RRB Group D Previous Year Paper (Held on: 11 Oct 2022 Shift 1)

Given series:

B Z C T B Z T E S B C Z T W A Z T F Z T U K R B Z T V

Condition to be checked:

Z immediately followed by T but not immediately preceded by B.

(not)B → Z → T

B Z C T B Z T E S B C Z T W A Z T F Z T U K R B Z T V

Thus, there are three such pattern (C Z T,  A Z T, F Z T) that is following the above conditions.

Hence, the correct answer is "Option 4".

Mistake Points

Immediately preceded by means immediately before or to come just before.

Immediately followed by means immediately after or to come just after.

The correct answer is India.

Key Points

• India reached this milestone in February 2022, becoming the first nation to play 1000 ODIs. This is a testament to the immense popularity of cricket in India and the country's consistent participation in international cricket.  India's journey to 1000 ODIs has been filled with memorable moments, including two World Cup victories (1983 and 2011) and numerous other triumphs. The sheer volume of matches played reflects the passion for the game in India and the constant demand for cricket entertainment.  This achievement also highlights the BCCI's (Board of Control for Cricket in India) role in organizing and promoting ODI cricket within the country and internationally.  India's reaching this milestone is a significant event in the history of ODI cricket.

Additional Information

• Australia:
• While Australia has a very long and storied ODI history and has played a massive number of ODIs, they were not the first to reach the 1000-match mark.
• They have won the Cricket World Cup multiple times and have been a dominant force in the format for many years.
• Australia's contribution to ODI cricket is immense, but in this particular race, they were second.
• Pakistan:
• Pakistan is another cricketing nation with a rich ODI history.
• They have produced many world-class players and have had their share of success in the format.
• However, they were not the first to reach the 1000 ODI milestone.
• While they have played a significant number of ODIs, they haven't yet reached the same number as India.
• Sri Lanka:
• Sri Lanka, while being a strong ODI team and having won the World Cup once, has played fewer ODIs than both India and Australia.
• They have a dedicated fan base and have contributed many exciting moments to ODI cricket.
• However, they were not even close to being the first to the 1000 ODI mark.

The correct answer is 1997.

Key Points

• The system of ad hoc treasury bills to finance the budget deficit was discontinued in India with effect from April 1, 1997.
• Ad Hoc Treasury Bills?
• Ad hoc treasury bills were a type of short-term debt instrument issued by the Reserve Bank of India (RBI) on behalf of the Indian government to finance its budget deficit. Essentially, they were a way for the government to borrow money from the RBI to cover the gap between its spending and its revenue. These bills were issued "on tap," meaning the government could obtain them whenever needed, and the interest rates were relatively low.
• The system of ad hoc treasury bills had several drawbacks:
• Automatic Monetization of Deficit:
• It led to the automatic monetization of the budget deficit, meaning the RBI essentially printed money to finance the government's spending. This could fuel inflation and undermine the central bank's ability to control monetary policy.
• Fiscal Indiscipline: T
• he easy availability of funds through ad hoc treasury bills could encourage fiscal indiscipline on the part of the government, as it reduced the pressure to manage spending and revenue effectively.
• Weakening of Monetary Policy:
• The system limited the RBI's independence and its ability to conduct monetary policy effectively. The central bank's primary role is to control inflation and maintain price stability, but the need to accommodate the government's borrowing needs could conflict with these objectives.
• Replaced
• The system of ad hoc treasury bills was replaced by Ways and Means Advances (WMA) with effect from April 1, 1997. WMA is a temporary overdraft facility provided by the RBI to the government to meet temporary mismatches in its receipts and expenditure. Unlike ad hoc treasury bills, WMA is not a source of financing the government's deficit. It is a short-term mechanism to help the government manage its cash flow.

The correct answer is 0°.

Key Points

• When a ray of light passes through the center of curvature (C) of a spherical mirror (whether concave or convex), it strikes the mirror perpendicularly to the surface at the point of incidence.
• This is a crucial point to understand.
• The normal to the spherical mirror at any point on its surface is a line that passes through the center of curvature.
• Since the incident ray is already along this normal (because it passes through C), the angle of incidence (the angle between the incident ray and the normal) is zero degrees.
• The law of reflection states that the angle of incidence is equal to the angle of reflection.
• Therefore, if the angle of incidence is 0 degrees, the angle of reflection must also be 0 degrees.
• This means the reflected ray will travel along the same path as the incident ray, but in the opposite direction.
• Essentially, the ray retraces its path back through the center of curvature.
• Imagine a line drawn from the center of curvature to any point on the mirror's surface.
• This line is perpendicular to the mirror's surface at that point.
• If a ray of light travels along this line (i.e., passes through the center of curvature), it hits the mirror at a 90-degree angle (normal incidence).
• Because the angle of incidence is zero, the angle of reflection is also zero.
• The reflected ray will then travel back along the same line, again passing through the center of curvature.

Given Statement: L ≤ H = P > O > D ≥ S = U

Now,

Conclusions:

Option 1: L ≤ P → True (L ≤ H = P It gives L ≤ P)

Option 2: U ≥ D → False (D ≥ S = U It gives D ≥ U)

Option 3: L > D → False (L ≤ H = P > O > D, there is no direct relation between L and D)

Option 4: L > O → False (L ≤ H = P > O, there is no direct relation between L and O)

Hence, the correct answer is "Option 2".

The correct answer is Kerela.

Key Points

• Kerala has the largest Christian population among Indian states, with 6.14 million Christians, making up 18.38% of the state's population, followed by Tamil Nadu with 4.41 million Christians (6.12% of the state population).
• While Kerala has the highest absolute number of Christians, states like Nagaland, Mizoram, and Meghalaya have a higher proportion of Christians in their population.
• Christianity is the third largest religion in India, with 27.8 million followers in 2011, constituting 2.3% of the total population.
• The Christian population is distributed across the country, with significant concentrations in the Northeast, South, and some parts of Western India.
• The 2011 Census data provides valuable insights into the religious demographics of India, highlighting the diversity and distribution of various faiths across the country.

Additional Information

• The Census of India 2011, conducted in two phases, provided a comprehensive snapshot of India's population, revealing demographic, social, and economic data, with key findings including a population of 1.21 billion, a sex ratio of 940 females per 1000 males, a literacy rate of 74%, and diverse religious and linguistic distributions.

The correct answer is Real wage rate is equal to the Marginal Productivity of Labour.

Key Points

• The real wage rate represents the purchasing power of wages, adjusted for inflation.
• It reflects the actual amount of goods and services a worker can buy with their earnings, rather than just the nominal value of their wages.
• Understanding the real wage rate is crucial for assessing living standards and the economic well-being of workers.
• While nominal wages might increase over time, if inflation rises faster, real wages can actually decline, meaning workers can afford less despite earning more in monetary terms.

Additional Information

• Calculating the real wage rate typically involves using a price index, such as the Consumer Price Index (CPI), to adjust nominal wages.
• The CPI measures changes in the price level of a basket of goods and services consumed by households.
• By dividing the nominal wage by the CPI and multiplying by 100, we can express real wages in constant dollars, effectively removing the impact of inflation.
• This allows for meaningful comparisons of purchasing power over different time periods.
• The real wage rate is a key indicator of economic health.
• Rising real wages generally suggest improved living standards, as workers have greater purchasing power.
• Conversely, declining real wages can lead to economic hardship and social unrest.
• Governments and policymakers often monitor real wage trends to gauge the effectiveness of their economic policies and to identify potential issues related to income inequality and poverty.

Shortcut Trick

Sum of ages after 5 years = 86 years.

Sum of present ages = 86 − (5 × 2) = 76 years.

Ratio of Arun to Uncle = 1 : 3 (Total parts = 4).

Arun's present age = (1 ÷ 4) × 76 = 19 years.

∴ The correct answer is 19 years.

Alternate Method

Given:

Ratio of Arun to Uncle = 1/3

Sum of ages after 5 years = 86

Let the present age of Arun be x and Uncle be 3x.

⇒ After 5 years, Arun's age = x + 5

⇒ After 5 years, Uncle's age = 3x + 5

⇒ (x + 5) + (3x + 5) = 86

⇒ 4x + 10 = 86

⇒ 4x = 76

⇒ x = 19

∴ The correct answer is 19 years.

Additional Information

Age Ratio Concepts

If the ratio of ages is a:b, their ages can be assumed as ax and bx. The difference between ages remains constant throughout life.

Sum of Ages after 'n' years

If there are 'k' people, the sum of their ages after 'n' years increases by (k × n).

Average Age

The average age of a group also increases by exactly 'n' years after 'n' years, provided no one leaves or joins the group.

The correct answer is Iron.

Key Points

• Iron is absolutely essential for the formation of human blood. It's the core component of hemoglobin, the protein within red blood cells responsible for oxygen transport.  Each hemoglobin molecule contains four iron atoms, and these are the very sites where oxygen molecules bind.  Without sufficient iron, the body cannot produce enough hemoglobin, leading to iron-deficiency anemia, characterized by fatigue, weakness, and shortness of breath due to reduced oxygen delivery to tissues.
• Here's the chemical information about iron:
• Atomic Number: 26 (meaning iron has 26 protons in its nucleus).
• Atomic Mass: Approximately 55.845 amu (atomic mass units). This is the average mass of an iron atom.
• Electronic Configuration: [Ar] 3d⁶ 4s². This notation describes how electrons are arranged in the atom's energy levels and orbitals. "[Ar]" represents the electron configuration of argon, the noble gas preceding iron. The 3d⁶ 4s² part indicates that iron has 6 electrons in its 3d orbitals and 2 electrons in its 4s orbital.
• Iron's ability to readily lose and gain electrons (due to its electronic configuration) is crucial for its role in hemoglobin. The iron atom in hemoglobin exists in two oxidation states: Fe²⁺ (ferrous) and Fe³⁺ (ferric). This allows it to reversibly bind and release oxygen.  The change in oxidation state of Iron is responsible for the red colour of blood.

Additional Information

• Nickel
• ​(Atomic Number: 28, Atomic Mass: 58.693 amu, Electronic Configuration: [Ar] 3d⁸ 4s²): Nickel plays some biological roles, including involvement in certain enzymes. However, it's not a direct constituent of hemoglobin or directly involved in the core process of oxygen transport in blood. Its role in human physiology is less central than iron's.
• Copper
• ​(Atomic Number: 29, Atomic Mass: 63.546 amu, Electronic Configuration: [Ar] 3d¹⁰ 4s¹): Copper is a trace mineral essential for various functions, including enzyme activity, iron metabolism, and connective tissue formation.  It plays an indirect role in blood formation by aiding iron absorption and utilization. Copper-containing enzymes are involved in hemoglobin synthesis.  However, copper is not a direct component of hemoglobin itself.
• Cobalt
• ​(Atomic Number: 27, Atomic Mass: 58.933 amu, Electronic Configuration: [Ar] 3d⁷ 4s²): Cobalt is a component of vitamin B12 (cobalamin), which is crucial for red blood cell production, DNA synthesis, and the maturation of red blood cells in the bone marrow.
• A deficiency in vitamin B12 (and thus cobalt) can lead to megaloblastic anemia.  However, like copper, cobalt's role is indirect. It's necessary for healthy red blood cell production, but it's not a constituent of hemoglobin.  Iron is the element that directly binds oxygen

The correct answer is Bishnoi.

Key Points

• The Bishnoi community in Rajasthan is renowned for its deep commitment to environmental conservation, particularly the protection of forests and wildlife.
• Their philosophy is rooted in the teachings of Guru Jambheshwar, who in the 15th century laid down 29 tenets (bish means twenty, noi means nine) that guide their lives.
• These principles emphasize living in harmony with nature, protecting animals, and conserving trees, especially the Khejri tree (Prosopis cineraria), which is vital in the arid landscape of Rajasthan.
• The Bishnois are particularly famous for their unwavering protection of the blackbuck antelope (Antilope cervicapra).
• Throughout history, there have been numerous instances where Bishnois have risked their lives to prevent the felling of trees and the poaching of animals, demonstrating their extraordinary dedication to conservation.
• The Chipko movement of the 1970s, although more prominent in Uttarakhand, was inspired by the Bishnoi's historical resistance to deforestation.
• The Bishnoi community's legacy is a powerful example of how cultural beliefs and religious principles can drive environmental stewardship and inspire others to protect nature.

Additional Information

• Bhil:
• The Bhil are a large tribal group in India, including Rajasthan.
• They have a rich cultural heritage and a traditional way of life closely connected to the forests.
• They possess valuable traditional knowledge of local ecosystems and have a deep respect for nature.
• However, their primary focus is not specifically on the conservation of forests and wildlife in the way the Bishnois are.
• Their traditions encompass a wider range of cultural practices and livelihoods.
• Chhipa:
• The Chhipa are a community traditionally involved in textile printing and dyeing.
• They are an important part of Rajasthan's cultural heritage, contributing significantly to the region's artistic traditions.
• However, their primary focus is on their craft and trade, not specifically on environmental conservation.
• Banjara:
• The Banjara are a nomadic trading community historically known for their travels across India.
• Their traditional lifestyle involved moving with their caravans, trading goods between different regions.
• While they have a connection to the land and its resources, their main focus was trade and livelihood, not specifically the conservation of forests and wildlife.

Given:

8.99 + 17.99 - 3.99 × 2.99 = ?

Formula used:

Basic Arithmetic Operations

Calculation:

8.99 + 17.99 - 3.99 × 2.99 = ?

⇒ 8.99 + 17.99 - (3.99 × 2.99)

⇒ 8.99 + 17.99 - 11.92

⇒ 26.98 - 11.92

⇒ 15.06

∴ The correct answer is option (3).

Shortcut Trick8.99 + 17.99 - 3.99 × 2.99 = ?

Closest approximate value :- 

8.99 = 9, 17.99 = 18, 3.99 = 4, 2.99 = 3.

⇒ 9 + 18 - 4 × 3 = ?

⇒ 27 - 12 = 15.

Shortcut Trick

Net deviation from the Arithmetic Mean is always zero: ∑ f_i(x_i − Mean) = 0.

Deviation of 3 from 4 is (3 − 4) = −1. Deviation of 7 from 4 is (7 − 4) = +3.

Total deviation: K(−1) + (K − 2)(+3) = 0

⇒ −K + 3K − 6 = 0 ⇒ 2K = 6 ⇒ K = 3.

∴ The correct answer is 3.

Alternate Method

Given:

Values (x): 3, 7

Frequencies (f): K, (K − 2)

Arithmetic Mean (χ): 4

Formula Used:

Arithmetic Mean = (∑ f_ix_i) ÷ (∑ f_i)

Calculations:

⇒ Mean = [3 × K + 7 × (K − 2)] ÷ [K + (K − 2)]

⇒ 4 = (3K + 7K − 14) ÷ (2K − 2)

⇒ 4 × (2K − 2) = 10K − 14

⇒ 8K − 8 = 10K − 14

⇒ 14 − 8 = 10K − 8K

⇒ 6 = 2K

⇒ K = 3

∴ The correct answer is 3.

Additional Information

Properties of Arithmetic Mean

The sum of the deviations of a set of observations from their arithmetic mean is always zero, i.e., ∑(x_i − χ) = 0.

Weighted Mean Formula

When values x₁, x₂, ..., x_n have weights w₁, w₂, ..., w_n, the weighted mean is calculated as (∑w_ix_i) ÷ ∑w_i.

Effect of Change of Origin and Scale

If each observation is increased by a constant a, the mean increases by a. If each observation is multiplied by h, the mean is multiplied by h.

Given: Six friends are sitting around a circular table facing the centre. 

1) Gabriel is sitting second to the right of Suchita.

2) Sourav is an immediate neighbour of both Gabriel and Dhruv.

3) Ritesh is sitting second to the right of Trinabh.

Thus, according to the final arrangement, Suchita is an immediate neighbour of both Ritesh and Trinabh.

Hence, "Option 1" is the correct answer.

Shortcut Trick

Total volume of 3 hemispheres = Volume of 1 new sphere.

3 × (2/3 × π × r³) = 4/3 × π × R³

2 × 2³ = 4/3 × R³ ⇒ 2 × 8 = 4/3 × R³

16 = 4/3 × R³ ⇒ 12 = R³ ⇒ R = ³√12

∴ The correct answer is ³√12 unit.

Alternate Method

Given: Radius of each hemisphere (r) = 2 units. Number of hemispheres = 3.

Formula Used: Volume of Hemisphere = 2/3πr³; Volume of Sphere = 4/3πR³.

Calculations:

⇒ Volume of 3 hemispheres = 3 × [2/3 × π × (2)³]

⇒ Volume of 3 hemispheres = 2 × π × 8 = 16π cubic units

⇒ Let the radius of the new sphere be R.

⇒ Volume of new sphere = 4/3 × π × R³

⇒ 4/3 × π × R³ = 16π

⇒ R³ = (16 × 3) ÷ 4

⇒ R³ = 12

⇒ R = ³√12 units

∴ The correct answer is ³√12 unit.

Additional Information

Recasting Rule

When one or more solid objects are melted and recast into a new shape, the total volume remains constant.

Surface Area of Sphere

The total surface area of a sphere with radius R is given by the formula 4πR².

Hemisphere Properties

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

Given: 9 + 7 ÷ 8 - 4 × 2 = ?

Decoding the given information:

 

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 9 × 7 + 8 ÷ 4 - 2

= 63 + 8 ÷ 4 - 2

⇒ 63 + 2 - 2

= 65 - 2 = 63

Hence, the correct answer is "Option 4".

The correct answer is Sodium bicarbonate (NaHCO3).

Key Points

• Sodium bicarbonate (NaHCO₃) is the scientific name for baking soda.
• It's a chemical compound commonly used in baking and cooking due to its ability to release carbon dioxide gas when heated or combined with an acid.
• This gas creates bubbles that cause dough or batter to rise, giving baked goods a light and airy texture.
• Sodium bicarbonate is also used in various other applications, including as an antacid to relieve heartburn, as a cleaning agent, and in some personal care products.
• It is a white crystalline powder that is soluble in water.
• The chemical reaction that produces carbon dioxide gas when baking soda is used in baking is a reaction between the bicarbonate ion (HCO₃⁻) and an acid.

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Additional Information

• Sodium carbonate (Na₂CO₃):
• Sodium carbonate is also known as washing soda.
• It's a stronger alkali than sodium bicarbonate and is not typically used in baking.
• Instead, it's used in cleaning products and as a water softener.
• It can be irritating to the skin and eyes and is not safe for consumption in the same way baking soda is.
• Chemically, it's a different compound with different properties.
• Sodium chloride (NaCl):
• Sodium chloride is common table salt.
• It's essential for human health in small amounts, but it doesn't have the leavening properties of baking soda.
• It's used primarily for flavoring food.  Chemically, it's an ionic compound formed from sodium and chloride ions, and it plays a very different role in cooking and other applications.
• Sodium sulfate (Na₂SO₄):
• Sodium sulfate is used in some industrial processes, as a drying agent, and sometimes as a laxative.
• It is not used in baking as a leavening agent.
• Chemically, it's a salt formed from sodium ions and sulfate ions.
• Its properties and uses are distinct from those of sodium bicarbonate.

The correct answer is Serena Williams.

Key Points

• Serena Williams is an American tennis legend, widely regarded as one of the greatest female tennis players of all time, who holds the record for the most Grand Slam singles titles won by a woman during the Open Era, with 23 titles.  Here's a deeper look at her remarkable career:
• Dominance in the Open Era: Her 23 Grand Slam singles titles are the most won by any female player since the Open Era began in 1968.
• Grand Slam Breakdown: Serena's Grand Slam titles are distributed across the four majors: 7 Australian Opens, 3 French Opens, 7 Wimbledons, and 6 US Opens.
• Multiple "Serena Slams": She has twice held all four Grand Slam titles simultaneously, a feat known as the "Serena Slam."
• Olympic Gold Medalist: Serena is also a four-time Olympic gold medalist, winning gold in singles (2012) and three times in doubles with her sister, Venus.
• Long Reign at World No. 1: She has held the world No. 1 ranking in singles for a total of 319 weeks, the third-longest reign in women's tennis history.
• Powerful Serve and Groundstrokes: Serena is known for her incredibly powerful serve and aggressive groundstrokes, which have overwhelmed opponents throughout her career.
• Sister Act: Her partnership with her sister, Venus, has been one of the most successful doubles teams in history, winning 14 Grand Slam doubles titles together.
• Impact Beyond the Court: Serena has been a vocal advocate for gender equality and racial justice, using her platform to inspire and empower others.
• Comeback from Childbirth: She returned to professional tennis after a difficult childbirth, demonstrating her resilience and determination.
• 23 Grand Slam Singles Titles: This is the core fact of her legendary status.
• Four Olympic Gold Medals: Highlighting her dominance not just in Slams, but also on the Olympic stage.
• 319 Weeks at World No. 1: Demonstrates her consistent high level of play over many years.
• 14 Grand Slam Doubles Titles (with Venus): Showcases their incredible synergy and success as a doubles team.

The correct answer is Science and Engineering Research Board (SERB).

Key Points

• Science and Engineering Research Board (SERB):
• SERB is a statutory body under the Department of Science and Technology (DST), Government of India.
• Its primary mandate is to promote and fund scientific research in various disciplines of science and engineering.
• SERB's mission aligns perfectly with the question's description:  It aims to improve the quality and global standing of Indian science and engineering through competitive funding.
• SERB supports a wide range of research activities, including basic research, applied research, and translational research.
• It provides grants to individual researchers, research groups, and institutions.
• SERB also fosters international collaborations and supports the development of research infrastructure.
• The organization emphasizes peer review and merit-based selection in its funding process to ensure that the most promising research proposals receive support.  SERB plays a crucial role in nurturing scientific talent and driving innovation in India.
• It strives to create a vibrant research ecosystem that can contribute to the nation's economic and social development.  SERB's funding mechanisms are designed to be flexible and responsive to the evolving needs of the research community.
• It actively seeks to identify and support emerging areas of research that have the potential to address critical challenges facing the country.
• SERB also works to promote science communication and outreach to enhance public understanding of science.

Additional Information

• Department of Science & Industrial Research (DSIR):
• The Department of Scientific and Industrial Research (DSIR) is a part of the Ministry of Science and Technology in the Indian government.
• While DSIR is involved in promoting scientific and industrial research, its focus is broader than just funding.
• It plays a key role in formulating policies related to science and technology, promoting technology transfer, and fostering collaboration between research institutions and industry.
• DSIR also supports autonomous research institutions and public sector undertakings.
• While funding is a component of its activities, DSIR's mandate encompasses a wider range of functions related to scientific and industrial development.  It plays a crucial role in linking research with industrial applications and promoting innovation.
• DSIR also works to create a conducive environment for research and development in the country.
• It supports the development of scientific infrastructure and promotes scientific temper among the public.
• While DSIR contributes significantly to the growth of Indian science and technology, SERB's specific focus on competitive research funding makes it the more accurate answer to the question.
• Department of Scientific Research:
• There isn't a specific Indian government department officially named "Department of Scientific Research."
• The Department of Science and Technology (DST) is the primary government body responsible for formulating and implementing policies related to science and technology in India.
• The DST plays a crucial role in funding scientific research, supporting research institutions, and promoting scientific temper in the country.
• It works to create a vibrant research ecosystem that can contribute to India's economic and social development.
• The DST also fosters international collaborations in science and technology.
• While the concept of "scientific research" is central to the work of many government departments, there's no single department with that exact name.
• Department of Space (DOS):
• The Department of Space (DOS) is responsible for the Indian space program.
• While the Indian space program involves a significant amount of scientific research and development, the DOS's primary focus is on space-related activities.
• This includes the development of launch vehicles, satellites, and other space technologies.
• The DOS also conducts scientific research related to space, such as astrophysics, planetary science, and remote sensing.
• However, the DOS's mandate is specifically focused on space, whereas the question asks about a more general national research funding agency covering diverse fields of science and engineering.
• ISRO, the Indian Space Research Organisation, functions under the DOS and is responsible for the execution of the Indian space program.
• While the research conducted under the DOS is of high quality, it is primarily directed towards space-related objectives.

According to the given Venn diagram:

The shaded region represents the number of children who play neither with barbie dolls nor with racing cars.

So, the number of children who play neither with barbie dolls nor with racing cars = 41

Hence, the correct answer is "Option 1".

Shortcut Trick

Diameter of the spherical capsule = 3.5 mm

Radius (r) = 3.5 ÷ 2 = 1.75 mm

Volume formula = (4/3) × π × r³

Volume ≈ 1.333 × 3.142 × (1.75)³ ≈ 22.458 mm³

∴ The correct answer is 22.46 mm³.

Alternate Method

Given:

Diameter (d) = 3.5 mm

Radius (r) = d ÷ 2 = 3.5 ÷ 2 = 1.75 mm = 7/4 mm

Formula Used:

Volume of a Sphere = $\frac{4}{3}$ π r³

Calculations:

⇒ Volume = $\frac{4}{3}$ × $\frac{22}{7}$ × (1.75)³

⇒ Volume = $\frac{4}{3}$ × $\frac{22}{7}$ × $\frac{7}{4}$ × $\frac{7}{4}$ × $\frac{7}{4}$

⇒ Volume = $\frac{1}{3}$ × 11 × $\frac{7}{2}$ × $\frac{7}{4}$

⇒ Volume = (11 × 49) ÷ (3 × 2 × 4) = 539 ÷ 24

⇒ Volume ≈ 22.45833...

⇒ Rounding to 2 decimal places, Volume = 22.46 mm³

∴ The correct answer is 22.46 mm³.

Additional Information

Surface Area of a Sphere

The total surface area of a sphere is given by the formula 4πr².

Volume of a Hemisphere

The volume of a hemisphere is exactly half of a sphere: (2/3)πr³.

Relation between Radius and Diameter

Radius (r) is always half of the diameter (d), i.e., r = d/2.

Given:

1(1)/(2) × 22 + 10 ÷ 5 - 2 × 8

Formula used:

BODMAS

Calculation:

1(1)/(2) × 22 + 10 ÷ 5 - 2 × 8

⇒ 1.5 × 22 + 10 ÷ 5 - 2 × 8

⇒ 33 + 2 - 16

⇒ 35 - 16

⇒ 19

∴ The correct answer is option (1).

The correct answer is Lucknow.

Key Points

• River Ganga:
• The River Ganga originates from the Gangotri glacier in Uttarakhand.
• Alaknanda River joins Bhagirathi at Devprayag and from there the river is called Ganga.
• Yamuna(Largest right bank tributary of Ganga), Damodar (Sorrow of Bengal), Ghagra, Gomti, Gandak, Ramganga, Kosi (Sorrow of Bihar), Son, Mahananda are major tributaries of River Ganga.
• It flows through the states of Uttarakhand, Uttar Pradesh, Bihar, Jharkhand, and West Bengal.
• It is a transboundary river, flows through India and Bangladesh.
• The total length of the river is 2525 km

The correct answer is Prasanta Chandra Mahalanobis.

Key Points 

• P.C. Mahalanobis
• P.C. Mahalanobis OBE, FNA, FASc, FRS (29 June 1893– 28 June 1972) was an Indian scientist and statistician.
• He is best remembered for the Mahalanobis distance, a statistical measure, and for being one of the members of the first Planning Commission of free India.
• He made pioneering studies in anthropometry in India. He founded the Indian Statistical Institute and contributed to the design of large-scale sample surveys.
• For his contributions, Mahalanobis has been considered the father of modern statistics in India.
• Mahalanobis was deeply influenced by the wisdom and guidance of Rabindranath Tagore and Brajendranath Seal.
• Under his leadership, the institute initiated and promoted the interaction of Statistics with natural and social sciences to advance the role of Statistics as a key technology by explicating the twin aspects – its general applicability and its dependence on other disciplines for its own development.

Additional Information

• Indian Statistical Institute (ISI) is a higher education and research institute which is recognized as an Institute of National Importance by the 1959 act of the Indian parliament.
• It grew out of the Statistical Laboratory set up by P.C. Mahalanobis in Presidency College, Kolkata.
• Established in 1931, this unique institution of India is one of the oldest institutions focused on statistics, and its early reputation led it to be adopted as a model for the first US institute of Statistics set up at the Research Triangle, North Carolina by Gertrude Mary Cox.
• The institute is now considered one of the foremost centers in the world for training and research in Computer science, Statistics, Quantitative Economics, and related sciences.

Thus, P.C. Mahalanobis established the Indian Statistical Institute.

Given:

Town C is south of the mid-point of the straight line joining town A and B.

Town B is to the East of Town A.

Town D is west of town C.

Town M is north-east of town B.

Thus, town D is to southwest of town M.

Hence, "Option 3" is the correct answer.

Given series:

N 4 & % L A * 6 T & C @ 4 B % 2 X L

Condition to be checked:

Numbers which are immediately preceded by a letter and also immediately followed by a symbol.

Letter → Number → Symbol

N 4 & % L A * 6 T & C @ 4 B % 2 X L

Thus there is one such pattern (N 4 &) that is following the above conditions.

Hence, "1" is the correct answer.

Mistake Points

Immediately preceded by means immediately before or to come just before.

Immediately followed by means immediately after or to come just after.

Shortcut Trick

In a continued proportion a : b : : b : c, the first term is calculated as y = b² ÷ c.

Given proportion is y : 196 : : 196 : 784.

⇒ y = (196 × 196) ÷ 784

⇒ y = 196 ÷ 4 = 49

∴ The correct answer is 49.

Alternate Method

Given: y : 196 : : 196 : 784

Formula Used: Product of Extremes = Product of Means

⇒ y ÷ 196 = 196 ÷ 784

⇒ y × 784 = 196 × 196

⇒ y = (196 × 196) ÷ 784

⇒ y = 38416 ÷ 784

⇒ y = 49

∴ The correct answer is 49.

Additional Information

Fourth Proportional

If four quantities a, b, c, d are in proportion, then a/b = c/d, where d is the fourth proportional.

Third Proportional

In a continued proportion a : b : : b : c, the term 'c' is called the third proportional to a and b.

Mean Proportional

The mean proportional between two numbers a and b is given by √(a × b).

The correct answer is 1 Ampere - 10 Ampere.

Key Points

• Fuse: A fuse is a safety device that protects electrical circuits from overcurrent. It's a thin wire designed to melt and break the circuit if the current exceeds a safe level.
• work:  When excessive current flows through the fuse, the wire heats up and melts. This breaks the circuit, preventing damage to appliances and wiring.  The melting of the fuse wire is due to the heat generated by the current flowing through it (Joule's Law).
• Fuses important: Fuses are crucial for preventing electrical fires and protecting valuable equipment. Overcurrent can cause wires to overheat, potentially igniting flammable materials.  They also protect appliances from damage due to power surges.
• Fuse Ratings: Fuses are rated in Amperes (A), which indicates the maximum current they can safely carry without melting.  The rating must be selected carefully based on the circuit's requirements.
• Domestic Fuse Ratings (1-10A):  Household circuits typically use fuses in the 1 to 10 Ampere range.  Lower amperage fuses (e.g., 1-3A) are often used for sensitive electronic devices, while higher amperage fuses (e.g., 5-10A) are used for lighting circuits and appliances like fans and refrigerators.
• Types of Fuses:  Various types of fuses exist, including cartridge fuses, plug fuses, and high-rupturing capacity (HRC) fuses.  Domestic wiring often uses cartridge or plug fuses.
• Choosing the Right Fuse:  It's essential to use the correct fuse rating for a given circuit. Using a fuse with a lower rating than required will cause it to blow prematurely, while using a fuse with a higher rating may not provide adequate protection.
• Replacing a Fuse:  When a fuse blows, it must be replaced with one of the same rating.  Never replace a fuse with one of a higher rating, as this can create a fire hazard.  It's always a good idea to identify the cause of the blown fuse before replacing it.
• Modern Circuit Breakers:  Many modern homes use circuit breakers instead of fuses. Circuit breakers perform the same function as fuses but can be reset after tripping, eliminating the need for replacement.  However, fuses are still used in some applications and are important to understand.
• Fuse Wire Material:  The fuse wire is usually made of a metal or alloy with a low melting point, such as tin or lead.  This ensures that the fuse melts quickly and reliably when the current exceeds the rated value.
• Importance of Correct Installation: Fuses should be installed correctly by a qualified electrician to ensure proper operation and safety.  Improperly installed fuses can be ineffective or even create a safety hazard.
• Regular Inspection: Fuses should be inspected periodically for signs of damage or deterioration.  A blown fuse indicates a problem in the circuit that needs to be addressed.
• Double-Pole Fuses: Some circuits, especially those for appliances like water heaters, may use double-pole fuses, which interrupt both the live and neutral wires.
• Fuse Symbol: Electrical diagrams use specific symbols to represent fuses, making it easy to identify them in circuit schematics.
• Fuse Testing:  A multimeter can be used to test a fuse to determine if it is still good.  A good fuse will show continuity, while a blown fuse will not.
• Safety Precautions: Always disconnect the power before replacing a fuse to avoid electric shock.  Use insulated tools when working with fuses.
• Fuse Box/Panel: Fuses are typically located in a fuse box or panel, which provides a central location for managing the electrical circuits in a building.
• Overcurrent Protection: Fuses are a vital part of the overall overcurrent protection system in a building's electrical wiring.
• Earthing and Fuses: Fuses work in conjunction with earthing (grounding) to provide comprehensive electrical safety.  Earthing provides a path for fault current to flow to ground, while fuses interrupt the current flow in case of an overcurrent.
• Understanding Fuse Characteristics:  Understanding the characteristics of different types of fuses, such as their time-current characteristics, is important for selecting the right fuse for a specific application.  The time-current characteristic describes how long it takes for a fuse to blow at different current levels.

The logic followed here is:

Logic: 1st number × 2 + 2nd number × 3 = 3rd number.

Now,

For (2, 6, 22):

⇒ 2 × 2 + 6 × 3

= 4 + 18 = 22.

For (4, 13, 47):

⇒ 4 × 2 + 13 × 3

= 8 + 39 = 47.

Similarly, 

Option 1) For (9, 5, 33):

⇒ 9 × 2 + 5 × 3

= 18 + 15 = 33.

Option 2) For (7, 4, 36):

⇒ 7 × 2 + 4 × 3

= 14 + 12 = 26, which is not equal to 36.

Option 3) For (29, 35, 68):

⇒ 29 × 2 + 35 × 3

= 58 + 105 = 163, which is not equal to 68.

Option 4) For (23, 41, 77):

⇒ 23 × 2 + 41 × 3

= 46 + 123 = 169, which is not equal to 77.

Hence, the correct answer is Option 1.

Shortcut Trick

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

tan 45° = 1 and cot 45° = 1.

Expression = (1 + 1²) ÷ (1 + 1²) = 2 ÷ 2 = 1.

Checking options: (1) tan² 45° = 1² = 1. Matches.

∴ The correct answer is tan² A.

Alternate Method

Given: Angle A is an acute angle.

Formula Used: 1 + tan²A = sec²A and 1 + cot²A = cosec²A

⇒ Expression = (1 + tan²A) ÷ (1 + cot²A)

⇒ Expression = sec²A ÷ cosec²A

⇒ Expression = (1/cos²A) ÷ (1/sin²A)

⇒ Expression = (1/cos²A) × (sin²A/1)

⇒ Expression = sin²A ÷ cos²A = tan²A

∴ The correct answer is tan² A.

Additional Information

Trigonometric Identities

Standard Pythagorean identities include sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Reciprocal Relations

tan A = sin A ÷ cos A and cot A = cos A ÷ sin A, which implies tan A = 1 ÷ cot A.

Acute Angle Range

An acute angle is an angle measuring between 0° and 90°, where all primary trigonometric ratios are positive.

Given word: BRIGHT

According to the question all the letters in the word given are arranged in English alphabetical order:

Thus, two letters i.e. B and T holds the same position in the word as its position in the English alphabetical order.

Hence, "Option 2" is the correct answer.

The correct answer is north to south direction.

Key Points

Magnetic field lines:

• A magnetic field line is an imaginary line such that tangent to it at any point gives the direction of the magnetic field at that point in space.
• Magnetic field lines are drawn to represent the magnetic fields.
• Magnetic field lines can be drawn with the help of a magnetic compass.
• Magnetic field lines are also called magnetic lines of force.

Properties of magnetic field lines:

1. The magnetic field lines of a magnet (or a solenoid) form continuous closed loops.
2. The magnetic field lines start from the north pole and end on a south pole outside the magnet. Inside the magnet, the magnetic field lines start from the south pole and end on the north pole.
3. The tangent to the field line at a given point represents the direction of the net magnetic field B at that point.
4. The larger the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B.
5. The magnetic field lines do not intersect with each other if they did, there will be two directions of the magnetic field at that point which is not possible.

The correct answer is heat.

Key Points

• Heat:
• Electrical losses in circuits primarily occur as heat.
• This is due to the resistance of the conductors, known as Joule heating.
• Electrons collide with atoms in the wire, causing vibrations and generating heat.
• The amount of heat is proportional to the square of the current and the resistance.
• Heat is a loss because it's energy not used for useful work.
• Excessive heat can damage components and cause fires.
• Minimizing resistive losses is crucial for efficient electrical systems.
• Thicker wires with lower resistance reduce heat losses.
• Superconductors eliminate heat losses but need extremely low temperatures.
• Heat dissipation is important in electronic device design to prevent overheating.
• Cooling mechanisms like heat sinks and fans remove waste heat.
• The efficiency of electrical devices is related to heat loss.

Additional Information

• Magnetic Losses:
• Magnetic fields are generated by electric currents.
• "Magnetic losses" refer to energy dissipated in ferromagnetic materials.
• Hysteresis losses occur due to magnetic domains lagging behind the changing field.
• Eddy currents are induced within the core, generating heat.
• These losses are significant in devices with magnetic cores.
• They are not the primary loss in simple conductive circuits like wires.
• Laminating the core reduces eddy current losses.
• Soft magnetic materials minimize hysteresis losses.
• Magnetic losses are important in transformers, motors, and electromagnetic devices.
• These losses contribute to the device's inefficiency.
• Sound:
• Some electrical devices produce sound.
• This sound is not the primary energy loss in a simple circuit.
• Sound energy is typically small compared to the heat generated.
• Sound can be produced by vibrations or electrical discharges.
• In some cases, sound indicates a problem in the circuit.
• In most basic circuits, the sound produced is negligible in energy loss.
• Light:
• Light is not the primary energy loss in a typical circuit.
• Some devices produce light as their function, not a loss.
• In a simple resistive circuit, energy is mainly lost as heat.
• Light can be produced by electrical discharges.
• The light produced by a simple resistive circuit is generally very small.
• Incandescent bulbs produce light by heating a filament, but this is the desired output.

Given: A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

1) C lives immediately above F, on an even numbered floor but not on the 6th floor. 

2) Only three people live between F and E. 

As there is no possible position for E in case 1, therefore is eliminated.

3) B lives two floors below E, and A is not on the topmost floor.

After positioning B and A only one position is left which will be occupied by the only person is left i.e. D.

Thus, according to the final arrangement, three people live exactly between D and C.

Hence, "Option 3" is the correct answer.

The correct answer is electromagnetic induction.

Key Points

• Faraday's law of electromagnetic induction: It states that an emf or voltage is induced in a current-carrying conductor if there is a change in magnetic flux through the coil and the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of the number of turns in the coil and flux associated with the coil.
• AC generator: A mechanical device that converts mechanical energy into AC electrical power is called an AC generator.
• It works on the principle of Faraday’s law of electromagnetic induction.
• In an AC generator, the electrical current reverses direction periodically.
• In an AC generator, the coil through which the current flows is fixed while the magnet moves. The construction is simple and costs are less.
• When the armature of the generator rotates between two poles of the magnet on an axis perpendicular to the magnetic field then the magnetic flux linkage of the armature changes continuously. Due to this change, an emf is induced in the armature and finally, the current is induced.

Additional Information

Magnetic field lines:

• A magnetic field line is an imaginary line such that tangent to it at any point gives the direction of the magnetic field at that point in space.
• Magnetic field lines are drawn to represent the magnetic fields.
• Magnetic field lines can be drawn with the help of a magnetic compass.
• Magnetic field lines are also called magnetic lines of force.

Properties of magnetic field lines:

1. The magnetic field lines of a magnet (or a solenoid) form continuous closed loops.
2. The magnetic field lines start from the north pole and end on a south pole outside the magnet. Inside the magnet, the magnetic field lines start from the south pole and end on the north pole.
3. The tangent to the field line at a given point represents the direction of the net magnetic field B at that point.
4. The larger the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B.
5. The magnetic field lines do not intersect with each other if they did, there will be two directions of the magnetic field at that point which is not possible.

Given: Six students, Madhu, Anshul, Avani, Aarav, Priti, and Shikha, gave their presentations on different days in the month of March. The presentation was from 11th March to 16th March. 

1) Anshul presented on 14th March and Shikha presented immediately before Anshul. 

2) Only one person presented between Shikha and Priti.

3. Shikha presented after Priti but before Avani. 

4) Avani presented immediately before Madhu.

As there is no possible position for Madhu in case 2, therefore is eliminated.

After positioning Madhu only one position is left which will be occupied by the only person left i.e. Aarav.

Thus, according to the final arrangement, Avani presented on 15th March.

Hence, "Option 4" is the correct answer.

Shortcut Trick

Profit% for a dishonest dealer = (Error ÷ True Value − Error) × 100

True weight = 250 kg, Actual weight given = 200 kg

Error = 250 − 200 = 50 kg

Profit% = (50 ÷ 200) × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given: Claimed selling weight = 250 kg, Actual weight delivered = 200 kg. Formulas: Profit% = (Profit ÷ Cost Price) × 100

⇒ Let the cost price (CP) of 1 kg be Rs. 1. ⇒ Total CP for 200 kg = Rs. 200. ⇒ Total selling price (SP) (charged for 250 kg at CP) = Rs. 250. ⇒ Profit = SP − CP = 250 − 200 = Rs. 50. ⇒ Profit% = (50 ÷ 200) × 100 = 25%.

∴ The correct answer is 25%.

Additional Information

Dishonest Dealer Concept

When a merchant claims to sell at cost price but uses lesser weight, the profit is calculated on the amount actually given to the customer, not the claimed amount.

Ratio Method

Profit ratio = (True Weight) : (False Weight). In this case, 250:200 which simplifies to 5:4. Since SP corresponds to 5 and CP to 4, Profit% = (1/4) × 100 = 25%.

The logic followed here is: 

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

Now,

For (15, 405, 9):

⇒ (15 × 9) × 3

= 135 × 3 = 405.

For (13, 273, 7)

⇒ (13 × 7) × 3

= 91 × 3 = 273.

Similarly, for Option 4: (11, 165, 5)

⇒ (11 × 5) × 3

= 55 × 3 = 165.

Hence, the correct answer is Option 4.

The correct answer is valence electrons.

Key Points

• Valence Electrons:
• Elements in the same group have the same number of valence electrons.
• Valence electrons are in the outermost shell.
• They are responsible for the element's chemical properties.
• The number of valence electrons determines how an element interacts with others.
• Elements in a group exhibit similar chemical behavior.
• This is because they have the same valence electron configuration.
• Group 1 elements (alkali metals) have one valence electron.
• Group 17 elements (halogens) have seven valence electrons.
• The periodic table is organized based on electronic configurations.
• Groups reflect recurring patterns in these configurations.
• Shared valence electrons are why elements in a group share properties.
• This is a fundamental principle of the periodic table.
• Understanding valence electrons is key to predicting compound formation.
• The number of valence electrons influences bond types.

Additional Information

• Shells:
• Elements in the same period have the same number of shells.
• Moving across a period, electrons are added to the same shell.
• The number of shells relates to an atom's size.
• Elements in the same group do not have the same number of shells.
• Lithium and Sodium are in the same group but have different numbers of shells.
• The number of shells increases down a group.
• Each period represents filling a new electron shell.
• The number of shells is related to the principal quantum number.
• Electrons:
• Elements in the same group do not have the same total number of electrons.
• Moving down a group, the atomic number increases.
• The number of protons (and electrons) increases.
• The total number of electrons is not a defining characteristic of a group.
• The total number of electrons determines atom size and some physical properties.
• Valence electrons dictate chemical behavior.
• The total number of electrons is related to the atomic number.
• The number of electrons must equal the number of protons in a neutral atom.
• Protons:
• Elements in the same group do not have the same number of protons.
• The number of protons is the atomic number.
• It defines which element it is.
• Each element has a unique number of protons.
• Moving down a group, the atomic number (and protons) increases.
• Protons are heavier than electrons and reside in the nucleus.
• The number of protons determines the nucleus's charge.
• The periodic table is arranged by increasing atomic number.
• Changing the number of protons changes the element's identity.

Shortcut Trick Find HCF of 408 and 1032 using division: 1032 = 408 × 2 + 216; 408 = 216 × 1 + 192; 216 = 192 × 1 + 24; 192 = 24 × 8 + 0. HCF = 24. Equation: 24 = 516m − 1008. 516m = 1032 ⇒ m = 2. ∴ The correct answer is 2. Alternate Method

Given: Numbers are 408 and 1032. Step 1: Calculate the HCF of 408 and 1032. ⇒ 1032 = 408 × 2 + 216 ⇒ 408 = 216 × 1 + 192 ⇒ 216 = 192 × 1 + 24 ⇒ 192 = 24 × 8 + 0 ⇒ HCF = 24 Step 2: Set the given expression equal to the HCF. ⇒ 516m − 252 × 4 = 24 ⇒ 516m − 1008 = 24 ⇒ 516m = 24 + 1008 ⇒ 516m = 1032 ⇒ m = 1032 ÷ 516 ⇒ m = 2 ∴ The correct answer is 2. Additional Information Euclid Division Lemma It states that for any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. HCF Property The Highest Common Factor (HCF) of two numbers is the largest positive integer that divides each of the integers without a remainder. Linear Combination The HCF of two numbers a and b can always be expressed in the form of am + bn for some integers m and n (Bezout's Identity).

The correct answer is Ethanol (C2H5OH).

Key Points

• Ethanol (C2H5OH)
• Ethanol is a product of alcoholic fermentation.
• This is another type of anaerobic respiration.
• It's carried out by some microorganisms, like yeast.
• Glucose is broken down into pyruvate.
• Pyruvate is converted into ethanol and carbon dioxide.
• This fermentation is used in producing alcoholic beverages.
• It's also used in some food products.
• Both lactic acid and alcoholic fermentation are anaerobic.
• But they produce different end products.
• The question specifies carbon dioxide and ATP as products.
• This corresponds to lactic acid fermentation in muscles.

Additional Information

• Lactic Acid:
• Anaerobic respiration occurs without oxygen.
• It generates ATP from glucose when oxygen is limited.
• Lactic acid fermentation is a common type of anaerobic respiration.
• Glucose is broken down into pyruvate during glycolysis.
• Without oxygen, pyruvate is converted into lactic acid.
• This conversion regenerates NAD+, essential for glycolysis.
• Lactic acid fermentation is used by some bacteria and animal muscle cells.
• It occurs during intense exercise when oxygen supply is limited.
• Lactic acid accumulation in muscles causes fatigue.
• Lactic acid is later transported to the liver.
• In the liver, it's converted back into glucose.
• Anaerobic respiration produces less ATP than aerobic respiration.
• It provides crucial energy for short bursts of activity.
• This process is vital for survival in low-oxygen environments.
• Pyruvate:
• Pyruvate is an intermediate product of glycolysis.
• Glycolysis is the first step in both aerobic and anaerobic respiration.
• In aerobic respiration, pyruvate is further oxidized.
• In anaerobic respiration, pyruvate is converted into lactic acid.
• Glycolysis is common to both aerobic and anaerobic pathways.
• Pyruvate is a key molecule in cellular metabolism.
• It serves as a branch point for different metabolic fates.
• If oxygen is present, pyruvate enters the citric acid cycle.
• If oxygen is absent, pyruvate is converted to fermentation products.
• Water:
• Water is a product of aerobic respiration.
• It's formed when oxygen is the final electron acceptor.
• This occurs in the electron transport chain.
• This process generates a large amount of ATP.
• Anaerobic respiration does not involve the electron transport chain.
• Therefore, water is not a direct product.
• Water is essential for many biological processes.
• But it's not a direct product of the anaerobic pathway described.

The correct answer is Intake of pills.

Key Points

• Intake of Pills (Hormonal Contraceptives):
• Birth control pills, also known as oral contraceptives, contain synthetic hormones, usually a combination of estrogen and progestin.
• These hormones work primarily by preventing the release of an egg from the ovaries (ovulation).
• They can also thicken cervical mucus, making it harder for sperm to reach the egg, and alter the lining of the uterus, making it less receptive to a fertilized egg.
• Because they introduce exogenous hormones, they directly change the body's natural hormonal balance.
• Different types of pills have varying dosages and combinations of hormones, affecting individuals differently.
• Hormonal pills are highly effective when used correctly and consistently.
• They offer some additional health benefits, such as regulating periods and reducing menstrual cramps.
• However, they can also have potential side effects, including mood changes, weight fluctuations, and, in rare cases, more serious health risks.
• It's important to consult a doctor before starting or stopping any hormonal contraceptive.
• The hormonal changes induced by the pill are reversible upon discontinuation.
• These pills affect the levels of hormones like estrogen and progesterone.
• They can impact the menstrual cycle and other hormone-related functions.

Additional Information

• Insertion of Copper-T (Intrauterine Device - IUD):
• The Copper-T is a type of intrauterine device (IUD) that releases copper into the uterus.
• Copper is toxic to sperm, creating an environment that is hostile to them and thus preventing fertilization.
• It primarily works by preventing sperm from surviving in the female reproductive tract.
• It does not primarily change the hormonal balance of the body.
• Some IUDs contain hormones, but the Copper-T specifically is non-hormonal.
• The copper IUD's effects are mainly localized to the uterus.
• It's a long-acting reversible contraceptive (LARC) method.
• It does not prevent ovulation in most women.
• It can sometimes cause heavier or more painful periods.
• Surgical Blockage of the Fallopian Tubes (Tubal Ligation):
• Tubal ligation is a surgical procedure that blocks or cuts the fallopian tubes.
• This prevents the egg from traveling from the ovaries to the uterus and thus prevents fertilization.
• It is a permanent method of contraception.
• It does not directly change the hormonal balance of the body.
• Hormone levels remain largely unaffected.
• It is considered a highly effective method of birth control.
• It is generally not easily reversible.
• It does not affect the menstrual cycle in most women.
• Use of Condoms (Barrier Method):
• Condoms are barrier methods of contraception.
• They prevent sperm from entering the vagina and reaching the egg.
• They do not change the hormonal balance of the body.
• They are a readily available and relatively inexpensive method of contraception.
• Condoms also offer protection against sexually transmitted infections (STIs).
• They are a temporary method of contraception.
• They are effective when used correctly and consistently.
• Their use does not interfere with natural hormone production.

Shortcut Trick

For any two co-prime numbers, the only common factor they share is 1.

Since there are no other common prime factors, their Least Common Multiple (LCM) is simply the product of the numbers.

Product = a × b.

∴ The correct answer is a × b.

Alternate Method

Given: Two numbers a and b are co-prime.

Formula Used: LCM × HCF = Product of two numbers

⇒ By definition, the Highest Common Factor (HCF) of co-prime numbers is 1.

⇒ Substitute HCF = 1 in the formula:

⇒ LCM × 1 = a × b

⇒ LCM = a × b

∴ The correct answer is a × b.

Additional Information

Co-prime Numbers

Numbers that have no common positive factor other than 1. Examples: (8, 9), (15, 16).

HCF and LCM Relation

For any two numbers x and y, HCF(x, y) × LCM(x, y) = x × y.

Prime Numbers

All pairs of distinct prime numbers are always co-prime, and their LCM is their product.

Shortcut Trick

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

If x² + 1/x² = m, then x⁴ + 1/x⁴ = m² − 2.

Given k = 2 ⇒ x² + 1/x² = 2² + 2 = 6.

Then, x⁴ + 1/x⁴ = 6² − 2 = 36 − 2 = 34.

∴ The correct answer is 34.

Alternate Method

Given: x − 1/x = 2

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

Calculations:

First, squaring both sides of the given equation:

⇒ (x − 1/x)² = 2²

⇒ x² + (1/x)² − 2 × x × (1/x) = 4

⇒ x² + 1/x² − 2 = 4

⇒ x² + 1/x² = 6

Now, squaring both sides again to reach the fourth power:

⇒ (x² + 1/x²)² = 6²

⇒ (x²)² + (1/x²)² + 2 × x² × (1/x²) = 36

⇒ x⁴ + 1/x⁴ + 2 = 36

⇒ x⁴ + 1/x⁴ = 36 − 2

⇒ x⁴ + 1/x⁴ = 34

∴ The correct answer is 34.

Additional Information

Algebraic Identities for Reciprocals

For any non-zero value x, the relation (x + 1/x)² = x² + 1/x² + 2 and (x − 1/x)² = x² + 1/x² − 2 are fundamental in solving higher power expressions.

Successive Squaring Property

To find the value of x⁴ + 1/x⁴, we must first find the value of x² + 1/x² as an intermediate step. The constant term 2 is added or subtracted based on the sign of the binomial being squared.

Conversion Rule

x² + 1/x² = (x − 1/x)² + 2 | x² + 1/x² = (x + 1/x)² − 2. Always check the given sign carefully before applying the constant adjustment.

The correct answer is aperture.

Key Points

• Aperture:
• The aperture of a lens is the diameter of the opening that controls how much light enters the lens.
• It's specifically the diameter of the effective circular outline through which light can pass. This might be smaller than the physical size of the lens.
• The aperture is a crucial factor in determining the lens's light-gathering ability and its depth of field.
• A larger aperture (wider opening) allows more light to enter, which is useful in low-light conditions.
• A smaller aperture (narrower opening) allows less light to enter but increases the depth of field (the portion of the image that appears in focus).
• Aperture is often expressed as an f-number (e.g., f/2.8, f/5.6), which is the ratio of the lens's focal length to the diameter of the aperture.
• The terms "aperture" and "effective diameter" are often used interchangeably in the context of lenses.
• The aperture is adjustable in many cameras and optical instruments.
• The size of the aperture affects the brightness of the image formed by the lens.
• It also plays a role in controlling diffraction, which can affect image sharpness.
• The aperture is a key parameter in photography, influencing exposure and artistic effects.

Additional Information

• Centre of Curvature:
• The center of curvature is the center of the sphere of which the lens surface is a part.
• It's a geometric point, not a physical diameter.
• It's important for understanding the lens's shape and how it refracts light.
• The radius of curvature is the distance from the center of curvature to the lens surface.
• Light rays passing through the center of curvature pass undeviated.
• The center of curvature is used in lens design and calculations.
• It's related to the focal length of the lens.
• It is not related to the amount of light entering the lens.
• Focus:
• The focus (or focal point) is the point where parallel light rays converge after passing through the lens.
• It's a point, not a diameter.
• The distance from the lens to the focus is called the focal length.
• The focus is crucial for image formation.
• A sharp image is formed when the object is at the correct distance for the lens to focus the light onto the image plane (e.g., film or sensor).
• The focal length determines the magnification of the lens.
• Different lenses have different focal lengths.
• The focus is not directly related to the light-gathering ability of the lens.
• Radius of Curvature:
• The radius of curvature is the distance from the center of curvature to the lens surface.
• It's a distance, not a diameter related to light entering the lens.
• It describes the curvature of the lens surface.
• It's related to the focal length of the lens.
• The radius of curvature is a parameter used in lens design.
• A shorter radius of curvature means a more curved lens surface.
• The radius of curvature is important for determining the lens's optical power.
• It is not the same as the aperture.

The correct answer is electrolysis of water.

Key Points

• Electrolysis of Water:
• Electrolysis is the process of using an electric current to drive a non-spontaneous chemical reaction.
• In the case of water, electrolysis involves passing a direct current (DC) through water.
• This causes the water molecules to split into their constituent elements: hydrogen and oxygen gas.
• The reaction occurs at two electrodes: the anode (positive) and the cathode (negative).
• At the anode, water molecules are oxidized, releasing oxygen gas and hydrogen ions (H+).
• At the cathode, hydrogen ions are reduced, forming hydrogen gas.
• The overall reaction is: 2H₂O(l) → 2H₂(g) + O₂(g)
• Electrolysis of water requires an electrolyte (like an acid or a salt) to be present in the water to carry the current. Pure water is a poor conductor of electricity.
• This process is used in various applications, including hydrogen production for fuel cells and other industrial uses.
• Electrolysis is a fundamental electrochemical process.
• It's a key method for producing pure hydrogen.

Additional Information

• Hydrolysis of Water:
• Hydrolysis is a chemical reaction in which water is used to break down a substance.
• While electrolysis of water is a type of reaction involving water, "hydrolysis" usually refers to reactions where water itself is a reactant in the breaking of chemical bonds, not simply being split itself by electricity.
• Hydrolysis can occur under acidic or basic conditions, or with the help of enzymes.
• It does not necessarily involve electricity.
• Examples of hydrolysis include the breakdown of carbohydrates into sugars and the breakdown of proteins into amino acids.
• While related to water, it's a broader term and not specific to the electrically driven splitting of water.
• Atomisation of Water:
• Atomization refers to the process of breaking a liquid into a fine spray of droplets.
• This is typically done mechanically (e.g., using a nozzle) or by using compressed gas.
• Atomization does not involve changing the chemical composition of the water. It is a physical process, not a chemical one.
• It's used in applications like fuel injection in engines, spray painting, and humidification.
• It's a physical process of dispersion, not a chemical change like the decomposition of water into its elements.
• Ionisation of Water:
• Ionization is the process of adding or removing electrons from an atom or molecule to create ions.
• Water undergoes a small degree of autoionization, where it forms hydronium ions (H₃O+) and hydroxide ions (OH-).
• However, this is a spontaneous and reversible process, not driven by electricity like electrolysis.
• Ionization is a fundamental concept in chemistry and physics.
• It plays a role in many chemical reactions and physical phenomena.
• While related to water's properties, it's not the term for the specific process of electrically splitting water into hydrogen and oxygen.

Given Statement: Y < V = X ≤ L < A > C ≥ H

Now,

Conclusions:

Option 1: X > Y → True (Y < V = X, so X > Y holds true)

Option 2: L ≥ V → True (V = X ≤ L, so L ≥ V holds true)

Option 3: X > A → False (X ≤ L < A , so X > A  not true)

Option 4: A > H → True (A > C ≥ H, so, A > H holds true)

Hence, the correct answer is "Option 3".

The correct answer is refractive index.

Key Points

• Refractive Index:
• The ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is defined as the refractive index.
• This relationship is known as Snell's Law: n₁sin(i) = n₂sin(r), where n₁ and n₂ are the refractive indices of the two media.
• The refractive index is a measure of how much light bends when it passes from one medium to another.
• It's a dimensionless quantity.
• A higher refractive index means that light bends more.
• The refractive index of a vacuum is defined as 1.
• The refractive index of other media is relative to the refractive index of a vacuum.
• When light travels from a medium with a lower refractive index to a medium with a higher refractive index, it bends towards the normal.
• When light travels from a medium with a higher refractive index to a medium with a lower refractive index, it bends away from the normal.
• The refractive index is dependent on the wavelength of light. This is why dispersion occurs.
• Snell's Law is fundamental to understanding how lenses and prisms work.

Additional Information

• Dispersion:
• Dispersion is the phenomenon of light splitting into its constituent colors (like a rainbow) when it passes through a prism or other medium.
• This happens because the refractive index of the medium varies slightly with the wavelength of light.
• Different colors of light bend by different amounts, causing them to separate.
• Dispersion is not the ratio of sin i to sin r, but a consequence of the fact that this ratio (refractive index) is wavelength-dependent.
• Prisms utilize dispersion to separate white light into its spectrum.
• Rainbows are a natural example of dispersion caused by raindrops acting as prisms.
• Magnification:
• Magnification is the apparent enlargement of an object by an optical instrument like a lens or a microscope.
• It's a measure of how much larger the image appears compared to the object.
• Magnification is not directly related to the ratio of sin i to sin r.
• Magnification is calculated based on the lens's focal length and the object/image distances.
• It can be linear (related to size) or angular (related to the angle subtended by the object/image).
• Refraction:
• Refraction is the bending of light as it passes from one medium to another.
• It's the phenomenon that is described by Snell's Law and the refractive index.
• Refraction is not the ratio of sin i to sin r itself, but the process governed by it.
• Refraction occurs because light travels at different speeds in different media.
• The change in speed causes the light to bend.
• Refraction is responsible for many optical illusions.

The correct answer is formation of lactic acid.

Key Points

• Formation of Lactic Acid:
• During heavy exercise, the demand for energy in muscle cells increases significantly.
• When the oxygen supply is limited, the muscle cells switch to anaerobic respiration to produce ATP (energy).
• Anaerobic respiration in muscle cells involves the breakdown of glucose into lactic acid.
• This process allows for the continued production of ATP even in the absence of sufficient oxygen.
• Lactic acid is a byproduct of this anaerobic process.
• The accumulation of lactic acid in muscle cells contributes to muscle fatigue and soreness.
• This is a temporary adaptation to meet the energy demands when oxygen is scarce.
• Once the exercise stops and oxygen becomes available, the lactic acid is converted back to pyruvate or glucose in the liver.
• This process provides a short-term solution for energy production during intense activity.
• It is less efficient than aerobic respiration, producing much less ATP per glucose molecule.
• This metabolic pathway is crucial for short bursts of high-intensity activity.

Additional Information

• Synthesis of Ethanol:
• Ethanol is a product of anaerobic respiration, but specifically alcoholic fermentation.
• Alcoholic fermentation is carried out by microorganisms like yeast, not by human muscle cells.
• Muscle cells do not produce ethanol during exercise.
• This process is used in the production of alcoholic beverages.
• It involves the conversion of pyruvate to ethanol and carbon dioxide.
• Accumulation of Pyruvate:
• Pyruvate is an intermediate product in the breakdown of glucose during glycolysis.
• If oxygen is available, pyruvate is further processed in the mitochondria to produce more ATP through aerobic respiration.
• When oxygen is limited, pyruvate is converted into lactic acid, not accumulated.
• The conversion of pyruvate to lactic acid is essential to regenerate NAD+, which is needed for glycolysis to continue.
• Accumulation of pyruvate would halt the energy production process during anaerobic conditions.
• Loss of Water:
• While the body does lose water during exercise through sweating, this is not directly related to the shift to anaerobic respiration.
• Sweating is a mechanism for thermoregulation (cooling the body).
• Water loss can lead to dehydration, which can impair performance.
• However, it's a separate process from the metabolic shift to lactic acid production.
• Dehydration can indirectly affect cellular respiration but is not the primary factor in anaerobic respiration taking place.
• s not the primary factor in anaerobic respiration taking place.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

(I) Some horses are peacocks → Follow (As all peacocks are cheetahs and all cheetahs are horses. As whole peacocks comes in cheetahs which whole comes in horses, therefore is true.)

(II) Some cheetahs are peacocks → Follow (As all peacocks are cheetahs. As whole peacocks comes in cheetahs, therefore is true.)

(III) All peacocks are horses → Follow (As all peacocks are cheetahs and all cheetahs are horses. As whole peacocks comes in cheetahs which whole comes in horses, therefore is true.

∴ Here, All conclusions I, II and III follow.​

Hence, the correct answer is "Option 3".

The correct answer is Zn (s) + CuSO4 (aq) ——→ ZnSO4 (aq) + Cu (s).

Key Points

Displacement reaction

• The chemical reaction in which a more reactive element displaces a less reactive element from its compound is called displacement reaction.
• Metal activity series: The metal reactivity series is an array of metals arranged in descending order of their reactivities. It is also known as the metal activity series.

Additional Information

• The top metals in the series (K, Na, Ca, Mg, and Al) are so reactive that they are never found as free elements in nature.
• The metals at the bottom of the activity series are the least reactive.
• Some of these metals can be found in their natural state in the earth's crust.

Given: Six girls with the initials V, M, S, E, N and C are sitting around a circular table, facing the centre and at equal distance from each other.

1) E sits second to the left of C.

2) C sits at the immediate left of V. 

3) S sits second to the right of V.

4) N sits second to the left of E.

After positioning N only one position is left which will be occupied by the only person left i.e. M.

Thus, according to the final arrangement, M sits at the immediate left of C.

Hence, "Option 3" is the correct answer.

Given Statement: The Union Road Transport and Highways Ministry is gearing up to build a super expressway to connect Delhi and Mumbai, which would allow commuters to finish the 1,400 km long journey within 12 hours.

Now,

Assumptions:

1. The road between the two cities is in very bad shape - Not Implicit (The statement does not provide any information about the current condition of the road between Delhi and Mumbai.)
2. Currently there are no roads to connect these two cities of India - Not Implicit (The statement mentions the construction of a super expressway to reduce travel time, but it does not imply that there are no existing roads connecting Delhi and Mumbai.)

Here, Neither assumption I nor II is implicit.

Hence, the correct answer is "Option 1".

Given:

 

Now, the group of letters is: YELLOW

Following the conditions:

Condition (iii) is applied: The letter O is present exactly twice in a word. So, the codes for these word is

After applying Condition (iii):

Hence, the correct answer is "Option 2".

Shortcut Trick

Convert all loans to an equivalent principal for 1 year at the initial rate (R%).

Equivalent Principal = P₁ + (P₂ × Rate Factor × Time Factor)

Equivalent Principal = 7250 + (3625 × 2 × 0.5) = 7250 + 3625 = ₹10,875

Rate (R) = (Total Interest ÷ Equivalent Principal) × 100

R = (335 ÷ 10875) × 100 ≈ 3.08%

∴ The correct answer is 3.08%.

Alternate Method

Given:

Initial Sum (P₁) = ₹7,250 | Time (T₁) = 1 year | Rate (R₁) = R%

Additional Sum (P₂) = ₹3,625 | Time (T₂) = 6 months = 0.5 year | Rate (R₂) = 2R%

Total Interest Earned = ₹335

Formula Used:

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

Calculations:

⇒ SI₁ = (7250 × R × 1) ÷ 100 = 72.5R

⇒ SI₂ = (3625 × 2R × 0.5) ÷ 100 = (3625 × R) ÷ 100 = 36.25R

⇒ Total SI = SI₁ + SI₂

⇒ 335 = 72.5R + 36.25R

⇒ 335 = 108.75R

⇒ R = 335 ÷ 108.75

⇒ R ≈ 3.080459...

⇒ R ≈ 3.08%

∴ The correct answer is 3.08%.

Additional Information

Simple Interest (SI) Properties

Interest is calculated only on the original principal for each period. It does not earn interest on interest.

Effective Rate of Interest

If multiple rates or time periods are involved, the average rate can be found by weighting the rates by the respective Principal × Time products.

SI vs Compound Interest (CI)

For the first period (e.g., 1 year with annual compounding), SI = CI. In subsequent periods, CI will always be greater than SI if interest is reinvested.

Given series: MN_ LMM PLM NP_MMNN _M

Option 1) NPNNMNLPL → MNN PLMMN NPLMM NNPLMMNNP LM → (It follows the pattern of: MNNPL - MMNNPL - MMNNPL - MMNNPL)

Option 2) NPNNMNLPP → MNN PLMMN NPLMM NNPLMMNNP LM → (It doesn't follow any pattern)

Option 3) NNNNMNLPL → MNN PLMMN NPLMM NNPLMMNNP LM → (It doesn't follow any pattern)

Option 4) MPNNMNLPL → MNN PLMMN NPLMM NNPLMMNNP LM → (It doesn't follow any pattern)

Hence, "Option 1" is the correct answer.

Shortcut Trick

Sum of interior angles of an 8-sided polygon = (8 − 2) × 180° = 1080°.

Sum of ratio parts = 1 + 3 + 4 + 6 + 7 + 11 + 13 + 15 = 60.

Value of 1 part = 1080° ÷ 60 = 18°.

Largest interior angle = 15 × 18° = 270°.

∴ The correct answer is 270°.

Alternate Method

Given:

Number of sides (n) = 8

Ratio of interior angles = 1 : 3 : 4 : 6 : 7 : 11 : 13 : 15

Formula Used:

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

Calculations:

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

⇒ Sum = 6 × 180° = 1080°

⇒ Let the angles be 1x, 3x, 4x, 6x, 7x, 11x, 13x, and 15x.

⇒ 1x + 3x + 4x + 6x + 7x + 11x + 13x + 15x = 1080°

⇒ 60x = 1080°

⇒ x = 1080° ÷ 60 = 18°

⇒ Largest interior angle = 15x = 15 × 18° = 270°

∴ The

The correct answer is To settle disputes and makes judgments between different level of governments.

Key Points

• Indian Parliament:
• The Indian Parliament is a bicameral legislature consisting of two houses – the Lok Sabha and the Rajya Sabha.
• The members of the Lok Sabha (House of the People) are directly elected by the people through the voting process.
• The members of the Rajya Sabha (Council of States) are elected by the members of the states’ legislative assemblies.
• The Parliament consists of the two Houses and the President of India.
• India has a parliamentary system of government.
• The Union Parliament is the supreme legislative body in the country.

 Additional Information

• Functions of Parliament:
• Legislative Functions:
• The Parliament legislates on all matters mentioned in the Union List and the Concurrent List.
• In the case of the Concurrent List, where the state legislatures and the Parliament have joint jurisdiction, the union law will prevail over the states unless the state law had received the earlier presidential assent.
• However, the Parliament can any time, enact a law adding to, amending, varying, or repealing a law made by a state legislature.
• Executive Functions (Control over the Executive):
• By a vote of no-confidence, the Parliament can remove the Cabinet (executive) out of power.
• It can reject a budget proposal or any other bill brought by the Cabinet.
• A motion of no-confidence is passed to remove a government from office.
• The MPs (Members of Parliament) can ask questions to the ministers on their ommissions and commissions.
• Any lapses on the part of the government can be exposed in the Parliament.
• Financial Functions:
• The Union Budget prepared by the Cabinet is submitted for approval by the Parliament.
• All proposals to impose taxes should also be approved by the Parliament.
• There are two standing committees (Public Accounts Committee and Estimates Committee) of the Parliament to keep a check on how the executive spends the money granted to it by the legislature.
• Amending Powers:
• The Parliament has the power to amend the Constitution of India.
• Both Houses of Parliament have equal powers as far as amending the Constitution is concerned.
• Amendments will have to be passed in both the Lok Sabha and the Rajya Sabha for them to be effective.

The correct answer is Jet stream.

Key Points

• Jet stream:
• Jet streams are fast-flowing, narrow air currents in the upper levels of the atmosphere.
• They are formed due to temperature differences between different air masses.
• The subtropical jet stream is a key factor in bringing western disturbances to India.
• These disturbances are extra-tropical cyclones that originate in the Mediterranean region.
• The jet stream acts as a carrier, steering these disturbances eastward towards the Indian subcontinent.
• Western disturbances bring winter rainfall to the northern parts of India, which is crucial for agriculture.
• They also influence the weather patterns in other parts of the subcontinent.
• The intensity and track of the jet stream can vary, affecting the timing and impact of western disturbances.
• These disturbances are important for replenishing groundwater and snowpack in the Himalayas.
• The interaction of western disturbances with the local weather systems can sometimes lead to severe weather events.

Additional Information

• Anabatic winds:
• Anabatic winds are local winds that blow upslope due to daytime heating.
• They are common in mountainous regions.
• The sun heats the mountain slopes, causing the air to rise.
• This rising air creates a localized upward current.
• Anabatic winds are not responsible for bringing western disturbances to India.
• They are a localized phenomenon driven by diurnal temperature variations.
• They influence local weather patterns in mountainous areas.
• Mango shower:
• Mango showers are pre-monsoon showers that occur in some parts of India, particularly in the southern states.
• They are associated with the heating of the land before the monsoon season.
• These showers are beneficial for mango crops, hence the name.
• They are a localized phenomenon and not related to western disturbances.
• They occur primarily in the pre-monsoon season (March-May).
• They are distinct from the winter rainfall brought by western disturbances.
• Relief rain:
• Relief rain, also known as orographic rain, occurs when moist air is forced to rise over mountains.
• As the air rises, it cools and condenses, leading to precipitation.
• This type of rainfall is common on the windward side of mountain ranges.
• While mountains can influence the path of western disturbances, relief rain is not the primary mechanism for their transport.
• Relief rain is a localized effect caused by the interaction of air masses with topography.

Shortcut Trick

When the base is the same, use the property a^m × a^−m = 1.

Here, the base is (y²x) and the powers are 4 and −4.

Product = (y²x)^{4 − 4} = (y²x)⁰ = 1.

∴ The correct answer is 1.

Alternate Method

Given: (y²x)⁴ × (y²x)⁻⁴ where x ≠ 0 and y ≠ 0.

Formula Used: a^m × aⁿ = a^m+n and a⁰ = 1 (for a ≠ 0).

⇒ (y²x)⁴ × (y²x)⁻⁴

⇒ (y²x)^{4 + (−4)}

⇒ (y²x)⁰

⇒ 1

∴ The correct answer is 1.

Additional Information

Product Law of Exponents

For any non-zero base a, a^m × aⁿ = a^m+n. Powers are added when multiplying the same base.

Zero Exponent Rule

Any non-zero expression raised to the power of zero is always equal to 1 (a⁰ = 1).

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the positive power: a⁻ⁿ = 1 / aⁿ.

The logic followed here is:

Hence, "Option 3" is the correct answer.

Shortcut Trick

If the sum of a number and its reciprocal is k, then the number is a root of the equation x² − kx + 1 = 0.

Here, k = 7, so the equation is x² − 7x + 1 = 0.

The roots of this quadratic equation are given by [k ± √(k² − 4)] / 2.

Substituting k = 7: [7 ± √(7² − 4)] / 2 = [7 ± √(49 − 4)] / 2 = (7 ± √45) / 2.

Simplified roots: (7 ± 3√5) / 2.

∴ The correct answer is (7 + 3√5)/2.

Alternate Method

Given:

The sum of a number (x) and its reciprocal (1/x) is 7.

Formula Used:

For a quadratic equation ax² + bx + c = 0, the roots are x = [−b ± √(b² − 4ac)] / 2a.

Calculations:

⇒ x + 1/x = 7

⇒ (x² + 1) / x = 7

⇒ x² + 1 = 7x

⇒ x² − 7x + 1 = 0

Comparing with ax² + bx + c = 0, we have a = 1, b = −7, and c = 1.

⇒ Discriminant (D) = b² − 4ac = (−7)² − 4(1)(1)

⇒ D = 49 − 4 = 45

⇒ x = [−(−7) ± √45] / (2 × 1)

⇒ x = (7 ± √(9 × 5)) / 2

⇒ x = (7 ± 3√5) / 2

The possible values for the number are (7 + 3√5) / 2 and (7 − 3√5) / 2.

∴ The correct answer is (7 + 3√5)/2.

Additional Information

Algebraic Identities for Reciprocals

If x + 1/x = k, then x² + 1/x² = k² − 2 and x³ + 1/x³ = k³ − 3k. These are frequently used in competitive exams for quick calculations.

Nature of Roots

When the discriminant D is positive but not a perfect square, the roots are irrational and always occur in conjugate pairs of the form (p + √q) and (p − √q).

Relation between Roots and Coefficients

For the equation ax² + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a. In this problem, the product of roots is 1/1 = 1, confirming they are reciprocals.

Given word: 'CAUTIONED'

After arranged in alphabetical order:

 

After arranged in alphabetical order I is the exact middle position after such arrangement.

Hence, the correct answer is "Option 2".

The correct answer is 2008.

Key Points

• The Centre for Excellence for Classical Tamil (CECT) was initially established in Mysore, Karnataka.
• It was later relocated to Chennai, Tamil Nadu, in 2008.
• The shift aimed to consolidate the center's operations and bring it closer to the heart of the Tamil linguistic and cultural community.
• Chennai, being the capital of Tamil Nadu, offered better infrastructure and resources for the center's activities.
• The move facilitated greater collaboration with Tamil scholars, institutions, and the general public.
• The CECT plays a crucial role in promoting research and study in Classical Tamil literature, linguistics, and culture.
• It supports various academic initiatives, including conferences, seminars, and workshops.
• The center also provides fellowships and scholarships to researchers and students.
• It works towards preserving and digitizing ancient Tamil texts.
• The CECT aims to make Classical Tamil literature accessible to a wider audience.
• It collaborates with universities and research institutions globally to promote Tamil studies.
• The center's activities contribute to the understanding and appreciation of the rich heritage of the Tamil language.
• Classical Tamil is recognized as one of the oldest surviving classical languages in the world.
• The CECT's work is essential for preserving this linguistic and cultural treasure.
• The shift to Chennai has strengthened the center's ability to achieve its objectives.
• The relocation has provided the CECT with a more conducive environment for its research and academic endeavors.
• The center actively engages in outreach programs to promote the study of Classical Tamil.
• It publishes research findings and educational materials related to Classical Tamil.
• The CECT serves as a hub for scholars and enthusiasts of the Tamil language and its literature.

The correct answer is In the 1980s.

Key Points

• This thinning of the ozone layer was particularly pronounced during the spring months (August-October) in the Southern Hemisphere.
• The phenomenon was termed the "ozone hole" due to the dramatic reduction in ozone concentration.
• Measurements from ground-based stations and satellite observations confirmed the rapid ozone depletion.
• The most significant and well-documented ozone hole is the one over Antarctica.
• Similar, though less severe, ozone depletion has also been observed over the Arctic region.
• The primary cause of this ozone depletion is the release of human-made chemicals, particularly chlorofluorocarbons (CFCs).
• CFCs were widely used in refrigerants, aerosols, and other industrial applications.
• When released into the atmosphere, CFCs drift up to the stratosphere.
• In the stratosphere, they are broken down by ultraviolet radiation, releasing chlorine atoms.
• Chlorine acts as a catalyst in the destruction of ozone molecules.
• A single chlorine atom can destroy thousands of ozone molecules.
• This catalytic destruction of ozone leads to the thinning of the ozone layer.
• The ozone layer is crucial for absorbing harmful ultraviolet (UV) radiation from the sun.
• Depletion of the ozone layer increases the amount of UV radiation reaching the Earth's surface.
• Increased UV radiation can have detrimental effects on human health, including increased risk of skin cancer and cataracts.
• It can also harm marine life and terrestrial ecosystems.
• The Montreal Protocol, an international treaty, was signed in 1987 to phase out the production and consumption of ozone-depleting substances like CFCs.
• Thanks to the Montreal Protocol, the ozone layer is slowly recovering.
• However, it is expected to take several decades for the ozone layer to fully recover to pre-1980 levels.
• Continued monitoring of the ozone layer is essential to ensure its long-term recovery.

Given:

1 - 2 × [{-2(2 + 3) × 20} ÷ 2]

Formula used:

BODMAS

Calculation:

1 - 2 × [{-2(2 + 3) × 20} ÷ 2]

⇒ 1 - 2 × [{-2(5) × 20} ÷ 2]

⇒ 1 - 2 × [{-10 × 20} ÷ 2]

⇒ 1 - 2 × {-200 ÷ 2}

⇒ 1 - 2 × {-100}

⇒ 1 - (-200)

⇒ 1 + 200

⇒ 201

∴ The correct answer is option (4).

Shortcut Trick

Total work remains same: 10 Women × 8 Days = 8 Men × 12 Days

Equating the work units: 80W = 96M

Simplifying the ratio of Efficiency (Work/Day): M/W = 80/96 = 5/6

∴ The correct answer is 5 : 6.

Alternate Method

Given:

Time taken by 10 women = 8 days

Time taken by 8 men = 12 days

Formula Used:

Total Work = Number of Persons × Efficiency × Days

⇒ Efficiency of 10 women = 480 ÷ 8 = 60 units/day

⇒ Efficiency of 1 woman (W) = 60 ÷ 10 = 6 units/day

⇒ Efficiency of 8 men = 480 ÷ 12 = 40 units/day

⇒ Efficiency of 1 man (M) = 40 ÷ 8 = 5 units/day

⇒ Ratio of Man : Woman = 5 : 6

∴ The correct answer is 5 : 6.

Additional Information

Work Equivalence Formula

The work done by different groups can be related as M₁D₁H₁E₁ = M₂D₂H₂E₂, where M is number of people, D is days, H is hours, and E is efficiency.

Efficiency vs Time

Efficiency is inversely proportional to the Time taken to complete a specific task. If ratio of time is a:b, ratio of efficiency is b:a.

The correct answer is Punjab.

Key Points

The correct answer is members of the samiti.

Key Points

• Members of the samiti:
• The Block Panchayat Samiti, also known as the Panchayat Samiti or Block Samiti, is a local government body at the intermediate level between the Gram Panchayat (village level) and the Zila Parishad (district level).
• The Chairman of the Block Panchayat Samiti is elected by and from among the elected members of the Samiti itself.
• These members are directly elected by the people residing within the block.
• The election of the Chairman usually takes place soon after the general elections for the Block Panchayat Samiti.
• The Chairman presides over the meetings of the Samiti and plays a key role in its functioning.
• The Chairman's responsibilities include coordinating development activities within the block.
• The Chairman works in close collaboration with other members and government officials.
• The position of Chairman is an important one in local governance, as it involves overseeing the implementation of various schemes and programs at the block level.
• The Chairman is accountable to the members of the Samiti and the people of the block.
• The tenure of the Chairman is usually the same as that of the elected members of the Samiti.

Additional Information

• Village Pradhan:
• The village Pradhan is the head of the Gram Panchayat, the village-level local government body.
• The Pradhan is elected directly by the residents of the village.
• The Pradhan's role is distinct from that of the Block Panchayat Samiti Chairman.
• The Pradhan focuses on village-level development and administration.
• The Pradhan does not have any direct role in the election of the Block Panchayat Samiti Chairman.
• Members of the State Legislative:
• Members of the State Legislative Assembly (MLAs) are elected by the people of their respective constituencies to the state legislative assembly.
• MLAs play a role in state-level legislation and policy-making.
• They do not have any direct involvement in the election of the Block Panchayat Samiti Chairman.
• Their responsibilities are at the state level, while the Block Panchayat Samiti operates at the block level.
• Members of the Zila Panchayat:
• Members of the Zila Panchayat are elected representatives at the district level.
• The Zila Panchayat is the apex body of the Panchayati Raj system at the district level.
• While there may be some coordination between the Zila Panchayat and the Block Panchayat Samiti, members of the Zila Panchayat do not elect the Chairman of the Block Panchayat Samiti.
• The Zila Panchayat's role is broader, encompassing the entire district.

The correct answer is parliamentary.

Key Points

• Parliamentary:
• India has a parliamentary form of government, also known as a Westminster system.
• In this system, the head of state (President) is different from the head of government (Prime Minister).
• The President is the nominal head of state, while the Prime Minister is the real executive authority.
• The Prime Minister is usually the leader of the party that commands a majority in the Lok Sabha (lower house of Parliament).
• The Prime Minister and the Council of Ministers are collectively responsible to the Lok Sabha.
• The government can remain in power as long as it enjoys the confidence of the Lok Sabha.
• The Lok Sabha can remove the government through a vote of no confidence.
• The executive branch (government) is drawn from and accountable to the legislative branch (Parliament).
• This system emphasizes collective responsibility and accountability of the government.
• India's parliamentary system is inspired by the British system but has its own unique features.
• The President is elected indirectly by an electoral college.
• The Rajya Sabha (upper house of Parliament) also plays a role in legislation and oversight.

Additional Information

• Communalism:
• Communalism refers to the tendency of people belonging to different religious or ethnic communities to prioritize their own group's interests over the interests of the nation as a whole.
• It is a social and political issue, not a form of government.
• Communalism can lead to tensions and conflicts between different communities.
• India is a secular country, and its Constitution guarantees equal rights and opportunities to all citizens regardless of their religion.
• The Indian government is committed to combating communalism and promoting social harmony.
• Monarchy:
• A monarchy is a form of government in which a single person, usually a king or queen, holds supreme power.
• The power is typically inherited.
• India is not a monarchy. It is a republic.
• The head of state is elected, not hereditary.
• Monarchies can be absolute or constitutional.
• In a constitutional monarchy, the monarch's power is limited by a constitution.
• Oligarchy:
• An oligarchy is a form of government in which a small group of people holds power.
• This group can be based on wealth, social status, or other factors.
• India is not an oligarchy. It is a democracy.
• Power rests with the people, who exercise it through elected representatives.
• Oligarchies are often characterized by inequality and lack of representation

The correct answer is ​A and B.

Key Points

• Absence of mobility:
• Plants are generally stationary, rooted in one place.
• This lack of movement significantly reduces their energy expenditure.
• Animals, on the other hand, require a lot of energy for locomotion, hunting, finding food, escaping predators, and other activities.
• Plants primarily use energy for growth, reproduction, and basic metabolic processes.
• These processes are less energy-intensive compared to the activities of mobile animals.
• Plants' sessile nature allows them to conserve energy.
• They don't need to expend energy searching for food or water in the same way animals do.
• Their energy needs are primarily met through photosynthesis.
• The absence of complex muscular systems also contributes to lower energy requirements.
• Plants' structural support comes from rigid cell walls, which require less energy to maintain than animal skeletons and muscles.
• This difference in lifestyle significantly contributes to the lower energy needs of plants.
• Presence of a large proportion of dead cells in the tissues:
• While it's true that plants have a significant proportion of dead cells in their tissues (like xylem), this is more of a consequence of their lower energy needs than the cause.
• The dead cells provide structural support, reducing the need for energy-intensive living tissues for that purpose.
• It's not the presence of dead cells that causes lower energy needs; it's the lack of mobility that allows for the efficient use of dead cells for structural support, reducing overall energy needs.
• The presence of dead cells is an adaptation to a stationary lifestyle.
• Plants synthesise their own food:
• Plants do synthesize their own food through photosynthesis.
• However, photosynthesis itself requires energy (sunlight).
• While plants don't need to hunt for food, they still need energy to carry out photosynthesis and other metabolic processes.
• The fact that plants are autotrophs (produce their own food) doesn't fully explain their lower energy needs compared to animals.
• It's more accurate to say that synthesizing their own food contributes to their ability to have lower energy needs, but the primary reason remains their lack of mobility.
• Plants release O2 during respiration:
• Plants release oxygen during photosynthesis, not respiration.
• During respiration, plants, like animals, consume oxygen and release carbon dioxide.
• Respiration is a process that consumes energy, not generates it in the way photosynthesis does.
• The fact that they release oxygen during photosynthesis is related to their ability to produce their own food, but it's not directly related to their lower energy needs compared to animals.

The correct answer is 18th group.

Key Points

• 18th group:
• An element with the electronic configuration 2, 8, 8 has a total of 18 electrons.
• Since it's a neutral atom, it also has 18 protons, meaning its atomic number is 18.
• The element with atomic number 18 is Argon (Ar).
• Argon is a noble gas, and noble gases are located in the 18th group (also known as Group 0) of the periodic table.
• The 18th group elements have a full outermost electron shell (either 8 electrons, as in the case of Argon, or 2 electrons for Helium).
• This full outer shell makes them chemically inert or very unreactive.
• Other noble gases include Helium (He), Neon (Ne), Krypton (Kr), Xenon (Xe), and Radon (Rn).
• The 18th group elements are often used in lighting, welding, and other applications where their inertness is beneficial.
• The stability of their electron configuration is the reason for their lack of reactivity.

Additional Information

• 10th group:
• The 10th group elements are transition metals.
• They do not have a simple electronic configuration ending in 8 like the element described.
• The 10th group includes elements like Nickel (Ni), Palladium (Pd), and Platinum (Pt).
• These elements have partially filled d orbitals.
• They are known for their catalytic properties and their use in various alloys.
• 4th group:
• The 4th group elements are also known as the carbon group.
• They have four valence electrons in their outermost shell.
• Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn), and Lead (Pb) are in this group.
• They exhibit a wide range of properties, from non-metallic (Carbon) to metallic (Tin and Lead).
• 6th group:
• The 6th group elements are also known as the oxygen group or the chalcogens.
• They have six valence electrons in their outermost shell.
• Oxygen (O), Sulfur (S), Selenium (Se), Tellurium (Te), and Polonium (Po) are in this group.
• Oxygen is essential for life, while other elements in the group have diverse applications.

The logic followed here is:

Hence, "Option 4" is the correct answer.

The correct answer is -1.

Key Points

• Given:
• Object distance (u) = -5 cm (negative because it's to the left of the mirror)
• Focal length (f) = -2.5 cm (negative for a concave mirror)
• Using the mirror formula: 1/v + 1/u = 1/f
• Substituting the values: 1/v + 1/(-5) = 1/(-2.5)
• Solving for image distance (v):
• 1/v = 1/(-2.5) + 1/5
• 1/v = (-2 + 1)/5
• 1/v = -1/5
• v = -5 cm
• Calculating magnification (m): m = -v/u
• Substituting the values: m = -(-5)/(-5)
• Therefore: m = -1

The correct answer is CH3OH and C2H5OH.

Key Points

• CH3OH and C2H5OH:
• A homologous series is a series of organic compounds with the same functional group but differing by a CH2 group in their carbon chain.
• CH3OH (methanol) and C2H5OH (ethanol) both belong to the alcohol family (functional group -OH).
• Ethanol has one more CH2 group than methanol.
• The difference in their molecular formulas is CH2 (C2H5OH - CH3OH = CH2).
• Therefore, they are consecutive members of the same homologous series (alcohols).
• Members of a homologous series have similar chemical properties due to the same functional group.
• Their physical properties show a gradual change with increasing carbon chain length.
• The general formula for alcohols is CnH2n+1OH.
• Methanol (CH3OH) has n=1.
• Ethanol (C2H5OH) has n=2.

Additional Information

• C3H7OH and CH3OH:
• C3H7OH (propanol) and CH3OH (methanol) are both alcohols.
• However, the difference between them is two CH2 groups (C3H7OH - CH3OH = C2H4), not one.
• While they belong to the same homologous series (alcohols), they are not consecutive members.
• For a correct pair, the difference should be exactly one CH2 unit.
• CH3OH and CH4:
• CH3OH (methanol) is an alcohol (functional group -OH).
• CH4 (methane) is an alkane (no functional group).
• They belong to different homologous series.
• Alkanes are hydrocarbons with only single bonds.
• Alcohols contain the hydroxyl (-OH) group.
• These two compounds have vastly different chemical properties due to the difference in their functional groups.
• CH3OH and C3H7OH:
• As explained before, both are alcohols, but the difference between them is two CH2 groups, not one.
• They are not consecutive members of the homologous series.
• The difference in their molecular formulas is C2H4.

The correct answer is 11.

Key Points

The Shanti Swaroop Bhatnagar Prize for Science and Technology is an award given by the Government of India to recognize outstanding contributions to science. It is considered one of the most prestigious awards in the country for scientific achievement.

• The award is named after Shanti Swaroop Bhatnagar, the founder and first Director-General of the Council of Scientific and Industrial Research (CSIR) in India.
• It is presented annually by the Prime Minister of India.
• The award recognizes scientists who have made exceptional contributions to any branch of science, including engineering, medical, agricultural, and mathematical sciences.
• Individuals of Indian origin engaged in research in any field of science and technology up to the age of 45 years are eligible for this award.
• The award consists of a citation, a plaque, and a cash prize.
• The cash prize is typically a significant amount, though the exact sum can vary.
• The Shanti Swaroop Bhatnagar Prize is awarded for research contributions made primarily in India during the five years preceding the award.
• The selection process is rigorous and involves a panel of eminent scientists who evaluate the nominations.
• The award is usually announced in September each year.
• The number of awardees can vary from year to year, depending on the quality of nominations received.
• There's no fixed number of awards given each year.
• It's not uncommon for the award to be shared by multiple scientists in a particular category.
• The Shanti Swaroop Bhatnagar Prize plays a vital role in promoting scientific excellence in India.
• It inspires young scientists to pursue careers in research and development.
• The award recognizes and celebrates the achievements of Indian scientists who are making significant contributions to their respective fields.

Shortcut Trick

Let the width be w.

Length = w + 5.

Area = Length × Width ⇒ w(w + 5) = 215.

Expanding gives w² + 5w − 215 = 0.

∴ The correct answer is w² + 5w − 215 = 0.

Alternate Method

Given:

Width of the rectangle = w cm

Length of the rectangle = w + 5 cm

Area of the rectangle = 215 cm²

Formula Used:

Area = Length × Width

Calculations:

⇒ 215 = (w + 5) × w

⇒ 215 = w² + 5w

⇒ w² + 5w − 215 = 0

∴ The correct answer is w² + 5w − 215 = 0.

Additional Information

Quadratic Equation Standard Form

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

Perimeter of a Rectangle

The distance around the outside of a rectangle is given by P = 2 × (Length + Width).

Nature of Roots

For a quadratic equation, the discriminant D = b² − 4ac determines if the roots are real or imaginary.

Given:

Expenditure (in thousands):

April = 35

May = 40

June = 45

August = 45

September = 45

October = 25

To find the average of the expenditures in April, May, June, August, September, and October.

Formula used:

Average = (Sum of expenditures) ÷ (Number of months)

Calculation:

Sum of expenditures = 35 + 40 + 45 + 45 + 45 + 25

⇒ Sum = 235

Number of months = 6

Average = 235 ÷ 6

⇒ Average = 39.16 = 39

∴ The approximate average expenditure is 39 thousand.

Shortcut Trick

Use the Algebraic Identity: a³ + b³ = (a + b)³ − 3ab(a + b)

Given Sum (a + b) = 25 and Product (ab) = 136.

⇒ Sum of cubes = 25³ − 3 × 136 × 25

⇒ Sum of cubes = 15625 − 10200 = 5425

∴ The correct answer is 5425.

Alternate Method

Given:

Sum of numbers (a + b) = 25

Product of numbers (ab) = 136

Formula Used:

1. a² + b² = (a + b)² − 2ab

2. a³ + b³ = (a + b)(a² − ab + b²)

Calculations:

⇒ a² + b² = 25² − 2 × 136

⇒ a² + b² = 625 − 272 = 353

⇒ a³ + b³ = 25 × (353 − 136)

⇒ a³ + b³ = 25 × 217

⇒ a³ + b³ = 5425

∴ The correct answer is 5425.

Additional Information

Difference of Cubes

The formula for the difference of two cubes is a³ − b³ = (a − b)(a² + ab + b²).

Square of a Trinomial

For three numbers, the identity is (a + b + c)² = a² + b² + c² + 2(ab + bc + ca).

Sum and Product Relation

The individual numbers can be found using the quadratic equation x² − (sum)x + (product) = 0.