RRB Technician Grade III Official Paper (Held On: 24 Dec, 2024 Shift 2) (Previous Year Paper)

Shortcut Trick

Difference in Amount = Interest for the difference in Time.

Interest for (5 − 2) = 3 years → ₹2,000 − ₹1,400 = ₹600.

Interest for 1 year = ₹200. ⇒ Interest for 2 years = ₹400.

Principal (P) = Amount_2yr − SI_2yr = 1,400 − 400 = ₹1,000.

Rate % = (Interest_1yr ÷ P) × 100 = (200 ÷ 1,000) × 100 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given: Amount in 2 years (A₁) = ₹1,400, Amount in 5 years (A₂) = ₹2,000.

Formula: Amount = Principal + (P × R × T ÷ 100)

⇒ Simple Interest (SI) for 3 years = A₂ − A₁ = 2,000 − 1,400 = ₹600.

⇒ SI for 1 year = 600 ÷ 3 = ₹200.

⇒ SI for 2 years = 200 × 2 = ₹400.

⇒ Principal (P) = Amount after 2 years − SI for 2 years = 1,400 − 400 = ₹1,000.

⇒ Rate (R) = (SI × 100) ÷ (P × T) = (400 × 100) ÷ (1,000 × 2)

⇒ R = 40,000 ÷ 2,000 = 20%.

∴ The correct answer is 20%.

Additional Information

Simple Interest Constant Property

In SI, the interest earned remains the same every year because it is always calculated on the original Principal.

Effective Rate of Interest

Rate of Interest = (SI for 1 year ÷ Principal) × 100. This is the fastest way to find R once P is known.

Difference between SI and CI

For the first year (if compounded annually), SI and CI are equal. From the second year, CI > SI.

The correct answer is Only a.

Key Points

• Phloem is primarily responsible for the transport of sugars and other metabolic products downward from the leaves to other parts of the plant.
• Xylem is the vascular tissue that is responsible for the transport of water and dissolved minerals absorbed from the soil.
• Root hairs significantly increase the surface area of roots, enhancing their ability to absorb water and nutrients from the soil.
• There is a continuous network of xylem channels that connect roots and leaves, facilitating the upward movement of water and minerals.

Additional Information

• Phloem Transport:
• Phloem tissue is composed of sieve tubes, companion cells, phloem fibers, and phloem parenchyma.
• It transports organic nutrients, particularly sucrose, from sources (e.g., leaves) to sinks (e.g., roots, fruits).
• Xylem Transport:
• Xylem is composed of tracheids, vessel elements, fibers, and xylem parenchyma.
• It facilitates the upward movement of water and minerals through capillary action, root pressure, and transpiration pull.
• Root Hair Function:
• Root hairs are extensions of root epidermal cells that greatly increase the root surface area for water and nutrient uptake.
• They play a crucial role in the absorption of minerals and water from the soil.
• Vascular Tissues:
• Xylem and phloem are the two main types of vascular tissues in plants.
• These tissues form a continuous network throughout the plant, ensuring efficient transport of water, minerals, and nutrients.

The logic followed here is:

Hence, "Option 1" is the correct answer.

The correct answer is Alok Shukla.

Key Points

• Alok Shukla is recognized for his efforts in environmental conservation and activism, particularly in the context of the Indian state of Chhattisgarh.
• He has been instrumental in leading community-driven initiatives to protect forests and water resources from industrial exploitation.
• Shukla’s work has significantly contributed to the preservation of biodiversity and the promotion of sustainable practices among local communities.
• The Goldman Environmental Prize is awarded annually to grassroots environmental activists from six continental regions, and Alok Shukla's efforts have earned him this prestigious recognition for 2024.
• The award highlights the critical role of local activism in addressing global environmental challenges and promoting ecological justice.

Additional Information

• Goldman Environmental Prize:
• Established in 1989 by Richard and Rhoda Goldman to honor grassroots environmental activists.
• Often referred to as the "Green Nobel," it recognizes individuals who have made significant efforts to protect and enhance the natural environment.
• The prize includes a monetary award to support the recipient's ongoing work and advocacy.
• Winners are selected from six regions: Africa, Asia, Europe, Islands & Island Nations, North America, and South & Central America.
• Environmental Activism:
• Involves efforts to address environmental issues through advocacy, education, and direct action.
• Focus areas include climate change, deforestation, pollution, conservation, and sustainable development.
• Grassroots activism is crucial for mobilizing local communities and influencing policy changes at higher levels.
• Biodiversity Conservation:
• Refers to the practice of protecting and managing biodiversity to ensure sustainable ecosystems.
• Key strategies include habitat preservation, species protection, and combating invasive species.
• Conservation efforts are essential for maintaining ecological balance and supporting human livelihoods.
• Sustainable Practices:
• Involve methods and processes that do not deplete natural resources or harm the environment.
• Include renewable energy, sustainable agriculture, and waste reduction techniques.
• Aim to meet current needs without compromising the ability of future generations to meet theirs.

The correct answer is 1 watt hour.

Key Points

• Energy consumption is calculated by multiplying power by time.
• 1 watt of power used for 1 hour equals 1 watt hour (Wh).
• 1 watt hour is the amount of energy consumed when a device with a power rating of 1 watt operates for 1 hour.
• It is a small unit of energy commonly used in household electrical appliances.

Additional Information

• Watt (W): A unit of power equivalent to one joule per second. It measures the rate of energy conversion or transfer.
• Watt Hour (Wh): A unit of energy representing the power consumption of one watt over the period of one hour.
• Kilowatt Hour (kWh): A larger unit of energy commonly used for measuring electricity consumption, equal to 1,000 watt hours.
• Energy Measurement: Energy can also be measured in other units such as joules (J), where 1 watt hour equals 3,600 joules.
• Power and Energy Relationship: Power is the rate at which energy is used, and energy is the total amount of work done or heat generated over time.

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

B sits third to the left of E.

Only E sits between K and F.

D is not an immediate neighbour of B.

F sits second to the left of C.

And G sit at remaining place.

So, Two people sit between G and F when counted from the right of G

Hence the correct answer is "Option 3"

Shortcut Trick

For any continued proportion a : b :: b : c, the property is b² = ac.

Here, x : 6 :: 6 : y ⇒ 6² = xy.

Taking square root on both sides: √xy = √(6²) = 6.

∴ The correct answer is 6.

Alternate Method

Given: x : 6 :: 6 : y

Formula Used: Product of Extremes = Product of Means

⇒ x/6 = 6/y

⇒ x × y = 6 × 6

⇒ xy = 36

⇒ √xy = √36

⇒ √xy = 6

∴ The correct answer is 6.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is √(ab). In the given question, 6 is the mean proportional of x and y.

Third Proportional

If a : b :: b : c, then c is called the third proportional to a and b, calculated as c = b²/a.

Fourth Proportional

If a : b :: c : d, then d is the fourth proportional, calculated as d = (b × c)/a.

Shortcut Trick Total Cost Price (CP) = (960 ÷ 0.96) + (840 ÷ 1.20) = 1000 + 700 = ₹1700. Total Selling Price (SP) = 960 + 840 = ₹1800. Since SP > CP, it is a Profit. Net Profit = 1800 − 1700 = ₹100. ∴ The correct answer is Profit, ₹100.

Alternate Method Given → SPshirt = ₹960, Loss% = 4%; SPsweater = ₹840, Profit% = 20%. Formulas: CP = [SP × 100] ÷ [100 ± Profit/Loss%]; Net Profit/Loss = Total SP − Total CP.

⇒ CP of Shirt = (960 × 100) ÷ (100 − 4) = 96000 ÷ 96 = ₹1000. ⇒ CP of Sweater = (840 × 100) ÷ (100 + 20) = 84000 ÷ 120 = ₹700. ⇒ Total CP = 1000 + 700 = ₹1700. ⇒ Total SP = 960 + 840 = ₹1800. ⇒ Net Profit = 1800 − 1700 = ₹100. ∴ The correct answer is Profit, ₹100.

Additional Information Profit and Loss Basics Profit occurs when Selling Price is greater than Cost Price. Profit = SP − CP. Net Transaction To find the Net Profit or Loss on multiple items, always calculate the sum of individual Cost Prices and compare it with the sum of individual Selling Prices.

The correct answer is World Para Athletics Championships.

Key Points

• Deepthi Jeevanji set a new world record in the women's T20 400-m event at the World Para Athletics Championships.
• The World Para Athletics Championships is a prominent event organized by the International Paralympic Committee (IPC).
• The Championships are held biennially, bringing together the best para-athletes from around the world.
• The T20 classification is for athletes with an intellectual impairment, ensuring fair competition among similarly challenged competitors.
• The 2023 edition of the World Para Athletics Championships took place in Paris, France.

Additional Information

• International Paralympic Committee (IPC)
• The IPC is the global governing body of the Paralympic Movement.
• It organizes the Paralympic Games and oversees the organization of World Para Athletics Championships.
• Founded on September 22, 1989, the IPC aims to enable para-athletes to achieve sporting excellence and inspire and excite the world.
• Classification in Para Athletics
• Classification ensures a level playing field by grouping athletes with similar impairments together.
• Classes include physical, visual, and intellectual impairments, with specific codes for each category.
• The T20 classification specifically caters to athletes with intellectual impairments.
• World Para Athletics Championships
• The Championships are a major event in the para-athletics calendar, held every two years.
• They feature a wide range of track and field events for athletes with various types of impairments.
• The event serves as a qualifying competition for the Paralympic Games.
• Records and Achievements
• Setting a world record is a significant achievement, highlighting the athlete's exceptional performance.
• World records are officially recognized by the IPC and require stringent verification processes.

The correct answer is Option 4.

Key Points

• Power of a lens is defined as the reciprocal of its focal length (P = 1/f).
• Larger focal length results in a smaller power as they are inversely proportional.
• Convex lenses have positive power since they converge light rays.
• Concave lenses have negative power since they diverge light rays.

Additional Information

• Focal Length (f):
• The distance between the center of a lens and its focus.
• Measured in meters (m).
• Power of a lens (P):
• Measured in diopters (D).
• Positive for convex lenses and negative for concave lenses.
• Convex Lens:
• A lens that converges light rays that are traveling parallel to its principal axis.
• Used in magnifying glasses, eyeglasses for farsightedness.
• Concave Lens:
• A lens that diverges light rays that are traveling parallel to its principal axis.
• Used in eyeglasses for nearsightedness.

The correct answer is Swapnil Kusale.

Key Points

• Swapnil Kusale won India's first-ever medal in the men's 50m Rifle 3-Positions final at the Paris 2024 Olympics.
• He achieved this historic feat by showcasing exceptional skill and precision in the event.
• The 50m Rifle 3-Positions event includes shooting in three different positions: kneeling, prone, and standing.
• Swapnil Kusale's victory is a significant milestone for Indian shooting sports, highlighting the country's growing talent in this field.

Additional Information

• 50m Rifle 3-Positions Event:
• This event requires shooters to fire a series of shots from three different positions: kneeling, prone, and standing.
• Each position tests different aspects of shooting skills, including stability, accuracy, and endurance.
• Indian Shooting Sports:
• India has a rich history in shooting sports, with several athletes achieving international success.
• The country has produced Olympic medalists such as Abhinav Bindra, who won gold in the 10m Air Rifle event at the 2008 Beijing Olympics.
• Olympic Shooting Events:
• The Olympics feature a variety of shooting events, including rifle, pistol, and shotgun disciplines.
• Shooting has been part of the modern Olympic Games since the first edition in 1896.
• Training for Shooting Sports:
• Shooters undergo rigorous training to develop their skills, including physical conditioning, mental focus, and technical precision.
• Advanced equipment and technology play a crucial role in training and competition.

The correct answer is Potassium and gold.

Key Points

• Potassium is the most reactive metal in the reactivity series. It reacts explosively with water and even moisture in the air.
• Gold is one of the least reactive metals and does not tarnish or corrode easily, maintaining its luster over time.
• The reactivity series is a list of metals arranged in order of decreasing reactivity to help predict their behavior in reactions.
• Potassium's high reactivity is due to its single electron in the outermost shell, which it loses easily to form positive ions.
• Gold's low reactivity is due to its full d-subshell and high ionization energy, making it less likely to participate in chemical reactions.

Additional Information

• Reactivity Series
• The reactivity series, also known as the activity series, is a ranking of metals based on their reactivity from highest to lowest.
• It helps predict how metals will react with acids, water, and other compounds.
• Metals high in the series, like potassium, sodium, and calcium, react more vigorously than those lower down, like gold, platinum, and silver.
• Reactivity of Alkali Metals
• Alkali metals, such as potassium and sodium, are highly reactive due to their single valence electron.
• They tend to lose this electron easily, forming positive ions and engaging in reactions with water, oxygen, and halogens.
• Gold's Chemical Properties
• Gold is known for its resistance to corrosion and tarnish, making it highly valuable in jewelry and electronics.
• It is a noble metal, meaning it is resistant to reacting with most chemicals.
• Applications of Reactivity Series
• The reactivity series is used in metallurgy to extract metals from their ores.
• It is also used in predicting the outcomes of displacement reactions in chemistry.

Family Chart:

Decoding the Symbols:

Given: 'X - Y × Z + A ÷ B'

So, A is brother to X

Hence, the correct answer is "Option 3".

Shortcut Trick

The product of n consecutive natural numbers is always divisible by n! (n factorial).

For four consecutive natural numbers, the product is divisible by 4!.

4! = 4 × 3 × 2 × 1 = 24.

To verify, take the smallest four consecutive natural numbers: 1, 2, 3, 4.

Product = 1 × 2 × 3 × 4 = 24.

∴ The correct answer is 24.

Alternate Method

Given: Four consecutive natural numbers.

Formula Used: Product of n consecutive integers is divisible by n!.

⇒ Let the four consecutive numbers be n, (n+1), (n+2), and (n+3).

⇒ Smallest set of natural numbers = 1, 2, 3, 4.

⇒ Product = 1 × 2 × 3 × 4 = 24.

⇒ Second set of natural numbers = 2, 3, 4, 5.

⇒ Product = 2 × 3 × 4 × 5 = 120.

⇒ HCF of 24 and 120 is 24.

⇒ Therefore, the greatest natural number that divides any such product is 24.

∴ The correct answer is 24.

Additional Information

Divisibility of Consecutive Integers

The product of r consecutive integers is always divisible by r!. This is because the number of ways to choose r items from n is an integer: ⁿC_r = P/r!, so P must be divisible by r!.

Factorial Definition

n! (n factorial) is the product of all positive integers from 1 up to n. For example, 3! = 3 × 2 × 1 = 6.

Natural Numbers

Natural numbers start from 1, 2, 3, .... If the question allowed for whole numbers (including 0), the product could be 0, which is divisible by any number.

The correct answer is When it is about to hit the ground..

Key Points

• When an object falls freely under gravity, its potential energy is converted to kinetic energy.
• The kinetic energy of an object is given by the formula KE = 0.5 * m * v², where 'm' is mass and 'v' is velocity.
• As the object falls, its velocity increases due to acceleration by gravity, leading to an increase in kinetic energy.
• The maximum kinetic energy is achieved just before the object hits the ground, as all potential energy has been converted to kinetic energy.

Additional Information

• Potential Energy (PE):
• It is the energy possessed by an object due to its position or height above the ground.
• PE is calculated using the formula PE = m * g * h, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is height.
• Law of Conservation of Energy:
• This law states that energy cannot be created or destroyed; it can only be transformed from one form to another.
• In the case of a falling object, potential energy is converted to kinetic energy.
• Acceleration due to Gravity (g):
• It is the acceleration experienced by an object due to the gravitational pull of the Earth.
• The standard value of 'g' is approximately 9.8 m/s².
• Free Fall:
• A condition in which the only force acting on an object is gravity, causing it to fall towards the Earth.
• During free fall, air resistance is considered negligible.

Shortcut Trick

Greater number = (Sum + Difference) ÷ 2

Smaller number = (Sum − Difference) ÷ 2

⇒ Greater number = (42 + 18) ÷ 2 = 60 ÷ 2 = 30

∴ The correct answer is 30.

Alternate Method

Given:

Sum of two numbers = 42

Difference between numbers = 18

Calculations:

Let the greater number be x and the smaller number be y.

⇒ x + y = 42 --- (1)

⇒ x − y = 18 --- (2)

Adding equations (1) and (2):

⇒ (x + y) + (x − y) = 42 + 18

⇒ 2x = 60

⇒ x = 30

∴ The correct answer is 30.

Additional Information

Linear Equations in Two Variables

To solve for two variables, we use the elimination method by adding or subtracting equations to remove one variable.

Sum and Difference Properties

Product of two numbers can also be derived: xy = [(x+y)² − (x−y)²] ÷ 4.

Logic followed here is,

Option 1) KRY

Option 2) YFM

Option 3) GNU

Option 4) BGT

Does not follow the same logic.

Hence the correct answer is "Option 4"

Logic followed here is,

Statement I indicates that high sugar consumption causes diabetes.

Statement II suggests people are reacting to the knowledge that sugar causes diabetes.

⇒ Statement I is the cause.

⇒ Statement II is the effect of Statement I.

∴ I is the cause and II is its possible effect.

Hence the correct answer is Option 2.

The correct answer is Shri Rajnath Singh.

Key Points

• Shri Rajnath Singh launched the ADITI 2.0 challenges and DISC 12 during DefConnect 4.0 on 7 October 2024.
• ADITI 2.0 aims to foster innovation and entrepreneurship in the defence sector.
• DISC 12 is part of the Defence India Startup Challenge series to promote 'Aatmanirbharta' or self-reliance in defence technologies.
• DefConnect 4.0 is an event organized to boost the defence startup ecosystem in India.
• The initiatives are intended to strengthen the collaboration between the government and the private sector in defence innovations.

Additional Information

• Defence India Startup Challenge (DISC):
• DISC is a flagship initiative under the Innovations for Defence Excellence (iDEX) framework.
• It encourages startups to develop products and solutions for defence and aerospace sectors.
• The challenge involves problem statements identified by the armed forces and is open to Indian startups and MSMEs.
• iDEX provides funding, mentorship, and support to the selected startups.
• Innovations for Defence Excellence (iDEX):
• Launched by the Ministry of Defence in 2018 to foster innovation and technology development in defence.
• iDEX aims to create an ecosystem that supports and nurtures startups and innovators.
• It provides access to defence testing facilities, funding, and expert mentorship.
• iDEX is managed by the Defence Innovation Organisation (DIO), a not-for-profit company set up by the Ministry of Defence.
• Aatmanirbhar Bharat:
• A flagship initiative by the Government of India to make the country self-reliant.
• It focuses on promoting local manufacturing, reducing dependency on imports, and boosting domestic industries.
• The initiative spans various sectors, including defence, healthcare, agriculture, and infrastructure.
• It aims to make India a global manufacturing hub by leveraging its demographic and technological advantages.
• DefConnect:
• DefConnect is an event organized by the Ministry of Defence to showcase innovations in the defence sector.
• It provides a platform for startups, MSMEs, and innovators to interact with the defence establishment.
• The event includes exhibitions, panel discussions, and networking opportunities.
• DefConnect aims to strengthen the collaboration between the government, industry, and academia.

The correct answer is Option 1.

Key Points

• The food we eat is digested by various enzymes in our body, which are biological catalysts.
• Enzymes are highly specific in their action, meaning each enzyme only acts on a particular substrate.
• Specific enzymes are required for the breakdown of particular substances; for example, amylase breaks down starch into sugars.
• This specificity is due to the unique shape of the enzyme's active site, which matches the shape of its substrate (lock-and-key model).

Additional Information

• Enzymes: Proteins that act as biological catalysts, speeding up chemical reactions in the body without being consumed.
• Substrate: The specific substance on which an enzyme acts.
• Active Site: The region on an enzyme where the substrate binds and the reaction occurs.
• Lock-and-Key Model: A model describing how enzymes and substrates fit together based on their specific shapes.
• Induced Fit Model: A model suggesting that enzyme active sites can adjust their shape to fit the substrate more snugly.

The correct answer is 1) 10 years.

Key Points

• The Pradhan Mantri Jan Dhan Yojana (PMJDY) was launched on 28 August 2014.
• As of 28 August 2024, PMJDY has completed 10 years since its launch.
• PMJDY is a national mission aimed at ensuring access to financial services like banking, savings and deposit accounts, remittance, credit, insurance, and pension.
• It is one of the world’s largest financial inclusion initiatives, aiming to provide universal access to banking facilities.
• The scheme was announced by Prime Minister Narendra Modi in his Independence Day address on 15 August 2014.

Additional Information

• Financial Inclusion:
• Financial inclusion refers to efforts to make financial products and services accessible and affordable to all individuals and businesses, regardless of their personal net worth or company size.
• It aims to remove barriers that exclude people from participating in the financial sector.
• Key Features of PMJDY:
• No minimum balance required.
• Accidental insurance cover of Rs. 2 lakh and life cover of Rs. 30,000.
• Overdraft facility up to Rs. 10,000 is available after six months of satisfactory operation.
• Impact of PMJDY:
• As of 2024, over 48 crore bank accounts have been opened under PMJDY, with a total balance of approximately Rs. 2 lakh crore.
• The scheme has significantly increased the penetration of banking services in rural and semi-urban areas.
• Challenges in Financial Inclusion:
• Lack of financial literacy among the population.
• Geographical barriers in reaching remote areas.
• Infrastructure limitations such as lack of bank branches and ATMs.

Shortcut Trick

Put θ = 90° in the expression.

⇒ sin 90° = 1 and cos 90° = 0.

⇒ [1 / (1 − 0)] + [(1 − 0) / 1] = 1 + 1 = 2.

Check options at θ = 90°: 2 cosec 90° = 2 × 1 = 2.

∴ The correct answer is 2 cosec θ.

Alternate Method

Given: Expression = [sin θ / (1 − cos θ)] + [(1 − cos θ) / sin θ]

Formula Used: sin²θ + cos²θ = 1 | cosec θ = 1 / sin θ

⇒ Take LCM of denominators: sin θ (1 − cos θ)

⇒ Expression = [sin²θ + (1 − cos θ)²] / [sin θ(1 − cos θ)]

⇒ Expression = [sin²θ + 1 + cos²θ − 2 cos θ] / [sin θ(1 − cos θ)]

⇒ Expression = [(sin²θ + cos²θ) + 1 − 2 cos θ] / [sin θ(1 − cos θ)]

⇒ Expression = [1 + 1 − 2 cos θ] / [sin θ(1 − cos θ)]

⇒ Expression = [2 − 2 cos θ] / [sin θ(1 − cos θ)]

⇒ Expression = 2(1 − cos θ) / [sin θ(1 − cos θ)]

⇒ Expression = 2 / sin θ

⇒ Expression = 2 cosec θ

∴ The correct answer is 2 cosec θ.

Additional Information

Trigonometric Identities

Fundamental identities include sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Reciprocal Relations

cosec θ = 1/sin θ, sec θ = 1/cos θ, and cot θ = 1/tan θ.

Value Substitution Method

For simplification questions, substituting standard angles like 30°, 45°, or 60° helps in verifying options quickly, provided no denominator becomes zero.

Given series:

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

Such Even digits are there, each of which is immediately preceded by a even digit and also immediately followed by an odd digit.

Even → Even → Odd

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

Thus, there are 2 such pairs(4 6 7, 2 8 3 )

Hence, the correct answer is "Option 4".

The correct answer is Both A and C.

Key Points

• Non-biodegradable substances are materials that cannot be broken down by natural processes like bacterial action, making them persistent in the environment.
• These substances can accumulate and remain in ecosystems for long periods, causing potential harm to wildlife, humans, and the environment.
• Materials such as plastics, synthetic chemicals, and certain metals are common examples of non-biodegradable substances.
• Due to their persistence, non-biodegradable substances can disrupt ecological balance and contribute to pollution and habitat destruction.

Additional Information

• Biodegradable substances: These are materials that can be broken down by natural processes, usually by microorganisms, into harmless substances that are absorbed into the environment.
• Environmental impact: The persistence of non-biodegradable substances in the environment can lead to soil and water pollution, harming flora, fauna, and potentially human health.
• Waste management: Proper disposal and recycling of non-biodegradable materials are essential to mitigate their environmental impact. Efforts include reducing plastic use, recycling programs, and developing biodegradable alternatives.
• Legislation and regulation: Governments and international bodies are implementing policies and regulations to manage and reduce the production and disposal of non-biodegradable substances, aiming for sustainable environmental practices.

Shortcut Trick

Check the divisibility of each number by small prime numbers like 2, 3, 5, 7, 11.

61, 71, and 31 are not divisible by any of these, making them prime.

91 is clearly divisible by 7 since 7 × 13 = 91.

∴ The correct answer is 91.

Alternate Method

Given: Numbers 61, 91, 71, 31.

Formula Used: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A composite number has more than two factors.

⇒ Factors of 61 = 1, 61 (Prime)

⇒ Factors of 71 = 1, 71 (Prime)

⇒ Factors of 31 = 1, 31 (Prime)

⇒ Factors of 91 = 1, 7, 13, 91

⇒ Since 91 has factors other than 1 and 91, it is a composite number.

∴ The correct answer is 91.

Additional Information

Prime Numbers 1-100

There are 25 prime numbers between 1 and 100. 2 is the only even prime number.

Composite Numbers

Numbers that have more than two factors. 1 is neither prime nor composite.

Divisibility Rule of 7

Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, the original number is divisible by 7.

The correct answer is nucleons.

Key Points

• The atomic mass of an atom is primarily determined by the total number of nucleons (protons and neutrons).
• Protons and neutrons are located in the nucleus of an atom and contribute most of the mass, as electrons have negligible mass.
• The mass number, which is approximately equal to the atomic mass, is the sum of the number of protons and neutrons in the nucleus.
• For example, Carbon-12 has 6 protons and 6 neutrons, giving it a mass number of 12.

Additional Information

• Protons:
• Positively charged particles located in the nucleus of an atom.
• The number of protons defines the atomic number and the element itself.
• Neutrons:
• Neutral particles located in the nucleus of an atom.
• Neutrons contribute to the stability of the nucleus.
• Electrons:
• Negatively charged particles that orbit the nucleus.
• Electrons have a much smaller mass compared to protons and neutrons.
• Isotopes:
• Atoms of the same element with the same number of protons but different numbers of neutrons.
• Isotopes have different mass numbers but the same chemical properties.

Shortcut Trick

Let M and N be the midpoints of AD and AC in ΔADC.

By the Midpoint Theorem, the line segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

⇒ MN = CD ÷ 2

⇒ 2 = CD ÷ 2 ⇒ CD = 4 units

⇒ Opposite side AB = CD = 4 units

Perimeter = 2 × (AD + CD) ⇒ 26 = 2 × (AD + 4) ⇒ AD + 4 = 13 ⇒ AD = 9 units

∴ The correct answer is 9 units.

Alternate Method

Given:

Perimeter of parallelogram ABCD = 26 units

Length of the line joining midpoints of AD and AC = 2 units

Formula Used:

Midpoint Theorem in a triangle: MN = 1/2 × third side

Perimeter of a parallelogram = 2 × (Sum of adjacent sides)

Calculations:

Consider ΔADC inside the parallelogram ABCD.

Let M be the midpoint of AD and N be the midpoint of AC.

⇒ MN = 2 units

Applying Midpoint Theorem in ΔADC:

⇒ MN = CD ÷ 2

⇒ 2 = CD ÷ 2

⇒ CD = 4 units

Since opposite sides of a parallelogram are equal:

⇒ AB = CD = 4 units

Now, let the length of AD be x units.

Perimeter of ABCD = 2 × (AD + CD)

⇒ 26 = 2 × (x + 4)

⇒ 13 = x + 4

⇒ x = 9 units

⇒ AD = 9 units

∴ The correct answer is 9 units.

Additional Information

Midpoint Theorem

The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is exactly half the length of that third side.

Properties of a Parallelogram

Opposite sides are parallel and equal in length. Opposite angles are equal, and adjacent angles are supplementary (sum to 180°).

The correct answer is Two.

Key Points

• There are two types of endoplasmic reticulum (ER) in cells: Rough ER and Smooth ER.
• Rough ER is studded with ribosomes, which gives it a "rough" appearance under a microscope.
• Smooth ER lacks ribosomes and appears smooth.
• Both types of ER are involved in the synthesis and transport of proteins and lipids within the cell.

Additional Information

• Rough ER
• Primarily involved in the synthesis of proteins due to the presence of ribosomes.
• Proteins synthesized on the rough ER are often destined for secretion or for use in the cell membrane.
• Smooth ER
• Involved in lipid synthesis, detoxification of drugs and poisons, and calcium ion storage.
• Lacks ribosomes, which is why it appears smooth under a microscope.
• Endoplasmic Reticulum (ER)
• ER is a network of membranous tubules and sacs called cisternae.
• It plays a key role in the biosynthesis, folding, modification, and transport of proteins and lipids.
• Cellular Functions
• The ER is essential for the production of proteins and lipids, which are critical for cell function and structure.
• It also helps in the detoxification of chemicals and the metabolism of carbohydrates.

Shortcut Trick Identify the nearest perfect squares: 702 = 4900 and 802 = 6400. Since 4900 < 6084 < 6400, the square root lies between 70 and 80. The unit digit of 6084 is 4, so the square root must end in 2 or 8 (22=4 or 82=64). Since 6084 is very close to 6400, the answer is 78. ∴ The correct answer is 78. Alternate Method Given: Number = 6084 Method: Prime Factorisation ⇒ 6084 = 2 × 3042 ⇒ 6084 = 2 × 2 × 1521 ⇒ 6084 = 2 × 2 × 3 × 507 ⇒ 6084 = 2 × 2 × 3 × 3 × 169 ⇒ 6084 = 2 × 2 × 3 × 3 × 13 × 13 ⇒ √6084 = √(22 × 32 × 132) ⇒ √6084 = 2 × 3 × 13 = 78 ∴ The correct answer is 78. Additional Information Unit Digit Property If a perfect square ends in 4, its square root ends in either 2 or 8. Estimation Method Always check the square of the middle value (752 = 5625). Since 6084 > 5625, the root must be > 75. Long Division Method Group digits in pairs from right (60 84) and find the largest divisor whose square is less than or equal to the first pair.

The correct answer is Rajdeep Sardesai.

Key Points

• Rajdeep Sardesai is a renowned Indian news anchor and author.
• The book "2024: The Election that Surprised India" is his analysis of the 2024 Indian general elections.
• He has previously authored books like "2014: The Election that Changed India" and "Newsman: Tracking India in the Modi Era".
• Rajdeep Sardesai is known for his in-depth political analysis and journalistic expertise.

Additional Information

• Book Overview
• The book provides a comprehensive analysis of the political climate leading up to and during the 2024 elections in India.
• It explores the key players, strategies, and unexpected outcomes that defined the election.
• Rajdeep Sardesai's Career
• He has worked with leading news channels like NDTV, CNN-IBN, and India Today.
• He is a recipient of numerous awards, including the Padma Shri in 2008.
• Context of the 2024 Elections
• The 2024 Indian general elections are a pivotal moment in Indian politics, shaping the future of governance and policy.
• The book delves into the social, economic, and political factors influencing voter behavior.
• Impact of the Book
• The book aims to provide readers with a deeper understanding of the complexities of Indian politics.
• It is a valuable resource for scholars, political enthusiasts, and anyone interested in contemporary Indian history.

Shortcut Trick

HCF is the highest common factor that divides all given numbers exactly.

Calculate differences between numbers: 20 − 16 = 4 and 24 − 20 = 4.

Since 4 divides 16 (4×4), 20 (4×5), and 24 (4×6), it is the HCF.

∴ The correct answer is 4.

Alternate Method

Given: Numbers 16, 20, and 24.

Method: Prime Factorization Method

⇒ Prime factors of 16 = 2 × 2 × 2 × 2 = 2⁴

⇒ Prime factors of 20 = 2 × 2 × 5 = 2² × 5

⇒ Prime factors of 24 = 2 × 2 × 2 × 3 = 2³ × 3

⇒ Common prime factors = 2 × 2

⇒ HCF = 2² = 4

∴ The correct answer is 4.

Additional Information

HCF (Highest Common Factor)

The greatest number which divides two or more numbers without leaving a remainder. Also known as GCD (Greatest Common Divisor).

LCM (Least Common Multiple)

The smallest number which is a multiple of two or more numbers. For 16, 20, 24, the LCM is 240.

Relationship Formula

For two numbers a and b: HCF(a, b) × LCM(a, b) = a × b.

Given, 

Jimmy starts from point A and drives 6 km towards the South.

He then takes two simultaneous left turns and drives 4 km and 6 km, respectively.

He then takes a final right turn and drives 4 km to reach point B.

He should drive 8 km toward West to reach Point A again.

Hence the correct answer is Option 4.

The logic followed here is:

Position of Drisha from the left = (Total number of people  - Position of Drisha from the right + 1)

Position of Drisha from the left = (19  - 17 + 1) = 3

Position of Vani from the left = 3^rd

Number of people between Drisha and Vani = Position of Vani from the left - Position of Drisha from the left - 1

Number of people between Drisha and Vani = 9 - 3 - 1 = 5

Hence, the correct answer is "Option 1".

Given, Seven people, A, B, C, L, X, Y and Z are sitting in a row, facing north.

Only two people sit to the left of A.

Only three people sit between A and Y.

L sits second to the right of A.

Only two people sit between L and Z.

C sits at some place to the right of B but at some place to the left of X.

So, 3 people sit to the right of C.

Hence the correct answer is "Option 3"

Shortcut Trick

Area of four walls = Total Cost ÷ Rate per m²

Area = 8640 ÷ 60 = 144 m²

Lateral Surface Area = 2 × (Length + Breadth) × Height

144 = 2 × (5 + 3) × Height ⇒ 144 = 16 × Height

Height = 144 ÷ 16 = 9 m

∴ The correct answer is 9 m.

Alternate Method

Given:

Length (L) of the office floor = 5 m

Breadth (B) of the office floor = 3 m

Total Cost of painting the walls = ₹8,640

Rate of painting = ₹60/m²

Formula Used:

1. Area of walls (Lateral Surface Area) = Total Cost ÷ Rate
2. Lateral Surface Area of Cuboid = 2 × (L + B) × h

Calculations:

⇒ Area of the four walls = 8640 ÷ 60

⇒ Area of the four walls = 144 m²

⇒ 2 × (L + B) × h = 144

⇒ 2 × (5 + 3) × h = 144

⇒ 2 × 8 × h = 144

⇒ 16 × h = 144

⇒ h = 144 ÷ 16

⇒ h = 9 m

∴ The correct answer is 9 m.

Additional Information

Lateral Surface Area of a Cuboid

It represents the sum of the areas of the four vertical walls, calculated as 2h(L + B).

Total Surface Area of a Cuboid

It includes the area of all six faces: 2(LB + Bh + hL).

Volume of a Cuboid

The space occupied by the cuboid is calculated as Length × Breadth × Height (L × B × h).

Diagonal of a Cuboid

The longest rod that can be placed inside the room is given by √(L² + B² + h²).

The correct answer is CH3OH(I).

Key Points

• Carbon monoxide (CO) reacts with hydrogen (H₂) to produce methanol (CH₃OH).
• This reaction is catalyzed by a mixture of copper, zinc oxide, and alumina.
• The reaction occurs at high temperatures (250-300°C) and pressures (50-100 atm).
• The chemical equation for the reaction is CO + 2H₂ → CH₃OH.

Additional Information

• Methanol (CH₃OH):
• Also known as wood alcohol, methanol is a light, volatile, colorless, and flammable liquid with a distinctive odor.
• It is used as an industrial solvent, antifreeze, and fuel.
• Methanol is also a key feedstock for the production of chemicals such as formaldehyde and acetic acid.
• Hydrogenation:
• Hydrogenation is a chemical reaction between molecular hydrogen (H₂) and another compound or element, usually in the presence of a catalyst.
• This process is widely used in the food industry to hydrogenate oils and in the petrochemical industry to produce various fuels and chemicals.
• Catalysts in Methanol Production:
• Catalysts are substances that increase the rate of a chemical reaction without being consumed in the process.
• In methanol production, commonly used catalysts include copper, zinc oxide, and alumina.
• Industrial Applications of Methanol:
• Methanol is used in the production of formaldehyde, which is a precursor to many other materials and chemical compounds.
• It is also used to make methyl tert-butyl ether (MTBE), a gasoline additive that improves combustion efficiency.

Given Equation: 12 D 15 B 3 C 6 A 5 = ?

BODMAS Rule:

Decoding the given information:

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

⇒ 12 - 15 ÷ 3 + 6 × 5 

⇒ 12 - 5 + 30 = 37

Hence, the correct option is "Option 2".

The correct answer is Vigyan Dhara.

Key Points

• In 2024, the Union Cabinet approved the continuation of three umbrella schemes merged into a unified central sector scheme under the Department of Science and Technology (DST) called Vigyan Dhara.
• The unified scheme aims to streamline and enhance the effectiveness of various science and technology initiatives by integrating them under a single framework.
• Vigyan Dhara focuses on promoting scientific research, fostering innovation, and providing comprehensive support to scientific institutions and researchers across the country.
• This scheme is expected to address critical areas such as technology development, research infrastructure, and human resource development in the field of science and technology.
• It underscores the Indian government's commitment to advancing scientific knowledge and leveraging technology for national development.

Additional Information

• Department of Science and Technology (DST)
• The DST was established in May 1971 to promote new areas of science and technology and to coordinate scientific and technological activities in the country.
• It plays a crucial role in formulating policies related to science and technology and oversees their implementation.
• The DST provides funding and support for various scientific research projects and initiatives.
• Scientific Research in India
• India has a rich tradition of scientific research, with significant contributions in fields such as space technology, pharmaceuticals, and information technology.
• The government supports numerous research institutions, including the Indian Institutes of Technology (IITs) and Indian Institutes of Science Education and Research (IISERs).
• Collaborative research programs with international institutions are encouraged to foster global scientific cooperation.
• Innovation and Technology Development
• Innovation is a key focus area under the Vigyan Dhara scheme, with the aim of translating scientific research into practical applications.
• Technology development initiatives are supported to enhance the competitiveness of Indian industries and contribute to economic growth.
• Startups and entrepreneurs in the technology sector receive support through various government programs and funding schemes.
• Human Resource Development in Science
• Building a strong scientific workforce is a priority, with programs aimed at nurturing young talent and providing advanced training opportunities.
• Fellowships, scholarships, and research grants are available to support students and researchers pursuing careers in science and technology.
• Collaborative initiatives with educational institutions aim to improve science education and inspire the next generation of scientists.

The logic follow here is:

TO-RM-PQ

And

WR-UP-ST  

Check each Option 

Option 1) XS-VQ-TW 

Option 2) SN-QL-OR 

Option 3) VQ-TO-RU 

Option 4) UP-SN-QR 

Only Option 4) follow same logic.

Hence, the correct answer is "Option 4".

Shortcut Trick

Net percentage increment for 2 years at 10% per year = 10 + 10 + (10 × 10)/100 = 21%.

Income in 2021 = Initial Income × (100 + Net %)/100

⇒ 21000 × 121% = 210 × 121 = 25410.

∴ The correct answer is ₹25410.

Alternate Method

Given:

Income in 2019 = ₹21,000

Annual increment rate (R) = 10%

Time period (n) = 2021 − 2019 = 2 years

Formula Used:

Final Value = P(1 + R/100)ⁿ

Calculations:

⇒ Income in 2020 = 21000 + (10% of 21000)

⇒ Income in 2020 = 21000 + 2100 = ₹23,100

⇒ Income in 2021 = 23100 + (10% of 23100)

⇒ Income in 2021 = 23100 + 2310 = ₹25,410

∴ The correct answer is ₹25410.

Additional Information

Successive Percentage Change

When a value changes by x% and then y% successively, the net change is given by [x + y + (xy/100)]%.

Compound Growth

Annual increments in salary or population growth follow the principle of Compound Interest where the base changes every year.

Multiplying Factor Method

For a 10% increase, the multiplying factor is 1.10. For 'n' years, the final amount is Initial Value × (1.10)ⁿ.

Given:

Rice consumed by Ravi in June = 9 kg

Rice consumed by Ravi in July = 12 kg

Rice consumed by Kapil in June = 8 kg

Rice consumed by Kapil in July = 10 kg

Formula used:

Difference = (Total rice consumed in July) - (Total rice consumed in June)

Calculations:

Total rice consumed in June and July by Ravi = 9 + 12 = 21 kg

Total rice consumed in June and July by Kapil = 8 + 10 = 18 kg

⇒ Difference = 21 - 18

⇒ Difference = 3 kg

∴ The difference between the total amount of rice consumed by Ravi and Kapil in the month of July and June is 3 kg.

Logic followed here is,

Logic: wind and dances is same in both language and snxk and vzod is same in both the code.

So, code for gracefully is Iwon.

Hence the correct answer is Option 2.

Given series: 

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

According to the question

12^th digit from the left = 6

2^nd digit from the right 7

Sum = 6 + 7 = 13

Hence, "Option 2" is the correct answer.

The correct answer is On a suitable stigma pollen tubes grow out of the pollen grain and travel through the style and reach the ovary..

Key Points

• Pollen tube formation is a critical step in the sexual reproduction of flowering plants, enabling the delivery of sperm cells to the ovule.
• The stigma is the receptive part of the pistil where pollen grains land and germinate.
• Once on the stigma, pollen grains germinate and form pollen tubes that grow through the style to reach the ovary.
• The pollen tube carries two sperm cells, one of which fertilizes the egg cell in the ovule.

Additional Information

• Fertilization:
• It is the process by which male and female gametes (sperm and egg cells) fuse to form a zygote.
• In flowering plants, fertilization typically occurs within the ovule.
• Ovary and Ovule:
• The ovary is the part of the pistil that houses the ovules.
• After fertilization, the ovule develops into a seed, and the ovary matures into a fruit.
• Embryo Development:
• The zygote undergoes cell division and differentiation to form an embryo.
• The embryo is the early developmental stage of the seed.
• Double Fertilization:
• Unique to flowering plants, involving two fertilization events.
• One sperm fertilizes the egg cell, forming a zygote, while the other fuses with two polar nuclei to form the endosperm, which nourishes the developing embryo.

Shortcut Trick

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

Rearranging this: Mode − Median = 2 Median − 2 Mean.

Factoring out 2: Mode − Median = 2 (Median − Mean).

This matches expression 1 exactly.

∴ The correct answer is 1.

Alternate Method

Given: Four expressions relating Mean, Median, and Mode.

Formula Used: Empirical Relationship: Mode = 3 Median − 2 Mean

Calculations:

⇒ Standard Formula: Mode = 3 Median − 2 Mean

⇒ Subtract Median from both sides: Mode − Median = 3 Median − 2 Mean − Median

⇒ Simplify the right side: Mode − Median = 2 Median − 2 Mean

⇒ Factor out 2: Mode − Median = 2 (Median − Mean)

⇒ This confirms expression 1 is correct.

⇒ Checking expression 3: Mode = 2 Median − Mean (Incorrect, should be 3 Median − 2 Mean).

⇒ Checking expression 4: Mean = (3 Median − Mode) ÷ 2 (Incorrect as given in option).

∴ The correct answer is 1.

Additional Information

Empirical Relationship

For a moderately skewed distribution, the relationship is Mode = 3 Median − 2 Mean.

Symmetrical Distribution

In a perfectly symmetrical distribution (like Normal Distribution), Mean = Median = Mode.

Skewness and Central Tendency

In a positively skewed distribution, Mean > Median > Mode. In a negatively skewed distribution, Mode > Median > Mean.

The correct answer is Biceps.

Key Points

• Biceps are voluntary muscles, meaning they are under conscious control.
• These muscles are part of the skeletal muscle group, which facilitates movement by attaching to bones.
• The primary function of the biceps is to flex the elbow and rotate the forearm.
• Skeletal muscles, including the biceps, are striated in appearance due to their fiber structure.

Additional Information

• Involuntary Muscles:
• These muscles operate without conscious control.
• Examples include muscles found in the heart, digestive system, and respiratory system.
• They play essential roles in bodily functions like heartbeats and digestion.
• Skeletal Muscles:
• These are voluntary muscles attached to bones.
• They are responsible for body movements and maintaining posture.
• Skeletal muscles are characterized by their striated appearance under a microscope.
• Cardiac Muscle:
• The heart muscle is involuntary and striated.
• It contracts rhythmically and continuously to pump blood throughout the body.
• Unlike other involuntary muscles, cardiac muscle can generate its own electrical impulses.
• Smooth Muscle:
• Found in walls of internal organs like the stomach, intestines, and blood vessels.
• These muscles are non-striated and involuntary.
• They help in functions such as peristalsis and regulation of blood pressure.

The correct answer is facilitate the marketing of tribal products and empower tribal people.

Key Points

• TRIFED (Tribal Cooperative Marketing Development Federation of India) was established in 1987 under the Ministry of Tribal Affairs.
• Its primary aim is to facilitate the marketing of tribal products and empower tribal people by improving their income and livelihood opportunities.
• TRIFED promotes tribal products by organizing exhibitions, fairs, and other marketing events to provide a platform for tribal artisans.
• The organization also engages in capacity-building activities to enhance the skills of tribal artisans and producers.
• TRIFED helps in the creation of sustainable economic opportunities for tribal communities by linking them with national and international markets.

Additional Information

• Ministry of Tribal Affairs:
• The Ministry of Tribal Affairs was formed in 1999 to provide more focused attention on the integrated socio-economic development of Scheduled Tribes (STs).
• It is responsible for planning, policy formulation, and coordination of programs for the development of STs.
• Van Dhan Vikas Kendra:
• Initiative under TRIFED to promote value addition, branding, and marketing of Minor Forest Produce (MFP) by establishing Van Dhan Vikas Kendras (VDVKs).
• It aims to provide livelihood opportunities to tribal gatherers and ensure fair prices for their produce.
• GI Tag for Tribal Products:
• TRIFED helps in obtaining Geographical Indication (GI) tags for tribal products to protect and promote unique tribal crafts and traditions.
• GI tagging helps in branding and marketing tribal products at higher prices, ensuring better income for tribal artisans.
• Tribes India:
• The retail arm of TRIFED, which markets tribal products through various outlets and e-commerce platforms.
• Tribes India promotes and sells a wide range of tribal products, including handicrafts, handlooms, and natural products.

The correct answer is option 1.

Key Points

• The gravitational force between two objects is directly proportional to the product of their masses.
• It is inversely proportional to the square of the distance between the two objects.
• This relationship is defined by Newton's law of universal gravitation.
• Newton's law states that every point mass attracts every other point mass by a force acting along the line intersecting both points.

Additional Information

• Newton's Law of Universal Gravitation: This law states that every mass attracts every other mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
• Gravitational Constant (G): The proportionality constant in Newton's law of gravitation is known as the gravitational constant, which has a value of approximately 6.674 × 10^-11 N(m/kg)².
• Inverse-square Law: The inverse-square law indicates that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity.
• Applications: Newton's law of gravitation applies to a wide range of physical phenomena, from the orbits of planets and moons to the trajectories of satellites and the motion of objects on Earth.

The correct answer is West Bengal.

Key Points

• The Aparajita Women and Child Bill, 2024, was passed by the Government of West Bengal in September 2024.
• The Bill aims to ensure the protection and empowerment of women and children in the state.
• It includes provisions for the safety, education, and health of women and children.
• The legislation focuses on creating a supportive environment for women and children, particularly those from marginalized communities.
• West Bengal has been proactive in implementing policies for women's and children's welfare, with several initiatives already in place.

Additional Information

• Women's Safety in India
• Women's safety has been a critical issue in India, with various laws and measures implemented to address it.
• The Nirbhaya Fund was established in 2013 to support initiatives aimed at enhancing the safety and security of women.
• Several states have launched helplines and mobile apps to offer immediate assistance to women in distress.
• Public awareness campaigns and self-defense training programs are also part of efforts to ensure women's safety.
• Child Welfare Policies
• India has implemented several policies to safeguard children's rights, including the Integrated Child Protection Scheme (ICPS).
• The Right to Education (RTE) Act, 2009 mandates free and compulsory education for children aged 6 to 14 years.
• Anganwadi centers under the Integrated Child Development Services (ICDS) scheme provide nutrition, health, and education services to children under six years of age.
• The Juvenile Justice (Care and Protection of Children) Act, 2015 focuses on the care and protection of children in conflict with the law and those in need of care and protection.
• Women's Empowerment Initiatives
• Various schemes such as Beti Bachao Beti Padhao, Pradhan Mantri Matru Vandana Yojana, and Mahila E-Haat aim to empower women economically and socially.
• The Self-Help Group (SHG) movement has been instrumental in empowering rural women through microfinance and entrepreneurship.
• The National Mission for Empowerment of Women (NMEW) works towards inter-sectoral convergence of all programs related to women's welfare and empowerment.
• Skill development programs like Skill India and PMKVY offer training to women in various trades to enhance their employability.
• Healthcare Initiatives for Women and Children
• Janani Suraksha Yojana (JSY) promotes institutional deliveries to reduce maternal and neonatal mortality.
• Rashtriya Bal Swasthya Karyakram (RBSK) aims to improve the overall health of children from birth to 18 years.
• Pradhan Mantri Matru Vandana Yojana (PMMVY) provides financial assistance to pregnant and lactating mothers for their first living child.
• Mission Indradhanush focuses on full immunization coverage for children and pregnant women.

Shortcut Trick

Identify the common factor in the required series.

Given series: 3² + 6² + 9² + ... + 30²

Each term is (3 × n)² = 3² × n² = 9 × n².

Factor out 3²: 9 × (1² + 2² + 3² + ... + 10²).

Required Value = 9 × 385 = 3465.

∴ The correct answer is 3465.

Alternate Method

Given: 1² + 2² + 3² + ... + 10² = 385

To Find: S = 3² + 6² + 9² + ... + 30²

⇒ S = (3×1)² + (3×2)² + (3×3)² + ... + (3×10)²

⇒ S = (3² × 1²) + (3² × 2²) + (3² × 3²) + ... + (3² × 10²)

⇒ S = 3² × (1² + 2² + 3² + ... + 10²)

⇒ S = 9 × (385)

⇒ S = 3465

∴ The correct answer is 3465.

Additional Information

Sum of squares of first n natural numbers

The formula is given by [n(n + 1)(2n + 1)] ÷ 6.

Property of Exponents

For any numbers a and b, (a × b)ⁿ = aⁿ × bⁿ.

Sum of first n natural numbers

The formula for the sum of the first n natural numbers is [n(n + 1)] ÷ 2.

Shortcut Trick

Effective Rate of Interest for 2 years at 10% Compound Interest = 10 + 10 + (10 × 10)/100 = 21%.

Total Amount = Principal × (100 + Effective Rate)%.

⇒ Amount = 12000 × 121% = 120 × 121 = ₹14520.

∴ The correct answer is ₹14520.

Alternate Method

Given:

Principal (P) = ₹12,000

Rate (R) = 10% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P(1 + R/100)ⁿ

Calculations:

⇒ A = 12000 × (1 + 10/100)²

⇒ A = 12000 × (110/100) × (110/100)

⇒ A = 12000 × (1.1) × (1.1)

⇒ A = 12000 × 1.21

⇒ A = ₹14520

∴ The correct answer is ₹14520.

Additional Information

Compound Interest (CI)

CI = Amount − Principal. It is the interest calculated on the initial principal and also on the accumulated interest of previous periods.

Successive Percentage Method

For two years, the effective rate can be calculated using the formula: x + y + (xy/100), where x and y are the rates for the first and second years.

Difference between CI and SI

For 2 years, the difference (D) between Compound Interest and Simple Interest is given by D = P(R/100)².

The logic follow here is:

LH-KG-JI

And

VR-UQ-TS 

Check each Option 

Option 1) TP-SN-RT

Option 2) TP-SO-RQ

Only Option 2) follow same logic.

Option 3) UP-SN-RQ

Option 4) UP-SO-RT

Hence, the correct answer is "Option 2".

The correct answer is Increase in humidity.

Key Points

• Humidity is the amount of water vapor present in the air. When humidity increases, the air becomes more saturated with water vapor, reducing the rate of evaporation.
• As the air becomes more saturated with moisture, the difference between the vapor pressure of the water and the air decreases, which slows down the evaporation process.
• High humidity levels mean that the air is close to being fully saturated with water vapor, leaving less room for additional water molecules to evaporate.
• Increased humidity directly affects the rate of evaporation because evaporation requires the removal of water vapor from the evaporating surface to the air.

Additional Information

• Evaporation: It is the process by which water changes from a liquid to a gas or vapor. Evaporation is a crucial part of the water cycle.
• Factors Affecting Evaporation: Key factors that affect the rate of evaporation include temperature, surface area, wind speed, and humidity.
• Temperature: Higher temperatures provide more energy to water molecules, increasing the rate of evaporation.
• Wind Speed: Increased wind speed removes the water vapor from the surface, enhancing the rate of evaporation.
• Surface Area: A larger surface area allows more water molecules to escape, increasing the rate of evaporation.

The correct answer is force.

Key Points

• The rate of change of momentum is directly proportional to the applied unbalanced force according to Newton's Second Law of Motion.
• Newton's Second Law states that F = ma, where F is the force applied, m is the mass, and a is the acceleration.
• This law implies that the force applied to an object is equal to the mass of the object multiplied by its acceleration.
• Momentum (p) is defined as the product of mass and velocity (p = mv). Hence, a change in momentum over time is influenced by the force applied.
• In formula terms, the rate of change of momentum (dp/dt) is equal to the force (F).

Additional Information

• Newton's First Law of Motion:
• Also known as the law of inertia, it states that an object will remain at rest or in uniform motion unless acted upon by an external force.
• Newton's Third Law of Motion:
• It states that for every action, there is an equal and opposite reaction.
• Conservation of Momentum:
• This principle states that the total momentum of a closed system is constant if no external forces are acting on it.
• Impulse:
• Impulse is the change in momentum of an object when a force is applied over a time interval. It is given by the product of force and time (Impulse = F * Δt).

The correct answer is Vascular tissue.

Key Points

• Vascular tissue in plants consists of xylem and phloem, which are essential for the transport of water, nutrients, and sugars throughout the plant.
• Xylem is responsible for the upward movement of water and minerals from roots to the rest of the plant.
• Phloem transports the products of photosynthesis, such as sugars, from the leaves to other parts of the plant.
• The development of vascular tissue has allowed plants to grow taller and larger, thereby outcompeting other plants for sunlight and resources.
• Vascular tissue supports the structural integrity of plants, enabling them to thrive in diverse terrestrial environments.

Additional Information

• Meristematic tissue: These are regions of actively dividing cells in plants, responsible for growth in length and girth.
• Connective tissue: Found in animals, this tissue supports, binds, and protects other tissues and organs.
• Epithelial tissue: Also found in animals, it forms the covering or lining of all internal and external body surfaces.
• Tracheophytes: These are vascular plants that have developed specialized vascular tissues (xylem and phloem) for conducting water and nutrients.
• Primary and secondary growth: Primary growth increases the length of the plant, while secondary growth increases the girth, both facilitated by vascular tissue.

The correct answer is 4) Variation.

Key Points

• Variation is essential for the process of natural selection to occur, which leads to evolution.
• It provides the genetic diversity necessary for populations to adapt to changing environments.
• Organisms with variations that provide a survival advantage are more likely to reproduce and pass on those beneficial traits.
• Variation can occur due to mutations, gene flow, and sexual reproduction, all of which contribute to the genetic pool of a species.

Additional Information

• Mutation: A change in the DNA sequence that can lead to new traits in an organism.
• Gene Flow: The transfer of genetic variation from one population to another, increasing genetic diversity.
• Natural Selection: The process by which organisms better adapted to their environment tend to survive and produce more offspring.
• Sexual Reproduction: A mode of reproduction that combines genetic material from two parents, leading to offspring with genetic variation.
• Genetic Drift: Random changes in the frequency of alleles in a population, which can lead to significant genetic differences over time.

Statements:

All belts are watches.

No belt is a tie.

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

Conclusions:

(I) No watch is a tie. → Not Follow (There is no direct relation between watch and tie.)

(II) At least some watches are belts. → Follow (As all belts are watches then at least some watches are belts.)

∴ Here, Only conclusion II follows

Hence, "Option 3" is the correct answer.

Logic followed here is, 

Logic : Alternate number increased by 23.

Hence the correct answer is "Option 2"

The correct answer is law of inertia.

Key Points

• The first law of motion is also known as the law of inertia.
• It states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
• This law was formulated by Sir Isaac Newton and is one of the fundamental principles of classical mechanics.
• The law of inertia explains the behavior of objects in the absence of external forces.

Additional Information

• Linear Momentum:
• Linear momentum is the product of the mass and velocity of an object.
• It is a vector quantity, having both magnitude and direction.
• Conservation of linear momentum is a fundamental principle in physics.
• Torque:
• Torque is a measure of the force that can cause an object to rotate about an axis.
• It is calculated as the product of force and the distance from the point of rotation.
• It is also a vector quantity.
• Angular Momentum:
• Angular momentum is the rotational equivalent of linear momentum.
• It depends on the object's moment of inertia and its angular velocity.
• Like linear momentum, angular momentum is also conserved in a closed system.
• Newton's Laws of Motion:
• Newton's first law is the law of inertia.
• Newton's second law states that force is equal to mass times acceleration (F=ma).
• Newton's third law states that for every action, there is an equal and opposite reaction.

Shortcut Trick

Ratio of students in Section A and Section B = 18 : 22 = 9 : 11.

Using weighted average formula: Average = (9 × 40 + 11 × 35) ÷ (9 + 11)

Average = (360 + 385) ÷ 20 = 745 ÷ 20 = 37.25 kg.

∴ The correct answer is 37.25 kg.

Alternate Method

Given:

Students in Section A (n₁) = 18, Average weight (w₁) = 40 kg

Students in Section B (n₂) = 22, Average weight (w₂) = 35 kg

Formula Used:

Combined Average = (n₁w₁ + n₂w₂) ÷ (n₁ + n₂)

Calculations:

⇒ Total weight of Section A = 18 × 40 = 720 kg

⇒ Total weight of Section B = 22 × 35 = 770 kg

⇒ Total weight of the whole class = 720 + 770 = 1490 kg

⇒ Total number of students = 18 + 22 = 40

⇒ Average weight of the whole class = 1490 ÷ 40 = 37.25 kg

∴ The correct answer is 37.25 kg.

Additional Information

Weighted Average Concept

When groups of different sizes are combined, the overall average is the sum of all individual values divided by the total count: A_avg = (Σn_ix_i) ÷ Σn_i.

Alligation Method

The ratio of the quantities is inversely proportional to the difference between their averages and the mean average: (n₁/n₂) = (A₂ − A_m) ÷ (A_m − A₁).

The correct answer is 4) 3 : 1.

Key Points

• Chlorine has two stable isotopes: Chlorine-35 and Chlorine-37.
• The natural abundance of Chlorine-35 is approximately 75.77%.
• The natural abundance of Chlorine-37 is approximately 24.23%.
• This results in a ratio of approximately 3:1 for Chlorine-35 to Chlorine-37 in nature.
• This ratio affects the atomic mass of chlorine, which is averaged to around 35.5 u.

Additional Information

• Isotopes:
• Atoms of the same element with different numbers of neutrons.
• Isotopes have the same atomic number but different mass numbers.
• Atomic Mass:
• The weighted average mass of the atoms in a naturally occurring element.
• Calculated based on the relative abundance of each isotope.
• Mass Spectrometry:
• A technique used to measure the mass-to-charge ratio of ions.
• Helps in determining the isotopic composition of an element.
• Chlorine:
• A halogen element with atomic number 17.
• Commonly found in nature as part of compounds, such as sodium chloride (table salt).

The correct answer is Formation of soap scum due to the reaction with calcium and magnesium ions..

Key Points

• Hard water contains high concentrations of calcium and magnesium ions.
• When soap is used in hard water, it reacts with these ions to form an insoluble precipitate called soap scum.
• This soap scum reduces the effectiveness of soap, making it less efficient for cleaning purposes.
• Soap scum can accumulate on surfaces, making them difficult to clean and potentially causing damage over time.
• The formation of soap scum is a common issue in areas with hard water and requires special detergents or water softeners to mitigate.

Additional Information

• Hard Water:
• Water that has high mineral content, primarily calcium and magnesium.
• Hard water can cause scaling in pipes, boilers, and other appliances.
• Water Softening:
• Process of removing calcium and magnesium ions from water.
• Common methods include ion-exchange resins and the use of water softening agents.
• Soap:
• Made from the reaction of fats and oils with an alkali, such as sodium hydroxide.
• Effective in soft water but forms scum in hard water.
• Detergents:
• Synthetic cleaning agents that are more effective in hard water compared to traditional soaps.
• Contain compounds that do not form scum with calcium and magnesium ions.

The correct answer is +10D.

Key Points

• Work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force.
• The formula for work done by a constant force is given by W = F × D, where W is the work, F is the force, and D is the displacement.
• Given that the force (F) is 10 N and the displacement (D) is in the direction of the force, the work done can be calculated as W = 10 × D.
• Therefore, the work done by a constant force of 10 N on an object that is displaced by D meters in the direction of the force is +10D Joules.

Additional Information

• Joule (J):
• The unit of work in the International System of Units (SI) is the Joule (J).
• 1 Joule is defined as the amount of work done when a force of 1 Newton displaces an object by 1 meter in the direction of the force.
• Force (N):
• The unit of force in the International System of Units (SI) is the Newton (N).
• 1 Newton is defined as the force required to accelerate a mass of 1 kilogram at a rate of 1 meter per second squared.
• Displacement:
• Displacement is a vector quantity that refers to the change in position of an object.
• It is measured in meters (m) in the International System of Units (SI).
• Work-Energy Principle:
• The work done on an object is equal to the change in its kinetic energy.
• This principle is fundamental in understanding the relationship between force, work, and energy.

Logic followed here is,

So, code for We is Hi.

Hence the correct answer is Option 1.

The correct answer is Centrifugation technique.

Key Points

• Centrifugation is a technique used to separate colloidal particles based on their size, shape, and density.
• During centrifugation, a mixture is spun at high speeds, causing denser particles to move outward to the bottom of the tube while lighter particles remain closer to the center.
• This method is particularly effective in separating particles that are too small to be filtered out by conventional filtration methods.
• Centrifugation is widely used in laboratories and industrial processes to isolate and purify biological molecules, cells, and sub-cellular components.

Additional Information

• Sublimation: A technique where a solid changes directly into a gas without passing through the liquid phase, typically used for purifying substances.
• Filtration: A method that separates solid particles from liquids or gases using a filter medium that allows the fluid to pass through but not the solid particles.
• Recrystallization: A technique used to purify chemicals by dissolving both impurities and a compound in an appropriate solvent, then allowing the compound to crystallize out.
• Colloids: These are mixtures where very small particles of one substance are evenly distributed throughout another without settling out or separating.
• Applications of Centrifugation: It is used in various fields including biochemistry, molecular biology, and medicine, for purposes like blood separation, DNA/RNA extraction, and purification of proteins.

The correct answer is Power is inversely proportional to focal length.

Key Points

• Power (P) of a lens is defined as the reciprocal of its focal length (f) in meters.
• The formula for calculating the power of a lens is P = 1/f, where P is in diopters (D) and f is in meters.
• As the focal length of a lens increases, the power of the lens decreases, and vice versa.
• This relationship signifies that a lens with a shorter focal length has higher power, enabling it to bend light more sharply.

Additional Information

• Diopters (D): The unit of measurement for the power of a lens, where one diopter is equivalent to a lens with a focal length of one meter.
• Convex Lens: A lens that converges light rays to a focal point, commonly used in magnifying glasses and corrective lenses for hyperopia (farsightedness).
• Concave Lens: A lens that diverges light rays away from a focal point, commonly used in corrective lenses for myopia (nearsightedness).
• Lens Formula: The relationship between the object distance (u), image distance (v), and focal length (f) of a lens, given by 1/f = 1/v + 1/u.
• Optical Power: A measure of how strongly a lens can converge or diverge light. Higher optical power indicates a stronger lens.

Shortcut Trick

Ratio of Length and Breadth = 5 : 3

Sum of ratio parts = 5 + 3 = 8 units

Semi-perimeter (L + B) = 112 ÷ 2 = 56 cm

1 unit = 56 ÷ 8 = 7 cm

Length = 5 × 7 = 35 cm, Breadth = 3 × 7 = 21 cm

Area = 35 × 21 = 735 cm²

∴ The correct answer is 735 cm².

Alternate Method

Given: Ratio of sides = 5 : 3, Perimeter = 112 cm

Formula Used: Perimeter = 2(Length + Breadth); Area = Length × Breadth

⇒ Let Length (L) = 5x and Breadth (B) = 3x

⇒ Perimeter = 2(5x + 3x) = 112

⇒ 2(8x) = 112

⇒ 16x = 112

⇒ x = 112 ÷ 16 = 7

⇒ Length = 5 × 7 = 35 cm

⇒ Breadth = 3 × 7 = 21 cm

⇒ Area = 35 × 21 = 735 cm²

∴ The correct answer is 735 cm².

Additional Information

Properties of Rectangle

A rectangle is a quadrilateral where opposite sides are equal and all angles are 90°. Diagonal d = √(L² + B²).

Perimeter and Area Relationship

For a given perimeter, the area of a rectangle is maximum when it is a square (L = B).

Diagonal of Rectangle

The diagonals of a rectangle are equal in length and bisect each other.

The correct answer is Regeneration is not the same as reproduction..

Key Points

• Regeneration is a biological process where organisms replace or restore lost or damaged tissues, organs, or body parts.
• While some organisms can regenerate parts of their bodies, this process does not always result in the creation of a new organism.
• Regeneration is distinct from reproduction, which involves the creation of a new organism from one or two parent organisms.
• Examples of organisms with high regenerative capabilities include starfish, planarians, and certain species of lizards.

Additional Information

• Planarians: Flatworms known for their remarkable regenerative abilities, capable of regrowing entire bodies from small segments.
• Autotomy: A defense mechanism in some animals, such as lizards, where they shed a body part (e.g., tail) to escape predators, which can later regenerate.
• Stem Cells: Undifferentiated cells that play a critical role in the regeneration process by differentiating into various cell types to replace damaged tissues.
• Asexual Reproduction: A mode of reproduction that does not involve the fusion of gametes, resulting in offspring genetically identical to the parent, distinct from regeneration.
• Epimorphosis: A type of regeneration where cells proliferate at the site of injury and differentiate to form new tissues, commonly seen in amphibians.

Given Equation: 15 × 5 - 56 + 28 ÷ 3 = ?

BODMAS Rule:

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

⇒ 15 - 5 × 56 ÷ 28 + 3

⇒ 15 - 5 × 2 + 3

⇒ 15 - 10 + 3 = 8

Hence, the correct option is "Option 2".

The correct answer is Option 1.

Key Points

• Thomson's model proposed that the atom is electrically neutral overall, with the positive and negative charges being equal in magnitude.
• The model suggested that the positive charge is uniformly spread throughout the atom, similar to the red edible part of a watermelon.
• Electrons were thought to be embedded within this positively charged sphere, akin to seeds in a watermelon.
• Thomson's model did not account for the nucleus; it assumed the atom was a single continuous positively charged entity.

Additional Information

• J.J. Thomson: An English physicist who is credited with the discovery of the electron in 1897, which led to the development of his atomic model.
• Plum Pudding Model: Thomson's atomic model is also known as the "plum pudding model" where electrons are like plums embedded in a positively charged "pudding."
• Limitations of Thomson's Model: The model was later refuted by Rutherford's gold foil experiment, which demonstrated the existence of a small, dense nucleus.
• Rutherford's Model: Introduced in 1911, it proposed that the atom consists of a dense nucleus surrounded by electrons, which provided a more accurate representation of atomic structure.
• Electron: A subatomic particle with a negative charge, discovered by J.J. Thomson, fundamental to the structure of atoms and chemistry.

Given:

Pattern: X : 108 : 9 : Y

Calculations:

Let's check each option:

Option 1: X = 12, Y = 81

If X = 12, then 12 : 108. 108 / 12 = 9.

So, the operation is multiply by 9.

If Y = 81, then 9 : 81.

81 / 9 = 9.

So, the operation is multiply by 9.

⇒ 12 × 9 = 108 and 9 × 9 = 81.

This pattern is correct.

Option 2: X = 14, Y = 81

If X = 14, then 14 : 108.

108 / 14 = 7.71 (not a whole number).

This option is incorrect.

Option 3: X = 16, Y = 145

If X = 16, then 16 : 108.

108 / 16 = 6.75 (not a whole number).

This option is incorrect.

Option 4: X = 12, Y = 126

If X = 12, then 12 : 108.

108 / 12 = 9.

So, the operation is multiply by 9.

If Y = 126, then 9 : 126.

126 / 9 = 14 (not 9).

This option is incorrect.

∴ The correct answer is option 1: X = 12, Y = 81.

Hence the correct answer is Option 1.

The correct answer is option 2.

Key Points

• The size of the particles of a colloid is typically between 1 and 1000 nanometers, which is not considered very large.
• The particles in a colloid are small enough to remain suspended and not settle out rapidly, which distinguishes them from those in a suspension.
• Colloidal particles are too small to be seen with the naked eye but large enough to scatter light, a phenomenon known as the Tyndall effect.
• Colloids are heterogeneous mixtures where the dispersed phase is distributed in the dispersion medium.

Additional Information

• Dispersed Phase: The phase that is dispersed or distributed in the form of very small particles in a dispersion medium within a colloidal solution.
• Dispersion Medium: The medium in which the colloidal particles are dispersed. It can be a solid, liquid, or gas.
• Tyndall Effect: The scattering of light by colloidal particles, making the path of the light beam visible. This is a key characteristic of colloidal solutions.
• Brownian Motion: The random, erratic movement of colloidal particles in a dispersion medium, resulting from collisions with molecules of the dispersion medium.
• Classification of Colloids: Colloids can be classified based on the physical state of the dispersed phase and dispersion medium (e.g., sol, gel, foam, emulsion, aerosol).

The correct answer is Gangue.

Key Points

• Gangue refers to the commercially worthless material that surrounds or is closely mixed with a wanted mineral in an ore deposit.
• During the extraction of minerals from ores, the gangue is separated from the ore minerals.
• It is a byproduct of the mining process and is typically discarded after the valuable minerals are extracted.
• The separation of gangue from ore is a crucial step in mineral processing to increase the purity of the extracted materials.

Additional Information

• Roasting:
• Roasting involves heating ore in the presence of excess air or oxygen to convert sulfide ores into oxides, releasing sulfur dioxide gas in the process.
• It is a step in the pyrometallurgical process used to extract metals from ores.
• Anode Mud:
• Anode mud is the residue left at the anode in an electrolytic cell during the purification of metals.
• It usually contains precious metals like gold and silver, which can be recovered through further processing.
• Calcination:
• Calcination is the process of heating a substance to a high temperature in the absence or limited supply of air or oxygen.
• This process is used to remove volatile substances and moisture from ores, making the ores easier to process.
• Mineral Processing:
• Mineral processing involves various techniques to separate valuable minerals from the gangue, such as crushing, grinding, magnetic separation, and froth flotation.
• It aims to produce a concentrated material rich in valuable minerals and a discardable waste material (gangue).

The correct answer is 3) October.

Key Points

• The Sahitya Akademi organised a two-day Birth Centenary Symposium in October 2024.
• The symposium was dedicated to 'Prabhjot Kaur and Colonel Narinder Pal Singh'.
• It marked the 100^th birth anniversary of both distinguished personalities.
• The event featured discussions, readings, and tributes to their contributions to literature and society.

Additional Information

• Sahitya Akademi:
• Established in 1954, it is India's National Academy of Letters.
• It promotes literature in 24 Indian languages, including English.
• Prabhjot Kaur:
• A renowned Punjabi writer known for her contributions to Punjabi literature.
• She authored several acclaimed novels, short stories, and poems.
• Colonel Narinder Pal Singh:
• A respected figure in Punjabi literature and military service.
• His works often reflect themes of patriotism and valor.
• Birth Centenary Celebrations:
• Such events commemorate the 100^th birth anniversary of notable individuals.
• They often include symposiums, exhibitions, and publication releases.

The correct answer is at the principal focus.

Key Points

• When parallel rays of light fall on a concave mirror, they reflect and meet at a single point known as the principal focus.
• This phenomenon occurs due to the converging nature of a concave mirror.
• The distance from the mirror's surface to this focal point is called the focal length.
• The principal focus is located on the principal axis of the mirror, halfway between the mirror's surface and its center of curvature.
• This property of concave mirrors makes them useful in applications such as telescopes, headlights, and solar furnaces.

Additional Information

• Principal Axis
• The principal axis is an imaginary line that passes through the center of curvature and the pole of a mirror.
• It is the line along which light rays parallel to it will converge or diverge after reflection.
• Focal Length
• Focal length is the distance between the pole of the mirror and the principal focus.
• It is denoted by the letter 'f' and is a crucial parameter in determining the mirror's reflective properties.
• Center of Curvature
• The center of curvature is the center of the sphere from which the concave mirror is a part.
• The distance from the center of curvature to the mirror's surface is called the radius of curvature.
• Reflection of Light
• Reflection is the phenomenon where light bounces off a surface.
• In concave mirrors, reflection follows the laws of reflection, where the angle of incidence equals the angle of reflection.

The correct answer is Vas deferens and scrotum.

Key Points

• Vas deferens is a duct that transports sperm from the testicles to the urethra, facilitating ejaculation.
• Scrotum is a sac that houses the testicles and regulates their temperature for optimal sperm production.
• The male reproductive system includes the testes, epididymis, vas deferens, ejaculatory ducts, urethra, and penis.
• The testes produce sperm and testosterone, the primary male sex hormone.
• The penis serves as the conduit for urine and semen to exit the body.

Additional Information

• Testosterone: This hormone is crucial for the development of male secondary sexual characteristics such as muscle mass, body hair, and voice deepening.
• Spermatogenesis: The process of sperm production that occurs within the seminiferous tubules of the testes.
• Prostate gland: Produces a fluid that nourishes and transports sperm during ejaculation.
• Seminal vesicles: These glands secrete a significant portion of the fluid that becomes part of semen.
• Erectile tissue: Tissue within the penis that becomes engorged with blood, leading to an erection necessary for sexual intercourse.

Shortcut Trick

Let Total Work (tank capacity) = LCM(60, 40) = 120 units.

Efficiency of A = 120 ÷ 60 = 2 units/min; Efficiency of B = 120 ÷ 40 = 3 units/min.

In first half-time (T/2), only B works → Work = 3 × (T/2).

In second half-time (T/2), A and B work together → Work = (2 + 3) × (T/2) = 5 × (T/2).

Total work = 1.5T + 2.5T = 4T = 120 ⇒ T = 30 minutes.

∴ The correct answer is 30 min.

Alternate Method

Given: Total time taken is T minutes.

Formula: Work = Efficiency × Time

⇒ Work done by B in first half = 3 × (T/2)

⇒ Work done by A + B in second half = (2 + 3) × (T/2) = 5 × (T/2)

⇒ Total Work = (3T/2) + (5T/2) = 8T/2 = 4T

⇒ 4T = 120

⇒ T = 120 ÷ 4

⇒ T = 30 minutes

∴ The correct answer is 30 min.

Additional Information

Pipes and Cisterns Efficiency

Efficiency is inversely proportional to time. If a pipe fills a tank in 'x' hours, its 1-hour work is 1/x.

Combined Work Formula

If pipe A fills in 'x' and pipe B fills in 'y', time together is (x × y) ÷ (x + y).

Inlet and Outlet Pipes

Inlet pipe efficiency is taken as positive (+), while outlet (leakage) pipe efficiency is taken as negative (−).

The correct answer is 1/3.

Key Points

• The magnification (m) of a lens is the ratio of the height of the image (h') to the height of the object (h), given by m = h'/h.
• In this case, the height of the image (h') is 10 cm and the height of the object (h) is 30 cm.
• Substituting the given values, m = 10 cm / 30 cm = 1/3.
• Since a concave lens always forms a virtual and erect image, the magnification is positive. Thus, m = 1/3 or approximately 0.33.

Additional Information

• Concave Lens:
• A concave lens is a diverging lens that spreads out light rays that have been refracted through it.
• It is thinner at the center than at the edges.
• Used in devices like peepholes, eyeglasses for nearsightedness, and certain types of cameras.
• Lens Formula:
• The lens formula relates the object distance (u), image distance (v), and the focal length (f) of the lens: 1/f = 1/v - 1/u.
• This formula is crucial for calculating the position and nature of the image formed by a lens.
• Magnification:
• Magnification (m) is the ratio of the height of the image to the height of the object.
• It can also be expressed as the ratio of the image distance to the object distance (m = v/u for lenses).
• Sign Conventions:
• For lenses, distances measured in the direction of the incident light are positive, and those against are negative.
• Heights measured above the principal axis are positive, and those below are negative.

The correct answer is Option 3.

Key Points

• Magnetic field lines are not parallel and equidistant when the field strength is zero. Instead, they are absent in regions where the magnetic field is zero.
• Magnetic field lines form closed loops, meaning they do not start or end anywhere, illustrating that magnetic monopoles do not exist.
• The relative strength of the magnetic field is indicated by the degree of closeness of the field lines; closer lines represent a stronger magnetic field.
• The direction of the magnetic field at any point corresponds to the direction in which the north pole of a magnetic compass needle points.

Additional Information

• Magnetic Field:
• A magnetic field is generated by moving electric charges and intrinsic magnetic moments of elementary particles.
• The Earth itself acts like a giant magnet with a magnetic field that affects compasses and the auroras.
• Magnetic Flux:
• Magnetic flux is the measure of the quantity of magnetism, taking into account the strength and the extent of a magnetic field.
• It is measured in Weber (Wb).
• Magnetic Monopoles:
• In theoretical physics, a magnetic monopole is a hypothetical particle that is an isolated magnet with only one magnetic pole.
• However, no magnetic monopoles have been observed in nature.
• Electromagnetism:
• Electromagnetism is the branch of physics that involves the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.
• It is one of the four fundamental forces of nature, alongside gravitation, weak interaction, and strong interaction.

Logic followed here is,

Option 1) RM-PT 

Option 2) LG-IM 

Option 2 does not follow the same logic.

Option 3) VQ-TX 

Option 4) ID-GK 

Hence the correct answer is "Option 2"

The correct answer is 2 N.

Key Points

• Newton’s Second Law of Motion:
• States that the force acting on an object is equal to the mass of the object multiplied by its acceleration, represented as F = m × a.
• This principle explains how the velocity of an object changes when subjected to an external force.
• The mass (m) of the body is given as 2 kg in the question.
• The velocity of the body changes from 8 m/s to 12 m/s.
• The change in velocity (Δv) can be calculated as: Δv = final velocity - initial velocity = 12 m/s - 8 m/s = 4 m/s.
• The time (t) over which this change occurs is given as 4 seconds.
• Using the formula for acceleration (a = Δv/t): a = 4 m/s ÷ 4 s = 1 m/s².
• To calculate the magnitude of the force, apply the formula F = m × a:
• Here, m = 2 kg and a = 1 m/s².
• Therefore, F = 2 kg × 1 m/s² = 2 N.
• Hence, the correct answer is Option 1: 2 N.

Additional Information

• Newton’s Second Law:
• It establishes the relationship between an object’s mass, acceleration, and the force applied to it.
• The unit of force in the SI system is the Newton (N), defined as the force required to accelerate a 1 kg mass by 1 m/s².
• This law is often used to calculate the acceleration of objects in motion when a force is applied.
• Acceleration:
• Defined as the rate of change of velocity with respect to time.
• It is a vector quantity, meaning it has both magnitude and direction.
• Acceleration is calculated using the formula: a = Δv/t, where Δv is the change in velocity and t is the time taken.
• Force:
• Force is a vector quantity that can change the motion of an object.
• It is calculated using the formula: F = m × a, where m is the mass and a is the acceleration.
• Velocity:
• Velocity is a vector quantity that represents the rate of change of an object’s position.
• It includes both speed and direction, distinguishing it from scalar quantities like speed.

Important Points

• SI Units:
• The Newton (N) is the standard unit of force in physics.
• One Newton is equivalent to 1 kg·m/s².
• Application of Newton’s Laws:
• Used widely in engineering, mechanics, and physics to understand the motion of objects.
• Examples include calculating the forces acting on vehicles, spacecraft, and falling objects.

The correct answer is b, d and e.

Key Points

• Plastids are present only in plant cells and include chloroplasts, which are crucial for photosynthesis.
• Vacuoles in plant cells are large central structures that help maintain cell rigidity and store nutrients and waste products.
• The cell wall is a rigid outer layer found only in plant cells, providing structure and protection. It is primarily composed of cellulose.
• Animal cells do not have plastids, large central vacuoles, or cell walls; these structures are unique to plant cells.

Additional Information

• Mitochondria: Present in both plant and animal cells, mitochondria are the powerhouse of the cell, generating ATP through respiration.
• Golgi apparatus: Found in both plant and animal cells, it processes and packages proteins and lipids.
• Lysosomes: These are present primarily in animal cells and contain digestive enzymes to break down waste materials and cellular debris.
• Chloroplasts: A type of plastid found in plant cells containing chlorophyll, essential for the process of photosynthesis.
• Cellulose: The primary component of the plant cell wall, providing structural support and protection to the plant cell.

The correct answer is Sublimation.

Key Points

• Sublimation is the process where a substance changes directly from the solid phase to the gaseous phase without passing through the liquid phase.
• This phenomenon occurs when the molecules of a solid gain enough energy to transition into the gas phase directly.
• Common examples of sublimation include dry ice (solid carbon dioxide) and iodine crystals.
• Sublimation is utilized in various industrial processes such as freeze-drying and purifying compounds.

Additional Information

• Fusion: The process where a substance changes from the solid state to the liquid state, also known as melting.
• Deposition: The reverse of sublimation, where a gas changes directly into a solid without passing through the liquid phase.
• Solidification: The process of a liquid becoming solid, commonly known as freezing.
• Evaporation: The process where a liquid changes to a gas at temperatures below its boiling point.
• Phase Transition: The transformation of a substance from one state of matter to another, such as from solid to liquid, liquid to gas, etc.

Shortcut Trick

Total Work (LCM of 9, 18, 12) = 36 units.

Efficiencies: P = 4, Q = 2, R = 3. Total for 1 cycle (3 hours) = 4 + 2 + 3 = 9 units.

Number of cycles = 36 ÷ 9 = 4 cycles.

Total time = 4 cycles × 3 hours/cycle = 12 hours.

∴ The correct answer is 12 hr.

Alternate Method

Step-by-step calculation:

⇒ Work done in Hour 1 (P) = 4 units

⇒ Work done in Hour 2 (Q) = 2 units

⇒ Work done in Hour 3 (R) = 3 units

⇒ Total work in 1 cycle (3 hours) = 4 + 2 + 3 = 9 units

⇒ Total time required = (Total Work ÷ Work per cycle) × Time per cycle

⇒ Total time = (36 ÷ 9) × 3

⇒ Total time = 4 × 3 = 12 hours

∴ The correct answer is 12 hr.

Additional Information

Alternate Work Pattern

In alternate work problems, calculate the work done in one complete cycle first. Total time = (Full cycles × items in cycle) + (remaining work ÷ next person's efficiency).

Efficiency and Time

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

LCM Method

The Least Common Multiple (LCM) of the individual times is assumed as the Total Work to simplify calculations into integers.

The correct answer is thermal decomposition.

Key Points

• Thermal decomposition is a chemical reaction where a compound breaks down into two or more products when heated.
• Limestone (CaCO₃) undergoes thermal decomposition to produce calcium oxide (CaO) and carbon dioxide (CO₂).
• This reaction requires a significant amount of heat and is typically performed in a lime kiln.
• The thermal decomposition of limestone is an endothermic reaction, meaning it absorbs heat from the surroundings.

Additional Information

• Calcium Carbonate (CaCO₃):
• A common substance found in rocks, also the main component of shells of marine organisms, snails, and eggshells.
• Used extensively in the construction industry and in the production of lime and cement.
• Calcium Oxide (CaO):
• Also known as quicklime, used in the manufacture of cement, steel, and glass.
• Highly reactive with water, forming calcium hydroxide (slaked lime).
• Endothermic Reaction:
• A reaction that absorbs heat from its surroundings.
• Characteristic of many decomposition reactions, requiring continuous heat supply.
• Lime Kiln:
• A kiln used to produce quicklime by the calcination of limestone (calcium carbonate).
• Operates at a high temperature, typically around 900-1000°C.

Shortcut Trick

multiplier SP = MP × (100 − D%) ÷ 100

SP = 620 × (100 − 15) ÷ 100

SP = 620 × 85 ÷ 100 = 62 × 8.5

SP = 527

∴ The correct answer is ₹527.

Alternate Method

Given → Marked Price (MP) = ₹620, Discount Percentage (D%) = 15% Formulas: Discount = (D% ÷ 100) × MP | SP = MP − Discount

⇒ Discount Value = (15 ÷ 100) × 620 ⇒ Discount Value = 0.15 × 620 = 93 ⇒ Selling Price (SP) = 620 − 93 ⇒ Selling Price (SP) = 527

∴ The correct answer is ₹527.

Additional Information

Marked Price & Discount

The Marked Price is the price printed on the label. Discount is always calculated on the MP unless specified otherwise.

Effective Price

The Selling Price is the actual amount a customer pays after the Discount is deducted from the Marked Price.