RRB Technician Grade III Official Paper (Held On: 29 Dec, 2024 Shift 1) (Previous Year Paper)

The correct answer is Electrolytic refining.

Key Points

• Electrolytic refining is a method used to purify impure metals by using electrolysis.
• In this process, the impure metal is made the anode, and a pure metal strip is made the cathode.
• An electrolyte solution containing the metal ions is used to facilitate the transfer of metal ions from the anode to the cathode.
• As a result, the pure metal is deposited on the cathode, while impurities either fall off as anode mud or remain in the solution.
• This method is commonly used for refining metals like copper, nickel, lead, and zinc.

Additional Information

• Electrolysis is the process of using an electric current to drive a non-spontaneous chemical reaction.
• In electrolytic refining, the energy supplied by the electric current helps in the separation of pure metal from its impurities.
• Anode refers to the electrode where oxidation occurs, while the cathode refers to the electrode where reduction occurs.
• Anode mud is the insoluble impurities that collect at the bottom of the electrolytic cell during the refining process.
• This method ensures high purity levels of the refined metal, often exceeding 99.9% purity.

The correct answer is 3) F2 > F1.

Key Points

• Force (F) is calculated using Newton's Second Law of Motion, which states that F = m × a, where m is mass and a is acceleration.
• For F1: The force needed to accelerate a 5 kg object at 10 m/s² is calculated as F1 = 5 kg × 10 m/s² = 50 N.
• For F2: The force needed to accelerate a 10 kg object at 12 m/s² is calculated as F2 = 10 kg × 12 m/s² = 120 N.
• Comparing F1 and F2: 50 N < 120 N, hence F2 > F1.

Additional Information

• Newton's Second Law of Motion: States that the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = m × a).
• SI Unit of Force: The SI unit of force is the Newton (N), which is defined as the force needed to accelerate a 1 kg mass by 1 m/s².
• Mass: Mass is a measure of the amount of matter in an object and is usually measured in kilograms (kg).
• Acceleration: Acceleration is the rate of change of velocity of an object and is measured in meters per second squared (m/s²).
• Application: Understanding the relationship between force, mass, and acceleration is crucial in fields such as engineering, physics, and various applied sciences.

Given:

(−18) + 6 ÷ 3 + 5

Formula used:

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

Calculations:

(−18) + 6 ÷ 3 + 5

⇒ (−18) + 2 + 5

⇒ −18 + 7

⇒ −11

∴ The correct answer is option (2).

Shortcut Trick

Identify numbers in the range 400 to 430 that are not divisible by 2, 3, 5, 7, 11, 13, 17, or 19.

Numbers to check: 401, 403, 407, 409, 413, 419, 421, 427, 429.

Eliminate: 403 (13×31), 407 (11×37), 413 (7×59), 427 (7×61), 429 (3×143).

Remaining Prime Numbers: 401, 409, 419, 421.

∴ The correct answer is 4.

Alternate Method

Given: Range of numbers between 400 and 430.

Method: To check if a number n is prime, test divisibility by all primes ≤ √n. Here, √430 ≈ 20.7, so test primes 2, 3, 5, 7, 11, 13, 17, 19.

⇒ 401: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19 → Prime

⇒ 403: 13 × 31 = 403 → Not Prime

⇒ 407: 11 × 37 = 407 → Not Prime

⇒ 409: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19 → Prime

⇒ 419: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19 → Prime

⇒ 421: Not divisible by 2, 3, 5, 7, 11, 13, 17, 19 → Prime

⇒ List of primes: {401, 409, 419, 421}

⇒ Total count = 4

∴ The correct answer is 4.

Additional Information

Definition of Prime Numbers

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Primality Test Rule

To check if N is prime, divide N by all prime numbers less than or equal to √N. If none divide N, then N is prime.

Twin Primes

Pairs of prime numbers that have a difference of 2 (e.g., 419 and 421 are twin primes).

Given:

(10)¹⁵⁰ ÷ (10)¹⁴⁶

Formula used:

a^m ÷ aⁿ = a^m−n

Calculations:

[(10)¹⁵⁰ ÷ (10)¹⁴⁶]

⇒ 10^(150−146)

⇒ 10⁴

⇒ 10 × 10 × 10 × 10

⇒ 10000

∴ The correct answer is option (3).

The correct answer is an erect and diminished image.

Key Points

• Convex mirrors always produce an erect image irrespective of the distance of the object from the mirror.
• The images formed by convex mirrors are always diminished, meaning they are smaller than the actual size of the object.
• Convex mirrors provide a wider field of view compared to plane or concave mirrors, which is crucial for vehicle safety.
• Due to these properties, convex mirrors are commonly used as rear-view mirrors in vehicles.
• The positioning of convex mirrors helps drivers see a larger area behind them, thereby reducing blind spots.

Additional Information

• Mirror Terminologies:
• Focal point (F): The point where parallel rays of light either converge or appear to diverge after reflecting from the mirror.
• Principal axis: The line passing through the center of curvature and the mirror's pole.
• Center of curvature (C): The center of the sphere of which the mirror is a part.
• Pole (P): The midpoint of the mirror's surface.
• Types of Mirrors:
• Plane mirrors: Produce virtual, erect, and same-sized images as the object.
• Concave mirrors: Can produce real, inverted images or virtual, erect images depending on the object distance from the mirror.
• Convex mirrors: Always produce virtual, erect, and diminished images.
• Applications of Convex Mirrors:
• Used in vehicle side mirrors for a wider field of view.
• Employed in surveillance systems in stores and public places.
• Utilized in road safety to give a view of oncoming traffic at blind curves and intersections.
• Image Formation by Mirrors:
• The nature, size, and orientation of the image formed depend on the type of mirror and the object's distance from the mirror.
• Convex mirrors always form virtual images as they diverge light rays.

Given Equation: 

27 ÷ 14 x 21 + 3 - 4 = ?

BODMAS Rule:

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

27 + 14 - 21 ÷3 x 4 

⇒ 27 + 14 - 7 x 4 

⇒ 41 - 28 = 13 

Hence, the correct option is "Option 1".

The correct answer is Colloid is a homogeneous mixture.

Key Points

• Colloids are mixtures where one substance of microscopically dispersed insoluble particles is suspended throughout another substance.
• Colloids cannot be separated by filtration due to the small size of the dispersed particles.
• Colloids are heterogeneous mixtures because the composition is not uniform throughout.
• Particles in a colloid do not settle down when left undisturbed because of their small size and constant motion caused by Brownian motion.

Additional Information

• Brownian Motion:
• The random movement of particles suspended in a fluid (liquid or gas) resulting from their collision with fast atoms or molecules in the gas or liquid.
• Tyndall Effect:
• The scattering of light by particles in a colloid or in a very fine suspension.
• Types of Colloids:
• Based on the state of the dispersed phase and the dispersion medium, colloids can be classified into various types like sols, gels, foams, and emulsions.
• Examples of Colloids:
• Milk (emulsion), fog (aerosol), and jelly (gel).

Shortcut Trick

For Mean Proportional (MP) between 18 and y:

MP² = 18 × y

⇒ 72 × 72 = 18 × y

⇒ y = (72 × 72) ÷ 18 = 4 × 72 = 288

∴ The correct answer is 288.

Alternate Method

Given:

First number = 18

Second number = y

Mean Proportional = 72

Formula Used:

Mean Proportional = √(a × b)

Calculations:

⇒ 72 = √(18 × y)

Squaring both sides:

⇒ 72² = 18 × y

⇒ 5184 = 18 × y

⇒ y = 5184 ÷ 18

⇒ y = 288

∴ The correct answer is 288.

Additional Information

Third Proportional

If a, b, and c are in continued proportion, then c is the third proportional where c = b²/a.

Fourth Proportional

For four numbers a, b, c, and d in proportion (a:b = c:d), d is the fourth proportional where d = (b × c)/a.

Continued Proportion

Three numbers a, b, c are in continued proportion if a/b = b/c, which implies b² = ac.

Shortcut Trick

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

Speed = 25 × (18/5) = 5 × 18 = 90 km/h.

∴ The correct answer is 90 km/h.

Alternate Method

Given:

Speed in m/s = 25 m/s

Formula Used:

Speed (km/h) = Speed (m/s) × (3600 / 1000)

Calculations:

⇒ 1 m = 1/1000 km

⇒ 1 sec = 1/3600 h

⇒ Speed = 25 × (1/1000) ÷ (1/3600)

⇒ Speed = 25 × (3600 / 1000)

⇒ Speed = 25 × (18 / 5)

⇒ Speed = 5 × 18

⇒ Speed = 90 km/h

∴ The correct answer is 90 km/h.

Additional Information

Speed Conversion Rules

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

Average Speed

Average Speed = Total Distance ÷ Total Time. For two equal distances with speeds x and y, Average Speed = 2xy/(x + y).

Relative Speed

Same direction: Subtract speeds (u − v). Opposite direction: Add speeds (u + v).

The correct answer is 1 : 1.

Key Points

• In the absence of air resistance, the acceleration due to gravity (g) is constant for all objects regardless of their masses.
• The time taken to fall from a certain height depends only on the height and the gravitational acceleration, not on the mass of the object.
• Both bodies, one of mass m and the other of mass 4m, will experience the same gravitational pull and will fall at the same rate.
• According to the equations of motion, the time taken to reach the ground is given by −−√t=2hg−−√t=2hg−−√t=2hg−−√[Math Processing Error]

t=2hg−−√t=2hg

             \\(t=\sqrt{\frac{2g}{h}} \\), which is the same for both bodies.

• Therefore, the ratio of the time taken by the two bodies to reach the ground is 1:1.

Additional Information

• Gravitational Acceleration (g)
• The acceleration of an object due to the Earth's gravity is approximately 9.8 m/s².
• It is denoted by the symbol "g" and is a constant value near the Earth's surface.
• Equations of Motion
• The equations of motion describe the relationship between the displacement, velocity, acceleration, and time of an object in motion.
• For free fall, the time taken to reach the ground is calculated using $t=\sqrt{\frac{2g}{h}}$−−√t=2hg−−√t=2hg−−√t=2hg−−√[Math Processing Error]

t=2hg−−√t=2hg

• Mass Independence
• In the absence of air resistance, the mass of an object does not affect the time it takes to fall to the ground.
• This principle was famously demonstrated by Galileo's experiments in the late 16th century.
• Free Fall
• Free fall is the motion of an object where gravity is the only force acting upon it.
• In free fall, all objects fall at the same rate regardless of their mass.

Shortcut Trick

For HCF, find the difference between the numbers: 360 − 240 = 120 and 480 − 360 = 120.

Since the minimum difference is 120, check if 120 divides all numbers.

240/120 = 2, 360/120 = 3, 480/120 = 4. All are divisible.

∴ The correct answer is 120.

Alternate Method

Given: Numbers are 240, 360, and 480.

Formula Used: Prime Factorization or Common Division Method.

⇒ Prime factors of 240 = 2⁴ × 3¹ × 5¹

⇒ Prime factors of 360 = 2³ × 3² × 5¹

⇒ Prime factors of 480 = 2⁵ × 3¹ × 5¹

⇒ HCF = Lowest power of common factors = 2³ × 3¹ × 5¹

⇒ HCF = 8 × 3 × 5 = 120

∴ The correct answer is 120.

Additional Information

HCF (Highest Common Factor)

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

Difference Method

HCF of a set of numbers is always a factor of the difference between any two numbers in that set.

LCM and HCF Relationship

For two numbers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF × LCM.

The correct answer is ATP.

Key Points

• ATP (Adenosine Triphosphate) is known as the energy currency of the cell as it provides energy for most cellular processes.
• ATP is produced in the mitochondria through cellular respiration, particularly during the process of oxidative phosphorylation.
• It releases energy when its phosphate bonds are hydrolyzed, converting ATP to ADP (Adenosine Diphosphate).
• ATP is crucial for various functions such as muscle contraction, nerve impulse propagation, and chemical synthesis.

Additional Information

• Cellular Respiration:
• The process by which cells convert glucose and oxygen into ATP, carbon dioxide, and water.
• It consists of three main stages: Glycolysis, the Citric Acid Cycle (Krebs Cycle), and Oxidative Phosphorylation.
• ADP (Adenosine Diphosphate):
• ADP is the product of ATP dephosphorylation and can be converted back into ATP through cellular respiration.
• Photosynthesis:
• In plants, ATP is also produced during the light reactions of photosynthesis, which occurs in the chloroplasts.
• Enzymes:
• Various enzymes like ATP synthase play a critical role in the formation of ATP during cellular respiration.

Shortcut Trick

Total Sum = Average × Count = 72 × 8

Least Number = 1/16 × Total Sum

Least Number = (1/16) × 72 × 8 = 72 ÷ 2 = 36

∴ The correct answer is 36.

Alternate Method

Given:

Average of 8 numbers = 72

Least number = 1/16 of the Total Sum

Calculations:

⇒ Total Sum = Average × n

⇒ Total Sum = 72 × 8 = 576

⇒ Least Number = (1/16) × 576

⇒ Least Number = 36

∴ The correct answer is 36.

Additional Information

Basic Average Formula

The Average is defined as the Sum of observations divided by the Number of observations. Formula: Average = Σx ÷ n.

Summation Rule

To find the Total Sum when the average is known, multiply the Average by the Total count (n).

Fractional Parts

If a value is a fraction 1/k of the total, the total can be represented as k units and the value as 1 unit.

The correct answer is Justice Ajay Manikrao Khanwilkar.

Key Points

• Justice Ajay Manikrao Khanwilkar has been appointed as the chairperson of the Lokpal in February 2024.
• He is a retired Judge of the Supreme Court of India, having served from May 2016 to July 2022.
• Justice Khanwilkar has a rich judicial career, including serving as the Chief Justice of the Madhya Pradesh High Court and as a Judge in the Bombay High Court.
• His appointment is expected to bring a wealth of experience and integrity to the Lokpal, India's anti-corruption ombudsman institution.

Additional Information

• Lokpal:
• The Lokpal and Lokayuktas Act, 2013, establishes a multi-member body to investigate and prosecute corruption cases against public servants in India.
• The Lokpal is an anti-corruption institution consisting of a chairperson and up to eight members.
• It has jurisdiction over all Members of Parliament and central government employees in cases of corruption.
• Previous Chairpersons:
• Justice Pinaki Chandra Ghose was the first chairperson of the Lokpal, appointed in March 2019.
• He served until his retirement in May 2022.
• Selection Process:
• The chairperson and members of the Lokpal are selected by a committee comprising the Prime Minister, the Chief Justice of India, the Lok Sabha Speaker, the Leader of the Opposition, and an eminent jurist nominated by the President.
• Role and Powers:
• The Lokpal has the authority to conduct preliminary inquiries, order investigations, and prosecute cases of corruption.
• It can also recommend disciplinary action against public servants found guilty of corruption.

The correct answer is Plasma membrane, nucleus and cytoplasm.

Key Points

• The plasma membrane surrounds the cell, providing structural support and regulating the movement of substances in and out of the cell.
• The nucleus houses the cell's genetic material (DNA) and is responsible for regulating gene expression and cell division.
• The cytoplasm is a gel-like substance where most cellular activities occur, including metabolic pathways and organelle function.
• These three features are fundamental to maintaining cell integrity and facilitating cellular processes.

Additional Information

• Mitochondria: Known as the powerhouse of the cell, mitochondria are responsible for producing ATP through cellular respiration.
• Golgi apparatus: Involved in modifying, sorting, and packaging proteins and lipids for secretion or delivery to other organelles.
• Endoplasmic Reticulum (ER): Exists in two forms, rough ER (with ribosomes) and smooth ER (without ribosomes), and is involved in protein and lipid synthesis.
• Lysosomes: Contain digestive enzymes to break down waste materials and cellular debris.
• Cytoskeleton: A network of protein filaments and tubules providing structural support and facilitating cell movement, shape, and division.

Statement:

Many trains on the Arakkonam-Chennai route are running several hours late today.

Reasons:

• Reason I: Railways has decided to run two holiday special trains between Kolkata and Patna from November to December 2023.
• Reason II: A major train accident occurred at Arakkonam Junction last night, where seven bogies of an express train derailed and fell across the tracks.

Analysis:

• Reason I: This reason is irrelevant to the statement. The fact that holiday trains are running between Kolkata and Patna has no direct impact on trains running on the Arakkonam-Chennai route.
• Reason II: This reason is highly relevant to the statement. A major train accident at Arakkonam Junction would directly cause delays and disruptions on the Arakkonam-Chennai route.

Conclusion:

Only Reason II (the train accident) is a possible and logical explanation for the delayed trains on the Arakkonam-Chennai route.

Therefore, the correct answer is option 2) Only II is a possible reason.

The correct answer is option 4.

Key Points

• Kinetic energy (KE) of a moving body is given by the formula KE = 0.5 * m * v².
• KE is directly proportional to the mass (m) of the body.
• KE is directly proportional to the square of the velocity (v²) of the body.
• Doubling the mass of the body will double its kinetic energy, keeping velocity constant.
• Doubling the velocity of the body will quadruple its kinetic energy, keeping mass constant.

Additional Information

• Kinetic Energy (KE): The energy possessed by an object due to its motion, dependent on mass and velocity.
• Mass (m): The amount of matter in a body, which directly influences the kinetic energy of the body.
• Velocity (v): The speed of an object in a particular direction, crucial in determining the kinetic energy as it is squared in the formula.
• Direct Proportionality: When one quantity increases, the other quantity increases at the same rate. KE is directly proportional to both mass and the square of velocity.
• Energy Conservation: In a closed system, the total energy remains constant. Kinetic energy can be transformed into other forms of energy but the total energy remains the same.

Shortcut Trick

According to the question, 60% of a number − 50 = 40.

Directly solving for the required value: 60% of the number = 40 + 50.

⇒ 60% of the number = 90.

∴ The correct answer is 90.

Alternate Method

Let the number be x.

Given: 60% of x − 50 = 40

⇒ (60/100) × x − 50 = 40

⇒ 0.6x − 50 = 40

⇒ 0.6x = 40 + 50

⇒ 0.6x = 90

The question asks for 60% of the same number, which is 0.6x.

⇒ Required Value = 90

∴ The correct answer is 90.

Additional Information

Percentage to Fraction Conversion

To simplify calculations, convert 60% to a fraction: 60/100 = 3/5. The equation becomes (3/5)x − 50 = 40.

Finding the Original Number

If the question asked for the original number: 0.6x = 90 → x = 90 ÷ 0.6 = 150.

Successive Percentage Change

For two successive changes of a% and b%, the net percentage change is [a + b + (ab/100)]%.

Family tree

In a certain code language,

'P + Q' means 'P is the father of Q',

'P - Q' means 'P is the wife of Q',

'P × Q' means 'P is the brother of Q' and

'P ÷ Q' means 'P is the sister of Q'.

Given,

‘A + B - C + D × E'

So,  A is Mother’s father to E

Hence the correct answer is "Option 1"

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

According to the question such symbols which are immediately preceded by an odd number and also immediately followed by an odd number:

Required condition: Odd - Symbol - Odd

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

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

Hence, "Option 1" is the correct answer.

The correct answer is 3) Both statements I and II are correct.

Key Points

• Non-metallic oxides such as CO₂ and SO₂ react with bases to form salt and water, demonstrating their acidic nature.
• Statement I is correct as it describes the neutralization reaction between a non-metallic oxide and a base.
• Statement II is correct as non-metallic oxides are indeed acidic in nature, meaning they react with bases.
• Examples include CO₂ reacting with NaOH to form Na₂CO₃ (sodium carbonate) and water.

Additional Information

• Acid-Base Reactions:
• Acid-base reactions involve the transfer of protons (H⁺) from the acid to the base.
• These reactions result in the formation of water and a salt.
• Examples of Non-Metallic Oxides:
• Carbon dioxide (CO₂), sulfur dioxide (SO₂), and nitrogen dioxide (NO₂) are common non-metallic oxides.
• These oxides typically react with water to form acids.
• Neutralization Reactions:
• In a neutralization reaction, an acid and a base react to form water and a salt.
• This type of reaction is essential in various industrial and biological processes.
• Properties of Acids and Bases:
• Acids have a sour taste and can turn blue litmus paper red.
• Bases have a bitter taste and can turn red litmus paper blue.

The correct answer is saliva.

Key Points

• The gastric glands in the stomach are responsible for secreting various substances that aid in digestion.
• These glands release pepsinogen, which is converted to pepsin in the presence of hydrochloric acid.
• Hydrochloric acid (HCl) is secreted by the parietal cells in the gastric glands and helps in maintaining an acidic environment.
• Mucus is also secreted by the gastric glands to protect the stomach lining from the corrosive effects of HCl and digestive enzymes.
• Saliva is not secreted by the gastric glands; it is produced by the salivary glands located in the mouth.

Additional Information

• Pepsinogen: An inactive enzyme precursor secreted by the chief cells in the stomach, which is activated to pepsin by the acidic environment.
• Hydrochloric Acid (HCl): Produced by the parietal cells in the stomach, it creates an acidic environment, which is essential for the activation of pepsin and for killing pathogens.
• Mucus: Secreted by the mucous cells in the stomach lining, it forms a protective barrier to prevent the stomach lining from being digested by gastric juices.
• Saliva: A digestive fluid produced by the salivary glands in the mouth, containing enzymes like amylase that begin the process of digestion.
• Gastric Glands: Located in the lining of the stomach, these glands include mucous cells, parietal cells, and chief cells, each secreting different substances necessary for digestion.

Shortcut Trick

Net Successive Discount = a + b − (a × b) ÷ 100

Here, a = 40 and b = 20.

Effective Discount = 40 + 20 − (40 × 20) ÷ 100

Effective Discount = 60 − 800 ÷ 100 = 60 − 8 = 52%.

∴ The correct answer is 52%.

Alternate Method

Given: First discount = 40%, Second discount = 20%. Formulas: SP = MP × (100 − d₁)% × (100 − d₂)% | Equivalent Discount = (MP − SP) ÷ MP × 100

⇒ Let the Marked Price (MP) be 100.

⇒ Price after 40% discount = 100 − 40 = 60.

⇒ Price after 20% additional discount = 60 − (20% of 60) = 60 − 12 = 48.

⇒ Total Discount = MP − Final SP = 100 − 48 = 52.

⇒ Equivalent Discount Percentage = (52 ÷ 100) × 100 = 52%.

∴ The correct answer is 52%.

Additional Information

Successive Discounts

When two or more discounts are applied one after another on the reduced price, they are called successive discounts. The net discount is always less than the sum of individual discount rates.

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). Selling Price (SP) = Marked Price − Discount.

The correct answer is Option 2: ₹125 crore.

Key Points

• The Board of Control for Cricket in India (BCCI) announced ₹125 crore as the prize money for the winner of the men's T20 World Cup 2024.
• This announcement aligns with BCCI's commitment to promoting cricket and providing substantial rewards for outstanding performances.
• The prize money reflects the increasing commercial success and popularity of T20 cricket globally.
• BCCI's decision aims to incentivize teams and players, enhancing the competitive spirit of the tournament.
• This amount is significantly higher than previous prize distributions, demonstrating the growing financial stakes in international cricket.

Additional Information

• Men's T20 World Cup:
• The ICC Men's T20 World Cup is an international cricket championship organized by the International Cricket Council (ICC).
• The tournament features teams from around the world competing in the T20 format, which is a shorter, more dynamic version of cricket.
• The first T20 World Cup was held in 2007, and it has since become one of the most popular events in the sport.
• BCCI (Board of Control for Cricket in India):
• BCCI is the governing body for cricket in India, overseeing all domestic and international cricket operations in the country.
• Founded in 1928, BCCI is one of the richest and most powerful cricket boards in the world.
• It is responsible for organizing major cricket tournaments in India, including the Indian Premier League (IPL).
• Commercial Success of T20 Cricket:
• T20 cricket has revolutionized the sport, attracting a wider audience with its fast-paced and entertaining format.
• It has led to significant commercial opportunities, including broadcasting rights, sponsorships, and merchandise sales.
• The format has also seen the emergence of various T20 leagues around the world, such as the IPL, Big Bash League (BBL), and Caribbean Premier League (CPL).
• Prize Money in Cricket:
• Prize money in cricket tournaments serves as a major incentive for teams and players, promoting higher levels of performance and competition.
• It also reflects the economic growth and financial health of the sport, driven by increasing viewership and commercial interests.
• Significant prize money allocations are seen in major tournaments like the ICC Cricket World Cup, IPL, and T20 World Cup.

Shortcut Trick

Ratio of A : B is found by the inverse of their fractional coefficients.

(1/2) × A = (1/3) × B ⇒ A : B = 2 : 3.

Total ratio parts = 2 + 3 = 5 units. Given 5 units = ₹2,000.

1 unit = 400. B's part (3 units) = 3 × 400 = ₹1,200.

∴ The correct answer is ₹1200.

Alternate Method

Given: Total sum = ₹2,000. Condition: (1/2) of A = (1/3) of B.

⇒ Let (1/2)A = (1/3)B = k

⇒ A = 2k and B = 3k

⇒ A + B = 2k + 3k = 5k

⇒ 5k = 2,000

⇒ k = 2,000 ÷ 5 = 400

⇒ B's part = 3k = 3 × 400 = 1,200

∴ The correct answer is ₹1200.

Additional Information

Ratio of Equality

If aA = bB, then the ratio A : B is b : a. This is often used in division problems involving fractions of shares.

Compound Ratio

The ratio of the products of the corresponding terms of two or more ratios is called the compound ratio (e.g., (a×c) : (b×d)).

Proportional Division

To divide a quantity S in ratio x : y, the parts are [x/(x+y)] × S and [y/(x+y)] × S.

The correct answer is 1.

Key Points

• NITI Aayog does not prepare the National Indicator Framework (NIF); this task is primarily undertaken by the Ministry of Statistics and Programme Implementation (MoSPI).
• The NIF is crucial for monitoring the progress of Sustainable Development Goals (SDGs) and is developed in consultation with various stakeholders, including government bodies, international agencies, and civil society organizations.
• NITI Aayog plays a significant role in fostering competitive federalism by encouraging states and Union Territories (UTs) to actively participate in achieving SDG targets.
• Benchmarking states based on SDG performance metrics is another crucial function of NITI Aayog, helping to identify areas that need improvement and promoting best practices.
• NITI Aayog serves as a collaborative platform for states and UTs, facilitating the exchange of ideas and strategies to achieve the SDGs effectively.

Additional Information

• Sustainable Development Goals (SDGs):
• The SDGs are a set of 17 global goals adopted by all United Nations Member States in 2015 as part of the 2030 Agenda for Sustainable Development.
• The goals cover a broad range of social, economic, and environmental development issues.
• They aim to end poverty, protect the planet, and ensure prosperity for all.
• NITI Aayog:
• The National Institution for Transforming India, known as NITI Aayog, is a policy think-tank of the Government of India, established with the aim to achieve sustainable development goals.
• It was formed on January 1, 2015, replacing the Planning Commission.
• NITI Aayog promotes cooperative federalism through structured support initiatives and mechanisms with the states.
• National Indicator Framework (NIF):
• The NIF is designed to track the progress of SDG targets in India.
• It includes a comprehensive set of indicators that are periodically reviewed and updated.
• The framework helps in identifying data gaps and areas that require policy intervention.
• Ministry of Statistics and Programme Implementation (MoSPI):
• MoSPI is responsible for the development and maintenance of statistical standards and the coordination of statistical activities in India.
• It is the nodal agency for the preparation of the National Indicator Framework.
• MoSPI ensures the availability of reliable, timely, and credible data for policymakers and stakeholders.

The correct answer is -4D.

Key Points

• The power of a lens (P) is calculated using the formula P = 1/f, where f is the focal length in meters.
• Given the focal length (f) is -25 cm, which is -0.25 meters (since 1 cm = 0.01 meters).
• Substituting the value into the formula: P = 1 / -0.25 = -4 Diopters (D).
• A negative power indicates that the lens is a diverging (concave) lens.
• Therefore, the power of the lens is -4D, making option 3 the correct answer.

Additional Information

• Diopter (D): A unit of measurement for the optical power of a lens, defined as the reciprocal of the focal length in meters.
• Focal Length (f): The distance between the center of a lens and its focus, where parallel rays of light converge or appear to diverge.
• Concave Lens: A lens that diverges light rays passing through it, typically used to correct myopia (nearsightedness).
• Convex Lens: A lens that converges light rays passing through it, typically used to correct hyperopia (farsightedness).
• 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.

The correct answer is 2) i - b, ii - c, iii - a, iv - d.

Key Points

• Ketone uses the suffix -one indicating the presence of a carbonyl group (C=O).
• Alkene uses the suffix -ene indicating the presence of a carbon-carbon double bond (-C=C-).
• Aldehyde uses the suffix -al indicating the presence of a formyl group (-CHO).
• Carboxylic acid uses the suffix -oic acid indicating the presence of a carboxyl group (-COOH).

Additional Information

• Keto Group (C=O):
• Found in ketones, characterized by the carbonyl group bonded to two carbon atoms.
• Example: Propanone (acetone), the simplest ketone.
• Alkene Group (-C=C-):
• Alkenes are hydrocarbons with at least one carbon-carbon double bond.
• Example: Ethene (ethylene), used in the production of polyethylene.
• Formyl Group (-CHO):
• Found in aldehydes, characterized by a carbonyl group bonded to at least one hydrogen atom.
• Example: Methanal (formaldehyde), used in the production of resins.
• Carboxyl Group (-COOH):
• Found in carboxylic acids, characterized by a carbonyl and hydroxyl group attached to the same carbon.
• Example: Ethanoic acid (acetic acid), a key component of vinegar.

Shortcut Trick

Ratio of Father : Son currently is 7 : 1 (diff = 6).

Ratio after 3 years is 5 : 1 (diff = 4). To equate difference, multiply 1st by 2 and 2nd by 3.

New ratios: 14 : 2 → 15 : 3. Change of 1 unit = 3 years. Current ages: 42 and 6.

Current total age = 48 years. Target total = 58 years. Required increase = 10 years.

Since two people are involved, years needed = 10 ÷ 2 = 5 years.

∴ The correct answer is 5 years.

Alternate Method

Given: Present age ratio 7:1. After 3 years, ratio becomes 5:1.

Let Son's present age = x and Father's present age = 7x.

⇒ (7x + 3) = 5 × (x + 3)

⇒ 7x + 3 = 5x + 15

⇒ 2x = 12 ⇒ x = 6

⇒ Father's present age = 42 years, Son's present age = 6 years.

⇒ Let after 'n' years, sum be 58: (42 + n) + (6 + n) = 58

⇒ 48 + 2n = 58 ⇒ 2n = 10 ⇒ n = 5

∴ The correct answer is 5 years.

Additional Information

Age Difference Property

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

Sum of Ages Property

If 'n' years pass, the sum of the ages of 'k' people increases by n × k years.

Ratio of Ages

Ratios of ages change over time; they can only be used directly if the time frame (present, past, future) is the same for all terms.

Shortcut Trick

Identify complementary angles: 48° + 42° = 90° and 40° + 50° = 90°.

Apply shortcut results for complementary pairs:

Numerator: sin² A + sin² (90−A) = 1.

Denominator: tan² B − cosec² (90−B) = tan² B − sec² B = −1.

Result = 1 ÷ (−1) = −1.

∴ The correct answer is -1.

Alternate Method

Given: Expression = (sin² 48° + sin² 42°) ÷ (tan² 40° − cosec² 50°)

Formula Used:

1. Complementary Angles: sin θ = cos(90° − θ) and cosec θ = sec(90° − θ)
2. Trigonometric Identities: sin² θ + cos² θ = 1 and sec² θ − tan² θ = 1

⇒ Numerator = sin² 48° + sin² (90° − 48°)

⇒ Numerator = sin² 48° + cos² 48° = 1

⇒ Denominator = tan² 40° − cosec² (90° − 40°)

⇒ Denominator = tan² 40° − sec² 40°

⇒ Since sec² θ − tan² θ = 1, then tan² θ − sec² θ = −1

⇒ Expression = 1 ÷ (−1) = −1

∴ The correct answer is -1.

Additional Information

Complementary Angle Relationships

For any angle θ, sin θ = cos(90° − θ), tan θ = cot(90° − θ), and sec θ = cosec(90° − θ).

Fundamental Trigonometric Identities

1. sin² θ + cos² θ = 1 | 2. 1 + tan² θ = sec² θ | 3. 1 + cot² θ = cosec² θ.

Sign Convention for Identities

Always check the order of terms; for example, sec² θ − tan² θ = 1, but tan² θ − sec² θ = −1.

The correct answer is abiotic components.

Key Points

• Abiotic components refer to the non-living physical and chemical elements in an ecosystem.
• These components include factors such as temperature, rainfall, wind, soil, and minerals.
• Abiotic factors significantly influence the types of organisms that can live in an ecosystem and their distribution.
• Examples of abiotic components also include sunlight, water, air, and nutrients.
• Abiotic components interact with biotic components (living organisms) to create a balanced ecosystem.

Additional Information

• Biotic Components:
• Biotic components are the living organisms in an ecosystem, such as plants, animals, fungi, and microorganisms.
• They interact with abiotic components to sustain life and maintain ecological balance.
• Decomposers:
• Decomposers are organisms like bacteria and fungi that break down dead organic matter, returning nutrients to the soil.
• They play a crucial role in nutrient cycling within ecosystems.
• Importance of Abiotic Factors:
• Abiotic factors determine the physical environment in which biotic components live.
• They influence growth rates, reproductive success, and survival of organisms.
• Interaction of Abiotic and Biotic Factors:
• Both sets of components interact to create a dynamic and functional ecosystem.
• Changes in abiotic factors can lead to shifts in the types of biotic communities present.

Logic followed here is,

Hence the correct answer is "Option 4"

The correct answer is It has a single chromosome..

Key Points

• Prokaryotic cells typically contain a single, circular chromosome, which is not enclosed in a nucleus.
• These cells lack a membrane-bound nucleus; instead, their genetic material is located in a nucleoid region.
• Prokaryotic cells do not possess membrane-bound organelles such as mitochondria or chloroplasts.
• Examples of prokaryotic cells include bacteria and archaea.

Additional Information

• Plasmids: Small, circular DNA molecules found in prokaryotes that are separate from the chromosomal DNA and can replicate independently.
• Ribosomes: Prokaryotic ribosomes are 70S, composed of 50S and 30S subunits, and are involved in protein synthesis.
• Cell Wall: Most prokaryotes have a rigid cell wall made of peptidoglycan (in bacteria) or pseudopeptidoglycan (in archaea) that provides structural support and protection.
• Binary Fission: Prokaryotic cells reproduce asexually through a process called binary fission, where the cell divides into two genetically identical daughter cells.

The correct answer is Both amino acids and sucrose.

Key Points

• Phloem transports multiple organic compounds, including both amino acids and sucrose, essential for plant growth and development.
• Sucrose is the primary form of carbohydrate transported through the phloem, providing energy to various parts of the plant.
• Amino acids are also transported through the phloem to support protein synthesis in growing regions.
• The transport of these substances ensures that non-photosynthetic parts of the plant, like roots and developing fruits, receive necessary nutrients.

Additional Information

• Phloem Structure:
• The phloem consists of sieve tube elements, companion cells, phloem fibers, and phloem parenchyma, which work together to transport nutrients.
• Translocation Process:
• The movement of nutrients through the phloem is known as translocation and is driven by pressure flow mechanisms.
• Source to Sink Movement:
• Nutrients are transported from 'source' regions (photosynthetic tissues) to 'sink' regions (growing or storage tissues).
• Role in Plant Health:
• Efficient phloem transport is crucial for overall plant health, affecting growth, reproduction, and response to environmental stresses.

BODMAS Rule:

Decoding the given information:

Now replacing the signs from left to right using BODMAS Rule in each option, we get:

Option 1) 28 D 39 A 3 C 12 B 7

⇒ 28 - 39 ÷ 3 + 12 × 7

⇒ 28 - 13 + 84

⇒ 15 + 84 = 99 (Matches)

Option 2) 28 C 39 B 3 D 12 A 7

⇒ 28 + 39 × 3 - 12 ÷ 7

⇒ 28 + 117 - 1.71 (approx.)

⇒ 145 - 1.71 = 143.29 (approx.) (Does not match 99)

Option 3) 28 A 39 D 3 B 12 C 7

⇒ 28 ÷ 39 - 3 × 12 + 7

⇒ 0.72 (approx.) - 36 + 7

⇒ -28.28 (approx.) (Does not match 99)

Option 4) 28 B 39 C 3 A 12 D 7

⇒ 28 × 39 + 3 ÷ 12 - 7

⇒ 1092 + 0.25 - 7

⇒ 1085.25 (Does not match 99)

Therefore, the correct answer is option 1) 28 D 39 A 3 C 12 B 7

The correct answer is a concave mirror.

Key Points

• A dentist uses a concave mirror to examine the teeth.
• Concave mirrors provide a magnified and upright image of the teeth, which helps in detailed examination.
• The curved surface of a concave mirror helps in focusing light, providing better illumination in the oral cavity.
• Concave mirrors are preferred because they allow dentists to see a larger area of the mouth clearly.

Additional Information

• Convex Mirror:
• A convex mirror diverges light rays and is used for a wider field of view, such as in vehicle side mirrors.
• It provides a smaller, upright, and diminished image, which is not suitable for dental examination.
• Plane Mirror:
• A plane mirror reflects light without altering the size of the image.
• It provides a virtual, upright image of the same size as the object, but it does not magnify, making it less useful for detailed dental work.
• Plano-Convex Mirror:
• A plano-convex mirror is typically used in focusing applications, such as in telescopes and laser systems.
• It is not used in dental practices due to its specific focusing properties.
• Optical Properties:
• Concave mirrors converge light rays to a focal point, allowing for magnification of the image.
• Convex mirrors and plane mirrors do not offer the same level of magnification and focus required for dental examinations.

The correct answer is 10g J.

Key Points

• The work done (W) by the porter on the luggage is calculated using the formula W = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
• Here, m = 10 kg, g = 9.8 m/s² (standard value of acceleration due to gravity), and h = 1 m.
• Substituting the values, W = 10 kg × 9.8 m/s² × 1 m.
• Thus, the work done by the porter is 10g joules (since g is the symbol for 9.8 m/s²).

Additional Information

• Work Done:
• In physics, work is defined as a measure of energy transfer that occurs when an object is moved over a distance by an external force.
• The formula for work done is W = F × d × cos(θ), where F is the force applied, d is the displacement, and θ is the angle between the force and displacement vectors.
• SI Unit of Work:
• The SI unit of work is the joule (J).
• 1 joule is equivalent to 1 newton-meter (N·m).
• Gravitational Force:
• Gravitational force is the force of attraction between two masses.
• It is given by the formula F = mg, where m is the mass and g is the acceleration due to gravity.
• Energy Transfer:
• Work is a form of energy transfer from one system to another.
• When work is done on an object, energy is transferred to the object, often resulting in a change in its kinetic or potential energy.

The correct answer is Union Bank of India.

Key Points

• Union Finance Minister inaugurated Nari Shakti Branches of Union Bank of India on 9 November 2024.
• The branches are located in Bengaluru, Chennai, Visakhapatnam, and Jaipur.
• Nari Shakti Branches aim to empower women by providing specialized banking services.
• The initiative is part of the bank's efforts to promote financial inclusion among women.

Additional Information

• Financial Inclusion:
• Financial inclusion refers to making financial services accessible and affordable to all individuals, especially those underserved by the banking sector.
• It aims to ensure that everyone has access to basic financial services like savings, credit, insurance, and pensions.
• Financial inclusion is crucial for reducing poverty and fostering economic growth.
• Women Empowerment:
• Women empowerment involves creating an environment where women can make independent decisions for their personal development.
• It includes providing access to education, employment, and financial services.
• Empowered women contribute significantly to the economic and social development of their communities.
• Union Bank of India:
• Union Bank of India is one of the largest government-owned banks in India.
• It was established in 1919 and has its headquarters in Mumbai.
• The bank provides a wide range of banking and financial services to its customers.

The correct answer is Soap.

Key Points

• Sodium or potassium salts of long chain carboxylic acids are commonly referred to as soaps.
• Soaps are produced through a chemical process called saponification, where fats and oils react with a base.
• In the saponification process, triglycerides (fats/oils) are hydrolyzed to produce glycerol and soap.
• Soaps are effective in cleaning because they are surfactants, which means they lower the surface tension of water, allowing it to mix with oils and dirt.

Additional Information

• Micelle:
• A micelle is an aggregate of surfactant molecules dispersed in a liquid colloid forming a molecular assembly.
• Micelles are formed when the concentration of surfactant molecules exceeds the critical micelle concentration (CMC).
• They play a key role in the cleansing action of soaps and detergents by trapping grease and dirt.
• Detergents:
• Detergents are synthetic cleaning agents, typically made from petrochemicals.
• Unlike soaps, detergents can perform well in hard water as they do not form scum.
• Detergents are also surfactants and work by emulsifying oils and dirt.
• Saponification:
• Saponification is a chemical reaction that produces soap from fats/oils and an alkali.
• The reaction results in the formation of glycerol and soap.
• This process is crucial in traditional soap making and industrial soap production.
• Surfactants:
• Surfactants are compounds that lower the surface tension between two liquids or a liquid and a solid.
• They are the active agents in soaps and detergents that enable them to clean effectively.
• Surfactants can be classified as anionic, cationic, nonionic, or amphoteric based on their charge.

Shortcut Trick

Using the ratio method: Principal (P) : Amount (A) = 12000 : 14520

Simplifying the ratio: P : A = 120 : 145.2 = 100 : 121

Since 100 : 121 = (10)² : (11)², which corresponds to (1 + 10%)², the time period is 2 years.

∴ The correct answer is 2 years.

Alternate Method

Given: Principal (P) = ₹12,000, Amount (A) = ₹14,520, Rate (R) = 10% per annum.

Formula Used: A = P × (1 + R/100)^t, where t is the time in years.

Calculations:

→ 14520 = 12000 × (1 + 10/100)^t

→ 14520 ÷ 12000 = (11/10)^t

→ 1452 ÷ 1200 = (1.1)^t

→ 121 ÷ 100 = (1.1)^t

→ 1.21 = (1.1)^t

→ (1.1)² = (1.1)^t

⇒ t = 2 years

∴ The correct answer is 2 years.

Additional Information

Compound Interest Formula

The amount accumulated on principal P at rate R% compound interest per annum compounded annually for t years is given by A = P(1 + R/100)^t.

Effective Rate of Interest

For a rate of 10% compounded annually, the effective rate for 2 years is calculated using successive percentage change: 10 + 10 + (10 × 10)/100 = 21%.

The correct answer is +1 Dioptre.

Key Points

• The power of a lens (P) in dioptres is the reciprocal of the focal length (f) in meters, represented as P = 1/f.
• If the power of the lens is +1 Dioptre, the focal length (f) can be calculated using the formula: f = 1/P.
• Substituting the given power, f = 1/1 = 1 meter.
• A positive dioptre value indicates that the lens is a converging lens, typically used for correcting hyperopia (farsightedness).

Additional Information

• Dioptre (D): A unit of measurement for the optical power of a lens, defined as the reciprocal of the focal length in meters (1/m).
• Focal Length (f): The distance between the lens and the point where parallel rays of light converge (for a converging lens) or appear to diverge (for a diverging lens).
• Converging Lens: Also known as a convex lens, it bends light rays inward, bringing them to a focus. Used in applications like magnifying glasses and corrective lenses for hyperopia.
• Diverging Lens: Also known as a concave lens, it spreads out light rays that have been refracted through it. Used in applications like corrective lenses for myopia (nearsightedness).
• Hyperopia (Farsightedness): A condition where distant objects are seen more clearly than near ones. Converging lenses with positive dioptre values are used for correction.

Logic followed here is,

Logic: Every letter is decreased by 7.

Given,

TQSO is related to MJLH

For, VSUQ is related to OLNJ

Similarly for ROQM is related to KHJF.

Hence the correct answer is "Option 2"

The correct answer is Displacement reaction.

Key Points

• A displacement reaction occurs when a more reactive metal displaces a less reactive metal from its compound.
• This type of reaction is typically observed in aqueous solutions where metals are involved.
• For example, when zinc is placed in a copper sulfate solution, zinc displaces copper, forming zinc sulfate and copper metal.
• Displacement reactions are a subset of redox reactions, where the more reactive metal is oxidized and the less reactive metal is reduced.
• These reactions are used in various industrial processes, including metal extraction and purification.

Additional Information

• Reactivity Series:
• The reactivity series is a list of metals arranged in order of decreasing reactivity.
• It helps predict the outcomes of displacement reactions.
• Highly reactive metals like potassium and sodium are at the top, while less reactive metals like gold and platinum are at the bottom.
• Redox Reactions:
• Redox reactions involve the transfer of electrons between two substances.
• Oxidation refers to the loss of electrons, while reduction refers to the gain of electrons.
• Displacement reactions are a specific type of redox reaction.
• Applications:
• Displacement reactions are used in metallurgy for extracting metals from their ores.
• They are also utilized in galvanic cells to generate electrical energy.
• These reactions are fundamental in the manufacturing of various chemicals.
• Examples:
• Iron displacing copper from copper sulfate solution: Fe + CuSO₄ → FeSO₄ + Cu
• Magnesium displacing zinc from zinc sulfate solution: Mg + ZnSO₄ → MgSO₄ + Zn

Logic follow here is that the first letter is decreased by 4 and second letter is decreased by 3.

Option 1) JNK

Option 2) OSP

Option 3) TXV

Does not follow the same logic.

Option 4) EIF

Hence the correct answer is "Option 3"

The correct answer is Option 2.

Key Points

• At maturity, the rate of general body growth in humans begins to slow down.
• This slowing down is primarily due to the completion of puberty and the end of the adolescent growth spurt.
• During puberty, the body undergoes rapid growth and changes, including the development of secondary sexual characteristics.
• Once maturity is reached, most individuals have achieved their maximum height, and the rate of growth in other body tissues also slows down significantly.

Additional Information

• Germ Cells: These are reproductive cells (sperm in males and eggs in females) that combine during sexual reproduction to form a new organism.
• Puberty: A developmental period in humans and other animals during which physical growth and sexual maturation occur rapidly.
• Adolescent Growth Spurt: A period of rapid physical growth and development during puberty, typically resulting in a significant increase in height.
• Secondary Sexual Characteristics: Physical traits that differentiate the sexes, such as breast development in females and facial hair in males, which develop during puberty.
• Reproductive Maturity: The stage in life when an individual is fully capable of reproduction, typically marked by the completion of puberty and the development of functional reproductive organs.

Given:

Manju ranked 8th from the top and 17nd from the bottom in his class.

Total students = Rank from Top + Rank from Bottom − 1

= 8 + 17− 1

= 25 − 1

= 24

Thus, total 24 students are there in the class.

Hence, the correct answer is "Option 2".

Shortcut Trick

Profit % = 11(1/9)% = 1/9 in fractional form.

This means for every 9 units of False Weight, the profit is 1 unit.

Ratio of True Weight to False Weight = (9 + 1) : 9 = 10 : 9.

Given 10 units = 1000 gm (1 kg).

⇒ 1 unit = 100 gm.

⇒ 9 units = 9 × 100 gm = 900 gm.

∴ The correct answer is 900 gm weight.

Alternate Method

Given:

Profit percentage = 11(1/9)% = 100/9%

True Weight = 1 kg = 1000 gm

Formula Used:

Profit % = [ (True Weight − False Weight) ÷ False Weight ] × 100

Calculations:

Let the False Weight used by the shopkeeper be x gm.

⇒ 100/9 = [ (1000 − x) ÷ x ] × 100

⇒ 1/9 = (1000 − x) ÷ x

⇒ x = 9 × (1000 − x)

⇒ x = 9000 − 9x

⇒ 10x = 9000

⇒ x = 900 gm

∴ The correct answer is 900 gm weight.

Additional Information

Dishonest Dealer Concept

When a dealer sells at Cost Price but uses less weight, the Profit % is always calculated on the False Weight (what he actually gives).

Case of Dual Profit

If a dealer marks up the price by a% and also uses a false weight giving b% less, the Total Profit % = [ (100 + a) / (100 − b) × 100 ] − 100.

Successive Percentage Method

For cheating while buying (x%) and selling (y%), the Net Profit % can be calculated using the formula: x + y + (xy/100).

Logic followed here is,

Logic: Every letter is increased by 5.

Given,

MPLO is related to RUQT

For, ILHK is related to NQMP.

Similarly for FIEH is related to KNJM.

Hence the correct answer is "Option 3"

The correct answer is stomach.

Key Points

• Pepsin is a proteolytic enzyme that is secreted by the chief cells in the stomach lining.
• The secretion is initially in the form of an inactive precursor called pepsinogen.
• Pepsinogen is converted to active pepsin in the acidic environment of the stomach, primarily due to the action of hydrochloric acid (HCl).
• Pepsin plays a crucial role in the digestion of proteins, breaking them down into smaller peptides.
• The pH level in the stomach, which ranges from 1.5 to 3.5, is optimal for pepsin activity.

Additional Information

• Chief Cells:
• These are cells in the stomach lining that secrete pepsinogen and gastric lipase.
• Chief cells are also known as zymogenic cells.
• Hydrochloric Acid (HCl):
• Produced by parietal cells in the stomach lining.
• Creates an acidic environment, which is necessary for the conversion of pepsinogen to pepsin.
• Gastric Mucosa:
• The mucous membrane layer of the stomach, which contains the glands and the gastric pits.
• Responsible for the secretion of gastric juices, including pepsinogen and HCl.
• Protein Digestion:
• Starts in the stomach with the action of pepsin.
• Continues in the small intestine with the help of other proteolytic enzymes like trypsin and chymotrypsin.

The correct answer is (20)/(7) Ω.

Key Points

• When resistors are connected in parallel, the reciprocal of the equivalent resistance (R_eq) is the sum of the reciprocals of the individual resistances.
• The formula used is: 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃.
• For resistors with values 5Ω, 10Ω, and 20Ω, the calculation is: 1/R_eq = 1/5 + 1/10 + 1/20.
• Solving the equation: 1/R_eq = (4 + 2 + 1)/20 = 7/20, thus R_eq = 20/7 Ω.

Additional Information

• Series vs. Parallel Circuits:
• In a series circuit, resistors are connected end-to-end, and the total resistance is the sum of individual resistances.
• In a parallel circuit, resistors are connected across the same two points, and the total resistance is less than the smallest individual resistance.
• 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.
• The formula is V = IR, where V is voltage, I is current, and R is resistance.
• Applications of Parallel Circuits:
• Parallel circuits are commonly used in household wiring, allowing multiple devices to operate independently.
• They ensure that if one component fails, the rest of the circuit can still function.
• Calculating Total Resistance:
• For multiple resistors in parallel, always use the reciprocal formula to find the total or equivalent resistance.
• This method ensures accurate calculation and understanding of how current divides among different branches.

Shortcut Trick

For an equilateral triangle, the relationship between Area and side (a) is: Area = (√3/4) × a².

Given Area = 16√3, we have 16√3 = (√3/4) × a².

Eliminate √3 from both sides: 16 = a²/4 ⇒ a² = 64.

Taking square root: a = 8 cm.

∴ The correct answer is 8 cm.

Alternate Method

Given:

Area of equilateral triangle = 16√3 cm²

Formula Used:

Area = (√3/4) × (side)²

Calculations:

⇒ 16√3 = (√3/4) × a²

⇒ 16 = a² / 4

⇒ a² = 16 × 4

⇒ a² = 64

⇒ a = √64

⇒ a = 8 cm

∴ The correct answer is 8 cm.

Additional Information

Height of Equilateral Triangle

The altitude or height (h) of an equilateral triangle is given by h = (√3/2) × a.

Perimeter of Equilateral Triangle

Since all three sides are equal, the perimeter (P) = 3 × a.

Inradius and Circumradius

Inradius (r) = a / (2√3) and Circumradius (R) = a / √3. Note that R = 2r.

Shortcut Trick

Check each pair for two conditions: 1. Both numbers must be composite (not prime). 2. Their HCF must be 1 (co-prime).

Option 1: (21, 35) → Both composite, but HCF = 7.

Option 2: (19, 27) → 19 is a prime number.

Option 3: (11, 17) → Both are prime numbers.

Option 4: (8, 25) → Both are composite and HCF = 1.

∴ The correct answer is (8, 25).

Alternate Method

Given: Pairs of numbers to check for non-prime and co-prime status.

Definitions: Prime Number has exactly 2 factors. Co-prime numbers have an HCF of 1.

⇒ Case 1: (21, 35) → Factors of 21: 1, 3, 7, 21; Factors of 35: 1, 5, 7, 35. HCF = 7 (Not co-prime).

⇒ Case 2: (19, 27) → 19 is a Prime Number (Violates first condition).

⇒ Case 3: (11, 17) → Both 11 and 17 are Prime Numbers (Violates first condition).

⇒ Case 4: (8, 25) → Factors of 8: 1, 2, 4, 8; Factors of 25: 1, 5, 25. Both are Composite and HCF = 1.

∴ The correct answer is (8, 25).

Additional Information

Co-prime Numbers

Two numbers are said to be co-prime if their Greatest Common Divisor (GCD) or HCF is 1. They do not need to be prime numbers themselves.

Composite Numbers

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

Twin Primes

A pair of prime numbers that have a difference of 2, such as (11, 13) or (17, 19).

The correct answer is primary consumer.

Key Points

• Honeybees collect nectar from flowers, which makes them primary consumers as they directly feed on producers (plants).
• Primary consumers are organisms that consume producers (plants) for energy.
• In the food chain, primary consumers are typically herbivores or omnivores.
• Honeybees play a crucial role in pollination, which supports the growth of plants and the ecosystem.

Additional Information

• Producers: Organisms that produce their own food using sunlight, water, and carbon dioxide (e.g., plants, algae).
• Primary Consumers: Organisms that feed directly on producers (e.g., herbivores like cows, and insects like honeybees).
• Secondary Consumers: Organisms that consume primary consumers (e.g., carnivores like lions, and omnivores like humans).
• Decomposers: Organisms that break down dead or decaying organisms, recycling nutrients back into the ecosystem (e.g., fungi, bacteria).
• Honeybees contribute to biodiversity by aiding in plant reproduction through the process of pollination.

The correct answer is 1) Cracking of voice.

Key Points

• Cracking of voice is typically associated with puberty in boys, not girls.
• During puberty, boys experience a deepening of the voice due to the growth of the larynx and lengthening of the vocal cords.
• Girls do not usually experience a significant change in voice pitch during puberty.
• The voice changes in girls during puberty are generally more subtle and less pronounced compared to boys.

Additional Information

• Oily Skin: An increase in the production of sebum due to hormonal changes often leads to oily skin during puberty in both boys and girls.
• Increase in Breast Size: One of the primary signs of sexual maturity in girls is the development and growth of breasts.
• Menstruation: The onset of menstruation is a key indicator of sexual maturity in girls, marking the beginning of reproductive capability.
• Puberty in Girls: Typically occurs between the ages of 8 and 13 and includes physical changes such as the development of secondary sexual characteristics and the onset of menstruation.
• Hormonal Changes: Puberty is driven by hormonal changes, primarily the increase in estrogen in girls, which leads to the development of secondary sexual characteristics.

Logic follows here is that the first letter and the second letter are increased by 2.

Option 1) TY-VA 

Option 2) DI-FK

Option 3) BG-DI 

Option 4) XB-YC 

Does not follow the same logic.

Hence the correct answer is "Option 4"

Given, A, B, E, F, P, Q and R are sitting around a circular table facing the centre.

Only three people sit between R and E when counted from the left of R.

Only two people sit between E and Q.

B sits third to the right of Q.

F sits to the immediate left of P

And A sits at the remaining place.

 So B sits to the immediate right of A.

Hence the correct answer is "Option 1"

The correct answer is First successful night landing at the Kargil airfield with a C-130J Super Hercules.

Key Points

• In January 2024, the Indian Air Force achieved a significant milestone by conducting the first successful night landing at the Kargil airfield using a C-130J Super Hercules.
• This operation demonstrated the IAF's enhanced night-time operational capabilities in high-altitude and tough terrains.
• The C-130J Super Hercules is known for its versatility, capable of landing on short and unpaved airstrips, making it ideal for such challenging missions.
• This achievement marks a strategic enhancement, ensuring better logistical and tactical support in the region, especially in times of conflict or emergency.

Additional Information

• C-130J Super Hercules:
• A military transport aircraft known for its versatility and reliability.
• Capable of performing a variety of missions, including transport, medevac, and aerial refueling.
• Equipped with advanced avionics and propulsion systems to handle short and unpaved runways.
• Kargil Airfield:
• Located in the challenging terrain of the Himalayan region.
• Strategically important due to its proximity to the Line of Control (LoC).
• Used primarily for transport and logistical purposes during the Kargil War in 1999.
• Night Operations:
• Require advanced navigation and landing systems.
• Enhance the operational readiness of the air force.
• Critical for surprise and stealth missions.
• Indian Air Force (IAF):
• The air arm of the Indian Armed Forces.
• Responsible for securing Indian airspace and conducting aerial warfare.
• Continuously upgrading its fleet and capabilities to handle modern-day threats and challenges.

Given:

Word: ARTICULATE

Rule: Vowels -> next letter, Consonants -> previous letter

Apply the rule to each letter:

• A -> B
• R -> Q
• T -> S
• I -> J
• C -> B
• U -> V
• L -> K
• A -> B
• T -> S
• E -> F

Resulting letters: B Q S J B V K B S F

B appears 3 times.

Conclusion:

Only the letter B appears more than twice.

Therefore, the correct answer is option 4) B.

Formula used:

Percentage of students qualified = (Qualified / Appeared) × 100

Calculations:

For State A:

2020: (100 / 500) × 100 = 20%

2021: (150 / 600) × 100 = 25%

For State B:

2020: (200 / 600) × 100 = 33.33%

2021: (250 / 800) × 100 = 31.25%

For State C:

2020: (50 / 400) × 100 = 12.5%

2021: (100 / 500) × 100 = 20%

For State D:

2020: (60 / 300) × 100 = 20%

2021: (80 / 400) × 100 = 20%

The percentage of students qualified did NOT change from 2020 to 2021 is from state D.

∴ The correct answer is option 2.

Logic followed here is

Logic : HELP is common in both the language and 2 4 6 1 is common in both the code.

So, code for W is 8.

Hence the correct answer is option (3).

The correct answer is 29.4 N.

Key Points

• The mass of the football is given as 3 kg.
• The acceleration due to gravity on Earth is 9.8 m/s².
• Weight is calculated using the formula: Weight (W) = Mass (m) × Acceleration due to gravity (g).
• Substituting the values, W = 3 kg × 9.8 m/s².
• The weight of the football on Earth is 29.4 N.

Additional Information

• Mass and Weight:
• Mass is a measure of the amount of matter in an object, typically measured in kilograms (kg).
• Weight is the force exerted by gravity on an object, measured in Newtons (N).
• Gravitational Force:
• Gravitational force is the attractive force between two masses.
• On Earth, this force is quantified as 9.8 m/s².
• Formula for Weight:
• The formula to calculate weight is W = m × g.
• Here, W represents weight, m represents mass, and g represents the gravitational force.
• Importance of Gravity:
• Gravity keeps planets in orbit around the sun.
• It gives weight to physical objects and is responsible for the free fall of objects.

Given:

Sets: (4, 12, 48) and (7, 21, 84)

Formula: First number × 3 = Second number

Formula: Second number × 4 = Third number

Given (4, 12, 48):

4 × 3 = 12

12 × 4 = 48

For (7, 21, 84):

7 × 3 = 21

21 × 4 = 84

Option 1) (5, 45, 180):

5 × 3 = 15 (Does not match 45)

45 × 4 = 180 (Matches the third number but second number does not match)

Option 2) (15, 25, 180):

15 × 3 = 45 (Does not match 25)

25 × 4 = 100 (Does not match 180)

Option 3) (15, 45, 180):

15 × 3 = 45

45 × 4 = 180

Only Option 3 satisfies both conditions.

Option 4) (15, 45, 170):

15 × 3 = 45

45 × 4 = 180 (Does not match 170)

Therefore, the correct answer is option 3) (15, 45, 180).

Given:

Pipe 1 fills the tank in 12 hours.

Pipe 2 empties the tank in 28 hours.

Formula used:

Work done = LCM of time taken

Efficiency = Total work / Time

Calculation:

LCM of 12 and 28 = 84

Let the total capacity of the tank be 84 units.

Efficiency of Pipe 1 (filling) = 84 / 12 = 7 units/hour

Efficiency of Pipe 2 (emptying) = 84 / 28 = 3 units/hour

Net efficiency when both pipes are open = 7 - 3 = 4 units/hour

One-third capacity of the tank = 84 / 3 = 28 units

Time taken to fill one-third of the tank = 28 / 4 = 7 hours

∴ The time taken to fill one-third of the tank is 7 hours.

The correct answer is Salt and hydrogen gas.

Key Points

• When acids react with metals, they produce a salt and hydrogen gas.
• This is a typical single displacement reaction where the metal displaces hydrogen from the acid.
• For example, when zinc (Zn) reacts with hydrochloric acid (HCl), it forms zinc chloride (ZnCl₂) and hydrogen gas (H₂).
• The general equation for this type of reaction is: Metal + Acid → Salt + Hydrogen gas.
• Common metals that react with acids include zinc, magnesium, and iron.

Additional Information

• Oxidation-Reduction Reaction: In the reaction between acids and metals, the metal undergoes oxidation (loses electrons) and hydrogen ions (H⁺) from the acid are reduced (gain electrons).
• Reactivity Series: Not all metals react with acids. The reactivity series of metals determines which metals will react with acids to produce hydrogen gas.
• Safety Precautions: The reaction between metals and acids can be vigorous and produce hydrogen gas, which is highly flammable. Proper safety measures should be taken.
• Applications: This type of reaction is utilized in various industrial processes including the production of hydrogen gas and in metal refining.

The correct answer is -2.

Key Points

• The magnification (m) of a mirror is calculated using the formula: m = -v/u, where 'v' is the image distance and 'u' is the object distance.
• Here, the object distance (u) is -20 cm (negative as it is in front of the mirror) and the image distance (v) is -40 cm (negative as it is a real image formed on the same side as the object).
• Substituting the values, m = -(-40 cm) / (-20 cm) = 40 / 20 = 2.0.
• Since the image is real and inverted, the magnification will be negative: m = -2.0.
• Thus, the correct magnification of the mirror is -2.0, which corresponds to option 4.

Additional Information

• Concave Mirrors:
• Concave mirrors are spherical mirrors that curve inward, resembling a portion of the interior of a sphere.
• They are known to converge light rays to a focal point, making them useful in applications like telescopes and shaving mirrors.
• Mirror Formula:
• The mirror formula relates object distance (u), image distance (v), and focal length (f) through the equation: 1/f = 1/u + 1/v.
• Magnification:
• Magnification (m) indicates how much larger or smaller the image is compared to the object.
• For mirrors, it is calculated as the ratio of the image height to the object height or -v/u for distances.
• Real vs. Virtual Images:
• Real images are formed when light rays converge and can be projected on a screen; they are inverted.
• Virtual images occur when light rays only appear to diverge from a point; they are upright.

The correct answer is Oxygen gas.

Key Points

• When electricity is passed through an aqueous solution of sodium chloride (brine), the main products formed are hydrogen gas, chlorine gas, and sodium hydroxide.
• Hydrogen gas is produced at the cathode due to the reduction of water molecules.
• Chlorine gas is generated at the anode by the oxidation of chloride ions.
• Sodium hydroxide is formed in the solution as a result of the ions remaining after the electrolysis process.
• Oxygen gas is not produced in this process as the primary reactions involve the decomposition of water and chloride ions, not oxygen.

Additional Information

• Electrolysis:
• Electrolysis is a chemical process that uses electric current to drive a non-spontaneous chemical reaction.
• In the electrolysis of brine, the solution conducts electricity due to the presence of ions.
• Brine Solution:
• Brine is a high-concentration solution of salt (sodium chloride) in water.
• It is commonly used in the chlor-alkali industry for the production of chlorine, hydrogen, and sodium hydroxide.
• Cathode and Anode Reactions:
• At the cathode: 2H₂O + 2e^- → H₂ + 2OH^-
• At the anode: 2Cl^- → Cl₂ + 2e^-
• Industrial Applications:
• The products of brine electrolysis are used in various industries: chlorine for disinfectants and PVC, hydrogen for fuel, and sodium hydroxide for soap and paper manufacturing.

The correct answer is Sir Isaac Newton.

Key Points

• Sir Isaac Newton was the first scientist to use a glass prism to discover the spectrum of sunlight.
• He conducted the experiment in 1666, demonstrating that white light is composed of different colors.
• Newton's work laid the foundation for the field of optics.
• He published his findings in the book "Opticks" in 1704.

Additional Information

• Prism:
• A prism is a transparent optical element with flat, polished surfaces that refract light.
• Prisms can be used to break light up into its constituent spectral colors (the colors of the rainbow).
• Optics:
• Optics is the branch of physics that studies the behavior and properties of light.
• It includes the study of reflection, refraction, dispersion, and the interaction of light with matter.
• White Light:
• White light is a combination of all colors in the visible spectrum.
• When passed through a prism, white light is dispersed into its component colors.
• Newton's Contributions:
• Isaac Newton made significant contributions to mathematics, physics, and astronomy.
• He is also known for his laws of motion and universal gravitation.

The correct answer is Russia.

Key Points

• India participated in the BRICS Literature Forum 2024 held in Russia to promote the dialogue of traditions, national values, and cultures among BRICS nations.
• The BRICS Literature Forum is a significant event that brings together writers, poets, and literary figures from BRICS countries to discuss and share their cultural and literary heritage.
• Russia hosted the 2024 forum, showcasing its commitment to fostering cultural cooperation and mutual understanding among BRICS countries.
• The forum included various literary discussions, workshops, and cultural performances aimed at enhancing the literary ties between the member countries.

Additional Information

• BRICS:
• BRICS is an acronym for five major emerging economies: Brazil, Russia, India, China, and South Africa.
• These countries are known for their significant influence on regional and global affairs.
• The BRICS grouping aims to promote peace, security, and development in the global economy.
• Cultural Exchange Programs:
• Cultural exchange programs are initiatives designed to foster mutual understanding and cooperation between different countries.
• Such programs often include exchanges in the fields of arts, literature, education, and sports.
• Literary Forums:
• Literary forums are platforms where writers, poets, and literary critics gather to discuss and promote literature.
• These forums play a crucial role in preserving and promoting cultural heritage and literary traditions.
• BRICS Cultural Cooperation:
• The BRICS countries have established various cultural cooperation initiatives to enhance mutual understanding and cultural exchange.
• These initiatives include film festivals, art exhibitions, and literary forums.

Shortcut Trick

For an equilateral triangle, the relationship between Area and Altitude (h) is given by:

Area = h² ÷ √3

⇒ Area = 12² ÷ √3 = 144 ÷ √3

⇒ Area = (144 × √3) ÷ 3 = 48√3 cm²

∴ The correct answer is 48√3 cm².

Alternate Method

Given: Altitude (h) of the equilateral triangle = 12 cm.

Formula Used:

1. Altitude (h) = (√3 ÷ 2) × side (a)
2. Area = (√3 ÷ 4) × a²

Calculations:

⇒ 12 = (√3 ÷ 2) × a

⇒ a = 24 ÷ √3 = 8√3 cm

⇒ Area = (√3 ÷ 4) × (8√3)²

⇒ Area = (√3 ÷ 4) × (64 × 3)

⇒ Area = (√3 ÷ 4) × 192

⇒ Area = 48√3 cm²

∴ The correct answer is 48√3 cm².

Additional Information

Properties of Equilateral Triangle

All three sides are equal, and each interior angle is 60°.

Inradius and Circumradius

Inradius (r) = a ÷ (2√3) and Circumradius (R) = a ÷ √3.

Perimeter of Equilateral Triangle

Perimeter = 3 × side (a).

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

No one sits to the right of Y.

Only two people sit between Y and C.

Only three people sit between B and L.

C sits to the immediate left of L.

Z sits to the immediate right of A.

X sits at the remaining place.

So 2 people sit between X and Z.

Hence the correct answer is "Option 4"

Shortcut Trick

For any expression of the form x + 1/x = k, the value of x² + 1/x² is given by the direct formula k² − 2.

Given k = 6.

⇒ x² + 1/x² = 6² − 2

⇒ 36 − 2 = 34

∴ The correct answer is 34.

Alternate Method

Given: x + 1/x = 6

Formula Used: (a + b)² = a² + b² + 2ab

Squaring both sides of the given equation:

⇒ (x + 1/x)² = 6²

⇒ x² + (1/x)² + 2 × x × (1/x) = 36

⇒ x² + 1/x² + 2 = 36

⇒ x² + 1/x² = 36 − 2

⇒ x² + 1/x² = 34

∴ The correct answer is 34.

Additional Information

Higher Power Relation (Cube)

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

Negative Sign Identity

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

Fourth Power Relation

To find x⁴ + 1/x⁴, square the result of (x² + 1/x²) and subtract 2.

The correct answer is cell wall.

Key Points

• The cell wall is a rigid layer that is found outside the plasma membrane in plant cells, bacteria, fungi, and some algae.
• In plants, the cell wall is primarily composed of cellulose, hemicellulose, and pectin.
• The cell wall provides structural support and protection, and it also acts as a filtering mechanism.
• It is crucial for maintaining the shape of the plant cell and preventing excessive water intake through osmosis.

Additional Information

• Plasma Membrane:
• A selectively permeable membrane that regulates the entry and exit of substances in and out of the cell.
• Composed of a phospholipid bilayer with embedded proteins.
• Cell Envelope:
• In bacteria, the cell envelope includes the plasma membrane, cell wall, and sometimes an outer membrane.
• Provides structural integrity and protection from environmental stress.
• Nuclear Membrane:
• A double membrane that encloses the nucleus in eukaryotic cells.
• Contains nuclear pores that allow the transport of molecules between the nucleus and cytoplasm.
• Composition of Plant Cell Walls:
• Primary Cell Wall: Thin and flexible, made of cellulose, hemicellulose, and pectin.
• Secondary Cell Wall: Thicker and more rigid, contains lignin in addition to cellulose and hemicellulose.

The correct answer is Chandrayaan-3 Team.

Key Points

• The Chandrayaan-3 Team of ISRO was awarded the Vigyan Team award in 2024.
• Chandrayaan-3 is the third lunar exploration mission by the Indian Space Research Organisation (ISRO).
• The mission aims to demonstrate the capability of soft-landing on the lunar surface and operate a rover.
• Chandrayaan-3 was built upon the experience gained from the Chandrayaan-2 mission.

Additional Information

• Chandrayaan-2
• Chandrayaan-2 was launched on 22 July 2019.
• It aimed to explore the south pole of the Moon.
• The mission included an orbiter, a lander named Vikram, and a rover named Pragyan.
• Aditya-L1 Mission
• Aditya-L1 is ISRO's mission to study the Sun.
• The mission aims to understand the dynamic processes of the Sun and its impact on the space environment.
• XPoSat Mission
• XPoSat (X-ray Polarimeter Satellite) is a dedicated mission to study cosmic X-ray sources.
• It aims to observe the polarization of X-rays from various sources like pulsars and black hole binaries.
• ISRO's Achievements
• ISRO has successfully launched missions like Mars Orbiter Mission (Mangalyaan) and various communication satellites.
• It has made significant contributions to space exploration and satellite technology.

Given

194, 249, 199, 244, 204,?

Logic follows here is,

Logic 

So, next number is 239.

Hence the correct answer is "Option 1"

Logic followed here is,

Hence the correct answer is "Option 2"

The correct answer is 3) The mass of an object is constant and does not change from place to place.

Key Points

• Mass is a fundamental property of an object that does not change regardless of location.
• The mass of an object is measured in kilograms (kg) and remains constant whether the object is on Earth, the Moon, or in space.
• Weight, on the other hand, is the force exerted by gravity on an object and can vary depending on the gravitational pull at different locations.
• Mass is a scalar quantity, meaning it only has magnitude, whereas weight is a vector quantity, having both magnitude and direction.

Additional Information

• Weight is calculated using the formula Weight = Mass × Gravitational Acceleration (W = mg).
• The gravitational acceleration on Earth is approximately 9.8 m/s², but this value can differ slightly depending on the location.
• On the Moon, the gravitational acceleration is about 1/6th of that on Earth, which is why objects weigh less on the Moon.
• Mass is commonly measured using a balance, which compares an unknown mass to a standard mass.
• Inertia is a concept related to mass, describing an object's resistance to changes in its state of motion.

Given series:

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

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

Required condition: Even - odd - Even

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

Thus, there are one such odd digit which are immediately preceded by an even digit and also immediately followed by an even digit.

Hence, "Option 1" is the correct answer.

Logic follows here is that the first letter is increased by 7 and the second letter is decreased by 4.

Option 1) CJF

Option 2) ELH

Option 3) IPL

Option 4) LSP

Does not follow the same logic.

Hence the correct answer is "Option 4"

The correct answer is Option 1.

Key Points

• Statement I is incorrect: Because the first Bharat Ratna awardees were three persons in 1954 — C. Rajagopalachari, S. Radhakrishnan, and C.V. Raman.
• Statement II is correct: Sachin Tendulkar was awarded the Bharat Ratna in 2014, and he is the first and only cricketer to receive this honor as of 2024.

Additional Information

• Bharat Ratna:
• It is the highest civilian award in India.
• Established in 1954, it is awarded for exceptional service towards the advancement of Art, Literature and Science, and in recognition of Public Service of the highest order.
• The award does not carry any monetary grant but a certificate (Sanad) signed by the President and a medallion.
• Sarvepalli Radhakrishnan:
• He was an Indian philosopher and statesman who served as the first Vice President of India and the second President of India.
• He was awarded the Bharat Ratna in 1954 for his contribution to education and philosophy.
• C. Rajagopalachari:
• He was an Indian politician, independence activist, lawyer, writer, and statesman.
• He was the last Governor-General of India and a founder of the Swatantra Party.
• He was awarded the Bharat Ratna in 1954 for his public service.
• Sachin Tendulkar:
• He is a former Indian cricketer and one of the greatest batsmen in the history of cricket.
• He was awarded the Bharat Ratna in 2014, making him the youngest recipient and the first sportsperson to receive the award.

Shortcut Trick

Total Simple Interest percentage = Rate × Time

Total % = 7% × 2 = 14%

Interest = 14% of ₹2,00,000 = 14 × 2000 = ₹28,000

∴ The correct answer is ₹28,000.

Alternate Method

Given:

Principal (P) = ₹2,00,000

Rate (R) = 7% per annum

Time (T) = 2 years

Formula Used:

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

Calculations:

⇒ SI = (2,00,000 × 7 × 2) ÷ 100

⇒ SI = 2,000 × 14

⇒ SI = 28,000

∴ The correct answer is ₹28,000.

Additional Information

Total Amount Formula

The total amount (A) to be paid after the time period is calculated as Amount = Principal + Simple Interest.

Constant Interest Property

In Simple Interest, the interest amount remains constant every year because it is always calculated on the original Principal.

Rate and Time Units

Ensure that the Rate and Time are in the same time units (e.g., if Rate is per annum, Time must be in years).

Logic:

Formula: First number / 9 = Second number

Given

(153, 17):

153 / 9 = 17

For (216, 24):

216 / 9 = 24

Option 1) (171, 18):

171 / 9 = 19 ≠ 18

Option 2) (243, 27):

243 / 9 = 27

Follow the same logic.

Option 3) (189, 31):

189 / 9 = 21 ≠ 31

Option 4) (225, 35):

225 / 9 = 25 ≠ 35

Conclusion:

Only Option 2 satisfies the given formula.

Therefore, the correct answer is option 2) (243, 27).

Statements:

All oil is paint.

All paint is brush.

Possible venn diagram is,

Conclusions:

(I) Some brushes are oil.→ follow(As from venn diagram All oil is paint and all paint is brush then some brushes are oil is possible)

(II) No brush is oil. → Not follow(As from venn diagram All oil is paint and all paint is brush then no brushes is oil is not possible)

Hence the correct answer is "Option 1"

Additional Information

Shortcut Trick

Rate of depreciation = 10% = 1/10.

Value ratio for 1 year = 10 : 9.

Value ratio for 2 years = 10² : 9² = 100 : 81.

Given, 81 units = ₹1,62,000 → 1 unit = ₹2,000.

Original value (100 units) = 100 × ₹2,000 = ₹2,00,000.

∴ The correct answer is ₹2,00,000.

Alternate Method

Given:

Present Value (V_p) = ₹1,62,000

Rate of depreciation (r) = 10%

Time period (n) = 2 years

Formula Used:

V_p = V₀ × (1 − r/100)ⁿ

Calculations:

⇒ 1,62,000 = V₀ × (1 − 10/100)²

⇒ 1,62,000 = V₀ × (90/100)²

⇒ 1,62,000 = V₀ × (9/10) × (9/10)

⇒ 1,62,000 = V₀ × (81/100)

⇒ V₀ = (1,62,000 × 100) ÷ 81

⇒ V₀ = 2,000 × 100

⇒ V₀ = 2,00,000

∴ The correct answer is ₹2,00,000.

Additional Information

Depreciation Formula

It is similar to Compound Interest but with a negative rate: Amount = Principal × (1 − R/100)^T.

Appreciation

If the value increases, the formula becomes: Future Value = Present Value × (1 + R/100)^T.

Successive Percentage Change

For two years of depreciation, the effective rate is −a − b + (ab/100). For 10% p.a., effective change = −10 − 10 + 1 = −19%.

Shortcut Trick

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

Efficiencies: A = 4, B = 3, C = 2. Combined = 9 units/day.

Work done in 3 days = 9 × 3 = 27 units.

Remaining work = 36 − 27 = 9 units.

Remaining work done by B and C = 9 ÷ (3 + 2) = 9/5 days.

∴ The correct answer is 9/5 days.

Alternate Method

Given: Time taken by A = 9 days, B = 12 days, C = 18 days. A leaves after 3 days.

Formula: Total Work = Efficiency × Time; Remaining Time = Remaining Work ÷ Efficiency of remaining workers.

⇒ Total work done by A, B, and C in 3 days = (4 + 3 + 2) × 3

⇒ Work done = 9 × 3 = 27 units

⇒ Remaining Work = 36 − 27 = 9 units

⇒ Remaining work done by B and C together = 9 ÷ (3 + 2)

⇒ Time taken = 9/5 days

∴ The correct answer is 9/5 days.

Additional Information

Total Work and Efficiency

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

Leaving/Joining Problems

When a person leaves mid-way, subtract the work they completed from the total work and divide the remainder by the efficiency of the remaining workforce.

Work and Wages

Wages are distributed in the ratio of the actual work done by each individual, which is Efficiency × Days worked.