ICAR Technician 2 March 2022 Shift 2 (Previous Year Paper)

The correct answer is Agra.

Key Points

• In 1526, Babur defeated the Sultan of Delhi at Panipat and occupied Delhi and Agra.
• The first battle of Panipat was fought in 1526.
• The first battle of Panipat was fought between the Mughal invader Babur and Ibrahim Lodi.
• It marked the beginning of the Mughal Empire, i.e, Babur defeated Lodi and captured the throne of Delhi.

Additional Information 

• ​The Second Battle of Panipat 
• It was fought on 5 November 1556
• It was fought between Akbar and Samrat Hem Chandra Vikramaditya (Hemu).
• Akbar defeated Hemu in this battle.
• The Third Battle of Panipat
• It was fought in 1761
• It was fought between the Afghan invader Ahmad Shah Abdali and the Marathas under Sadashivrao Bhau Peshwa of Pune.
• Abdali won this battle.
• The war led to a power vacuum, which later led to the British conquest of India.

The correct answer is A person, who is not associated with any government scheme or organization, can be below the poverty line.

Key Points

• Poverty means that the income level from employment is so low that basic human needs can't be met.
• The poverty line varies with time and place.
• Hence, Statement 1 is true.
• A poor household is defined as one with an expenditure level below a specific poverty line.
• Hence, Statement 2 is not true.
• As per the Rangarajan committee report (2014), the poverty line is estimated as Monthly Per Capita Expenditure of Rs. 1407 in urban areas and Rs. 972 in rural areas.
• A common method used to measure poverty is based on income.
• Hence, Statement 3 is true.
• Poverty line estimation in India is based on consumption expenditure and not on income levels.
• Poverty is measured based on consumer expenditure surveys of the National Sample Survey Organisation.
• The incidence of poverty is measured by the poverty ratio, which is the ratio of the number of poor to the total population expressed as a percentage. It is also known as head-count ratio.
• Alagh Committee (1979) determined a poverty line based on a minimum daily requirement of 2400 and 2100 calories for an adult in Rural and Urban area respectively.
• The measurement limits of the poverty line may be based on the consumption levels of the population.
• Hence, Statement 4 is true.

Additional Information

• According to the World Bank, Poverty is a pronounced deprivation in well-being and comprises many dimensions.
• It includes low incomes and the inability to acquire the basic goods and services necessary for survival with dignity.
• Poverty also encompasses low levels of health and education, poor access to clean water and sanitation, inadequate physical security, lack of voice, and insufficient capacity and opportunity to better one's life.

The correct answer is Sanket Mahadev Sargar.

Key Points

• Sanket Mahadev Sargar won a gold medal in the Men's 55 kg snatch category at the ongoing Commonwealth Weightlifting Championships 2021 in Tashkent on 7 December 2021.
• He lifted the weight of 113 kg.
• With this lift, Sargar also created the new snatch national record.
• The championship is currently being held concurrently in Tashkent along with World Weightlifting Championships.

Additional Information

• Sathish Sivalingam is an Indian weightlifter who won gold medals in the men's 77 kg weight class at both the 2014 and 2018 Commonwealth Games.
• Jeremy Lalrinnunga is an Indian weightlifter from Aizawl, Mizoram. He represented India in the 2018 Summer Youth Olympics in Buenos Aires.
• He won the gold medal in the Boys' 62 kg category weightlifting with a lift of 274 kg.

The correct answer is Senior citizens.

Key Points 

• The government has come up with an online employment exchange platform to cater to senior citizens seeking job opportunities.
• The SACRED portal launched by the Government of India in October 2021 is for the employment of SACRED.
• The portal developed by the Ministry of Social Justice and Empowerment is named Senior Able Citizens for Re-Employment in Dignity (SACRED).
• The International Day of Older Persons is observed on 1st October each year.

Additional Information

• Citizens above 60 years of age can register on the portal and find jobs and work opportunities.
• The Employment Portal will serve not only the senior citizens seeking employment, but also the employers, the Self Help Groups (SHGs), the senior citizens gaining skills, and other agencies or individuals.
• A number of Rs. 10 Cr would be provided for funding for the platform development along with a maintenance grant of Rs. 2 Cr per year for 5 years.
• The portal is shaped on the recommendations of the Empowered Expert Committee (EEC) report on startups for the elderly.

The correct answer is National Payments Corporation of India.

Key Points 

• The Ministry of Electronics and Information Technology prepared a draft framework for the use of blockchain technology in government services.
• The Ministry intends to use the technology in the areas of property record keeping, digital certificates, power distribution, health records as well as supply chain management.
• With the Ministry of Electronics and Information Technology, is involved in offering Blockchain as a Service under the National Blockchain Strategy:
• National Informatics Center Service Institute
• National Informatics Center
• Center for Advanced Computing Development (C-DAC)
• **Hence, National Payments Corporation of India is not correct.**​

Important Points

• The blockchain technology operates on a distributed ledger system that is owned by everyone, participants can read, write, or make changes to the ledger.
• The national framework has suggested that blockchain could be set up in one of the four architectures-
• public and permission less
• public but with permissions
• private and permission less
• private and with permissions

Additional Information

• National Payments Corporation of India was the initiative of the Reserve Bank of India (RBI) and the Indian Banks Association (IBA).
• National Payments Corporation of India (NPCI) is an umbrella organization for operating retail payments and settlement systems in India.
• National Payments Corporation of India has been incorporated as a “Not for Profit” Company.
• RuPay debit card is the product of the National Payments Corporation of India.
• BHIM App (Bharat Interface for Money) is also the product of the National Payments Corporation of India.

The correct answer is Dumhal.

Key Points 

• Dumhal is performed in Jammu and Kashmir by the Wattal tribe.
• Dumhal dancer wears colorful costume while the men wear tall conical hat.
• Other dances of Kashmir:
• Rauf
• Hikat
• Mandjas
• Kud Dandi Nach
• Damali

Additional Information

• 'Chholiya' is the famous dance form of Kumaon, Uttarakhand.
• It is generally performed at the Kumaoni weddings.
• It is a sword dance that accompanies a marriage procession.
• The Hurka Baul dance is performed during the cultivation of paddy and maize in Uttarakhand.
• The dance name is derived from Hurka, the drum which is the only musical accompaniment, and baul, the song.
• In the Hurka Baul dance, the singer narrates the story of battles and heroic deeds, while the performers enter from two opposite sides and enact the stories in a series of crisp movements.
• Charkula is a dance performed in the Braj region of Uttar Pradesh.
• In this dance, veiled women balancing large multi-tiered circular wooden pyramids on their heads dance to songs about Krishna.

The correct answer is Canara Bank.

Key Points 

• Syndicate Bank has become the fourth largest public sector bank in India after its merger with Canara Bank with effect from 01 April 2020.
• The Reserve Bank of India (RBI) excluded six Public Sector Banks (PSBs) from the second schedule of the RBI Act,1934, due to their merger with the other banks effectively from the April 1st, 2020.

Additional Information

• The six banks which are excluded recently from the second schedule of the RBI are Syndicate Bank, Oriental Bank of Commerce, United Bank of India, Andhra Bank, Corporation Bank, and Allahabad bank.

 Banks mergers with other banks are - 

The correct answer is Sodium hydrogen carbonate.

Key Points

• Sodium hydrogen carbonate is also an ingredient in antacids.
• Being alkaline, it neutralizes excess acid in the stomach and provides relief.
• It is also used in soda-acid fire extinguishers.
• Uses of sodium hydrogen carbonate (NaHCO3):
• For making baking powder, which is a mixture of baking soda (sodium hydrogen carbonate) and a mild edible acid such as tartaric acid. When baking powder is heated or mixed in water, the following reaction takes place –
• NaHCO3+ H+→ CO2+ H2O + Sodium salt of an acid.

Additional Information

• Sodium carbonate (washing soda) is used in glass, soap and paper industries.
• It is used in the manufacture of sodium compounds such as borax.
• Chile Saltpetre is the common name for Sodium Nitrate (NaNO3).
• It is an alkali metal nitrate salt.
• Sodium hydroxide is used for making soaps and detergents.
• It is used for making artificial textile fibers.
• It is used in the manufacture of paper.
• It is used in purifying bauxite ore from which aluminium metal is extracted.

The correct answer is Delhi.

Key Points 

• The Pradhan Mantri UDAY (PM-UDAY) scheme, launched in October 2021, provides ownership rights to residents of unauthorized colonies in Delhi.
• Under PM Uday Yojana, residents from unauthorized colonies in Delhi would be eligible to apply for the rights of ownership via a dedicated online portal.
• In case the application under DDA pm uday yojana is approved, the applicant would receive the registry papers just by the payment of a small fee.
• The complete procedure of dda pm uday is being conducted by DDA – Delhi Development Authority (DDA pm uday).

Additional Information

• In Delhi there are around 50 lakh people living in unauthorized/illegal colonies.
• In 2021 around 4 lakh applications were received by the government.
• It is estimated that around 50 lakh people across Delhi live in different unauthorized colonies that are usually located on public or private land.

The correct answer is Allahabad​.

Key Points

• The “Central Organization for Railway Electrification” was founded in 1979.
• Its headquarter is located in Allahabad (Now Prayagraj), Uttar Pradesh.
• The unit of this organization operates in -

Important Points

• The other organizations involved in the electrification of the Indian railway include -
• RVNL (Rail Vikas Nigam Limited)
• IRCON (International or Indian railway construction limited)
• PGCIL (Power Grid Corporation of India Limited)
• RITES (Rail India Technical and Economic Services)

Additional Information

• The headquarter has several departments such as -
• Electrical
• Signal and Telecommunication
• Civil engineering
• Vigilance and Financial department

The correct answer is Mission Poshan 2.0.

Key Points 

• As per Budget 2021-22, Supplementary Nutrition Program and Poshan Abhiyaan were to be merged and launched as Mission Poshan 2.0.
• The objectives of the mission are-
• To strengthen nutritional content, delivery, outreach, and outcome
• Merging the Supplementary Nutrition Programme and the Poshan Abhiyan
• Intensified strategy to be adopted to improve nutritional outcomes across 112 Aspirational Districts
• Mission Poshan 2.0 is a part of Health and Wellbeing which is one of the six pillars of the Union Budget.

Additional Information

• Rs. 2,23,846 crore outlay for Health and Wellbeing in 2021-22 as against Rs. 94,452 crore in BE 2020-21 – an increase of 137%
• The focus will be on strengthening three areas:
• Preventive
• Curative
• Wellbeing
• Rs. 64,180 crore outlay over 6 years for PM AatmaNirbhar Swasth Bharat Yojana – a new centrally sponsored scheme to be launched, in addition to National Health Mission.
• The Budget proposals for 2021-2022 rest on 6 pillars-
• Health and Wellbeing
• Physical & Financial Capital, and Infrastructure
• Inclusive Development for Aspirational India
• Reinvigorating Human Capital
• Innovation and R&D
• Minimum Government and Maximum Governance

The correct answer is Vedika.

Key Points 

• ​The wooden or stone railing that surrounds the stupa called Vedika.
• The stupa is enclosed by a vedika.
• At Barhut, Sanchi, and Amaravati the vedika consisted of upright pillars with three transverse bars known as the suchi.
• A Stupa is a dome-shaped sacred burial mound of brick that was used to house Buddha's relics,
• It is used to commemorate significant facts and events related to Buddhism.
• Sanchi, Sarnath, Amaravati, and Bharhut are among the oldest known stupas.

Additional Information

• Characteristic of Stupa:
• Initially, mounds of Earth are encased in bricks.
• Stupas are usually built on a foundation laid with blocks of stone or bricks.
• On this foundation, a hemispherical dome was raised called Anda.
• The drum of the stupa became more elongated and elevated.
• It took the form of a cylindrical vessel.
• On the truncated top of the hemisphere, a harmika is placed, surrounded by a railing.
• The railing is provided with four gateways.
• A path of circumambulation runs around the stupa at the ground level within the railing called Pradakshinapath.
• Toranas were ceremonial gateways around the stupas

The correct answer is Pensioners.

Key Points 

• Union Minister Jitendra Singh launched  Unique face recognition for pensioners.
• This face recognition technique of giving life certificates is a historic and far-reaching reform since it will touch the lives of not only 68 lakh central government pensioners but also those under EPFO and state government.
• Face recognition technology will benefit pensioners across the country in providing Life Certificate by simply using the mobile app.

Additional Information

• Face recognition technology is a way of recognizing a human face through technology.
• This technology uses biometrics to map facial features from a photograph or video and compares the information with a database of known faces to find a match.

The correct answer is Vegetables.

Key Points 

• Fruits and vegetables are called protective foods as they are rich in vitamins and minerals that keep us healthy and protect us from diseases.
• Protective foods are the foods that contain adequate amounts of vitamins, minerals, and high quality proteins, and they protect against development of a deficiency disease.
• The food is includes of leafy or yellow vegetables, citrus fruits, meat, milk, eggs.

Additional Information

• Based on the functions that are performed by various types of food items available, they can be broadly divided into three groups.
• Energy giving food: 
• ​Foods containing fats and  carbohydrates are also called ‘energy-giving foods’.
• Carbohydrates mainly provide energy to our bodies.
• Fats give much more energy as compared to the same amount of carbohydrates.
• **Carbohydrate-**containing food items are rice, potato, sugar, etc.
• Fats containing food items are butter and ghee.
• Bodybuilding food: 
• ​Foods containing proteins are often called ‘body-building foods’.
• Proteins are needed for the growth and repair of our bodies.
• Examples of food items containing proteins are pulses, milk, meat, etc.
• Regulatory and protective food: 
• ​Vitamins and minerals help in protecting our bodies against diseases.
• They also help in keeping our eyes, bones, teeth, and gums healthy.
• Fruits and vegetables contain vitam ins and minerals.

The correct answer is Charminar.

Key Points 

• Charminar was reported as the first building of Hyderabad.
• The Charminar is located in Telangana, India. 
• It was constructed in 1591 by Muhammad Quli Qutb Shah.
• It is a monument and mosque.  Muhammad Quli Qutb Shah built it in 1591 after shifting his capital from Golkonda to the city of Hyderabad.
• It has become a symbol of Hyderabad.
• It is listed as an archaeological and architectural treasure on the official “List of Monuments” prepared by the Archaeological Survey of India.
• It has been officially incorporated as the Emblem of Telangana for the state of Telangana.

Additional Information

• Chowmahalla Palace or Chowmahallat is the palace of the Nizams of Hyderabad State in Hyderabad, Telangana, India.
• Falaknuma Palace is a rare blend of Italian and Tudor architecture.
• It was built by Nawab Viquar-ul- Umra Bahadur, the fifth Emir from the noble Paigah family of Deccan India.
• Golconda fort was built by the Kakatiya dynasty in the 13th century.
• It is considered one of India's most outstanding citadels.

The correct answer is Manipur.

Key Points 

• Manipur won the Senior Women's Football Championship in December 2021.
• This was Manipur’s 21st title in what was the 26th edition of the senior national women’s football championship.

Important Points 

• 2021–22 Senior Women's National Football Championship:
• It is also known as Hero Senior Women's National Football Championship.
• It was the 26th edition of the Championship.
• Manipur came out to be the winners, defeating Railways by 2–1.

The correct answer is 1990.

Key Points 

• SIDBI is the principal development financial institution for promotion, financing, and development of Micro, Small, and Medium Enterprises (MSME) sector in India.
• It was established on April 2, 1990, under an Act of Parliament.
• The headquarters of the SIDBI is located in Lucknow, Uttar Pradesh.​

Important Points

• It aims to facilitate and strengthen credit flow to MSMEs and address both financial and developmental gaps in the MSME ecosystem across the country.
• It coordinates the functions of institutions engaged in similar activities.

The correct answer is Nokrek.

Key Points 

• Nokrek Biosphere Reserve is a Biosphere Reserve, a part of the Garo Hills in Meghalaya.
• The representative parts of natural and cultural landscapes extending over large areas of terrestrial or coastal/ marine ecosystems or a combination of both designated by the United Nations Educational, Scientific and Cultural Organisation (UNESCO)  is called a Biosphere Reserve.

Additional Information

Important Biosphere reserves:

The correct answer is Ribosomes.

Key Points

• Prokaryotic cells are primitive cells, i.e. they lack a true membrane-bound nucleus.
• Most of the prokaryotes are bacteria.
• Prokaryotic genetic material lies naked in the cytoplasm, and replication of DNA occurs in the cytoplasm only.
• Ribosomes are found in prokaryotic cells.
• Several prokaryotic bacterial cells like Nostoc, Anabaena are capable of nitrogen fixation, they can fix atmospheric nitrogen into ammonia.
• Autotrophic prokaryotes synthesize organic molecules from inorganic molecules of carbon dioxide.
• Plasmids are double-stranded, closed circular, symbiotic DNA molecules that occur naturally in bacteria (prokaryote), outside the bacterial chromosome.

Additional Information

• The mitochondrion is a membrane-bound structure with outer and inner membranes.
• Mitochondria are said to be the sites of aerobic respiration.
• They produce cellular energy in the form of ATP, hence they are called ‘power houses’ of the cell.
• Vacuoles are membrane-bound organelles.
• It is present in both plant and animal cells.
• Vacuoles are storage sacs for solid or liquid contents. It is also used to store food for the cell.
• Lysosomes are membrane-bound vesicular structures formed by the process of packaging in the Golgi apparatus.
• These are also called ''Suicidal bags'' because of their phagocytic activity.

The correct answer is 1829.

Key Points 

• On 4 December 1829, Lord Bentinck issued Regulation XVII, declaring Sati to be illegal and punishable in criminal courts.
• Lord William Bentinck served as Governor-General of India between 1828 and 1835.
• Raja Ram Mohan Roy was the social reformer who worked hard for the abolition of this 'Sati Pratha' ritual.
• Due to the fierce campaign and lobbying of Raja Rammohan Roy and others, Sati practice was formally banned in all the lands under Bengal Presidency by Lord William Bentinck on 4 December 1829.

Additional Information 

• 'Sati pratha' was a Hindu ritual where the widow had to sit on her husband's funeral pyre and burn alive.
• The Portuguese banned the practice in Goa by 1515.
• In the 16th century, Humayun was the first to try a royal agreement against the practice. Akbar was next to issue official orders prohibiting Sati, and since then it was done voluntarily by women.

The correct answer is 1949.

Key Points 

• The Government of India decided in May 1949 to take steps to develop a systematic collection of data on population size, its growth, etc. and set up a Census Organization in the Ministry of Home Affairs under the Registrar General of India and ex-officio Census Commissioner.
• This organization was created to prepare data on population figures, including vital statistics and census.
• Later, this office was also entrusted with the task of implementation of the Birth and Death Registration Act, 1969 in the country.
• It is a family of 34 numbers of Directorates of Census Operations is functioning under the aegis of its Headquarters—Office of the Registrar General & Census Commissioner, India, New Delhi.

Additional Information

• The responsibility of conducting the decennial Census rests with the Office of the Registrar General and Census Commissioner, India under the Ministry of Home Affairs, Government of India.
• The Census Act was enacted in 1948 to provide for the scheme of conducting a population census with the duties and responsibilities of census officers.
• Current Registrar General and Census Commissioner, India- Dr. Vivek Joshi

The correct answer is 1878.

Key Points

• The Vernacular Press Act was passed in 1878.
• The Act was modelled on Irish Press Laws.
• It provided the government with extensive rights to censor reports and editorials in the vernacular press.
• The government kept records of vernacular newspapers published.
• It was enacted to curtail the freedom of the non-English press.

Additional Information

• Criticism of the Vernacular Press Act
• Lytton's successor as viceroy, Lord Ripon (who ruled from 1880 to 1884), abolished the statute in 1881.
• The hatred it engendered among Indians, became one of the drivers for India's rising independence movement.
• Among the act’s most vocal critics was the Indian Association (founded 1876), which is generally considered to be one of the precursors of the Indian National Congress (founded 1885).

The correct answer is 2004.

Key Points 

• Tamil is the first language in India that received the classical status.
• Tamil was declared as a classical language in 2004.
• Odia is the latest addition to the list of classical languages in India.
• Odia was given the status of the classical language in 2014.
• At present, there are six languages that enjoy the 'Classical' status in India.
• All six classical languages are listed in the eighth schedule of the constitution.

Additional Information

• Sanskrit was declared as a classical language in 2005.
• Kannada was declared as a classical language in 2008.
• Telugu was declared as a classical language in 2008.
• Malayalam was declared as a classical language in 2013.

The answer is Nickel, Tungsten, Aluminum, Copper.

Important Points 

• Electrical resistivity of some substances at 20 °C:

• Silver is the best conductor because the resistivity of silver is the lowest among all, i.e., 1.6 x 10-8 Ωm.
• Hence Nickel, Tungsten, Aluminum, Copper is correct order.

Additional Information 

• Resistivity:
• Resistivity is a measure of the resistance of a given size of a specific material to electrical conduction.
• The resistivity is a figure that enables comparisons of the way in which different materials allow or resist current flow.
• The SI unit of electrical resistivity is the ohm metre (Ωm).
• It is commonly represented by the Greek letter ρ, rho.

The correct answer is Odisha.

Key Points

• The first Physical National Yogasana Championships will be held in Bhubaneshwar, Odisha from November 11 to 13, 2021.
• The event will be organized by the National Yogasana Sports Federation (NYSF) in association with the Odisha government.
• Yogasana sport for both male and female categories has also been included in Khelo India Youth Games 2021.

Additional Information 

• About Khelo India Programme:
• Khelo India was formed by merging three schemes: Rajiv Gandhi Khel Abhiyan, Urban Sports Infrastructure Scheme, and National Sports Talent Search Scheme.
• It works to promote “Sports for All” and “Sports for Excellence”.
• Its aim is the mass participation of youth in annual sports competitions through a structured competition.

Shortcut Trick

Apply alligation on the fraction of acid in both vessels:

Acid fraction in X = 3/10, Acid fraction in Y = 1/4, Target acid fraction = 5/18.

Ratio of X to Y = (5/18 − 1/4)  ∶  (3/10 − 5/18)

⇒ Ratio = (1/36)  ∶  (1/45) = 45  ∶  36 = 5  ∶  4.

∴ The correct answer is 5 : 4.

Alternate Method

Given:

⇒ Ratio of acid to water in Vessel X = 3  ∶  7

⇒ Ratio of acid to water in Vessel Y = 1  ∶  3

⇒ Required ratio of acid to water in the final mixture = 5  ∶  13

Formula Used:

By the rule of alligation:

⇒ (Quantity of Vessel X) / (Quantity of Vessel Y) = |Concentration in Y − Mean Concentration| / |Concentration in X − Mean Concentration|

Calculations:

⇒ Fraction of acid in Vessel X = 3 / (3 + 7) = 3/10

⇒ Fraction of acid in Vessel Y = 1 / (1 + 3) = 1/4

⇒ Fraction of acid in final mixture = 5 / (5 + 13) = 5/18

⇒ Applying alligation to the acid fractions:

⇒ Difference on Vessel X side = 3/10 − 5/18 = (27 − 25) / 90 = 2/90 = 1/45

⇒ Difference on Vessel Y side = 5/18 − 1/4 = (10 − 9) / 36 = 1/36

⇒ Required ratio of mixing Vessel X and Vessel Y = (1/36)  ∶  (1/45)

⇒ Required ratio = 45  ∶  36

⇒ Required ratio = 5  ∶  4

∴ The correct answer is 5 : 4.

Additional Information

Rule of Alligation

It is used to find the proportion in which two or more ingredients at their respective prices must be mixed to obtain a mixture at a specified mean price.

Single Component Focus

While solving mixture problems involving ratios, always perform calculations on only one of the components (either completely on acid or completely on water) to ensure quick and consistent results.

Mean Concentration Formula

For mixtures mixed in ratio q₁  ∶  q₂ with concentrations c₁ and c₂, the resulting concentration c_m is calculated as c_m = (c₁ × q₁ + c₂ × q₂) / (q₁ + q₂).

Given:

Reena bought a mobile phone at a discount of 20%

Had the discount received was 25%, she would have saved ₹2,000 more.

Concept used:

Cost price = Actual price × (100 - discount)%

Calculation:

Let the actual price of the phone be 100x

Cost price of Reena = 100x × (100 - 20)%

⇒ 100x × 80%

⇒ 80x

If 25% discount is given then,

Cost price of Reena = 100x × (100 - 25)%

⇒ 75x

According to the question,

80x - 75x = 2000

⇒ 5x = 2000

⇒ x = 400

So, actual cost price of Reena = 80 × 400

⇒ 32000

∴ She paid 32000 (in ₹) for the mobile phone.

Shortcut TrickAt first she received a 20% discount, 

Later, the second rate of discount is 25%,

⇒ Difference between rates = 25% - 20% = 5%

According to the question, 

⇒ 5%(MP) = 2,000

⇒ 5/100(MP) = 2,000

⇒ MP = 40,000

Now, the SP at 20% discount is, 

⇒ 80%(40,000)

⇒ 4/5 × 40,000

⇒ 32,000

∴ She paid 32000 (in ₹) for the mobile phone.

Given:

Ratio of efficiencies of X and Y is 5 : 4

X and Y can complete the same work in 10 days

Concept used:

Total work = Total time × total efficiency

Calculation:

Efficiencies ratio X to Y = 5 ∶ 4 

Total work = (5 + 4) × 10 = 90 

Work done by Y in 5 days = 4 × 5 = 20

Remaining work = 90 – 20 = 70

Remaining work completed by X in = 70/5

⇒ 14 days i.e a

Again,

The efficiency of X and Z = 70/7

⇒ 10

Efficiency of Z = 10 - 5

⇒ 5

Remaining work completed by Z in = 70/5

⇒ 14 days i.e b

So, ratio of a and b = 14 : 14

⇒ 1 : 1

∴ The value of a : b is 1 : 1.

Calculation:

Increase in production of C in 2020 = 350 - 250

⇒ 100

% increase = (100/250) × 100

⇒ 40%

Increase in production of D in 2020 = 375 - 350

⇒ 25

% increase = (25/350) × 100

⇒ 50/7%

Increase in production of E in 2020 = 400 - 320

⇒ 80

% increase = (80/320) × 100

⇒ 25%

Now,

New production of C = 350 + 350 × 40%

⇒ 490  i.e x

New production of D = 375 + 375 × 50/7%

⇒ 375 + $26\frac{11}{14}$

⇒ $401\frac{11}{14}$ i.e y

New production of E = 400 + 400 × 25%

⇒ 500 i.e z

Now,

x + y + z = 490 + $401\frac{11}{14}$ + 500

⇒ $1391 \frac{11}{14}$

∴ The sum (in lakh tonnes) of x + y + z is $1391 \frac{11}{14}$.

Given:

55% of the total voters are males and the rest are females.

40% of the males are illiterate and 40% of the females are literate.

Calculation:

Let total voters be 100x

So, Male voters = 100x × 55%

⇒ 55x

Female voters = 100x - 55x

⇒ 45x

Now,

Literate males = 55x × (100 - 40)%

⇒ 55x × 60%

⇒ 33x

So, illiterate males = 55x - 33x

⇒ 22x

Literate females = 45x × 40%

⇒ 18x

So, illiterate females = 45x - 18x

⇒ 27x

Now,

a = [(33x - 27x)/27x] × 100

⇒ a = 6/27 × 100

⇒ a = 200/9

b = [(22x - 18x)/22x] × 100

⇒ b = 4/22 × 100

⇒ b = 200/11

Now,

a : b = 200/9 : 200/11

⇒ a : b = 1/9 : 1/11

⇒ a : b = 11 : 9

∴ The value of a : b is 11 : 9.

Formula Used:

C.P [100 - loss%]% = S.P

Profit% = [Profit/C.P] × 100

Profit = S.P - C.P

Calculation:

$23 \frac{1}{3}$% = 7/30 and $33 \frac{1}{3}$% = 1/3

Let the original selling price be Rs. 30

According to the question

New selling price = 30 × $23 \frac{1}{3}$%

⇒ Rs. 7

Here, loss =  $33 \frac{1}{3}$%

According to formula used

C.P [100 - 33.33]% = 7

⇒ C.P × (2/3) = 7

⇒ C.P = Rs. 21/2 or Rs. 10.5

Now, S. P when selling at 65% of original S.P = 30 × 65%

⇒ Rs.19.5

Profit% = [(19.5 - 10.5)/10.5] × 100

⇒ 9/10.5 × 100

⇒ $85 \frac{5}{7}$%

∴ Required profit is $85 \frac{5}{7}$%.

Shortcut Trick

Add both given equations directly to eliminate y:

(3x + y − 5) + (2x − y − 5) = 0 ⇒ 5x − 10 = 0 ⇒ x = 2

Substitute x = 2 into the first equation:

3(2) + y − 5 = 0 ⇒ 6 + y − 5 = 0 ⇒ y = −1

The point of intersection is (α, β) = (2, −1), so α + β = 2 + (−1) = 1.

∴ The correct answer is 1.

Alternate Method

Given:

Equation 1: 3x + y − 5 = 0

Equation 2: 2x − y − 5 = 0

Intersection point is P(α, β).

O X Y

3x + y = 5

2x - y = 5

P(2, -1)

2

-1

Calculations:

From Equation 1, express y in terms of x:

⇒ y = 5 − 3x

Substitute the value of y into Equation 2:

⇒ 2x − (5 − 3x) − 5 = 0

⇒ 2x − 5 + 3x − 5 = 0

⇒ 5x − 10 = 0

⇒ 5x = 10

⇒ x = 2

Now, substitute x = 2 back into the expression for y:

⇒ y = 5 − 3(2)

⇒ y = 5 − 6 = −1

The point of intersection P(α, β) is (2, −1).

Therefore, α = 2 and β = −1.

Now, calculate the required value (α + β):

⇒ α + β = 2 + (−1) = 1

∴ The correct answer is 1.

Additional Information

Linear Equations in Two Variables

The general form is ax + by + c = 0. Its graph always represents a straight line on the coordinate plane.

Intersection of Two Lines

Two distinct linear equations intersect at exactly one unique point if their slopes are different, forming a unique mathematical solution.

Coordinates and Solutions

The intersection point (α, β) is the only point that simultaneously satisfies the algebraic conditions of both linear equations.

Shortcut Trick

Ratio of B profit to Total profit = 600 : 2000 = 3 : 10

Since the time period for both is same, Profit Ratio = Investment Ratio

B investment share = 3/10 of the total investment

B investment = (3 ÷ 10) × 15,000 = 4,500

∴ The correct answer is 4,500.

Alternate Method

Given:

Total investment (A + B) = ₹15,000

Total profit at the end of the year = ₹2,000

B profit share = ₹600

Formula: Profit Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂)

A Profit: 1400

B Profit: 600

Total Investment = 15,000 (10 units) B's Investment Ratio = 3 / 10

⇒ A profit = Total profit − B profit = 2000 − 600 = 1400

⇒ Profit Ratio (A : B) = 1400 : 600 = 7 : 3

⇒ Since time is equal (1 year each), Investment Ratio (A : B) = Profit Ratio = 7 : 3

⇒ Total investment units = 7 + 3 = 10 units

⇒ 10 units = 15,000

⇒ 1 unit = 15,000 ÷ 10 = 1,500

⇒ B investment = 3 units = 3 × 1,500 = 4,500

∴ The correct answer is 4,500.

Additional Information

Basic Partnership Rule

When the time period of investment is the same for all partners, the profit is distributed directly in the ratio of their capitals: P₁ : P₂ = C₁ : C₂.

Compound Partnership

When partners invest for different time periods, the profit ratio is calculated as the product of capital and time: P₁ : P₂ = C₁T₁ : C₂T₂.

Working vs Sleeping Partner

A working partner manages the business and may receive a fixed percentage of profit as salary before the remaining profit is divided based on investment ratios.

Given:

Four bells ring at intervals of 6, 8, 9 and 10 seconds.

Concept used:

For this type of question, we take the LCM of the times as the answer

Calculation:

LCM of 6, 8, 9 and 10 = 360 sec

360 sec = 6 minutes

∴ After 6 minutes they will ring together again.

Given:

The sides of a triangle are 11 cm, 60 cm and 61 cm.

Formula used:

s = (a + b + c)/2

Area of triangle = √[s (s – a) (s – b) (s – c)]

Circumradius of a triangle = abc/4Δ

Here,

a, b and c are the sides of the triangle

Δ = Area of the triangle

Calculation:

As we know,

s = (11 + 60 + 61)/2

⇒ 132/2 = 66

Now,

​Area of triangle = √[66(66 – 11)(66 – 60)(66 – 61)]

⇒ √[66 × 55 × 6 × 5]

⇒ 11 × 6 × 5

⇒ 330

Now,

Circumradius = (11 × 60 × 61)/(4 × 330)

⇒ 61/2

⇒ 30.5

∴ The radius of the circle circumscribing this triangle is 30.5 cm.

Given:

The length of the entire capsule is 16 mm and the radius of the capsule is 3 mm

Concept used:

Volume of a cylinder = πr²h

Volume of a hemisphere = 2/3πr3

Here,

r = radius

h = height or length

Calculation:

Length of the cylindrical portion of the capsule = 16 - 2 × 3

⇒ 10 mm

According to the question,

Total volume of the capsule = Volume of the cylindrical portion + 2 × Volume of the hemispherical portion

Now,

Total volume of the capsule = π3² × 10 + 2 × (2/3)π3³

⇒ π32 × 10 + 2 × 2π32

⇒ π32 × 10 + 4π32

⇒ π32(1 × 10 + 4)

⇒ π32(10 + 4)

⇒ π32 × 14

⇒ 22 × 9 × 2

⇒ 396

∴ The maximum amount (in mm3) of medicine that can be filled in it is 396.

Given:

Time taken by pipe A to fill the tank = 16 minutes

Time taken by pipe B to empty the tank = 24 minutes

Calculation: 

Efficiency of pipe A = 1/16

Efficiency of pipe B = 1/24

Filling of the tank by pipe A in 20 minutes = 20 × 1/16

⇒ 5/4 

Amount of water filled by pipe A which is in excess after filling the tank = 5/4 – 1 = 1/4 

This excess water is emptied by pipe B when they open together.

Time taken by pipe B to empty excess water = (1/4)/(1/24)

⇒ 6 minutes

∴ After 6 minutes if pipe B is closed, the tank will be filled in 20 minutes

Given:

Time = 2 years

Rate = 20%

Concept used:

C.I = P[(1 + R/100)^T - 1]

When half yearly interest is calculated

Rate = R/2

Time = 2T

Here,

P = Sum

R = Rate

T = Time

Calculation:

Let the sum be Rs. P

According to the question,

$\rm P[(1 +\frac{10}{100})^4 - 1] - P[(1+\frac{20}{100})^2-1] = 1205$

⇒ $\rm P[(1 +\frac{1}{10})^4 - 1] - P[(1+\frac{1}{5})^2-1] = 1205$

⇒ $\rm P[(\frac{11}{10})^4 - 1] - P[(\frac{6}{5})^2-1] = 1205$

⇒ $\rm P[(\frac{14641}{10000}) - 1] - P[(\frac{36}{25})-1] = 1205$

⇒ $\rm P[(\frac{14641-10000}{10000})] - P[(\frac{36-25}{25})] = 1205$

⇒ $\rm P[(\frac{4641}{10000})] - P[(\frac{11}{25})] = 1205$

⇒ $\rm P[(\frac{4641}{10000}) - (\frac{11}{25})] = 1205$

⇒ $\rm P[(\frac{4641-4400}{10000})] = 1205$

⇒ $\rm P[(\frac{241}{10000})] = 1205$

⇒ P = 5 × 10000

⇒ P = 50000

So, sum = Rs. 50000

Now,

Amount = 50000(1 + 10/100)²

⇒ 50000(1 + 1/10)2

⇒ 50000(11/10)2

⇒ 50000 × 121/100

⇒ 60500

∴ Required amount is ₹ 60500.

Given:

Three batches of student = 80, 70, 65

The average marks of three batches = 70, 65, 75

Formula Used:

Average = sum of data/No. of data

Calculation:

Sum of marks of 80 student = 80 × 70 

⇒ 5600 

Sum of marks of 70 student = 70 × 65 

⇒ 4550 

Sum of marks of 65 student = 65 × 75 

⇒ 4875

Now,

(5600 + 4550 + 4875)/(80 + 70 + 65)

⇒ 15025/215

⇒ 69.88 ≈ 70

∴ The average marks of all students is 70.

Calculation:

Silver medals won by A = (55 - 11) × 6/11

⇒ 44 × 6/11

⇒ 24

Silver medals won by B = (72 - 18) × 5/9

⇒ 54 × 5/9

⇒ 30

Silver medals won by C = (118 - 31) × 2/3

⇒ 87 × 2/3

⇒ 58

Silver medals won by E = (80 - 15) × 8/13

⇒ 65 × 8/13

⇒ 40

Total number of silver medals won by A, B, C, and E = 24 + 30 + 58 + 40

⇒ 152

Average = 152/4

⇒ 38

∴ Required answer is 38.

Given:

(5x - 3)3 + (3x - 5)3 + (3x - 1)3 = 45 (x - $\frac 3 5$) (3x - 5) (x - $\frac 1 3$)

Concept used:

If (a + b + c) = 0

Then a³ + b³ + c³ = 3abc

Calculation:

(5x - 3)3 + (3x - 5)3 + (3x - 1)3 = 45 (x - $\frac 3 5$) (3x - 5) (x - $\frac 1 3$)

⇒ (5x - 3)3 + (3x - 5)3 + (3x - 1)3 = 45 ( $\frac {5x -3}{5}$) (3x - 5)( $\frac {3x-1}{3}$)

⇒ (5x - 3)3 + (3x - 5)3 + (3x - 1)3 = 3(5x - 3)(3x - 5)(3x - 1)

So,

(5x - 3) + (3x - 5) + (3x - 1) = 0

⇒ 5x - 3 + 3x - 5 + 3x - 1 = 0

⇒ 11x - 9 = 0

⇒ 11x = 9

⇒ x = 9/11

Now,

($\frac {11} 9$x + 5)3 = ($\frac {11} 9$ × $\frac {9}{11}$ + 5)3

⇒ (1 + 5)3

⇒ 63

⇒ 216

∴ Required answer is 216.

Given:

$0 . \overline{32}+0.5 \overline{48}-0.2 \overline{9}+(0.6 \overline{5} \div 0 . \overline{59})$

Concept used:

$0.\bar{ab} = \frac{ab}{99}$

$0.a\bar{b} = \frac{ab - a}{90}$

$a.b\bar{c} = \frac{abc - ab}{90}$

Calculation:

$0 . \overline{32}+0.5 \overline{48}-0.2 \overline{9}+(0.6 \overline{5} \div 0 . \overline{59})$

⇒ $0 . \overline{32}+0.5 \overline{48}-0.2 \overline{9}+(\frac{65 - 6}{90} \div \frac{59}{99})$

⇒ $0 . \overline{32}+0.5 \overline{48}-0.2 \overline{9}+(\frac{59}{90} \div \frac{59}{99})$

⇒ $0 . \overline{32}+0.5 \overline{48}-0.2 \overline{9}+(\frac{59}{90} \times \frac{99}{59})$

⇒ $\frac{32}{99}+\frac{548-5}{990}- \frac{29 - 2}{90}+\frac{11}{10}$

⇒ $\frac{32}{99}+\frac{543}{990}- \frac{27}{90}+\frac{11}{10}$

⇒ $\frac{320+543-297+1089}{990}$

⇒ $\frac{1655}{990}$

⇒ $\frac{1671 - 16}{990}$

⇒ $1.6 \overline{71}$

∴ The required answer is $1.6 \overline{71}$.

Shortcut Trick

Third proportional a = (0.8 × 0.8) ÷ 0.4 = 1.6

Mean proportional b = √(13.5 × 0.24) = √3.24 = 1.8

Required value (a + b) = 1.6 + 1.8 = 3.4

∴ The correct answer is 3.4.

Alternate Method

Given:

a = Third proportional of 0.4 and 0.8

b = Mean proportional of 13.5 and 0.24

Formula Used:

Third proportional of x and y is a = y² ÷ x

Mean proportional of x and y is b = √(x × y)

0.4 : 0.8 :: 0.8 : a a = 1.6 13.5 : b :: b : 0.24 b = 1.8 Final Sum: a + b = 3.4

Calculations:

⇒ a = (0.8 × 0.8) ÷ 0.4

⇒ a = 0.64 ÷ 0.4 = 1.6

⇒ b = √(13.5 × 0.24)

⇒ b = √(3.24) = 1.8

⇒ a + b = 1.6 + 1.8 = 3.4

∴ The correct answer is 3.4.

Additional Information

Fourth Proportional

If four quantities a, b, c, and d are in proportion (a:b :: c:d), then d is the fourth proportional, calculated as d = (b × c) ÷ a.

Continued Proportion

Three quantities a, b, and c are in continued proportion if a:b = b:c, which leads to the relation b² = ac.

Duplicate Ratio

The duplicate ratio of two numbers x and y is the ratio of their squares, expressed as x² : y².

Given:

$45 \div 20 - \frac{5}{4}$ of $\left(\frac{8}{3} \times \frac{9}{16}\right) + \left(\frac{9}{8} \times \frac{3}{4}\right) - \left(\frac{5}{32} \div \frac{15}{21}\right) + \left(\sqrt{16} \times \frac{\sqrt{1875}}{\sqrt{3888}} \div \frac{\sqrt{1200}}{\sqrt{768}}\right) \times \frac{\sqrt{175}}{\sqrt{1792}}$

Formula used:

BODMAS Rule

Calculations:

$45 \div 20 - \frac{5}{4}$ of $\frac{3}{2} + \frac{27}{32} - \frac{7}{32} + \left(4 \times \frac{25}{36} \div \frac{5}{4}\right) \times \frac{5}{16}$

⇒ $\frac{9}{4} - \left(\frac{5}{4} \times \frac{3}{2}\right) + \frac{20}{32} + \left(\frac{20}{9} \times \frac{5}{16}\right)$

⇒ $\frac{9}{4} - \frac{15}{8} + \frac{5}{8} + \frac{25}{36}$

⇒ $\frac{18 - 15}{8} + \frac{5}{8} + \frac{25}{36}$

⇒ $\frac{3}{8} + \frac{5}{8} + \frac{25}{36}$

⇒ $1 + \frac{25}{36} = \frac{61}{36}$

∴ The correct answer is option (3).

Given:

The speed of a boat in still water is 25 km/h.

The speed of the stream is 3 km/h.

Concept used:

Time = Distance/speed

Upstream = Speed of the object - Speed of the stream

Downstream = Speed of the object + Speed of the stream

Calculation:

Upstream speed = 25 - 3

⇒ 22 km/h

Downstream speed = 25 + 3

⇒ 28 km/h

Now,

x = (112/28) + (44/22)

⇒ x = 6

y = (112/22) + (44/28)

⇒ y = 513/77

Now,

x + y = 6 + 513/77

⇒ (6 + 513)/77

⇒ (975)/77

∴ The value of x + y in hours is $\frac{975}{77}$.

Given:

An amount of ₹ 1,450 was given as a loan at the beginning of the year at a certain percentage per annum. After 8 months, another amount of ₹ 725 was given as loan but this time the rate was double than before

Total interest = Rs. 67

Concept used:

S.I = (P × T × R)/100

Here,

P = Sum

T = Time

R = Rate

Calculation:

Let the rate of interest be x

According to the question,

$\frac{1450 × x}{100} + \frac{725 × 4 × 2x}{100 × 12} = 67$

⇒ $\frac{1450x}{100} + \frac{1450x}{300} = 67$

⇒ $\frac{4350x + 1450x}{300} = 67$

⇒ $\frac{5800x}{300} = 67$

⇒ x = (67 × 3)/58

⇒ x = 3.465 ≈ 3.47%

∴ The original interest rate is 3.47%.

Given:

OO' = 12 cm and AB = 16 cm

Concept used:

We know that perpendicular from the centre of the circle to a chord bisects the chord.

Calculation:

Equal circles have same radius.

So, Radius of the both circles will be R.

Since ΔOCA and ΔO’CA are congruent triangles.

OC = OC = OO’/2

⇒ 12/2 = 6 cm

AB is chord and OC is perpendicular to AB.

So, AC = AB/2

⇒ 16/2 = 8 cm

In ΔOCA,

By the Pythagoras Theorem,

OA² = OC² + AC²

⇒ R² = 6² + 8²

⇒ R2 = 36 + 64

⇒ R2 = 100

⇒ R = 10 cm

So, diameter = 10 × 2

⇒ 20 cm

∴ The diameter (in cm) of each circle is 20.

Given:

The ratio of the speeds (in km/h) of A and B is 6 : 7

Concept used:

Speed of A/Speed of B = √Time of B/Time of A

Calculation:

$5 \frac{4}{9}$ = $\frac{49}{9}$

Now,

6/7 = √[p/(49/9)]

⇒ 6/7 = √[9p/49]

Squaring on both sides

36/49 = 9p/49

⇒ 9p = 36

⇒ p = 4

∴ The value of p is 4.

Given:

Side of cube = 5 m = 500 cm

Side of small cube = 12.5 cm

Formula used: 

Volume of cube = (side)³

Calculation:

Let the number of small cubes be N.

According to the question,

Volume of cube = N × volume of small cube

⇒ 500³ = N × 12.5³

⇒ N = (500/12.5)³

⇒ N = 403

⇒ N = 64000

∴ 64000 small cubes can be obtained.

Given:

The angles of elevation of the top of the lighthouse are 30° and 45° respectively

Concept used:

Calculation:

Let BD be the lighthouse and A and C be the positions of the ships.

Then, BD = 100 m, 

∠BAD = 30°, ∠BCD = 45°

In ΔABD, we have

tan30° = BD/BA

⇒ 1/√3 = 100/BA

⇒ BA = 100√3

In ΔCBD, we have

tan45° = BD/BC

⇒ 1 = 100/BC

⇒ BC=100 m

Distance between the two ships = AC = BA + BC

⇒ 100√3 + 100

⇒ 100(√3 + 1)

⇒ 100(1.73 + 1)

⇒ 100 × 2.73

⇒ 273 m

∴ The distance (in m) between the two ships (closest to an integer) is 273.

The correct answer is Chlorine gas at the anode and hydrogen gas at the cathode.

Concept:

• Electrolysis is a process caused by passing an electric current through a substance.
• It is carried out in an electrolytic cell.
• It is used in metallurgical processes such as the extraction or purification of metals from ores or compounds.
• Ions are moved to an electrode during electrolysis.
• Ions cannot move in solid states, making them unsuitable for electrolysis.

Explanation:

• Brine is a water-based, highly concentrated solution of sodium chloride (NaCl).
• Sodium chloride is decomposed by electrolysis and forms sodium hydroxide at the cathode.
• During this process, chlorine gas (Cl) gets liberated at the anode, and Hydrogen (H) gas is liberated at the cathode.
• At anode
• 2Cl^- → Cl₂ (g) + 2e^-
• At cathode
• 2H⁺ + 2e^- → H₂ (g)

Concept:

Refraction of Light: 

• The bending of the ray of light passing from one medium to the other medium is called refraction.

Refractive Index (n):

• n = sin i / sin r, where 'i' =  angle of incidence  and 'r' = angle of refraction.
• Also, n = c/v, where c = speed of light in a vacuum, and v = speed of light in a medium.

Explanation:​

Relative refractive index:

• It refers to the refractive index of one material medium with respect to another one.
• $n_{21}= \frac{n_{2}}{n_{1}}$

Refractive index of glass with respect to benzene:

∴ n = \(\frac{Refractiveindexofglass}{Refractiveindexofbenzene}\) = $\frac{1.65}{1.5}$ = 1.1

• Greater the refractive index, the denser the medium.
• Thus, glass (1.65) is denser than benzene (1.5).
• When the ray of light moves from a denser to a rarer medium, the refracted ray moves away from the normal.
• When the ray of light moves from a rarer to a denser medium, the refracted ray moves towards the normal.
• Thus, when a light ray will move from crown glass to dense flint glass, it will move towards the normal.

As here light moves from rarer (benzene) to a denser medium (glass) it will move towards the normal and refractice index of glass w.r.t. is 1.1

The correct answer is The solution will become more acidic and the pH will decrease.

Concept:

• pH means the potential of Hydrogen.
• The pH of a solution is a measure of the number of hydrogen ions present.
• The higher the concentration of hydrogen gas, the lower the pH of the solution.
• It is used to determine whether a solution is acidic or alkaline.
• The pH scale ranges from 0 to 14.
• If the pH is lesser than 7, the solution is acidic.
• If the pH is greater than 7, the solution is basic.
• If the pH is 7, the solution is neutral.

Explanation:

• The pH of an acid is less than of neutral and basic solutions.
• When we add acid to neutral water, the concentration of hydrogen ions increases.
• As a result, when HCl is added to the solution, the acidity increases and pH decreases.
• If a few drops of HCl are added to a solution (pH of 6.5), then pH will become a little less than 6.5.

The correct answer is In the 1970s.​

Key Points

• Chipko movement ('Hug the Trees Movement'):
• It was a forest conservation movement in India.
• Chipko movement is also called  'Chipko Andolan'.
• The movement started in 1973 at Reni village in the Chamoli district of the Garhwal region in Uttarakhand, then a part of Uttar Pradesh.
• This movement was mainly about hugging the trees to protect them from wood cutters from cutting them.
• The Chipko Movement was launched by Chandi Prasad Bhatt and Sunder Lal Bahuguna against the large-scale cutting of trees by timber contractors in the Uttarakhand hills.
• Sunder Lal Bahuguna has spent a large portion of his life fighting for the preservation of forests in the Himalayas.
• Local hill women from villages were organized and made aware of the ecological threats in the hills.
• They actively participated in the campaign.
• They embraced or hugged the trees when the timber contractors reached and forced them to leave.
• The participation of local people led to the efficient management of forests.
• This novel campaign for saving hill forests and greenery spread all along the hill region and to Karnataka in the South also in 1983.

Therefore**,** from the following given options, option three (In the 1970s) would be the most appropriate answer.

Concept:

Resistance: The property of any conductor that opposes the flow of electric current through it and depends on the shape and size of the materials, temperature, and nature of the materials is called resistance.

• It is denoted by R and the SI unit is the ohm (Ω).

⇒ R = $\frac{ρ L}{A}$

• where ρ is resistivity, L is the length and A is the area of the cross-section.

Resistivity (ρ): The property of a conductor that opposes the flow of electric current through them and is independent of the shape and size of the materials but depends on the nature and temperature of the materials is called resistivity.

• The unit for resistivity is the ohm-meter (Ω-m).
• The resistivity of a material depends on its nature and the temperature of the conductor.

Calculation:

Given Data:

• As the C is the midpoint of AB hence the length of AC and CB is the same then we take this length as l

​∴ AC = CB = l

• The radius of AC is 2r and CB is r
• The resistivity of wire AC is ρ, and wire CB is 1.5ρ
• ​Let us take the value of resistance of AC as R₁ and CB as R₂

​⇒ Resistance of wire AC is

∴ R₁ = $\frac{\rho × l}{\pi(2r)^2}$       (∵ R = $\frac{ρ L}{A}$)

∴ R1 = $\frac{\rho l}{4\pi r^2}$  ..................(1)

​⇒ Resistance of wire CB is

∴ R2 = $\frac{1.5\rho l}{\pi r^2}$  ..................(2)

• We know that in the series connection of wire the value of current remains the same and from ohm's law we also know that V = IR
• Voltage from wire AC is given as V₁

⇒ V₁ = I × R₁

⇒ V2 = I × R2

∴ $\frac{V_1}{V_2}$ = $\frac{I\cdot R_1}{I\cdot R_2}$

∴  $\frac{V_1}{V_2}$ = $\frac{R_1}{R_2}$

∴  $\frac{V_1}{V_2}$= $\frac{\frac{\rho \times l}{4\pi r^2}}{\frac{1.5\rho l}{\pi r^2}}$    ( ∵ from eq 1 and 2 )

∴  $\frac{V_1}{V_2}$ = $\frac{\rho l}{4\pi r^2}\times\frac{\pi r^2}{1.5\rho l}$

∴  $\frac{V_1}{V_2}$ = $\frac{1}{4\times 1.5}$ = $\frac{1}{6}$

The correct answer is the Tincture of iodine.

Concept:

• Most of the common solutions are made by dissolving solids in liquids, but this is not always so.
• In fact, solutions can be made by dissolving: solids in solids, solids in liquids, liquids in liquids, gases in liquids, and gases in gases.
• The various types of solutions are: 
• Solution of Solid in a Solid
• Solution of Solid in a Liquid
• Solution of Liquid in a Liquid
• Solution of Gas in a Liquid
• Solution of Gas in a Gas

Explanation:

Tincture of iodine

• A tincture of iodine is a 2-3 percent solution in an alcohol-water mixture.
• It has antiseptic properties.
• It is used to treat wounds.
• In a tincture of iodine, iodine is the solute and alcohol is the solvent.
• The presence of alcohol distinguishes tincture solutions.

Solution of Solid in a Liquid:

• This is the most common type of solution.
• Sugar solution and salt solution are the solutions of solids in liquids.
• A solution of iodine in alcohol called "tincture of iodine", is also a 'solid in a liquid type of solution.
• This is because it contains a solid dissolved in a liquid.

Key Points

• A solvent is a substance in which a solute dissolves to form a homogeneous mixture.
• A solute is a substance that dissolves in a solvent to form a homogeneous mixture.

Additional InformationSolution of Solid in a Solid:

• Metal alloys are solid-in-solid solutions.
• Example, Brass is a zinc-copper solution.
• Brass is proposed by cooling a mixture of molten zinc and molten copper.

Solution of Liquid in a Liquid:

• Vinegar is an acetic acid solution in water.
• It is a liquid in a liquid solution.

**Solution of Gas in a Liquid:**​

• Soda water is a carbon dioxide gas solution in water.
• It is a gas in a liquid solution.

Solution of Gas in a Gas:

• Air is a solution of gases like oxygen, argon, carbon dioxide, and water vapor, etc. in nitrogen gas.
• In air, nitrogen is the solvent, and all other gases are solutes.

Concept:

Power is the ability to bend light and it is equal to the reciprocal of the focal length of the lens/mirror in meters.

$Power;(P) =\frac{1}{f}$

Where f is the focal length of the lens or mirror.

• The unit of power of a lens is Dioptre when the focal length of the lens is taken in meters (m).
• The focal length of the concave lens is negative and hence its power is also negative.
• The focal length of the convex lens is positive and hence its power is also positive.

Lens formula:

⇒  $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ 

where f is focal length, v is the image distance, and u is object distance.

Power of lens: It is the reciprocal of the focal length of the lens.

$P=\frac{1}{f}$ where f is the focal length in meters. 

P = $\frac{100}{f}$ where f is the focal length in centimeters.

Explanation:

For convex lens

$Power;(P) =\frac{1}{f}$

∴ f  = $\frac{1}{p}$ = $\frac{100}{2.5}$ = 40 cm

Given Data:

Object distance u = 0.6 m = -60 cm, Focal length f = 40 cm

⇒ By using the lens formula

$⇒\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

∴ $\frac{1}{40} = \frac{1}{v} - \frac{1}{-60}$

∴ $\frac{1}{40} = \frac{1}{v} + \frac{1}{60}$

∴ $\frac{1}{40} - \frac{1}{60} = \frac{1}{v}$

∴ $\frac{1}{v} = \frac{3-2}{120}$

∴ $\frac{1}{v} = \frac{1}{120}$

∴ v = 120 cm

For concave lens

⇒ f = $\frac{1}{p}$ = $\frac{100}{-2.5}$ = - 40 cm

Given Data:

Object distance u = -130 - ( -120)= - 130 + 120 = - 10 cm,

focal length f = - 40 cm

⇒ By using the lens formula

⇒$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

∴ $\frac{1}{-40} = \frac{1}{v} - \frac{1}{-10}$

∴ $\frac{1}{-40} = \frac{1}{v} + \frac{1}{10}$

∴ $\frac{1}{-40} - \frac{1}{10} = \frac{1}{v}$

∴ $\frac{1}{v} =-\frac{1}{40} - \frac{1}{10}$

∴ $\frac{1}{v} = \frac{-1-4}{40} = \frac{-5}{40} = \frac{-1}{8}$

∴ v = - 8 cm 

Distance between original object and final image = 60 + (130- 8) = 60 + 122 = 182 cm = 1.82 m.

The correct answer is A is ammonia, B is nitrite, and C is nitrate.

Explanation:

Nitrogen Cycle- 

• The process of cycle of events by which free atmospheric nitrogen gets converted into its various chemical forms is called Nitrogen cycle.

 

Nitrogen fixation process

• In this process, the atmospheric nitrogen is fixed which is to be used by plants.
• In this step, the molecular nitrogen is converted into inorganic nitrogenous compounds like ammonia, nitrite, and nitrate.
• Nitrogen fixation is of two types-
• Physical nitrogen fixation-
• The process of conversion of N2 to inorganic nitrogenous compounds without the involvement of microorganisms is called physical nitrogen fixation.

       2NH3 + 3O2 → 2 NO2 - + 2H + + 2 H2O

        (ammonia)                    (nitrite)

       2NO2- + O2 → 2 NO3-

       (nitrite)                       (nitrate)

• Biological nitrogen fixation-
• The process in which atmospheric nitrogen gets converted into inorganic nitrogenous compounds through microorganisms are called biological nitrogen fixation.
• Very few organisms can utilize atmospheric nitrogen, only certain prokaryotes are capable of fixing nitrogen.
• The reduction of nitrogen to ammonia by living organisms is called biological nitrogen fixation.

​​$N \equiv N \xrightarrow{Nitrogenase}NH_3$

The correct answer is Testis.

Concept:

• The male reproductive system consists of the following:
• Primary sex organ: Testis
• Secondary or accessory sex organs:
• Accessory ducts: Rete testis, vasa efferentia, epididymis, and vas deferens.
• Accessory glands: Seminal vesicle, prostate, and bulbourethral glands.
• External genitalia: Penis.

 

Explanation:

• A pair of the testis is situated outside the abdominal cavity in a sac of skin called the scrotum.
• The scrotum is a thick skin sac that protects and surrounds the testis.
• The scrotum keeps the testis at a temperature of 2 - 2.5 degrees celsius lower than the internal body temperature, which is necessary for the synthesis of sperms.
• Each testis is oval in shape, and measures about 4 -5 cm in length and 2 - 3 cm in width.
• Generally, the left testis hangs lower than the right.
• Each testis is divided into 250 compartments.
• Sperms are produced in the seminiferous tubules.
• Each seminiferous tubule is lined on its inside, by two highly specialized cells called male germ cells and Sertoli cells.
• Functions of the testis:
• Production of sperms by seminiferous tubules.
• Production of male sex hormone, testosterone, by Leydig cells.

Concept:

Convex mirror: 

The mirror in which the rays diverge after falling on it is known as the convex mirror.

• Convex mirrors are also known as diverging mirrors.
• The focal length of a convex mirror is positive according to the sign convention.

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

where v = image distance, u = object distance and f = focal length.

Magnification (m) = \(\frac{heightofimage}{heightofobject}\) = $\frac{h_i}{h_o}$

also, m = $-\frac{v}{u}$

⇒ m = $\frac{hi}{ho} = \frac{-v}{u}$

Cartesian Sign Convention for Spherical Mirror: 

• All signs are taken from the Pole of the spherical mirror, which is often called the origin or origin point.
• The sign is taken as – (negative) on the left side of the pole.
• So, the object distance is always taken as – (negative) in the case of both types of spherical mirrors, i.e. concave and convex mirrors.
• The sign is taken as + (positive) on the right side of the pole.
• The height is taken as + (positive) above the principal axis and taken as – (negative) below the principal axis.

​Explanation:

Given Data:

Object distance u = -1 m, focal length f = 0.5 m

height of object ho = 1 cm

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

∴ $\frac{1}{0.5} = \frac{1}{v} + \frac{1}{-1}$

∴ $\frac{1}{0.5} = \frac{1}{v} - \frac{1}{1}$

∴ $\frac{1}{v} = 2+1$

∴v = $\frac{1}{3}$ m = 100/3 cm

⇒  M= $\frac{hi}{ho} = \frac{-v}{u}$

∴ $\frac{hi}{1} =- \frac{-\frac{1}{3}}{1}$

∴ h_i = $\frac{1}{3}$ m = $\frac{100}{3}$ cm

The image is formed at v = 1/3 m = 100/3 cm and its height h_i = 100/3 cm.

The correct answer is 12.044 × 1023.

Calculation:

1 mole of CO_{2 =} 12 + 32 = 44gm (molar mass of CO2)

Number of C in 1 molecule of CO₂ = 1

44g CO2 contains 1 mole C

88g CO2 contains =  $\frac{1}{44}\times 88$  = 2 mole carbon

1 mole = 6.022 × 1023

2 mole C = 2 × 6.022 × 1023 C atoms

= 12.044 × 1023

Thus, 12.044 × 1023  carbon atoms are present in 88 g of carbon dioxide.

Key Points

• In the human body, the iris of the eye is made up of smooth muscles.
• The cells of smooth muscle are spindle-shaped, which are wide in the middle and tapered at the ends.
• These cells are uninucleate and have the capacity to contract and relax.
• Thus, they are able to change the cell shape by contraction or relaxation.
• These cells are under involuntary control.

Explanation:

• In the given figure, the first cell shape indicates the smooth muscle cell in the relaxed state, where it can reach a length of up to 300 µm.
• The cells lack myofibrils, but contain myosin and actin proteins which cause contraction of the cells.
• The contraction ability of the smooth muscle cells in the iris help in controlling the size of the pupil.
• This regulates the amount of light entering the eye.

Therefore, the shape-changing cells shown in the figure are found in the iris of eye in the human body.

Concept:

Chemical reaction:

• It is a process in which one or more substances, the reactants, are converted to one or more different substances, the products.
• A chemical reaction rearranges the constituent atoms of the reactants to create different substances as products.

Bases:

• They are bitter in taste and soapy to the touch.
• They turn red litmus blue.
• They have a pH value greater than 7.

Explanation

• Element A is acidic as it turns the blue litmus red.
• The element B is basic as it turns the red litmus blue
• Acids and bases dissolve in water because they increase the concentration of either protons or hydroxide ions, they suppress water self-ionization.Hence

It will be soluble in water - It is correct

Its aqueous solution will not conduct electricity - Incorrect

It will be flexible and malleable - Incorrect

It will have a low melting point - Incorrect

Concept:

• Rate of energy dissipated is actually the Power.
• Power usage of the Resistor is calculated as

⇒ P = V × I = I²R

• Where V is the voltage across the resistor
• I = Current flow through the resistor
• R = Value of the Resistance of a resistor

​Current division rule:

• By using the current division rule,
• The current flows through the resistor R­1

⇒  ${I_1} = \frac{{I\left( {{R_2}} \right)}}{{\left( {{R_1} + {R_2}} \right)}}$

• The current flows through the resistor R­2

⇒ ${I_2} = \frac{{I\left( {{R_1}} \right)}}{{\left( {{R_1} + {R_2}} \right)}}$

Explanation:

 

Given Data: Voltage of Battery V = 11 volt,

• R_A = 12 Ω, R_B = 24 Ω, R_C = 12 Ω, R_D = 24 Ω

​As R_A and R_B are connected in parallel their resultant resistance is R_AB

∴ $\frac{1}{R_{AB}}=\frac{1}{R_A}+\frac{1}{R_B}$

∴ $\frac{1}{R_{AB}}=\frac{1}{12}+\frac{1}{24}$

∴ $\frac{1}{R_{AB}}=\frac{3}{24}$

∴ R_AB = 8 Ω

Now this Resultant Resistance of A and B (R_AB) is connected in series with RC and R_D.

So the total resistance R_T of the circuit will be

∴ R_T = R_AB + R_C + R_D

∴ RT = 8 + 12 + 24

∴ RT = 44 Ω

• Now we have the voltage V and total resistance R_T of the circuit so the value of current **I_T **will be found by using Ohm's Law

∴ I_T = $\frac{V}{R_T}$

∴ I_T = $\frac{11}{44}$ = $\frac{1}{4}$ A

• Because the Resistors C and D are in series hence the current flow these resistors are actually total current flow through the whole circuit.

The rate of energy dissipated through Resistance C (R_C) is P_C

⇒  P_C = (I_T)² × R_C

∴ P_C = $(\frac{1}{4})$² × 12

∴ PC = $\frac{12}{16}$ = $\frac{3}{4}$ watt  ...................(1)

• The total current I_T is split between resistors A and B.

​We can find the current flown through resistor A by using the Current division rule which is given as

⇒ I_A = $\frac{I_T\cdot R_B}{R_A+R_B}$

• Where I_A = Current flow through Resistor A
• I_T = Total current flow through parallel circuit = (1/4 A)

∴ I_A = $\frac{(\frac{1}{4})\cdot (24)}{12+24}$

∴ I_A = $\frac{6}{36}$ = $\frac{1}{6}$ A

⇒ The rate of energy dissipated through Resistance A (RA) is PA

∴ P_A = (IA)2 × RA

∴ PA = ($\frac{1}{6}$)² × 12

∴ PA = $\frac{1}{3}$ watt  ..............(2)

• Now the ratio of P_A and P_C is

⇒ $\frac{P_A}{P_C}$ = $\frac{\frac{1}{3}}{\frac{3}{4}}$ = $\frac{1}{3}\times\frac{4}{3}$

⇒ $\frac{P_A}{P_C}$ = $\frac{4}{9}$

• As Rate of energy dissipated for Resistors A and C is given as P_A : P_C = 4 : 9

Key Points

• Complicated organs cannot be generated by a single DNA change
• They will be created bit-by-bit over generations
• This step-by-step change over many generations and millions of years produces complex organisms
• This is called evolution by stages
• It does not happen in one stage but required many stages of gradual change
• At each successive evolutionary stage, the organ becomes more complex and adapted

Hence, evolution by stages, means complex organs arise as a result of small changes over several generations (option 4)

Important Points

• Eye is a very popular adaptation, found in insects, octopuses, and vertebrates
• Structure of the eye in each organism is different, indicating separate evolutionary origin
• The rudimentary eye evolved to become complex and adapted to the requirement of different species
• Evolutionary change that is useful for one property can later be used for a different function
• Feathers started out as a means for providing insulation but became useful for flight
• Similarly, for eyes, they can be simple, complex, with different rotation, and multiple lenses depending on the requirements of the species
• All these eyes probably started as rudimentary eyes but became complex as organisms continued to evolve
• There was no single event or change making them this complex, i.e., it did not happen in a single stage
• It happened slowly over millions of years, i.e., in many stages.

Explanation:

Tracing evolutionary relationship - 

• These morphological changes in the eye or any such evolving organ are accompanied by a similar change in the DNA
• This DNA change can be used for tracing evolutionary relationship
• Comparing the DNA of different species gives us an estimate of how DNA changed during formation of species
• This method is now used to identify evolutionary relationships.

Key Points

• Adenosine 5'-triphosphate (ATP) is the principal molecule for storing and transferring energy
• Called the energy currency of the cell
• ATP is an organic compound composed of

1. three phosphate groups
2. adenine
3. sugar ribose

• Triphosphate tail of ATP is the actual power
• Energy is contained in the bonds between the phosphate groups
• Energy is released when phosphate bonds are broken
• This is done by hydrolysis, addition of water molecule
• Usually, only outer phosphate group is removed from ATP to yield energy
• ATP – Adenosine triphosphate is converted into ADP – adenosine diphosphate
• ADP is formed which has only two phosphates and a phosphate group is released
• The above energy-releasing reaction can be written as
• ATP → ADP + Pi

Hence, the correct option is (1)

Important Points

• Plant make sugar molecules by process of photosynthesis
• Animals consume plant products and other animals for their carbohydrate or sugar needs
• During the process of respiration, the sugar molecules are broken down
• The energy released during the breakdown of sugar molecules is used to produce ATP
• ATP is formed by capturing chemical energy from the digested food molecules
• ATP molecules are synthesized by Mitochondria
• Mitochondria are called the powerhouse of the cell
• ATP  is the energy-carrying molecule found in the cells of all living things
• Energy stored in ATP is later released for different cellular processes like walking, eating, etc.

The correct answer is 15.

Concept:

Periodic table:

• The modern periodic table contains 18 vertical columns called groups and seven horizontal rows called periods.
• Periods:
• The elements in the periods have the same valence shell or energy shell.
• The formula 2n², where n is the number of shells from the nucleus, can be used to calculate the number of elements present in a period.
• Groups:
• The group consists of elements with the same number of electrons in the valence shell, or the atom's outermost shell.
• As the elements in a group move down the periodic table, the number of shells increases by one unit.

Inert gas configuration:

• The general electronic configuration of the inert gases is ns²np⁶.
• Therefore, the noble gases' outermost valence shells can be considered 'full.'
• Thus, the total number of electrons in inert gases is 18.

Explanation:

• An element 'X' belongs to the third period of the periodic table and forms X^3- anion to get the inert gas configuration it accepts 3 electrons.
• Thus, it means it belongs to the 15th group.
• Element X belongs to the 3rd period
• 3rd period means there are 3 shells.
• So, the atom will have three shells, and five electrons will be present in its valence shell.
• Therefore, the electronic configuration is 2, 8, 5.
• Thus, the atomic number of X is 2+8+5 = 15.

Concept:

Convex lens

• A convex lens is thick in the middle and thin at the edges.
• A convex lens is a spherical lens whose two surfaces are bent outwards. A convex lens is also known as a converging lens
• As seen from the table when the object placed between F1 and optic centre O the image is vertual,erect and enlarged.

​

Additional Information​The image formation of a convex lens is given by

Concept:

• Resistance (R) It is a measure of the opposition to current flow in an electrical circuit.
• It is measured in ohms, symbolized by the Greek letter omega (Ω).
• $R = \frac{ρ l}{A}$ where ρ is resistivity, l is length, and A is the area of the cross-section of the wire.

Explanation: 

• Suppose original length = L, Area of cross-section = A, radius of wire = r and Resistance = R
• Since the wire is the same, the resistivity ρ will be the same.
• After the increase in length, let us take new length = L', radius of wire = r' and new resistance = R'

∴ L' = $\frac{125L}{100}$ = $\frac{5L}{4}$  ( because there is 25% length increased)

• The volume of the wire remains the same.
• So, Volume of Original Wire = volume of new wire

∴ π r2 L = π ( r ')2 L'

∴ r2L = ( r') 2 L'

∴ r' 2 = r2 $\frac{L}{L'}$

∴ r' 2 = $r^2 \frac{L}{\frac{5L}{4}}$

∴ (r')2 = $\frac{4r^2}{5}$ ...................(1)

• Now the increase in resistance in percentage is given as

⇒ Increase in resistance = ΔR = $\frac{R'-R}{R}$ × 100

∴ ΔR  = $\frac{\frac{\rho L'}{A'}-\frac{\rho L}{A}}{\frac{\rho L}{A}}$ × 100

∴ ΔR = $\frac{\frac{\rho L'}{\pi (r')^2} - \frac{\rho L}{\pi r^2}}{ \frac{\rho L}{\pi r^2} } × 100$

∴ ΔR = $\frac{\frac{L'}{(r')^2} - \frac{L}{r^2}}{ \frac{L}{r^2} } × 100$

∴ ΔR = $\frac{{\frac{5L× 5}{4× 4r^2}}-\frac{L}{r^2}}{\frac{L}{r^2}}$ × 100          (∵ Putting values of L' and r')

∴ ΔR = $\frac{\frac{25L}{16r^2}-\frac{L}{r^2}}{\frac{L}{r^2}}$ × 100

∴ ΔR = $\frac{\frac{25L - 16 L}{16r^2}}{\frac{L}{r^2}}$ × 100

∴ ΔR = $\frac{9L}{16r^2}×{\frac{r^2}{L}}$ × 100

∴ ΔR = $\frac{9}{16}$ × 100 = 56.25 %

• Thus the resistance will be increased by 56.25% if the length of the wire increases by 25 % for the same volume.