RRB Group D Previous Year Paper (Held on: 13 Sept 2022 Shift 1)

The correct answer is 9th.

Key Points

• Ramadan or Ramazan is the ninth month of Islamic calendar and is observed by Muslims worldwide as a month of fasting.
• Ramadan is considered as the holiest month in the Islamic calendar.
• During Ramadan, Muslims fast from dawn until sunset, abstaining from food, drink, and other physical needs.
• It is believed that fasting during Ramadan is a way to purify the soul and gain a deeper understanding of Allah's blessings.
• The end of Ramadan is marked by Eid al-Fitr, a major festival in the Islamic calendar.

Additional Information

• The Muslim calendar and Islamic calendar are other terms used to refer to the Hijri calendar in English.
• It is a lunar calendar with 12 lunar months and 354 or 355 days in a year.
• It is employed to ascertain the appropriate dates for Islamic holidays and customs, including the annual fasting period and the time of the big pilgrimage.

The correct answer is Option 4.

Key Points

• Since the attractive forces between molecules are weak, it doesn't take much energy to disrupt them and thus organic molecules have low melting and boiling points. Ionic compounds, in general, do not burn in oxygen.
• An organic compound is any of a large class of chemical compounds in which one or more atoms of carbon are covalently linked to atoms of other elements, most commonly hydrogen, oxygen, or nitrogen.
• Life is based on carbon; organic chemistry studies compounds in which carbon is a central element.
• The properties of carbon make it the backbone of the organic molecules which form living matter.
• Carbon is such a versatile element because it can form four covalent bonds.
• Carbon skeletons can vary in length, branching, and ring structure.
• The functional groups of organic molecules are the parts involved in chemical reactions.
• Organic molecules important for life include relatively small monomers as well as large polymers.​

Additional Information

• Ionic Bond:
• The ionic bond is the electrostatic force of attraction that holds two oppositely charged ions together.
• The complete transfer of one or more electrons from one atom to the other forms a chemical link between two atoms, causing the atoms to acquire their closest inert gas configuration.
• Examples - KCl, AlCl3, NaCl

The correct answer is Asymmetric Digital Subscriber Line.

Key Points

• Asymmetric Digital Subscriber Line is the correct full name of ADSL technology.
• Asymmetric refers to the fact that ADSL provides higher download speeds than upload speeds.
• ADSL technology provides high transmission speeds for video and voice to homes over an ordinary copper telephone wire.
• ADSL uses different frequencies for upstream and downstream data transmission.

Additional Information

• Asynchronized refers to a communication mode where data is transmitted without a clock signal, but ADSL uses a clock signal for synchronization.
• Algorithm refers to a set of rules or instructions for solving a problem, but ADSL is a specific technology for data transmission over copper telephone lines.
• Arithmetic refers to mathematical operations like addition, subtraction, multiplication, and division, but ADSL technology does not involve arithmetic operations.

The logic followed here is:

1. PRVW → P - Q P - R R R - R S S S - T - U V - V V V - W W W W 2. QRUW → P - Q Q - R R R - R S S S - T - U U - V V V - W W W W 3. QSVW → P - Q Q - R R R - S S S S - T - U V - V V V - W W W W 4. QSUW → P - Q Q - R R R - S S S S - T - U U - V V V - W W W W

Letters are increased as per the English dictionary starting from P to W with increase in number of repetition.

Hence, 'QSUW' is the correct answer.

The correct answer is Option 2. 

Key Points

• The energy change that takes place in an electromagnet is electrical energy to magnetic energy.
• An electromagnet is a device consisting of a core of magnetic material surrounded by a coil, through which an electric current is passed to magnetize the core.
• An electromagnet is used wherever controllable magnets are required.
• Electromagnetism is directly proportional to the number of turns of the coil, the current flow through the coil, and the material of the coil.
• As the flow of current and number of turns increases, the strength of the electromagnet increases.
• Using a soft core increase the strength of the electromagnet because when the core is made up of a soft or hard magnetic material. Soft iron will magnetize more readily than steel.​
• Electromagnets are controllable.
• Electromagnets have adjustable power levels.
• They are used in MRI and Generators.
• Electromagnetic strength is directly proportional to the number of turns and the current flowing through it.

Additional Information

• Electric Energy - 
• The commercial unit of electric energy is Kilowatt-hour.
• One kilowatt-hour is defined as the energy consumed by the power consumption of 1kW during 1 hour.
• One kilowatt-hour is equal to 3600 kilojoules.
• The SI unit of electrical energy is Joule.
• Magnetic Energy - 
• Magnetic field: If a current is passed through a wire a magnetic field is produced around it.
• lenz's Law: According to this law, the direction of induced emf or current in a circuit is such as to oppose the cause that produces it.
• This law gives the direction of induced emf/induced current.
• This law is based upon the law of conservation of energy.

The logic followed here is:

Similarly,

Hence, 'NRWZN' is the correct answer.

The correct answer is Option 1. 

Key Points

• All C3H8, C2H6, CH4  saturated carbon compounds with the general formula: Cn​H2n+2​ whereas C4​H8​ is an alkene with general formula Cn​H2n.
• Homologous series is defined as a series of compounds in which the same functional group substitutes for hydrogen in a carbon chain.
• This series will be differing with a successive member of CH2.
• Some examples are methane (CH4), ethane (C2H6), propane (C3H8) as they differ by CH2 and they have the same functional group called alkanes (General formula CnH2n+2).​

Additional Information

• Homologous series - 
• Homologous series is a series of compounds with similar chemical properties and some functional groups differing from the successive member by CH2.
• Carbon chains of varying lengths have been observed in organic compounds having the same general formula.
• Such organic compounds that vary from one another by a repeating unit and have the same general formula form a series of compounds.
• Alkanes with the general formula CnH2n+2, alkenes with the general formula CnH2n, and alkynes with the general formula CnH2n-2 form the most basic homologous series in organic chemistry.
• The same thing can be observed in the case of alkenes in which the first member is ethene and the successive members are C3H6, C4H8, and C5H10.
• They differ from each other by a –CH2 unit. The Alkene formula is written as CnH2n.​

Shortcut Trick

For two numbers in ratio a ∶ b with HCF = H:

LCM = a × b × H

Given: a = 5, b = 7, H = 8

⇒ LCM = 5 × 7 × 8 = 35 × 8 = 280

∴ The correct answer is 280.

Alternate Method

Given:

Ratio of numbers = 5 ∶ 7

HCF (Highest Common Factor) = 8

Calculations:

Let the two numbers be 5x and 7x, where x is the HCF.

⇒ x = 8

⇒ First Number = 5 × 8 = 40

⇒ Second Number = 7 × 8 = 56

We know the property: Product of two numbers = HCF × LCM

⇒ 40 × 56 = 8 × LCM

⇒ LCM = (40 × 56) ÷ 8

⇒ LCM = 5 × 56 = 280

∴ The correct answer is 280.

Additional Information

Fundamental Property

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

Ratio and HCF relationship

If two numbers are in the ratio p ∶ q (where p and q are co-prime), their LCM is always p × q × HCF.

Co-prime Numbers

If two numbers are co-prime, their HCF is 1 and their LCM is simply their product.

The correct answer is Option 4. 

Key Points

• When light passes from one medium to any other medium say air, a glass of water then a part of the light is absorbed by particles of the medium preceded by its subsequent radiation in a particular direction. This phenomenon is termed a scattering of light.
• Rayleigh's law of scattering:-
• According to Rayleigh's law of scattering, the intensity of light of wavelength λ present in the scattered light is inversely proportional to the fourth power of λ, provided the size of the scattering particles is much smaller than λ. Mathematically,
• $I \propto \frac{1}{\lambda^4 }$
• Thus the scattered intensity is maximum for a shorter wavelength.

Additional Information

• The molecules of air and other fine particles in the atmosphere have a size smaller than the wavelength of visible light.
• These are more effective in scattering light of shorter wavelengths at the blue end than the light of longer wavelengths at the red end.
• The red light has a wavelength of about 1.8 times greater than blue light.
• Thus, when sunlight passes through the atmosphere, the fine particles in the air scatter the blue colour (shorter wavelengths) more strongly than red.
• The scattered blue light enters our eyes.
• The red colour of the sun at sunrise is due to the scattering of light.
• Dispersion of Light  - It means the splitting of white light when it passes through a glass prism into its constituent spectrum of colors (i.e. Violet, Indigo, Blue, Green, Yellow, Orange, and Red).
• Refraction: When a ray of light passes from one medium to another it suffers a change in direction at the boundary of two media is called refraction.

The change in direction is because the speed of light travels at different speeds in different mediums. The Refractive Index of a medium defines that it is denser or rarer.

Examples of refraction of light:

• Twinkling of stars in a clear sky.
• Pool of water appears to be less deep than it actually is.
• Rainbow formation in the sky.

Reflection

• The property of light to fall on a surface and then reflect back the same medium is known as reflection.
• As a result, the medium of light does not change during reflection.
• Reflection is the change in direction of light when it strikes a surface.
• In the case of reflection, the light returns to the medium from which it originated.​

Shortcut Trick

Scheme (I): Successive discount = a + b − (a × b) ÷ 100 = 15 + 20 − (15 × 20) ÷ 100 = 35 − 3 = 32%.

Scheme (II): Discount% = [Free Items ÷ Total Items] × 100 = [4 ÷ (5 + 4)] × 100 = 4 ÷ 9 × 100 = 44.44%.

∴ The correct answer is 32%, 44.44%.

Alternate Method

Given → Scheme I: 15% and 20% successive; Scheme II: Buy 5 Get 4 Free. Formulas: Successive = a + b − ab/100 | Scheme II Discount% = [Free ÷ (Buy + Free)] × 100.

⇒ For Scheme I: Successive Discount = 15 + 20 − (15 × 20)/100 = 35 − 3 = 32%. ⇒ For Scheme II: MP of 9 items = 9 units; Free items = 4 units. ⇒ Discount % = (4 ÷ 9) × 100 = 44.44%.

∴ The correct answer is 32%, 44.44%.

Additional Information

Successive Discounts

When two or more discounts are applied one after another, the net discount is less than the sum of individual percentages.

Buy X Get Y Free

In this offer, the customer pays for X items but receives X + Y items. The discount is calculated on the total (X+Y) items provided.

Shortcut Trick

Value of 2 × number = 342 − (3 × 52) = 342 − 156 = 186.

Required sum = (4 × number) + (2 × 52).

Since 4 × number = 2 × (2 × number) = 2 × 186 = 372.

Required sum = 372 + 104 = 476.

∴ The correct answer is 476.

Alternate Method

Given:

Sum of twice a number and three times of 52 = 342

Formula Used:

Linear Equation: ax + b = c

Calculations:

Let the number be x.

⇒ 2x + 3 × 52 = 342

⇒ 2x + 156 = 342

⇒ 2x = 342 − 156

⇒ 2x = 186

⇒ x = 186 ÷ 2 = 93

Now, we need to find the sum of four times the number and two times 52:

⇒ 4x + 2 × 52

⇒ 4 × 93 + 104

⇒ 372 + 104 = 476

∴ The correct answer is 476.

Additional Information

Linear Equation in One Variable

An equation which can be written in the form ax + b = 0, where a and b are constants and x is the variable.

Transposition Rule

When a term is moved from one side of the equation to the other, its sign changes (+ becomes −, and × becomes ÷).

BODMAS Rule

Always follow the order: Brackets, Orders, Division, Multiplication, Addition, and Subtraction for multi-step calculations.

The correct answer is Option 1. 

Key Points

• According to ohm's law Current (I) = Potential difference (V) / Resistance(R)
• ​​​​​​If the potential difference is maintained constant and the resistance is changed - Current (I) is inversely proportinal to the reisistance (R) ⇒  I ∝ 1/R
• So If current is doubled and potential difference is reduced to half, then resistance will become one-fourth.

Additional Information

• Resistance:
• It is defined as the hurdles in the path of flow of current.
• The SI unit of resistance is the ohm.
• It is denoted by the symbol Ω.
• It depends on the material of the conductor and the dimensions of the conductor.
• In other words, we can say it is the ratio of voltage to the current.
• R= (rho×length)/area
• Note: rho=Resistivity

The correct answer is 10 lakh.

Key Points

• Municipal Corporations are the governing bodies responsible for the development and administration of urban areas in India.
• The population of a Metropolitan City with more than 10 lakh inhabitants is managed by a Municipal Corporation.
• The Municipal Corporation is responsible for providing basic amenities such as water supply, sanitation, and maintenance of roads and infrastructure.
• The Municipal Corporation also collects taxes and fees from the citizens to fund its activities and projects.

Additional Information

• 2 lakh and 5 lakh are a relatively small population, and such cities are usually managed by a Municipal Council or a Nagar Panchayat.
• 12 lakh is a large population, and such cities are usually managed by a Metropolitan Development Authority or a Metropolitan Planning Committee.
• Panchayat Raj institutions are the local government authorities in rural areas.
• Village panchayats are the local governing bodies at the village level.
• They are referred to as panchayat samitis at the block level.
• They are referred to as zilla parishads at the district level.

The correct answer is All - A, B and C.

Key Points

• Capital receipts refer to the inflow of funds that create liabilities or reduce assets for the government.
• Loans taken by the government from the public, borrowings from foreign countries and institutes, and disinvestment of assets are all examples of capital receipts.
• Loans taken by the government from the public are a form of borrowing and create a liability for the government.
• Borrowings from foreign countries and institutes also create a liability for the government and are usually accompanied by conditions and terms of repayment.
• Disinvestment of assets refers to the sale of government-owned assets like shares, land, or buildings, and generates revenue for the government.

Additional Information

• Capital receipts are earnings from non-routine or infrequently occurring activity.
• An organization's primary or consistent source of income is not capital receipts.
• Additionally, due to their capital nature, these receipts are displayed on a company's balance sheet rather than in the income statement or profit and loss account.
• The recording of these receipts follows the accrual method.
• Additionally, unlike revenue receipts, capital receipts cannot be used for the distribution of profit due to their non-recurring nature.

Given equation: 24 × 6 ÷ 5 - 3 + 2 = ?

After replacing the symbols by their meaning, we get:

24 ÷ 6 × 5 + 3 - 2 = ?

⇒ 4 × 5 + 3 - 2 = ?

⇒ 23 - 2 = ?

⇒ 21 = ?

Hence, '21' is the correct answer.

The logic followed here is:

Similarly,

Hence, '45447' is the correct answer.

Six persons are sitting around a circular table facing the centre.

1. Madhuram is an immediate neighbour of both Rahim and Amit.

2. Sumit is sitting second to the right of Rahim.

3. David is sitting third to the left of Amit.

4. Prem is an immediate neighbour of both Sumit and Amit.

The above condition cannot be satisfies in Case I, so it is eliminated.

Clearly, Amit is an immediate neighbour of both Madhuram and Prem.

Hence, ‘Amit’ is the correct answer.

Pattern: Letter Letter Number

(Left) B F % 6 J Q 6 H & K M 8 1 5 T Z # @ K L 9 (Right)

Clearly, three such letters are there which are immediately preceded by a letter and also immediately followed by a number.

Hence, ‘3’ is the correct answer.

The correct answer is Property taxes.

Key Points

• Variable costs are expenses that vary with the level of production or sales.
• They increase as production or sales increase and decrease as production or sales decrease.
• In contrast, fixed costs are expenses that do not vary with production or sales levels.
• Commissions and labor costs are both examples of variable costs.
• Commissions are paid based on the level of sales, so they increase when sales increase and decrease when sales decrease.
• Labor costs similarly increase as production increases and decrease as production decreases.
• Packing costs could be either a variable or fixed cost depending on how they are structured.
• If the cost of packing materials and labor varies with the level of production, then it is a variable cost.
• If it is a fixed cost that does not vary with production levels, then it is a fixed cost.
• Property taxes, on the other hand, are typically a fixed cost.
• They are based on the assessed value of the property and do not vary with production or sales levels.

Additional Information

• Commissions are payments made to salespeople or other employees based on their level of sales or performance.
• They are a form of incentive compensation that is designed to motivate employees to work harder and sell more.
• Property taxes are taxes that are levied on real estate property.
• They are typically assessed by local governments and are based on the value of the property.
• They are used to fund a variety of local services, such as schools, police, and fire departments.
• Labor costs are the wages and benefits paid to employees.
• They are a major expense for many companies and can vary widely depending on the type of work being done and the location of the company.
• Packing costs are the expenses associated with packaging and shipping products.
• They can include the cost of materials, labor, and shipping fees.

The logic followed here is:

Hence, '15, 1' is the correct answer.

Shortcut Trick

To be divisible by 2, 3, and 5, a number must be divisible by their LCM.

LCM(2, 3, 5) = 2 × 3 × 5 = 30.

Check Divisibility Rules: Unit digit must be 0 (for 2 and 5) and sum of digits must be divisible by 3.

Only 3150 ends in 0 and 3+1+5+0 = 9 (divisible by 3).

∴ The correct answer is 3150.

Alternate Method

Given: Divisors are 2, 3, and 5.

Divisibility Rule for 2: Last digit must be even (0, 2, 4, 6, 8).

Divisibility Rule for 5: Last digit must be 0 or 5.

⇒ Combining 2 and 5, the last digit must be 0.

⇒ Options (3) 14175 and (4) 54332 are eliminated.

Divisibility Rule for 3: Sum of digits must be divisible by 3.

⇒ For 2240: 2 + 2 + 4 + 0 = 8 (Not divisible by 3).

⇒ For 3150: 3 + 1 + 5 + 0 = 9 (Divisible by 3).

∴ The correct answer is 3150.

Additional Information

Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3.

Divisibility by 10

A number is divisible by 10 if its last digit is 0.

LCM Property

If a number is divisible by several coprime numbers, it is also divisible by their product.

Shortcut Trick

Mean Proportional of two numbers a and b is √(a × b).

⇒ Mean Proportional = √(25 × 36)

⇒ Mean Proportional = 5 × 6 = 30

∴ The correct answer is 30.

Alternate Method

Given: First number (a) = 25, Second number (b) = 36

Formula Used: If x is the mean proportional between a and b, then a : x = x : b

⇒ x² = a × b

⇒ x² = 25 × 36

⇒ x = √(900)

⇒ x = 30

∴ The correct answer is 30.

Additional Information

Third Proportional

For two numbers a and b, the third proportional c is such that a : b = b : c, calculated as c = b² ÷ a.

Fourth Proportional

For three numbers a, b, and c, the fourth proportional d is such that a : b = c : d, calculated as d = (b × c) ÷ a.

Compound Ratio

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

The correct answer is Original Jurisdiction.

Key Points

• Original Jurisdiction refers to the power of a court to hear a case for the first time, instead of on appeal or by review of another court's decision.
• In the United States, the Supreme Court has original jurisdiction in a limited number of cases, such as disputes between states or cases involving ambassadors or other public ministers.

Additional Information

• Appellate Jurisdiction refers to the power of a court to review and revise the decisions of a lower court.
• The Supreme Court has appellate jurisdiction over most cases, and it is the highest court of appeal in the United States.
• Advisory Jurisdiction refers to the power of a court to provide legal advice or opinions, rather than to decide specific cases.
• The Supreme Court does not have advisory jurisdiction in the United States.
• Writ Jurisdiction refers to the power of a court to issue writs, or orders, to government officials or agencies.
• The Supreme Court has writ jurisdiction, and it can issue writs such as habeas corpus, mandamus, and certiorari.

Shortcut Trick

Surface Area = 4πr² = 196π ⇒ r² = 49 ⇒ r = 7 cm.

Volume = (4/3)πr³ = (4/3) × π × 7³.

Volume = (4 × 343 × π) ÷ 3 = 1372π/3 cm³.

∴ The correct answer is 1372π/3 cm³.

Alternate Method

Given:

Surface Area of sphere = 196π cm²

Formula Used:

Surface Area = 4πr²

Volume = (4/3)πr³

Calculations:

⇒ 4 × π × r² = 196 × π

⇒ 4r² = 196

⇒ r² = 196 ÷ 4

⇒ r² = 49

⇒ r = √49 = 7 cm

⇒ Volume = (4/3) × π × (7)³

⇒ Volume = (4/3) × π × 343

⇒ Volume = (1372π)/3 cm³

∴ The correct answer is 1372π/3 cm³.

Additional Information

Properties of Sphere

A sphere has only one surface, so its Total Surface Area and Curved Surface Area are the same: 4πr².

Hemisphere Formulas

For a hemisphere of radius r: Volume = (2/3)πr³, CSA = 2πr², and TSA = 3πr².

Ratio of Volume and Surface Area

The ratio of the Volume to the Surface Area of a sphere is always r/3.

Given equation: 12 × 3 - 25 ÷ 25 + 25 = ?

After replacing the symbols by their meaning, we get:

12 ÷ 3 × 25 + 25 - 25 = ?

⇒ 4 × 25 + 25 - 25 = ?

⇒ 100 + 25 - 25 = ?

⇒ 125 - 25 = ?

⇒ 100 = ?

Hence, '100' is the correct answer.

The correct answer is Option 2. 

Key Points Oxidation is the loss of hydrogen. Reduction is the gain of hydrogen.

• Reduction Reaction is always accompanied by an oxidation reaction where the reactant loses one or more electron.
• Reduction-oxidation reactions are often called redox equations.
• A reduction reaction is only one half of a redox reaction. The other half is the oxidation reaction.​

Additional Information

• Oxidation Reaction refers to a reaction in which either the addition of Oxygen takes place or the removal of Hydrogen takes place.
• Rusting is an example of an oxidation reaction.
• The iron reacts with water and oxygen to form hydrated iron oxide, which we see as rust.

iron + water + oxygen → hydrated iron oxide

• Decomposition is the process of breakdown of the complex organic matter into a simpler inorganic matter like carbon dioxide, water, and nutrients.  The fungi, bacteria, and flagellates initiate the process of decomposition and are known as decomposers.

Given equation: 20 × 5 ÷ 5 - 5 + 3 = ?

After interchanging the symbols, we get:

20 ÷ 5 × 5 + 5 - 3 = ?

⇒ 4 × 5 + 5 - 3 = ?

⇒ 20 + 5 - 3 = ?

⇒ 25 - 3 = ?

⇒ 22 = ?

Hence, '22' is the correct answer.

Shortcut Trick

Product of LCM and HCF = Product of the two numbers.

Other number = (LCM × HCF) ÷ Given number

⇒ (459 × 3) ÷ 51 = 9 × 3 = 27.

∴ The correct answer is 27.

Alternate Method

Given:

LCM = 459

HCF = 3

First Number (A) = 51

Formula Used:

A × B = LCM × HCF

Calculations:

⇒ 51 × Second Number (B) = 459 × 3

⇒ Second Number (B) = (459 × 3) ÷ 51

⇒ Second Number (B) = 1377 ÷ 51

⇒ Second Number (B) = 27

∴ The correct answer is 27.

Additional Information

HCF Properties

The HCF (Highest Common Factor) is always a factor of the LCM (Least Common Multiple).

Co-prime Numbers

For two co-prime numbers, the HCF is always 1 and their LCM is the product of the numbers.

Ratio and HCF

If two numbers are in the ratio x : y and their HCF is H, then the numbers are Hx and Hy, and their LCM = H × x × y.

Shortcut Trick

Assume total distance is LCM of denominators (3, 4) × 100 = 1200 km.

Distances: D₁ = 400 km, D₂ = 300 km, D₃ = 500 km.

Times: T₁ = 400/25 = 16 h, T₂ = 300/30 = 10 h, T₃ = 500/50 = 10 h.

Average Speed = Total Distance ÷ Total Time = 1200 ÷ 36 = 100/3 = 33(1/3) km/h.

∴ The correct answer is 33(1/3) km/h.

Alternate Method

Given: Speeds are 25 km/h, 30 km/h, and 50 km/h for 1/3, 1/4, and remaining journey.

Formula Used: Average Speed = Total Distance / Total Time

⇒ Let total distance be D.

⇒ Remaining distance = D − (D/3 + D/4) = D − 7D/12 = 5D/12.

⇒ Total Time = (D/3)/25 + (D/4)/30 + (5D/12)/50

⇒ Total Time = D/75 + D/120 + D/120 = D/75 + 2D/120 = D/75 + D/60

⇒ Total Time = (4D + 5D)/300 = 9D/300 = 3D/100.

⇒ Average Speed = D ÷ (3D/100) = 100/3 = 33(1/3) km/h.

∴ The correct answer is 33(1/3) km/h.

Additional Information

Average Speed (Equal Distances)

If two equal distances are covered at speeds u and v, then Average Speed = 2uv/(u + v).

Average Speed (General Case)

It is always the weighted harmonic mean of the speeds: Total Distance ÷ ∑(d_i/s_i).

Relative Speed

When moving in the same direction, speed = S₁ − S₂. When moving in opposite directions, speed = S₁ + S₂.

Shortcut Trick

For any expression of the form x − 1/x = k, the value of x³ − 1/x³ is given by the formula k³ + 3k.

Given: k = 6

Value = 6³ + 3(6)

Value = 216 + 18 = 234

∴ The correct answer is 234.

Alternate Method

Given: x − 1/x = 6

Formula Used: (a − b)³ = a³ − b³ − 3ab(a − b)

Applying the cubic identity by cubing both sides of the given equation:

⇒ (x − 1/x)³ = 6³

⇒ x³ − (1/x)³ − 3 × x × (1/x) × (x − 1/x) = 216

⇒ x³ − 1/x³ − 3(1)(6) = 216

⇒ x³ − 1/x³ − 18 = 216

⇒ x³ − 1/x³ = 216 + 18

⇒ x³ − 1/x³ = 234

∴ The correct answer is 234.

Additional Information

Standard Algebraic Identity for Sum

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

Relationship with Squares

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

Conversion Formula

The relation between sum and difference is (x + 1/x)² = (x − 1/x)² + 4.

Shortcut Trick

Use the direct formula for two people working together: Time = (a × b) ÷ (a − b)

Where a = time taken by boy (10 days) and b = time taken together (6 days).

⇒ Friend's time = (10 × 6) ÷ (10 − 6)

⇒ Friend's time = 60 ÷ 4 = 15 days.

∴ The correct answer is 15 days.

Alternate Method

Given:

Time taken by Boy alone = 10 days

Time taken by Boy + Friend together = 6 days

Formula: Efficiency = Total Work ÷ Time

Calculations:

⇒ Friend's efficiency = (Boy + Friend) efficiency − Boy efficiency

⇒ Friend's efficiency = 5 − 3 = 2 units/day

⇒ Time taken by Friend alone = Total Work ÷ Friend's efficiency

⇒ Time = 30 ÷ 2 = 15 days

∴ The correct answer is 15 days.

Additional Information

Total Work Assumption

Total work is always assumed as the LCM of individual days taken by the workers to simplify efficiency calculations.

Combined Efficiency Rule

If person A takes x days and B takes y days, their combined efficiency is (1/x + 1/y), and time taken together is (xy) ÷ (x + y).

Work & Wages Relation

Wages are always distributed in the ratio of work done or the ratio of efficiencies when people work for the same duration.

Each of A, B, C, D and E has an exam on a different day of a week, starting from Monday and ending on Friday of the same week.

1. C has the exam on Thursday.
2. Only one person has the exam between B and A.
3. B has the exam on the day immediately before D. 

Hence, ‘A’ is the correct answer.

Shortcut Trick

Put standard trigonometric values and basic identities directly into the expression.

Use: tan² θ − sec² θ = −1 and cosec² θ − cot² θ = 1

Expression = [(√3)² + (√3)²] / (−1) − [1 + 1] / 1

= (3 + 3) / (−1) − (2) / 1

= −6 − 2 = −8

∴ The correct answer is -8.

Alternate Method

Given:

(tan² 60° + cot² 30°) / (tan² 20° − sec² 20°) − (sin 90° + cos 0°) / (cosec² 20° − cot² 20°)

Formula and Values Used:

⇒ sec² θ − tan² θ = 1 ⇒ tan² θ − sec² θ = −1

⇒ cosec² θ − cot² θ = 1

⇒ tan 60° = √3, cot 30° = √3

⇒ sin 90° = 1, cos 0° = 1

Calculations:

⇒ First part numerator: tan² 60° + cot² 30° = (√3)² + (√3)² = 3 + 3 = 6

⇒ First part denominator: tan² 20° − sec² 20° = −1

⇒ Second part numerator: sin 90° + cos 0° = 1 + 1 = 2

⇒ Second part denominator: cosec² 20° − cot² 20° = 1

⇒ Expression Value = (6 / −1) − (2 / 1)

⇒ Value = −6 − 2 = −8

∴ The correct answer is -8.

Additional Information

Pythagorean Identities

sin² θ + cos² θ = 1 | 1 + tan² θ = sec² θ | 1 + cot² θ = cosec² θ

Key Trigonometric Values

sin 90° = 1, cos 0° = 1, tan 45° = 1, tan 60° = √3, cot 30° = √3.

Complementary Angles

sin(90° − θ) = cos θ | tan(90° − θ) = cot θ | sec(90° − θ) = cosec θ

The correct answer is Option 3.

Key Points

• Calcium Sulphate Dihydrate (CaSO4.2H2O) is commonly known as “Gypsum”.
• When Gypsum is heated, it gets converted into Calcium Sulphate Hemihydrate (CaSO4.1/2H2O) or “Plaster of Paris (POP)”.
• This is prepared by heating the gypsum which contains calcium sulfate dihydrate (CaSO4.2H2O) to a temperature of about 150 deg C.
• When added water to the plaster of Paris (PoP), it will re-form into gypsum.​

Additional Information Some common chemical compounds with their common names are:-

Calculation

45 students qualified from Institute

25% → 45

The students qualified from Institute 4 = 10%

10% → 45/25 × 10 = 18

The answer is 18.

The correct answer is Option 3. 

Key Points Energy conversion in water pump is from electrical to mechanical.

• An electric motor uses electromagnetic induction to convert electrical energy into mechanical energy.
• Electric energy is converted into mechanical energy by a direct current (DC) motor, and mechanical energy is converted into electrical energy by an alternating current (AC) generator.
• The electric motor is used as an important component in **electric fans, refrigerators, mixers, washing machines, computers, MP3 players, etc.**​

Additional Information

• Dynamo - A dynamo is an electrical generator that uses a commutator to generate direct current.
• Inverter - An inverter converts direct current (DC) electricity from sources such as batteries or fuel cells to alternating current (AC).The electricity can be at any voltage required; in an instance, it can power AC equipment designed for mains operation or be rectified to produce DC at any voltage required.
• Potentiometer - A potentiometer is a device that we use to measure the electromagnetic force of the cell. Potentiometers operate on the Wheatstone bridge principle, which means no current flows through the meter.

The correct answer is Option 4. 

Key Points 

Carbon is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent-making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Three isotopes occur naturally and are stable.

• Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard and brittle crystalline solid with a blue-grey metallic cluster, and it is a tetravalent metalloid and semiconductor. It is relatively unreactive.
• Germanium is a chemical element with the symbol Ge and atomic number 32. It is a lustrous, hard-brittle, greyish-white metalloid in the carbon group, chemically similar to its group neighbor's silicon and tin. Pure germanium is a semiconductor with an appearance similar to elemental silicon.​

Additional InformationModern Periodic Table has 18 Groups and 7 Periods.

• It has 118 Elements.
• Each of the tables has a vertical row is called group. Elements in groups have similar chemical and physical properties because they have the same number of outer electrons.
• Each of the tables has horizontal rows is called periods. During a period, a gradual change in chemical properties occurs from one element to another.
• The elements are arranged in the modern periodic table on the basis of Mosely law, which states that the physical and chemical properties of elements are the periodic function of their atomic number.
• The Structure of it is like a bird Grid.
• The Modern Periodic table is used to organize all the known elements.
• Advantages of Modern Periodic Table:- 
• It is easier to remember the properties of an element if its position in the periodic table is known.
• It made the study of Chemistry Systematic and Easy.

Modern Periodic Table:-

The correct answer is Option 4. 

Key Points

• Two chambered heart
• ​The heart of some animals, like fish, only has two chambers. There is only one ventricle and one auricle in their heart.
• The sinus venosus, which leads to the atrium, and the bulbus arteriosus, which follows the ventricle, are on their flanks.
• The sinus venosus is where the deoxygenated blood enters the atrium. It enters the ventricle from here.
• When the blood is pumped out of the ventricle, the pressure is much higher than that at the gills, which are the next place the blood goes.
• Because of their thin walls, the gills run the risk of being damaged by high blood pressure. As a result, the blood pressure that comes out of the ventricle is adjusted by the bulbus arteriosus.
• The blood's pressure must still be sufficient to circulate the fluid throughout the body, even though the decreased pressure may prevent damage to the lungs.
• As a result, a fish's blood circulation relies on a delicate balance between low pressure for the gills and sufficient circulation. Fishes do not have double circulation, unlike humans.

Additional Information 

• Three chambered heart
• ​With the exception of crocodiles, the hearts of all reptiles have three chambers, with two auricles and one ventricle. Compared to fish, this type is more advanced, but not as advanced as mammals.
• However, the ventricle is divided into two sub chambers by an incomplete partition. The right ventricle, also known as the Calum pulmonale, and the left ventricle, also known as the Calum venosum, are the two sub chambers.
• A third sub chamber, the cavum arteriosum, is located toward the top of the ventricle. A valve connects it to the left ventricle.
• Blood that has lost oxygen makes its way into the right atrium and into the right sub chamber of the ventricle. However, it also leaks into and fills the left ventricle as a result of incomplete separation.
• After that, the blood ascends the ventricle and enters the lungs for oxygenation. This descends once more and clogs the third chamber, the cavum arteriosum, temporarily.
• After that, the blood flows into the left ventricle, where it reaches the rest of the body.

The least possible Venn diagram is:    

Conclusions:

I. All cups are pans. → Follows (As, All cups are bottles and All bottles are pans, So the conclusion definitely follows.)

II. All bottles are cups. → Does not follow (As, All cups are bottles → Some bottles are cups)

III. All pans are cups. → Does not follow (As, All cups are bottles and All bottles are pans → Some pans are cups)

IV. Some pans are bottles. → Follows (As, All bottles are pans, So the conclusion definitely follows.)

Hence, only conclusions I and IV follow.

Concept used

Rombus: The diagonal of a rhombus is a line segment that joins any two non-adjacent vertices of a rhombus.

 A rhombus has two diagonals that bisect each other at right angles, thus, they form 4 right-angled congruent triangles.

Kite: The two diagonals of a kite bisect each other at 90 degrees. The main diagonal of a kite bisects the other diagonal. 

Square: A diagonal divides a square into two isosceles right-angled triangles.

Calculation

The diagonals of Parallelogram do not intersect at 90$^\circ$

L J + K - Y % T # U P

If all symbols are dropped from the series, then the newly formed series will be:

L J K Y T U P

Clearly, Y is at the middle most position in the newly formed series.

Hence, ‘Y’ is the correct answer.

1. P = T → False (As, T ≥ Y > U < I ≤ O = P → The relation between P and T cannot be determined) 2. Y > I → False (As, T ≥ Y > U < I ≤ O = P → The relation between Y and I cannot be determined) 3. U > P → False (As, T ≥ Y > U < I ≤ O = P → U < P) 4. T > U → True (As, T ≥ Y > U < I ≤ O = P → T > U)

Hence, ‘T > U’ is the correct answer.

Teachers who are also farmers but NOT from China is shown below:

Hence, ‘20’ is the correct answer.

The correct answer is Anukriti .net.

Key Points

• Anukriti.net is a website that provides information on Sanskrit language and literature.
• Anukriti.net is a translation service and information site developed jointly by the Central Institute of Indian Languages, Sahitya Akademi and National Book Trust in 2002.
• It was developed by the Rashtriya Sanskrit Sansthan, an autonomous organization under the Ministry of Human Resource Development.
• It offers resources for learning and studying Sanskrit language and literature.

Additional Information

• Praroop.net is a website that provides information on Indian languages and scripts.
• It was developed by the Centre for Development of Advanced Computing (C-DAC) in Pune.
• It offers tools and resources for learning and using various Indian languages.
• Anuvaad.net is a website that offers machine translation services for Indian languages.
• It was launched by the Ministry of Electronics and Information Technology (MeitY) in 2019.
• It uses artificial intelligence and machine learning algorithms to provide accurate translations.
• Pratilipi.net is a website that offers a platform for Indian language writers and readers.
• It was founded in 2014 and has a collection of over 400,000 books and stories in various Indian languages.
• It allows users to read, write, and share stories in their preferred Indian language.

The logic followed here is:

Similarly,

Hence, '(3, 83, 8)' is the correct answer.

Shortcut Trick

Identify prime numbers from the given list of 2-digit numbers.

Prime numbers identified: 79, 31, 29, 37, 43.

Sum → 79 + 31 + 29 + 37 + 43 = 219.

∴ The correct answer is 219.

Alternate Method

Given series: 78, 25, 96, 36, 14, 45, 76, 79, 39, 34, 31, 38, 29, 24, 26, 16, 37, 43

Check each number for primality (divisibility only by 1 and itself):

⇒ 78 (Even), 25 (5×5), 96 (Even), 36 (Even), 14 (Even), 45 (5×9), 76 (Even) → Composite

⇒ 79 (Prime)

⇒ 39 (3×13), 34 (Even) → Composite

⇒ 31 (Prime)

⇒ 38 (Even) → Composite

⇒ 29 (Prime)

⇒ 24 (Even), 26 (Even), 16 (Even) → Composite

⇒ 37 (Prime)

⇒ 43 (Prime)

Calculations:

⇒ Sum = 79 + 31 + 29 + 37 + 43

⇒ Sum = 110 + 29 + 37 + 43

⇒ Sum = 139 + 80

⇒ Sum = 219

∴ The correct answer is 219.

Additional Information

Prime Numbers

Numbers greater than 1 that have exactly two factors: 1 and the number itself. The only even prime is 2.

Composite Numbers

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

Co-prime Numbers

A pair of numbers whose HCF is 1. Example: (8, 15).

10 friends of a class appeared for a class test. Each friend got different marks in test.

1. Rama scored more than 4 friends only.
2. Usha scored less than 3 friends only.

Clearly, only 1 friend scored more than Rama but less than Usha.

Hence, ‘1’ is the correct answer.

The logic followed here is:

Hence, '83' is the correct answer.

The correct answer is A - Transverse section; B - Longitudinal section

Key Points

• The difference in appearance of the two diagrams is due to the orientation of the tissue in each section.
• In a longitudinal section, the tissue is cut along its length and appears elongated, while in a transverse section, the tissue is cut perpendicular to its length and appears circular.
• Sclerenchyma tissue is a type of plant tissue that provides mechanical support to the plant.
• It is composed of cells with thick, lignified cell walls.

Additional Information

• Sclerenchyma tissue is divided into two types: fibers and sclereids.
• Fibers are elongated cells that provide tensile strength to the plant, while sclereids are shorter cells that provide compressive strength.
• Lignin is a complex organic polymer that is deposited in the cell walls of sclerenchyma cells.
• It makes the cells rigid and waterproof, and gives them their characteristic woody texture.
• Longitudinal sections are often used to study the internal structure of plant organs such as stems and roots, while transverse sections are useful for studying the arrangement of tissues in leaves and flowers.

The logic followed here is:

Similarly,

Hence, 'HKW : NQC' is the correct answer.

The correct answer is 9/8.

Key Points

• Refractive index is the measure of the bending of light as it passes through a medium.
• The refractive index of medium A with respect to medium B can be calculated by dividing the refractive index of medium A by the refractive index of medium B.
• Therefore, the refractive index of medium A with respect to medium B is 3/2 divided by 4/3 = 9/8.

Additional Information

• How much light is bent, or refracted, as it enters a material is determined by its refractive index.
• In mathematical formulae and descriptive texts, the letter n or n' is most frequently used to represent the refractive index variable.
• The velocity of light of a certain wavelength in empty space, c, divided by its velocity in a substance, v, yields the refractive index, which is also equal to n = c/v.

The correct answer is Nirbhaya Fund.

Key Points

• The One Stop Centre (OSC) scheme was launched by the Ministry of Women and Child Development in 2015 to provide support and assistance to women affected by violence.
• Facilitating access to a wide range of assistance for women affected by abuse is the scheme's main goal.
• The Nirbhaya Fund was set up in 2013 in the aftermath of the Delhi gang-rape case to support initiatives aimed at enhancing the safety and security of women in India.

Additional Information

• The PM National Relief Fund is a fund set up to provide assistance to people affected by natural calamities and other emergencies.
• Durga Vahini Fund is a fund set up by the Vishwa Hindu Parishad to support initiatives aimed at promoting Hindu culture and values.
• Women Empowerment Fund is a general term and could refer to any fund set up to support initiatives aimed at empowering women.

The correct answer is Cu(s) + PbCl2(aq) → CuCl2(aq) + Pb(s).

Key Points

• A displacement reaction occurs when a more reactive element displaces a less reactive element from its compound.
• Cu(s) + PbCl2(aq) → CuCl2(aq) + Pb(s) is not possible because copper is less reactive than lead, so it cannot displace lead from its compound.
• In Pb(s) + CuCl2(aq) → PbCl2(aq) + Cu(s), lead is more reactive than copper, so it displaces copper from its compound.
• In Fe(s) + CuSO4(aq) → FeSO4(aq) + Cu(s), iron is more reactive than copper, so it displaces copper from its compound.
• In Zn(s) + CuSO4(aq) → ZnSO4(aq) + Cu(s), zinc is more reactive than copper, so it displaces copper from its compound.

Additional Information

• Copper is a moderately reactive metal that is commonly used in electrical wiring, plumbing, and construction materials.
• It is also an essential nutrient for plants and animals.
• Lead is a highly toxic metal that can cause serious health problems, including brain damage, kidney damage, and developmental delays.
• It is commonly found in old paint, plumbing, and soil.
• Iron is the most significant metal, but it rusts easily, making it a mysterious material.
• The majority is utilized in the production of steel, in manufacturing, and in civil engineering (reinforced concrete, girders, etc.).
• Rubber, medications, and metal goods are among the things that employ zinc.
• Roughly 75% of the zinc that is used is used as metal, primarily in the form of rolled zinc, zinc-based die casting alloy, alloying metal for making bronze and brass, and a coating to prevent iron and steel from corroding.

The correct answer is To preserve natural ecosystems.

Key Points

• Protected areas are established to conserve and protect natural ecosystems, including flora, fauna, and their habitats.
• These areas are also established to maintain biodiversity and ecological processes that are essential for the survival of various species.
• Protected areas also serve as a buffer zone against human activities such as deforestation, mining, and agriculture that can negatively impact the environment.
• They also provide opportunities for scientific research and education, which can help in understanding the complex ecological systems and developing conservation strategies.

Additional Information

• The Wildlife Protection Act of 1972 established India's four kinds of protected areas.
• Areas covered by national parks and wildlife sanctuaries make up tiger reserves.
• In India, there are 53 tiger reserves.
• India's protected areas accounted for 173,629.52 square kilometers as of January 2023, or around 5.28% of the nation's total land area.

The correct answer is It is the branch of science concerned with the origin, structure and composition of rocks.

Key Points

• Petrology is the branch of science concerned with the origin, structure and composition of rocks.
• Petrology is derived from the Greek word "petra" which means rock and "logos" which means study or discourse.
• It is a sub-discipline of geology that focuses on the study of rocks, including their formation, mineralogy, and texture.
• Petrologists use various techniques such as microscopy, X-ray diffraction, and chemical analysis to study rocks and understand their properties.
• The study of petrology is important in understanding the geologic history of the Earth, as rocks provide clues about past geological events and processes.

Additional Information

• The branch of science concerned with the origin, structure and composition of petroleum is called Petroleum Geology.
• The sedimentary rock formed out of deposits of glaciers is called Glacial Till or Glacial Sediment.
• Any naturally occurring solid mass or combination of minerals or mineraloid materials is referred to as rock in geology. 
• Igneous rocks, sedimentary rocks, and metamorphic rocks are the three main categories into which rocks are typically divided.
• Lava cooling on the surface or beneath the ocean creates igneous rocks.
• Magma cooling in the Earth's crust also produces igneous rocks.
• The weathering, movement, and deposition of pre-existing rocks result in the diagenesis and lithification of sediments, which in turn form sedimentary rocks.
• When pre-existing rocks are exposed to extreme temperatures and pressures that cause them to change without significantly melting, new rocks known as metamorphic rocks are created.

Calculation

The sum of the maximum marks obtained in Mathematics and the minimum marks obtained in Hindi = 85 + 85

Average = (85 + 85)/2 = 85

The answer is 85.

Shortcut Trick

Expand the cubic term on the Left-Hand Side (LHS): (x + 2)³ = x³ + 6x² + 12x + 8.

Expand the Right-Hand Side (RHS): x(x² − 1) = x³ − x.

Equate LHS = RHS: x³ + 6x² + 12x + 8 = x³ − x.

Subtract x³ from both sides and combine like terms: 6x² + 12x + x + 8 = 0.

The Standard Form is 6x² + 13x + 8 = 0.

∴ The correct answer is 6x² + 13x + 8 = 0.

Alternate Method

Given Equation: (x + 2)³ = x(x² − 1)

Formula Used: (a + b)³ = a³ + 3a²b + 3ab² + b³

⇒ LHS = (x)³ + 3(x)²(2) + 3(x)(2)² + (2)³

⇒ LHS = x³ + 6x² + 12x + 8

⇒ RHS = x × x² − x × 1

⇒ RHS = x³ − x

Equating both sides:

⇒ x³ + 6x² + 12x + 8 = x³ − x

⇒ x³ − x³ + 6x² + 12x + x + 8 = 0

⇒ 0 + 6x² + 13x + 8 = 0

⇒ 6x² + 13x + 8 = 0

∴ The correct answer is 6x² + 13x + 8 = 0.

Additional Information

Standard Form of a Quadratic Equation

A quadratic equation is typically written in the form ax² + bx + c = 0, where a ≠ 0.

Algebraic Expansion

The identity (a + b)³ = a³ + 3a²b + 3ab² + b³ is essential for expanding cubic binomials.

Degree of Equation

When the highest power (degree) of the variable after simplification is 2, the equation is quadratic. If the cubic terms do not cancel, it remains a cubic equation.

Amongst six friends A, B, C, D, E an F, each has a different height.

1. F is taller than only two other friends.

__ > __ > __ > F > __ > __

2. A is shorter than only one friend.

__ > A > __ > F > __ > __

3. D is shorter than F but taller than C.

F > D > C

4. E is shorter than B.

B > E

From 1, 2, 3 and 4, we get:

B > A > E > F > D > C

Clearly, E is the third tallest among all the friends.

Hence, ‘E’ is the correct answer.

Shortcut Trick

The numbers 597 and 603 are equidistant from 600.

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

Here, a = 600 and b = 3.

Result = 600² − 3² = 360000 − 9 = 359991.

∴ The correct answer is 359991.

Alternate Method

Given:

Expression: 597 × 603

Formula Used:

(a − b)(a + b) = a² − b²

Calculations:

⇒ 597 × 603 = (600 − 3) × (600 + 3)

⇒ 597 × 603 = (600)² − (3)²

⇒ 597 × 603 = 360000 − 9

⇒ 597 × 603 = 359991

∴ The correct answer is 359991.

Additional Information

Difference of Two Squares

The identity (a + b)(a − b) = a² − b² is used to simplify products of numbers close to a multiple of 10 or 100.

Unit Digit Method

Multiplying the last digits: 7 × 3 = 21. The result must end in 1, which helps eliminate wrong options quickly.

Digital Sum Rule

Digital sum of 597 (5+9+7=21→3) × 603 (6+0+3=9). Product DS = 3 × 9 = 27 → 9. The answer must have a digital sum of 9.

Shortcut Trick

Mean proportional between a and b is √(a × b).

Here, a = 4(2 + √2) and b = 3(2 − √2).

Product ab = 12 × (2 + √2)(2 − √2) = 12 × (4 − 2) = 12 × 2 = 24.

Mean proportional = √24 = 2√6.

∴ The correct answer is 2√6.

Alternate Method

Given: First number (a) = 8 + 4√2, Second number (b) = 6 − 3√2.

Formula Used: Mean proportional = √(a × b)

⇒ Let Mean Proportional be x.

⇒ x = √[(8 + 4√2) × (6 − 3√2)]

⇒ x = √[4(2 + √2) × 3(2 − √2)]

⇒ x = √[12 × (2² − (√2)²)]

⇒ x = √[12 × (4 − 2)]

⇒ x = √[12 × 2] = √24

⇒ x = 2√6

∴ The correct answer is 2√6.

Additional Information

Third Proportional

For two numbers a and b, the third proportional c is such that a : b = b : c, giving c = b²/a.

Fourth Proportional

For three numbers a, b, and c, the fourth proportional d is such that a : b = c : d, giving d = (b × c)/a.

Algebraic Identity

The identity (x + y)(x − y) = x² − y² is used to simplify the product of conjugate surds.

The correct answer is the same, opposite.

Key Points

• In both cases, the induced potential differences are of the same magnitude.
• In case (a), the induced potential difference has the same sign as that of the magnet's north pole, i.e., it is positive.
• In case (b), the induced potential difference has the opposite sign as that of the magnet's south pole, i.e., it is negative.
• The magnitude of the induced potential difference depends on the rate of change of magnetic flux through the coil, which, in turn, depends on the speed and orientation of the magnet.
• The induced potential difference is given by the formula: V = -N du/dt, where V is the induced potential difference, N is the number of turns in the coil, and du/dt is the rate of change of magnetic flux through the coil.

Additional Information

• Induced potential difference refers to the voltage generated in a conductor when it is subjected to a changing magnetic field.
• An electric potential difference is created in the coil by the pace at which the number of magnetic field lines connected to the loop changes while the magnet and loop are moving relative to one another or by a change in current in a nearby conductor.
• The circuit resistance is inversely proportional to the induced current, and it is proportional to the induced electromotive force.
• Although there is no current when the circuit is open, there may be an induced electromotive force.

The correct answer is second.

Key Points

• Neeraj Chopra
• Neeraj Chopra on 24 July 2022 won a Silver medal in the men's javelin throw event at World Athletics Championships in Eugene, US.
• Chopra grabbed the 2nd position with his best throw of 88.13 metres.
• Grenadian Anderson Peters won the gold medal with a throw of 90.54 meters.
• With this win, Neeraj Chopra has become the first-ever Indian to win a silver medal at World Athletics Championships.
• He is the second Indian after former long jumper Anju Bobby George, who won a bronze medal in long jump at 2003 in Paris.

Additional Information ​Sports:

• Indian weightlifter Harshada Garud on 18 July 2022 won a gold medal in the 2022 Asian Youth and Junior Weightlifting Championship.
• The Netherlands clinched their ninth FIH Women’s Hockey World Cup by beating Argentina 3-1 in the final on 17 July 2022.
• Youth World Boxing champions Alfiya Pathan & Gitika won gold medals at the first edition of the Elorda Boxing Cup in Nur-Sultan, Kazakhstan on 4 July 2022.
• Archers Jyothi Surekha Vennam and Abhishek Verma won the gold medal in the compound mixed team event at the Archery World Cup 2022 Stage- 3 in Paris on 25 June 2022.
• Cyclist Ronaldo Singh made history by winning a silver medal in the senior category sprint event at the Asian Track Cycling Championship 2022 (41st edition) held in New Delhi.
• Neeraj Chopra won the gold medal at the Kuortane Games in Finland on 18 June 2022.
• On 14 June 2022, Chopra also broke his own national record with a throw of 89.30m at the Paavo Nurmi Games 2022.
• Indian para-powerlifters Manpreet Kaur and Parmjeet Kumar have won bronze medals in World Para-powerlifting 2022 Asia Oceania Open Championships

The least possible Venn diagram is: 

Conclusions:

I. All sofas are cots. → Follows (As, All beds are cots and All sofas are beds)

II. Some beds are sofas. → Follows (As, All sofas are beds)

Hence, both conclusions I and II follow.

P, Q, R, S, T, U and V are sitting on a wall in a straight row, and all of them are facing north.

1. Q is at one of the extreme end and has T as his immediate neighbour. 2. V is the immediate neighbour of T and U.

3. S is sitting third from the extreme right end.

The above condition cannot be satisfied in Case I, so it is eliminated.

4. R is on the immediate right of S.

P, the only person left will occupy the vacant position.

Clearly, PQ is sitting at each of the extreme end.

Hence, ‘PQ’ is the correct answer.

The correct answer is Rent.

Key Points

• Rent is a fixed cost as it remains constant regardless of the level of production or sales.
• It is a cost that is incurred regularly and does not vary with the quantity produced or sold.
• Examples of other fixed costs include salaries, insurance, and property taxes.
• Fixed costs are important to consider when calculating the breakeven point for a business.

Additional Information

• Distribution costs can be variable or fixed, depending on the method of distribution.
• If a company uses a third-party logistics provider, the cost may be variable based on the volume of goods shipped.
• If a company has its own distribution network, the cost may be fixed as it is a regular expense.
• Other variable costs in distribution may include fuel costs and transportation expenses.
• Packaging costs can be variable or fixed, depending on the type of packaging used.
• If a company uses custom packaging for each product, the cost may be variable based on the quantity produced.
• If a company uses standard packaging for all products, the cost may be fixed as it is a regular expense.
• Other variable costs in packaging may include materials and labor costs.
• Raw material costs are typically considered variable costs as they vary with the quantity produced.
• The cost of raw materials may fluctuate based on supply and demand, weather conditions, and other factors.
• It is important for companies to monitor raw material costs and adjust pricing or production levels accordingly.
• Other variable costs in production may include labor costs and energy costs.

Shortcut Trick

Total age after 8 years = 80 + (8 × 2) = 96 years.

Sum of ratio parts = 17 + 15 = 32 units.

32 units = 96 years ⇒ 1 unit = 3 years.

B’s age after 8 years = 15 × 3 = 45 years.

Present age of B = 45 − 8 = 37 years.

∴ The correct answer is 37 years.

Alternate Method

Given: Sum of present ages of A and B = 80 years.

Ratio of ages after 8 years = 17 : 15.

⇒ Let ages of A and B after 8 years be 17x and 15x.

⇒ Present age of A = 17x − 8

⇒ Present age of B = 15x − 8

⇒ (17x − 8) + (15x − 8) = 80

⇒ 32x − 16 = 80

⇒ 32x = 96

⇒ x = 3

⇒ Present age of B = 15(3) − 8 = 45 − 8 = 37 years.

∴ The correct answer is 37 years.

Additional Information

Age Sum Shift

If the sum of ages of 'n' people is S at present, then after 't' years, the sum will be S + (n × t).

Ratio and Proportion in Ages

When a ratio a : b is given for a future or past time, always adjust the current sum or individual ages to that specific time frame before applying the ratio parts.

Constant Difference

The difference between the ages of two individuals remains constant regardless of the number of years passed.

The correct answer is Natural resources.

Key Points

• Natural resources are the foundation of sustainability.
• They provide the essential resources for human well-being, including food, water, and energy.
• Proper management of natural resources ensures their availability for future generations.
• This includes sustainable practices such as conservation, restoration, and responsible use.
• Natural resources also play a crucial role in mitigating climate change and promoting biodiversity.
• For example, forests absorb carbon dioxide, while wetlands provide habitat for a variety of wildlife.

Additional Information

• While industries provide employment opportunities and contribute to economic growth, they can have negative impacts on the environment if not managed properly.
• For example, industrial activities can lead to air and water pollution, as well as contribute to greenhouse gas emissions.
• The choice of crop varieties can impact the environment.
• Some crops require more water and pesticides than others, which can lead to negative impacts Mining activities can have negative impacts on the environment, including water pollution, soil erosion, and habitat destruction.
• The by-products of mining, such as tailings and waste rock, can also have negative impacts on the environment if not managed properly.

The correct answer is Eastern Ghat.

Key Points Shevroy Hills 

• Shevroy Hills and the Javadi Hills are located to the southeast of the Eastern Ghats.
• The Western Ghats and the Eastern Ghats mark the western and the eastern edges of the Deccan Plateau respectively.
• The Western Ghats are higher than the Eastern Ghats.
• The Eastern Ghats stretch from the Mahanadi Valley to the Nilgiris in the south.
• Mahendragiri (1,501 meters) is the highest peak in the Eastern Ghats.
• The Western Ghats cause orographic rain by facing the rain-bearing moist winds to rise along the western slopes of the Ghats.
• The highest peaks include the Anai Mudi (2,695 meters) and the Doda Betta (2,637 meters).

I. Monthly benefits will keep the employees happy.

Only assumption I is implicit as it is clearly stated in the question that In order to retain employees, we must reward them with monthly benefits.

II. The employees will be punctual.

Assumption II is not implicit as there is no statement regarding the punctuality of employees.

Hence, only assumption I is implicit.

Shortcut Trick

Assume the annual installment is 100%.

Total units for 5 years = (100 + 40) + (100 + 30) + (100 + 20) + (100 + 10) + 100 = 600%.

Interest parts = Rate × Sum of years remaining = 10 × (4 + 3 + 2 + 1 + 0) = 100%.

Given 600% = ₹9,600 ⇒ 1% = 16.

Installment (100%) = 100 × 16 = ₹1,600.

∴ The correct answer is ₹1,600.

Alternate Method

Given:

Total debt (A) = ₹9,600

Rate of interest (R) = 10% per annum

Time period (n) = 5 years

Formula Used:

A = n × x + [R × x × n(n − 1) / 200]

Where x = annual installment.

Calculations:

⇒ 9,600 = 5 × x + [10 × x × 5 × 4 / 200]

⇒ 9,600 = 5x + [200x / 200]

⇒ 9,600 = 5x + x

⇒ 9,600 = 6x

⇒ x = 9,600 / 6

⇒ x = 1,600

∴ The correct answer is ₹1,600.

Additional Information

Definition of Debt

The debt (or amount due) is the sum of all installments and the simple interest earned by each installment from the time of payment until the end of the total period.

Installment Interest Pattern

For n years, the 1^st installment earns interest for (n − 1) years, the 2^nd for (n − 2) years, and the final installment earns 0 interest.

SI Installment General Formula

Installment (x) = [100 × A] / [100n + R × n(n − 1)/2], where A is Total Debt, R is Rate, and n is Time.

Shortcut Trick

Side of cube (a) = √³(Volume) = √³(512) = 8 cm.

Main Diagonal of cube = a√3.

Diagonal = 8√3 cm.

∴ The correct answer is 8√3 cm.

Alternate Method

Given: Volume of cube = 512 cm³.

Formula Used: Volume = a³ | Main Diagonal = a√3 (where a is the side).

⇒ a³ = 512

⇒ a = √³(8 × 8 × 8)

⇒ Side (a) = 8 cm

⇒ Main Diagonal = a × √3

⇒ Diagonal = 8√3 cm

∴ The correct answer is 8√3 cm.

Additional Information

Surface Area of Cube

The Total Surface Area (TSA) of a cube is 6a² and the Lateral Surface Area (LSA) is 4a².

Face Diagonal

The diagonal of any single square face of the cube is given by a√2.

In-radius and Circum-radius

The In-radius (r) is a/2 and the Circum-radius (R) of the cube is (a√3)/2.

Shortcut Trick

For a regular polygon, the sum of its interior angle and exterior angle is always 180°.

⇒ Exterior angle = 180° − Interior angle = 180° − 144° = 36°

For any regular polygon, the number of sides (n) = 360° ÷ Exterior angle

⇒ n = 360° ÷ 36° = 10

∴ The correct answer is 10.

Alternate Method

Given:

Each interior angle of a regular polygon = 144°

Formula Used:

Each interior angle of a regular polygon having n sides = [(n − 2) × 180°] ÷ n

Calculation:

⇒ 144° = [(n − 2) × 180°] ÷ n

⇒ 144n = 180n − 360

⇒ 360 = 180n − 144n

⇒ 360 = 36n

⇒ n = 360 ÷ 36

⇒ n = 10

∴ The correct answer is 10.

Additional Information

Sum of Interior Angles of a Polygon

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

Sum of Exterior Angles

The sum of all exterior angles of any convex polygon is always 360°.

Exterior Angle of a Regular Polygon

Each exterior angle of a regular polygon is equal to 360° ÷ n.

Shortcut Trick

For three equal distances, Average Speed = (3 × s₁ × s₂ × s₃) ÷ (s₁s₂ + s₂s₃ + s₃s₁)

Average Speed = (3 × 5 × 8 × 6) ÷ (5×8 + 8×6 + 6×5) = 720 ÷ (40 + 48 + 30)

Average Speed = 720 ÷ 118 = 360 ÷ 59 = 6(6/59) km/h

∴ The correct answer is 6(6/59) km/h.

Alternate Method

Given: Speeds s₁ = 5 km/h, s₂ = 8 km/h, s₃ = 6 km/h. Distances are equal.

Formula: Average Speed = Total Distance ÷ Total Time

⇒ Let the equal distance be LCM(5, 8, 6) = 120 km each.

⇒ Time t₁ = 120 ÷ 5 = 24 hours

⇒ Time t₂ = 120 ÷ 8 = 15 hours

⇒ Time t₃ = 120 ÷ 6 = 20 hours

⇒ Total Distance = 120 + 120 + 120 = 360 km

⇒ Total Time = 24 + 15 + 20 = 59 hours

⇒ Average Speed = 360 ÷ 59 = 6(6/59) km/h

∴ The correct answer is 6(6/59) km/h.

Additional Information

Average Speed for Two Equal Distances

When a person covers two equal distances at speeds x and y, the average speed is given by (2xy) ÷ (x + y).

Harmonic Mean Property

When distances are equal, average speed is the Harmonic Mean of the individual speeds.

Relative Speed

In the same direction, relative speed is s₁ − s₂; in the opposite direction, it is s₁ + s₂.

The correct answer is It depends only upon the nuclear charge.

Key Points

• Down the group, the effective nuclear charge experienced by the valence electrons decreases as  the outermost electrons move further away from the nucleus .
• These electrons can be easily lost.
• Thus, the metallic property decreases in a period and moves down the group.
• The effective nuclear charge increases in period from left to right as the table unfolds.

Additional Information

• The word "effective" is used because shielding effect The negatively charged electron prevents the higher energy electrons from experiencing the full nuclear charge of the nucleus due to the repulsive effect of the inner layer.
• The effective nuclear charge experienced by an electron is also called the core charge.
• A higher effective nuclear charge causes greater attraction for electrons, pulling the electron cloud closer to the nucleus resulting in a smaller atomic radius.

The logic followed here is:

Logic: 1st digit × (3/2) = 2nd digit

12 ∶ 18 → 12 × (3/2) = 18

28 : 42 → 28 × (3/2) = 42

Similarly,

10 ∶ ? → 10 × (3/2) = 15

Hence, '15' is the correct answer.

The correct answer is Lysosomes.

Key Points

• Lysosomes: These are membrane-bound vesicular structures formed by the process of packaging in the Golgi apparatus. These are formed by the fusion of vesicles that have budded off from the trans-Golgi apparatus.
• These are also called ''Suicidal bags'' because of their phagocytic activity. Lysosome keeps the cell clean by digesting any foreign material as well as worn-out cell organelles.
• If any cell or cell organelle gets damaged, the lysosome digest the damaged cell or cell organelle by the application of hydrolytic enzymes (hydrolases – lipases, proteases, carbohydrates).

Additional Information

According to given conditions,

Clearly, Yogesh's home is to the South-West of his Sister's home.

Hence, ‘South-west’ is the correct answer.