RRB Group D Previous Year Paper (Held on: 22 Aug 2022 Shift 3)

Given Statement:  A = F ≥ S > H < Z > R = G

Now,

Conclusions:

I. S < G → False (S > H < Z > R = G it gives no definite relation between S and G)

II. S ≥ A → False (A = F ≥ S it gives A ≥ S)

Here, Both conclusions I and II are false.

Hence, the correct answer is "Option 2".

The correct answer is violet

Key Points

• Violet light deviates the most when passing through a glass prism.
• This is due to the fact that violet light has the shortest wavelength of all the colors in visible light, and shorter wavelengths are refracted more than longer wavelengths.
• The phenomenon of light splitting into its constituent colors is called dispersion, and it occurs because different wavelengths of light are refracted by different amounts.
• The order of colors from least to most deviation through a prism is red, orange, yellow, green, blue, indigo, and violet (often remembered by the acronym ROYGBIV).

Additional Information

• Isaac Newton was the first to demonstrate that white light is made up of a spectrum of colors by using a glass prism.
• When white light enters a prism, it slows down and bends. Each color bends by a different amount because each color travels at a different speed in the glass.
• This separation of light into different colors is what produces the spectrum.
• In natural phenomena, dispersion is responsible for the formation of rainbows, where sunlight is dispersed by water droplets in the atmosphere.

The correct answer is NV Ramana

Key Points

• NV Ramana served as the Chief Justice of India as of March 2022.
• He was appointed as the 48th Chief Justice of India on April 24, 2021.
• Justice NV Ramana has played a significant role in several landmark judgments and has been an advocate for judicial reforms.
• He emphasized the need for a robust judicial system to uphold the rule of law and ensure justice for all citizens.

Additional Information

• The Chief Justice of India is the head of the judiciary of India and the Supreme Court of India.
• The Chief Justice is appointed by the President of India and serves until the age of 65.
• The Supreme Court of India was established on January 28, 1950, and is the highest judicial forum and final court of appeal under the Constitution of India.
• The Chief Justice plays a crucial role in the administration of justice and the functioning of the judiciary in India.
• The Supreme Court consists of the Chief Justice and a maximum of 33 other judges.

The correct answer is It helps in maintaining temperature 2-3 degrees lower than the body for sperm formation

Key Points

• Testes are located outside the abdominal cavity in a pouch called the scrotum.
• This positioning helps in maintaining the temperature 2-3 degrees lower than the body temperature, which is essential for sperm formation.
• The scrotum acts as a climate control system for the testes, ensuring an optimal environment for the production and storage of sperm.
• Temperature regulation is crucial because spermatogenesis (the production of sperm) requires a temperature slightly lower than the core body temperature.

Additional Information

• The scrotum has a layer of muscle called the dartos muscle which contracts or relaxes to move the testes closer to or further from the body, thus regulating their temperature.
• In colder conditions, the cremaster muscle also contracts to pull the testes closer to the body for warmth.
• This temperature regulation mechanism is vital for maintaining sperm viability and fertility.
• Additionally, the lower temperature in the scrotum helps in preventing damage to the developing sperm cells.

Shortcut Trick Total Eggs = 12 dozen = 144 eggs. Cost Price (CP) = 144 × 5 = ₹720. Remaining Eggs = 144 − 12 = 132 eggs. Selling Price (SP) = 132 × 6 = ₹792. Profit % = (792 − 720) ÷ 720 × 100 = 72 ÷ 720 × 100 = 10%. ∴ The correct answer is 10%.

Alternate Method

Given: Quantity bought = 12 dozen = 12 × 12 = 144 eggs Rate of purchase = ₹5 per egg Broken eggs = 12 Rate of sale = ₹6 per egg Formula Used: Profit Percentage = [(SP − CP) ÷ CP] × 100 Calculations: ⇒ Total Cost Price (CP) = 144 × 5 = ₹720 ⇒ Remaining eggs = 144 − 12 = 132 ⇒ Total Selling Price (SP) = 132 × 6 = ₹792 ⇒ Profit = 792 − 720 = ₹72 ⇒ Profit % = (72 ÷ 720) × 100 ⇒ Profit % = 10% ∴ The correct answer is 10%.

Additional Information Profit and Loss Basics Profit occurs when Selling Price (SP) > Cost Price (CP). Loss occurs when CP > SP. Percentage Change Percentage change is always calculated on the Initial Value (CP) unless stated otherwise: % Change = (Difference ÷ Initial) × 100. Impact of Wastage Wastage or breakage effectively increases the CP per unit of the remaining items, as the total cost is now spread over fewer units.

According to the given Venn diagram:

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Now, 

Option 1) The number of teachers who are both writers and poets is 20.

The shaded area shows the "the number of teachers who are both writers and poets" = 20.

Option 2) The number of poets who are also teachers is 44.

The shaded area shows the "The number of poets who are also teachers".

Option 3) The number of writers who are neither teachers nor poets is 10.

The shaded area shows the " The number of writers who are neither teachers nor poets".

Option 4) The number of poets who are also teachers but not writers is 48.

The shaded area shows the "The number of poets who are also teachers but not writers".

So, only Option 1 is correct.

Hence, the correct answer is " Option 1".

Given: 

A certain number of people are sitting in a row, facing north.

Now,

1) D is at the extreme right end of the row. 

2) D is to the immediate right of H.

3) Only three people sit between H and L.

4) L is fifth to the right of C.

5) A is third to the left of C

So, The total number of person seated in the row is 14.

Hence the correct answer is "Option 4".

The correct answer is to have services proactively anticipate citizens’ needs before they approach the services.

Key Points

• The aim of the Digital Government Mission launched by the Ministry of Electronics and Information Technology in January 2022 is to have services proactively anticipate citizens' needs before they approach the services.
• This initiative is part of the broader effort to enhance the efficiency and responsiveness of government services through digital means.
• The mission seeks to leverage technology to provide seamless and efficient service delivery to citizens.
• Proactive service delivery can significantly reduce the time and effort required by citizens to access government services.

Additional Information

• The Digital Government Mission is a step towards transforming the governance model in India to be more citizen-centric and technology-driven.
• It aligns with the vision of a Digital India, aiming to ensure that government services are made available to citizens electronically by improving online infrastructure and increasing internet connectivity.
• This mission is expected to enhance transparency, efficiency, and ease of access to public services.
• Other initiatives under the Digital India program include digital literacy campaigns, e-governance initiatives, and the development of digital infrastructure.

The logic followed here is:

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

Given,

(5, 62, 7)

⇒ 5² + 7² - (5 + 7)

⇒ 74 - 12 = 62.

And, (8, 188, 12) 

⇒ 82 + 122 - (8 + 12)

⇒ 208 - 20 = 188.

Now, checking the options:

Option 1) (10, 181, 9)

⇒ 102 + 92 - (10 + 9)

⇒ 181 - 19 = 162 ≠ 181.

.Option 2) (6, 117, 19 )

⇒ 62 + 192 - (6 + 19)

⇒ 397 - 25 = 372 ≠ 117.

Option 3) (11, 390, 13)

⇒ 112 + 132 - (11 + 13)

⇒ 190 - 24 = 166 ≠ 390.

Option 4) (7, 114, 9) 

⇒ 72 + 92 - (7 + 9)

⇒ 130 - 16 = 114.

 Hence, the correct option is "Option 4".

Shortcut Trick

When the distance covered is same for both ways, use the Harmonic Mean formula.

Average Speed = (2 × x × y) ÷ (x + y)

Average Speed = (2 × 4 × 20) ÷ (4 + 20)

Average Speed = 160 ÷ 24 = 20/3 km/h

∴ The correct answer is 20/3 km/h.

Alternate Method

Given:

Speed to school (S₁) = 4 km/h

Return speed (S₂) = 20 km/h

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Let the distance to school be D.

⇒ Time taken to go = D/4 hours

⇒ Time taken to return = D/20 hours

⇒ Total Time = D/4 + D/20 = (5D + D) ÷ 20 = 6D/20 = 3D/10 hours

⇒ Total Distance = D + D = 2D

⇒ Average Speed = 2D ÷ (3D/10) = (2D × 10) ÷ 3D

⇒ Average Speed = 20/3 km/h

∴ The correct answer is 20/3 km/h.

Additional Information

Average Speed (Different Distances)

If distances are not equal, always use the basic formula: (d₁ + d₂ + ...) ÷ (t₁ + t₂ + ...).

Relative Speed

Objects moving in the same direction: S₁ − S₂. Objects moving in opposite directions: S₁ + S₂.

Unit Conversion

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

The position and positional values or English Alphabets are:

Now,

HCM : MHR

FET : KJY 

Let's check each Option One by One.

Option 1) PRT : TPS 

 

Option 2) UPJ : ZUO

Option 3) UFL : LKU

Option 4) GHK : HKJ

So, Only UPJ : ZUO follows the pattern of given letter cluster.

Hence, the correct answer is 'Option 2'

Concept:

Concave Mirror Formula:

• The relationship between object distance (u), image distance (v), and focal length (f) of a concave mirror is given by the mirror formula:
• Mirror Formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
• Here, f is the focal length (cm), v is the image distance (cm), and u is the object distance (cm).
• The focal length (f) of a concave mirror is negative, and the image distance (v) for a real image is also negative.
• Real Image: An image formed where the light rays converge. It is inverted and can be projected onto a screen.
• SI Unit: The SI unit of focal length is meter (m), but in this context, we use centimeters (cm).
• Dimensional Formula: The dimensional formula for focal length is [L].

 

Calculation:

Given,

Focal length, f = -20 cm

Image distance, v = -60 cm

Using mirror formula,

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

⇒$\frac{1}{-20} = \frac{1}{-60} + \frac{1}{u}$

⇒$\frac{1}{u} = \frac{1}{-20} - \frac{1}{-60}$

⇒ $\frac{1}{u} = \frac{-3 + 1}{60}$

⇒ $\frac{1}{u} = \frac{-2}{60}$

⇒$\frac{1}{u} = -\frac{1}{30}$

⇒ u = -30 cm

∴ The object distance is -30 cm.

The correct answer is Article 40.

Key Points

• Article 40 of the Constitution of India enshrines one of the Directive Principles of State Policy.
• It states that "the State shall take steps to organise village panchayats and endow them with such powers and authority as may be necessary to enable them to function as units of self-government."
• This directive aims at promoting local self-governance and empowering rural areas.
• Article 40 is part of Part IV of the Indian Constitution, which outlines the Directive Principles of State Policy.
• These principles are fundamental in the governance of the country, intended to be applied by the government in making laws.

Additional Information

• The Directive Principles of State Policy are guidelines for the framing of laws by the government. They are not enforceable by any court, but they are considered fundamental in the governance of the country.
• The Constitution of India was adopted on 26th November 1949 and came into effect on 26th January 1950.
• The Constitution aims to establish India as a sovereign, socialist, secular, and democratic republic.
• It assures its citizens justice, equality, and liberty, and endeavors to promote fraternity among them.
• Article 40 is among the various articles in the Constitution that aim to promote social and economic welfare and to ensure a just society.

The correct answer is Iron-ore

Key Points

• The Gua mines in Jharkhand are primarily known for their Iron-ore deposits.
• Iron-ore is a critical raw material for the production of steel and is one of the most abundant minerals found in the region.
• The Gua mines have been a significant contributor to India’s iron-ore production, supporting both domestic steel industries and export markets.

Additional Information

• Jharkhand is rich in mineral resources and has some of the largest iron-ore mines in India.
• The state also produces other minerals such as coal, bauxite, and copper, but the Gua mines are specifically known for iron-ore.
• Iron-ore mining in Jharkhand contributes significantly to the economy and provides employment to a large number of people in the region.
• The quality of iron-ore from the Gua mines is considered to be of high grade, making it a valuable asset for industrial use.

Shortcut Trick

Count the decimal places: both numerator and denominator have 6 decimal places.

Remove decimals: √(30625 ÷ 1225).

Divide directly: 30625 ÷ 1225 = 25.

√25 = 5.

∴ The correct answer is 5.

Alternate Method

Given: √(0.030625 ÷ 0.001225)

Step 1: Equalize decimal places by multiplying numerator and denominator by 1,000,000.

⇒ √(30625 ÷ 1225)

Step 2: Factorize the numbers.

⇒ 30625 = 175²

⇒ 1225 = 35²

Step 3: Calculate the square root.

⇒ √(175² ÷ 35²) = 175 ÷ 35

⇒ 5

∴ The correct answer is 5.

Additional Information

Square Root of Decimals

If the number of decimal places is the same in the numerator and denominator, they cancel out each other.

Squares ending in 25

A number ending in 25 is a perfect square only if the digits before 25 are a product of two consecutive integers n × (n+1).

BODMAS Rule

Always solve terms inside the square root (grouping symbol) before final extraction.

The correct answer is only iii.

Key Points

• Dobereiner's Triads: Johann Wolfgang Döbereiner was a German chemist who is best known for his work that led to the development of the periodic table. He identified groups of three elements (triads) that had similar properties and observed that the atomic weight of the middle element was approximately the average of the atomic weights of the other two elements.
• The triads mentioned in the options are as follows:
• (i) Li, Na, K
• (ii) Ca, Sr, Ba
• (iii) N, P, Sb
• (iv) Cl, Br, I
• Explanation:
• Option (i): Li, Na, K - This is a valid Dobereiner's triad as Lithium (Li), Sodium (Na), and Potassium (K) all belong to Group 1 (Alkali metals) and show similar properties.
• Option (ii): Ca, Sr, Ba - This is a valid Dobereiner's triad as Calcium (Ca), Strontium (Sr), and Barium (Ba) all belong to Group 2 (Alkaline earth metals) and show similar properties.
• Option (iii): N, P, Sb - This is NOT a valid Dobereiner's triad. Nitrogen (N), Phosphorus (P), and Antimony (Sb) do not form a triad with similar properties and the atomic weight of P is not the average of N and Sb.
• Option (iv): Cl, Br, I - This is a valid Dobereiner's triad as Chlorine (Cl), Bromine (Br), and Iodine (I) all belong to Group 17 (Halogens) and show similar properties.
• Conclusion: Therefore, the triad that is NOT a Dobereiner's triad is Option (iii): N, P, Sb.

Shortcut Trick

Net Interest Percentage = Rate × Time = 5% × 3 = 15%

Total Amount Percentage = 100% (Principal) + 15% (Interest) = 115%

Amount = 115% of ₹1,232 = 1.15 × 1232

Amount = ₹1,416.80

∴ The correct answer is ₹1416.80.

Alternate Method

Given:

Principal (P) = ₹1,232

Rate (R) = 5% per annum

Time (T) = 3 years

Formula Used:

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

Amount (A) = Principal (P) + Simple Interest (SI)

Calculations:

⇒ SI = (1232 × 5 × 3) ÷ 100

⇒ SI = (1232 × 15) ÷ 100

⇒ SI = 18480 ÷ 100

⇒ SI = ₹184.80

⇒ Amount = 1232 + 184.80

⇒ Amount = ₹1,416.80

∴ The correct answer is ₹1416.80.

Additional Information

Simple Interest Formula

Simple interest is calculated only on the initial principal. Formula: SI = P × R × T ÷ 100.

Compound Interest Comparison

Unlike SI, Compound Interest is calculated on the principal plus accumulated interest. Amount A = P(1 + R/100)^T.

Rate and Time relationship

If the Rate is given half-yearly, the time must be doubled and the rate must be halved for calculations.

Shortcut Trick

Income ratio (Anuj : Mathew) = 5 : 7

Expenditure ratio (Anuj : Mathew) = 2 : 3

Savings are equal (₹10,000), so equate the ratio differences: (5−2) ≠ (7−3). New ratios with equal difference: (5 : 7) × (3−2) = 5 : 7 and (2 : 3) × (7−5) = 4 : 6.

Difference in ratio units (5−4 or 7−6) = 1 unit → ₹10,000.

Anuj’s Income = 5 units = 5 × ₹10,000 = ₹50,000.

∴ The correct answer is ₹50,000.

Alternate Method

Given: Ratio of incomes = 5 : 7, Savings = ₹10,000 each, Ratio of expenditure = 2 : 3.

Formula: Income − Savings = Expenditure

⇒ Let Anuj’s income be 5x and Mathew’s income be 7x.

⇒ (5x − 10000) / (7x − 10000) = 2 / 3

⇒ 3 × (5x − 10000) = 2 × (7x − 10000)

⇒ 15x − 30000 = 14x − 20000

⇒ 15x − 14x = 30000 − 20000

⇒ x = 10000

⇒ Anuj’s Income = 5x = 5 × 10000 = ₹50,000

∴ The correct answer is ₹50,000.

Additional Information

Income-Expenditure Relationship

Income is always the sum of Expenditure and Savings. Formula: Income = Expenditure + Savings.

Cross-Multiplication Method

Used when ratios change by a fixed value. (Product of means − Product of extremes) in ratios equals the constant difference effect.

Ratio Balancing

If Savings are equal for both, the difference between income units and expenditure units must be made equal by multiplying the ratios with the difference of the other ratio.

Shortcut Trick

Sum of roots = 7/3 + 12/5 = (35 + 36)/15 = 71/15

Product of roots = (7/3) × (12/5) = 84/15

The quadratic equation is 15x² − (Sum × 15)x + (Product × 15) = 0.

Required equation: 15x² − 71x + 84 = 0.

∴ The correct answer is 15x² − 71x + 84 = 0.

Alternate Method

Given:

The roots of the required quadratic equation are α = 7/3 and β = 12/5.

Formula Used:

A quadratic equation with given roots α and β is formed as:

x² − (α + β)x + αβ = 0

Calculations:

⇒ Sum of roots (α + β) = 7/3 + 12/5

⇒ α + β = ( (7 × 5) + (12 × 3) ) / 15

⇒ α + β = (35 + 36) / 15 = 71/15

⇒ Product of roots (αβ) = (7/3) × (12/5)

⇒ αβ = 84/15

⇒ Substituting these values into the standard form:

⇒ x² − (71/15)x + 84/15 = 0

⇒ Multiply the entire equation by the LCM of denominators (15):

⇒ 15(x²) − 15(71/15)x + 15(84/15) = 0

⇒ 15x² − 71x + 84 = 0

∴ The correct answer is 15x² − 71x + 84 = 0.

Additional Information

Relationship between Roots and Coefficients

For any quadratic equation ax² + bx + c = 0, the sum of roots (α + β) = −b/a and the product of roots (αβ) = c/a.

Discriminant and Nature of Roots

The nature of roots is determined by D = b² − 4ac. If D ≥ 0 and a perfect square, the roots are rational and distinct (provided a, b, c are rational).

Formation of Equation

If the roots are reciprocal to each other, then the product αβ = 1, which implies the coefficients a = c.

The correct answer is Bible

Key Points

• The Bible is the sacred text of Christianity.
• It consists of two main parts: the Old Testament and the New Testament.
• The Old Testament is essentially the Hebrew text of the time of Jesus.
• The New Testament includes writings about Jesus Christ and the early church.

Additional Information

• The Bible is divided into chapters and verses for reference.
• It is considered the word of God by Christians and is used in worship and instruction.
• The Old Testament contains books such as Genesis, Exodus, and Psalms.
• The New Testament contains the Gospels, Acts, Epistles, and Revelation.
• The Bible has been translated into numerous languages and is one of the most widely read and distributed books in the world.

Given Statements:

Some purses are keys.

All lockers are keys.

All keys are pins.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some pins are purses. - True (Because, some purses are keys and all keys are pins implies that some pins are definitely purses).

II. No pin is a purse.  - False (Because, some purses are keys and all keys are pins implies that some pins are definitely purses).

So, Only conclusion I follow.

Hence, the correct answer is "Option 3".

The correct answer is 44th

Key Points

• Tripura celebrated the 44th Kokborok Day on 19th January 2022.
• Kokborok is one of the state languages of Tripura, predominantly spoken by the Tripuri people.
• The celebration of Kokborok Day marks the recognition and promotion of the Kokborok language and its cultural significance.
• The day is observed with various cultural programs, events, and activities aimed at preserving and promoting the language.

Additional Information

• Kokborok, also known as Tripuri, is a Tibeto-Burman language spoken in the Indian state of Tripura and neighboring areas.
• The language has a rich oral tradition and has been an integral part of the cultural heritage of the indigenous Tripuri people.
• The Tripura government has taken several initiatives to promote the use of Kokborok in education and official communication.
• The celebration of Kokborok Day serves as a reminder of the importance of preserving indigenous languages and cultures.

The correct answer is Heptene

Key Points

• Heptene is the next member in the homologous series of hexene.
• A homologous series is a series of compounds with the same functional group and similar chemical properties where each successive member differs by a CH₂ unit.
• Hexene has the chemical formula C₆H₁₂, and adding a CH₂ unit will result in Heptene with the formula C₇H₁₄.
• Members of the alkenes (olefins) homologous series, to which hexene and heptene belong, have the general formula CₙH₂ₙ.

Additional Information

• Alkenes are hydrocarbons that contain at least one carbon-carbon double bond (C=C).
• They are unsaturated hydrocarbons and are more reactive than alkanes due to the presence of the double bond.
• Alkenes are used in the production of polymers, alcohols, and other chemicals.
• Examples of alkenes include ethene (C₂H₄), propene (C₃H₆), and butene (C₄H₈).

Given: L, M, N, O, P, Q and R, are sitting in a straight row, facing north.

1) Only three people sit between Q and N.

2. M and O are immediate neighbors.

3. O is at the extreme right end of the row.

4) R is at the immediate left of N.

So, N is at the fifth position from the left end of the row.

Hence, the correct answer is "Option 4".

The correct answer is CO.

Key Points

• CO acts as a reducing agent in the given reaction.
• In the reaction: Fe₂O₃ + 3CO → 2Fe + 3CO₂, carbon monoxide (CO) reduces ferric oxide (Fe₂O₃) to iron (Fe).
• A reducing agent is a substance that loses electrons and reduces another substance by giving electrons.
• Here, CO is oxidized to CO₂ while reducing Fe₂O₃ to Fe.

Additional Information

• In redox reactions, the substance that gets oxidized (loses electrons) is the reducing agent.
• Fe₂O₃ is the oxidizing agent as it gains electrons and gets reduced to Fe.
• The reaction is a classic example of the reduction of metal oxides using carbon monoxide.
• Such reactions are commonly used in metallurgy for extracting metals from their ores.

Given: Few birds (One each of Orange, Yellow, Black, Green, Grey, Red colour and three White coloured) were sitting in a row facing north.

1. The black bird was an immediate neighbour of both, the red and the grey bird.

2. The yellow bird was sitting to the immediate right of the green bird.

3. Only three birds were sitting between the orange and the red bird and all these three birds were white.

4. The yellow bird sat third to the right of the black bird.

So, the Orange colour bird was sitting at the leftmost end and the Yellow colour bird was sitting at the rightmost end of the row.

Hence, the correct answer is "Option 4".

Given Statements:

Some beds are tables.

Some tables are cupboards.

Some cupboards are chairs.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some chairs are beds - False (Because, No definite relation is given between chairs and beds, so some chairs are beds can be a possibility only).

II. Some beds are cupboards - False (Because, No definite relation is given between beds and cupboards, some beds are cupboards can be a possibility only)

So, Neither conclusion I nor II follow.

Hence, the correct answer is "Option 4".

Calculation:

Fans sold = 28%

Ovens sold = 8%

According to the question:

⇒ (28% - 8%) of 16800 = 3360.

∴ Option 4 is the correct answer.

The correct answer is option 3

Key Points

• Option 3 correctly represents the order of metallic character: Mg < Na < Ba < Cs.
• Metallic character increases down a group and decreases across a period in the periodic table.
• Cesium (Cs) has the highest metallic character among the given elements, followed by Barium (Ba), Sodium (Na), and Magnesium (Mg).
• This order is determined by the elements' ability to lose electrons, which is a key property of metals.

Additional Information

• The metallic character is directly related to the atomic size and ionization energy of the elements.
• Cesium (Cs), being at the bottom of Group 1, has the largest atomic size and the lowest ionization energy, making it the most metallic.
• Barium (Ba) is in Group 2 and has a larger atomic size and lower ionization energy than Sodium (Na) and Magnesium (Mg), making it more metallic than both.
• Sodium (Na) is in Group 1 but is above Cesium, making it less metallic than Cesium and Barium but more metallic than Magnesium.
• Magnesium (Mg) is in Group 2 and has the smallest atomic size and highest ionization energy among the given elements, making it the least metallic.

Solution:

Two resistors of 2 ohm are connected in series.

So, Equivalent resistor = 2 + 2 = 4 ohm

Now, use ohm's law:

V = I R_eq

⇒ 4 = I × 4

⇒ I = 4/4 = 1 A

Hence, the total current in the circuit is 1 A.

Shortcut Trick

Profit Ratio = (Capital × Time)

Ratio (S : G : Si) = (4000 × 6) : (8000 × 8) : (6000 × 8)

Ratio = 24 : 64 : 48 ⇒ 3 : 8 : 6

Total units = 3 + 8 + 6 = 17 units → ₹34,000

Mr. Gupta share (8 units) = (34000 ÷ 17) × 8 = ₹16,000

∴ The correct answer is ₹16,000.

Alternate Method

Given:

Investment of Mr. Sharma (I₁) = ₹4,000, Time (T₁) = 6 months

Investment of Mr. Gupta (I₂) = ₹8,000, Time (T₂) = 8 months

Investment of Ms. Sinha (I₃) = ₹6,000, Time (T₃) = 8 months

Total Profit = ₹34,000

Formula Used:

Profit Ratio = (I₁ × T₁) : (I₂ × T₂) : (I₃ × T₃)

Calculations:

⇒ Ratio = (4000 × 6) : (8000 × 8) : (6000 × 8)

⇒ Ratio = 24000 : 64000 : 48000

⇒ Ratio = 24 : 64 : 48 = 3 : 8 : 6

⇒ Sum of ratios = 3 + 8 + 6 = 17

⇒ Share of Mr. Gupta = (8 ÷ 17) × 34000

⇒ Share of Mr. Gupta = 8 × 2000 = ₹16,000

∴ The correct answer is ₹16,000.

Additional Information

Partnership Basics

When investments are for different time periods, the profit is distributed in the ratio of the product of capital and time (Equivalent Capital).

Working vs Sleeping Partner

A working partner may receive a fixed percentage or salary from the profit before the remaining profit is distributed according to the investment ratio.

Ratio of Capitals

If profits are shared in ratio P₁:P₂ and time periods are T₁:T₂, then the ratio of capitals C₁:C₂ = (P₁/T₁) : (P₂/T₂).

The correct answer is Consumer Empowerment Week

Key Points

• The Consumer Empowerment Week was initiated by the Department of Consumer Affairs in 2022.
• The program aims to raise awareness among consumers about their rights and responsibilities.
• It includes various activities and campaigns to educate consumers on how to make informed decisions and seek redressal for grievances.
• The initiative also focuses on promoting digital literacy and safe online transactions among consumers.

Additional Information

• The Department of Consumer Affairs operates under the Ministry of Consumer Affairs, Food and Public Distribution.
• The objective of the department is to protect the rights of consumers and ensure fair trade practices.
• Various consumer helplines and portals have been set up to assist consumers in lodging complaints and seeking resolution.
• The department also collaborates with state governments and other stakeholders to implement consumer protection laws effectively.

The correct answer is zygote is kept outside and development takes place in a test tube.

Key Points

• In IVF (in vitro fertilisation), fertilisation occurs outside the body.
• The zygote is typically formed and allowed to develop for a few days outside the body.
• After initial development, the zygote is placed in the uterus for further growth and development.
• Complete development of the baby takes place in the uterus, not outside the body.
• Option 1 is incorrect because complete development does not occur in a test tube.

Additional Information

• IVF is a common solution for women with blocked oviducts, allowing them to conceive.
• This process involves hormone treatments to stimulate egg production, retrieval of eggs, fertilisation in the lab, and transfer of the embryo back to the uterus.
• IVF has been a revolutionary procedure in assisted reproductive technology, helping many couples achieve pregnancy.

Given: L, G, K, P, H and Z live on eight different floors of the same multistorey building with 2 floors being vacant.

The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 8.

1) H lives on floor No. 1, K on No. 2, and P on No. 8.

 

2) One immediate floor above and one immediate floor below Z are vacant.

3)  G’s floor is immediately above the floor on which L lives.

Case I: 

 

Case II:

 

4) G’s floor is also immediately below P’s floor - from this statement Case II canceled, so considering case I.

Case I:

 

So, 'Z' lives on floor number 4.

Hence, the correct answer is "Option 1".

Shortcut Trick

Put x = 45° because the expression is independent of x.

⇒ Value = 1/(1 + 1²)² + 1²/(1 + 1²)² + 1/(1 + 1²)

⇒ Value = 1/4 + 1/4 + 1/2 = 1/2 + 1/2 = 1.

∴ The correct answer is 1.

Alternate Method

Given: Expression = 1/(1 + cot²x)² + tan²x/(1 + tan²x)² + 1/(1 + tan²x)

Formula Used: 1 + cot²x = cosec²x; 1 + tan²x = sec²x; 1/cosec²x = sin²x; 1/sec²x = cos²x

⇒ 1/(cosec²x)² + tan²x/(sec²x)² + 1/sec²x

⇒ 1/cosec⁴x + (sin²x/cos²x) × (1/sec⁴x) + cos²x

⇒ sin⁴x + (sin²x/cos²x) × cos⁴x + cos²x

⇒ sin⁴x + sin²x cos²x + cos²x

⇒ sin²x (sin²x + cos²x) + cos²x

⇒ sin²x (1) + cos²x

⇒ sin²x + cos²x = 1

∴ The correct answer is 1.

Additional Information

Trigonometric Identities

Standard Pythagorean identities include sin²x + cos²x = 1, 1 + tan²x = sec²x, and 1 + cot²x = cosec²x.

Reciprocal Relations

tan x = sin x / cos x, cot x = cos x / sin x, and sec x = 1 / cos x.

Value Substitution Method

In objective exams, for expressions containing tan, cot, sec, or cosec, substituting 45° (where defined) is the fastest way to verify the result.

The correct answer is Transpiration, diffusion and storage

Key Points

• Transpiration, diffusion, and storage are the different ways of excretion in plants.
• Transpiration is the process by which water evaporates from the aerial parts of the plant, primarily through the stomata in the leaves.
• Diffusion involves the movement of substances from an area of higher concentration to an area of lower concentration.
• Storage refers to the accumulation of waste products in certain parts of the plant, such as leaves, bark, and vacuoles, where they can be isolated from the rest of the plant's cellular activities.

Additional Information

• Plants have evolved various mechanisms to deal with waste products generated during metabolic activities.
• Excretion in plants is not as complex as in animals because plants produce fewer toxic wastes.
• Other methods of excretion in plants include the shedding of leaves, bark, and fruits.
• Some plants also excrete waste substances through their roots into the soil.

The logic followed here is:

So, '114' is the missing number in the given series.

Hence, the correct answer is "Option 2".

The correct answer is Sikkim.

Key Points

• Saga Dawa festival is celebrated in the state of Sikkim.
• This festival is one of the most significant events for the Buddhist community in the state.
• It marks the birth, enlightenment, and death of Gautama Buddha.
• During the festival, devotees visit monasteries, offer prayers, and participate in various religious activities.

Additional Information

• Sikkim is known for its rich cultural heritage and diverse traditions.
• The state is home to several indigenous tribes, each with its own unique festivals and customs.
• Other important festivals in Sikkim include Losar, Tendong Lho Rum Faat, and Bhumchu.
• The capital city of Sikkim is Gangtok.

Shortcut Trick

For any two similar triangles, the ratio of any corresponding linear dimensions (such as sides, medians, altitudes, and perimeters) is always equal to the constant scale factor of similarity (k).

However, the angles of similar triangles are always equal, meaning their ratio is always 1:1, which is independent of the ratio of their medians.

Thus, the statement Ratio of any two angles = Ratio of any two medians is mathematically incorrect and is NOT a property of similar triangles.

∴ The correct answer is Ratio of any two angles = Ratio of any two medians.

Alternate Method

Given: Two similar triangles, ΔABC and ΔPQR (i.e., ΔABC ˜ ΔPQR).

Properties of Similar Triangles:

⇒ Corresponding angles are equal: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.

⇒ Corresponding sides are proportional: AB ÷ PQ = BC ÷ QR = AC ÷ PR = k (where k is the scale factor).

Verification of Options:

⇒ Option 1: Ratio of corresponding sides = Ratio of corresponding medians. Since the triangles are similar, the ratio of their medians BM₁ ÷ QM₂ is equal to the ratio of their corresponding sides AB ÷ PQ = k. This is a valid property.

⇒ Option 2: Ratio of corresponding sides = Ratio of corresponding perimeters. The perimeter of ΔABC is AB + BC + AC, and for ΔPQR it is PQ + QR + PR. Since each side is scaled by k, the ratio of perimeters is also k. This is a valid property.

⇒ Option 3: Ratio of corresponding sides = Ratio of corresponding altitudes. The ratio of altitudes is also equal to the ratio of corresponding sides (k). This is a valid property.

⇒ Option 4: Ratio of any two angles = Ratio of any two medians. The ratio of any two angles in similar triangles is always 1 (since corresponding angles are equal), whereas the ratio of medians is k (which can be any positive real number). Thus, this statement is NOT a property of similar triangles.

∴ The correct answer is Ratio of any two angles = Ratio of any two medians.

Additional Information

Ratio of Areas of Similar Triangles

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. For example, Area(ΔABC) ÷ Area(ΔPQR) = (AB ÷ PQ)².

Ratio of Inradii and Circumradii

The ratio of the inradii (r₁ ÷ r₂) and circumradii (R₁ ÷ R₂) of two similar triangles is also equal to the ratio of their corresponding sides.

Similarity Criteria

Two triangles are similar if they satisfy the AAA (Angle-Angle-Angle), SAS (Side-Angle-Side), or SSS (Side-Side-Side) similarity theorems.

Given Equation: 42 + 7 ÷ 24 × 6 - 3 = ?

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

New Equation: 42 ÷ 7 + 24 - 6 × 3 = ?

Now, using BODMAS rule, we get:

⇒ 42 ÷ 7 + 24 - 6 × 3 = ?

⇒ 6 + 24 - 6 × 3 = ?

⇒ 6 + 24 - 18 = ?

⇒ 30 - 18 = 12

Hence, the correct answer is "Option 2".

The correct answer is ZnO is reduced to Zn.

Key Points

• In the reaction ZnO + C → Zn + CO, ZnO is reduced to Zn.
• This reaction is a redox reaction where ZnO acts as an oxidizing agent and gets reduced.
• Carbon acts as a reducing agent and is oxidized to CO.
• The reduction of ZnO to Zn involves the gain of electrons by Zn²⁺ ions.

Additional Information

• In redox reactions, the substance that gains electrons is reduced, and the substance that loses electrons is oxidized.
• Reduction refers to the decrease in oxidation state, while oxidation refers to the increase in oxidation state.
• Zinc oxide (ZnO) has zinc in the +2 oxidation state, and elemental zinc (Zn) has an oxidation state of 0, indicating reduction.
• Carbon (C) starts with an oxidation state of 0 and ends up in carbon monoxide (CO) with an oxidation state of +2, indicating oxidation.

Shortcut Trick

Check the conditions directly using the Options.

Condition 1: Sum of digits = 9. All options (45, 18, 27, 36) satisfy this.

Condition 2: Number = (5 × Ones digit) + 6.

For 36: Ones digit is 6. ⇒ (5 × 6) + 6 = 30 + 6 = 36. This matches the number.

∴ The correct answer is 36.

Alternate Method

Let the tens digit be x and the ones digit be y.

Given: Sum of digits = 9 ⇒ x + y = 9 — (i)

Given: The value of the number (10x + y) is 6 more than 5 times the ones digit (y).

⇒ 10x + y = 5y + 6

⇒ 10x − 4y = 6

⇒ 5x − 2y = 3 — (ii)

Substitute y = 9 − x from (i) into (ii):

⇒ 5x − 2(9 − x) = 3

⇒ 5x − 18 + 2x = 3

⇒ 7x = 21 ⇒ x = 3

⇒ y = 9 − 3 = 6

⇒ Number = 10(3) + 6 = 36.

∴ The correct answer is 36.

Additional Information

Standard Form of a Two-Digit Number

Any two-digit number with tens digit a and units digit b is represented as 10a + b.

Digit Reversal Rule

If digits are reversed, the new number is 10b + a. The difference between the original and reversed number is always 9 × |a − b|.

Three-Digit Number Expansion

A three-digit number with digits x, y, and z is written as 100x + 10y + z.

Shortcut Trick

Recognize the Perfect Square Identity: a² − 2ab + b² = (a − b)².

In the equation x² − 6x + 9 = 0, we have a = x and b = 3.

Since 2 × x × 3 = 6x and 3² = 9, the expression is a complete square.

Therefore, x² − 6x + 9 = (x − 3)².

∴ The correct answer is (x − 3)² = 0.

Alternate Method

Given: x² − 6x + 9 = 0

Method: Factorisation by splitting the middle term.

⇒ Find two numbers that multiply to 9 and add to −6. The numbers are −3 and −3.

⇒ x² − 3x − 3x + 9 = 0

⇒ x(x − 3) − 3(x − 3) = 0

⇒ (x − 3)(x − 3) = 0

⇒ (x − 3)² = 0

∴ The correct answer is (x − 3)² = 0.

Additional Information

Perfect Square Trinomial

A quadratic expression is a perfect square if it can be written as (ax + b)². For x² + bx + c, this occurs when c = (b/2)².

Discriminant and Equal Roots

For a Quadratic Equation ax² + bx + c = 0, if the discriminant D = b² − 4ac = 0, the roots are real and equal, and the equation is a perfect square.

Algebraic Identities

Common identities used for factorisation include (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Given Word: OPTICAL

Conditions:

1. Each vowel in the given word is changed to the letter following it alphabetically i.e. +1 in the positional value. 2. Each consonant is changed to the letter preceding it alphabetically i.e. -1 in the positional value.

After applying the conditions, we get:

Thus, the letter which appear twice in the group of letters is 'B'.

Hence, the correct answer is "Option 4".

The logic followed here is: (1^st number - 3^rd number)² = 2^nd number

Checking all the options:

Option 1) (26, 56, 8)

⇒ (26 - 8)² 

(18)² = 324

324 ≠ 56.

Option 2) (21, 144, 32)

⇒ (21 - 32)²

(11)² = 121

121 ≠ 144.

Option 3) (24, 169, 11)

⇒ (24 - 11)² 

(13)² =169

169 = 169.

Option 4) (30, 49, 11)

⇒ (30 - 11)²

(19)² = 361

361 ≠ 49.

Hence, the correct answer is "Option 3".

The correct answer is the induced potential difference in the coil increases.

Key Points

• When a magnet is moved near a coil, an induced potential difference is produced in the coil due to electromagnetic induction.
• Increasing the speed of the magnet near the coil increases the rate of change of magnetic flux through the coil.
• The induced potential difference in the coil is directly proportional to the rate of change of magnetic flux.
• Therefore, increasing the speed of the magnet will increase the induced potential difference in the coil.

Additional Information

• This phenomenon is described by Faraday's Law of Electromagnetic Induction.
• Faraday's Law states that the induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.
• In practical applications, this principle is used in the working of electrical generators and transformers.
• Factors affecting the induced potential difference include the strength of the magnet, the number of turns in the coil, and the speed at which the magnet is moved.

Shortcut Trick

In parallel lines intersected by a transversal, the sum of angles forming a linear pair is always 180°.

Given angle = 30°

Angle 1 = 180° − 30° = 150°

∴ The correct answer is 150°.

Alternate Method

Given:

Line l is parallel to line m (l ∥ m).

Line p is the transversal.

One of the angles is given as 30°.

Property Used:

The sum of angles on a straight line (linear pair) is 180°.

Calculations:

⇒ Angle 1 + 30° = 180° (Linear pair on line l)

⇒ Angle 1 = 180° − 30°

⇒ Angle 1 = 150°

∴ The correct answer is 150°.

Additional Information

Corresponding Angles

When two parallel lines are cut by a transversal, the angles in matching corners are equal.

Alternate Interior Angles

Angles between the parallel lines on opposite sides of the transversal are equal.

Consecutive Interior Angles

Angles between the parallel lines on the same side of the transversal are supplementary (sum = 180°).

 

 

Now, the group of numbers and symbols is: 4 6 $ 7 4 # @ 2

Here, only first condition followed in the given group,

Thus, 4 → Z and 2 → H

Then, the code for '4 6 $ 7 4 # @ 2' is 'ZFEMHTPH'.

Hence, the correct answer is "Option 2".

Shortcut Trick

Direct formula: Product of two numbers = HCF × LCM

1472 = 8 × LCM

LCM = 1472 ÷ 8 = 184

∴ The correct answer is 184.

Alternate Method

Given:

Product of numbers = 1472

HCF = 8

Formula Used:

Number₁ × Number₂ = HCF × LCM

Calculations:

⇒ 1472 = 8 × LCM

⇒ LCM = 1472 ÷ 8

⇒ LCM = 184

∴ The correct answer is 184.

Additional Information

HCF and LCM Relation

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

Co-prime Numbers

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

HCF of Fractions

HCF = (HCF of Numerators) ÷ (LCM of Denominators).

LCM of Fractions

LCM = (LCM of Numerators) ÷ (HCF of Denominators).

Given Word: INCURABLE

Conditions:

1. Each vowel in the given word is changed to the letter following it alphabetically → +1 in the positional value. 2. Each consonant is changed to the letter preceding it alphabetically → -1 in the positional value.

After applying the conditions, we get:

Thus, only one vowel is there in the new word formed.

Hence, the correct answer is "Option 1".

The correct answer is option 3) a, c and d.

Key PointsEfforts for Sustainability of Resources:

• Switching off unnecessary lights and fans: This helps in conserving electricity, which is a crucial resource. By reducing the consumption of electricity, we are helping in the reduction of fossil fuel usage, which is often used to generate electricity.
• Repairing leaking taps for conserving water: Water is a precious resource, and repairing leaking taps prevents wastage, ensuring that more water is available for future use.
• Using empty containers to store things: Reusing containers reduces waste and minimizes the need to produce new storage materials, which in turn saves resources and energy.

Options b and e, on the other hand, are not considered efforts towards sustainability:

• Using lift instead of stairs: Using stairs instead of lifts is a more sustainable practice as it saves electricity. Therefore, option b is not useful for sustainability.
• Going to school by your own car instead of cycling: Using a car increases fuel consumption and emissions, whereas cycling is a more sustainable and eco-friendly mode of transport. Therefore, option e is not useful for sustainability.

Hence, the correct answer is 3) a, c and d.

According to given information:

So, the distance between starting point and end point is: 14 + 13 + 10 = 37 m

Thus, Shyam is 37 m from starting point.

Hence, the correct answer is "Option 1".

Solution:

Value of total export in 2019 = 280 cr

Number of containers in 2019 = 130

Average value of goods sold per container in 2019 = 280/130 = 2.15 cr

If number of containers in 2020 remains unchanged then new approximate value of total exports (in crores) in 2020 = 2.15 × 180 = 387 cr

∴ Option 4 is the correct answer.

The correct answer is in the long run, all inputs are fixed.

Key Points

• Option 4 states that "In the long run, all inputs are fixed," which is incorrect.
• In the long run, all inputs are variable, meaning firms can adjust all factors of production.
• This allows firms to change their scale of operations, unlike in the short run where some inputs are fixed.
• The correct understanding is that in the long run, firms have the flexibility to alter all input levels to optimize production and costs.

Additional Information

• Total cost is indeed the sum of the total variable cost and the total fixed cost.
• The Average fixed cost curve is downward sloping because fixed costs are spread over a larger number of units as production increases.
• Both marginal cost and average variable cost curves are typically 'U'-shaped due to economies and diseconomies of scale.
• Understanding the distinction between short run and long run is crucial in economics, as it affects how firms make production decisions.

To calculate the energy consumed by electrical appliances, we use the formula:

• Energy = Power × Time

For the electric heater:

Power = 1000 W = 1 kW

Time = 4 hours/day

Energy consumed by the heater daily = 1 KW × 4 H = 4 KWH

​For the electric geyser:

Power = 2000 W = 2 kW

Time = 4 hours/day

Energy consumed by the geyser daily = 2 KW × 4 H = 8 KWH

Now, let's find the total energy consumed by both appliances in one day:

Total energy consumed (in 1 day) = 4 KWH + 8 KWH = 12KWH

And, energy consumed in 10 days = 12 × 10 = 120 KWH

Therefore, the energy consumed in 10 days is 120KWh.

Given:

Statement:

Team A students lost 14 out of 20 games they played last season.

I. Team A students are more interested in academics than sports - False (Because it is not mentioned in the statement that they are good at academics,they can be interested in other events also.) 

Il Team A students are unlucky - False (It is also doesn't follow as they loss in the match, there might be some other reasons of loosing the match.)

So, Neither conclusion I nor II follows.

Hence, the correct answer is "Option 3".

The logic followed here is:

For, ‘CURRY is written as BSONT’,

For, 'KHAKI is written as JFXGD’,

Similarly, for 'BHEEM'

So, 'BHEEM' will be written as 'AFBAH'.

Hence, the correct answer is "Option 3".

The correct answer is 2 Only.

Key Points

• Statement-I: Ionic compounds are generally brittle and break into pieces when pressure is applied.
• This statement is true.
• Ionic compounds have a rigid and brittle crystal lattice structure.
• When pressure is applied, the ions of the same charge are forced closer together, resulting in repulsive forces that cause the crystal to shatter.
• Statement-II: Ionic compounds have low melting and boiling points.
• This statement is false.
• Ionic compounds typically have high melting and boiling points due to the strong electrostatic forces of attraction between the oppositely charged ions in their lattice structure, which require a significant amount of energy to overcome.
• Hence, Statement-I is true, and Statement-II is false.

Shortcut Trick

List of first 8 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19

Sum of these primes = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77

Result = Sum ÷ 7 = 77 ÷ 7 = 11

∴ The correct answer is 11.

Alternate Method

Given: The first 8 prime numbers.

Formula Used: Required Value = (Sum of first 8 prime numbers) ÷ 7

⇒ First 8 prime numbers = 2, 3, 5, 7, 11, 13, 17, 19

⇒ Sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19

⇒ Sum = 77

⇒ Required Value = 77 ÷ 7

⇒ Required Value = 11

∴ The correct answer is 11.

Additional Information

Prime Numbers

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

The Number 2

The number 2 is the smallest prime number and the only even prime number.

First 10 Prime Numbers

The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

The correct answer is are finger-like structures.

Key Points

• Alveoli have an extensive network of blood vessels which facilitates gas exchange.
• They are thin-walled to allow easy diffusion of gases.
• Alveoli possess a large surface area to maximize the efficiency of gas exchange.
• The structure of alveoli is not finger-like; instead, they are more sac-like or balloon-shaped.

Additional Information

• The alveoli are the primary sites of gas exchange in the lungs, where oxygen is absorbed into the blood, and carbon dioxide is expelled.
• The thin walls of the alveoli are composed of a single layer of epithelial cells and a thin basement membrane, which aids in the rapid exchange of gases.
• The large surface area of the alveoli is due to the presence of numerous alveolar sacs, each containing many alveoli, providing a vast surface for gas exchange.
• Surfactant, a substance produced by alveolar cells, reduces surface tension within the alveoli, preventing their collapse and ensuring they remain open for gas exchange.

Calculation:

⇒ $\rm \frac{3}{2}x^2+2x-\frac{3}{2}+\frac{x^2}{2}-6x+\frac{1}{2}$

⇒ $\rm \frac{3}{2}x^2+\frac{x^2}{2}+2x-6x-\frac{3}{2}+\frac{1}{2}$

⇒ 2x² - 4x - 1

∴ Option 1 is the correct answer.

Logic:

In one hour, minutes hand covers angular distance = 360°

In one minutes, minutes hand covers angular distance = 360º / 60 = 6°

So, in 3 hours 10 minutes, minutes hand covers = 6° × (3 × 60 + 10)

= 6° × 190 = 1140°

So, the minutes hand will cover 1140° angular distance in 3 hours and 10 minutes.

Hence, the correct answer is "Option 1".

Shortcut Trick

Apply the Conditional Identity: If a + b + c = 0, then a³ + b³ + c³ = 3abc.

For numerator: (4x² − 9y²) + (9y² − 49z²) + (49z² − 4x²) = 0.

For denominator: (2x − 3y) + (3y − 7z) + (7z − 2x) = 0.

Expression = [3(4x² − 9y²)(9y² − 49z²)(49z² − 4x²)] ÷ [3(2x − 3y)(3y − 7z)(7z − 2x)].

Factorize each term (a² − b²) in the numerator to cancel out denominator terms.

∴ The correct answer is (2x + 3y)(3y + 7z)(7z + 2x).

Alternate Method

Given: Algebraic expression with sum of cubes in fractional form.

Formula Used: If a + b + c = 0, then a³ + b³ + c³ = 3abc; also m² − n² = (m − n)(m + n).

⇒ Let A = 4x² − 9y², B = 9y² − 49z², C = 49z² − 4x²

⇒ A + B + C = 4x² − 9y² + 9y² − 49z² + 49z² − 4x² = 0

⇒ Numerator = 3(4x² − 9y²)(9y² − 49z²)(49z² − 4x²)

⇒ Let p = 2x − 3y, q = 3y − 7z, r = 7z − 2x

⇒ p + q + r = 2x − 3y + 3y − 7z + 7z − 2x = 0

⇒ Denominator = 3(2x − 3y)(3y − 7z)(7z − 2x)

⇒ Value = [3(2x − 3y)(2x + 3y)(3y − 7z)(3y + 7z)(7z − 2x)(7z + 2x)] ÷ [3(2x − 3y)(3y − 7z)(7z − 2x)]

⇒ Value = (2x + 3y)(3y + 7z)(7z + 2x)

∴ The correct answer is (2x + 3y)(3y + 7z)(7z + 2x).

Additional Information

Algebraic Cube Identity

The general identity is a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca). If (a + b + c) = 0, the right side becomes zero.

Difference of Squares

For any two terms, m² − n² is always equal to the product of their sum and difference: (m + n)(m − n).

Factorization of Higher Powers

Terms like (4x² − 9y²) are perfect squares since 4x² = (2x)² and 9y² = (3y)², allowing for easy cancellation in algebraic fractions.

Shortcut Trick

Efficiency ratio of A : B = 100 : 125 = 4 : 5.

Total efficiency (A + B) = 4 + 5 = 9 units/day.

Total work = Combined efficiency × Total days = 9 × 8 = 72 units.

Time taken by A alone = Total work ÷ Efficiency of A = 72 ÷ 4 = 18 days.

∴ The correct answer is 18 days.

Alternate Method

Given:

⇒ Time taken by (A + B) = 8 days

⇒ B is 25% more efficient than A

Calculations:

⇒ Let efficiency of A = 4x

⇒ Efficiency of B = 4x + 25% of 4x = 5x

⇒ Combined efficiency of (A + B) = 4x + 5x = 9x

⇒ Total Work = (A + B) efficiency × Time = 9x × 8 = 72x

⇒ Time for A alone = Total Work ÷ Efficiency of A

⇒ Time for A = 72x ÷ 4x = 18 days

∴ The correct answer is 18 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete a work. If the efficiency ratio of A:B is x:y, then the time ratio is y:x.

Work & Wages

Wages are generally distributed in the ratio of efficiency or the actual work done by each person.

Total Work Formula

Total Work = Number of Persons × Efficiency × Time (Days/Hours).

Given equation: [{(44 + 36) - (4 × 4)} ÷ (1 - 5)] × 2 = 8 

BODMAS Table: 

Let's check each option one by one.

Option 1) + and × 

Given equation: [{(44 + 36) - (4 × 4)} ÷ (1 - 5)] × 2 = 8 

After interchanging the signs we get;

⇒ [{(44 × 36) - (4 + 4)} ÷ (1 - 5)] + 2 = 8

⇒ [{1584 - 8} ÷ (- 4)] + 2 = 8 

⇒  [1576 ÷ (- 4)] + 2 = 8 

⇒ - 394 + 2 = 8 

⇒ - 392 ≠ 8

⇒ LHS ≠ RHS

Option 2) + and ÷ 

Given equation: [{(44 + 36) - (4 × 4)} ÷ (1 - 5)] × 2 = 8 

After interchanging the signs we get;

⇒  [{(44 ÷ 36) - (4 × 4)} + (1 - 5)] × 2 = 8 

⇒  [{ 1.22 - 16} + (-4**)**] × 2 = 8

⇒  [-15.78 - 4] × 2 = 8

⇒ -19.78 × 2 = 8

⇒ - 39.56 ≠ 8

⇒ LHS ≠ RHS

Option 3) + and -

Given equation: [{(44 + 36) - (4 × 4)} ÷ (1 - 5)] × 2 = 8 

After interchanging the signs we get;

⇒ [{(44 - 36) + (4 × 4)} ÷ (1 + 5)] × 2 = 8

⇒ [{8 + 16} ÷ 6] × 2 = 8

⇒ [24 ÷ 6] × 2 = 8

⇒ 4 × 2 = 8

⇒ 8 = 8

⇒ LHS = RHS

Option 4) × and ÷

Given equation: [{(44 + 36) - (4 × 4)} ÷ (1 - 5)] × 2 = 8 

After interchanging the signs we get;

⇒ [{(44 + 36) - (4 ÷ 4)} × (1 - 5)] ÷ 2 = 8

⇒ [{80 - 1} × (-4)] ÷ 2 = 8

⇒ [79 × (-4)] ÷ 2 = 8

⇒ -316 ÷ 2 = 8

⇒ -158 ≠ 8

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 3".

The correct answer is Stomata

Key Points

• Stomata are tiny openings or pores found on the surface of leaves and stems.
• They are crucial for gas exchange, allowing the intake of carbon dioxide and the release of oxygen during photosynthesis and respiration.
• Stomata are surrounded by guard cells that regulate their opening and closing.
• In addition to gas exchange, stomata play a significant role in the process of transpiration, helping to regulate water loss in plants.

Additional Information

• The location and density of stomata can vary among different plant species and environments.
• In most plants, stomata are more numerous on the lower epidermis of the leaf to reduce water loss.
• Stomatal behavior is influenced by environmental factors such as light, carbon dioxide concentration, and humidity.

Given equation: 5 × 4 ÷ 10 - 8 + 2 = 8

BODMAS Table: 

Let's check each option one by one.

Option 1) + , ÷

Given: 5 × 4 ÷ 10 - 8 + 2 = 8

After interchanging the numbers we get;

⇒ 5 × 4 + 10 - 8 ÷ 2 = 8

⇒ 5 × 4 + 10 - 4 = 8

⇒ 20 + 10 - 4 = 8

⇒ 30 - 4 = 8

⇒ 26 ≠ 8

⇒ LHS ≠ RHS

Option 2) ×, ÷

Given: 5 × 4 ÷ 10 - 8 + 2 = 8

After interchanging the numbers we get;

⇒ 5 ÷ 4 × 10 - 8 + 2 = 8

⇒ 1.25 × 10 - 8 + 2 = 8

⇒ 12.5 - 8 + 2 = 8

⇒ 14.5 - 8  = 8

⇒ 6.5 ≠ 8

⇒ LHS ≠ RHS

Option 3) +, ×

Given: 5 × 4 ÷ 10 - 8 + 2 = 8

After interchanging the numbers we get;

⇒ 5 + 4 ÷ 10 - 8 × 2 = 8

⇒ 5 + 0.4 - 8 × 2 = 8

⇒ 5 + 0.4 - 16 = 8

⇒ 5.4 - 16 = 8

⇒ -10.6 ≠ 8

⇒ LHS ≠ RHS

Option 4) +, -

Given: 5 × 4 ÷ 10 - 8 + 2 = 8

After interchanging the numbers we get;

⇒ 5 × 4 ÷ 10 + 8 - 2 = 8

⇒ 5 × 0.4 + 8 - 2 = 8

⇒ 2 + 8 - 2 = 8

⇒ 10 - 2 =8

⇒ 8 = 8

⇒ LHS = RHS

Hence, the correct answer is "Option 4".

The correct answer is both the statements are true.

Key Points

• Statement-I: Washing soda is produced from sodium chloride.
• This statement is true.
• Washing soda, also known as sodium carbonate (Na₂CO₃), is produced from sodium chloride (NaCl) through the Solvay process.
• The Solvay process involves the reaction of sodium chloride with ammonia and carbon dioxide in water to form sodium bicarbonate, which is then heated to produce sodium carbonate (washing soda).
• Statement-II: It attacks dirt and grease to form water soluble products, which are then washed away on rinsing with water.
• This statement is also true.
• Washing soda is an effective cleaning agent because it can react with the fatty acids in grease and dirt to form soluble salts, which can be easily rinsed away with water.
• Since both Statement-I and Statement-II are true, the correct answer is option 2.

The correct answer is Oxidation reaction

Key Points

• The conversion of ethanol to ethanoic acid is an example of an oxidation reaction.
• In this reaction, ethanol (C₂H₅OH) is oxidized to form ethanoic acid (CH₃COOH).
• Oxidation reactions involve the gain of oxygen or the loss of hydrogen.
• This process is significant in organic chemistry and biochemistry, where alcohols are often oxidized to carboxylic acids.

Additional Information

• Ethanol can be oxidized to ethanoic acid using oxidizing agents such as potassium dichromate (K₂Cr₂O₇) in the presence of sulfuric acid (H₂SO₄).
• This reaction is commonly performed in laboratories and has industrial applications.
• Oxidation reactions are crucial in various metabolic pathways in living organisms.

To determine the minimum rating of the fuse wire to be connected to the electric heater, we need to calculate the current drawn by the heater. The formula for calculating the current (I) is:

• I = P / V.

Where,

P is the power rating of the heater (2200 W)

V is the voltage (220 V).

Substituting the given values:

I = 2200 / 220 = 10 A.

Thus, the current drawn by the heater is 10 A. The fuse should be rated slightly higher than the operating current to avoid nuisance blowing, so the appropriate fuse rating should be higher than 10 A.

Therefore, the minimum fuse rating required for safe operation is 10 A.

Given series: Q I O M J E S T R U L E B A C K J M N

Correct pattern is: Consonant → Consonant → Vowel.

consonants which are immediately preceded by a consonant and immediately followed by a vowel are

Q I O M J E S T R U L E B A C K J M N

There are 'two' consonants which are immediately preceded by a consonant and immediately followed by a vowel.

Hence, the correct answer is "Option 4".

**Mistake PointsImmediately preceded by means immediately before or to come just before.**Immediately followed by means immediately after or to come just after.

Shortcut Trick

For the least number of cubes, the side of each cube must be the HCF of the dimensions.

HCF of 12, 24, and 30 → 6 cm.

Number of cubes = (12 × 24 × 30) ÷ (6 × 6 × 6)

Number of cubes = 2 × 4 × 5 = 40.

∴ The correct answer is 40.

Alternate Method

Given: Dimensions of the cuboidal block are 12 cm, 24 cm, and 30 cm.

Formula Used: Volume of cuboid = Length × Breadth × Height; Volume of cube = Side³.

⇒ To minimize the number of cubes, we must maximize the side (a) of each cube.

⇒ Side of cube (a) = HCF(12, 24, 30)

⇒ Factors of 12 = 2 × 2 × 3

⇒ Factors of 24 = 2 × 2 × 2 × 3

⇒ Factors of 30 = 2 × 3 × 5

⇒ HCF = 2 × 3 = 6 cm

⇒ Total Volume of Cuboid = 12 × 24 × 30 = 8640 cm³

⇒ Volume of one Cube = 6 × 6 × 6 = 216 cm³

⇒ Number of cubes = 8640 ÷ 216 = 40

∴ The correct answer is 40.

Additional Information

HCF Application

When a larger object is divided into identical smaller objects with no wastage, the dimension of the smaller object is the Highest Common Factor (HCF) of the larger dimensions.

Volume Invariance

The sum of the volumes of all small identical cubes is always equal to the total volume of the original cuboid.

Surface Area Change

While the volume remains constant during cutting, the total surface area increases because new faces are exposed with every cut.

The correct answer is South Maubuang

Key Points

• South Maubuang became the first open-defecation free (ODF) Plus village of Mizoram in January 2022.
• This achievement is part of the ongoing efforts under the Swachh Bharat Mission to improve sanitation and hygiene in rural areas.
• The ODF Plus status indicates that the village has sustained its ODF status and has implemented solid and liquid waste management systems.
• This milestone is a significant step towards improving public health and environmental sustainability in the region.

Additional Information

• The Swachh Bharat Mission (SBM) was launched on 2nd October 2014 by the Government of India, with the aim to eliminate open defecation and improve solid waste management.
• Under SBM, villages across India are encouraged to achieve ODF status, which means no visible feces in the environment or village surroundings.
• The ODF Plus status is an advanced stage where villages not only maintain their ODF status but also implement effective waste management practices.
• Continued community participation and government support are crucial for sustaining the ODF Plus status and ensuring a clean and healthy environment.

Given:

3x-2 + 3x = 7290

Calculation:

⇒ 3x-2 + 3x = 7290

⇒ 3x/3² + 3x = 729 × 10

⇒ 3x/9 + 3x = 3⁶ × 10

⇒ 3x[1/9 + 1] = 36 × 10

⇒ 3x[10/9] = 36 × 10

⇒ 3x/3² = 36 × 10

⇒ 3x-2 = 36

⇒ x - 2 = 6

 

⇒ x = 8

 

Therefore the value of x is 8.

The correct answer is Part III

Key Points

• Part III of the Indian Constitution contains Articles 12 to 35, which deal with Fundamental Rights.
• The Fundamental Rights are essential for the overall development of individuals and are guaranteed by the Constitution to all citizens.
• These rights ensure civil liberties so that all Indians can lead their lives in peace and harmony as citizens of India.
• They include rights such as the right to equality, the right to freedom, the right against exploitation, the right to freedom of religion, cultural and educational rights, and the right to constitutional remedies.
• Part III is often referred to as the cornerstone of the Indian Constitution and is crucial for safeguarding the democratic fabric of the country.

Additional Information

• Article 12 defines the term 'State' for the purposes of Part III.
• Article 13 declares that any law in violation of the Fundamental Rights is void.
• Fundamental Rights are justiciable, meaning individuals can approach the courts for enforcement of these rights.
• The Constitution provides for the suspension of these rights during emergencies, but certain rights such as the right to life and personal liberty (Article 21) cannot be suspended.
• The Fundamental Rights have been amended from time to time to address changing societal needs and interpretations.

The correct answer is - Increase of UV radiations reaching Earth’s surface.

Key Points

• The ozone layer is a stratosphere layer, the second layer of the Earth's atmosphere. The stratosphere is a layer of protective gases that clings to our planet.
• The ozone layer, like a sponge, absorbs solar radiation that hits Earth. Although we require some of the sun's radiation to survive, too much of it can be harmful to living things. The ozone layer acts as a protective layer for life on Earth.
• The ozone layer is shrinking. Chlorofluorocarbons (CFCs) are responsible for the thinning of the ozone layer. A chlorofluorocarbon is a molecule composed of carbon, chlorine, and fluorine. CFCs are ubiquitous, most notably in refrigerants and plastics.
• Businesses and consumers use them because they are inexpensive, do not easily catch fire, and do not usually poison living things.
• However, once CFCs reach the stratosphere, they begin to deplete the ozone layer.
• Ozone molecules, which are simply three joined oxygen atoms, are constantly being destroyed and reformed by nature. However, CFCs in the air make it extremely difficult for ozone to reform once it has been broken apart.

Additional Information 

 Globally, the ozone layer has been shown to be depleting, and halocarbon emissions are most likely to blame. Ozone loss raises the amount of biologically hazardous solar UV light that reaches Earth's surface, which has a number of negative consequences, including a rise in the prevalence of skin cancer. International production limits on ozone-depleting compounds are set down in the 1985 Vienna Convention.

The logic followed here is:

So, '246' will be the next number in the given series.

Hence, the correct answer is 'Option (1)'.

The correct answer is 14

Key Points

• 14 private banks were nationalized by Indira Gandhi during the Fourth Five Year Plan in 1969.
• The nationalization of banks was a major economic policy shift aimed at providing the government more control over credit delivery.
• It was intended to ensure that banking institutions serve the needs of development and the economy in general.
• This move was part of a larger strategy to implement socialistic policies and reduce the influence of large industrial houses over banking.

Additional Information

• Indira Gandhi was the Prime Minister of India from 1966 to 1977 and then again from 1980 until her assassination in 1984.
• The nationalization of banks was announced on 19th July 1969.
• The banks that were nationalized included major institutions like the Bank of India, Punjab National Bank, and Central Bank of India.
• This policy was followed by further nationalization of six more banks in 1980.
• Nationalization aimed to spread banking infrastructure to rural and remote areas and to make credit available to agriculture, small industries, and entrepreneurs.

Shortcut Trick

Increase in Surface Area = 4π((r+2)² − r²) = 704

4 × (22/7) × (4r + 4) = 704

(88/7) × 4(r + 1) = 704

r + 1 = (704 × 7) ÷ (88 × 4) = 14

r = 14 − 1 = 13 cm

∴ The correct answer is 13 cm.

Alternate Method

Given: Increase in radius = 2 cm, Increase in Area = 704 cm²

Formula: Surface Area of Sphere = 4πr²

⇒ 4π(r + 2)² − 4πr² = 704

⇒ 4 × (22/7) [ (r² + 4r + 4) − r² ] = 704

⇒ (88/7) [ 4r + 4 ] = 704

⇒ 4r + 4 = (704 × 7) ÷ 88

⇒ 4r + 4 = 8 × 7

⇒ 4r + 4 = 56

⇒ 4r = 52

⇒ r = 13 cm

∴ The correct answer is 13 cm.

Additional Information

Volume of a Sphere

The total space occupied by a sphere is given by V = $\frac{4}{3}$πr³.

Hemisphere Properties

Curved Surface Area = 2πr² and Total Surface Area = 3πr².

Ratio of Areas

If the ratio of radii is a:b, then the ratio of their surface areas is a²:b² and volumes is a³:b³.

The correct answer is Meghalaya

Key Points

• The Zoological Survey of India (ZSI) highlighted green rules to help the living root bridges of Meghalaya get the UNESCO world heritage site tag.
• These living root bridges are a unique type of bridge found in the northeastern state of India, Meghalaya.
• They are made from the aerial roots of rubber fig trees (Ficus elastica) and have been used by the local Khasi and Jaintia tribes for centuries.
• The bridges are not only a marvel of bioengineering but also a testament to the harmonious relationship between the local communities and their natural environment.
• Efforts to get the UNESCO world heritage site tag aim to preserve these structures and promote sustainable tourism in the region.

Additional Information

• The living root bridges are part of the rich cultural heritage of Meghalaya and showcase the ingenious methods used by the indigenous people to adapt to their environment.
• UNESCO world heritage site status can help in attracting global attention and resources for the conservation of these unique structures.
• Meghalaya is known for its high rainfall and diverse ecosystems, which provide the perfect conditions for the growth of rubber fig trees used in the construction of these bridges.
• Conservation efforts will also focus on educating the local communities and tourists about the importance of preserving these natural wonders.

The correct answer is V.

Key Points

• The S.I unit of induced-potential difference is Volt (V).
• The volt is the derived unit for electric potential, electric potential difference (voltage), and electromotive force.
• It is named after the Italian physicist Alessandro Volta.
• 1 Volt is defined as the potential difference across a conductor when a current of 1 ampere dissipates 1 watt of power.
• The symbol for volt is V.

Additional Information

• The concept of electric potential difference is essential in understanding how electric circuits work.
• It is a measure of the work needed to move a charge from one point to another in an electric field.
• In practical terms, it is what drives electric current through a circuit.
• Various instruments like voltmeters are used to measure the potential difference in circuits.
• Volt is a crucial unit in both theoretical and applied physics, especially in the fields of electronics and electrical engineering.

The correct answer is Kerala.

Key Points

• Monazite ore is predominantly found in the coastal beach sands of Kerala, particularly in the Palakkad and Kollam districts.
• These areas hold some of the world's richest deposits of monazite, making Kerala a key source of this valuable mineral in India.
• While monazite can be found in trace amounts in other states like Odisha and Tamil Nadu, it's mainly Kerala that boasts significant commercially viable reserves.

Additional Information

• Monazite :
• It's a phosphate mineral primarily containing rare-earth elements (REEs) like lanthanum (La), cerium (Ce), neodymium (Nd), and thorium (Th).
• It appears as small, reddish-brown grains or crystals and is quite heavy.
• Due to its composition, it's considered an ore for REEs and thorium but also contains phosphates.
• It is found in igneous and metamorphic rocks and as placer deposits in beach sands.
• Major locations with significant monazite reserves include India (particularly Kerala), South Africa, Madagascar, Vietnam, Brazil, and the United States.
• It's radioactive due to the presence of thorium.
• Thorium has historically been used in nuclear materials, but its use is decreasing due to safety concerns and alternatives.