RRB Technician Grade III Official Paper (Held On: 27 Dec, 2024 Shift 1) (Previous Year Paper)

The correct answer is Plasma.

Key Points

• Plasma has the highest kinetic energy of particles compared to other states of matter.
• In plasma, particle (ions and free electrons) move at extremely high speeds due to high temperatures, making it the most energetic state.
• Plasma is found in environments like stars (including the Sun) and lightning, where temperatures are very high.
• The formation of plasma requires energy input to ionize gases, leading to the creation of charged particles.
• Unlike gases, plasma consists of charged particles and exhibits unique properties like electrical conductivity and responsiveness to magnetic fields.

Additional Information

• Kinetic Theory of Matter:
• This theory explains that particles of matter are always in motion.
• The energy of these particles increases with temperature.
• It applies to all states of matter - solids, liquids, and gases.
• Temperature and Kinetic Energy:
• Kinetic energy of particles is directly proportional to the temperature.
• Higher temperatures mean higher kinetic energy and vice versa.
• Comparison of States of Matter:
• Solids have the least kinetic energy due to tightly packed particles.
• Liquids have more kinetic energy than solids but less than gases.
• Gases have the highest kinetic energy among the three states.
• Behavior of Gases:
• They expand to fill their container.
• They are easily compressible due to the large spaces between particles.

The correct answer is Vadodara.

Key Points

• On 28 October 2024, Prime Minister Narendra Modi and Spanish PM Pedro Sanchez jointly inaugurated the Tata Aircraft Complex in Vadodara, Gujarat.
• The Tata Aircraft Complex is India's first private facility dedicated to the construction of military aircraft.
• This facility is expected to enhance India's self-reliance in the defense sector by manufacturing key military planes domestically.
• Vadodara was chosen due to its strategic location and existing infrastructure supporting the aerospace industry.

Additional Information

• Make in India:
• Launched by PM Narendra Modi in 2014, it is an initiative to encourage companies to manufacture their products in India.
• It aims to increase the GDP growth and tax revenue by producing quality products domestically.
• Defense Industrial Corridors:
• India has established two defense industrial corridors, one in Uttar Pradesh and another in Tamil Nadu.
• These corridors aim to develop a robust defense manufacturing ecosystem in the country.
• Strategic Partnership Model:
• This model encourages Indian private firms to collaborate with foreign original equipment manufacturers (OEMs).
• It aims to boost indigenous production of defense equipment.
• Aerospace and Defense Policies:
• Several state governments have introduced policies to attract investments in the aerospace and defense sectors.
• These policies offer incentives like subsidies, tax rebates, and infrastructural support to manufacturers.

The correct answer is kg, N.

Key Points

• Mass is a fundamental property of matter that quantifies the amount of substance in an object, and its SI unit is the kilogram (kg).
• Weight is the force exerted on a body due to gravity, and its SI unit is the Newton (N).
• Weight is calculated as the product of mass and gravitational acceleration (W = mg), where g is approximately 9.81 m/s² on Earth.
• The kilogram (kg) is the base unit of mass in the International System of Units (SI).
• The Newton (N) is derived from the SI units as 1 N = 1 kg·m/s².

Additional Information

• Mass vs Weight:
• Mass is a scalar quantity and does not change with location, while weight is a vector quantity and changes with the gravitational field strength.
• Mass is measured using a balance, while weight is measured using a spring scale.
• SI Units:
• The International System of Units (SI) is the modern form of the metric system and the most widely used system of measurement.
• It includes seven base units: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).
• Gravitational Acceleration:
• Gravitational acceleration (g) varies slightly over the surface of the Earth, generally taken as 9.81 m/s².
• Weight varies slightly depending on altitude and latitude due to variations in gravitational acceleration.
• Historical Context:
• The kilogram was originally defined in 1795 as the mass of one liter of water.
• In 2019, the definition of the kilogram was redefined based on the Planck constant, making it more stable and accurate.

Shortcut Trick

Interest Percentage = (Interest ÷ Principal) × 100

Interest Percentage = (1050 ÷ 2100) × 100 = 50%

Time = Total Interest % ÷ Rate % per annum

Time = 50% ÷ 10% = 5 years

∴ The correct answer is 5 years.

Alternate Method

Given:

Principal (P) = ₹2,100

Simple Interest (SI) = ₹1,050

Rate (R) = 10% per annum

Formula Used:

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

Calculations:

⇒ 1050 = (2100 × 10 × T) ÷ 100

⇒ 1050 = 210 × T

⇒ T = 1050 ÷ 210

⇒ T = 5 years

∴ The correct answer is 5 years.

Additional Information

Simple Interest Definition

Simple interest is calculated only on the original principal amount for the entire period of the loan or investment.

Amount Formula

The total amount (A) is the sum of the principal and interest: A = P + SI or A = P(1 + RT/100).

Rate and Time Consistency

Ensure that the Rate (R) and Time (T) are in the same time units (usually years). If time is in months, divide by 12.

Given:

A = 8³ × 5⁴

B = 8⁵ × 5³

Formula used:

a^m × aⁿ = a^m+n

(a^m)ⁿ = a^mn

Calculations:

A × B = (8³ × 5⁴) × (8⁵ × 5³)

⇒ A × B = 8³⁺⁵ × 5⁴⁺³

⇒ A × B = 8⁸ × 5⁷

⇒ A × B = (2³)⁸ × 5⁷

⇒ A × B = 2^3×8 × 5⁷

⇒ A × B = 2²⁴ × 5⁷

∴ The correct answer is option (3).

Shortcut Trick

Apply Trigonometric Identities: sin² θ + cos² θ = 1 and sec² θ − tan² θ = 1.

Substitute values: 1 − 1 + cot θ sin θ + cos θ.

Since cot θ sin θ = (cos θ / sin θ) × sin θ = cos θ.

Expression becomes: 0 + cos θ + cos θ = 2 cos θ.

∴ The correct answer is 2 cos θ.

Alternate Method

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

Formulas Used:

1. Pythagorean Identity: sin² θ + cos² θ = 1
2. Secant Identity: sec² θ − tan² θ = 1
3. Quotient Identity: cot θ = cos θ / sin θ

Calculations:

⇒ [sin² θ + cos² θ] − [sec² θ − tan² θ] + [(cos θ / sin θ) × sin θ] + cos θ

⇒ 1 − 1 + cos θ + cos θ

⇒ 0 + 2 cos θ

⇒ 2 cos θ

∴ The correct answer is 2 cos θ.

Additional Information

Trigonometric Identities

Fundamental relations like cosec² θ − cot² θ = 1 are essential for simplifying complex trigonometric expressions.

Reciprocal Relations

Always remember that tan θ × cot θ = 1 and sin θ × cosec θ = 1 for quick cancellations.

Substitution Method

If stuck, substitute a standard value like θ = 45° to check options, provided the terms remain defined.

Shortcut Trick

Let the cost of production be CP.

Successive multipliers: 1.10 (10% gain), 1.15 (15% gain), and 1.25 (25% gain).

CP × 110/100 × 115/100 × 125/100 = 1265

CP × 11/10 × 23/20 × 5/4 = 1265

CP = (1265 × 10 × 20 × 4) ÷ (11 × 23 × 5) = 800

∴ The correct answer is ₹800.00.

Alternate Method

Given: Retail Price = ₹1,265, Manufacturer profit = 10%, Wholesale profit = 15%, Retailer profit = 25%.

Formula: Final Price = Initial Price × (100 + P₁)/100 × (100 + P₂)/100 × (100 + P₃)/100

⇒ Let CP be x.

⇒ Price after Manufacturer = x × (110/100) = 1.1x

⇒ Price after Wholesaler = 1.1x × (115/100) = 1.265x

⇒ Price after Retailer = 1.265x × (125/100) = 1.58125x

⇒ 1.58125x = 1265

⇒ x = 1265 ÷ 1.58125 = 800

∴ The correct answer is ₹800.00.

Additional Information

Chain of Profit

When goods pass through multiple hands, the Selling Price of one becomes the Cost Price for the next. The overall multiplier is the product of individual profit multipliers.

Effective Profit Percentage

To find the total profit percent over the initial cost, use the successive formula for two stages: a + b + (a × b)/100.

The logic followed here is:

Logic: 3rd number - 2nd number = 1st number.

For, (45, 96, 141)

⇒ 141 - 96 = 45

For, (12, 16, 28)

⇒ 28 - 16 = 12

Let's check options one by one.

Option 1) (10, 7, 18)

⇒ 18 - 7 = 11 ≠ 10.

Here, doesn't follow the pattern 

Option 2) (16, 20, 36)

⇒ 36 - 20 = 16

Here, follow the pattern 

Option 3) (13, 15, 30)

⇒ 30 - 15 = 15 ≠ 13

Here, doesn't follow the pattern 

Option 4) (14, 17, 32)

⇒ 32 - 17 = 14 ≠ 15

Here, doesn't follow the pattern 

Hence. the correct answer is "Option 2".

The correct answer is v/u.

Key Points

• Magnification (M) produced by a lens is defined as the ratio of the image distance (v) to the object distance (u).
• The formula for magnification is given by M = v/u, where v is the distance from the lens to the image, and u is the distance from the lens to the object.
• This relationship holds true for both convex and concave lenses.
• Magnification can also be expressed in terms of the heights of the image (h') and the object (h), M = h'/h.

Additional Information

• Lens Formula:
• The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens: 1/f = 1/v - 1/u.
• This formula is applicable to both convex and concave lenses.
• Types of Lenses:
• Convex Lens: Converging lens that brings parallel rays of light to a focus.
• Concave Lens: Diverging lens that spreads parallel rays of light outward.
• Real and Virtual Images:
• Real Image: Formed when light rays actually converge and can be projected on a screen; always inverted.
• Virtual Image: Formed when light rays appear to diverge from a point; cannot be projected on a screen; always upright.
• Optical Instruments:
• Microscopes and telescopes use lenses to magnify objects and provide a closer view.
• These instruments utilize the principles of magnification and lens formulas.

The logic followed here is:

Option 1) CYU

Option 2) FOZ

Option 3) JFB

Option 4) TPL

Hence, the correct answer is "Option 2".

Shortcut Trick

Net percentage change formula = a + b + (a × b)/100

Here, a = −40% (decrease) and b = +50% (increase).

Net change = −40 + 50 + [(−40 × 50)/100] = 10 − 20 = −10%.

Negative sign indicates a loss or decrease.

∴ The correct answer is 10%.

Alternate Method

Let the Initial Salary be ₹100.

⇒ Salary after 40% decrease = 100 − 40% of 100 = 100 − 40 = ₹60.

⇒ Salary after 50% increase = 60 + 50% of 60 = 60 + 30 = ₹90.

⇒ Total Loss = Initial Salary − Final Salary = 100 − 90 = 10.

⇒ Loss Percentage = (10 / 100) × 100 = 10%.

∴ The correct answer is 10%.

Additional Information

Successive Percentage Change

When a value is changed by x% and then by y%, the net effect is [x + y + (xy/100)]%. Use positive for increase and negative for decrease.

Fractional Equivalent Method

A 40% decrease is a multiplier of 3/5, and a 50% increase is a multiplier of 3/2. Net multiplier = (3/5) × (3/2) = 9/10, representing a 1/10 or 10% loss.

Shortcut Trick

Let the two numbers be a and b.

Using the options, we can check which pair satisfies both conditions: sum = 35 and LCM = 306.

For option (3) with values 17 and 18:

Sum = 17 + 18 = 35

Since 17 is a prime number, LCM(17, 18) = 17 × 18 = 306. Both conditions are satisfied.

∴ The correct answer is 17, 18.

Alternate Method

Given:

Sum of two numbers (a + b) = 35

LCM of two numbers = 306

Formula Used:

For two co-prime numbers (or numbers with HCF = 1), their product is equal to their LCM.

The quadratic equation with roots a and b is given by: x² − (a + b)x + ab = 0

Calculations:

Let the HCF of the two numbers be 1. Then their product ab = LCM = 306.

⇒ x² − 35x + 306 = 0

⇒ x² − 18x − 17x + 306 = 0

⇒ x(x − 18) − 17(x − 18) = 0

⇒ (x − 17)(x − 18) = 0

⇒ x = 17 or x = 18

∴ The correct answer is 17, 18.

Additional Information

Product of Two Numbers Formula

For any two positive integers a and b, Product of numbers (a × b) = HCF(a, b) × LCM(a, b).

Co-prime Numbers

If two numbers have no common factor other than 1, their HCF is 1, and their LCM is equal to their product.

The correct answer is Chlorofluorocarbons.

Key Points

• Chlorofluorocarbons (CFCs) are synthetic compounds containing carbon, chlorine, and fluorine.
• They are primarily used in refrigeration, air conditioning, and as propellants in aerosol sprays.
• CFCs are known to cause the depletion of the ozone layer in the stratosphere.
• When CFCs are released into the atmosphere, they rise to the stratosphere where they are broken down by UV radiation, releasing chlorine atoms that destroy ozone molecules.
• The use of CFCs has been largely phased out under the Montreal Protocol, an international treaty adopted in 1987 to protect the ozone layer.

Additional Information

• Ozone Layer:
• The ozone layer is a region of Earth's stratosphere that contains a high concentration of ozone (O₃) and absorbs most of the Sun's harmful ultraviolet radiation.
• It is crucial for protecting living organisms on Earth from UV radiation, which can cause skin cancer, cataracts, and other health issues.
• Montreal Protocol:
• The Montreal Protocol is an international treaty designed to protect the ozone layer by phasing out the production of numerous substances, including CFCs, that are responsible for ozone depletion.
• It was agreed upon on September 16, 1987, and has been ratified by 198 countries, making it one of the most successful environmental agreements.
• Ultraviolet (UV) Radiation:
• UV radiation is a type of electromagnetic radiation that comes from the Sun and is invisible to the human eye.
• It is divided into three types based on wavelength: UVA, UVB, and UVC, with UVB being the most harmful to the skin and DNA.
• Alternatives to CFCs:
• Hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs) are alternatives to CFCs that do not deplete the ozone layer.
• However, HFCs are potent greenhouse gases and contribute to global warming, leading to the development of more sustainable alternatives like hydrofluoroolefins (HFOs).

The correct answer is Option 2.

Key Points

• The potential difference (V) across a conductor can be calculated using Ohm's Law: V = I × R, where I is the current and R is the resistance.
• Given a current (I) of 2 A and a resistance (R) of 12 Ω, the potential difference (V) is calculated as V = 2 A × 12 Ω = 24 V.
• Option 2, which states 24 V, is the correct answer.
• Ohm's Law is fundamental in understanding the relationship between voltage, current, and resistance in electrical circuits.

Additional Information

• Ohm's Law: Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
• Resistance (R): Resistance is a measure of the opposition to the flow of current in an electrical circuit, measured in ohms (Ω).
• Current (I): Current is the rate of flow of electric charge in a circuit, measured in amperes (A).
• Voltage (V): Voltage is the electrical potential difference between two points in a circuit, measured in volts (V).
• Applications: Understanding these concepts is crucial for designing and analyzing electrical circuits used in various applications, from household wiring to complex industrial systems.

The logic followed here is:

Option 1) PVZ

Option 2) VAF

Option 3) TYD

Option 4) AFK

Hence, the correct answer is "Option 1".

The correct answer is The National Human Rights Commission (NHRC).

Key Points

• The National Human Rights Commission (NHRC) is a statutory body established under the Protection of Human Rights Act, 1993.
• NHRC's primary function is to protect and promote human rights in India.
• On 9 September 2024, NHRC emphasized the importance of safety and social audits in cities and institutions to address women's safety issues.
• These audits aim to identify gaps and issues in the current safety measures and provide insights for improvement.

Additional Information

• Women's Safety in India:
• Women's safety is a critical issue in India, with numerous initiatives and laws aimed at reducing violence and harassment.
• Despite these efforts, challenges such as social norms, lack of enforcement, and inadequate support systems persist.
• Social Audits:
• Social audits are a process of reviewing official records and determining whether reported expenditures reflect the actual money spent on the ground.
• They involve the participation of the community and aim to ensure transparency and accountability.
• National Commission for Women (NCW):
• The NCW is another statutory body, established in 1992, dedicated to protecting and promoting the interests of women.
• It reviews existing laws and suggests amendments to ensure the legal protection of women.
• Crimes Against Women:
• Crimes against women in India include domestic violence, sexual harassment, dowry deaths, and trafficking.
• Efforts to combat these crimes include stricter laws, awareness campaigns, and dedicated support services.

The correct answer is Undiminished in all directions.

Key Points

• According to Pascal's Law, fluid pressure is transmitted equally and undiminished in all directions in a confined fluid.
• This principle applies to fluids at rest, ensuring the pressure at any point in the fluid is the same in every direction.
• Pascal's Law is fundamental in hydraulic systems where pressure applied at one point is transmitted to another point using an incompressible fluid.
• Examples of applications include hydraulic presses, car brakes, and hydraulic jacks.

Additional Information

• Pascal's Law:
• Formulated by Blaise Pascal, a French mathematician, physicist, and inventor.
• States that a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
• Hydraulic Systems:
• Utilize Pascal's Law to multiply force by using fluid pressure.
• Commonly found in machinery like excavators, hydraulic presses, and braking systems.
• Pressure in Fluids:
• Pressure is defined as force per unit area and is measured in Pascals (Pa) or atmospheres (atm).
• In fluids, pressure increases with depth due to the weight of the fluid above.
• Incompressible Fluids:
• Fluids that do not change in volume when pressure is applied, ideal for hydraulic systems.
• Examples include liquids like water and oil.

The logic followed here is:

Logic: - 1 in the positional value of letters.

Hence, the correct answer is "Option 1".

The logic followed here is:

The code for "T" is 2.

Hence, the correct answer is "Option 4".

Shortcut Trick

For circular motion, distance covered in one revolution is the circumference = 2πr.

Speed v = Distance ÷ Time

v = 2πr ÷ 2

v = πr metre/sec

∴ The correct answer is πr metre/sec.

Alternate Method

Given:

Radius of the circular path = r

Time taken for one revolution (T) = 2 seconds

Formula Used:

Speed (v) = Distance ÷ Time

In a circular path, Distance = Circumference = 2×π×Radius

Calculations:

⇒ Distance = 2πr

⇒ v = (2πr) ÷ 2

⇒ v = πr metre/sec

∴ The correct answer is πr metre/sec.

Additional Information

Angular Velocity (ω)

It is the rate of change of angular displacement, ω = 2π/T. In this case, ω = 2π/2 = π rad/sec.

Relation between v and ω

Linear speed v is related to angular speed ω by the formula v = rω.

Centripetal Acceleration

For an object in uniform circular motion, acceleration a = v²/r = ω²r directed towards the center.

The correct answer is Waheeda Rehman.

Key Points

• Veteran actress Waheeda Rehman was honored with the prestigious 53rd Dadasaheb Phalke Award in 2023.
• The Dadasaheb Phalke Award is India's highest award in cinema, presented annually by the Government of India.
• Waheeda Rehman has had a prolific career in Indian cinema spanning over six decades, known for her exemplary performances in films such as "Pyaasa", "Guide", and "Khamoshi".
• She was recognized for her lifetime achievement in contributing significantly to Indian cinema.

Additional Information

• Dadasaheb Phalke Award:
• The award is named after Dhundiraj Govind Phalke, revered as the 'Father of Indian Cinema'.
• It was instituted in 1969, and the first recipient was actress Devika Rani.
• The award includes a Swarna Kamal (Golden Lotus) medallion, a shawl, and a cash prize.
• Waheeda Rehman's Career:
• She began her career with the Telugu film "Rojulu Marayi" and gained prominence in Hindi cinema with Guru Dutt's "CID".
• Waheeda has worked with iconic filmmakers like Satyajit Ray, Raj Khosla, and Yash Chopra.
• She is also a recipient of several other awards, including the Padma Bhushan and the Padma Shri.
• Significance of the Award:
• The Dadasaheb Phalke Award is a recognition of outstanding contribution to the growth and development of Indian cinema.
• It is considered one of the most coveted honors in the Indian film industry.
• Other Notable Recipients:
• Previous recipients include legends like Raj Kapoor, Lata Mangeshkar, Amitabh Bachchan, and Rajinikanth.
• The award showcases the diverse talents and contributions of individuals across different facets of Indian cinema.

The correct answer is H+ ions and OH- ions.

Key Points

• In an aqueous solution, acids release H+ ions (hydrogen ions), which are responsible for the acidic properties of the solution.
• Bases, on the other hand, release OH- ions (hydroxide ions) in an aqueous solution, which are responsible for the basic properties.
• The interaction of H+ ions from acids and OH- ions from bases leads to the formation of water (H₂O) and is termed as a neutralization reaction.
• This phenomenon is fundamental to the concept of pH, which measures the acidity or basicity of a solution.
• According to the Brønsted-Lowry theory, acids are proton donors (H+), and bases are proton acceptors (OH-).

Additional Information

• pH Scale:
• The pH scale ranges from 0 to 14, with 7 being neutral.
• A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic solution.
• The pH scale is logarithmic, meaning each whole number change represents a tenfold change in H+ ion concentration.
• Strong vs. Weak Acids and Bases:
• Strong acids and bases dissociate completely in water, releasing more H+ or OH- ions, respectively.
• Weak acids and bases partially dissociate in water, releasing fewer H+ or OH- ions.
• Neutralization Reaction:
• This is a chemical reaction in which an acid and a base react to form water and a salt.
• The general equation for a neutralization reaction is: Acid + Base → Salt + Water.
• Neutralization reactions are exothermic, releasing heat.
• Applications of Acids and Bases:
• Acids are used in various industries, including food preservation, cleaning agents, and chemical manufacturing.
• Bases find applications in soap making, cleaning products, and as antacids in medicine.

The correct answer is Iron stick.

Key Points

• In an iron stick, particles are held together by strong metallic bonds, which are among the strongest types of chemical bonds.
• Metallic bonds involve a lattice of positive metal ions surrounded by a sea of delocalized electrons, creating a strong attraction between particles.
• Iron, being a metal, has a crystalline structure that contributes to the strong binding forces between its particles.
• The strong interatomic forces in iron result in its high melting and boiling points, as well as its hardness and strength.

Additional Information

• States of Matter:
• In solid state, particles are closely packed in a fixed position, leading to a definite shape and volume.
• In liquid state, particles are close together but can move past each other, giving liquids a definite volume but no fixed shape.
• In gaseous state, particles are far apart and move freely, resulting in neither a definite shape nor a definite volume.
• Intermolecular Forces:
• Intermolecular forces are forces of attraction or repulsion between neighboring particles (atoms, molecules, or ions).
• Different types of intermolecular forces include Van der Waals forces, dipole-dipole interactions, hydrogen bonds, and ionic bonds.
• Metallic Bonding:
• Metallic bonding is a type of chemical bonding that arises from the electrostatic attractive force between conduction electrons and positively charged metal ions.
• It is responsible for many physical properties of metals such as electrical conductivity, thermal conductivity, ductility, and malleability.
• Crystalline Structure of Metals:
• Metals typically have a crystalline structure where atoms are arranged in a highly ordered and repeating pattern.This structure contributes to the strength and durability of the metal.

The correct answer is SBI.

Key Points

• State Bank of India (SBI) launched the new term deposit scheme 'Amrit Vrishti' in July 2024.
• The scheme has a tenure of 444 days, providing a unique investment opportunity for customers.
• 'Amrit Vrishti' is designed to commemorate India's 75 years of Independence.
• This scheme is part of SBI's continuous efforts to offer attractive investment options with competitive interest rates.
• The deposit scheme is available across all SBI branches and can be accessed through online banking as well.

Additional Information

• State Bank of India (SBI)
• SBI is the largest public sector bank in India, with a rich history dating back to 1806.
• It offers a wide range of banking products and services to its customers, including savings accounts, loans, and term deposits.
• SBI is known for its extensive network of branches and ATMs across the country.
• The bank continuously innovates to provide modern banking solutions and enhance customer experience.
• Term Deposit Schemes
• Term deposits are investment options where money is deposited for a fixed tenure at a predetermined interest rate.
• They offer higher interest rates compared to regular savings accounts, providing better returns on investment.
• The interest rates and tenure options for term deposits vary among banks and financial institutions.
• Term deposits are considered safe investment options as they are not affected by market fluctuations.
• Investment Options
• Diversifying investments across various financial instruments can help in managing risks effectively.
• Besides term deposits, other popular investment options include mutual funds, stocks, bonds, and real estate.
• Investors should consider factors like risk appetite, investment horizon, and financial goals while choosing investment options.
• Consulting with a financial advisor can help in making informed investment decisions.
• Online Banking
• Online banking allows customers to manage their bank accounts and conduct financial transactions via the internet.
• It provides convenience and accessibility, enabling customers to perform banking tasks anytime and anywhere.
• Features of online banking include fund transfers, bill payments, account statements, and investment services.
• Ensuring cybersecurity measures like strong passwords and two-factor authentication is crucial for safe online banking.

Shortcut Trick

Let total work be the LCM of 2.4 and 4 = 12 units.

Efficiency of (A + B) = 12 ÷ 2.4 = 5 units/hr.

Efficiency of B = 12 ÷ 4 = 3 units/hr.

Efficiency of A = 5 − 3 = 2 units/hr ⇒ Time for A = 12 ÷ 2 = 6 hours.

Total capacity = Time × Filling rate = 6 × 100 = 600 litres.

∴ The correct answer is 600 litres.

Alternate Method

Given:

Time taken by Pipe A and Pipe B together = 2.4 hours

Time taken by Pipe B alone = 4 hours

Filling rate of Pipe A = 100 litres/hour

Calculations:

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

⇒ Efficiency of Pipe A = 5 − 3 = 2 units/hour

⇒ Time taken by Pipe A alone = Total Work ÷ Efficiency of A

⇒ Time taken by Pipe A = 12 ÷ 2 = 6 hours

⇒ Capacity of the cistern = Time taken by Pipe A × Rate of Pipe A

⇒ Capacity of the cistern = 6 × 100 = 600 litres

∴ The correct answer is 600 litres.

Additional Information

Pipes & Cisterns

If a pipe can fill a tank in x hours, the part filled in 1 hour is 1/x. If another pipe empties it in y hours, the net part filled in 1 hour is (1/x − 1/y).

Work & Efficiency Relation

Time taken is inversely proportional to efficiency. Total Work = Time taken × Efficiency.

Negative Work

In pipes and cisterns, leakages or emptying pipes perform negative work, so their efficiency is strictly subtracted from the efficiency of the filling pipes.

The correct answer is Option 2.

Key Points

• Magnetic field lines inside a current-carrying solenoid are uniform and parallel to each other along the axis of the solenoid.
• The field inside the solenoid is the same at all points and is considered to be uniform in strength.
• The field lines do not intersect each other; they run parallel to the axis and are evenly spaced, indicating a uniform field.
• The statement that the field lines are "ellipsoidal and intersect with each other" is incorrect, as magnetic field lines never cross each other.

Additional Information

• Current-Carrying Solenoid:
• A solenoid is a coil of wire designed to create a magnetic field when an electric current passes through it.
• When current flows through the solenoid, it generates a magnetic field similar to that of a bar magnet, with distinct north and south poles.
• Magnetic Field Lines:
• Magnetic field lines are a visual representation of the magnetic field, showing the direction and strength of the field.
• They always form closed loops, emerging from the north pole and entering the south pole of a magnet.
• Properties of Magnetic Field Lines:
• Magnetic field lines never intersect; if they did, it would imply multiple directions for the magnetic field at a single point, which is impossible.The density of the field lines indicates the strength of the magnetic field; closer lines represent a stronger field.
• Applications of Solenoids:
• Solenoids are used in various applications including electromagnets, inductors, valves, and as components in electromechanical devices such as relays.
• They are also used in scientific experiments and magnetic resonance imaging (MRI) machines to create controlled magnetic fields.

Shortcut Trick

Empirical formula: Mode − Mean = 3 × (Median − Mean)

Also, Mode − Median = 2 × (Median − Mean)

Given Mode − Median = 24.12

Required value = Median − Mean = 24.12 ÷ 2 = 12.06

∴ The correct answer is 12.06.

Alternate Method

Given: Mode − Median = 24.12

Formula Used: Mode = 3 × Median − 2 × Mean

⇒ Mode = 3 Median − 2 Mean

⇒ Subtracting Median from both sides:

⇒ Mode − Median = (3 Median − 2 Mean) − Median

⇒ Mode − Median = 2 Median − 2 Mean

⇒ Mode − Median = 2 × (Median − Mean)

⇒ 24.12 = 2 × (Median − Mean)

⇒ Median − Mean = 24.12 ÷ 2

⇒ Median − Mean = 12.06

∴ The correct answer is 12.06.

Additional Information

Empirical Relationship

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

Symmetrical Distribution

In a perfectly symmetrical distribution, the Mean, Median, and Mode are all equal (Mean = Median = Mode).

Skewness

If Mean > Median > Mode, the data is positively skewed. If Mode > Median > Mean, the data is negatively skewed.

Given: 'R - S × T + U - V × W'

Decoding the relation of symbols.

 'R - S × T + U - V × W' → It means that R is the husband of S, S is the mother of T, T is the sister of U, U is the husband of V, V is the mother of W.

Thus, S is the Father's mother of of W.

Thus, the correct answer is "Option 2".

The correct answer is By changing the amount of water in them.

Key Points

• Plants such as the Mimosa pudica move their leaves in response to touch through changes in turgor pressure, which is the pressure of water inside the plant cells.
• Turgor pressure is controlled by the movement of water into and out of the cells in the pulvini, which are the swollen bases of the leaf stalks.
• When touched, the cells on the inner side of the pulvini lose water and shrink, causing the leaves to fold.
• This rapid movement is an example of a nastic movement, which is a non-directional response to a stimulus.

Additional Information

• Turgor Pressure: The force within the cell that pushes the plasma membrane against the cell wall, crucial for maintaining the plant's structure and function.
• Pulvini: Specialized motor organs at the base of a leaf or leaflet that facilitate movement through changes in turgor pressure.
• Nastic Movements: Non-directional responses to stimuli, such as the folding of leaves in response to touch or light changes.
• Mimosa pudica: A plant species known for its rapid leaf movements in response to touch, commonly referred to as the "sensitive plant" or "touch-me-not."
• Hydraulic Mechanism: The process involving water movement within plant cells that enables quick movements such as the folding of leaves in response to touch.

Shortcut Trick

Since the wage per hour for both male workers and female workers is the same (₹20), the average wage must also be ₹20.

Equal rates for all groups → Average = Rate.

∴ The correct answer is ₹20.

Alternate Method

Given:

Number of male workers = 25

Wage of male worker = ₹20 per hour

Number of female workers = 15

Wage of female worker = ₹20 per hour

Formula Used:

Average Wage = (Total Wages) ÷ (Total Number of Workers)

Calculations:

⇒ Total wage of males = 25 × 20 = ₹500

⇒ Total wage of females = 15 × 20 = ₹300

⇒ Total number of workers = 25 + 15 = 40

⇒ Total wages paid = 500 + 300 = ₹800

⇒ Average wage = 800 ÷ 40

⇒ Average wage = ₹20

∴ The correct answer is ₹20.

Additional Information

Weighted Average

When groups have different sizes (n₁, n₂) and different values (x₁, x₂), the average is (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Constant Value Rule

If every observation in a data set is a constant k, then the arithmetic mean of the data set is also k.

The correct answer is Thu Aug 08 2024 00:00:00 GMT+0530 (India Standard Time).

Key Points

• The Mussalman Wakf (Repeal) Bill, 2024, was introduced in the Lok Sabha on August 8, 2024.
• The bill seeks to repeal the Mussalman Wakf Act, 1923, which was an outdated legislation.
• The introduction of the bill is part of the government's initiative to remove redundant laws.
• The bill was introduced by the Ministry of Minority Affairs.

Additional Information

• Wakf: A Wakf is a permanent dedication of property by a Muslim for religious, pious, or charitable purposes as recognized by Muslim law.
• Mussalman Wakf Act, 1923: This act was enacted to provide for the better governance of Wakf properties.
• Repeal of Outdated Laws: The government periodically reviews and repeals outdated laws to streamline the legal framework.
• Ministry of Minority Affairs: This ministry is responsible for the development and welfare of minority communities in India.
• Lok Sabha: The Lok Sabha is the lower house of India's bicameral Parliament, responsible for law-making.

Given: John, Kelly, Lisa, Mike, Nancy, and Owen-are sitting in a straight line, facing north.

Only one person sits to the left of Kelly. Exactly two people sit between Kelly and Lisa. John sits to the immediate right of Lisa.

Mike sits second to the right of Owen. Mike is not an immediate neighbor of Lisa.

Final arrangement,

Thus. Owen  is sitting extreme left end of the line.

Hence, the correct answer is "Option 2".

The correct answer is 25 degree Celsius.

Key Points

• The Kelvin scale is an absolute temperature scale starting at absolute zero, where 0 K is the coldest possible temperature.
• To convert temperature from Kelvin to Celsius, subtract 273.15 from the Kelvin temperature.
• Given temperature: 298 K
• Conversion: 298 K - 273.15 = 24.85 degree Celsius (rounded to 25 degree Celsius)
• Correct conversion: 298 K is approximately 25 degree Celsius, not 32 degree Celsius. The correct answer should be option 4.

Additional Information

• Kelvin Scale:
• The Kelvin scale is used primarily in scientific contexts because it is an absolute scale based on absolute zero.
• 0 Kelvin (K) is the point at which particles have minimal thermal motion.
• Celsius Scale:
• The Celsius scale, also known as the centigrade scale, is used for most everyday temperature measurements.
• The scale is defined by the freezing point (0°C) and boiling point (100°C) of water at 1 atmosphere of pressure.
• Absolute Zero:
• Absolute zero is the lowest possible temperature where nothing could be colder and no heat energy remains in a substance.
• It is 0 K, which is equivalent to -273.15°C or -459.67°F.
• Temperature Conversion:
• To convert Celsius to Kelvin, add 273.15 to the Celsius temperature.
• To convert Kelvin to Celsius, subtract 273.15 from the Kelvin temperature.

Shortcut Trick

For any expression in the form a + 1/a = k, the value of a² + 1/a² is given by the formula k² − 2.

Given: k = 8

⇒ Result = 8² − 2 = 64 − 2 = 62

∴ The correct answer is 62.

Alternate Method

Given:

a + 1/a = 8

Formula Used:

(x + y)² = x² + y² + 2xy

Calculations:

Squaring both sides of the given equation:

⇒ (a + 1/a)² = 8²

⇒ a² + (1/a)² + 2 × a × (1/a) = 64

⇒ a² + 1/a² + 2 = 64

⇒ a² + 1/a² = 64 − 2

⇒ a² + 1/a² = 62

∴ The correct answer is 62.

Additional Information

Higher Power Identities

If a + 1/a = k, then a³ + 1/a³ = k³ − 3k and a⁴ + 1/a⁴ = (k² − 2)² − 2.

Negative Sign Identity

If a − 1/a = k, then a² + 1/a² = k² + 2.

Given:

3^{(K − 2)} × 3^K = 729

Formula used:

a^m × aⁿ = a^{(m + n)}

Calculations:

3^{(K − 2)} × 3^K = 729

⇒ 3^{(K − 2 + K)} = 3⁶

⇒ 3^{(2K − 2)} = 3⁶

Comparing the powers:

⇒ 2K − 2 = 6

⇒ 2K = 6 + 2

⇒ 2K = 8

⇒ K = 4

∴ The correct answer is option (1).

The logic followed here is:

For, JF-BE-HG

For, MI-EH-KJ

Let's check options one by one:

Option 1) PM-IL-OK

Option 2) QM-IL-ON

Here, follow the pattern.

Option 3) QM-IK-ON

Option 4) PM-IL-OJ

Hence, the correct answer is "Option 2".

The logic followed here is:

For, JH-KI-LN

For, LJ-MK-NP

Let's check options one by one.

Option 1) RP-SQ-TU

Option 2) QO-RP-ST

Option 3) OM-PN-QS

Here, follow the pattern.

Option 4) SQ-TR-UV

Hence, the correct answer is "Option 3".

The correct answer is Combination reaction.

Key Points

• A combination reaction occurs when two or more reactants combine to form a single product.
• In the given reaction, calcium oxide (CaO) reacts with water (H₂O) to form a single product, calcium hydroxide (Ca(OH)₂).
• This reaction is highly exothermic, releasing a significant amount of heat.
• The chemical equation for this combination reaction is: CaO + H₂O → Ca(OH)₂.

Additional Information

• Combination Reaction:
• Also known as a synthesis reaction, it involves two or more substances combining to form a single compound.
• Examples include the formation of water (H₂O) from hydrogen (H₂) and oxygen (O₂).
• Exothermic Reaction:
• A reaction that releases energy in the form of heat.
• These reactions often occur spontaneously and result in an increase in temperature.
• Calcium Oxide (CaO):
• Also known as quicklime or burnt lime.
• It is a white, caustic, alkaline substance used in various industrial processes.
• Slaked Lime (Calcium Hydroxide, Ca(OH)₂):
• A compound formed by the reaction of calcium oxide with water.
• It is used in various applications such as water treatment, construction, and chemical manufacturing.

Given:

First number = -5/9

Resulting sum = -5/6

Formula used:

Required number (x) = Resulting sum − Given number

Calculations:

Let the number to be added be x.

⇒ -5/9 + x = -5/6

⇒ x = -5/6 − (-5/9)

⇒ x = -5/6 + 5/9

Taking LCM of 6 and 9 which is 18:

⇒ x = (-5 × 3 + 5 × 2) / 18

⇒ x = (-15 + 10) / 18

⇒ x = -5/18

∴ The correct answer is option (1).

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

L sits third to the left of K.  C sits to the immediate right of K. C sits second to the left of E.

Only two people sit between E and F when counted from the left of F. B is not an immediate neighbour of L.

Final arrangement,

Thus, D is sitting third to the right of B.

Hence, the correct answer is "Option 4".

The correct answer is Sulphuric acid.

Key Points

• When ferrous sulphate (FeSO₄) is heated, it undergoes thermal decomposition to form ferric oxide (Fe₂O₃), sulphur dioxide (SO₂), and sulphur trioxide (SO₃).
• Ferrous sulphate decomposes in the following manner:
  

2 FeSO₄ → Fe₂O₃ + SO₂ + SO₃

• Sulphuric acid (H₂SO₄) is not formed in this reaction.
• The decomposition typically occurs at temperatures between 480°C and 500°C.

Additional Information

• Ferrous Sulphate (FeSO₄):
• It is a green crystalline solid.
• It is used in various applications such as water treatment, and as a precursor to other iron compounds.
• Thermal Decomposition:
• It is a chemical decomposition caused by heat.
• It involves breaking down compounds into simpler substances when heated.
• Sulphur Dioxide (SO₂):
• It is a toxic gas with a pungent, irritating smell.
• It is used as a preservative and in the production of sulphuric acid.
• Sulphur Trioxide (SO₃):
• It is a chemical compound that is used in the production of sulphuric acid.
• It is highly reactive and can cause severe burns on contact.

The correct answer is 1.5 m.

Key Points

• Work is defined as the product of the force applied and the displacement caused in the direction of the force.
• The formula for work is: W = F × d, where W is the work done, F is the force applied, and d is the displacement.
• In this problem, the given values are:
• Work (W) = 3 J
• Force (F) = 2 N
• To find the displacement, rearrange the formula: d = W / F.
• Substituting the given values:
• d = 3 J / 2 N = 1.5 m
• Thus, the displacement caused by the force is 1.5 meters.
• The correct option is Option 2, which corresponds to 1.5 m.

Additional Information

• Work
• Work is a scalar quantity that has magnitude but no direction.
• The unit of work is the joule (J), where 1 joule = 1 newton meter (N·m).
• Work is only done when the force has a component in the direction of the displacement.
• Force
• Force is a vector quantity that can change the state of motion of an object.
• Its unit is the newton (N), where 1 newton = 1 kg·m/s².
• Force can act through contact (e.g., friction) or at a distance (e.g., gravity).
• Displacement
• Displacement is a vector quantity that represents the shortest path between two points.
• It is measured in meters (m) and considers both magnitude and direction.
• Displacement differs from distance, which is a scalar quantity and does not consider direction.

The correct answer is Muscular tissue.

Key Points

• Muscular tissue is responsible for producing movement in animals.
• This tissue contracts and relaxes to cause movement, including voluntary actions like walking and involuntary actions like the beating of the heart.
• There are three types of muscular tissues: skeletal, smooth, and cardiac, each with distinct roles in the body.
• Skeletal muscles control voluntary movements, smooth muscles control involuntary actions in organs, and cardiac muscles are responsible for heartbeats.

Additional Information

• Epithelial tissue:
• It forms the covering or lining of all internal and external body surfaces.
• It functions in protection, absorption, secretion, and sensation.
• Meristematic tissue:
• It is found in plants and is responsible for growth.
• These tissues are composed of cells that can divide and differentiate into other types of cells.
• Connective tissue:
• It supports, binds together, and protects tissues and organs of the body.
• Includes various types like bone, blood, adipose, and cartilage.

The correct answer is International Institute of Sports Management (IISM).

Key Points

• The International Institute of Sports Management (IISM) launched India's first-ever book on Sports Psychology on 5 April 2024.
• The book aims to provide comprehensive insights into the psychological aspects of sports and athletic performance.
• This initiative by IISM marks a significant milestone in the field of sports education and research in India.
• The book is intended to serve as a valuable resource for athletes, coaches, sports psychologists, and students of sports management and psychology.

Additional Information

• Sports Psychology:
• Sports psychology involves the study of how psychological factors affect performance and how participation in sports and exercise affect psychological and physical factors.
• Key areas include motivation, performance anxiety, and the psychological benefits of sports and exercise.
• Sports psychologists work with athletes to improve performance and increase motivation.
• They also help athletes cope with the pressures of competition and recover from injuries.
• International Institute of Sports Management (IISM):
• Founded in 2010, IISM is India's premier sports management education institute.
• It offers undergraduate and postgraduate courses in sports management.
• IISM collaborates with various sports organizations and professionals to provide practical training and exposure to its students.
• The institute aims to contribute to the professional development of the sports industry in India.
• Importance of Sports Psychology:
• Enhances athletic performance by improving focus and mental resilience.
• Helps in managing stress and anxiety associated with competitive sports.
• Assists athletes in setting realistic goals and maintaining motivation.
• Supports injury recovery by addressing the psychological impact of injuries.
• Psychological Skills Training (PST):
• PST involves techniques such as visualization, self-talk, and relaxation training.
• These techniques help athletes enhance their mental skills and improve their performance.
• Regular practice of PST can lead to better focus, confidence, and coping strategies.

The correct answer is Cilia.

Key Points

• Cilia are hair-like structures that cover the outer surface of Paramecium.
• They beat in a coordinated manner to create water currents, directing food particles towards the oral groove.
• These structures aid in locomotion as well as in food capture and ingestion.
• Cilia play a crucial role in the feeding mechanism of Paramecium by transporting food to the cell mouth (cytostome).

Additional Information

• Parapodia: These are paired, lateral appendages found in polychaete worms, aiding in locomotion and respiration.
• Pseudopodia: These are temporary, arm-like projections of the cell membrane in amoeboid cells, used for movement and capturing prey.
• Flagella: Long, whip-like structures that aid in locomotion for many protozoa and bacteria; they are different from cilia in number and beating pattern.
• Oral Groove: A channel on the surface of Paramecium where cilia direct food particles to the cell mouth for ingestion.

The logic followed here is:

Logic: - 18 and ÷ 2 respectively in each next step.

Hence, the correct answer is "Option 2".

Shortcut Trick

Net discount for two successive discounts a% and b% = (a + b − ab ÷ 100)%.

Given a = 2% and b = 5%.

Equivalent discount = (2 + 5 − (2 × 5) ÷ 100)% = (7 − 10 ÷ 100)%.

Equivalent discount = (7 − 0.1)% = 6.9%.

∴ The correct answer is 6.9%.

Alternate Method

Given: First discount = 2%, Second discount = 5%.

Formulas: Successive Discount = a + b − ab ÷ 100 | Selling Price = MP × (100 − D₁)% × (100 − D₂)%

⇒ Let the Marked Price (MP) be 100 units.

⇒ Price after 1st discount = 100 − (2% of 100) = 100 − 2 = 98 units.

⇒ Price after 2nd discount = 98 − (5% of 98) = 98 − 4.9 = 93.1 units.

⇒ Total discount amount = 100 − 93.1 = 6.9 units.

⇒ Equivalent single discount = (6.9 ÷ 100) × 100 = 6.9%.

∴ The correct answer is 6.9%.

Additional Information

Successive Discounts

When a series of discounts are applied one after another on the reducing balance, they are called successive discounts. The total effective discount is always less than the simple sum of individual discounts.

Marked Price & Selling Price

Discount is always calculated on the Marked Price (MP). The price after deducting the discount is the Selling Price (SP).

Shortcut Trick

A consistent system of equations means there is at least one solution.

Intersecting lines provide exactly one solution (unique).

Coincident lines provide infinitely many solutions.

Since both cases yield solutions, a consistent pair must be intersecting or coincident.

∴ The correct answer is intersecting or coincident.

Alternate Method

Given: A pair of linear equations is consistent.

Consider the general form: a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0.

A system is consistent if it has one or more solutions.

⇒ Case 1: Unique Solution (Intersecting Lines)

⇒ Condition: a₁/a₂ ≠ b₁/b₂

⇒ Case 2: Infinite Solutions (Coincident Lines)

⇒ Condition: a₁/a₂ = b₁/b₂ = c₁/c₂

⇒ If the system is inconsistent, it has no solution (Parallel Lines).

⇒ Condition: a₁/a₂ = b₁/b₂ ≠ c₁/c₂

∴ The correct answer is intersecting or coincident.

Additional Information

Inconsistent System

A pair of linear equations with no solution is called inconsistent, representing parallel lines.

Dependent Equations

A pair of dependent linear equations is always consistent and has infinitely many solutions (coincident lines).

The correct answer is Metal salt.

Key Points

• In the electrolytic refining process, the electrolyte used is a solution of metal salt.
• This solution contains ions of the metal that is being refined.
• The impure metal is made the anode, and a thin sheet of pure metal acts as the cathode.
• During the process, metal ions from the electrolyte deposit on the cathode, while impurities are left behind at the anode.

Additional Information

• Electrolytic Refining:
• It is a method used to purify metals by using electrolysis.
• Commonly refined metals include copper, zinc, aluminum, and nickel.
• The process ensures the removal of impurities and the production of high-purity metal.
• Anode Mud:
• The residue left behind at the anode during electrolytic refining is known as anode mud.
• Anode mud can contain precious metals like gold and silver, which can be recovered separately.
• Cathode and Anode:
• The cathode is the electrode where reduction (gain of electrons) takes place.
• The anode is the electrode where oxidation (loss of electrons) occurs.
• Electrolyte:
• The electrolyte is a conducting solution that allows the flow of ions during electrolysis.
• In electrolytic refining, the electrolyte is typically a solution of the metal salt corresponding to the metal being refined.

The correct answer is two cells.

Key Points

• Binary fission is a type of asexual reproduction commonly found in prokaryotes such as bacteria.
• In binary fission, a single organism divides into two parts, each of which develops into a new individual.
• This process results in the formation of two genetically identical daughter cells.
• Binary fission involves the replication of the parent organism's DNA followed by the division of the cytoplasm.

Additional Information

• Multiple Fission:
• A process where one organism divides to form multiple daughter cells.
• Commonly seen in some protozoans like Plasmodium.
• Prokaryotes vs. Eukaryotes:
• Prokaryotes are unicellular organisms that lack a nucleus, such as bacteria.
• Eukaryotes have a defined nucleus and include organisms such as plants, animals, and fungi.
• Mitosis:
• A type of cell division that occurs in eukaryotic cells, resulting in two genetically identical daughter cells.
• Involves stages like prophase, metaphase, anaphase, and telophase.
• Cell Cycle:
• Consists of stages G1, S, G2, and M phase (mitosis) in eukaryotic cells.
• Ensures proper replication and division of genetic material.

The correct answer is Castor and Balsam.

Key Points

• Castor and Balsam plants have fruits that burst open with sudden jerks, aiding in the dispersal of seeds over a wide area.
• This method of seed dispersal is known as explosive or ballistic dispersal.
• In Castor (Ricinus communis), the fruits dry out and split open forcefully to scatter seeds.
• In Balsam (Impatiens), the fruits burst open upon slight touch, dispersing seeds in different directions.
• This mechanism helps in reducing competition among seedlings and allows colonization of new areas.

Additional Information

• Seed Dispersal
• Seed dispersal is the movement or transport of seeds away from the parent plant.
• It can occur through various mechanisms such as wind, water, animals, and explosive mechanisms.
• Effective seed dispersal is crucial for the survival and spread of plant species.
• Explosive Mechanism
• Plants like Castor and Balsam exhibit an explosive mechanism where the fruit dehisces (splits open) suddenly to release seeds.
• This mechanism involves the buildup of tension in the fruit's tissues, which is released suddenly to scatter seeds.
• Other Plants with Explosive Dispersal
• Other plants that use explosive seed dispersal include Touch-Me-Not (Mimosa pudica) and Pea family members like Lupins.
• Advantages of Explosive Dispersal
• Reduces competition for resources among seedlings.
• Helps in the colonization of new areas.
• Ensures genetic diversity by spreading seeds over a wider area.

The logic followed here is:

Logic: + 1 in the place value of letters.

Hence, the correct answer is "Option 3".

The correct answer is Firozabad.

Key Points

• Firozabad was awarded the first prize under the Medium-sized Cities category (Population between 3 lakh and 10 lakh) in the Swachh Vayu Survekshan 2024.
• Swachh Vayu Survekshan is an initiative by the Ministry of Environment, Forest and Climate Change (MoEFCC) to monitor and improve air quality in Indian cities.
• The award recognizes the city’s efforts in implementing effective measures for air pollution control and management.
• Firozabad’s initiatives included promoting the use of electric vehicles, enhancing green cover, and strict monitoring of industrial emissions.

Additional Information

• Swachh Vayu Survekshan
• Launched by the MoEFCC to assess and rank cities based on air quality management efforts.
• The survey covers various parameters including vehicular pollution, industrial emissions, and waste management.
• Aims to encourage cities to adopt sustainable and effective practices for improving air quality.
• Electric Vehicles (EVs)
• EVs are vehicles that use electric motors powered by electricity from batteries or fuel cells.
• They produce zero tailpipe emissions, contributing significantly to the reduction of urban air pollution.
• Green Cover
• Refers to the presence of vegetation such as trees, shrubs, and grasses in urban areas.
• Enhancing green cover helps in improving air quality by absorbing pollutants and providing oxygen.
• Industrial Emissions
• Emissions from industrial activities include pollutants like sulfur dioxide, nitrogen oxides, and particulate matter.
• Strict monitoring and regulation of these emissions are crucial for maintaining air quality.

Shortcut Trick

Number of diagonals = n(n − 3) ÷ 2 = 20

⇒ n(n − 3) = 40

⇒ By observation, 8 × 5 = 40, so n = 8 (Octagon).

⇒ Sum of interior angles = (n − 2) × 180°

⇒ (8 − 2) × 180° = 6 × 180° = 1080°.

∴ The correct answer is 1080°.

Alternate Method

Given: Number of diagonals = 20

Formula Used:

1. Number of diagonals in an n-sided polygon = [n(n − 3)] / 2
2. Sum of interior angles = (n − 2) × 180°

Calculations:

⇒ [n(n − 3)] / 2 = 20

⇒ n² − 3n = 40

⇒ n² − 3n − 40 = 0

⇒ n² − 8n + 5n − 40 = 0

⇒ n(n − 8) + 5(n − 8) = 0

⇒ (n − 8)(n + 5) = 0

⇒ Since n (number of sides) cannot be negative, n = 8.

⇒ Sum of interior angles = (8 − 2) × 180°

⇒ 6 × 180° = 1080°.

∴ The correct answer is 1080°.

Additional Information

Sum of Exterior Angles

For any convex polygon, the sum of all exterior angles is always constant and equal to 360°.

Individual Interior Angle

In a regular polygon, each interior angle is calculated as [(n − 2) × 180°] / n.

Relation between Angles

At any vertex of a polygon, the Interior Angle + Exterior Angle = 180°.

Shortcut Trick

Area to be painted = Area of 4 walls + Area of ceiling

Area = [2 × Height × (Length + Breadth)] + (Length × Breadth)

Area = [2 × 21 × (15 + 17)] + (15 × 17) = 1344 + 255 = 1599 m²

Total Cost = Area × Rate = 1599 × 42 = ₹67,158

∴ The correct answer is ₹67,158.

Alternate Method

Given:

Length (L) = 15 m, Breadth (B) = 17 m, Height (H) = 21 m

Rate of painting = ₹42/m²

Formula Used:

Area of 4 walls = 2H(L + B)

Area of ceiling = L × B

Total Cost = (Area of 4 walls + Area of ceiling) × Rate

Calculations:

⇒ Area of 4 walls = 2 × 21 × (15 + 17)

⇒ Area of 4 walls = 42 × 32 = 1344 m²

⇒ Area of ceiling = 15 × 17 = 255 m²

⇒ Total surface area to be painted = 1344 + 255 = 1599 m²

⇒ Total cost = 1599 × 42

⇒ Total cost = ₹67,158

∴ The correct answer is ₹67,158.

Additional Information

Total Surface Area (TSA) of Cuboid

The total surface area including all six faces is given by 2(LB + BH + HL).

Volume of Cuboid

The amount of space occupied by the cuboid is calculated as Length × Breadth × Height.

Diagonal of Cuboid

The longest rod that can be placed in a cuboidal room is the diagonal, √(L² + B² + H²).

The correct answer is Unisexual flower - Watermelon.

Key Points

• Watermelon (Citrullus lanatus) is known for producing unisexual flowers, meaning that each flower is either male or female.
• In watermelon plants, male flowers produce pollen, while female flowers develop into the fruit after pollination.
• Unisexual flowers in watermelons help in ensuring cross-pollination, which can lead to better genetic diversity and fruit production.
• Pollination in watermelons is typically carried out by bees, which transfer pollen from male to female flowers.

Additional Information

• Unisexual Flowers:
• Unisexual flowers contain either male (staminate) or female (pistillate) reproductive organs, but not both.
• Examples of plants with unisexual flowers include cucumbers, pumpkins, and corn.
• Bisexual Flowers:
• Bisexual flowers contain both male and female reproductive organs within the same flower.
• Examples include roses, lilies, and tomatoes.
• Pollination:
• Pollination is the process of transferring pollen from the male part of the flower (anther) to the female part (stigma).
• It can occur via wind, water, or animals (particularly insects like bees).
• Cross-Pollination:
• Cross-pollination involves the transfer of pollen from the flower of one plant to the flower of another plant of the same species.
• This process enhances genetic diversity within a plant species.

The correct answer is Odisha.

Key Points

• The state of Odisha won the 14th Hockey India Senior Men National Championship held in 2024.
• Odisha secured the title by defeating Maharashtra in the final match.
• The championship saw participation from numerous state teams, showcasing high-level competition.
• This victory highlights the growing prominence of Odisha in Indian hockey, furthering their reputation as a strong contender in national tournaments.
• The tournament was organized by Hockey India, the governing body for field hockey in India.

Additional Information

• Hockey India:
• Hockey India is the governing body for field hockey in India, responsible for the promotion and development of the sport at all levels.
• It was established in 2009 and is recognized by the Indian Olympic Association and the International Hockey Federation (FIH).
• Hockey India organizes various national championships and league competitions, contributing to the growth of the sport in the country.
• Field Hockey in India:
• Field hockey is one of the most popular sports in India, with a rich history of success in international competitions.
• India has won multiple Olympic gold medals in hockey, with the first victory coming in 1928.
• The sport is governed by Hockey India, which oversees the national teams and domestic competitions.
• Odisha's Contribution to Indian Hockey:
• Odisha has emerged as a significant contributor to Indian hockey, hosting major tournaments and providing infrastructure support.
• The state government has invested in the development of hockey facilities, including the Kalinga Stadium in Bhubaneswar.
• Several prominent Indian hockey players have emerged from Odisha, contributing to the national team's success.
• National Championships:
• The Hockey India Senior Men National Championship is an annual tournament that brings together state teams from across the country.
• The championship serves as a platform for identifying and nurturing talent for the national team.
• It provides an opportunity for players to showcase their skills and compete at a high level.

The correct answer is Tendon.

Key Points

• Tendons are strong, fibrous connective tissues that attach muscles to bones.
• They transmit the force generated by the muscle to the bone, enabling movement.
• Tendons are composed of collagen fibers, making them both strong and flexible.
• Examples of tendons include the Achilles tendon, which connects the calf muscle to the heel bone.

Additional Information

• Ligaments:
• Ligaments are fibrous connective tissues that connect bones to other bones at joints.
• They provide stability to joints and limit their range of motion.
• Examples include the anterior cruciate ligament (ACL) in the knee.
• Cartilage:
• Cartilage is a flexible connective tissue found in joints, rib cage, ear, nose, bronchial tubes, and intervertebral discs.
• It provides cushioning and reduces friction between bones.
• There are three types of cartilage: hyaline, fibrocartilage, and elastic cartilage.
• Muscles:
• Muscles are tissues that have the ability to contract, producing movement in or maintaining the position of parts of the body.
• There are three types of muscles: skeletal, cardiac, and smooth muscles.
• Skeletal muscles are attached to bones and are responsible for voluntary movements.
• Fibroblasts:
• Fibroblasts are cells that produce collagen and other fibers found in connective tissues.
• They play a crucial role in wound healing and maintaining the structural integrity of connective tissues.
• They are found in various tissues, including tendons, ligaments, and skin.

The correct answer is old xylem.

Key Points

• In plants, old xylem tissue is commonly used to store waste products such as resins and gums.
• Old xylem, also known as heartwood, is formed from dead cells and serves as a repository for various secondary metabolites.
• These waste products are often transported to the heartwood to prevent them from interfering with the plant's metabolic processes.
• Storing waste in old xylem helps in maintaining the overall health and functionality of the living tissues in plants.

Additional Information

• Heartwood and Sapwood:
• Heartwood is the central, non-living part of a tree trunk, which is usually darker and denser than the outer sapwood.
• Sapwood is the outer, living layers of the tree trunk that actively conduct water and nutrients.
• Secondary Metabolites:
• These are organic compounds not directly involved in the normal growth, development, or reproduction of organisms.
• In plants, secondary metabolites include alkaloids, terpenoids, and phenolic compounds.
• Function of Xylem:
• Xylem is a type of vascular tissue in plants responsible for the transport of water and nutrients from the roots to the rest of the plant.
• Xylem also provides structural support due to the lignification of its cells.
• Resins and Gums:
• Resins are sticky, viscous substances secreted by some plants, particularly conifers, as a defense mechanism.
• Gums are water-soluble polysaccharides produced by certain plants and used in various industries for their adhesive and thickening properties.

Shortcut Trick

Total Simple Interest required = 1,860 − 1,500 = ₹360.

Interest per year = 8% of 1,500 = 1500 × (8/100) = ₹120.

Time (T) = Total Interest ÷ Interest per year = 360 ÷ 120 = 3 years.

∴ The correct answer is 3 years.

Alternate Method

Given:

Principal (P) = ₹1,500

Amount (A) = ₹1,860

Rate (R) = 8% per annum

Formula Used:

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

Amount (A) = P + SI

Calculations:

⇒ SI = A − P

⇒ SI = 1,860 − 1,500 = ₹360

⇒ 360 = (1,500 × 8 × T) ÷ 100

⇒ 360 = 15 × 8 × T

⇒ 360 = 120 × T

⇒ T = 360 ÷ 120

⇒ T = 3 years

∴ The correct answer is 3 years.

Additional Information

Simple Interest (SI)

Calculated only on the Principal amount. SI = (P × R × T)/100 remains constant every year if P, R, and T are fixed.

Compound Interest (CI)

Interest calculated on the Principal plus accumulated interest. Formula: A = P(1 + R/100)^T.

Rate of Interest (R)

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

Shortcut Trick

Area of path around a rectangular field (inside) = 2w(L + B − 2w)

Given: Length (L) = 50 m, Breadth (B) = 42 m, Width (w) = 6 m

Area = 2 × 6 × (50 + 42 − 2 × 6)

Area = 12 × (92 − 12) = 12 × 80 = 960 m²

∴ The correct answer is 960 m².

Alternate Method

Given: External Length = 50 m, External Breadth = 42 m, Path Width = 6 m

Formula Used: Area of path = External Area − Internal Area

⇒ External Area = 50 × 42 = 2100 m²

⇒ Internal Length = 50 − (2 × 6) = 50 − 12 = 38 m

⇒ Internal Breadth = 42 − (2 × 6) = 42 − 12 = 30 m

⇒ Internal Area (Lawn) = 38 × 30 = 1140 m²

⇒ Area of Path = 2100 − 1140 = 960 m²

∴ The correct answer is 960 m².

Additional Information

Path Outside a Rectangle

If the path is built outside the field, the area of the path is given by 2w(L + B + 2w), where w is the width of the path.

Cross Paths in Middle

For two paths of width w crossing each other in the middle of a field, the total area of paths = w(L + B − w).

Area and Perimeter

Area of rectangle = L × B and Perimeter = 2(L + B). Always ensure units are consistent before calculation.

Given: 24 + 4 - 15 ÷ 2 × 12 = ?

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

24 + 4 - 15 ÷ 2 × 12 = ? ⇒ 24 ÷ 4 × 15 + 2 - 12 = ?

⇒ 24 ÷ 4 × 15 + 2 - 12 = ?

⇒ 90 + 2 - 12 = ?

⇒ 92 - 12 = 80

Hence, the correct answer is "Option 1".

Given: 9 - 2 × 20 +4 ÷ 11 = ?

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

9 - 2 × 20 +4 ÷ 11 = ? ⇒ 9 × 2 - 20 ÷ 4 + 11 = ?

⇒ 9 × 2 - 20 ÷ 4 + 11 = ?

⇒ 18 - 5 + 11 = ?

⇒29 - 5 = 24

Hence, the correct answer is "Option 3".

The correct answer is 1.2.

Key Points

• The pH of gastric juice is typically around 1.2, indicating its highly acidic nature.
• This acidity is primarily due to the presence of hydrochloric acid (HCl) in the stomach.
• The acidic environment helps in the breakdown of food and activation of digestive enzymes such as pepsin.
• Hydrochloric acid in gastric juice also plays a crucial role in killing harmful bacteria and pathogens ingested with food.

Additional Information

• Hydrochloric Acid (HCl)
• It is secreted by the parietal cells in the stomach lining.
• The concentration of hydrochloric acid in gastric juice is about 0.5% (5000 ppm).
• Pepsin
• Pepsin is a digestive enzyme that breaks down proteins into peptides.
• It is activated from its precursor, pepsinogen, in the presence of hydrochloric acid.
• Gastric Mucosa
• The inner lining of the stomach is called the gastric mucosa.
• It contains various glands that secrete mucus, hydrochloric acid, and digestive enzymes.
• pH Scale
• The pH scale measures the acidity or alkalinity of a solution.
• A pH value below 7 indicates acidity, 7 is neutral, and above 7 indicates alkalinity.

Given: 

Amit starts from Point A and drives 35 km towards East.

He then takes a right turn, drives 17 km, turns right and drives 15 km.

He then takes a left turn and drives 13 km.

He takes a final right turn, drives 20 km and stops at Point P.

Thus,  he drive 30 km towards North in order to reach Point A again.

Hence, the correct answer is "Option 3".

The correct answer is Option 2.

Key Points

• Antonie van Leeuwenhoek, a Dutch scientist, is credited with discovering free-living cells in pond water for the first time in 1674.
• He is often referred to as the "Father of Microbiology" due to his significant contributions to the field.
• Leeuwenhoek used a single-lens microscope that he designed and built himself to observe these microscopic organisms.
• His observations included bacteria, protozoa, and other microorganisms, which he called "animalcules."

Additional Information

• Microscope: An optical instrument used for viewing very small objects, typically magnified several hundred times.
• Animalcules: A term used by Leeuwenhoek to describe the microorganisms he observed, which included bacteria and protozoa.
• Microbiology: The branch of science that deals with microorganisms and their effects on other living organisms.
• Robert Hooke: An English scientist who, in 1665, published "Micrographia," where he detailed his observations of cells in cork, coining the term "cell."
• Protozoa: A diverse group of unicellular eukaryotic organisms, many of which can be found in pond water.

The correct answer is -2.0 m, concave lens.

Key Points

• The focal length of a lens is given by the inverse of the power of the lens (f = 1/P).
• Given the eye power of -0.5D, the focal length (f) = 1/(-0.5) = -2.0 m.
• A negative power indicates that the lens is concave, which is used to correct myopia (nearsightedness).
• Concave lenses are diverging lenses, meaning they spread out light rays that have been refracted through them.
• The student should therefore use a concave lens with a focal length of -2.0 meters to correct her vision defect.

Additional Information

• Myopia (Nearsightedness)
• Myopia is a common vision condition where close objects are seen clearly, but distant objects appear blurry.
• It occurs when the eyeball is too long or the cornea is too curved, causing light rays to focus in front of the retina.
• Concave Lenses
• Concave lenses are thinner at the center than at the edges.
• They cause parallel rays of light to diverge, spreading out from a point.
• Lens Power
• The power of a lens is measured in diopters (D), which is the reciprocal of the focal length in meters (P = 1/f).
• Negative power indicates a concave lens, while positive power indicates a convex lens.
• Corrective Lenses
• Corrective lenses are designed to bend light rays to compensate for the refractive errors of the eye.
• They help focus light directly on the retina, providing clear vision.

Shortcut Trick

Passing marks = Marks scored + Failing margin = 20 + 40 = 60 marks

According to the question, 40% = 60 marks

Maximum marks (100%) = (60 ÷ 40) × 100 = 1.5 × 100 = 150 marks

∴ The correct answer is 150.

Alternate Method

Given:

Marks scored by Y = 20

Marks by which Y fails = 40

Passing percentage = 40%

Calculations:

⇒ Passing Marks = 20 + 40 = 60 ⇒ Let Maximum Marks be M. ⇒ 40% of M = 60 ⇒ (40 ÷ 100) × M = 60 ⇒ 0.4 × M = 60 ⇒ M = 60 ÷ 0.4 ⇒ M = 600 ÷ 4 = 150

∴ The correct answer is 150.

Additional Information

Passing Marks Formula

Passing Marks = (Pass Percentage × Maximum Marks) ÷ 100. This determines the minimum score required to pass an examination.

Percentage to Fraction Conversion

Converting percentage to fraction simplifies calculations: 40% = 40/100 = 2/5. Multiplying the total marks by 2/5 gives the 40% value.

Relationship between Scored and Passing Marks

If a student fails, Passing Marks = Marks Obtained + Failing Margin. If a student passes with extra marks, Passing Marks = Marks Obtained − Excess Marks.

Shortcut Trick

Ratio of ages of Ishan and Surya = 7 : 8

Difference in ratio parts = 8 − 7 = 1 unit

Given age difference = 3 years ⇒ 1 unit = 3 years

Ishan age = 7 units = 7 × 3 = 21 years

∴ The correct answer is 21 years.

Alternate Method

Given:

Ratio of Ishan age to Surya age = 7 : 8

Let the ages be 7x and 8x.

Calculations:

⇒ Age of Surya − Age of Ishan = 3

⇒ 8x − 7x = 3

⇒ x = 3

⇒ Ishan age = 7x = 7 × 3

⇒ Ishan age = 21 years

∴ The correct answer is 21 years.

Additional Information

Ratio and Proportion

If two quantities are in ratio a:b, they can be represented as ax and bx, where x is the common multiplier.

Age Difference Constant

The numerical difference between the ages of two persons always remains constant regardless of the number of years passed or preceding.

Unitary Method in Ratios

Difference in ratio units corresponds to the actual numerical difference. 1 unit = (Actual Difference) ÷ (Difference in Ratio parts).

The correct answer is Particles of the solution can be seen by the naked eye.

Key Points

• A solution is defined as a homogeneous mixture of two or more substances.
• In a solution, the solute is uniformly distributed within the solvent.
• The particles of a solution are of molecular size, usually less than 1 nanometer, making them invisible to the naked eye.
• Solute particles in a solution do not settle down when left undisturbed, ensuring the mixture remains stable over time.
• Solute particles cannot be separated from the solvent by ordinary filtration methods.

Additional Information

• Homogeneous Mixture:
• A mixture in which the composition is uniform throughout the sample.
• Examples include saltwater, air, and alloys.
• Solvent:
• The substance in which the solute dissolves, typically present in a greater amount.
• Common solvents include water, ethanol, and benzene.
• Solute:
• The substance that is dissolved in the solvent.
• Examples include salt in saltwater or sugar in sugar water.
• Tyndall Effect:
• The scattering of light by particles in a colloid or in very fine suspensions.
• True solutions do not exhibit the Tyndall effect, as the particles are too small to scatter light.

The correct answer is Option 2.

Key Points

• Work done is calculated as the product of the force applied and the displacement in the direction of the force.
• Formula: Work (W) = Force (F) × Displacement (d).
• Given: Force (F) = 5 N and Displacement (d) = 3 m.
• Calculation: W = 5 N × 3 m = 15 Joules.
• Thus, the work done by the force is 15 Joules, which corresponds to option 2.

Additional Information

• Work: In physics, work is defined as the energy transferred to or from an object via the application of force along a displacement.
• Joule: The unit of work or energy in the International System of Units (SI). It is defined as the amount of work done when a force of one newton displaces an object by one meter.
• Force: A push or pull on an object that can cause it to change velocity (to accelerate), measured in newtons (N).
• Displacement: The vector quantity that denotes the change in position of an object, measured in meters (m).
• Direction of Force: For work to be done, the force applied must have a component in the direction of the displacement.

Given: (Left) $ 1 & 8 4 7 £ * 5 3 @ 2 % 9 + Ω 6 # (Right)

Condition: Number - Number - Number

(Left) $ 1 & 8 4 7 £ * 5 3 @ 2 % 9 + Ω 6 # (Right)

Here, only one pair which follow the logic " 8 4 7 ".

Hence, the correct answer is "Option 4".

Shortcut Trick

Let Total Work (LCM of 20, 24, 15) = 120 units.

Efficiency of Pipe A = 6, Pipe B = 5, and (A + B + C) = 8.

Efficiency of Emptying Pipe C = 8 − (6 + 5) = −3 units/min.

Since 3 units/min corresponds to 3 gallons/min, 1 unit = 1 gallon.

∴ The correct answer is 120 gallons.

Alternate Method

Calculations:

⇒ Total efficiency of filling pipes (A + B) = 6 + 5 = 11 units/min.

⇒ Efficiency of waste pipe C = (A + B + C) − (A + B) = 8 − 11 = −3 units/min.

⇒ Negative sign indicates emptying.

⇒ Time taken by Pipe C to empty the tank = 120 ÷ 3 = 40 minutes.

⇒ Capacity of tank = Rate of emptying × Time taken = 3 gallons/min × 40 min = 120 gallons.

∴ The correct answer is 120 gallons.

Additional Information

Pipes and Cisterns Efficiency

Efficiency of a filling pipe is taken as positive, while the efficiency of an emptying pipe is taken as negative.

Capacity Formula

The total capacity of a tank is calculated as the Rate of flow × Time taken to fill or empty the tank.

LCM Method

Total Work is assumed as the Least Common Multiple of individual time periods to simplify efficiency calculations.

The correct answer is ₹13,000 crore.

Key Points

• The Pradhan Mantri Vishwakarma Yojana (PM Vishwakarma Scheme) is allocated a budget of ₹13,000 crore for the period from 2023-24 to 2027-28.
• This scheme aims to provide financial support to traditional artisans and craftsmen in India.
• PM Vishwakarma Scheme focuses on the upliftment and enhancement of skills of the Vishwakarma community, who are engaged in traditional crafts.
• The initiative is in line with the government's vision of empowering the artisan community and preserving traditional craftsmanship.
• The scheme will include various components such as skill training, financial assistance, and market linkages to ensure holistic development.

Additional Information

• Vishwakarma Community:
• The Vishwakarma community comprises traditional artisans such as carpenters, blacksmiths, goldsmiths, potters, sculptors, and masons.
• They have a significant role in preserving India's cultural heritage through their craftsmanship.
• Skill Development:
• The scheme includes skill development programs to enhance the existing skills of artisans.
• Training will be provided to improve the quality and productivity of their crafts.
• Financial Assistance:
• Financial support will be provided to artisans for procuring raw materials and modern tools.
• This will help them to scale their operations and improve their income.
• Market Linkages:
• The scheme aims to create market linkages for traditional crafts to ensure better market access.
• It will help artisans to reach a wider customer base and increase their sales.
• Preservation of Heritage:
• The scheme is a step towards preserving India's rich cultural heritage and traditional crafts.
• It aims to encourage the younger generation to take up traditional crafts as a viable career option.

The correct answer is Option 2.

Key Points

• When a soft iron bar is introduced inside a current-carrying solenoid, the magnetic field inside the solenoid increases significantly.
• Soft iron has high magnetic permeability, which means it enhances the magnetic field by becoming magnetized itself.
• The magnetic domains in the soft iron align with the magnetic field created by the solenoid, thus amplifying the overall magnetic field.
• This phenomenon is used in electromagnets to create strong magnetic fields by inserting a core of soft iron inside the solenoid.

Additional Information

• Magnetic Permeability:
• It is a measure of how easily a material can become magnetized or how well it can support the formation of a magnetic field within itself.
• Materials with high magnetic permeability, like soft iron, are used to enhance magnetic fields in various applications.
• Electromagnet:
• An electromagnet is formed by passing an electric current through a coil of wire wrapped around a magnetic core (usually soft iron).
• The current generates a magnetic field, which magnetizes the core, thus creating a strong magnetic field.
• Solenoid:
• A solenoid is a cylindrical coil of wire acting as a magnet when carrying electric current.
• Solenoids are widely used in various devices where control of a magnetic field is needed, such as in relays, valves, and inductors.
• Magnetic Domains:
• Magnetic domains are regions within a material where the magnetic moments of atoms are aligned with each other.
• In the presence of an external magnetic field, these domains align in the direction of the field, increasing the material's overall magnetic strength.

Shortcut Trick

Convert all weights to grams (1 kg = 1000 g).

Total Weight = 12650 g

Chocolate Weight = 6350 g

Box Weight = 12650 − 6350 = 6300 g.

∴ The correct answer is 6300 g.

Alternate Method

Given:

Weight of box + chocolates = 12.650 kg

Weight of chocolates = 6 kg 350 g

Formula Used:

Weight of empty box = Total Weight − Weight of chocolates

Calculations:

⇒ Total weight = 12.650 × 1000 = 12650 g

⇒ Weight of chocolates = (6 × 1000) + 350 = 6350 g

⇒ Weight of empty box = 12650 g − 6350 g

⇒ Weight of empty box = 6300 g

∴ The correct answer is 6300 g.

Additional Information

Unit Conversion

Standard unit of mass is Kilogram (kg). 1 kg = 1000 grams (g) and 1 g = 1000 milligrams (mg).

Gross vs Net Weight

Gross Weight is the total weight (Box + Contents), while Net Weight is the weight of the contents only. Tare Weight refers to the weight of the empty container.

The logic followed here is:

The code for "needs" is "cy".

Hence, the correct answer is "Option 1".

Given:

Total cost incurred by the company in 2020 = $100,000

Electricity cost percentage = 5%

Formula used:

Electricity Cost = Total Cost × (Electricity Cost Percentage / 100)

Calculation:

Electricity Cost = $100,000 × (5 / 100)

⇒ Electricity Cost = $100,000 × 0.05

⇒ Electricity Cost = $5,000

∴ The correct answer is option (4).

Shortcut Trick

When the time intervals are equal (1 hour each), the Average Speed is simply the Arithmetic Mean of the individual speeds.

Average Speed = (S₁ + S₂) ÷ 2

Average Speed = (90 + 60) ÷ 2 = 150 ÷ 2 = 75 km/h.

∴ The correct answer is 75 km/h.

Alternate Method

Given:

Speed in 1^st hour (S₁) = 90 km/h

Speed in 2^nd hour (S₂) = 60 km/h

Time (t₁ = t₂) = 1 hour

Formula Used:

Average Speed = Total Distance ÷ Total Time

Distance = Speed × Time

Calculations:

⇒ Distance covered in 1^st hour = 90 × 1 = 90 km

⇒ Distance covered in 2^nd hour = 60 × 1 = 60 km

⇒ Total Distance = 90 + 60 = 150 km

⇒ Total Time = 1 + 1 = 2 hours

⇒ Average Speed = 150 ÷ 2

⇒ Average Speed = 75 km/h

∴ The correct answer is 75 km/h.

Additional Information

Average Speed (Equal Distance)

If a body travels equal distances at speeds x and y, the average speed is given by the harmonic mean: 2xy ÷ (x + y).

Average Speed (Equal Time)

If a body travels for equal time intervals at speeds x and y, the average speed is the arithmetic mean: (x + y) ÷ 2.

Unit Conversion

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

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

Condition: sum of the 5th digit from the left and the 2nd digit from the right.

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

⇒ 5th digit from the left = 0

⇒2nd digit from the right = 6

⇒ sum of the 5th digit from the left and the 2nd digit from the right is (0 + 6) = 6.

Hence, the correct answer is "Option 1".

The correct answer is Option 2.

Key Points

• Olfactory receptors are responsible for the sense of smell.
• When the nose is blocked, the passage of air to the olfactory receptors is obstructed.
• This obstruction prevents the olfactory receptors from detecting odor molecules effectively.
• Smell is directly linked to the function of olfactory receptors, which are located in the nasal cavity.

Additional Information

• Olfactory System:
• The olfactory system is the sensory system used for smelling (olfaction).
• It includes the olfactory receptors, olfactory bulb, and various brain regions involved in processing smell.
• Olfactory Receptors:
• These are specialized sensory cells located in the nasal cavity.
• They detect odor molecules and send signals to the brain.
• Function of Smell:
• Smell is vital for detecting dangers, such as smoke or spoiled food.
• It also plays a role in taste perception and memory recall.
• Blockage of the Nose:
• Nasal blockage can be caused by colds, allergies, or sinus infections.
• This blockage hinders the ability to smell by preventing odor molecules from reaching the olfactory receptors.

Statements:

All wigs are plastics.

All stones are plastics.

The least possible Venn diagram is given:

Conclusion:

(I) All plastics are wigs - False(because, All wigs are plastics and All stones are plastics it implies that part of plastic which is stone has no direct relation between wigs, so it cannot be definite, but possible only).

(II) Some wigs are stones - False(because, there is no direct relation between wigs and stone, so it can be possible only).

Thus, Neither conclusion (I) nor (II) follows.

Hence, the correct answer is "Option 4".

The correct answer is 2) Roots.

Key Points

• Roots exhibit positive geotropism, meaning they grow in the direction of gravitational pull, which is downwards.
• This downward growth of roots helps in anchoring the plant firmly in the soil.
• The primary role of roots is to absorb water and nutrients from the soil, which is essential for the plant's survival and growth.
• Root cap at the tip of the root protects the growing root tip as it pushes through the soil.
• Specialized root structures such as root hairs increase the surface area for absorption.

Additional Information

• Geotropism:
• It is a growth response to gravity observed in plants.
• Roots show positive geotropism (growth towards gravity), while shoots show negative geotropism (growth away from gravity).
• Root System Types:
• Taproot system: A single main root grows downwards with smaller lateral roots (e.g., carrot).
• Fibrous root system: Many small roots spread out from the base of the stem (e.g., grass).
• Root Functions:
• Anchorage: Roots hold the plant in place in the soil.
• Absorption: Roots absorb water and minerals from the soil.
• Storage: Roots can store food and nutrients (e.g., sweet potatoes).
• Root Adaptations:
• Aerial roots: Roots that grow above the ground (e.g., mangroves).
• Adventitious roots: Roots that grow from unusual places like stems or leaves (e.g., banyan tree).

The correct answer is Option 2 (C5H12).

Key Points

• Pentane is an alkane with the chemical formula C₅H₁₂.
• It consists of five carbon atoms and twelve hydrogen atoms, arranged in a straight chain.
• Alkanes are hydrocarbons that contain only single bonds between carbon atoms, following the general formula C_nH_2n+2.
• Pentane is used as a solvent and in the production of polystyrene foam.

Additional Information

• Isomers of Pentane:
• Pentane has three structural isomers: n-pentane, isopentane (2-methylbutane), and neopentane (2,2-dimethylpropane).
• Physical Properties:
• Pentane is a colorless, volatile liquid at room temperature with a boiling point of approximately 36°C (97°F).
• Combustion:
• Like other alkanes, pentane undergoes combustion, producing carbon dioxide and water.
• Role in Industry:
• Pentane is used as a blowing agent in the production of polystyrene foam and as a solvent for various chemical reactions.