compounds exchange their ions to form new compounds.
• The reaction between sodium sulfate (Na₂SO₄) and barium chloride (BaCl₂) produces two new compounds: barium sulfate (BaSO₄) and sodium chloride (NaCl).
• Barium sulfate (BaSO₄) forms as an insoluble precipitate, which is the hallmark of a double displacement reaction.
• This reaction can be represented as: AB + CD → AD + CB, where ions are exchanged between the reactants.
• In this case: AB = Na₂SO₄, CD = BaCl₂, AD = BaSO₄, and CB = NaCl.
• The formation of a solid precipitate (BaSO₄) confirms the occurrence of a chemical reaction.
• Double displacement reactions are commonly observed in aqueous solutions and are often used for qualitative analysis in chemistry.

 Additional Information

• Fe(s) + CuSO₄ (aq) → FeSO₄ (aq) + Cu(s)
• This is an example of a single displacement reaction, not a double displacement reaction.
• In this reaction, iron (Fe) displaces copper (Cu) from copper sulfate (CuSO₄) to form iron sulfate (FeSO₄) and copper metal (Cu).
• Pb(s) + CuCl₂ (aq) → PbCl₂ (aq) + Cu(s)
• This is also an example of a single displacement reaction.
• Here, lead (Pb) replaces copper (Cu) in copper chloride (CuCl₂) to produce lead chloride (PbCl₂) and copper metal (Cu).
• Zn(s) + CuSO₄ (aq) → ZnSO₄ (aq) + Cu(s)
• This is yet another example of a single displacement reaction.
• In this reaction, zinc (Zn) replaces copper (Cu) in copper sulfate (CuSO₄) to form zinc sulfate (ZnSO₄) and copper metal (Cu).

Logic follows here is that the first letter and the second letter are increased by 7.

Option 1) VCJ

Option 2) EMS

Does not follow the same logic.

Option 3) AHO

Option 4) HOV

Hence the correct answer is "Option 2"

The correct answer is Hyderabad.

Key Points

• TakeMe2Space (TM2Space) is an innovative space technology firm based in Hyderabad, India.
• Hyderabad has emerged as a hub for space technology, startups, and research and development in India.
• TakeMe2Space specializes in developing advanced space technology and contributes to India's space missions.
• Hyderabad is home to several prominent organizations like ISRO's National Remote Sensing Centre (NRSC) and the Research Centre Imarat (RCI), which supports the growth of space-related industries.
• The city provides a robust ecosystem for space startups with access to skilled workforce, infrastructure, and government initiatives.
• TakeMe2Space also collaborates with other space agencies and organizations to promote satellite development, space exploration, and innovation.
• Hyderabad's strategic focus on technology and innovation makes it a preferred location for companies like TakeMe2Space.

 Additional Information

• New Delhi
• New Delhi is the capital of India and a major hub for policy-making and administration.
• It is home to ISRO's headquarters and other national-level institutions that contribute to India's space programs.
• While New Delhi is critical for policy and governance, it is not the base of TakeMe2Space.
• Chennai
• Chennai is a key city in southern India and houses the ISRO Propulsion Complex (IPRC), which plays a vital role in space propulsion systems.
• It has a growing technology sector but is not the location for TakeMe2Space.
• Kolkata
• Kolkata, located in eastern India, is known for its rich history and culture but is not a prominent hub for space technology startups.
• While it has institutions contributing to science and technology, it is not the base for TakeMe2Space.

Given:

One-third part of a number exceeds its one-fifth part by 6.

Formula used:

Let the number be x.

One-third part = x/3

One-fifth part = x/5

Calculations:

According to the question:

⇒ x/3 − x/5 = 6

⇒ (5x − 3x) / 15 = 6

⇒ 2x / 15 = 6

⇒ 2x = 6 × 15

⇒ 2x = 90

⇒ x = 45

Now, find one-third part of the number:

⇒ One-third part = x / 3

⇒ One-third part = 45 / 3

⇒ One-third part = 15

∴ The correct answer is option (4).

The Correct answer is Short and branched.

Key Points

• Dendrites are specialized structures of neurons that are primarily responsible for receiving electrochemical signals from other neurons or sensory inputs.
• They are typically short and exhibit a branched structure, which increases the surface area for receiving signals.
• The branching nature of dendrites allows them to form connections with multiple neurons, facilitating the integration of information in the nervous system.
• Dendrites contain specialized structures called dendritic spines, which are tiny protrusions where synapses are formed with other neurons.
• They play a crucial role in processes such as learning and memory by strengthening or weakening synaptic connections based on activity.
• In contrast to axons, which transmit signals away from the neuron, dendrites are primarily involved in receiving and processing incoming signals.

 Additional Information

• Short and unbranched
• Neuronal structures like axon terminals may sometimes appear short and unbranched, but this description does not apply to dendrites.
• Unbranched structures are typically not suited for integrating multiple inputs, which is the primary function of dendrites.
• Long and branched
• Axons, not dendrites, are more likely to be long and may occasionally exhibit branching, especially near their terminals.
• Axons are involved in transmitting signals over long distances, which differs from the function of dendrites.
• Long and unbranched
• This description is characteristic of certain axons, which are responsible for conducting signals away from the neuron over long distances.
• Dendrites, in contrast, are short and branched to facilitate the reception of multiple signals.

The Correct answer is Boundary Lab.

Key Points

• Boundary Lab is the title of the book authored by Nandan Kamath, which won the prestigious Sports Book of the Year award in 2024.
• The book explores various aspects of sports law, governance, and ethics in the context of modern sports.
• It is a significant contribution to the understanding of legal and regulatory frameworks in sports, making it highly relevant for those involved in sports administration, athletes, and legal professionals.
• Nandan Kamath is an eminent sports lawyer and has been actively involved in promoting better governance and legal practices in sports.
• The award highlights the importance of literature that bridges the gap between sports and legal perspectives, encouraging informed decision-making and ethical conduct in the sports industry.
• The book has received acclaim for its in-depth analysis and comprehensive approach, making it a valuable resource for academicians, policymakers, and sports enthusiasts.

 Additional Information

• Spirit of Sports
• The title suggests a focus on the emotional, cultural, and inspirational aspects of sports, but it is not authored by Nandan Kamath or related to the Sports Book of the Year award in 2024.
• It might represent a thematic exploration of how sports inspire unity, teamwork, and resilience globally.
• The Winning Mindset
• This book likely deals with the psychological aspects of sports, such as focus, determination, and mental preparation, but it is not authored by Nandan Kamath.
• The concept of a "Winning Mindset" is widely discussed in sports psychology and performance enhancement.
• Playing It My Way
• This book is the autobiography of Sachin Tendulkar, the legendary Indian cricketer.
• It recounts his life and career, but it is unrelated to the Sports Book of the Year award in 2024.
• Published in 2014, it became a bestseller and provides insights into the life of one of India's greatest sports icons.

Given series:

(Left) 2 1 6 8 3 9 5 2 7 6 3 2 9 9 7 3 9 6 4 6 3 2 6 2 2 0 3 4 7 2 (Right)

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

Required condition:  odd - Even - odd 

(Left) 2 1 6 8 3 9 5 2 7 6 3 2 9 9 7 3 9 6 4 6 3 2 6 2 2 0 3 4 7 2 (Right)

Thus, there are four such even digits (2, 6, 2, 4)  which are immediately preceded by an odd digit and also immediately followed by an odd digit

Hence, "Option 4" is the correct answer.

The correct answer is Retired Sportsperson Empowerment Training (RESET) Programme.

Key Points

• The Retired Sportsperson Empowerment Training (RESET) Programme was launched by the government on National Sports Day 2024.
• This initiative is aimed at providing career opportunities, skill development, and financial stability to retired sportspersons.
• RESET focuses on helping athletes transition from their sports careers to alternative professional fields.
• The programme includes training in areas such as coaching, sports management, fitness training, and entrepreneurship.
• It also provides access to certifications, workshops, and mentorship programs to enhance employability.
• The RESET Programme is part of the government’s efforts to recognize the contribution of athletes and ensure their well-being beyond their playing years.
• This initiative aligns with the larger vision of promoting sports culture and holistic support for athletes in India.

 Additional Information

• National Sports Scholarship Scheme
• This option refers to a hypothetical initiative involving scholarships for athletes.
• While scholarships are an important part of supporting young athletes, there is no specific announcement of a National Sports Scholarship Scheme in 2024.
• Fit India Movement
• The Fit India Movement was launched by the Government of India in August 2019 to encourage citizens to adopt a healthy and active lifestyle.
• It focuses on fitness awareness and promoting physical activities but is unrelated to the RESET Programme.
• National Fitness Challenge
• This option suggests an initiative promoting fitness challenges, but no such specific programme was launched on National Sports Day 2024.
• The term aligns with general fitness campaigns but does not pertain to the RESET Programme.

The Correct answer is Bronze.

Key Points

• Bronze is an alloy primarily made of copper (Cu) and tin (Sn). The typical ratio used is approximately 88% copper and 12% tin.
• This alloy has been in use since the Bronze Age (around 3300 BCE to 1200 BCE), marking a significant advancement in human technology.
• Bronze is known for its strength, durability, and resistance to corrosion, making it suitable for creating tools, weapons, and sculptures.
• The addition of tin to copper reduces its melting point and increases its hardness, which are crucial properties for crafting robust materials.
• It is widely used in the manufacturing of statues, coins, musical instruments, and bearings.
• Some historical artifacts, such as the famous Bronze sculptures from ancient civilizations, showcase the significance of this alloy in early societies.

 Additional Information

• Solder
• Solder is another alloy, commonly composed of tin (Sn) and lead (Pb). It is primarily used in electronics and plumbing for joining metal components.
• Solder has a low melting point, making it ideal for creating secure connections without damaging sensitive materials.
• Gold
• Gold is a pure metal rather than an alloy. It is known for its malleability, ductility, and resistance to tarnish.
• Gold is widely used in jewelry, electronics, and financial reserves.
• Brass
• Brass is another alloy, made of copper (Cu) and zinc (Zn).
• It is known for its golden appearance and is commonly used in decorative items, musical instruments, and plumbing fittings.

Logic followed here is

Logic : ROM is common in both the language and 3 5 8 is common in both the code.

So, code for A is 2.

Hence the correct answer is option (2).

The Correct answer is Indian Film Festival of Melbourne (IFFM) 2024.

Key Points

• The Indian Film Festival of Melbourne (IFFM) is one of the most prestigious film festivals held annually in Melbourne, Australia, celebrating Indian cinema and its global impact.
• In 2024, renowned actor Ram Charan was honored with the title of Ambassador for Indian Art and Culture.
• This recognition highlights his contribution to promoting Indian cinema and culture on a global platform.
• The festival serves as a bridge between Indian and Australian cultural ties, fostering understanding through the medium of films.
• Ram Charan, known for his remarkable performances in films like RRR, has gained international acclaim, making him a fitting choice for this honor.
• The IFFM often features screenings, panel discussions, and cultural events, providing a platform for Indian artists to showcase their talents to a global audience.
• This award not only celebrates Ram Charan's achievements but also emphasizes the growing influence of Indian cinema in the global entertainment industry.

 Additional Information

• Cannes Film Festival
• The Cannes Film Festival is an annual film festival held in Cannes, France, showcasing new films from around the world.
• It is one of the most prestigious and highly publicized events in the global film industry.
• The festival features categories such as the Palme d'Or, awarded for the best film.
• Although Indian films are often featured, this event did not host the specific recognition for Ram Charan in 2024.
• International Film Festival of India (IFFI)
• The International Film Festival of India (IFFI) is held annually in Goa, India, showcasing the best of Indian and world cinema.
• It is one of the most significant film festivals in Asia, organized by the Government of India.
• While IFFI highlights Indian cinema extensively, Ram Charan received his award at the IFFM 2024, not at this event.
• Toronto International Film Festival (TIFF)
• The Toronto International Film Festival (TIFF) is one of the largest publicly attended film festivals in the world, held annually in Toronto, Canada.
• It is known for its diverse lineup of films and often serves as a launchpad for award-season contenders.
• Although Indian films have been showcased here, Ram Charan's recognition as an ambassador happened at the IFFM 2024.

Given:

Statement: In City X, the number of car accidents has spiked recently due to poor road conditions and lack of adequate signage.

Course of Action I: The city should launch an awareness campaign to educate drivers on safe driving practices.

Course of Action II: Immediate Road repair and installation of proper signage should be carried out.

Explanation:

The statement clearly mentions that the car accidents are due to poor road conditions and lack of signage.

Course of Action I suggests an awareness campaign.

While it might be helpful, it doesn't directly address the root causes of the accidents.

Course of Action II suggests immediate road repair and installation of proper signage.

This directly addresses the problems mentioned in the statement.

Therefore, Course of Action II is the logical and effective solution.

∴ Only Course of Action II follows.

Shortcut Trick Let Total Capacity of the tank be LCM(40, 60) = 120 units. Efficiency of A = 120 ÷ 40 = 3 units/min | Efficiency of B = 120 ÷ 60 = 2 units/min. Pipe A remains open for the full 30 minutes, filling 3 × 30 = 90 units. Remaining work (120 − 90 = 30 units) is done by Pipe B. Time for Pipe B = 30 ÷ 2 = 15 minutes. ∴ The correct answer is 15 min. Alternate Method Given: Pipe A fills in 40 min, Pipe B fills in 60 min, Total time = 30 min. Formula Used: Total Work = Time × Efficiency.

Person Days Total Work Efficiency

Pipe A 40 120 3

Pipe B 60 2

⇒ Total capacity = 120 units. ⇒ Work done by Pipe A in 30 minutes = 30 × 3 = 90 units. ⇒ Remaining work to be done by Pipe B = 120 − 90 = 30 units. ⇒ Time for which Pipe B was open = 30 ÷ 2 = 15 minutes. ∴ The correct answer is 15 min. Additional Information Pipes and Cisterns Concept If a pipe can fill a tank in x hours and another can empty it in y hours, the net part filled in 1 hour = (1/x − 1/y) where y > x. Work and Wages Wages are always distributed in the ratio of the Efficiency of the workers or the ratio of Work Done by them. Alternate Day Work In alternate work problems, calculate the work done in one cycle (sum of efficiencies) and then find the number of cycles required.

The correct answer is I = I1 + I2 + I3.

Key Points

• In a parallel circuit, the total current (I) flowing through the circuit is the sum of the currents flowing through each branch. Hence, I = I1 + I2 + I3.
• The voltage across each resistor in a parallel combination is the same, but the current varies depending on the resistance of each branch.
• Ohm's Law (V = IR) is used to calculate the current through each resistor when the resistance and voltage are known.
• In parallel circuits, the total current is distributed among the branches, and this is one of the key characteristics of such circuits.
• The principle of current conservation is applied here, which states that the total current entering a junction equals the total current leaving the junction.
• Parallel circuits are commonly used in electrical systems where components need to operate independently, such as in home wiring systems.

 Additional Information

• R_eq = R3 + (R2R1)/(R2 + R1)
• This formula is incorrect for calculating the equivalent resistance in a parallel circuit. The correct formula involves the reciprocal of resistances.
• For two resistors in parallel, the equivalent resistance is given by 1/Req = 1/R1 + 1/R2 + ....
• 1/I = 1/I1 + 1/I2 + 1/I3
• This equation is incorrect as it misrepresents the relationship between the total current and individual branch currents in a parallel circuit.
• The reciprocal rule applies to resistances in parallel, not currents.
• R_eq = R1 + (R2R3)/(R2 + R3)
• This formula is also incorrect as it doesn't represent the correct calculation of equivalent resistance in a parallel circuit.
• In a parallel circuit, the equivalent resistance is always smaller than the smallest individual resistance.

The Correct answer is 4.

Key Points

• To balance the given chemical equation 3Fe + xH₂O → Fe₃O₄ + 4H₂, we need to ensure that the number of atoms of each element on both sides of the equation is equal.
• On the product side, Fe₃O₄ contains 3 iron (Fe) atoms and 4 oxygen (O) atoms. Additionally, there are 4 molecules of hydrogen gas (H₂), which account for 8 hydrogen (H) atoms on the product side.
• On the reactant side, there are 3 iron (Fe) atoms provided by the 3Fe. However, to balance the 4 oxygen atoms and 8 hydrogen atoms on the product side, we require 4 water molecules (H₂O), as each water molecule contains 1 oxygen atom and 2 hydrogen atoms.
• Thus, the balanced equation becomes: 3Fe + 4H₂O → Fe₃O₄ + 4H₂.
• Here, the value of x = 4, which corresponds to the number of water molecules required to balance the equation.
• This balanced equation ensures the conservation of mass, as the total number of atoms of each element is the same on both sides.

 Additional Information

• Importance of Balancing Chemical Equations:
• Balancing chemical equations ensures the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.
• It helps in determining the stoichiometric proportions of reactants and products in a reaction.
• Balanced equations are essential for calculating the quantities of reactants and products in chemical processes.
• Fe₃O₄ (Magnetite):
• Magnetite is a naturally occurring iron oxide mineral with a chemical formula of Fe₃O₄.
• It is widely used as a source of iron in the steel manufacturing industry.
• Magnetite is also known for its magnetic properties, making it useful in various industrial applications.

The Correct answer is Amoeba.

Key Points

• Amoeba is a unicellular organism that belongs to the phylum Protozoa.
• It is known for its ability to change its shape continuously by extending and retracting its cytoplasm to form structures called pseudopodia.
• Pseudopodia are used for movement and capturing food, a process called phagocytosis.
• This organism is commonly found in freshwater environments such as ponds, lakes, and streams.
• The cell structure of Amoeba is simple, consisting of a nucleus, cytoplasm, and a flexible cell membrane.
• Amoebas reproduce through a process called binary fission, where the cell divides into two identical daughter cells.
• Its ability to change shape is due to the absence of a rigid cell wall, making its membrane highly adaptable.
• It is an excellent example of how unicellular organisms can carry out all life processes independently.

 Additional Information

• Yeast
• Yeast is a unicellular fungus commonly used in the food and beverage industry for fermentation.
• It reproduces mainly through a process called budding, rather than changing shape like Amoeba.
• Yeasts are important for making bread, beer, and wine.
• Bacteria
• Bacteria are unicellular organisms belonging to the domain Prokaryota.
• They have a rigid cell wall and generally maintain a fixed shape such as spherical (cocci), rod-shaped (bacilli), or spiral (spirilla).
• Bacteria are found in diverse environments and play roles in decomposition, nitrogen fixation, and causing diseases.
• Paramoecium
• Paramoecium is a unicellular organism belonging to the phylum Ciliophora.
• It has a fixed slipper-like shape and moves using hair-like structures called cilia.
• Paramoecium is commonly found in freshwater habitats and feeds on microorganisms like bacteria and algae.

The Correct answer is First woman mahout.

Key Points

• Parbati Baruah is renowned for being the first woman mahout in India, a remarkable achievement in a field traditionally dominated by men.
• A mahout is a person who works with, rides, and tends to elephants. In India, mahouts are integral to wildlife conservation, forest management, and religious ceremonies involving elephants.
• She hails from the state of Assam, a region known for its rich wildlife and cultural connection with elephants.
• Parbati Baruah has spent years mastering the art of handling elephants and has deep knowledge of their behavior, health, and habitat.
• Her work has significantly contributed to elephant conservation, particularly in the northeast region of India, which faces challenges due to habitat destruction and human-elephant conflicts.
• She is celebrated for breaking gender stereotypes in a male-dominated profession and inspiring women to pursue unconventional careers.
• The recognition of her work by the Padma Shri award in 2024 emphasizes the importance of her contribution to wildlife conservation and cultural heritage.

 Additional Information

• Tiger conservation
• Tiger conservation refers to efforts aimed at protecting and increasing the population of tigers, which are endangered due to poaching, habitat loss, and human-wildlife conflict.
• India is home to the largest population of wild tigers in the world, with conservation programs like Project Tiger launched in 1973.
• Protected areas such as Ranthambore, Sundarbans, and Bandhavgarh are key tiger habitats.
• Rhino conservation
• Rhino conservation focuses on protecting the Indian rhinoceros, commonly found in Assam's Kaziranga National Park.
• Efforts include anti-poaching measures, habitat preservation, and breeding programs.
• India has made significant progress in rhino conservation, with the population of the one-horned rhino increasing due to these initiatives.
• Lion conservation
• Asiatic lions are primarily found in the Gir Forest National Park in Gujarat, India.
• Conservation efforts include habitat restoration, anti-poaching measures, and raising public awareness to prevent human-lion conflict.
• The population of Asiatic lions has shown a steady increase due to these efforts.

Logic followed here is,

Hence the correct answer is "Option 2"

The Correct answer is large central vacuole.

Key Points

• Most mature plant cells have a large central vacuole, which is a membrane-bound organelle filled with cell sap.
• The large central vacuole is essential for maintaining the turgidity of the cell, ensuring that the cell remains rigid and supports the plant structure.
• It plays a vital role in storage, holding water, nutrients, ions, and even waste materials.
• The vacuole helps in maintaining the osmotic balance within the plant cell, which is crucial for its survival.
• It contains enzymes that aid in the breakdown of complex molecules and cellular debris, contributing to the cell's detoxification processes.
• The vacuole also contributes to the plant's defense mechanisms by storing harmful or bitter-tasting compounds to deter herbivores.
• The vacuole is surrounded by a specialized membrane known as the tonoplast, which helps regulate the movement of substances in and out of the vacuole.
• In addition, the vacuole can store pigments like anthocyanins, which provide coloration to flowers and fruits, aiding in pollination and seed dispersal.

 Additional Information

• Chromoplasts
• Chromoplasts are specialized organelles responsible for storing pigments that give fruits, flowers, and other parts of plants their vivid colors.
• They play a significant role in attracting pollinators and aiding in seed dispersal.
• Unlike the large central vacuole, chromoplasts do not maintain turgidity or store waste substances.
• Leucoplasts
• Leucoplasts are non-pigmented organelles primarily involved in the storage of starch, oils, and proteins.
• They are commonly found in non-photosynthetic tissues of plants, such as roots and seeds.
• Leucoplasts do not contribute to maintaining turgidity or storing waste substances like the central vacuole.
• Small ribosome
• Small ribosomes are cellular organelles responsible for protein synthesis.
• They are present in both plant and animal cells and are not involved in maintaining turgidity or storing substances.
• Ribosomes are often found floating freely in the cytoplasm or attached to the endoplasmic reticulum.

The Correct answer is Shri Manoj Sinha.

Key Points

• Shri Manoj Sinha assumed office as the Lieutenant Governor of Jammu and Kashmir following the scrapping of Article 370.
• He became the second Chief Minister-level leader to hold office after the abrogation of Article 370, marking a significant transition in the region's political administration.
• Manoj Sinha is a seasoned politician and former Member of Parliament from the Ghazipur constituency in Uttar Pradesh.
• His appointment symbolized a shift in governance as Jammu and Kashmir transitioned from a state to a Union Territory.
• Manoj Sinha is known for his administrative capabilities and focus on development-oriented policies.
• He succeeded Girish Chandra Murmu, the first Lieutenant Governor of Jammu and Kashmir after it became a Union Territory.
• Under his leadership, the region witnessed steps toward grassroots democracy and efforts to boost economic growth and infrastructure.

 Additional Information

• Shri Omar Abdullah
• Omar Abdullah is the former Chief Minister of Jammu and Kashmir and a prominent leader of the National Conference Party.
• He served as Chief Minister from 2009 to 2015 but did not assume office after the abrogation of Article 370.
• He is known for his opposition to the scrapping of Article 370, which granted special status to Jammu and Kashmir.
• Shri Farooq Abdullah
• Farooq Abdullah, father of Omar Abdullah, is also a former Chief Minister of Jammu and Kashmir.
• He is a veteran politician and a member of the National Conference Party.
• Farooq Abdullah has served multiple terms as Chief Minister but was not in office following the removal of Article 370.
• Mehbooba Mufti
• Mehbooba Mufti is the former Chief Minister of Jammu and Kashmir and leader of the PDP (People’s Democratic Party).
• She was the first woman to hold the Chief Minister position in the region.
• Her tenure ended before the scrapping of Article 370, and she was a strong critic of the decision to revoke Jammu and Kashmir’s special status.

The Correct answer is Combination Reaction.

Key Points

• A combination reaction is a type of chemical reaction where two or more substances combine to form a single product.
• In the given reaction, CaO (calcium oxide), also known as quicklime, reacts with H₂O (water) to form Ca(OH)₂ (calcium hydroxide), which is commonly known as slaked lime.
• The reaction is highly exothermic as it releases a significant amount of heat.
• The general form of a combination reaction is: A + B → AB.
• In this reaction, CaO (A) combines with H₂O (B) to form Ca(OH)₂ (AB).
• Combination reactions are also called synthesis reactions as they result in the formation of a new compound.
• The product, calcium hydroxide, is an important compound used in various applications such as whitewashing, water treatment, and soil stabilization.

 Additional Information

• Wurtz Fitting Reaction
• The Wurtz Fitting reaction is a chemical reaction where an aromatic halide reacts with an alkyl halide in the presence of metallic sodium in dry ether to form an aromatic hydrocarbon.
• This reaction is used for the synthesis of alkylbenzenes.
• It is different from the given reaction and does not involve the combination of substances to form a single product.
• Decomposition Reaction
• A decomposition reaction is a chemical reaction where a single compound breaks down into two or more simpler substances.
• It is the reverse of a combination reaction and often requires the input of energy such as heat, light, or electricity.
• An example of a decomposition reaction is: 2H₂O → 2H₂ + O₂.
• Wurtz Reaction
• The Wurtz reaction involves the reaction of an alkyl halide with metallic sodium in dry ether to form a higher alkane.
• This reaction is used in organic chemistry for the synthesis of alkanes.
• It is not related to the combination reaction of calcium oxide and water.

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

Only two people sit to the left of B.

Only three people sit between B and R.

P sits second to the right of B.

Only two people sit between P and A.

G sits at some place to the right of E but at some place to the left of Q.

So, three people sit to the right of G.

Hence the correct answer is "Option 3"

Logic followed here is

Logic : EAM is common in both the language and 9 8 3 is common in both the code.

So, code for B is 4.

Hence the correct answer is option (3).

Shortcut Trick

Let the third number be 100.

First number = 100 − 30 = 70

Second number = 100 − 37 = 63

Required percentage = (63 ÷ 70) × 100 = 9 × 10 = 90%

∴ The correct answer is 90%.

Alternate Method

Given:

Let the Third Number (N₃) = 100

Formula Used:

Percentage = (Value ÷ Base Value) × 100

Calculations:

⇒ First Number (N₁) = 100 − (30% of 100) = 70

⇒ Second Number (N₂) = 100 − (37% of 100) = 63

⇒ Required % = (N₂ ÷ N₁) × 100

⇒ Required % = (63 ÷ 70) × 100

⇒ Required % = 0.9 × 100 = 90%

∴ The correct answer is 90%.

Additional Information

Percentage Base Change

When comparing two numbers relative to a third, always assume the third number as 100 to simplify the calculations of the other two values.

Percentage Decrease Formula

New Value = Original Value × (100 − Decrease%) ÷ 100. This is the direct multiplier method for percentage reduction.

Relative Percentage

To find what percent X is of Y, the formula is (X/Y) × 100. Here, Y is the denominator/base of the comparison.

Given series:

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

According to the question, such even digits which are immediately preceded by perfect square and also immediately followed by an odd digit:

Required condition:  perfect square - Even - odd 

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

Thus, there are 2 such even digits which are immediately preceded by a perfect square and also immediately followed by an odd digit

Hence, "Option 4" is the correct answer.

Given:

Value 1 = -3/13

Value 2 = 4

Formula used:

Result = Value 1 − Value 2

Calculations:

Result = -3/13 − 4

⇒ Result = (-3 − (4 × 13)) / 13

⇒ Result = (-3 − 52) / 13

⇒ Result = -55/13

∴ The correct answer is option (2).

Shortcut Trick To compare surds like 21/2, 31/3, and 41/4, find the LCM of the denominators of the powers (2, 3, 4) = 12. Raise each number to the power of 12: (21/2)12 = 26 = 64; (31/3)12 = 34 = 81; (41/4)12 = 43 = 64. Since 81 is the largest value, the corresponding original number is the greatest. ∴ The correct answer is 31/3. Alternate Method

Given: Numbers are √2, 31/3, and 41/4. Formula: To compare a1/n and b1/m, raise both to the power of LCM(n, m). ⇒ √2 = 21/2 ⇒ 31/3 = 31/3 ⇒ 41/4 = (22)1/4 = 22/4 = 21/2 ⇒ Comparing 21/2 and 31/3: ⇒ LCM of 2 and 3 is 6. ⇒ (21/2)6 = 23 = 8 ⇒ (31/3)6 = 32 = 9 ⇒ Since 9 > 8, 31/3 is the greatest number. ∴ The correct answer is 31/3. Additional Information Comparison of Indices If the powers are in fraction form, convert them to a common denominator using LCM to compare the bases directly. Laws of Surds (am)n = am×n and (a × b)n = an × bn are essential for simplifying radical expressions. Equality of Terms Note that √2 and 41/4 are mathematically equal as (22)1/4 = 22/4 = 21/2.

The Correct answer is Mithun Chakraborty.

Key Points

• Mithun Chakraborty, a veteran Indian film actor, has been chosen as the recipient of the Dadasaheb Phalke Lifetime Achievement Award for the year 2022. This was announced on 30th September 2024 by Union Minister for Information and Broadcasting, Ashwini Vaishnaw.
• The Dadasaheb Phalke Award is the highest honor in Indian cinema, instituted by the Government of India in 1969 to commemorate Dadasaheb Phalke, the father of Indian cinema.
• Mithun Chakraborty is renowned for his contributions to Indian cinema, particularly for his iconic performances in Bollywood and regional films. He has acted in over 350 films in various languages, including Hindi, Bengali, and Tamil.
• He gained prominence with his National Film Award-winning performance in the film "Mrigayaa" in 1976, directed by Mrinal Sen.
• He is also celebrated for his role in the dance revolution in Bollywood through his famous film "Disco Dancer" (1982), which made him a cultural icon.
• Beyond acting, he has served as a politician and has been involved in various social initiatives.
• This award recognizes his lifetime achievement in the field of Indian cinema and his significant influence on the film industry.

 Additional Information

• Asha Bhosle
• Asha Bhosle is a legendary Indian playback singer known for her versatility and a career spanning over seven decades.
• She holds the Guinness World Record for the most studio recordings, having recorded over 11,000 songs.
• She has received numerous awards, including the Dadasaheb Phalke Award in 2000.
• Shah Rukh Khan
• Shah Rukh Khan, popularly known as the "King of Bollywood", is one of the most successful Indian actors globally.
• He has appeared in over 80 Bollywood films and is known for his charismatic performances.
• He has not received the Dadasaheb Phalke Lifetime Achievement Award but has earned numerous other accolades, including 14 Filmfare Awards.
• Rajinikanth
• Rajinikanth is one of the most iconic actors in Indian cinema, particularly in the Tamil film industry.
• He was honored with the Dadasaheb Phalke Award in 2020.
• His unique style, larger-than-life performances, and philanthropic work have made him a cultural phenomenon.

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

Only three people sit between D and F when counted from the left of D.

D sits to the immediate right of E.

Only three people sit between E and L.

B sits to the immediate right of C.

And K sits at the remaining place.

There are two people sit between K and C when counted from the left of C. 

Hence the correct answer is "Option 3"

The Correct answer is Helium.

Key Points

• Helium is a noble gas and belongs to Group 18 of the periodic table.
• Noble gases are characterized by their full valence electron shell, which makes them extremely stable and chemically inert.
• Due to this inertness, Helium does not typically form molecules and exists as monoatomic particles.
• It is the second lightest element in the periodic table after hydrogen.
• Helium is used in various applications such as cryogenics, as a cooling agent in MRI machines, and in balloons and airships due to its lightweight nature.
• It is the second most abundant element in the universe, primarily produced through nuclear fusion in stars.
• Helium is non-toxic, non-flammable, and does not react with other elements under normal conditions.

 Additional Information

• Hydrogen
• Hydrogen is the lightest element in the periodic table and exists primarily as a diatomic molecule (H₂) under standard conditions.
• It is highly reactive and can easily form compounds with other elements.
• Hydrogen is widely used in industries for applications such as fuel cells, ammonia production, and rocket fuel.
• This element is the most abundant in the universe and plays a critical role in stellar nuclear fusion processes.
• Oxygen
• Oxygen exists as a diatomic molecule (O₂) and is essential for life on Earth due to its role in respiration.
• It is highly reactive and forms oxides with almost all elements.
• Oxygen is the third most abundant element in the universe and is used in applications such as medical oxygen therapy and industrial processes.
• Nitrogen
• Nitrogen is a diatomic molecule (N₂) and makes up about 78% of the Earth's atmosphere.
• It is relatively inert due to the strong triple bond between its atoms, which makes it useful in preserving food and creating an inert environment for industrial processes.
• Nitrogen is essential for life and is a key component of amino acids and DNA.
• It is used in the production of fertilizers, explosives, and cryogenics.

The Correct answer is Enzymes.

Key Points

• Enzymes are biological molecules that act as catalysts in living organisms.
• They speed up biochemical reactions by lowering the activation energy required for the reaction to occur.
• Enzymes are typically made up of proteins, though some RNA molecules can also function as enzymes (e.g., ribozymes).
• Each enzyme is highly specific to the substrate it acts upon due to the unique structure of its active site.
• They play a crucial role in various processes such as digestion, respiration, and DNA replication.
• Examples of enzymes include amylase (breaks down starch), lipase (breaks down fats), and protease (breaks down proteins).
• Enzymes are sensitive to environmental factors such as temperature and pH, which can affect their activity.

 Additional Information

• Hydrochloric acid
• Hydrochloric acid (HCl) is a component of gastric juice in the stomach.
• It helps in the digestion process by creating an acidic environment, which activates the enzyme pepsin for protein breakdown.
• HCl also kills bacteria and other pathogens in the food.
• Mucus
• Mucus is a slippery secretion produced by mucous membranes in the body.
• It plays a role in protecting tissues, such as the lining of the stomach, from damage caused by digestive acids and enzymes.
• Mucus also helps in lubricating food for easier swallowing and movement through the digestive system.
• Digestive juices
• Digestive juices are fluids secreted by the digestive organs, including the stomach, pancreas, and intestines.
• They contain enzymes, such as amylase, lipase, and protease, which help in breaking down carbohydrates, fats, and proteins, respectively.
• While digestive juices aid digestion, they are not catalysts themselves; instead, they carry enzymes which perform catalytic functions.

Shortcut Trick

Profit ratio is equal to the investment ratio when the time period is constant.

Ratio of Profit (A : B) = 30,000 : 24,000 = 5 : 4.

Total ratio parts = 5 + 4 = 9 units.

9 units = Rs. 13,500 ⇒ 1 unit = 13,500 ÷ 9 = Rs. 1,500.

Share of A = 5 × 1,500 = Rs. 7,500.

∴ The correct answer is Rs. 7,500.

Alternate Method

Given: Investment of A = Rs. 30,000, Investment of B = Rs. 24,000, Total Profit = Rs. 13,500, Time = 1 year. Formulas: Profit Share = Investment × Time | Profit Ratio = (I_A × T_A) : (I_B × T_B)

⇒ Profit Ratio (A : B) = (30,000 × 1) : (24,000 × 1) ⇒ Ratio = 30 : 24 = 5 : 4 ⇒ Let A's share be 5x and B's share be 4x ⇒ 5x + 4x = 13,500 ⇒ 9x = 13,500 ⇒ x = 1,500 ⇒ A's Share = 5 × 1,500 = 7,500

∴ The correct answer is Rs. 7,500.

Additional Information

Partnership Concepts

In a simple partnership, the capital is invested for the same period. The profit is distributed in the ratio of their investments.

Compound Partnership

When capitals are invested for different time periods, the profit is distributed in the ratio of (Capital × Time). Profit Ratio = C₁T₁ : C₂T₂.

The Correct answer is Spirogyra.

Key Points

• Spirogyra is a genus of filamentous green algae that reproduces by a method called fragmentation.
• Fragmentation is an asexual mode of reproduction where the filament breaks into smaller fragments, and each fragment grows into a new individual.
• Spirogyra is commonly found in freshwater habitats like ponds, ditches, and slow-moving streams.
• The name Spirogyra comes from the characteristic spiral arrangement of its chloroplasts within the cells.
• Fragmentation occurs naturally in Spirogyra due to mechanical damage or decay of older cells in the filament.
• This method of reproduction allows rapid multiplication, especially in favorable environmental conditions, ensuring the survival of the species.
• Spirogyra contributes to the oxygenation of water bodies and serves as a food source for various aquatic organisms.

 Additional Information

• Amoeba
• Amoeba reproduces asexually through a process called binary fission, where the parent cell divides into two identical daughter cells.
• Amoeba is a single-celled organism found in freshwater, soil, and decaying organic matter.
• It lacks a fixed shape and moves using pseudopodia.
• Hydra
• Hydra reproduces both sexually and asexually, but its common mode of asexual reproduction is budding.
• In budding, a small outgrowth develops on the parent organism, which eventually detaches and becomes a new individual.
• Hydra is a freshwater organism belonging to the phylum Cnidaria.
• Plasmodium
• Plasmodium is a parasitic protozoan that causes malaria in humans.
• It reproduces asexually through a process called schizogony and sexually in the gut of the Anopheles mosquito.
• Plasmodium primarily resides in red blood cells and the liver of the host.

The Correct answer is chemotropism.

Key Points

• Chemotropism refers to the growth or movement of an organism, typically plants, in response to a chemical stimulus.
• The growth of pollen tubes towards the ovules is guided by the secretion of chemical attractants from the ovules, making it a classic example of chemotropism.
• This phenomenon ensures that the male gametes carried by the pollen tube reach the ovules for fertilization, facilitating sexual reproduction in plants.
• Chemotropism is crucial for the process of pollination and fertilization in flowering plants, contributing to the production of seeds and fruits.
• It is a directional response, meaning the growth of the pollen tube is oriented specifically towards the source of the chemical stimulus.
• Examples of chemicals involved in this process include calcium ions and other signaling molecules released by the ovules.

 Additional Information

• Hydrotropism
• Hydrotropism is the growth or movement of plants in response to water stimuli.
• An example is the growth of plant roots towards moist areas in the soil to absorb water.
• It plays a vital role in the plant's ability to locate water sources, especially in arid conditions.
• Phototropism
• Phototropism refers to the growth of plants in response to light stimuli.
• Plants exhibit positive phototropism when their shoots grow towards the light source and negative phototropism when their roots grow away from light.
• Phototropism is primarily controlled by a plant hormone called auxin.
• Geotropism
• Geotropism, also known as gravitropism, refers to a plant's growth in response to gravity.
• Roots exhibit positive geotropism as they grow downward into the soil, while shoots exhibit negative geotropism by growing upward against the force of gravity.
• This response ensures that plants maintain their orientation for optimal nutrient and light absorption.

Given

81, 108.6, 136.2, 163.8, ? 

Logic follows here is,

Logic 

So, next number is 191.4.

Hence the correct answer is "Option 1"

The Correct answer is Stretching a rubber band.

Key Points

• Potential energy is the energy stored within an object due to its position, condition, or configuration.
• When a rubber band is stretched, it undergoes a change in its configuration, storing elastic potential energy.
• The energy stored depends on the extent of stretching, governed by the material's elastic properties.
• Elastic potential energy is a type of mechanical energy that can be released when the object returns to its original shape.
• This concept is widely applied in various devices, such as springs, slingshots, and bows, which depend on the storage and release of elastic potential energy.
• Stretching a rubber band demonstrates the principle of energy conservation, where potential energy transforms into other forms, such as kinetic energy, when released.

 Additional Information

• Pushing a vehicle on a plane road
• Pushing a vehicle involves kinetic energy, which is the energy of motion, rather than potential energy.
• The energy exerted here is used to overcome frictional forces and move the vehicle forward.
• This scenario does not involve storing energy in the system.
• Moving a pencil across a table
• Similar to pushing a vehicle, moving a pencil involves kinetic energy instead of potential energy.
• The energy is applied to overcome surface friction and move the object.
• No energy is stored in this process.
• Lighting a matchstick
• Lighting a matchstick is a process that involves chemical energy, not potential energy.
• The chemical energy stored in the matchstick is released as heat and light energy when ignited.
• This scenario does not represent the storage of energy but rather its conversion.

The Correct answer is CH₂.

Key Points

• The successive members of a homologous series differ by a common unit, which is CH₂.
• A homologous series is a group of organic compounds that have a similar structure and functional group but differ by a fixed unit in their molecular formula.
• In the series provided (CH₄, C₂H₆, C₃H₈), the molecular formulas show a successive difference of CH₂ units between each compound.
• The molecular formula of methane (CH₄) and ethane (C₂H₆) differs by one CH₂ unit, and similarly, ethane (C₂H₆) and propane (C₃H₈) also differ by one CH₂ unit.
• Each member of a homologous series has similar chemical properties but shows a gradual change in physical properties like boiling point, melting point, and density due to the addition of the CH₂ group.
• The concept of homologous series is crucial in organic chemistry as it simplifies the study of organic compounds by grouping them into families.

 Additional Information

• CH₄
• CH₄, also known as methane, is the simplest alkane and the first member of the alkane homologous series.
• Methane is a major component of natural gas and is widely used as a fuel source.
• It is a colorless, odorless gas at room temperature and is a potent greenhouse gas.
• CH
• CH is not a stable molecule in the context of hydrocarbons and does not represent a homologous series unit.
• It is a radical and may exist in some transient chemical reactions.
• CH₃
• CH₃ is a methyl group, which is a part of many organic compounds but does not represent the common difference in a homologous series.
• It is often seen as a substituent or functional group in organic chemistry.

The Correct answer is in front of, behind.

Key Points

• The centre of curvature of a spherical mirror is the center of the sphere from which the mirror is made.
• For a concave mirror, the reflecting surface curves inward, and the centre of curvature lies in front of the mirror. This is because the center of the sphere is located on the same side as the reflecting surface.
• For a convex mirror, the reflecting surface curves outward, and the centre of curvature lies behind the mirror. The center of the sphere is located on the opposite side of the reflecting surface.
• The pole, radius of curvature, and principal axis are other important terms related to spherical mirrors. These terms help define the geometry and behavior of these mirrors.
• Understanding the position of the centre of curvature is essential for ray diagrams and calculating focal lengths in optics.

 Additional Information

• Behind, in front of
• This option incorrectly states the positions of the centre of curvature for concave and convex mirrors.
• In a concave mirror, the centre of curvature is always in front, not behind.
• In front of, in front
• This option incorrectly suggests that the centre of curvature for both concave and convex mirrors lies in front.
• However, in a convex mirror, the centre of curvature is behind because the reflecting surface curves outward.
• Behind, behind
• This option incorrectly states that the centre of curvature for both types of mirrors is behind.
• In reality, the concave mirror's centre of curvature is in front, while the convex mirror's is behind.

The logic follow here is:

UQ-VR-WY 

And

RN-SO-TV 

Only Option 2) follow same logic.

OK-PL-QS 

  

Hence, the correct answer is "Option 2".

The Correct answer is Urethra.

Key Points

• The urethra in males serves as a common passage for both urine and sperm.
• It is a tube-like structure that connects the urinary bladder to the external part of the body for the excretion of urine.
• During ejaculation, sperm from the testes passes through the urethra and exits the body.
• The urethra is part of both the urinary system and the reproductive system in males.
• This dual function is facilitated by a special muscular valve called the internal urethral sphincter, which prevents urine from mixing with sperm during ejaculation.
• Located at the tip of the penis, the urethra opens to the outside of the body, allowing for the discharge of fluids.
• It plays a crucial role in maintaining proper functioning of the male reproductive and urinary systems.

 Additional Information

• Vas deferens
• The vas deferens is a tube that transports sperm from the testes to the urethra.
• It is part of the male reproductive system but does not serve as a passage for urine.
• The vas deferens plays a role in storing and carrying sperm during ejaculation.
• Scrotum
• The scrotum is a pouch-like structure that houses the testes.
• It maintains the optimal temperature for sperm production but does not function as a passage for urine or sperm.
• Its primary role is in the reproductive system, ensuring proper functioning of the testes.
• Urinary bladder
• The urinary bladder is a muscular organ that stores urine until it is excreted through the urethra.
• It is part of the urinary system and does not play any role in the passage of sperm.
• The bladder ensures controlled release of urine from the body through the urethra.

Shortcut Trick

Interest for 1 year = 520 ÷ 8 = ₹65.

Rate % = (Interest per year ÷ Principal) × 100.

Rate % = (65 ÷ 1300) × 100 = 5%.

∴ The correct answer is 5%.

Alternate Method

Given:

Principal (P) = ₹1,300

Simple Interest (SI) = ₹520

Time (T) = 8 years

Formula Used:

SI = (P × R × T) ÷ 100

Calculations:

⇒ 520 = (1300 × R × 8) ÷ 100

⇒ 520 = 13 × R × 8

⇒ 520 = 104 × R

⇒ R = 520 ÷ 104

⇒ R = 5%

∴ The correct answer is 5%.

Additional Information

Simple Interest Components

Simple interest is calculated only on the principal amount. Amount (A) = Principal (P) + Interest (SI).

Rate of Interest

The rate of interest is the percentage of the principal charged as interest for a specific period (usually per annum).

Rule of SI

Interest remains constant for every year in Simple Interest if the Principal and Rate are unchanged.

Statements:

Some pulses are flours.

All biscuits are curds.

All biscuits are flours.

Possible Venn diagram is,

Conclusions:

(I) All flours are curds.→ Not follow (some flour are curds is possible, but we can't say that all flours are curds by the given statement.)

(II) Some biscuits are pulses. → Not follow (As there is no direct link between biscuits and pulses.)

Hence the correct answer is "Option 1"

Additional Information

The Correct answer is Mitochondria.

Key Points

• Mitochondria are known as the powerhouses of the cell because they are the site of ATP production, which is the energy currency of the cell.
• ATP (Adenosine Triphosphate) is synthesized through cellular respiration, primarily in the mitochondria, using energy derived from the breakdown of glucose or other nutrients.
• The process of ATP production occurs through oxidative phosphorylation in the inner mitochondrial membrane, where the electron transport chain is located.
• Mitochondria are double-membrane organelles, with the inner membrane folded into structures called cristae, which increase surface area for energy production.
• The mitochondria are responsible for driving endothermic reactions within the cell by providing the necessary energy through ATP hydrolysis.
• These organelles are found in most eukaryotic cells and play a crucial role in energy metabolism, as well as other functions such as regulation of the cell cycle and apoptosis.

 Additional Information

• Ribosome
• Ribosomes are the sites of protein synthesis in the cell.
• They are composed of ribosomal RNA (rRNA) and proteins and are found either floating freely in the cytoplasm or attached to the endoplasmic reticulum (forming rough ER).
• Ribosomes are not directly involved in energy production but play a critical role in translating genetic information into functional proteins.
• Lysosome
• Lysosomes are membrane-bound organelles containing digestive enzymes that break down waste materials and cellular debris.
• They are primarily involved in the degradation and recycling of cellular components and are not directly related to ATP synthesis.
• Lysosomes are known as the "suicidal bags" of the cell because they can initiate autophagy or programmed cell death under certain conditions.
• Chloroplast
• Chloroplasts are found in plant cells and are the sites of photosynthesis, where light energy is converted into chemical energy stored in glucose.
• While chloroplasts are involved in energy production, they do not produce ATP for cellular processes but instead synthesize glucose, which can be metabolized by mitochondria to generate ATP.
• Chloroplasts contain the pigment chlorophyll, which captures sunlight, and are unique to plant and algal cells.

Logic:

First number + Third number = Second number.

Given:

For (12, 38, 26):

12 + 26 = 38.

For (50, 75, 25):

50 + 25 = 75.

Option 1: (21, 40, 15)

21 + 15 = 36, which is not 40.

Option 2: (14, 42, 28)

14 + 28 = 42.

Option 3: (8, 32, 7)

8 + 7 = 15, which is not 32.

Option 4: (9, 28, 16)

9 + 16 = 25, which is not 28.

∴ The set (14, 42, 28) follows the same logic.

Hence the correct answer is "Option 2"

The correct answer is A solution is basic with a high hydroxide ion concentration.

Key Points

• A solution with a pH value of 10 is classified as basic or alkaline.
• The pH scale ranges from 0 to 14, where a pH less than 7 indicates an acidic solution, 7 indicates a neutral solution, and greater than 7 indicates a basic solution.
• A basic solution has a high hydroxide ion concentration (OH⁻) and a lower concentration of hydrogen ions (H⁺).
• In a solution with a pH of 10, the concentration of hydroxide ions (OH⁻) is much higher than that of hydrogen ions (H⁺).
• The relationship between pH and hydroxide ion concentration is governed by the equation: pH + pOH = 14, where pOH represents the hydroxide ion concentration.
• At a pH of 10, the corresponding pOH is 4, indicating a high concentration of hydroxide ions.
• Basic solutions are commonly associated with substances like soaps, detergents, and baking soda, which have a pH greater than 7.

 Additional Information

• A solution is acidic with a high hydroxide ion concentration
• This statement is incorrect because an acidic solution has a high concentration of hydrogen ions (H⁺), not hydroxide ions.
• Acidic solutions have a pH less than 7 and are typically associated with substances like lemon juice, vinegar, and hydrochloric acid.
• A solution is acidic with a high hydrogen ion concentration
• This statement is incorrect because the given solution has a pH of 10, which is in the basic range, not acidic.
• An acidic solution would have a pH below 7, indicating a higher concentration of H⁺ ions.
• A solution is basic with a high hydrogen ion concentration
• This statement is incorrect because a basic solution has a high concentration of hydroxide ions (OH⁻), not hydrogen ions.
• A high concentration of hydrogen ions is characteristic of an acidic solution.

The Correct answer is Zn(s) + CuSO4(aq) → ZnSO4(aq) + Cu(s).

Key Points

• This is a type of displacement reaction, where one element replaces another element in a compound.
• In this reaction, zinc (Zn) is more reactive than copper (Cu), so zinc replaces copper from copper sulfate (CuSO4) to form zinc sulfate (ZnSO4) and copper.
• Displacement reactions generally occur when a more reactive metal displaces a less reactive metal from its compound.
• Zinc belongs to the higher position in the reactivity series compared to copper, making it capable of displacing copper.
• This reaction is an example of a redox reaction, where oxidation and reduction occur simultaneously. Zinc is oxidized, and copper is reduced.
• Such reactions are widely used in applications like metal extraction and refining processes.

 Additional Information

• C(s) + O2(g) → CO2(g)
• This reaction represents a combustion reaction, not a displacement reaction.
• Carbon reacts with oxygen to produce carbon dioxide, releasing energy in the form of heat and light.
• Combustion reactions are commonly used in applications like energy production and are crucial for fuel-based systems.
• CaO(s) + H2O(l) → Ca(OH)2(aq)
• This is a combination reaction, where two reactants combine to form a single product.
• Calcium oxide (CaO), also known as quicklime, reacts with water to form calcium hydroxide (Ca(OH)2), commonly known as slaked lime.
• Such reactions are widely used in industries, especially in the preparation of lime mortar and water treatment.
• 2AgCl(s) → 2Ag(s) + Cl2(g)
• This is a type of decomposition reaction, where a single compound splits into two or more simpler substances.
• Silver chloride (AgCl) decomposes into silver metal and chlorine gas when exposed to light, a phenomenon called photodecomposition.
• This reaction is used in photographic processes and demonstrates the sensitivity of certain compounds to light.

The Correct answer is It has a single chromosome.

Key Points

• Prokaryotic cells are simpler and lack a well-defined nucleus.
• The genetic material in prokaryotes is present in a region called the nucleoid, which is not surrounded by a nuclear membrane.
• These cells typically have a single, circular chromosome that contains the genetic information needed for cellular processes.
• Prokaryotic cells do not have membrane-bound organelles such as mitochondria, endoplasmic reticulum, or Golgi apparatus.
• Examples of prokaryotic cells include bacteria and archaea.
• The single chromosome in prokaryotes is often associated with plasmids, which are small, circular DNA molecules that can replicate independently.
• Prokaryotic cells reproduce asexually through processes like binary fission, which allows for rapid multiplication.
• The simplicity of prokaryotic cells makes them highly adaptable to various environments, including extreme conditions.

 Additional Information

• Nuclear region is well defined and surrounded by nuclear membrane
• Prokaryotic cells lack a well-defined nucleus. Instead, their genetic material is located in the nucleoid region, which is not enclosed by a membrane.
• In contrast, eukaryotic cells possess a nuclear membrane surrounding their genetic material.
• It has more than one chromosome
• Prokaryotic cells generally have a single circular chromosome. Multiple chromosomes are a characteristic of eukaryotic cells.
• Membrane-bound cell organelles are present
• Prokaryotic cells lack membrane-bound organelles such as mitochondria, chloroplasts, or the endoplasmic reticulum. These features are exclusive to eukaryotic cells.

The Correct answer is Ovary.

Key Points

• After fertilisation, the ovary begins to grow rapidly and undergoes transformations to eventually form the fruit.
• The ovary is a reproductive organ in flowering plants (angiosperms) that encloses the ovules.
• Once fertilisation occurs, the ovules develop into seeds, and the surrounding ovary tissues mature into the fruit.
• The petals, sepals, stamens, style, and stigma typically shrivel and fall off as they are no longer required for reproductive processes.
• The transformation of the ovary into fruit ensures the protection and dispersal of the seeds.
• This process is critical for the plant’s life cycle and plays a vital role in ensuring reproduction and survival.
• Examples of ovary-to-fruit transformation include the development of mangoes, apples, tomatoes, and oranges.

 Additional Information

• Ovule
• The ovule is the structure within the ovary that develops into a seed after fertilisation.
• It contains the female gametophyte and is the site of fertilisation by the male gamete.
• While the ovule itself becomes the seed, it does not grow into the fruit.
• Gynoecium
• The gynoecium refers to the collective term for the female reproductive structures in a flower, including the ovary, style, and stigma.
• While it plays a role in reproduction, only the ovary undergoes transformation to form the fruit.
• Pistil
• The pistil is the single or compound unit of the gynoecium. It includes the ovary, style, and stigma.
• While it aids in reproduction, the pistil as a whole does not grow into a fruit; only the ovary does.

Preparing the family tree using the following symbols:

 

Thus 'H + J × K ÷ M - L means

Here, we can see that H is Mother's mother of L.

Hence, Option (2) is correct.

Shortcut Trick

Net Discount % = x + y − (x × y)/100

Here, x = 25 and y = 8

Net Discount % = 25 + 8 − (25 × 8)/100

Net Discount % = 33 − 200/100 = 33 − 2 = 31%

∴ The correct answer is 31%.

Alternate Method

Given:

Trade Discount = 25%

Cash Discount = 8%

Formula used:

Selling Price (SP) = Marked Price (MP) × (100 − D₁)% × (100 − D₂)%

MP = 100 75 Net SP = 69

−25% (Trade)

−8% (Cash on 75)

Total Discount = 100 − 69 = 31%

Calculation:

Let the Marked Price be 100.

⇒ Price after trade discount = 100 − 25% of 100

⇒ Price after trade discount = 100 − 25 = 75

⇒ Price after cash discount = 75 − 8% of 75

⇒ Price after cash discount = 75 − (8/100) × 75

⇒ Price after cash discount = 75 − 6 = 69

⇒ Net Discount = Marked Price − Final Selling Price

⇒ Net Discount = 100 − 69 = 31

⇒ Net Discount % = (31/100) × 100 = 31%

∴ The correct answer is 31%.

Additional Information

Successive Discount for Three Terms

For three successive discounts a%, b%, and c%, the equivalent discount is [1 − (1 − a/100)(1 − b/100)(1 − c/100)] × 100.

Marked Price and Cost Price Relation

MP/CP = (100 + Profit%)/(100 − Discount%). This is useful when both profit and discount percentages are given.

Effective Discount on Buy X Get Y Free

Discount % = [Free Items / (Free Items + Paid Items)] × 100.

The Correct answer is 105.

Key Points

• The Global Hunger Index (GHI) is a tool designed to comprehensively measure and track hunger at the global, regional, and national levels.
• India was ranked 105th out of 125 countries in the 2024 Global Hunger Index (GHI).
• The GHI scores are based on four key indicators:
• Undernourishment: The share of the population with insufficient caloric intake.
• Child Wasting: The share of children under the age of five who have low weight for their height, reflecting acute undernutrition.
• Child Stunting: The share of children under the age of five who have low height for their age, reflecting chronic undernutrition.
• Child Mortality: The mortality rate of children under the age of five.
• The GHI is published annually by Concern Worldwide and Welthungerhilfe.
• India's rank highlights the persistent challenges of malnutrition and hunger in the country despite efforts to improve food security and nutrition.
• The index emphasizes the need for effective policy implementation, increased agricultural productivity, and better nutritional programs to combat hunger.
• India's ranking in the GHI is often criticized as it brings attention to inequalities in food distribution and the inadequacy of food security measures.

 Additional Information

• The Global Hunger Index (GHI) is calculated on a scale of 0 to 100, where 0 is the best score (no hunger) and 100 is the worst.
• The GHI is often used to track progress towards achieving Sustainable Development Goal 2 (Zero Hunger).
• India has previously ranked poorly in the GHI, which has sparked debates over the accuracy of the methodology used to measure hunger.
• India's significant population size means that even a small percentage of undernourished individuals translates into a large absolute number of people suffering from hunger.

Logic:

First number - Third number = Second number.

Given:

For (25, 5, 20):

25 - 20 = 5.

For (40, 8, 32):

40 - 32 = 8.

Check each option,

Option 1: (80, 14, 64)

80 - 64 = 16, which is not 14.

Option 2: (100, 16, 64)

100 - 64 = 36, which is not 16.

Option 3: (80, 16, 64)

80 - 64 = 16.

Option 4: (80, 16, 60)

80 - 60 = 20, which is not 16.

∴ The set (80, 16, 64) follows the same logic.

Hence the correct answer is "Option 3"

Shortcut Trick

For consecutive integers, the average is the middle term (7^th term).

Smallest term (1^st) = Average − ((n − 1) ÷ 2) = 36 − 6 = 30.

Largest term (13^th) = Average + ((n − 1) ÷ 2) = 36 + 6 = 42.

Required Sum = (2 × 30) + 42 = 60 + 42 = 102.

∴ The correct answer is 102.

Alternate Method

Given: Number of integers (n) = 13, Average = 36.

Formula: Average of n consecutive integers = (First + Last) ÷ 2 = Middle Term.

⇒ Middle term (7^th term) = 36.

⇒ Smallest term = 36 − (7 − 1) = 30.

⇒ Largest term = 36 + (13 − 7) = 42.

⇒ Required Value = (2 × Smallest) + Largest

⇒ Required Value = (2 × 30) + 42 = 60 + 42 = 102.

∴ The correct answer is 102.

Additional Information

Average of Arithmetic Progression

For any series in AP, Average = (First term + Last term) ÷ 2. For odd number of terms, it is exactly the middle term.

Consecutive Integers Property

In a set of n consecutive integers, the difference between the largest and smallest integer is always (n − 1).

Sum of N terms

Sum = Average × Number of terms. For 13 terms with average 36, Sum = 13 × 36 = 468.

Statements:

Some games are boards.

No board is a dice.

No remote is a game.

Possible Venn diagram is,

Conclusions:

(I) No game is a dice.→ Not follow (We can't say as there is no direct link between game and dice)

(II) Some remotes are boards. → Not follow (We can't say as there is no direct link between remotes and boards.)

Hence the correct answer is "Option 1"

Additional Information

The Correct answer is Grass.

Key Points

• Grass is a biotic component of the ecosystem.
• Biotic components refer to living organisms or once-living organisms in an ecosystem.
• Grass is a type of plant and plays a significant role as a producer in the food chain.
• It converts solar energy into chemical energy through the process of photosynthesis.
• Grass serves as a primary source of food for herbivores, and indirectly for higher trophic levels.
• Unlike abiotic components, grass interacts with other living organisms such as animals, fungi, and microorganisms in the ecosystem.

 Additional Information

• Rainfall
• Rainfall is an abiotic component as it is a non-living factor in the ecosystem.
• It plays a crucial role in the water cycle and supports plant and animal life by providing essential water.
• Rainfall impacts soil moisture, vegetation growth, and habitats of various species.
• Soil
• Soil is also an abiotic component that provides a medium for plant growth.
• It contains minerals and organic matter, which are essential for plant nutrition.
• Soil supports the ecosystem by storing water and nutrients and hosting various microorganisms.
• Wind
• Wind is an abiotic factor that influences weather patterns and the distribution of seeds and pollen.
• It affects temperature regulation and the evaporation of water in ecosystems.
• Wind also plays a role in shaping landforms through erosion and deposition.

Given, D, E. F. G, L, M and N are sitting around a circular table facing the centre.

F sits third to the left of L.

L is an immediate neighbour of both D and N.

N sits second to the left of E.

G is not an immediate neighbour of F.

And M sits at the remaining place.

There two people sit between M and N when counted from the right of M.

Hence the correct answer is "Option 1"

The correct answer is Proteins and sugars.

Key Points

• The matrix of cartilage is composed mainly of proteins and sugars, which give it its characteristic flexibility and resilience.
• Cartilage contains a protein called collagen, which provides structural support and tensile strength.
• It also contains proteoglycans, a combination of proteins and sugars, which help in retaining water and maintaining the elasticity of cartilage.
• The sugars present are often in the form of glycosaminoglycans (GAGs) like chondroitin sulfate and hyaluronic acid, which contribute to the cushioning and lubrication properties of cartilage.
• Cartilage is found in areas of the body such as the joints, ear, nose, and respiratory tract, where flexibility and smooth movement are required.
• Unlike bone, cartilage does not contain calcium and phosphorus, making it softer and more pliable.
• Cartilage plays a crucial role in the development of the skeletal system and the smooth functioning of joints.

 Additional Information

• Phosphorus and sugars
• Phosphorus is primarily found in bones, where it combines with calcium to form calcium phosphate, which provides strength and rigidity to the skeletal system.
• Cartilage does not rely on phosphorus for its structural composition; it focuses more on proteins and sugars for flexibility.
• Proteins and fats
• Fats are not a significant component of cartilage. They are primarily found in adipose tissues and serve as energy reserves.
• Cartilage requires proteins like collagen and sugars for its structure and function rather than fats.
• Calcium and sugars
• Calcium is a major component of bone tissue, not cartilage. It is essential for the hard and rigid structure of bones.
• Cartilage lacks calcium, which is why it remains flexible and soft compared to bone tissue.

Shortcut Trick

Apply trigonometric identities: sin² θ + cos² θ = 1 and sec² θ − tan² θ = 1.

Expression ⇒ 1 − 1 + tan θ cos θ + sin θ

Since tan θ cos θ = sin θ, the expression becomes 0 + sin θ + sin θ = 2 sin θ.

∴ The correct answer is 2 sin θ.

Alternate Method

Given: sin² θ + cos² θ − (sec² θ − tan² θ) + tan θ cos θ + sin θ

Formula Used: sin² θ + cos² θ = 1; sec² θ − tan² θ = 1; tan θ = sin θ / cos θ

⇒ Substitute identities: (1) − (1) + (sin θ / cos θ × cos θ) + sin θ

⇒ 1 − 1 + sin θ + sin θ

⇒ 0 + 2 sin θ

⇒ 2 sin θ

∴ The correct answer is 2 sin θ.

Additional Information

Pythagorean Identities

Fundamental identities include sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Reciprocal Relations

Key relations: tan θ = sin θ / cos θ, sec θ = 1 / cos θ, and cosec θ = 1 / sin θ.

The Correct answer is Joseph Proust.

Key Points

• Joseph Proust, a French chemist, proposed the 'Law of Constant Proportions', also known as the 'Proust's Law'.
• This law states that in a chemical substance, the elements are always present in definite proportions by mass, regardless of the source or method of preparation.
• The law emphasizes that the composition of a pure compound is fixed and does not vary, which is a fundamental concept in chemistry.
• For example, in water (H₂O), the mass ratio of hydrogen to oxygen is always 1:8, irrespective of whether the water is sourced from a river, a lake, or synthesized in a laboratory.
• Proust's work laid the foundation for the development of modern chemical stoichiometry and the study of chemical reactions.
• This law is a crucial part of Dalton's atomic theory, which further validated the idea of fixed atomic ratios in compounds.

 Additional Information

• Ernest Rutherford
• Ernest Rutherford, known as the father of nuclear physics, discovered the nucleus of the atom and proposed the Rutherford atomic model.
• He is famous for his gold foil experiment, which demonstrated that atoms have a small, dense, and positively charged nucleus.
• His work provided insights into the structure of the atom but was not related to the 'Law of Constant Proportions'.
• E. Goldstein
• E. Goldstein is credited with the discovery of canal rays (positively charged rays), leading to the identification of protons.
• His work focused on atomic structure and the discovery of subatomic particles, not on chemical laws like the 'Law of Constant Proportions'.
• J.J. Thomson
• J.J. Thomson discovered the electron and proposed the plum pudding model of the atom.
• His contributions include the study of cathode rays and the measurement of the charge-to-mass ratio of electrons.
• Thomson's work was foundational in atomic physics but unrelated to the 'Law of Constant Proportions'.

The Correct answer is same.

Key Points

• Resistivity is a material property that measures how strongly a material opposes the flow of electric current.
• The resistivity of a conductor is dependent only on the material's nature and is independent of its shape and size, such as its cross-sectional area or length.
• When the cross-sectional area of a conductor is doubled, the resistance is affected (resistance decreases), but the resistivity remains unchanged.
• This is because resistivity is defined as a constant for a specific material at a given temperature, regardless of changes in its dimensions.
• The formula for resistivity is ρ = R × (A / L), where ρ represents resistivity, R is resistance, A is the cross-sectional area, and L is the length of the conductor.
• From the formula, resistivity is independent of the conductor's dimensions; it is solely determined by the intrinsic properties of the material.
• Thus, doubling the cross-sectional area affects the resistance but does not alter the inherent resistivity of the conductor.

 Additional Information

• halved
• Halving the resistivity would imply a change in the fundamental properties of the material, which does not happen by altering the conductor's dimensions.
• Resistivity is constant for a specific material and is independent of changes in cross-sectional area.
• one fourth
• The term one fourth might apply to changes in resistance when the cross-sectional area is quadrupled, but it does not affect resistivity, as resistivity depends solely on the material.
• doubled
• Doubling resistivity would require a fundamental alteration of the material properties, which is not related to changes in physical dimensions like cross-sectional area.

Given:

Chart showing exports of companies X and Y.

Formula used:

Absolute difference = Export of X in Feb - Export of Y in April.

Calculations:

Export of company X in February = 35.

Export of company Y in April = 55.

Difference = 55 - 35 = 20

The difference between the export by company X in February and export by company Y in April is 20 crore.

The Correct answer is A mixture of iron nails in water.

Key Points

• A homogeneous mixture is a mixture where the composition is uniform throughout, and the components are not visibly distinguishable.
• A mixture of iron nails in water is not homogeneous because the iron nails do not dissolve in water. Instead, they remain separate and visible, forming a heterogeneous mixture.
• In a heterogeneous mixture, the components are physically distinct and can often be separated by physical methods such as filtration or decanting.
• Iron nails are made of metal and are insoluble in water, making the mixture uneven in composition.
• Examples of homogeneous mixtures include substances like salt water and sugar water, where the solute dissolves completely in the solvent.
• This distinction between homogeneous and heterogeneous mixtures is important in chemistry for understanding the properties of materials and how they interact.

 Additional Information

• A mixture of copper sulphate in water
• Copper sulphate dissolves completely in water, forming a homogeneous solution.
• It is commonly used in agriculture as a fungicide and in laboratories for experiments.
• Its blue color is due to the presence of hydrated copper ions.
• A mixture of salt in water
• Salt water is a homogeneous mixture where the salt (sodium chloride) dissolves fully in water, forming a uniform solution.
• It is widely used in cooking, cleaning, and medical applications.
• A mixture of sugar in water
• Sugar water is another example of a homogeneous mixture as sugar dissolves completely in water.
• It is often used in beverages, syrups, and medical oral rehydration solutions.

Shortcut Trick

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

Measure of each exterior angle = 360° ÷ n (where n is the number of sides).

For a regular octagon, n = 8.

⇒ Angle = 360° ÷ 8 = 45°.

∴ The correct answer is 45°.

Alternate Method

Given: Shape is a regular octagon.

Formula Used: Exterior Angle = 360° / n

Calculations:

⇒ Number of sides (n) in an octagon = 8

⇒ Sum of all exterior angles of a polygon = 360°

⇒ Measure of each exterior angle = 360° ÷ 8

⇒ Measure of each exterior angle = 45°

∴ The correct answer is 45°.

Additional Information

Interior Angle Formula

The measure of each interior angle of a regular polygon is given by [(n − 2) × 180°] / n.

Relationship between Angles

At any vertex, the Interior Angle + Exterior Angle = 180° (Linear Pair).

Sum of Interior Angles

The sum of all interior angles of a polygon with n sides is (n − 2) × 180°.

Given:

Total length of wire = 70 cm

Ratio of one piece to the other = 2/5

Formula used:

Ratio of two pieces = a : b

Length of shorter piece = (a / (a + b)) × Total Length

Calculations:

Let the length of the longer piece be x cm.

Length of the shorter piece = (2/5) × x

⇒ Ratio of pieces = (2/5)x : x

⇒ Ratio = 2 : 5

Sum of ratio parts = 2 + 5 = 7 units

⇒ 7 units = 70 cm

⇒ 1 unit = 10 cm

⇒ Shorter piece (2 units) = 2 × 10

⇒ Shorter piece = 20 cm

∴ The correct answer is option (3).

The Correct answer is Centripetal force.

Key Points

• The motion of the moon around the Earth is governed by the centripetal force.
• Centripetal force is a force that acts toward the center of a circular path, keeping an object in circular motion.
• In the case of the moon, this force is provided by the gravitational pull of the Earth.
• The gravitational force acts as the centripetal force, pulling the moon toward the Earth and preventing it from moving off in a straight line due to its inertia.
• Without this force, the moon would follow a straight-line path into space, as per Newton's first law of motion.
• The balance between the moon's tangential velocity and the centripetal force keeps it in a stable orbital motion around the Earth.
• This principle applies to all celestial bodies in orbit, including planets, satellites, and stars in their respective systems.

 Additional Information

• Centrifugal force
• Centrifugal force is a fictitious force that appears to act outward on a body in a rotating reference frame.
• It is not a real force but rather the result of inertia when viewed in a non-inertial, rotating frame.
• In contrast to the centripetal force, it does not play a role in the moon's motion, as the moon orbits due to the Earth's gravitational pull.
• Coriolis force
• The Coriolis force is an apparent force caused by the rotation of the Earth.
• It primarily affects the motion of objects over large distances, such as air currents and ocean currents, causing them to deflect to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
• It is not responsible for the orbital motion of celestial bodies.
• Coulomb force
• The Coulomb force refers to the electrostatic force between two charged particles.
• It has no role in the motion of the moon, as the moon and the Earth interact primarily through gravitational force, not electrostatic force.

The Correct answer is 14.

Key Points

• The number of neutrons in an element can be calculated using the formula: Neutrons = Mass Number - Atomic Number.
• Aluminium (Al) has an atomic number of 13 and a mass number of 27.
• Using the formula: Neutrons = 27 - 13 = 14.
• Hence, Aluminium has a total of 14 neutrons.
• The atomic number represents the number of protons in an element, which is equal to the number of electrons in a neutral atom.
• The mass number is the sum of the number of protons and neutrons in the nucleus.
• Aluminium is a widely used metal known for its lightweight, non-corrosive, and ductile properties.

 Additional Information

• 15
• The value 15 does not correspond to the number of neutrons in Aluminium.
• It is important to correctly subtract the atomic number from the mass number to avoid errors.
• 27
• 27 is the mass number of Aluminium, not the number of neutrons.
• The mass number includes the total number of protons and neutrons in the nucleus of an atom.
• 13
• 13 is the atomic number of Aluminium, representing the number of protons or electrons in a neutral atom.

The Correct answer is Yellow.

Key Points

• When light passes through a glass prism, it undergoes refraction, and its constituent colors bend at different angles due to their varying wavelengths.
• The phenomenon of different colors bending by different amounts is called dispersion of light.
• Yellow light, which lies in the middle of the visible spectrum, has a wavelength of approximately 570–590 nm.
• Because the bending of light is inversely proportional to its wavelength, longer wavelengths bend less than shorter wavelengths.
• Compared to violet, blue, and green light, yellow light is bent through a minimum angle as it has a relatively longer wavelength.
• This property of light is significant in optics, including in the design of prisms and lenses.

 Additional Information

• Green Light
• Green light has a shorter wavelength than yellow light, approximately 495–570 nm.
• Because of its shorter wavelength, it bends more than yellow light when passing through a prism.
• Green light is situated in the middle of the visible spectrum and contributes to the perception of white light.
• Blue Light
• Blue light has a wavelength range of 450–495 nm, shorter than both green and yellow light.
• Due to its shorter wavelength, it bends more than green and yellow light when refracted through a prism.
• Blue light is commonly associated with technologies such as LED screens and smartphones.
• Violet Light
• Violet light has the shortest wavelength in the visible spectrum, approximately 380–450 nm.
• As a result, violet light bends the most among all visible colors when it passes through a prism.
• It is located at the extreme end of the visible spectrum and is responsible for the highest level of dispersion in white light.

Given Equation: 

11 ÷ 12 + 4 - 5 × 6 = ?

BODMAS Rule:

After interchanging  ‘+' and ‘÷' and ‘×' and ‘-’, we get

11 + 12 ÷ 4 × 5 - 6 

⇒ 11 + 3 × 5 - 6 

⇒ 11 + 15 - 6 = 20

Hence, the correct option is "Option 3".

Shortcut Trick

List Price = 150, Final SP = 105. Total multiplier = 105 ÷ 150 = 0.7.

Second discount = 12.5% ⇒ Multiplier = (100 − 12.5) ÷ 100 = 0.875.

First discount multiplier = Total multiplier ÷ Second multiplier = 0.7 ÷ 0.875 = 0.8.

First discount % = (1 − 0.8) × 100 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given → List Price (MP) = Rs. 150, Final Selling Price (SP) = Rs. 105, Second Discount (d₂) = 12.5%. Formulas: SP = MP × (100 − d₁)/100 × (100 − d₂)/100

⇒ Let the First Discount be x%.

⇒ Price after first discount = 150 × (100 − x)/100.

⇒ Final Price = [150 × (100 − x)/100] × (100 − 12.5)/100 = 105.

⇒ 150 × [(100 − x)/100] × 87.5/100 = 105.

⇒ (100 − x)/100 = (105 × 100) ÷ (150 × 87.5) = 10500 ÷ 13125 = 0.8.

⇒ 100 − x = 80 ⇒ x = 20%.

∴ The correct answer is 20%.

Additional Information

Successive Discounts

When two discounts a% and b% are given successively, the Equivalent Single Discount is calculated as: (a + b − ab/100)%.

Marked Price and Selling Price

The Selling Price is the final amount paid by the customer after all discounts are subtracted from the Marked Price (List Price).

Given Equation: 21 D 3 B 4 C 5 A 22 = ?

BODMAS Rule:

Decoding the given information:

 

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 21 ÷ 3 - 4 × 5 + 22

⇒ 7 - 20 + 22 = 9

Hence, the correct option is "Option 2".

Given series:

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

According to the question, such odd digits which are immediately preceded by perfect square and also immediately followed by an even digit:

Required condition:  perfect square - odd - Even

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

Thus, there is no such odd digits which are immediately preceded by perfect square and also immediately followed by an even digit.

Hence, "Option 4" is the correct answer.

The Correct answer is Ovule.

Key Points

• After fertilisation, the ovule develops a tough outer coat known as the seed coat.
• The ovule is gradually converted into a seed, which contains the embryo formed by the repeated division of the zygote.
• The embryo is the future plant enclosed within the seed, surrounded by protective layers, aiding in its development under suitable conditions.
• The ovule contains the female gametophyte, which is fertilised by the male gametes during reproduction.
• Post fertilisation, the ovule undergoes changes such as the formation of the seed coat, storage of nutrients, and maturation into a functional seed.
• This process is crucial for the reproductive success of flowering plants, ensuring the dispersal and germination of the next generation.

 Additional Information

• Pistil
• The pistil is the female reproductive organ of a flower, consisting of the stigma, style, and ovary.
• Although it plays a role in reproduction, it is not directly converted into a seed.
• The pistil facilitates the transfer of pollen to the ovary but does not form the embryo.
• Ovary
• The ovary is the part of the pistil that contains one or more ovules.
• Post fertilisation, the ovary develops into a fruit, enclosing the seeds.
• While important in reproduction, the ovary itself does not become the seed.
• Gynoecium
• The gynoecium refers collectively to the female reproductive structures in a flower, including pistils.
• It is the overall organ system, not a specific part that develops into a seed.
• Its primary function is to house and support fertilisation processes.

The Correct answer is P = VI.

Key Points

• The formula P = VI is the fundamental expression for calculating
• in a circuit.
• Power (P) in an electrical circuit represents the rate at which electrical energy is transferred or converted into another form of energy, such as heat or light.
• The formula indicates that power is the product of voltage (V) and current (I), where:
• Voltage (V) is the potential difference across two points in the circuit, measured in volts.
• Current (I) is the flow of electric charge through a conductor, measured in amperes.
• This formula is derived from the basic definition of power: Power = Work / Time. In the context of electricity, work is the product of charge and potential difference, and dividing it by time leads to the formula P = VI.
• It is a widely used formula in analyzing electrical circuits, determining the efficiency of devices, and calculating energy consumption.
• This relationship is valid for both direct current (DC) and alternating current (AC) circuits, though in AC circuits, factors such as phase difference and power factor may need to be considered.
• For example, if the voltage across a circuit is 10 volts and the current is 2 amperes, the power is calculated as:
• P = VI = 10 × 2 = 20 watts

 Additional Information

• P = V/I
• This formula is incorrect because dividing voltage by current gives resistance (R), not power.
• The relationship is derived from Ohm's Law, which states that V = IR, where R is resistance.
• P = V²I
• This formula is incorrect and does not follow the principles of power calculation. It appears to be a misrepresentation of the power equation.
• P = V²/I
• This formula is also incorrect. It is not consistent with the physical laws governing electrical circuits.

Logic follows here is that the first letter is decreased by 5 and the second letter is increased by 3.

Option 1) SN-QU

Does not follow the same logic.

Option 2) UP-SV

Option 3) QL-OR

Option 4) OJ-MP

Hence the correct answer is "Option 1"

Logic followed here is,

Given,

SDFG is related to YJKM

For, QBZE is related to WHEK

Similarly for ITOW is related to RYOM.

Hence the correct answer is "Option 1"

The Correct answer is Increasing the displacement.

Key Points

• The work done by a force on an object is calculated using the formula: Work = Force × Displacement × cos(θ), where θ is the angle between the force and displacement vectors.
• Increasing the displacement directly increases the work done if the force and displacement are in the same direction (θ = 0 degrees).
• The work done depends on the magnitude of the displacement, as a larger displacement under the same force results in higher work.
• If the displacement increases while the force remains constant, the object moves farther, contributing to more work being done.
• In physics, work is a measure of the energy transfer that occurs when an object is moved over a distance by an external force.
• Thus, increasing the displacement is a practical way to enhance the work done, provided the force remains constant and is applied in the same direction.
• This concept is widely applied in real-life scenarios, such as in machinery, where increasing the range of motion can yield higher energy output.

 Additional Information

• Reducing the mass
• Reducing the mass does not directly affect the work done, as work depends on force and displacement, not the mass of the object.
• However, a lighter object requires less force to move, which can indirectly influence how much work is done under varying conditions.
• Reducing the displacement
• Reducing the displacement decreases the work done, as work is proportional to the magnitude of displacement.
• This option is incorrect because it contradicts the principle of maximizing work by increasing displacement.
• Reducing the force
• Reducing the force also decreases the work done, as work is directly proportional to the applied force.
• This option is incorrect because lowering the force reduces the energy transfer to the object, resulting in less work being done.