RRB Group D Previous Year Paper (Held on: 25 Aug 2022 Shift 1)

According to the given information,

1) B is 20 m to the west of C.

2) C is 30 m to the north of E.

3) F is 60 m to the south of E.

4) A is 60 m to the west of B.

5) D is 30 m to the south of B.

Here, we can see that A is in west direction with reference to C.

Hence, the correct answer is "West".

The correct answer is CH3COOH, H2CO3

Key Points

• CH3COOH (acetic acid) and H2CO3 (carbonic acid) are weak acids.
• Weak acids only partially ionize in water, meaning they do not completely dissociate into their ions.
• HCl (hydrochloric acid), H2SO4 (sulfuric acid), and HNO3 (nitric acid) are strong acids, which completely ionize in water.
• Weak acids have higher pKa values and lower ionization constants (Ka) compared to strong acids.
• Weak acids are important in various chemical and biological processes due to their ability to act as buffering agents, maintaining pH levels within a narrow range.

Additional Information

• Acids are classified based on their ability to donate protons (H⁺) in an aqueous solution.
• The strength of an acid is determined by its ionization constant (Ka) and its ability to donate protons.
• In aqueous solutions, strong acids completely dissociate, leading to a higher concentration of hydrogen ions (H⁺), while weak acids only partially dissociate.
• The pH of a solution containing a weak acid is higher (less acidic) compared to a solution of the same concentration containing a strong acid.
• Common examples of weak acids include acetic acid (vinegar), citric acid (found in citrus fruits), and carbonic acid (found in carbonated beverages).
• Understanding the difference between strong and weak acids is crucial in fields such as chemistry, biology, environmental science, and medicine.

According to the given information,

The reflection effect can be found by subtracting the given time from 12:00, since in a mirror image, every hour has an opposite position. Start with the given time, 3:55.

Formula: 11 : 60 - Given Time

Subtract 3:55 from 12:00 to determine the actual time: First, subtract the minutes: [{60 minutes (in 1 hour)} - 55 {minutes} = 5 minutes}] 

Since we borrowed 1 hour to do the minute subtraction, we have to subtract 1 hour from 12 hours: [11 {hours} - 3 {hours} = 8 hours}]

So, the actual time is 8:05. 

Hence, the correct answer is "8 : 05".

The correct answer is enzymes are unable to break down plastics

Key Points

• We should refrain from using plastics because enzymes are unable to break down plastics.
• Plastics are synthetic materials made from polymers, which are long chains of molecules.
• These polymers are not easily broken down by natural processes, leading to their accumulation in the environment.
• The inability of natural enzymes to degrade plastics means they persist for hundreds of years, causing significant environmental pollution.
• Plastics can harm wildlife, contaminate water sources, and enter the food chain, posing health risks to humans and animals.

Additional Information

• Efforts are being made to develop biodegradable plastics and promote recycling to mitigate the environmental impact of plastic waste.
• Biodegradable plastics are designed to be broken down by natural processes, reducing their persistence in the environment.
• Recycling helps to reduce the amount of plastic waste that ends up in landfills and oceans, conserving resources and energy.
• Public awareness and policies aimed at reducing plastic use, such as bans on single-use plastics, are crucial steps toward addressing plastic pollution.

The correct answer is NITI Aayog

Key Points

• NITI Aayog released the 'Banking on electric vehicles in India' report in collaboration with Rocky Mountain Institute and RMI India in January 2022.
• The report focuses on the financial sector's role in accelerating India's electric vehicle (EV) adoption.
• It provides a roadmap for banks and non-banking financial companies (NBFCs) to increase their lending to the EV sector.
• The report highlights the importance of financing in achieving India's EV goals and reducing carbon emissions.

Additional Information

• NITI Aayog stands for National Institution for Transforming India.
• It was established in 2015 to replace the Planning Commission with the aim of fostering cooperative federalism.
• NITI Aayog acts as a policy think tank of the Government of India and provides directional and policy inputs.
• Rocky Mountain Institute (RMI) is a US-based non-profit organization that focuses on sustainability and energy efficiency.
• RMI India is the Indian subsidiary of Rocky Mountain Institute, working on similar goals within the Indian context.

The correct answer is 3 Ω.

Key Points

• The formula for equivalent resistance (R_eq) in a parallel circuit is 1/R_eq = 1/R1 + 1/R2 + 1/R3.
• For three resistors of 9 Ω each connected in parallel, the calculation becomes 1/R_eq = 1/9 + 1/9 + 1/9.
• This simplifies to 1/R_eq = 3/9, hence R_eq = 3 Ω.
• The equivalent resistance is always less than the resistance of the smallest individual resistor in a parallel circuit.
• For resistors in parallel, the total resistance decreases as more resistors are added to the circuit.

Additional Information

• Ohm’s Law
• It defines the relationship between voltage (V), current (I), and resistance (R): V = I × R.
• It is a fundamental principle used in circuit analysis and design.
• Parallel Circuit
• In a parallel circuit, the total voltage across all components is the same, but the total current is the sum of the individual currents.
• The equivalent resistance decreases as more resistors are added in parallel.
• Resistance
• Resistance is a measure of how much a material opposes the flow of electric current.
• It is measured in ohms (Ω) and can be calculated using Ohm's law.
• Calculating Total Resistance in Parallel
• The total resistance in a parallel circuit is always less than the smallest resistance in the circuit.
• This is because the current has multiple paths to flow through, reducing overall resistance.

Shortcut Trick

Find the LCM of 15, 24, 35, and 42.

LCM(15, 24, 35, 42) = 840.

Smallest 5-digit number (10000) ÷ 840 gives remainder 760.

Number = 10000 + (840 − 760) + 13 = 10093.

∴ The correct answer is 10093.

Alternate Method

Given: Divisors are 15, 24, 35, 42 and the remainder is 13.

Formula: Required number = (Multiple of LCM of divisors) + Remainder

⇒ Prime factors: 15 = 3 × 5, 24 = 2³ × 3, 35 = 5 × 7, 42 = 2 × 3 × 7

⇒ LCM = 2³ × 3 × 5 × 7 = 8 × 3 × 5 × 7 = 840

⇒ Divide 10000 by 840: 10000 = 840 × 11 + 760

⇒ Next multiple of 840 = 840 × 12 = 10080

⇒ Required Number = 10080 + 13 = 10093

∴ The correct answer is 10093.

Additional Information

LCM Method for Remainders

When a number leaves the same remainder 'r' for divisors a, b, c, the general form is k × LCM(a, b, c) + r.

Smallest n-digit number

To find the smallest n-digit number divisible by L, use 10^n-1 + (L − Remainder of 10^n-1/L).

Divisibility Rule of 3 and 5

For a remainder of 13 when divided by 15, the number must end in 3 or 8 (based on 5) and sum of digits minus 13 must be divisible by 3.

The correct answer is Jainism

Key Points

• The Digambara sect is one of the two main sects in Jainism.
• Digambara means "sky-clad" and its monks traditionally do not wear any clothes, symbolizing their renunciation of worldly possessions.
• This sect believes that women must be reborn as men to achieve liberation.
• The other main sect in Jainism is the Svetambara sect, which differs in its practices and beliefs regarding asceticism and liberation.
• Both sects follow the teachings of Lord Mahavira, the 24th Tirthankara in Jainism.

Additional Information

• Jainism is an ancient Indian religion that emphasizes non-violence, truth, and asceticism.
• The religion is known for its teachings on the five great vows: non-violence (Ahimsa), truth (Satya), non-stealing (Asteya), celibacy (Brahmacharya), and non-possessiveness (Aparigraha).
• Jain temples are often characterized by their intricate architecture and detailed carvings.
• Jains celebrate various festivals such as Paryushana and Mahavir Jayanti, which honor the teachings and life of Lord Mahavira.
• The Jain community is known for its contributions to Indian art, culture, and philosophy.

The correct answer is Devendra Jhajharia

Key Points

• Devendra Jhajharia became the first para-athlete of India to receive the Padma Bhushan in the year 2022.
• The Padma Bhushan is the third-highest civilian award in India, recognizing distinguished service of a high order in any field.
• Devendra Jhajharia is a javelin thrower and has won multiple medals in the Paralympics, including gold medals in 2004 and 2016.
• His achievements have been a source of inspiration for many aspiring para-athletes in India.

Additional Information

• Pramod Bhagat is a para-badminton player who has also made significant contributions to Indian sports.
• Harvinder Singh is known for his achievements in para-archery.
• Manoj Sarkar is another notable para-badminton player from India.
• The Padma Awards are one of the highest civilian honors in India and are announced annually on the eve of Republic Day.

The correct answer is Plants produced are genetically different from the parent plant.

Key Points

• In vegetative propagation, plants bear flowers and fruits earlier than those produced from seeds.
• Plants produced through vegetative propagation are genetically identical to the parent plant, making option 2 incorrect.
• Plants can be grown from root, stem, and leaves using vegetative propagation methods.
• Vegetative propagation allows the growth of plants that have lost the capacity to produce seeds.

Additional Information

• Vegetative propagation is a type of asexual reproduction in plants where new plants grow from parts of the parent plant.
• This method is commonly used in horticulture to produce plants with desirable traits.
• Examples of vegetative propagation include the growth of new plants from cuttings, tubers, runners, and bulbs.
• It is an efficient way to propagate plants that do not produce viable seeds or have a long seed germination period.

The logic followed here is,

Hence, the correct answer is "IPXF".

The correct answer is low

Key Points

• The doldrums are an area of low pressure around the equator.
• This region is characterized by calm prevailing winds, which can lead to periods of no wind at all.
• The calm conditions are caused by the convergence of trade winds from both the Northern and Southern Hemispheres.
• The doldrums are known for their unpredictable weather and can pose challenges for maritime navigation.

Additional Information

• The doldrums are also referred to as the Intertropical Convergence Zone (ITCZ).
• This zone migrates with the seasons, moving north during the Northern Hemisphere summer and south during the Northern Hemisphere winter.
• The doldrums can significantly impact global weather patterns and are linked to the formation of tropical storms.

The correct answer is INDICoV-Om

Key Points

• INDICoV-Om is the first indigenous RT-PCR kit developed by 'CSIR - Central Drug Research Institute' for testing the omicron variant.
• The development of this kit marks a significant achievement in India's efforts to combat the COVID-19 pandemic, particularly the detection of the highly transmissible omicron variant.
• The RT-PCR kit is designed to provide accurate and quick results, enhancing the country's testing capabilities.
• This indigenous development reduces dependency on imported testing kits and boosts local innovation and production capabilities.

Additional Information

• The CSIR - Central Drug Research Institute (CDRI) is one of the premier research organizations in India, focusing on drug research and development.
• CDRI has been actively involved in various research initiatives to address the challenges posed by the COVID-19 pandemic.
• The institute's contributions include the development of diagnostic kits, therapeutic drugs, and vaccines.
• The introduction of the INDICoV-Om RT-PCR kit aligns with the government's 'Make in India' initiative, promoting self-reliance in critical healthcare technologies.

Given codes for the number/ symbol is shown below,

The given question to be coded: 7 # $ 4 6 @ 4 ! 8 3

→ Here, we can see that the condition (iv) applies here. So, the codes will be used directly.

Hence, the correct answer is "KYPTULTEQW".

The correct answer is into the plane of paper.

We can use $\vec F= q (\vec v \times \vec B) \ \$

Taking the curl we get the direction. if velocity is in +y direction and magnetic field is in x direction then the curl of them will be into the plane

Key Points

• To determine the direction of the force experienced by a proton moving in a magnetic field, we can use the right-hand rule.

• Point your fingers in the direction of the proton's velocity. In the diagram, the proton's velocity is pointing upward.

• Point your palm in the direction of the magnetic field. The magnetic field is directed to the right.

• The direction your thumb points is the direction of the force on a positive charge (proton).

• Applying the right-hand rule to this scenario:

• Fingers point up (proton's velocity).

• Palm faces right (magnetic field direction).

• Thumb points into the screen (towards you).

• Therefore, the force experienced by the proton will be into the screen (towards the observer).

Given:

Company M sales:

2019 = 235

2020 = 340

2021 = 765

Total sales of Company M (2019-2021) = 235 + 340 + 765 = 1340

Formula used:

Percentage share = $\frac{\text{Sales in 2019}}{\text{Total sales}} \times 100$

Calculations:

Percentage share of 2019 sales = $\frac{235}{1340} \times 100$

⇒ Percentage share = 17.54%

∴ The percentage share of sales of Company M in 2019 is 17.54%.

Given:

12.998 + 20.009 ÷ 4.998 - 2.999 × 2.998 = ?

Formula Used:

Order of Operations (BODMAS/BIDMAS): Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication, Addition and Subtraction.

Calculation:

We have,

⇒ 12.998 + 20.009 ÷ 4.998 - 2.999 × 2.998

First, perform the division:

⇒ 20.009 ÷ 4.998 ≈ 4

Next, perform the multiplication:

⇒ 2.999 × 2.998 ≈ 9

Now, substitute these values back into the equation:

⇒ 12.998 + 4 - 9

Perform the addition and subtraction from left to right:

⇒ 12.998 + 4 = 16.998

⇒ 16.998 - 9 = 7.998

Since we need the closest approximate value:

⇒ 7.998 ≈ 8

∴ The correct answer is option 1.

The correct answer is N

Key Points

• Nitrogen (N) has the highest valency among the given elements.
• Valency is the combining capacity of an element, and it typically corresponds to the number of electrons an atom can lose, gain, or share.
• Nitrogen has a valency of 3 or 5, depending on the compound it forms, while the other elements (Ca, Al, Li) have lower valencies.
• Calcium (Ca) has a valency of 2, Aluminum (Al) has a valency of 3, and Lithium (Li) has a valency of 1.

Additional Information

• Valency and oxidation states are fundamental concepts in chemistry that help in understanding how elements interact and form compounds.
• Valency is often determined by the number of electrons in the outermost shell of an atom.
• Elements in the same group of the periodic table typically have similar valencies.
• Understanding valency is crucial for predicting the types of bonds that an element can form.

According to the given information,

1) Only two people sit to the left of K.

2) J is at the extreme left end of the row.

3) P is an immediate neighbour of both K and N.

4) L is to the immediate right of N.

5) O and L are immediate neighbours.

Thus, the final arrangement is,

Here, we can see that O sits at the extreme right end.

Hence, the correct answer is "O".

The given statement is: An online teaching platform has reported to earn almost double through subscriptions ever since they started LIVE problem-solving classes on the platform.

Conclusions:

I. No other online teaching platform offers LIVE problem-solving classes → False (The statement does not provide any information about other online teaching platforms or their offerings).

II. Students who opt for LIVE problem-solving sessions on the said platform have to pay double the fees as compared to those who opt for regular classes → False (There is no specific mention of fee structures or comparative pricing between LIVE problem-solving sessions and regular classes. The increase in platform earnings could be due to a higher number of subscriptions, not necessarily the cost difference between classes).

Hence, the correct answer is "Neither I nor II can be concluded".

Shortcut Trick

Multiply the coefficient of m² (√3) and the constant term (7√3) to get the product: √3 × 7√3 = 21.

Find two factors of 21 that sum up to the middle coefficient (10): These are 7 and 3.

Divide the factors by the coefficient of m² and change their signs to find the roots.

Roots ⇒ m₁ = −7/√3 and m₂ = −3/√3 = −√3.

∴ The correct answer is −7/√3 and −√3.

Alternate Method

Given Equation: √3m² + 10m + 7√3 = 0

Method: Factorisation by Splitting the Middle Term.

⇒ √3m² + 3m + 7m + 7√3 = 0

⇒ √3m(m + √3) + 7(m + √3) = 0

⇒ (m + √3)(√3m + 7) = 0

⇒ Case 1: m + √3 = 0 ⇒ m = −√3

⇒ Case 2: √3m + 7 = 0 ⇒ √3m = −7 ⇒ m = −7/√3

∴ The correct answer is −7/√3 and −√3.

Additional Information

Standard Quadratic Equation

Any equation of the form am² + bm + c = 0 is a quadratic equation where a ≠ 0.

Discriminant and Nature of Roots

The term D = b² − 4ac determines the nature. If D > 0, roots are real and unequal; if D = 0, roots are real and equal.

Sum and Product of Roots

For the equation am² + bm + c = 0, the Sum of roots = −b/a and the Product of roots = c/a.

The correct answer is Nagaland

Key Points

• In July 2022, the Lok Sabha passed the Family Courts (Amendment) Bill, 2022.
• This amendment was necessary to address the issue of lack of jurisdiction of Family Courts in the States of Himachal Pradesh and Nagaland.
• The amendment validates the existence and functioning of Family Courts in these states retrospectively.
• Family Courts are established to promote conciliation and secure speedy settlement of disputes relating to marriage and family affairs.

Additional Information

• The Family Courts Act was enacted in 1984 to provide for the establishment of Family Courts with a view to promote conciliation and secure speedy settlement of disputes relating to marriage and family affairs.
• The amendment ensures that all the actions taken by the Family Courts in Himachal Pradesh and Nagaland are validated from the date of their respective establishments.
• This move is expected to enhance the accessibility and efficiency of the judicial system in addressing family-related cases in these states.

The correct answer is Growth of nails

Key Points

• Growth of nails is a continuous process that happens throughout life and is not specifically a change that marks the onset of puberty.
• Puberty is characterized by several physiological changes, such as a change in voice, change in body shape, and a sudden increase in height.
• These changes are driven by hormonal changes in the body during adolescence.
• Understanding the distinct changes that occur during puberty helps in identifying the normal developmental process.

Additional Information

• Puberty typically begins between ages 8 and 14 for girls and 9 and 16 for boys.
• It is initiated by the release of hormones such as estrogen in girls and testosterone in boys.
• Other changes that occur during puberty include the development of secondary sexual characteristics, such as breast development in girls and facial hair growth in boys.
• Emotional and psychological changes also accompany the physical changes during this period.

The correct answer is Dec 28 2021 

Key Points

• Dec 28 2021 is the date on which the Consumer Protection (Direct Selling) Rules, 2021 were introduced by the Government of India.
• These rules are part of the Consumer Protection Act, which aims to protect the interests of consumers in India.
• The rules provide a regulatory framework for direct selling and aim to prevent unfair trade practices.
• They also ensure that direct sellers and direct selling entities comply with certain obligations to safeguard consumer interests.
• The introduction of these rules marks a significant step in enhancing consumer rights and promoting fair trade practices in the direct selling industry.

Additional Information

• The Consumer Protection Act, 2019 was enacted to replace the Consumer Protection Act, 1986, and it came into force on 20th July 2020.
• The Act provides for the establishment of the Central Consumer Protection Authority (CCPA) to promote, protect, and enforce the rights of consumers.
• The Act includes provisions for the prevention of unfair trade practices, product liability, and the establishment of consumer dispute redressal commissions.
• The Consumer Protection (Direct Selling) Rules, 2021 are part of the comprehensive legal framework aimed at strengthening consumer protection in India.
• Direct selling entities must adhere to these rules to operate legally in India, ensuring transparency and accountability in their business practices.
• The rules also mandate that direct sellers provide accurate information about the products and services they offer, thereby protecting consumers from misleading claims.

Shortcut Trick

Total frequency n = 60, so n/2 = 30.

Cumulative frequency (cf) before the 80-90 class is 6 + 8 + 15 = 29.

Since 30 falls after 29, the Median Class is 80-90.

Applying the linear interpolation: Median = 80 + [(30 − 29) ÷ 20] × 10.

Median = 80 + (1 ÷ 20) × 10 = 80 + 0.5 = 80.5.

∴ The correct answer is 80.5 units.

Alternate Method

Given: Monthly consumption distribution of 60 consumers.

Formula Used: Median = l + [((n ÷ 2) − cf) ÷ f] × h

Where: l = lower limit of median class, n = total frequency, cf = cumulative frequency of preceding class, f = frequency of median class, h = class size.

Step-by-step Calculations:

⇒ Total Consumers (n) = 6 + 8 + 15 + 20 + 11 = 60

⇒ n ÷ 2 = 60 ÷ 2 = 30

⇒ Cumulative Frequencies (cf): 6, 14, 29, 49, 60

⇒ Median class is 80-90 (as cf 49 > 30)

⇒ l = 80, cf = 29, f = 20, h = 10

⇒ Median = 80 + [(30 − 29) ÷ 20] × 10

⇒ Median = 80 + [1 ÷ 20] × 10

⇒ Median = 80 + 0.5 = 80.5 units

∴ The correct answer is 80.5 units.

Additional Information

Empirical Relationship

The relationship between central tendencies is given by: Mode = 3 Median − 2 Mean.

Mode of Grouped Data

Calculated as: Mode = l + [(f₁ − f₀) ÷ (2f₁ − f₀ − f₂)] × h, where f₁ is the frequency of the modal class.

Mean of Grouped Data

The Mean is calculated using the Direct Method: Σf_ix_i ÷ Σf_i, where x_i is the class mark.

The correct answer is West Bengal

Key Points

• Kaal Baisakhi is a local term for the pre-monsoon thunderstorms that occur in the Indian state of West Bengal.
• These storms typically occur in the late afternoon or evening and are characterized by strong winds, heavy rain, and sometimes hail.
• Kaal Baisakhi is most common during the months of April and May, just before the onset of the monsoon season.
• It is also known as the "Nor'wester" due to the direction from which the storms usually approach.

Additional Information

• West Bengal is located in the eastern part of India and shares its borders with Bangladesh, Bhutan, and Nepal.
• The state experiences a tropical climate, with hot summers, heavy monsoon rains, and mild winters.
• West Bengal is known for its rich cultural heritage, including its contributions to literature, music, and art.
• The state capital, Kolkata, is one of the largest cities in India and an important cultural and economic hub.
• In addition to Kaal Baisakhi, West Bengal also experiences other weather phenomena such as the monsoon season and occasional cyclones.

The correct answer is AIADMK

Key Points

• AIADMK (All India Anna Dravida Munnetra Kazhagam) is a regional political party in the Indian state of Tamil Nadu and the union territory of Puducherry.
• The party was established in 1972 by M.G. Ramachandran, a popular actor and politician in Tamil Nadu.
• AIADMK has been a significant player in Tamil Nadu politics and has formed the state government multiple times.
• The party's symbol is "Two Leaves" and it has a strong base among the rural and urban population in Tamil Nadu.

Additional Information

• AIADMK has been known for its welfare schemes and populist measures aimed at improving the socio-economic conditions of the people in Tamil Nadu.
• The party has faced several internal splits and leadership challenges, especially after the demise of its prominent leaders.
• AIADMK has also played a crucial role in national politics, often aligning with major national parties to form coalition governments.
• The party's influence extends to cultural and social spheres, with strong ties to the Tamil film industry.
• AIADMK's rival party in Tamil Nadu is the DMK (Dravida Munnetra Kazhagam), and the political landscape of the state is often dominated by the contest between these two major parties.

The least possible venn diagram is shown below,

Conclusions:

I. No sugar is sweetener → True (All sugars are jaggery and no jaggery is sweetener implies that no sugar is sweetener).

II. Some jaggeries are sweeteners → False (No jaggery is sweetener implies that some jaggery can't be sweetener).

III. Some jaggeries are sugars → True (All sugars are jaggery implies that some jaggeries are definitely sugar).

Hence, the correct answer is "Only conclusion I and III follow".

According to the give information,

1) Rahul is at the 8th place from the left end of the row.

2) Only 11 persons are sitting between Rahul and Samar.

3) Samar is at some place towards the right of Rahul.

4) Mohit is to the immediate left of Zeeshan, who is sitting at the extreme right end.

5. Samar is at the 9th place from the extreme right end.

The total number of persons seated here = (7 + 1 + 11 + 1 + 6 + 1 + 1) = 28

Hence, the correct answer is "28".

Shortcut Trick

Sum of ratio parts = 3 + 5 + 4 + 6 = 18 units.

Total sum of angles in a quadrilateral = 360º.

Value of 1 unit = 360º ÷ 18 = 20º.

Required value (3p + 2r) in units = 3(3) + 2(4) = 9 + 8 = 17 units.

Final value = 17 × 20º = 340º.

∴ The correct answer is 340º.

Alternate Method

Given: Ratio of angles p : q : r : s = 3 : 5 : 4 : 6.

Formula Used: Sum of interior angles of a quadrilateral = 360º.

⇒ Let the measures of the angles be 3x, 5x, 4x, and 6x.

⇒ 3x + 5x + 4x + 6x = 360º

⇒ 18x = 360º

⇒ x = 360º ÷ 18 = 20º

⇒ p = 3x = 3 × 20º = 60º

⇒ r = 4x = 4 × 20º = 80º

⇒ Value of 3p + 2r = 3(60º) + 2(80º)

⇒ 3p + 2r = 180º + 160º = 340º

∴ The correct answer is 340º.

Additional Information

Angle Sum Property of Polygons

The sum of the interior angles of a polygon with n sides is (n − 2) × 180º. For a quadrilateral, n = 4, so (4 − 2) × 180º = 360º.

Ratio and Proportion

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

Types of Quadrilaterals

Common types include Parallelogram, Rectangle, Square, Rhombus, and Trapezium, all of which follow the 360º angle sum rule.

Shortcut Trick

Sum of two numbers (a + b) = 55

Product of two numbers (a × b) = HCF × LCM = 5 × 120 = 600

Sum of reciprocals = (a + b) ÷ (a × b)

Sum of reciprocals = 55 ÷ 600 = 11/120

∴ The correct answer is 11/120.

Alternate Method

Given:

Sum of two numbers (x + y) = 55

HCF = 5, LCM = 120

Formula Used:

Product of two numbers = HCF × LCM

Sum of reciprocals = (1/x) + (1/y) = (x + y) / (xy)

Calculations:

⇒ Product of numbers = 5 × 120 = 600

⇒ Sum of reciprocals = (x + y) ÷ (xy)

⇒ Sum of reciprocals = 55 ÷ 600

⇒ Sum of reciprocals = (11 × 5) ÷ (120 × 5)

⇒ Sum of reciprocals = 11/120

∴ The correct answer is 11/120.

Additional Information

HCF and LCM Relationship

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

Reciprocal Property

The sum of reciprocals of two numbers is always equal to (Sum of numbers) / (Product of numbers).

Co-prime Factors

Numbers can be represented as Hx and Hy where x and y are co-prime integers and H is the HCF.

The logic followed here is:

Logic: (Second number) = (First number - 1)² × (First number)

6 ∶ 150

→ 150 = (6 - 1)² × 6

→ 150 = (5)² × 6

→ 150 = 25 × 6

4 ∶ 36

→ 36 = (4 - 1)2 × 4

→ 36 = (3)2 × 4

→ 36 = 9 × 4

Similarly,

5 ∶ ?

→ ? = (5 - 1)2 × 5

→ ? = (4)2 × 5

→ ? = 16 × 5 = 80

Hence, the correct answer is "80".

The correct answer is N2 + H2 → 2NH3

Key Points

• Combination reactions are chemical reactions where two or more substances combine to form a single product.
• In the given options, option 2 (N2 + H2 → 2NH3) is an example of a combination reaction as nitrogen and hydrogen combine to form ammonia.
• Other options represent different types of reactions:
• Option 1 (ZnCO3 → ZnO + CO2) is a decomposition reaction.
• Option 3 (MgCl2 + Na → 2NaCl + Mg) is a displacement reaction.
• Option 4 (2NaCl → 2Na + Cl2) is also a decomposition reaction.

Additional Information

• Combination reactions are also known as synthesis reactions.
• These reactions are generally exothermic in nature, meaning they release heat.
• Examples of combination reactions include the formation of water (H2 + O2 → H2O) and the formation of calcium carbonate (CaO + CO2 → CaCO3).

The given three letter words are: (Left) NAT PAL COT TAN (Right)

If in each of the words, each letter is changed to the next letter in the English alphabetical order, we get:

→ (Left) OBU QBM DPU UBO (Right)

Here, we can see that there is one word (QBM) which has no vowel.

Hence, the correct answer is "One".

The correct answer is 42nd Amendment

Key Points

• The 42nd Amendment to the Indian Constitution is also known as the Constitution (Forty-second Amendment) Act, 1976.
• This amendment is one of the most comprehensive amendments and is often referred to as a "mini-Constitution" due to its wide-ranging impact.
• It substituted the words 'sovereign democratic republic' with 'sovereign socialist secular democratic republic' in the Preamble of the Constitution.
• It also replaced the words 'unity of the Nation' with 'unity and integrity of the Nation' in the Preamble.
• This amendment was enacted during the Emergency period under Prime Minister Indira Gandhi's tenure.
• It aimed at reducing the power of the judiciary and increasing the power of the central government.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26th November 1949 and came into effect on 26th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Seventh Schedule of the Constitution contains three lists which delineate the subjects under the Union, State, and Concurrent lists.
• Amendments to the Constitution can be made through a process outlined in Article 368.
• The Union List has been amended several times to meet the evolving needs of the nation.

The logic followed here is:

Logic: Second number = First number + (Third number)²

(12, 61, 7)

→ 61 = 12 + (7)²

→ 61 = 12 + 49

(15, 51, 6)

→ 51 = 15 + (6)2

→ 51 = 15 + 36

Now, let's check each option,

1) (20, 54, 5)

→ 54 = 20 + (5)2

→ 54 ≠ 20 + 25 

2) (14, 78, 8)

→ 78 = 14 + (8)2

→ 78 = 14 + 64 ⇒ Follows the logic.

3) (12, 46, 4)

→ 46 = 12 + (4)2

→ 46 ≠ 12 + 16 

4) (16, 70, 9)

→ 70 = 16 + (9)2

→ 70 ≠ 16 + 81

Here, we can see that only Option 2 follows the logic.

Hence, the correct answer is "(14, 78, 8)".

Shortcut Trick

Net discount percentage = a + b − (a × b) ÷ 100

Net discount = 20 + 15 − (20 × 15) ÷ 100 = 35 − 3 = 32%

Selling Price (SP) = 100% − 32% = 68% of Marked Price (MP)

SP = 68% of 2,000 = (68 ÷ 100) × 2,000 = 1,360

∴ The correct answer is Rs. 1,360.

Alternate Method

Given → Marked Price (MP) = Rs. 2,000 | First Discount (d₁) = 20% | Second Discount (d₂) = 15% Formulas: SP = MP × (100 − d₁)% × (100 − d₂)%

⇒ Step 1: Price after 20% discount = 2,000 − (20% of 2,000) = 2,000 − 400 = 1,600 ⇒ Step 2: Price after second 15% discount = 1,600 − (15% of 1,600) = 1,600 − 240 ⇒ Final SP = 1,360

∴ The correct answer is Rs. 1,360.

Additional Information

Successive Discounts

When a series of discounts are applied, each subsequent discount is calculated on the reduced price after the previous discount. The order of application does not change the final price.

Marked Price & Selling Price

Marked price is the price printed on an item. The selling price is the final amount paid by the customer after all discounts: SP = MP × (1 − d₁/100) × (1 − d₂/100).

The correct answer is Beyond centre of curvature

Key Points

• A concave mirror forms a real, inverted, and diminished image of an object when the object is placed beyond the centre of curvature.
• In this position, the rays of light converge at a point between the focus and the centre of curvature after reflecting from the mirror, forming a smaller image.
• This characteristic of concave mirrors is utilized in devices such as telescopes and certain types of cameras.

Additional Information

• Concave mirrors have a reflecting surface that curves inward, resembling a portion of the interior of a sphere.
• The focus of a concave mirror is the point where light rays parallel to the principal axis converge after reflection.
• The centre of curvature is the center of the sphere of which the mirror is a part, and it lies on the principal axis.
• When the object is placed at the centre of curvature, the image formed is real, inverted, and of the same size as the object.
• If the object is placed between the focus and centre of curvature, the image formed is real, inverted, and magnified.
• When the object is placed at the focus, the reflected rays become parallel, and the image is formed at infinity.
• Concave mirrors are commonly used in applications requiring focused light, such as in headlights, solar furnaces, and shaving mirrors.

Shortcut Trick

The age difference between two people remains constant regardless of time.

Age difference = 12 years (given for 6 years hence, so it is the same now and 1 year ago).

1 year ago: Krishna (4x) and Kavitha (x). Difference = 3x = 12 ⇒ x = 4.

1 year ago: Krishna = 16, Kavitha = 4. Present ages: Krishna = 17, Kavitha = 5.

∴ The correct answer is 17 ∶ 5.

Alternate Method

Given:

Ratio 1 year ago = 4 ∶ 1

Difference 6 years hence = 12 years

Calculations:

⇒ Let ages 1 year ago be 4x and x.

⇒ Age difference = 4x − x = 3x.

⇒ Since age difference is constant, 3x = 12 ⇒ x = 4.

⇒ Krishna's age 1 year ago = 4 × 4 = 16 years.

⇒ Kavitha's age 1 year ago = 1 × 4 = 4 years.

⇒ Present age of Krishna = 16 + 1 = 17 years.

⇒ Present age of Kavitha = 4 + 1 = 5 years.

⇒ Required Ratio = 17 ∶ 5.

∴ The correct answer is 17 ∶ 5.

Additional Information

Constant Age Difference

The difference between the ages of two individuals never changes over time. If A is 10 years older than B today, A will always be 10 years older than B.

Ratio Balancing

When solving age problems with ratios, ensure the difference between ratio parts is consistent with the actual age difference to simplify calculations.

PY - RW - TU

EN - GL - IJ

Now, let's check each option,

1) MT - OR - QP

⇒ Follows the logic.

2) DE - EF - FG

3) XC - YB - ZA

4) UV - TU - ST

Here, we can see that only Option 1 follows the logic.

Hence, the correct answer is "MT - OR - QP".

Shortcut Trick

Volume of Cube = Volume of Cuboid

Side³ = Length × Width × Height

18 × 18 × 18 = 27 × Width × 7

Width = (18 × 18 × 18) ÷ (27 × 7) = (2 × 18 × 18) ÷ (3 × 7) = 216 ÷ 7 ≈ 30.85 m

∴ The correct answer is 30.8 m.

Alternate Method

Given:

Edge of Cube (a) = 18 m

Length of Cuboid (L) = 27 m

Height of Cuboid (H) = 7 m

Formula Used:

Volume of Cube = a³

Volume of Cuboid = L × B × H

Calculations:

⇒ Volume of Milk = 18 × 18 × 18 = 5832 m³

⇒ Volume of Cuboid = 27 × Width × 7

⇒ 5832 = 189 × Width

⇒ Width = 5832 ÷ 189

⇒ Width = 30.857... m

⇒ Width ≈ 30.8 m

∴ The correct answer is 30.8 m.

Additional Information

Surface Area of Cube

Total surface area of a cube is 6a² and lateral surface area is 4a².

Surface Area of Cuboid

Total surface area of a cuboid is 2(LB + BH + HL).

Diagonal of Cube and Cuboid

Diagonal of cube is √3 × a and diagonal of cuboid is √(L² + B² + H²).

The given statement is: J > H = N ≥ B ≤ C < E

Now, let's check each option,

1) H < B → False (There is a definite relation; H = N ≥ B)

2) N > C → False (The relation is uncertain between them; N ≥ B ≤ C)

3) N > E → False (There is a definite relation; N ≥ B ≤ C < E)

4) B < J → True (There is a definite relation; J > H = N ≥ B)

Hence, the correct answer is "B < J".

The venn diagram representing recipes using exactly any two of the given ingredients is shown below,

Hence, the correct answer is "33".

The correct answer is Mumbai

Key Points

• Mumbai has been named as the host of the International Olympic Committee session in 2023.
• This marks a significant event as it is the first time in four decades that India will host such a session.
• The last time India hosted an IOC session was in 1983 in New Delhi.
• The decision was made during the 139th IOC Session held in Beijing, China.
• Mumbai was selected unanimously, reflecting the city's robust infrastructure and capacity to host international events.

Additional Information

• The International Olympic Committee (IOC) is a non-governmental sports organization based in Lausanne, Switzerland.
• Founded by Pierre de Coubertin and Demetrios Vikelas in 1894, the IOC is the authority responsible for organizing the modern Olympic Games.
• IOC sessions are significant as they involve discussions and decisions regarding the Olympic movement, including the selection of host cities for future games.
• Hosting an IOC session is a prestigious event and provides the host city with an opportunity to showcase its culture and infrastructure to a global audience.
• India's selection as a host reflects its growing importance and influence in the global sports arena.

The correct answer is 3 Only.

Key Points

• Plaster of Paris is a quick-setting gypsum plaster consisting of a fine white powder (calcium sulfate hemihydrate), which hardens when moistened and allowed to dry.
• It is commonly used for making toys, materials for decoration, and for making surfaces smooth. Hence, Option 3 is correct.
• It is not used in the manufacture of glass, soap and paper as mentioned in Option 1.
• Plaster of Paris is not a cleaning agent for domestic purposes as stated in Option 2.
• It is also not used for baking as mentioned in Option 4.

The correct answer is Endoplasmic reticulum

Key Points

• Endoplasmic reticulum (ER) is the cell organelle responsible for detoxifying toxins and drugs.
• The ER is divided into two types: rough ER and smooth ER.
• The smooth ER is particularly involved in the detoxification process.
• It contains enzymes that facilitate the breakdown and removal of harmful substances.
• These detoxifying enzymes in the smooth ER convert lipid-soluble toxins into water-soluble substances that can be easily excreted from the cell.

Additional Information

• The rough ER is studded with ribosomes and is involved in protein synthesis.
• The smooth ER also plays a role in lipid metabolism and calcium ion storage.
• Other cell organelles like mitochondria are mainly involved in energy production, while Golgi bodies are involved in packaging and transport of proteins.
• Ribosomes are the sites of protein synthesis and do not play a role in detoxification.

Shortcut Trick

Difference in fractions = 5/4 − 3/4 = 2/4 = 1/2

Given that 1/2 of the number is 6.

Full number (1 unit) = 6 × 2 = 12

∴ The correct answer is 12.

Alternate Method

Let the number be x.

According to the question:

⇒ (5/4) × x − (3/4) × x = 6

⇒ (5x − 3x) / 4 = 6

⇒ 2x / 4 = 6

⇒ x / 2 = 6

⇒ x = 12

∴ The correct answer is 12.

Additional Information

Fraction basics

When denominators are the same, subtract or add the numerators directly over the common denominator.

Linear Equations

Translate greater than as an equation where (Value 1) − (Value 2) = Difference.

According to the given information,

1) C has the exam on Tuesday.

2) E has exam on Sunday.

3) Only one person has the exam between A and G, A has exam before G.

4. D has the exam on the day immediately before A, but not on Thursday. 

5) F's exam is on one of the days before E but after B. 

Here, we can see that B has the exam on Monday.

Hence, the correct answer is "B".

The given codes of the number/symbol is shown below,

The given question to be coded is: 6 # % 3 8 5 # 4

→ Here, we can see that condition (ii) applies here. So, the codes of second and the fifth elements are to be interchanged.

Now, the code of the given question →

Hence, the correct answer is "R B K W P G P U".

The correct answer is H = IR2t

Key Points

• The formula H = IR²t does not correctly represent the heat produced in a conductor due to the flow of electric current.
• The correct formulae to represent the heat produced in a conductor are H = (V²/R)t, H = I²Rt, and H = VIt.
• These formulae are derived from the principles of Joule's law of heating, which states that the heat produced in a conductor is proportional to the square of the current, the resistance of the conductor, and the time for which the current flows.

Additional Information

• Joule's law of heating states that the heat produced in a resistor is directly proportional to the square of the current passing through it, the resistance of the resistor, and the time for which the current passes through it.
• The formula H = I²Rt is the most direct representation of Joule's law, where H is the heat produced, I is the current, R is the resistance, and t is the time.
• The formula H = (V²/R)t is derived from Ohm's law, where V is the voltage across the conductor.
• The formula H = VIt is another representation that combines both voltage and current to calculate the heat produced.

The correct answer is uniform and non-zero

Key Points

• The magnetic field strength inside a current carrying solenoid is uniform and non-zero.
• A solenoid is a long coil of wire wound in the form of a helix, and when an electric current passes through it, a magnetic field is generated.
• Inside the solenoid, the magnetic field lines are parallel and evenly spaced, indicating a uniform field.
• The strength of the magnetic field inside the solenoid is given by the formula: B = μ₀nI, Where: B is the magnetic field, μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current.
• This uniform magnetic field is a result of the superposition of the magnetic fields created by each turn of the wire.

Additional Information

• At the ends of the solenoid, the magnetic field lines start to spread out, causing the field to become weaker and less uniform.
• Outside the solenoid, the magnetic field is much weaker compared to the inside.
• Solenoids are widely used in various applications such as electromagnets, inductors, and transformers.
• The concept of a solenoid is fundamental in electromagnetism and is essential for understanding the behavior of magnetic fields in different configurations.

According to the given information,

1) B is the third box from the top.

2) G is immediately above B.

3) Exactly two boxes are kept between C and D with C placed above D.

4) Exactly two boxes are kept between D and E with D placed above E.

5) F is immediately below A.

Here, we can see that Box F is just above Box E.

Hence, the correct answer is "F".

The correct answer is coal

Key Points

• Carbonisation is a process in which dead plant material is converted into coal over millions of years.
• This process involves the decomposition of plant material in the absence of oxygen, leading to the formation of carbon-rich substances.
• The stages of coal formation include peat, lignite, bituminous coal, and anthracite, with each stage representing a higher degree of carbon content.
• Coal is a crucial fossil fuel used for electricity generation, steel production, and as a source of energy in various industries.

Additional Information

• Coal formation is a slow geological process that takes millions of years.
• Different types of coal have varying uses; for instance, anthracite is used in residential heating due to its high carbon content and low impurities.
• The carbonisation process is crucial for the fossil fuel industry and plays a significant role in the global energy supply.
• Coal mining and usage have environmental impacts, including greenhouse gas emissions and habitat destruction, necessitating efforts for sustainable and cleaner energy alternatives.

The correct answer is Punjab

Key Points

• NESTLE India Ltd. set up its first factory in 1961 in the state of Punjab.
• This factory marked the beginning of Nestle's manufacturing operations in India.
• The choice of Punjab was strategic due to its rich agricultural base, which provided easy access to raw materials.
• The factory primarily focused on producing dairy products, which aligned with the state's strong dairy industry.
• Nestle's establishment in Punjab contributed to the industrial growth of the region and provided employment opportunities.

Additional Information

• NESTLE India Ltd. is a subsidiary of Nestlé S.A., a Swiss multinational food and drink processing conglomerate.
• The company has a significant presence in India with multiple manufacturing facilities across various states.
• Besides dairy products, NESTLE India Ltd. produces a wide range of products including beverages, prepared dishes, and cooking aids, chocolates, and confectioneries.
• The establishment of the factory in Punjab was a part of Nestle's broader strategy to cater to the Indian market and expand its global footprint.

Shortcut Trick

Ratio of efficiency (A : B) = 3 : 1

Total combined efficiency = 3 + 1 = 4 units/min

Total work (Capacity) = Combined efficiency × Time = 4 × 36 = 144 units

Time taken by Pipe A alone = Total Work ÷ Efficiency of A = 144 ÷ 3 = 48 min

∴ The correct answer is 48 min.

Alternate Method

Given:

Efficiency of Pipe A is 3 times that of Pipe B.

Time taken by (A + B) together = 36 min.

Formula Used:

Total Work = Efficiency × Time

Time = Total Work ÷ Efficiency

Calculations:

⇒ Let Efficiency of Pipe B = 1 unit/min

⇒ Efficiency of Pipe A = 3 × 1 = 3 units/min

⇒ Combined Efficiency (A + B) = 3 + 1 = 4 units/min

⇒ Total Capacity of tank = 4 × 36 = 144 units

⇒ Time taken by Pipe A = 144 ÷ 3 = 48 min

∴ The correct answer is 48 min.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken. If efficiency ratio is x : y, the time ratio is y : x.

Pipes and Cisterns Concept

Inlet pipes have positive efficiency while outlet/leakage pipes have negative efficiency.

Work Equivalence

Total Work = (E₁ × T₁) = (E₂ × T₂). This constant can be used to find any unknown variable.

Shortcut Trick

Age ratio 10 years ago: Son : Father = 1 : 8 (Difference = 7 units)

Present age ratio: Son : Father = 9 : 37 (Difference = 28 units)

Equalize differences: Multiply 10-year ago ratio by 4 → 4 : 32

Increase in units = 37 − 32 = 5 units. Given 5 units = 10 years ⇒ 1 unit = 2 years

Present age of Father = 37 × 2 = 74 years.

∴ The correct answer is 74 years.

Alternate Method

Given: Ratio 10 years ago = 1/8; Present Ratio = 9/37.

Formula Used: Age Equation Method.

Let the present age of the Father be F and Son be S.

⇒ S = (9/37)F

⇒ 10 years ago: (S − 10) = (1/8) × (F − 10)

⇒ 8 × ((9F/37) − 10) = F − 10

⇒ (72F / 37) − 80 = F − 10

⇒ (72F / 37) − F = 80 − 10

⇒ (72F − 37F) / 37 = 70

⇒ 35F / 37 = 70

⇒ F = (70 × 37) / 35

⇒ F = 2 × 37 = 74 years.

∴ The correct answer is 74 years.

Additional Information

Ratio Difference Method

To solve age problems quickly, always equalize the difference between the ratio parts for different time periods as the age gap remains constant.

Algebraic Verification

If present ages are in ratio a:b, then after 'n' years the ratio becomes (ax+n)/(bx+n) = c/d.

Linear Equations in Ages

Most age problems can be modeled as linear equations with one or two variables, where time shifts apply equally to all persons involved.

The correct answer is Leucoplast

Key Points

• Leucoplasts are a type of plastid found in plant cells.
• They are primarily involved in the storage of starch, proteins, and oil granules.
• Leucoplasts are colorless and found in non-photosynthetic tissues of plants, such as roots, seeds, and tubers.
• They play a crucial role in the storage and synthesis of essential biomolecules.

Additional Information

• Chloroplasts are involved in photosynthesis and contain chlorophyll, giving them a green color.
• Chromoplasts contain pigments that give flowers and fruits their distinctive colors.
• Protoplasts refer to the living part of the cell that is enclosed by the plasma membrane, excluding the cell wall.
• Plastids are classified into different types based on their functions and the pigments they contain, such as chloroplasts, chromoplasts, and leucoplasts.

Shortcut Trick

Sum of first n odd natural numbers = n².

Number of terms (n) = [(Last term − First term) ÷ Difference] + 1

n = [(21 − 1) ÷ 2] + 1 = 11.

Sum = 11² = 121.

∴ The correct answer is 121.

Alternate Method

Given: Arithmetic Progression (AP) = 1, 3, 5, 7, ..., 21

Formula Used: Sum of AP (S_n) = (n/2) × [a + l], where a is the first term and l is the last term.

⇒ First term (a) = 1

⇒ Last term (l) = 21

⇒ Common difference (d) = 3 − 1 = 2

⇒ l = a + (n − 1)d

⇒ 21 = 1 + (n − 1) × 2

⇒ 20 = (n − 1) × 2

⇒ 10 = n − 1

⇒ n = 11

⇒ S₁₁ = (11/2) × [1 + 21]

⇒ S₁₁ = (11/2) × 22

⇒ S₁₁ = 11 × 11 = 121

∴ The correct answer is 121.

Additional Information

Sum of first n natural numbers

The sum is calculated using the formula: S_n = [n(n + 1)] ÷ 2.

Sum of first n even natural numbers

The sum is calculated using the formula: S_n = n(n + 1).

Sum of squares of first n natural numbers

The sum is calculated using the formula: S_n = [n(n + 1)(2n + 1)] ÷ 6.

The correct answer is Bile salts

Key Points

• Bile salts reduce the size of large fat globules, allowing enzymes to work more effectively.
• Bile salts are a component of bile, which is produced by the liver and stored in the gallbladder.
• They play a crucial role in the digestion and absorption of fats in the small intestine.
• By emulsifying fats, bile salts increase the surface area available for enzyme action, particularly for the enzyme lipase.

Additional Information

• Hydrochloric acid is secreted by the stomach and helps in the digestion of proteins but does not emulsify fats.
• Pancreatic juice contains enzymes that digest carbohydrates, proteins, and fats but does not emulsify fats.
• Succus entericus is the intestinal juice that contains various digestive enzymes but does not emulsify fats.
• Emulsification of fats is essential for the efficient digestion and absorption of dietary fats.

The correct answer is Differentiation

Key Points

• Differentiation is the process in plants where cells of meristematic tissue lose their ability to divide, take up a permanent shape and size, and specialize to perform a specific function.
• This process is crucial for the development of various tissues and organs in plants, allowing them to perform specialized functions.
• Meristematic tissues are regions of active cell division, and as cells differentiate, they transition into permanent tissues with specific roles.
• Examples of differentiated cells include xylem and phloem, which are specialized for water and nutrient transport, respectively.

Additional Information

• Regeneration refers to the process of renewal, restoration, and growth of cells or tissues.
• Development is the overall process by which an organism grows and develops, involving cell division and differentiation.
• Proliferation is the rapid multiplication of cells.
• Meristematic tissues are found in zones of the plant where growth can take place, such as the tips of roots and shoots.
• Plants have three main types of meristematic tissues: apical meristems, lateral meristems, and intercalary meristems.

Given:

Total number of boys from places J and M in 2017 = Boys from J (2017) + Boys from M (2017)

Boys from J in 2017 = 10 thousand

Boys from M in 2017 = 8 thousand

Total number of boys in 2017 from J and M = 10 + 8 = 18 thousand

Girls from M in 2016 = 9 thousand

Girls from M in 2017 = 7 thousand

Girls from M in 2018 = 4 thousand

Girls from M in 2019 = 11 thousand

Girls from M in 2020 = 12 thousand

Girls from M in 2021 = 18 thousand

∴ The year is 2021 when the total number of girls from M is 18 thousand.

Shortcut Trick

Put a specific value for acute angle A, say A = 45°.

Expression = (cos 45° − sin 45° + 1) ÷ (cos 45° + sin 45° − 1)

⇒ (1/√2 − 1/√2 + 1) ÷ (1/√2 + 1/√2 − 1) = 1 ÷ (√2 − 1)

⇒ Rationalizing: 1 × (√2 + 1) = √2 + 1

Check options at A = 45°: cot 45° + cosec 45° = 1 + √2. Matches.

∴ The correct answer is cot A + cosec A.

Alternate Method

Given: (cos A − sin A + 1) ÷ (cos A + sin A − 1)

Formula Used: cosec²A − cot²A = 1

Divide numerator and denominator by sin A:

⇒ (cos A/sin A − sin A/sin A + 1/sin A) ÷ (cos A/sin A + sin A/sin A − 1/sin A)

⇒ (cot A − 1 + cosec A) ÷ (cot A + 1 − cosec A)

⇒ [cot A + cosec A − (cosec²A − cot²A)] ÷ (cot A + 1 − cosec A)

⇒ [(cot A + cosec A) − (cosec A − cot A)(cosec A + cot A)] ÷ (cot A + 1 − cosec A)

⇒ (cot A + cosec A)[1 − (cosec A − cot A)] ÷ (cot A + 1 − cosec A)

⇒ (cot A + cosec A)(1 − cosec A + cot A) ÷ (1 − cosec A + cot A)

⇒ cot A + cosec A

∴ The correct answer is cot A + cosec A.

Additional Information

Trigonometric Identities

Standard identities: sin²A + cos²A = 1, 1 + tan²A = sec²A, and 1 + cot²A = cosec²A.

Complementary Angles

For an acute angle A, sin(90°−A) = cos A and tan(90°−A) = cot A.

Reciprocal Relations

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

The correct answer is Hornbill Festival

Key Points

• The Hornbill Festival is celebrated in Nagaland, India, every December.
• It is named after the hornbill bird, which is a symbol of the state.
• This festival plays a crucial role in reviving, protecting, and sustaining the rich culture and traditions of Nagaland.
• It showcases the heritage of Nagaland's 16 tribes through traditional music, dance, food, and crafts.
• The festival attracts tourists from all over the world, promoting cultural exchange and tourism in the region.

Additional Information

• Nagaland is known for its diverse indigenous tribes, each with its own unique culture and traditions.
• The Hornbill Festival is often referred to as the "Festival of Festivals" in Nagaland.
• It is organized by the State Tourism and Art & Culture Departments and is held at the Naga Heritage Village, Kisama, about 12 km from Kohima, the state capital.
• The festival provides a platform for the tribes to display their traditional arts, dances, folk songs, and games.
• It also includes a variety of other activities such as rock concerts, fashion shows, and traditional wrestling.

The logic followed here is,

Hence, the correct answer is "191".

The correct answer is option 3

Key Points

• Electrolytic Decomposition Reaction involves the decomposition of a compound using electric current.
• Option 3: 2H2O → 2H2 + O2 is an example of electrolytic decomposition where water is decomposed into hydrogen and oxygen gases by passing an electric current through it.
• Other options represent different types of decomposition reactions but not electrolytic decomposition.

Additional Information

• In electrolytic decomposition, the electrolyte is usually in a molten or dissolved state to allow the flow of ions and electric current.
• This process is used in various applications such as electrolysis of water for hydrogen production, electrorefining, and electroplating.
• Electrolytic decomposition is distinct from thermal decomposition, which requires heat, and photochemical decomposition, which requires light.

The given numbers are: (Left) 86547231 (Right)

If 1 is added to each odd digit and 1 is subtracted from each even digit in the number, we get → (Left) 75638142 (Right)

Digit which is third from the left → 6

Digit which is third from the right → 1

Difference between the digits = (6 - 1) = 5

Hence, the correct answer is "5".

The correct answer is marketed surplus

Key Points

• The portion of agricultural product that is sold by farmers in the market is popularly known as marketed surplus.
• Marketed surplus refers to the quantity of produce that is sold off by the farmers after meeting their own consumption needs.
• This surplus is crucial as it forms the basis of the agricultural supply in the market and affects the overall food security and economy.
• Understanding marketed surplus helps in planning and policy-making for agricultural marketing, pricing, and storage.

Additional Information

• Marketed surplus is different from marketable surplus, which is the total quantity of produce that can be sold in the market after accounting for storage, wastage, and other losses.
• The concept of marketed surplus is significant for understanding the market dynamics and the income of farmers.
• Policies to improve the marketed surplus can include better storage facilities, efficient transportation, and fair pricing mechanisms.
• Accurate data on marketed surplus helps in framing agricultural policies and ensuring that farmers get a fair price for their produce.

Shortcut Trick

For parallel lines, the sum of interior angles on the same side of the transversal is always 180°.

m∠1 + m∠2 = 180°

35° + m∠2 = 180°

m∠2 = 180° − 35° = 145°

∴ The correct answer is 145°.

Alternate Method

Given:

m∠1 = 35°

∠1 and ∠2 are consecutive interior angles.

Formula Used:

Sum of consecutive interior angles = 180°

Calculations:

⇒ m∠1 + m∠2 = 180°

⇒ 35° + m∠2 = 180°

⇒ m∠2 = 180° − 35°

⇒ m∠2 = 145°

∴ The correct answer is 145°.

Additional Information

Corresponding Angles

When two parallel lines are cut by a transversal, the

Shortcut Trick Apply the direct relation: Median = (Mode + 2 × Mean) ÷ 3 Median = (23 + 2 × 65) ÷ 3 Median = (23 + 130) ÷ 3 = 153 ÷ 3 Median = 51 ∴ The correct answer is 51.

Alternate Method Given: Mean = 65 Mode = 23 Formula Used: The Empirical Formula relating the three measures of central tendency is: Mode = 3 × Median − 2 × Mean

Calculations: ⇒ 23 = 3 × Median − 2 × 65 ⇒ 23 = 3 × Median − 130 ⇒ 3 × Median = 23 + 130 ⇒ 3 × Median = 153 ⇒ Median = 153 ÷ 3 ⇒ Median = 51 ∴ The correct answer is 51.

Additional Information Empirical Relationship In a moderately skewed distribution, the distance between mean and median is about one-third of the distance between mean and mode. Symmetrical Distribution For a perfectly symmetrical frequency distribution (like a Normal Distribution), the values of Mean, Median, and Mode are all equal (Mean = Median = Mode). Skewness Property If Mean > Median > Mode, the distribution is positively skewed. If Mean < Median < Mode, it is negatively skewed.

Shortcut Trick

Identify the signs of the cross-product terms in the expression: −6ab, +6bc, and −2ac.

The term +6bc is positive, which implies that b and c must have the same sign.

The terms −6ab and −2ac are negative, which implies that a must have the opposite sign of b and c.

Looking at the options, only (a − 3b − c)² satisfies these conditions (positive a, negative b and c).

∴ The correct answer is (a − 3b − c)².

Alternate Method

Given Expression: a² + 9b² + c² − 6ab + 6bc − 2ac

Formula Used: (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

We need to represent the given terms as squares and pairs:

⇒ x² = a² → x = a

⇒ y² = 9b² = (−3b)² → y = −3b (chosen negative to match the −6ab term)

⇒ z² = c² = (−c)² → z = −c (chosen negative to match the −2ac and +6bc terms)

Now, verify the cross-products:

⇒ 2xy = 2 × a × (−3b) = −6ab

⇒ 2yz = 2 × (−3b) × (−c) = +6bc

⇒ 2zx = 2 × a × (−c) = −2ac

All terms match the original expression, so:

⇒ a² + 9b² + c² − 6ab + 6bc − 2ac = (a + (−3b) + (−c))²

⇒ (a − 3b − c)²

∴ The correct answer is (a − 3b − c)².

Additional Information

Square of a Trinomial

The general expansion is (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca. The sign of the squared terms is always positive for real numbers.

Sign Convention

When one or more variables are negative, the sign of the product terms (ab, bc, ca) changes accordingly. For example, (a − b + c)² = a² + b² + c² − 2ab − 2bc + 2ca.

Perfect Square Identification

To identify a perfect square trinomial, check if the square root of the squared terms, when multiplied by 2 in pairs, matches the remaining terms of the expression.

The correct answer is 1.03, towards.

Key Points

• The refractive index of a medium is a measure of how much the speed of light is reduced when it travels through that medium compared to a vacuum.
• The refractive index of turpentine oil is given as 1.47, and the refractive index of glass is given as 1.52.
• The refractive index of glass with respect to turpentine oil is calculated using the formula:
  

Refractive index (glass w.r.t. turpentine oil) = (Refractive index of glass) / (Refractive index of turpentine oil) = 1.52 / 1.47 ≈ 1.03.

• When light travels from a medium with a lower refractive index (turpentine oil) to a medium with a higher refractive index (glass), it bends towards the normal. This is because the speed of light decreases as it enters the denser medium (glass).
• Hence, the correct refractive index is 1.03, and the light bends towards the normal.

Additional Information

• Refractive Index:
• The refractive index is a dimensionless quantity and is a fundamental property of transparent materials.
• It is defined as the ratio of the speed of light in a vacuum to the speed of light in the given medium. Formula: n = c/v, where c is the speed of light in a vacuum, and v is the speed of light in the medium.
• Snell's Law:
• Snell's Law governs the refraction of light as it passes between two media with different refractive indices. It states:
  

n₁ sinθ₁ = n₂ sinθ₂, where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction, respectively.

• If n₂ > n₁, the light bends towards the normal. If n₂ < n₁, the light bends away from the normal.
• Practical Applications of Refractive Index:
• Used in designing lenses for spectacles, cameras, and microscopes to control the bending of light.
• Helps in determining the purity of liquids like oils and alcohols based on their refractive indices.
• Plays a crucial role in fiber optics technology for efficient signal transmission.

Important Points

• Refractive Index of Common Materials:
• Vacuum: 1 (absolute reference).
• Air: Approximately 1.0003 (close to vacuum).
• Water: 1.33.
• Glass: Varies between 1.5 to 1.9 depending on the type of glass.
• Bending of Light:
• Light bends towards the normal when it enters a denser medium (higher refractive index).
• Light bends away from the normal when it enters a rarer medium (lower refractive index).
• Critical Angle and Total Internal Reflection:
• The critical angle is the angle of incidence beyond which light is totally reflected back into the denser medium.
• This phenomenon is used in optical fibers and prism-based instruments.

The correct answer is less than 1, erect.

Key Points

• The focal length of the concave lens is –20 cm (negative for concave lens).
• The object is placed at a distance of 10 cm (object distance u = –10 cm). Using the lens formula: 1/f = 1/v - 1/u.
• Substituting values: 1/(-20) = 1/v - 1/(-10). Solving for v, we get the image distance v = -6.67 cm (negative, meaning the image is virtual and formed on the same side as the object).
• The magnification (m) is given by: m = -v/u. Substituting the values: m = -(-6.67)/(-10) = 0.667, which is less than 1.
• The image is virtual, erect, and diminished (as magnification is less than 1).

Additional Information

• Concave Lens:
• Also known as a diverging lens.
• Always forms a virtual, erect, and diminished image for any object placed in front of it.
• Has a negative focal length.
• Lens Formula:
• 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
• Sign convention: For concave lenses, focal length is negative, object distance is negative when the object is in front of the lens, and image distance is negative for virtual images.
• Magnification:
• m = -v/u. The magnification indicates the size and orientation of the image.
• For concave lenses, the magnification is always less than 1 (diminished) and positive for virtual, erect images.
• Virtual Images:
• Formed when the rays diverge after passing through the lens, but they appear to converge on the same side of the object.
• Always upright and smaller than the object for concave lenses.

The correct answer is Option 1

Key Points

• Butane and 2-methyl propane are isomers of each other, meaning they have the same molecular formula but different structural formulas.
• An isomeric pair consists of two compounds that share the same molecular formula but differ in the arrangement of atoms within the molecules.
• Butane (C₄H₁₀) and 2-methyl propane (C₄H₁₀) both have four carbon atoms and ten hydrogen atoms, but their structures are different.
• In butane, the carbon atoms are arranged in a straight chain, whereas in 2-methyl propane, the carbon atoms form a branched chain.

Additional Information

• Isomers are important in chemistry because they can have significantly different chemical and physical properties despite having the same molecular formula.
• There are different types of isomers including structural isomers, geometric isomers, and stereoisomers. Butane and 2-methyl propane are examples of structural isomers.
• The concept of isomerism is crucial in the study of organic chemistry and is widely applied in the synthesis and analysis of chemical compounds.

The correct answer is National Bank for Agriculture and Rural Development

Key Points

• National Bank for Agriculture and Rural Development (NABARD) is an apex development financial institution in India.
• It was established on 12 July 1982 by a special act of the Parliament.
• NABARD is responsible for the development of the small industries, cottage industries, and any other such village or rural projects.
• The organization provides financial support and policy guidance to various institutions in the rural sector.
• NABARD also plays a crucial role in implementing government schemes and initiatives aimed at rural development.

Additional Information

• The establishment of NABARD was recommended by the B. Sivaraman Committee (Committee to Review Arrangements for Institutional Credit for Agriculture and Rural Development).
• NABARD's headquarters is located in Mumbai, Maharashtra.
• The institution also focuses on innovation and technology in agriculture, promoting sustainable and inclusive growth.
• NABARD's initiatives include microfinance, financial inclusion, and capacity building programs for rural communities.
• It also supports agricultural research and development to enhance productivity and efficiency in the sector.

Formula Used:

To solve this, we need to perform operations on fractions step by step.

Calculation:

We have,

⇒ $\frac{2}{3} + \frac{1}{1 + \frac{4}{5}} - \frac{5}{6}$

First, simplify 1/[(1 + 4/5]

⇒ 1 + 4/5 = 5/5 + 4/5 = 9/5

⇒1)/(9/5) = 5/9

So, the expression becomes:

⇒ 2/3 + 5/9 - 5/6

Find the common denominator (LCM of 3, 9, and 6 is 18):

⇒ (2 × 6)/(3 × 6) + (5 × 2)/(9 × 2) - (5 × 3)/(6 × 3)

⇒ 12/18 + 10/18 - 15/18

Combine the fractions:

⇒ (12 + 10 - 15)/(18)

⇒ 7/18

Hence, the correct answer is option 2 i.e : 7/18.

The logic followed here is,

Conclusions:

I. No wire is a pipe → True (All wires are switches and no switch is a pipe implies that no wire is a pipe).

II. No bulb is a switch → True (All bulbs are pipes, and no switch is a pipe implies that no bulb is a switch).

Hence, the correct answer is "Both conclusions I and II follow".

The correct answer is Article 324

Key Points

• Article 324 of the Indian Constitution envisages the Election Commission of India (ECI).
• The Election Commission of India is a constitutional body established to conduct and regulate elections in the country.
• It ensures free and fair elections to the Parliament, State Legislatures, and the offices of the President and Vice-President in India.
• The ECI operates under the authority of the Constitution per Article 324, ensuring the electoral process is transparent and impartial.

Additional Information

• The Election Commission of India was established on 25th January 1950.
• Article 324(1) states that the superintendence, direction, and control of the preparation of the electoral rolls and the conduct of elections shall be vested in the Election Commission.
• The ECI is an autonomous constitutional authority responsible for administering election processes in India at both the national and state levels.
• The Commission consists of the Chief Election Commissioner and such number of other Election Commissioners as the President may from time to time fix.
• The Chief Election Commissioner and the Election Commissioners are appointed by the President of India.
• The ECI ensures the model code of conduct is followed by political parties and candidates during elections.
• The Constitution of India mandates that elections to the House of the People and to the Legislative Assemblies of States be held on the basis of adult suffrage.

The correct answer is Option 1

Key Points

• Group 18 of the periodic table represents elements with zero valency.
• This group is also known as the noble gases which include Helium, Neon, Argon, Krypton, Xenon, and Radon.
• Noble gases are characterized by their inert nature due to having a complete valence shell, making them highly stable and unlikely to react with other elements.
• These elements are used in various applications such as lighting, welding, and in inert gas shields for arc welding.

Additional Information

• The concept of valency is crucial in understanding how elements interact and bond with each other to form compounds.
• Elements in Group 18 are often used in scientific experiments where a non-reactive environment is required.
• Due to their stability, noble gases are also used in the preservation of historical documents and in the filling of incandescent light bulbs to prevent oxidation of the filament.
• Helium, a noble gas, is also utilized in cryogenics and as a cooling medium for nuclear reactors.

According to the given information,

1) Beena is sitting to the immediate left of Ketaki. 

2) Only Ketaki is sitting between Beena and Elisa.

3) Hema is sitting to the immediate right of Zoya.

Here, we can see that Zoya is sitting to the immediate right of Elisa.

Hence, the correct answer is "Zoya".

The correct answer is Nepal

Key Points

• India and Nepal agreed to line up a joint task force on a "proposal to construct a hydropower project" from investments of both countries in February 2022.
• This initiative aims to enhance bilateral cooperation in the energy sector and promote sustainable hydropower development.
• The task force will explore potential projects, investment opportunities, and address any challenges in the implementation of such projects.
• This agreement further strengthens the longstanding relationship between India and Nepal, particularly in the area of energy cooperation.

Additional Information

• India and Nepal share a long history of cooperation in the hydropower sector, with several joint projects already in operation or under development.
• The collaboration between the two countries in the energy sector is seen as a key driver for economic growth and development in the region.
• Hydropower projects are crucial for Nepal as they provide a sustainable and renewable source of energy, contributing to the country's energy security.
• For India, such collaborations help in meeting its growing energy demands and also strengthen regional ties.
• The agreement to form a joint task force signifies a commitment to work together towards mutual benefits and addressing common challenges in the hydropower sector.

The correct answer is Mangrove Forests

Key Points

• Mangrove Forests are the most commonly home to the Royal Bengal tiger.
• The Sundarbans, which is the largest mangrove forest in the world, is the primary habitat of the Royal Bengal tiger.
• Mangrove forests provide a unique ecosystem that supports a diverse range of wildlife, including the Bengal tiger.
• The dense mangrove vegetation and the intricate network of waterways create an ideal environment for the tigers to thrive.

Additional Information

• The Sundarbans is a UNESCO World Heritage Site and is located in the delta region of Padma, Meghna, and Brahmaputra river basins.
• It spans across India and Bangladesh and is renowned for its unique flora and fauna.
• Conservation efforts are in place to protect the Royal Bengal tiger and its habitat in the Sundarbans.
• The mangrove ecosystem also acts as a natural barrier against coastal erosion and storm surges, providing environmental protection to the region.

Shortcut Trick

Surface area of a sphere = 4 × π × r²

For r = 7 cm, Area = 4 × (22/7) × 7 × 7

Area = 88 × 7 = 616 cm²

∴ The correct answer is 616 cm².

Alternate Method

Given:

Radius (r) = 7 cm

π = 22/7

Formula Used:

Total Surface Area (A) = 4πr²

Calculations:

⇒ Surface Area = 4 × (22/7) × (7)²

⇒ Surface Area = 4 × (22/7) × 7 × 7

⇒ Surface Area = 4 × 22 × 7

⇒ Surface Area = 88 × 7

⇒ Surface Area = 616 cm²

∴ The correct answer is 616 cm².

Additional Information

Volume of Sphere

The amount of space occupied by a sphere is given by V = (4/3)πr³.

Hemisphere Properties

For a hemisphere, Curved Surface Area = 2πr² and Total Surface Area = 3πr².

Circle Area vs Sphere Area

The surface area of a sphere is exactly 4 times the area of its great circle (πr²).

The correct answer is continues to rise

Key Points

• As long as MP (marginal product) remains higher than the average product (AP), the average product continues to rise.
• This is because the marginal product contributes positively to the average product when it is higher than the current average.
• Once the marginal product falls below the average product, the average product will start to decline.
• The relationship between marginal product and average product is crucial in understanding the stages of production and efficiency in economics.
• Monitoring these metrics helps businesses optimize their production processes and resource allocation.

Additional Information

• Marginal Product (MP) is the additional output produced by adding one more unit of a specific input, keeping all other inputs constant.
• Average Product (AP) is the total output produced divided by the number of units of the input used.
• The Law of Diminishing Marginal Returns states that as more units of an input are added, the additional output produced by each additional unit will eventually decrease.
• Understanding MP and AP helps in determining the most efficient level of production and the optimal combination of inputs.

Shortcut Trick

Put the values of x = 7 and y = 3 directly into the expression.

Expression = (7² + 3²) ÷ (7² − 3²)

Expression = (49 + 9) ÷ (49 − 9) = 58 ÷ 40

Simplified Ratio = 29 ÷ 20

∴ The correct answer is 29 ∶ 20.

Alternate Method

Given: x ∶ y = 7 ∶ 3

Formula Used: Ratio Substitution Method

⇒ Let x = 7k and y = 3k

⇒ (x² + y²) = (7k)² + (3k)² = 49k² + 9k² = 58k²

⇒ (x² − y²) = (7k)² − (3k)² = 49k² − 9k² = 40k²

⇒ Required Ratio = 58k² ∶ 40k²

⇒ Required Ratio = 58 ∶ 40 = 29 ∶ 20

∴ The correct answer is 29 ∶ 20.

Additional Information

Componendo and Dividendo

If a/b = c/d, then (a+b)/(a−b) = (c+d)/(c−d). This rule is useful for simplifying expressions involving fractions and ratios.

Homogeneous Functions

In expressions where the sum of powers in every term of the numerator and denominator is the same, constant k cancels out, allowing direct substitution of ratio values.

Duplicate Ratio

The duplicate ratio of a ∶ b is a² ∶ b². Here, x² ∶ y² = 49 ∶ 9.

Shortcut Trick

Net Profit or Loss% = a + b + (a × b) ÷ 100

Where a is the markup percentage (+26) and b is the discount percentage (−13).

Net Gain% = 26 − 13 + (26 × (−13)) ÷ 100

Net Gain% = 13 − (338 ÷ 100) = 13 − 3.38 = 9.62%.

∴ The correct answer is 9.62.

Alternate Method

Given: Markup Percentage = 26%, Discount Percentage = 13%.

Formulas: Marked Price (MP) = CP × (100 + Markup%) ÷ 100 | Selling Price (SP) = MP × (100 − Discount%) ÷ 100 | Gain% = (SP − CP) ÷ CP × 100

⇒ Let Cost Price (CP) = 100.

⇒ Marked Price (MP) = 100 + 26% of 100 = 126.

⇒ Selling Price (SP) = 126 − 13% of 126.

⇒ SP = 126 − 16.38 = 109.62.

⇒ Gain% = (109.62 − 100) ÷ 100 × 100 = 9.62%.

∴ The correct answer is 9.62.

Additional Information

Successive Percentage Change

When a value is increased by x% and then decreased by y%, the net change is given by [x − y − (xy/100)]%.

Relationship between CP, MP, and SP

The ratio of CP to MP can be expressed as: CP/MP = (100 − Discount%)/(100 + Profit%).