ICAR Technician 4 March 2022 Shift 2 (Previous Year Paper)

The correct answer is 6 to 12 months.

Key Points

• Children between 6 to 12 months old are generally at high risk of falling prey to Protein-energy malnutrition since they are more vulnerable to infections, especially gastrointestinal and measles.
• Protein-energy malnutrition or PEM is the condition of lack of energy due to the deficiency of all the macronutrients and many micronutrients.
• It can occur suddenly or gradually.
• It can be graded as mild, moderate, or severe.
• The symptoms of PEM include:
• Apathy and irritability
• Weakness.
• Impaired cognition and consciousness.
• Temporary lactose deficiency.
• Diarrhea.
• PEM can be treated by providing a balanced diet.

The correct answer is Arpinder Singh.

Key PointsTo make a triple jump you must make a raid, a second jump, a third and fall.Arpinder Singh

• He was born in Punjab.
• He won the gold medal at the event of Asian Games in 2018.

Suresh Babu

• Suresh Babu won the bronze medal for long jump in 1978 commonwealth games.
• He also won the Gold medal in Asian game 1978.

Vijay Singh Chauhan

• He was born in Uttar Pradesh.
• Won the Gold Medal in Asian Games 1974.

Renjith Maheswary

• He was born in Kerala.
• Won Asian championship in 2007.

Additional Information

• First Arjuna Award was given in 1961.
• The Arjuna Award symbol is the Bronze Statue of Arjuna with his “Bow and Scroll”.
• The sports persons receiving this award are given 15 Lakh Rupees in cash.
• This is the second-highest sporting honor of India.
• The award is conferred by the Ministry of Youth Affairs and Sports, Government of India.
• At present Anurag Thakur is the Minister of Youth Affairs and Sports.

The correct answer is 14.30 Crores.

Key Points

• Khelo India is our endeavor to make India one of the top 10 countries in the 2028 olympics.
• The sports Ministry, in June 2020 planned to open 1000 new Khelo India Centers over a period of 4 years.

Additional Information

• Present Minister of Youth affairs and Sports is Anurag Thakur.
• First Khelo India Youth Game organized in 2018 at Delhi.
• Its headquaters is in New Delhi.
• Host state for Khelo India 2022 is in Madhya Pradesh (Bhopal).
• State-Wise Khelo India Centers and Budget allocation:-

The correct answer is 27.5.

Key Points

• India ranks 101^st out of 116 Countries in the 2021 ranking.
• Global Hunger Index is the 16^th edition of the Hunger Index in 2021 (since 2006).
• Global Hunger Index ranks countries on a 0 to 100 point scale.
• Global Hunger Index ranks the Countries based on the following Data
• Undernourishment
• Child Stunting
• Child Wasting
• Child Mortality​

Additional Information

• India is ranked behind most of the neighboring countries
• Pakistan - 92
• Sri Lanka - 65
• Nepal - 76
• Bangladesh - 76

The correct answer is 2.2.

Key PointsTotal Fertility Rate (TFR) :-

• Average number of children born to a woman “At the end of her reproductive period”.
• There are five states whose TFR is higher than 2 :- Bihar (3), Meghalaya (2.9), Uttar Pradesh (2.4), Jharkhand (2.3) and Manipur (2.2).
• The total fertility rate was found to be the lowest in West Bengal and Maharashtra is 1.6.
• The survey of NHFS - 5 is Conducted by the Ministry of Health and Family Welfare.
• The survey provides state and national information for India Based on:
• Reproductive health
• Nutrition
• Fertility
• Infant and child mortality
• Maternal and Child health
• The practice of family planning
• Utilization and quality of health and family planning services​

Additional Information

• The Present Minister of Health and Family Welfare is Mansukh L Mandaviya.
• Sex Ratio: NFHS - 5 data shows there were 1020 Women for 1000 Men.

The correct answer is Rajaraja Chola I.

• Brihdeshwar temple also known as Rajarajeshwar temple is attributed to Lord Shiva.

Key Points

• Rajaraja Chola I (985 - 1014 CE)
• Rajaraja Chola I defeated the ruler of Sri Lanka, Mahendra V, and conquered the northern region of Sri Lanka.
• Rajaraja Chola I conquered Maldives with the help of his mighty navy.
• He was the first Chola ruler who got the land metered and fixed the tax on the basis of metering.
• He was a follower of Shaivism.

Additional Information 

Rajendra - I

• Rajendra-1 defeated the Pala King Mahipala and took the title Gangaikondachola.
• He built a city called Gangaikondacholapuram.
• He conquered the whole of Ceylon or Sri Lanka.

Rajendra II

• Rajadhiraja probably died while fighting with the Chalukya king Someshvara.
• At the same time Rajendra II consecrated his kingdom in the Rann region.
• Rajendra II defeated  Someshvara in the battle of Koppam.

Rajadhiraja

• He was also called Jayamkonda Chola.
• He destroyed the Chalukyas cities such as Kalyani and planted a Jaystambh at Yadgir.

The correct answer is Murali Sreeshankar.

Key Points

• Murali Sreeshankar broke his own national record and won the gold medal in the Federation Cup Senior National Athletics Championships in Patiala, Punjab in March 2021.
• He jumped for 8.26 meters.
• After this, he secured his berth for the Tokyo Olympics 2021.
• Murali Sreeshankar was born in Palakkad, Kerala on March 27, 1999.

 

Additional Information

The correct answer is 1838.

Key Points

• Matthias Schleiden:
• He is a German botanist who in 1838, examined a large number of plants, and concluded that all plant tissues are made up of cells and that an embryonic plant arises from a single cell.
• He observed that all plants are composed of different kinds of cells which form the tissues of the plant.
• Theodore Schwann:
• He was a British Zoologist who in 1839, studied different types of animal cells.
• On the basis of this, Schwann proposed the hypothesis that the bodies of animals and plants are composed of cells and products of cells.
• Schleiden and Schwann together formulated the cell theory and stated that every living being is composed of cells.

Additional Information

• Cell theory:
• All living organisms are composed of cells and products of cells.
• All cells arise from pre-existing cells.
• Cell theory was first developed in 1839 by Matthias Jakob Schleiden and Theodor Schwann.
• There are three observations of cell theory:
• All organisms are made of cells.
• Cells are the basic units of life.
• Cells arise from pre-existing cells.
• The third part was described by Rudolf Virchow in 1858.

The  correct answer is 8598 m.

Key Points

• Kanchenjunga is the world's third-highest mountain, with an elevation of 28,169 feet (8598meters).
• It is situated in the eastern Himalayas on the border between Sikkim state, northeastern India, and eastern Nepal, 46 miles (74 km) north-northwest of Darjiling, Sikkim.

Important Points  

Additional Information

• Mount Everest is Earth's highest mountain above sea level, located in the Mahalangur Himalaya sub-range of the Himalayas.

1. The China–Nepal border runs across its summit point.
2. Its elevation of 8,848.86 m was most recently established in 2020 by the Chinese and Nepali authorities.

• Dhaulagiri-Dhaulagiri is the seventh highest mountain in the world at 8172 metres above sea level, and the highest mountain in Nepal.

The correct answer is 1948.

Key Points 

• The Census Act,1948 (Act No.37 of 1948) was amended in 1994.
• An act to provide for certain matters in connection with the taking of the Census.
• Whereas it is expedient to provide for the taking of the census in India or any part thereof whenever necessary or desirable and to provide for certain matters in connection with the taking of such census;
• It is hereby enacted as follows:

1. This Act may be called the Census Act, 1948.
2. It extends to the whole of India.​

Additional Information 

• Census 2011 - Salient features.
• It is the 15^th census since 1872.
• 7^th census since Independence.
• The largest census in human history ever conducted by any Government till now.

The correct answer is Call Your Cop.

In News 

• Nagaland DGP T. John Longkumer officially launched the ‘Call your Cop’ mobile App on 29 November 2021 at Police Headquarters in Kohima.
• The app will enable all citizens of the state, especially those in distress to get in touch directly with the police with just one click.
• The app was developed by the Police Headquarters CID branch in collaboration with Excellogics Tech Solutions Pvt Ltd.

Additional Information

• About Nagaland:
• In 1962, Nagaland was created as a separate state.
• Its capital is Kohima.
• Its current Governor is Jagdish Mukhi.
• Its current Chief Minister is Neiphiu Rio.​
• It shares an international border with Myanmar.
• Nagaland has the lowest Scheduled Caste Population.

The correct answer is 1992.

Key Points

• 71^st constitution amendment act 1992 deals with the addition of Konkani, Manipuri, and Nepali in the eighth schedule of the constitution of India.

Additional Information

• Eighth Schedule
• It is the list of 22 official languages.
• Part 17 of the Indian constitution describes the official languages in Articles 343 to 351.
• 14 languages were initially included in the constitution of India.
• 21^st constitution amendment act of 1967 deals with the addition of the Sindhi language.
• 92^nd constitution amendment act of 2003 deals with the addition of Bodo, Dogri, Maithili, And Santhali languages.

The correct answer is The Reserve Bank of India.

Key Points

• Repo Rate – The interest rate that the RBI lends money to a commercial bank is called the repo rate.
• Reverse Repo Rate – The interest rate that the RBI borrows money from commercial banks is called the reverse repo rate.
• It is used by RBI to withdraw money from the market.

Additional Information

• Reserve Bank of India
• It was established on April 1, 1935. (Reserve Bank of India Act, 1934)
• It was initially established in Calcutta but was permanently moved to Mumbai in 1937.
• It was nationalized in 1949.
• It is also known as Banker’s Bank (owned by Govt. of India).
• It regulates the credit and currency system in India.
• Sir Osborne Smith was the first RBI Governor and C. D. Deshmukh was the first Indian RBI Governor.
• Important tools of Monetary Policy
• Cash Reserve Ratio (CRR), Statutory Liquidity Ratio (SLR), Bank Rate, Repo Rate, Reverse Repo Rate, Open Market Operations

The correct answer is Rs 20,000 crores.

Key Points

• Development Financial Institutions
• It provides long-term credit for capital-intensive investments spread over a long period and low-yielding rates of return.
• It provides credit to such sectors as urban infrastructure, mining and heavy industry, and irrigation systems.
• Union Budget 2022-23
• According to Article 112 of the Indian Constitution, the union budget of a year is referred to as the Annual Financial Statement (AFS).
• A financial year begins on 1^st April of the current year and ends on 31^st March of the following year.

Additional Information

• Key Highlights of Union Budget 2022-23
• The Budget 2022 states that India’s economic growth is estimated at 9.2%.
• Digital Rupee is to be issued by RBI using blockchain technologies.
• Issuance of E-passport with embedded chip and futuristic technology to be rolled out.
• Sovereign green bonds are to be issued.
• The Budget provides an impetus for growth along with four priorities:
• PM GatiShakti
• Inclusive Development
• Financing of investments
• Productivity Enhancement & Investment, Sunrise opportunities, Energy Transition, and Climate Action

The correct answer is Indira PP Bora.

• Sattriya dance is a 500-year-old dance that comes from **Assam state.**​

Key Points

• In 2022, Padma Awards were given to 128 Persons on the eve of the Country’s 73^rd Republic Day.
• Total Persons in three categories of Padma Awards
• Padma Vibhushan – 4
• Padma Bhushan – 17
• Padma Shri – 107
• Pranab Mukherjee, Bhupen Hazarika, and Nanaji Deshmukh were awarded by Bharat Ratna 2019.

Important Points

• Padma Awards 
• It is one of the highest civilian honours in India and announces annually on the eve of Republic Day.
• ​Padma Vibhushan is given exceptional and distinguished service. It is the second-highest civilian award in India.
• Padma Bhushan is given distinguished service of a high order. It is the third-highest civilian award in India.
• Padma Shri is given distinguished service. It is the fourth highest civilian award in India.
• Bharat Ratna 
• It is the highest civilian award in the country. It is awarded in recognition of exceptional service/performance of the highest order in any field of human endeavor.

The correct answer is 1983.

Key Points

• Taj Mahal
• It is an immense mausoleum of white marble.
• It was built in Agra between 1631 and 1648 by Mughal Emperor Shah Jahan in memory of his wife Mumtaz Mahal.
• It was made of Ivory white marble.
• The main architect of the Taj Mahal was Ustad Ahmad Lahori.
• It is located on the bank of the Yamuna river in Agra, UP.

Additional Information

• UNESCO
• Full Name – United Nations Educational, Scientific and Cultural Organization
• Headquarters – Paris, France
• Founded – 16 Nov 1945 (London, UK)
• Director-General – Audrey Azoulay
• It aimed at promoting world peace and security through international cooperation in education arts, sciences, and culture.
• At present, there are 40 world heritage sites in India declared by UNESCO.

The correct answer is Antoine Lavoisier.

Key Points

• The Principle of Conservation of Mass was described by Antoine Lavoisier in 1789.
• "Mass is neither created nor destroyed in chemical reactions".
• During a chemical reaction, the total mass and number of atoms of the reactants are equal to the total mass and number of atoms of the products.

\(\underset{\rm 80g}{\underbrace{\begin{matrix}\rm CH_4\\ \rm Methane\\ \rm 16g\end{matrix}+\begin{matrix}\rm 2O_2\\ \rm Oxygen\\ \rm 2^{*}32g\end{matrix}}}= \underset{\rm 80g}{\underbrace{\begin{matrix}\rm CO_2\\ \rm Carbon \ dioxide\\ \rm 44g\end{matrix}+\begin{matrix}\rm 2H_2O\\ \rm water\\ \rm 2^{*}18g\end{matrix}}}\)

Important Points

• Antoine Lavoisier recognized and also named oxygen (1778) and hydrogen (1783).
• Antoine Lavoisier is known as "the father of modern chemistry", mainly discovered the Role of oxygen in combustion and respiration, proved the law of conservation, and reformed the chemical nomenclature.

Additional Information

• John Dalton
• John Dalton is Known for Dalton's atomic theory and the Law of multiple proportions.
• ​Dalton's atomic theory - All Matter is made up of individual particles called Atoms.
• Linus Carl Pauling 
• ​Linus Carl Pauling received the 1954 Nobel Prize in Chemistry for his research into "the nature of the chemical bond and its applications to the elucidation of the structure of complex substances".
• Joseph Proust
• Joseph Proust gave the Law of Definite Proportion in 1797.
• Law of Definite Proportion states that "the samples of a compound will always have the same proportion of the elements by mass."

The correct answer is Regulating Act of 1773.

Key Points

• The main objective of Regulating Act of 1773 was "To Bring about a change in the management of the East India Company's governance in India
• Regulating Act of 1773:
• This act was based on the report of the Lord North(British PM) Committee.
• By this act, the Governance of the East India Company was put under British parliamentary control.
• By this act, the Governor of Bengal was nominated as Governor-General for all the three Presidents of Calcutta, Bombay, and Madras (Warren Hastings was the first such governor-general).
• By this act, a Supreme Court was established in Calcutta in 1774.

Additional Information

• Pitt's India Act, 1784​ 
• The Act introduced a Board of Controllers (6 members), which was responsible for the company's political issues.
• By this act, Trade and commerce-related issues were under the purview of the Court of Directors of the company.
• Government of India Act, 1858​
• This act granted the British Empire control over India without any popular participation in the administration of the country.
• This act changed the office of the Governor-General of India to the office of the Viceroy of India. Lord Canning became the first Viceroy of India.
• Indian Councils Act, 1892
• The Act increased the number of private members in the central and provincial legislatures.
• For the first time, the Governing Council had the power to discuss the budget and address questions to the executive.

The correct answer is IIT Kanpur.

Key Points

• Prime Minister Narendra Modi launched a blockchain-powered technology-based digital degree developed by IIT Kanpur under the National Blockchain Project in December 2021 on the occasion of the 54^th Convocation Ceremony of IIT Kanpur.
• The National Blockchain Project has been launched to develop e-governance solutions using blockchain technology.
• A blockchain is a digital database or ledger where information is stored as "blocks" which together form a "chain".

Additional Information

• IIT Kanpur and Ordnance Factory Medak (OFMK), Telangana, in a joint effort have developed India's first soft recovery system (SRS) for a supersonic projectile.
• IIT Roorkee has launched a mobile app, under the Gramin Krishi Mausam Sewa (GKMS) project, named ‘KISAN’ for the farmers.
• Through this app, agro-meteorological advisory services will be provided to the farmers.
• IIT Roorkee launches Earthquake Early Warning Mobile App.
• IIT-Kharagpur develops an Early Cyclone Detection Technique.

The correct answer is 2021.

Key Points

• The National Bank for Financing Infrastructure and Development Bill was passed in Lok Sabha in 2021.
• This Act may be called the National Bank for Financing Infrastructure and Development Act, 2021.
• The act establishes the National Bank for Financing Infrastructure and Development (NBFID) as the principal development financial institution (DFIs) for infrastructure financing.
• NBFID is set up for providing long-term finance for such segments of the economy where the risks involved are beyond the acceptable limits of commercial banks and other ordinary financial institutions.

Important Points

• NBFID will be set up as a corporate body with an authorized share capital of one lakh crore rupees.
• Initially, the central government will own 100% shares of NBFID which may subsequently be reduced up to 26%.
• Chairman of NBFID is K V Kamath (March 2022).

The correct answer is 12.

Key Points

• As of September 2021, The Indian banking system consists of 12 public sector banks, 22 private sector banks, 46 foreign banks.
• 12 public sector banks are;

1. State Bank of India
2. Punjab National Bank (With Merger of Oriental Bank of Commerce and United Bank of India)
3. Bank of Baroda
4. Canara Bank (With Merger of Syndicate Bank)
5. Union Bank of India (With Merger of Andhra Bank and Corporation Bank)
6. Bank of India
7. Indian Bank (With Merger of Allahabad Bank)
8. Central Bank of India
9. Indian Overseas Bank
10. UCO Bank
11. Bank of Maharashtra
12. Punjab & Sind Bank.

• Public Sector Banks (PSBs) in India are those banks whose majority stake (i.e. more than 50%) is owned by the Ministry of Finance, Government of India.

The correct answer is Torana.

Key Points

• Toranas
• Toranas typically consist of two pillars carrying two or three transverse beams that extend beyond the pillars on either side.
• Toranas are associated with Buddhist stupas like the Great Stupa in Sanchi, as well as with Jain and Hindu structures, and also with several secular structures.

Additional Information

• Harmika
• A small platform with a railing located on top of a stupa.
• Medhi
• A circular terrace surrounded by a three-bar railing in stupa.
• Vedica
• A protective fence made of hewn and polished stones that surrounds a Buddhist stupa and symbolically separates the inner sacred from the surrounding secular sphere.

The correct answer is 1914.

Key Points

• The Simla Convention between Great Britain, China, and Tibet, was an ambiguous treaty concerning the status of Tibet negotiated by representatives of the Republic of China, Tibet and Great Britain in Simla in 1914.
• The Simla Convention provided that Tibet would be divided into "Outer Tibet" and "Inner Tibet".
• Outer Tibet would "remain in the hands of the Tibetan Government at Lhasa under Chinese suzerainty", but China would not interfere in its administration.
• "Inner Tibet" would be under the jurisdiction of the Chinese government.
• The convention with its annexes also defines the boundary between Tibet and China and that between Tibet and British India with the latter coming to be known as the Mcmohan Line.

Additional Information

• Radcliffe Line
• On 17 August 1947, the borderline that separated India from Pakistan, known as the Radcliffe Line was revealed.
• The Radcliffe line is spread through the Rann of Kutch in Gujarat to the international border in Jammu in Jammu & Kashmir, dividing India and Pakistan into two different countries. Radcliffe divided India into three halves:
• West Pakistan
• East Pakistan and
• India
• It demarcated between the Indian and Pakistani portions of the Punjab Province and Bengal Presidency of British India.
• It was named after its architect, Cyril Radcliffe, who, as the joint chairman of the two boundary commissions for the two provinces, received the responsibility to equitably divide 450,000 km² of territory with 88 million people.
• Today, its western side is part of the India-Pakistan border and its eastern side serves as the Bangladesh-India border (known as International Border now).

The correct answer is Akshaya Patra Foundation.

Key Points

• PM-POSHAN scheme is a revamp of Mid Day Meal Scheme.
• Mid-Day Meal Scheme
• Launched in 1995 to increase school enrolment and improve the nutritional status of millions of undernourished children across the country.
• Supreme Court in 2001 ordered state governments to provide free lunches to students in all state-run elementary schools.
• PM-POSHAN scheme
• The Union Cabinet approved the Pradhan Mantri Poshan Shakti Nirman or PM-POSHAN in September 2021, for providing one hot cooked meal in Government and Government-aided schools with a financial outlay of Rs 1.31 trillion.
• Meals will now be extended to students studying in pre-primary levels or BalVatikas of government and government-aided primary schools.
• Primary and upper primary school children are entitled to 100 grams and 150 grams of food grains per working day each, to ensure a minimum of 700 calories.
• It has been launched for a period of five years, from 2021-2022 to 2025-2026, with contributions from both Union and state governments.

The correct answer is Prime Minister.

Key Points 

• PM Narendra Modi is the Chairperson of NITI Aayog.
• The NITI Aayog (National Institution for Transforming India) is a policy think tank of the Government of India, formed on January 1, 2015.
• Headquarters: New Delhi

Additional Information

• NITI Aayog replaced Planning Commission with emphasis on the 'Bottom - Up' approach to envisage the vision of Maximum Governance, Minimum Government.
• On 7 June 2018, the Prime Minister approved the reconstitution of NITI Aayog to include Ex-officio members and Special Invitees consisting of Experts and Specialists with domain knowledge.
• There will be a maximum of five Ex-Officio members and three Special Invitees from the Union Council of ministers nominated by the Prime Minister.
• The Governing Council of NITI Aayog, with the Prime Minister as its Chairman, comprises Chief Ministers of all States and Lt. Governors of Union Territories (UTs).

Given:

The income of A is 48% more than the income of B

the income of C is 25% less than the combined income of A and B

Calculation:

Let the income of B be 100 unit

So, The income of A = 100 × 148%

⇒ The income of A = 148 

Now, According to the question 

Income of C = (100 + 148) × 75%

⇒ The income of C = 248 × 3/4 = 186

Now,

Income of C - Income of A = 186 - 148

⇒ Income of C - Income of A = 38

So, The required Percent = (38/148) × 100%

⇒ 25.675 ≈ 25.7

∴ The income of C is 25.7% more than that of A.

Given:

The radius of a sphere is 20 cm

The height of a cylinder is 20% more than the radius of the sphere

Formula Used:

Volume of Speher = 4πR³/3

Volume of Cylinder = πr²h

Where, R = Radius of sphere 

r = Radius of cylinder, h = Height of cylinder

In a right angled Δ 

h² = p² + b²

Where, h = Hypotenuse, p = Perpendicular, 

b = Base

Calculation:

Here In this figure AC = 2R = 2 × 20 = 40 cm 

And BC (Height of cylinder) = 120% of 20 = 24 cm 

According to the figure 

ΔABC is a right angled triangle, ∠B = 90° 

So, AC² = AB² + BC²

⇒ 40² = AB2 + 242

⇒ AB2 = 1600 - 576

⇒ AB2 = 1024 = 32²

⇒ AB (Diameter of base of cylinder) = 32

Radius of cylinder = 32/2 = 16 cm 

Now,

Volume of (Cylinder : Spehere) = πr2h : 4πR3/3

⇒ Volume of (Cylinder : Spehere) = 3r2h : 4R3

⇒ Volume of (Cylinder : Spehere) = 3 (16)2 × 24 : 4(20)3

⇒ Volume of (Cylinder : Spehere) = 3 × 16 × 16 × 24 : 4 × 8000

⇒ Volume of (Cylinder : Spehere) = 72 : 125

∴ The required ratio is 72 : 125.

Given:

The ratio of the investment of A and B = 2 : 3

Calculation:

According to the question

The total salary of A = 36000x

The total salary of B = 30000x

Remaining profit after distributing salaries

⇒ 768000 - (36000x + 30000x)

⇒ 768000 - 66000x

Share of A in the remaining profit = (768000 - 66000x) × 2/5

The total profit share of A = \(36000x\ +\ {{2\over 5}\ × (768000\ -\ 66000x)}\ \)

⇒\(\ 36000x\ +\ 307200\ -\ 26400x \ =\ 9600x\ +\ 307200\)

Share of B in the remaining profit = (768000 - 66000x) × 3/5

The total profit share of B = \(30000x\ +\ {{3\over 5}\ × (768000\ -\ 66000x)}\ \)

⇒\(\ 30000x\ +\ 460800\ -\ 39600x \ =\ -9600x\ +\ 460800\)

Now, According to the question 

Their total share are same 

So, 9600x + 307200 = -9600x + 460800

⇒ 19200x = 153600

⇒ x = 8 months

∴ The required result will be 8 months.

Given:

The compounded amount = Rs. 5989.50

Formula used:

\(Compounded\ amount\ =\ {P\ \times (1\ +\ {R\over 100})^T} \)

\({Simple\ Interest\ =\ {P\ \times\ R\ \times\ T\over 100}} \)     

Where P = Principle, R = Rate and T = Time

Calculation:

Let the simple interest  be X and the principle be P

The effective rate of interest = \({15\ \times 8\over 12}\ =\ 10%\)

The effective time = 2 years = 24 months = \({24\over 8}\ =\ 3\)

According to the question

⇒ \(5989.5\ =\ {P\ \times (1\ +\ {10\over 100})^3}\)

⇒ \(5989.5\ =\ {P\ \times {({11\over 10})^3}}\)

⇒ \(P\ =\ {5989.5\over 1.331}\ =\ 4500 \)

The simple interest on the same sum = \({4500\ \times {14\over 3}\ \times 19\over 100}\ \)

⇒ \(\ {45\ \times {14\over 3}\ \times 19}\ =\ 3990\)

∴ The required simple interest will be Rs. 3990.

Given:

The ratio of the number of Rs. 5 notes to the number of Rs. 10 notes is 11 : 8

The ratio of the number of Rs. 10 notes to the number of Rs. 20 notes is 10 : 7

The total amount in the bag is Rs. 3,705

Concept Used:

Number of Rs. 5 notes × 5 = Total amount of Rs. 5 notes 

Number of Rs. 10 notes × 10 = Total amount of Rs. 10 notes 

Number of Rs. 20 notes × 20 = Total amount of Rs. 10 notes 

Calculation:

According to the question 

Rs. 5 notes : Rs. 10 notes = 11 : 8     ----(i)

Rs. 10 notes : Rs. 20 notes = 10 : 7     ----(ii)

On doing (i) × 5 and (ii) × 4, we get 

Rs. 5 notes : Rs. 10 notes = 55 : 40     ----(iii)

Rs. 10 notes : Rs. 20 notes = 40 : 28     ----(iv)

Form equation (iii) and (iv), we get 

Rs. 5 notes : Rs. 10 notes : Rs. 20 notes = 55 : 40 : 28

Now, Let the ratio be x 

So, Number of Rs. 5 notes = 55x 

Number of Rs. 10 notes = 40x 

Number of Rs. 20 notes = 28x 

Now, According to the concept used

55x × 5 + 40x × 10 + 28x × 20 = 3705

⇒ 275x + 400x + 560x = 3705

⇒ 1235x = 3705

⇒ x = 3

So, Rs. 10 notes = 40x

⇒ 40 × 3 = 120

∴ The number of Rs. 10 notes is 120.

Shortcut Trick

Total Volume (V) = πr²h = 3.14 × (2.5)² × 3 = 58.875 m³.

Volume of water removed = 47.1 kilolitres = 47.1 m³.

Remaining Volume = 58.875 − 47.1 = 11.775 m³.

Percentage level drop to = (Remaining Volume ÷ Total Volume) × 100.

⇒ (11.775 ÷ 58.875) × 100 = 1/5 × 100 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given:

Radius (r) = 2.5 m = 5/2 m

Height (H) = 3 m

Water removed = 47.1 kilolitres = 47.1 m³ (since 1 kl = 1 m³)

π = 3.14

Formula Used:

Volume of Cylinder = πr²h

Percentage level = (Current Height ÷ Total Height) × 100

Calculations:

⇒ Base Area of tank = πr²

⇒ Base Area = 3.14 × (2.5)² = 3.14 × 6.25 = 19.625 m²

⇒ Height of water removed (h_removed) = Volume removed ÷ Base Area

⇒ h_removed = 47.1 ÷ 19.625 = 2.4 m

⇒ New water level height = Total Height − Height removed

⇒ New height = 3 − 2.4 = 0.6 m

⇒ Percentage drop to = (New height ÷ Total height) × 100

⇒ Percentage drop to = (0.6 ÷ 3) × 100

⇒ Percentage drop to = 0.2 × 100 = 20%

∴ The correct answer is 20%.

Additional Information

Volume of a Cylinder

The volume of a cylinder with radius r and height h is given by V = πr²h.

Kilolitre and Cubic Meter Relationship

1 kilolitre (kl) is exactly equal to 1 cubic meter (m³). 1 litre = 1000 cm³.

Percentage Level in Uniform Cross-section

For a tank with a uniform base (like a cylinder or prism), the percentage of volume is directly proportional to the percentage of height.

Given:

\(\frac{{0.\overline 4 + 0.5\overline {67} - 0.5\overline 9 }}{{(0.2\overline {26} \div 0.7\overline 5 ) \times 3.4 \div 2.\overline {54} \times 3.\overline 3 }}\)

Calculation:

\(\frac{\frac{4}{9} + \frac{567 - 5}{990} - \frac{59 - 5}{90}}{(\frac{226 -2}{990} \div \frac{75-7}{90}) \times \frac{34}{10} \div \frac{254- 2}{99} \times \frac{33-3}{9}} \)

⇒ \(\frac{\frac{4}{9} + \frac{562}{990} - \frac{54}{90}}{(\frac{224}{990} \div \frac{68}{90}) \times \frac{34}{10} \div \frac{252}{99} \times \frac{30}{9}} \)

⇒ \(\frac{\frac{440 + 562 - 594 }{990} }{(\frac{4}{3})} \)

⇒ \(\frac{\frac{408}{990} }{(\frac{4}{3})} \)

⇒ \({\frac{408}{990} } \times \frac{3}{4}=0.309\)

∴ The value lies between 0.3 to 0.4.

Given:

The cost price of each A and B is Rs. 800

The marked price of both are the same 

He sells A at a discount of 35% but earns Rs. 175

He sells B at a discount of 28%

Formula Used:

Selling Price = M.P (100 - D%)

Profit% = [(S.P - C.P)/C.P] × 100%

S.P = C.P + Profit

Calculation:

Let the Marked Price (M.P) of articles be x

According to the question 

S.P of A = 800 + 175 

⇒ S.P of A = Rs. 975

Now, S.P of A = M.P × (100 - 35)%

⇒ S.P of A = 13x/20

So, 13x/20 = 975

⇒ x = 1500

So, The M.P of B = Rs. 1500

S.P of B = 1500 × (100 - 28)%

⇒ S.P of B = 1080

Profit on selling B = 1080 - 800 = 280

% Profit on selling B = (280/800) × 100%

∴ The % Profit on selling B is 35%.

Given:

 \(x =√2 - 1\) and \(y= {3\over√2}\),     ----(i)

Calculation:

At first we have to find the value of (x - 2y + 1)

From (i)

⇒ (√2 - 1) - 2 × \({3\over √ 2}\) + 1

⇒ √2 - 3√2 = -2√2     ----(ii)

Now, We have to find the value of 

⇒ (x2 + 4y2 + 2y + 2xy + 2x + 1)

From (i), we have 

⇒ (√2 - 1)² + 4 × \({({3\over √ 2})^2}\) + 2 × \({3\over √ 2}\) + 2 × (√2 - 1) × \({3\over √ 2}\) + 2 × (√2 - 1) + 1

⇒ 2 + 1 - 2√2 + 18 + 3√2 + 6 - 3√2 + 2√2 - 2 + 1

⇒ (x2 + 4y2 + 2y + 2xy + 2x + 1) = 26      ----(iii)

Now, We have to find the value of 

(x - 2y + 1) (x2 + 4y2 + 2y + 2xy + 2x + 1)

So, From (ii) and (iii), we get

⇒ 26 × -2√2 = -52√2

∴ The required result will be -52√2.

Given:

The LCM of two numbers = 28 × HCF of two numbers

Sum of LCM and HCF = 493

Difference between numbers = 51

Concept:

LCM:- The least common multiple of two numbers is the smallest non zero common number which is a multiple of both the numbers

HCF:- The highest common factor of two or more numbers is the greatest factor that divides the numbers.

LCM × HCF = Product of Numbers

Calculation:

Let the numbers be X and Y and HCF and

LCM of the numbers be p and q respectively

According to the question

q = 28p and p + q = 493

On solving these, we get

⇒ p + 28p = 493

⇒ 29p = 493

⇒ p = 17 and q = 476

Again, According to the concept used

⇒ XY = 476 × 17 = 8092     ----(1)

⇒ X - Y = 51     ----(2)

⇒ X + Y = s     ----(3)

On solving the equations (1) and (2), we get

⇒ X² - 51X - 8092 = 0

⇒ X = 119, and Y = 68

⇒ By equation (3)

⇒ X + Y = s

⇒ s = 119 + 68 = 187

The sum of the digits of s = 1 + 8 + 7 = 16

∴ The required result will be 16.

Given:

The profit % in 2016 = 45%

The profit % in 2017 = 65%

The profit % in 2018 = 40%

The profit % in 2019 = 60%

The profit % in 2020 = 58%

Formula used:

Profit = P% × [S.P/(100 + P%)]

Where, P = Profit, SP = Selling price, and CP = Cost price

Calculation:

The profit earned in 2016 = \({232\over 145}\ × 45\ =\ 72\)

The profit earned in 2017 = \({297\over 165}\ × 65\ =\ 117\)

The profit earned in 2018 = \({182\over 140}\ × 40\ =\ 52\)

The profit earned in 2019 = \({216\over 160}\ × 60\ =\ 81\)

The profit earned in 2020 = \({237\over 158}\ × 58\ =\ 87\)

The total profit in 2016 & 2020 = 72 + 87 = 159

The total profit in 2017, 2018, & 2019 = 117 + 52 + 81 = 250

The required percentage = \({159\over 250}\ × 100\ =\ 63.6%\)

∴ The required result will be 63.6%.

Given:

The average of 54 numbers = 65.5

Formula used:

Average = Sum of all the terms/Total number of terms

Calculation:

Let the average of the remaining three numbers be X

According to the question

The sum of the 54 numbers = 65.5 × 54 = 3537

The sum of first 28 numbers = 28 × 54.5 = 1526

The sum of the last 23 numbers = 23 × 78 = 1794

The sum of the last three numbers = 3537 - 1526 - 1794 = 3537 - 3320 = 217

The average of the last three numbers = 217/3 = 72.33

∴ The required result will be 72.3.

Shortcut Trick

Initial Acid : Water ratio = 62.5% : 37.5% = 5 : 3.

Resulting ratio after adding 4L Acid = 13 : 7.

Make Water constant: (5 : 3) × 7 = 35 : 21 and (13 : 7) × 3 = 39 : 21.

Increase in Acid = 39 − 35 = 4 units ⇒ 4 units = 4 litres ⇒ 1 unit = 1 litre.

Initial solution x = 35 + 21 = 56 units = 56.

∴ The correct answer is 56.

Alternate Method

Given: Initial volume = x litres, Acid concentration = 62.5%, Added Acid = 4 litres, Final Ratio = 13 : 7.

Formula Used: Ratio = (Component 1) / (Component 2)

⇒ Initial Acid = 62.5% of x = (5/8)x

⇒ Initial Water = 37.5% of x = (3/8)x

⇒ After adding 4 litres of Acid, New Acid = (5x/8) + 4

⇒ New Ratio of Acid to Water = ((5x/8) + 4) ÷ (3x/8) = 13/7

⇒ (5x + 32) ÷ 3x = 13/7

⇒ 7 × (5x + 32) = 13 × 3x

⇒ 35x + 224 = 39x

⇒ 4x = 224

⇒ x = 56

∴ The correct answer is 56.

Additional Information

Percentage to Fraction Conversion

Common percentages in mixture problems: 12.5% = 1/8, 37.5% = 3/8, 62.5% = 5/8, and 87.5% = 7/8.

Ratio Balancing Rule

When only one substance is added or removed from a mixture, the quantity of the other substance remains constant. Adjust the ratios such that the constant component has the same number of units.

Initial Mixture Calculation

Total quantity = (Sum of ratio parts) × (Value of one unit). Here, (35 + 21) × 1 = 56.

Given:

The mobile phone was sold by A and B in February = 1944

Formula used:

\({GM%}\ =\ {GM\over TM}\ × 100\)   

Where, GM = Gain marks, and TM = Total marks

Calculation:

Let the total number of mobile phones sold by A and B in all months be X

⇒ X = \({1944\over 18}\ × 100\) = 10800

The total mobile sold in May = 10800 × 0.21 = 2268

The total mobile sold in March = 10800 × 0.15 = 1620

The phone was sold in May by A = \({8\over 21}\ \times 2268\ =\ 864\)

The phone was sold in May by B = \({13\over 21}\ \times 2268\ =\ 1404\)

The phone was sold in March by A = \({11\over 15}\ \times 1620\ =\ 1188\)

The phone was sold in March by B = \({4\over 15}\ \times 1620\ =\ 432\)

The total mobile sold by A in March and May = 1188 + 864 = 2052

The total mobile sold by B in March and May = 1404 + 432 = 1836

The required difference = 2052 - 1836 = 216

∴ The required result lies between "215 and 220".

Given:

A sofa set is available for Rs. 48,500 cash or 

For Rs. 10,500 cash down payment followed by three equal monthly installments

The rate of interest charged under the installment plan = 16% p.a

Calculation:

Let the equal monthly installment be Rs. x

Cash Payment = Rs. 10500

Remaining amount to be paid = Rs. 48500 - 10500

⇒ Rs. 3800

Interest paid at the end of 1^st month

⇒ [(3800 × (16/12)]/100

⇒ 15200/300

Principal for 2^nd Month = (3800 - x)

Interest for 2^nd month  

⇒ [(3800 - x) × (16/12)]/100

⇒ 4(3800 - x)/300

Principal for 3^rd Month = (3800 - 2x)

Interest for 3^rd month  

⇒ [(3800 - 2x) × (16/12)]/100

⇒ 4(3800 - 2x)/300

Now, According to the question 

3x = 3800 + 15200/300 + 4(3800 - x)/300 + 4(3800 - 2x)/300

⇒ (3x - 3800) × 300 = [15200 + 15200 - 4x + 15200 - 8x]

⇒ 900x - 3800 × 300 = 45600 - 12x

⇒ 912x = 1185600

⇒ x = 1300

∴ The amount of equal installment is 1300.

Given:

The A and B together can fill the tank = 30 hours

Formula used:

W = E × T   

Where, W = Work, E = Efficiency, T = Time

Calculation:

Let A, B, and C alone can fill and empty the tank in A, B, and C hours respectively

According to the question

The one hour work of A = \({1\over A}\)

The one hour work of B = \({1\over B}\)

The one hour work of C = \(-{1\over C}\)

When A, B, and C work together then

The time taken by them = \({30\ \times {4\over 3}}\ =\ 40\ hours\)

⇒ \({1\over A}\ +\ {1\over B}\ =\ {1\over 30}\)     ----(1)

⇒ \({1\over A}\ +\ {1\over B}\ -\ {1\over C}\ =\ {1\over 40}\)     ----(2)

From equations (1) and (2)

⇒ \({1\over 30}\ -\ {1\over C}\ =\ {1\over 40}\)

⇒ \({1\over C}\ =\ {1\over 30}\ -\ {1\over 40}\)

⇒ \({1\over C}\ =\ {4\ -\ 3\over 120}\)

The C can alone empty the tank = 120 hours

∴ The required result will be 120 hours.

Given:

if one is subtracted from the numerator and denominator then it become = \( {1 \over 4}\)

If 5 is added to each of the numerator and denominator then fraction = \(1\over 2\)

Calculation:

Let the fraction be \({x\over y}\).

According to the question

⇒ \({x\ -\ 1\over y\ -\ 1}\ =\ {1\over 4}\)

⇒ 4x - 4 = y - 1

⇒ 4x - y = 3     ----(1)

⇒ \({x\ +\ 5\over y\ +\ 5}\ =\ {1\over 2}\)

⇒ 2x + 10 = y + 5

⇒ 2x - y = - 5     ----(2)

By solving equation (1) and (2)

⇒ x = 4, y = 13

The 11 times the numerator = 11 × 4 = 44

The 3 times the denominator = 3 × 13 = 39

The required difference = 44 - 39 = 5

∴ The required result will be 5.

Given:

A is 60% more efficient than B

B is 10% less efficient than C

C alone can complete the work in 36 hours

Formula used:

W = E × T   

Where, W = Work, E = Efficiency, and T = Time

Calculation:

Let the A, and B can complete the work in A, and B, days respectively

And C will complete the remaining work in X days

The efficiency of A = \({1\over A}\)

The efficiency of B = \({1\over B}\)

The efficiency of C = \({1\over 36}\)

According to the question

⇒ \({9\over 10} \times {1\over 36}\ =\ {1\over B}\)

⇒ \({1\over B}\ =\ {1\over 40}\)

⇒ \({1\over 40}\ \times {8\over 5}\ =\ {1\over A}\)

⇒ \({1\over A}\ =\ {1\over 25}\)

Now, According to the question

⇒ \({5\over 25}\ +\ {5\over 40}\ +\ {X\over 36}\ =\ 1\)

By solving the equation

⇒ X = 24.3 hours 

∴ The required time to complete the remaining work by C is 24.3 hours.

Additional Information 

 If we assume total work = 36, then the efficiency of C = 1, B = 0.9 and A = 1.44. When A and B worked together for 5 hours, they completed 5 x (0.9+1.44) =  11.7 out of the total 36 work. So the remaining work 36 -11.7 = 24.3 will be completed by C in 24.3 hours as the efficiency of C is 1.

Given:

In ΔPQR, QS \( \bot\) PR, RT \( \bot\) PQ and

QS and RT intersect each other at O

The bisector of ∠OQR and ∠ORQ meet at M

∠QPR = 56°

Formula Used:

In ΔABC if OB and OC are the bisectors of ∠B and ∠C

Then, ∠BOC = 90° + ∠A/2

Calculation:

From Figure 

∠PTO = 180° - 90°    [linear pair of angle]

⇒ ∠PTO = 90°      -----(i)

And, ∠PSO = 180° - 90°    [linear pair of angle]

⇒ ∠PSO = 90°      -----(ii)

Now, In quadrilateral PTSO

∠PTO + ∠P + ∠PSO + ∠TOS = 360° 

⇒ 90° + 56° + 90° + ∠TOS = 360° 

⇒ ∠TOS = 124° = ∠QOR   [Vertically opp. Angle]

Now, In ΔQOR we can see that 

QM and RM are the angle bisectors of ∠OQR and ∠ORQ

So, By the formula Used

∠QMR = 90° + 124°/2 = 152° 

∴ The measurement of ∠QMR is 152°.

Given:

Anil beats Bhushan by 30 seconds

Bhushan beats Raghav by 60 seconds

Bhushan's speed is the average speed of Anil and Raghav

Formula used:

\({S\ =\ {D\over T}}\)     

Where, S = Speed, D = Distance, and T = Time

Calculation:

Let the time taken by Anil be t sec

So, Time taken by Bhushan = t + 30 sec.

So, Time taken by Raghav = t + 90 sec.

Since, Distance travelled by them is constant 

So, Speed ∝ 1/Time

So, Speed Ratio = 1/t : 1/(t + 30) : 1/(t+ 90)

Now, According to the question 

2/(t + 30) = 1/t + 1/(t+ 90)

⇒ 2 t (t + 90) = (t + 30) (2t + 90)

⇒ 2t² + 180t = 2t² + 150t + 2700

⇒ 30t = 2700 

⇒ t = 90 sec

∴ The time taken by A is 90 seconds.

Given:

The time is taken by boat upstream = \(2 {2\over 3}\) hours

Formula used:

\({S\ =\ {D\over T}}\)   

Where, S = Speed, D = Distance, and T = Time

Calculation:

Let the speed of the boat and speed of the current be 13s and 3s respectively, 

The distance be D and the time taken in return journey be T

The upstream speed = 13s - 3s = 10s

The downstream speed = 13s + 3s = 16s

According to the question

\(2 {2\over 3}\) = \({D\over 10s}\)     ----(1)

T = \({D\over 16s}\)     ----(2)

By equations (1) and (2)

⇒ \(2 {2\over 3}\) × 10s = T × 16s

⇒ \({8\over 3}\) × 10 = 16T

⇒ T = \({5\over 3}\)

The time is taken in return journey = \( 1{2 \over 3}\) hours

∴ The required result will be \( 1{2 \over 3}\).

Given:

Height of pole = 500√3m

The angle of depression from P on A and B are  60° and 30° respectively

Time taken by Car to travel from A to B = 80 sec

Formula Used:

Speed = Distance/ Time 

1 m/s = 18/5 km/hr

tanθ = p/b

Calculation:

We know that

The angle of depression = Angle of elevation

So, ∠A = ∠APC = 60° and

∠B = ∠BPD = 30°

Now, In ΔAPQ, ∠Q = 90° 

So, tanA = PQ/AQ

⇒ tan60° = (500√3)/AQ

⇒ √3 = 500√3/AQ

⇒ AQ = 500m       ----(i)

And in ΔPQB, ∠Q = 90° 

TanB =  PQ/BQ

⇒ tan30° = (500√3)/BQ

⇒ 1/√3  = (500√3)/BQ

⇒ BQ = 1500m       ----(ii)

Form the figure, we have 

AB = AQ + BQ

Form (i) and (ii)

⇒ AB =  500m + 1500m  = 2000 m

Now, According to the formula used

Speed = (2000/80) m/sec

⇒ Speed = 25 m/sec = 25 × 18/5 km/hr

⇒ Speed = 90 km/hr

∴ The speed of car is 90 km/hr.

Shortcut Trick

For a circle where diameter PQ and produced chords PR and QS meet at T:

The direct relation is ∠PTQ = 90° − (∠ROS / 2)

Given ∠ROS = 48°

∠PTQ = 90° − (48° / 2) = 90° − 24° = 66°

∴ The correct answer is 66°.

Alternate Method

Given:

PQ is the diameter of the circle with centre O.

Chords PR and QS meet at T when produced.

∠ROS = 48°

Formula Used:

Angle subtended by an arc at the centre is double the angle at the circumference: ∠Central = 2 × ∠Circumference

Angle formed by two secants outside a circle: ∠T = 1/2 × (Measure of Major Arc − Measure of Minor Arc)

Calculations:

⇒ Arc PQ is a semi-circle, so its measure = 180°.

⇒ The angle subtended by arc RS at the centre is ∠ROS = 48°, so the measure of Arc RS = 48°.

⇒ According to the exterior angle theorem for secants:

⇒ ∠PTQ = 1/2 × (Arc PQ − Arc RS)

⇒ ∠PTQ = 1/2 × (180° − 48°)

⇒ ∠PTQ = 1/2 × 132°

⇒ ∠PTQ = 66°

∴ The correct answer is 66°.

Additional Information

Angle in a Semicircle

Any angle subtended by the diameter at the circumference of the circle is always a right angle (90°).

Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of its intercepted arc. (∠Circumference = 1/2 × Arc measure).

Angles Outside the Circle

If two secants, two tangents, or a secant and a tangent intersect outside a circle, the angle formed is half the positive difference of the intercepted arcs.

Given:

The profit of the entire transaction = Rs. 558

Formula used:

P = SP - CP     

Where, P = Profit, SP = Selling price,

And CP = Cost price

Calculation:

Let the cost price of the good be X

S.P of \(66{2 \over 3}\) of the goods = 1.30 × \({2\over 3}\) × X = \({2.6\over 3}\)X

S.P of 75% of the remaining goods = \({1\over 3}\) × 0.75 × 1.16 × X

⇒ \({0.87\over 3}\)X

The reaming goods sell at 40% loss then,

S.P of the goods = \({1\over 3}\)× 0.25 × 0.60 × X = \({0.15\over 3}\)X

The total selling price =  \({2.6\over 3}\)X +  \({0.87\over 3}\)X + \({0.15\over 3}\) 

⇒ \({3.62\over 3}\)X

According to the question

⇒ \({3.62\over 3}\)X - X = 558

⇒ 3.62X - 3X = 558 × 3

⇒ 0.62X = 1674

⇒ X = 2700

∴ The cost price of the goods is 2700.

Given:

The number = 9386x378y

Concept:

If the sum of digits is divisible by 9 then the number itself is divisible by 9

If the last 3 digits of the number are divisible by 8 then the number itself is divisible by 8

Calculation:

The possible value of y = 4

Then the last three-digit of the number will be divisible by 8 = \({784\over 8}\ =\ 98\)

The possible value of x = 6

The sum of the digits = 9 + 3 + 8 + 6 + 6 + 3 + 7 + 8 + 4 = 54 which is divisible by 9

Now, x² + y² = 6² + 4² 

⇒ 36 + 16 = 52

⇒ x² - y² = 6² - 4² 

⇒ 36 - 16 = 20

The required ratio = \({13\over 5}\)

∴ The required result will be \({13\over 5}\).

The correct answer is Loading.

Concept: 

Mixture:

• A mixture is a substance that consists of two or more elements or compounds not chemically combined together.
• For example, a mixture of salt and sand.

Separation of mixtures:

• The constituents of mixtures have different physical properties such as density, size of particles, solubility, etc.
• These differences are used to separate the constituents of the mixtures.
• The various physical processes which are used to separate the constituents of a mixture are Loading, crystallization, filtration, chromatography, etc.

Explanation:

Chromatography:

• Chromatography is a technique of separating two or more dissolved solids which are present in a solution in very small quantities.
• This separation is based on the fact that though two or more substances are soluble in the same solvent but their solubilities may be different.
• A special type of paper called “chromatography paper” is used for carrying out separations by chromatography.

Filtration:

• Filtration is a process by which insoluble solids can be removed from a liquid by using filter paper.
• A filter paper is a special type of paper that has pores that are tiny enough to let only liquids pass through it.
• The clear liquid obtained is called filtrate while the insoluble solids left on filter paper are called the residue.

Loading:

• It is a process in which chemicals like alum are used to increase the rate of sedimentation.
• The alum particles deposit fine clay particles and make them heavier so that they settle down at the bottom of the beaker easily.

Crystallization:

• It is a process in which a pure solid is separated from an impure solution in the form of crystals.
• The mixture is dissolved in the minimum amount of water and then heated strongly.
• The hot, concentrated solution is allowed to cool and crystals of pure solids are formed.
• The impure solids remain dissolved in the solution.

So, the most effective technique for separating very fine mud particles suspended in water is loading.

The correct answer is restoring forests.

Concept:

Forest conservation: It is the practice of planting and maintaining forested areas for the benefit and sustainability of future generations. 

Explanation:

Silviculture:

• It is a branch of forestry dealing with the development and care of forests.
• It can also be defined as the art and science of managing forests for desired outcomes, such as wildlife habitat, aesthetics, and timber production.

Additional Information​ Water harvesting:

• It is the activity of the direct collection of rainwater.
• The rainwater collected can be stored for direct use or can be recharged into the groundwater.

Organic farming:

• It is the agricultural system that uses ecologically based pest controls and biological fertilizers derived largely from animal and plant wastes and nitrogen-fixing cover crops.

The correct answer is 30 cm; 0.5 cm.

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) = height of image / height of object = h_i / h_o 

Also, m = -v/ u 

So, 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: Object distance, u = -120 cm, focal length, f = 40 cm, height of object, h_o = 2 cm

\(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)(\frac{1}{v} = \frac{4}{120}\)

\(\frac{1}{40} = \frac{1}{v} + \frac{1}{-120}\)

\(\frac{1}{40} = \frac{1}{v} - \frac{1}{120}\)

\(\frac{3+1}{120} = \frac{1}{v} \)

\(\frac{4}{120} = \frac{1}{v}\)

\(\frac{1}{v} = \frac{1}{30} \)

v = 30 cm

m = \(\frac{hi}{ho} = \frac{-v}{u}\)

\(\frac{hi}{2} = \frac{-30}{-120} = \frac{1}{4}\)

\(hi = \frac{2}{4} = \frac{1}{2} = 0.5 \) cm

The image is formed at v = 30 cm and its height hI = 0.5 cm.

The correct answer is Amalgam.

Concept:

Alloy:  An alloy is a homogeneous mixture of two or more metals, or a metal and a non-metal. 

Mineral: Minerals are naturally occurring inorganic solids with a crystalline structure and a definite range of chemical formulas.

Ore: Ores are concentrations of minerals in rock that are high enough to be economically extracted for use.

Explanation:

Cinnabar:

• It is bright red or brownish-red mineral formed of mercuric sulfide (mercury(II) sulfide).
• It is found close to areas of volcanic activity and hot springs.
• It is the main commercial source of mercury.
• Chemical Formula: HgS.

Amalgam

• It is an alloy of mercury and one or more other metals.
• It is crystalline in structure, except for those with a high mercury content, which is liquid.

So, the metal extracted from cinnabar ore by strong heating is Mercury and the alloys of this metal with other metals are collectively known as amalgam.

Additional Information

• Nichrome: It is an alloy of nickel, chromium, and iron (Ni + Cr + Fe).
• Steel:  It is an alloy of iron and carbon (Fe + C).
• German silver: It is an alloy of copper, zinc, and nickel (Cu + Zn + Ni).

The correct answer is Fish.

Concept:

Evolution: It is the process by which the various forms of plants, animals, and other life forms have developed due to the accumulation of variations in pre-existing organisms over millions of years.

Fossils:

• Fossils are the preserved remains of plants and animals whose bodies were buried in sediments, such as sand and mud, under ancient seas, lakes, and rivers.
• Fossils are commonly found in sedimentary rocks.

Explanation:

Formation of sedimentary rocks:

• These rocks get their name from the Latin word sedimentum which means settle down.
• These rocks are formed by the settling down of sediments.
• Sediments are the smaller particles/fragments that are formed by breaking down rocks when they roll down, crack and hit each other.
• These sediments are transported by wind, water, etc., and form sedimentary rocks when compressed and hardened.
• These also contain fossils of plants, animals, and other microorganisms that once lived on them.
• The oldest fossils are buried in the deepest.

Evolution of animals: ​

• Life first originated in water.
• Out of all chordates, fish were the first to evolve, then came amphibians, then reptiles, followed by mammals, and lastly birds.
• So, on the evolutionary timeline, fish would have evolved first, then scaly dinosaurs (reptile), then feathery dinosaurs (reptile) followed by birds.
• When we will start digging, we will first find the most recent fossils and as we go deeper and deeper, older and older fossils will be found.
• Thus, fish are most likely to be found in the deepest layer of the earth.

The correct answer is 36.

Concept:

Resistance in series:

• When resistors are connected end-to-end in a circuit, they are said to be in "series."
• R = R1 + R2 + R3....
• Current remains the same across all the resistors connected in series.

Resistance in parallel: 

• When both ends of resistors are connected, they are said to be in parallel.
• 1/R = 1/R1 + 1/R2 = 1/R3 ....
• The potential difference across all the resistors connected in parallel remains the same.

Electric Power:

• The energy consumed per unit of time or the rate of doing work is called power.
• Power = work done / time taken = Vq / t = VI = V²/R = I²R

Explanation:

Resistors A (2 Ω), B (3 Ω), and C (6 Ω) are connected in parallel.

Equivalent resistance, 1/R1 = 1/2 + 1/3 +1/6 = 3+2+1/ 6 = 6/6 = 1 Ω

Now, the resistors R1, D, F, and G are in series.

R2 = 1 + 2 + 3 + 6 = 12 Ω

Equivalent current, I in the circuit = V/R2 = 6/12 1/2 A.

Potential difference across C = IR1 = 1/2 × 1 = 1/2 V

P_G = I²G = 1/2 × 1/2 × 6 = 3/2 Watt       (since current remains same in series combination)

P_C = V²/C = (1/2 × 1/2) / 6 = 1/24 Watt  (since voltage remains same in parallel combination)

The ratio (PG/PC) = 3/2 × 24 = 3 × 12 = 36.

The correct answer is 40 u.

Concept:

The Modern Periodic Table:

• In 1913, Henry Moseley showed that the atomic number of an element is a more fundamental property than its atomic mass.
• Modern Period Law: The physical and chemical properties of elements are the periodic function of their atomic number.
• The modern periodic table contains 18 vertical columns known as groups and seven horizontal rows known as periods.
• On moving from left to right in a period, the number of valence electrons increases from 1 to 8 in the elements present but the number of shells remains the same.
• All the elements of a group of the periodic table have the same number of valence electrons.

Explanation:

Period:

• The periods have the same elements that have the same valence shell or the energy shell.
• The number of elements present in a period can be determined by the formula 2n², where n is the number of the shell from the nucleus.
• For example, the first period has two elements only as they have only 1 valence shell and the second period** has **8 elements with 2 shells.
• Also, the elements have the same no. of shells as their period no. So, an element belonging to period 4 will have 4 shells.

​Groups:

• The group consists of elements that have the same number of electrons in the valence shell or outermost shell of the atom.
• The number of shells increases by one unit as the elements move down in the periodic table in a group.
• Group number indicates the valence electrons of the atom. Group1 and 2 have 1 and 2 valence electrons in the outermost shell respectively.
• But for group no. 13-18 it is calculated by subtracting 10 from group no. For example, an element belonging to group 13 will have 13-10 = 3 valence electrons.

Element X belongs to the 3^rd period and 2^nd group.

• 3^rd period means there are 3 shells.
• 2^nd group means 2 valence electrons in its outermost shell.
• So, its electronic configuration will be 2, 8, 2.
• Element X is Magnesium with atomic number 12 and an atomic mass of 24 u.
• Element Y belongs to the 2^nd period and 16^th group.
• 2^nd period means there are 2 shells.
• 16^th group means 16-10 = 6 valence electrons in the outermost shell.

Electronic configuration = 2, 6 

Element Y is Oxygen with atomic number 8 and atomic mass 16 u.

**The molecular mass of compound XY = mass of X + mass of Y = 24 + 16 = 40 u.**​

The correct answer is Fungi.

Concept:

Classification of organisms: 

• Classification is the process of grouping organisms into different categories on the basis of their similarities and dissimilarities.
• It makes the study of organisms easier and more convenient.

Explanation: 

Five Kingdom classification system:

• It was given by R.H. Whittaker in 1969.
• He divided all organisms into five categories namely**, Monera, Protista, Fungi, Plantae, and Animalia.**
• This classification was based upon certain characteristics like mode of nutrition, thallus organization, cell structure, phylogenetic relationships, and reproduction.

Yeast belongs to the kingdom Fungi.

The correct answer is 51%.

Concept:

Resistance (R): 

• Resistance 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).
• Ohms is named after George Simon Ohm (1784-1854), a German physicist who studied the relationship between voltage, current and resistance.
• \(R = \frac{ρ l}{A}\) 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 decrease in length, let us take new length = L', radius of wire = r' and new resistance = R'

L' = 70 L/ 100 ( since there is 30% decrease)

The volume of the wire remains the same ( given).

So, Volume of Original Wire = volume of new wire 

π r² L = π r ' ² L'

r²L = r' 2 L'

r' 2 = r2 L /  L'

r' ² = 100 r² L / 70 L

r' 2 = 100 r2  / 70 

Decrease in resistance = \(\frac{R-R'}{R} × 100\)

\(\frac{\frac{\rho L}{A} -\frac{\rho L'}{A'}}{\frac{\rho L}A} × 100\)

\(\rm \frac{\left(\frac{\rho L}{A}-\frac{\rho L{'}}{A}\right)}{\frac{\rho L}{A}}\times100\)

\(\rm \frac{\left(\frac{\rho L}{r r^2}-\frac{\rho L{'}}{r r'^2}\right)}{\frac{\rho L}{r r'}}\times100\)

\(\rm \frac{\frac{\rho}{\pi}\left(\frac{L}{r^2}-\frac{70 \ L}{180\ r'^2}\right)}{\frac{\rho}{\pi}\times\frac{L}{r^2}}\times100\)

\(\rm \frac{\left(\frac{L}{r^2}-\frac{70 \ L}{180\ r'^2}\right)}{\frac{L}{r^2}}\times100\)

\(\rm \frac{\frac{100\ r_1^2-70\ Lr^2}{100\ r^2\ r"^2}}{\frac{L}{r^2}}\)

\(\rm \frac{\frac{100\times100\ r^2}{70}-70\ Lr^2}{\frac{100}{70}r^2}\)

\(\rm \frac{10000r^2-4900r^2}{\frac{70\times100\times r^2}{70}}\)

\(=\frac{5100\ r^2}{100\ r^2}\)

= 51%

The resistance decreases by 51%.

The correct answer is 18.

Concept:

Resistance:

• It is the opposition offered to the flow of current passing through a conductor.
• It is measured in Ohms (Ω).
• R = ρL/ A where ρ is resistivity, L is the length of conductor and A is the area of cross-section.

Ohm's Law:

• Ohm’s law states that the amount of electric current through a metal conductor in a circuit is directly proportional to the voltage impressed across it, for any given temperature.
• V = IR, where V is voltage, I is current and R is resistance.

Explanation:

 In the above-drawn circuit, we can refer to the two sections of wire as two different resistors in series. Current remains same in series connection. So, here we will take current = I. 

For Wire AC

length = L, resistivity= ρ , Radius = 3r 

Area of cross-section of wire = π r² = π (3r)² = 9 π r²

R1 = ρ L/ A = ρ L / 9 π r2

V1 = I R1 = I ρ L / 9 π r2

For wire BC 

length = L, resistivity= 2ρ , Radius = r 

Area of cross-section of wire = π r2 

R2 = 2ρ L/ A = 2ρ L /  π r2

V2 = I R2 =  2ρ I L /  π r2

Ratio of V2 to V1 = V2/ V1 =  \(\frac{\frac{2\rho IL}{\pi r^2}}{\frac{\rho I L}{9\pi r^2}}\) = \(\frac{2\rho IL}{\pi r^2}\) × \(\frac{9 \pi r^2}{\rho IL}\) = 2 × 9 = 18 

The ratio (V2 / V1) is 18.

The correct answer is real and of the same size.

Concept: 

 Convex lenses:

• A convex lens is thicker at the center than at the edges.
• It is called a converging lens because the rays of light that pass through it are brought closer together (they converge).
• When parallel rays of light pass through a convex lens the refracted rays converge at one point called the principal focus.
• The distance between the principal focus and the center of the lens is called the focal length.
• A double convex lens has two foci F1 and F2 and two centers of curvature 2F1 and 2F2.

Explanation:

Image formed by a convex lens when Object is at 2F1:

A same-sized, real, and inverted image is formed at the center of curvature, 2F2 when the object is placed at the center of curvature, 2F1 of a convex lens.

Additional Information All six cases of image formation by the convex lens:

The correct answer is A precipitate is formed.

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.

Explanation:

Types of Chemical Reactions:

Combination reaction:

• Two or more elements or compounds combine together to form a single compound.
• Such reactions are represented by equations of the following form:     A + B → AB.

Decomposition reaction:

• The opposite of a combination reaction, a complex molecule breaks down to make simpler ones.
• Such reactions are represented by equations of the following form: AB → A + B.

Precipitation reaction:

• Two solutions of soluble salts are mixed resulting in an insoluble solid (precipitate) forming.
• Such reactions are represented by equations of the following form: A + Soluble salt B  → Precipitate + soluble salt C.
• Lead nitrate + Potassium iodide → Lead Iodide (yellow precipitate) + Potassium nitrate
• Pb(NO₃)₂ + KI → PbI₂  + KNO₃

Neutralization reaction:

• An acid and a base react with each other. Generally, the product of this reaction is salt and water.
• Such reactions are represented by equations of the following form: Acid + Base → Salt + Water.

Combustion reaction:

• Oxygen combines with a compound to form carbon dioxide and water.
• These reactions are exothermic, meaning they give off heat.
• Such reactions are represented by equations of the following form: A + O2 → H2O + CO2.

Displacement reaction:

• One element takes place with another element in the compound.
• Such reactions are represented by equations of the following form: A + BC → AC + B.

The correct answer is Both arrows are operational but unequal (the amount of water entering is not equal to the amount of water exiting).

Concept:

Osmosis: 

• It is the movement of water molecules through a semi-permeable membrane.
• The water molecules move from a region of higher concentration to a region of lower concentration.

Types of solutions: 

• Hypertonic Solution: A solution having a higher concentration of solute with respect to another solution, is called a hypertonic solution.
• Hypotonic Solution: A solution having a higher concentration of solvent with respect to another solution, is called a hypotonic solution.
• Isotonic Solution: A solution that has exactly the same water concentration with respect to another solution, is called an isotonic solution.

Explanation:

• When a cell is placed in a hypotonic solution, the cell has less water and more solute as compared to the solution.
• The water molecules will move in both directions that is from the solution into the cell and vice versa.
• But the amount of water entering the cell will be more as compared to the water coming out of it.
• The net effect seen will be water entering the cell.

The correct answer is the Law of conservation of mass.

Concept:

Law of conservation of mass:

• It was discovered by Antoine Lavoisier in 1789.
• It states that mass is neither created nor destroyed in chemical reactions.
• In other words, the mass of any one element at the beginning of a reaction will equal the mass of that element at the end of the reaction.

Mole:

• It is the SI unit of the amount of substance.
• One mole contains exactly 6.022×1023 atoms/molecules. This number is the fixed numerical value of the Avogadro constant (NA).
• The mass of one mole of a substance in grams is called its molar mass.
• The molar mass in grams is numerically equal to atomic/molecular/formula mass in u.

So, 1 mole = 6.022 × 1023 atoms/molecules = Atomic/molecular mass of an element/compound.

​Explanation:

On heating Calcium carbonate,  calcium oxide, and carbon dioxide are formed.

     CaCO₃                 +      heat      \(\to\)   CaO + CO₂

1.5-1 = 0.5 mole                                    28g     22g 

1 mole of  CaCO₃  = Molar mass of  CaCO₃  = 40 + 12 + 3 × 16 = 52 + 48 = 100 g

0.5 mole of  CaCO3  = 0.5 × 100 = 50 g

According to law of conservation, the total mass of reactants should be equal to total mass of products.

• Mass of reactant = 50 g
• Mass of products = mass of CaO + mass of CO₂ = 28 + 22 = 50 g
• Mass of reactant = Mass of products = 50 g

So, the above chemical reaction demonstrates the Law of conservation of mass.

The correct answer is Calcium hydroxyapatite.

Concept:

Tooth decay: 

• Tooth decay is damage to a tooth's surface or enamel.
• It happens when bacteria in our mouth make acids that attack the enamel.
• Enamel is the hardest part of the human body, made up of calcium phosphate.

Explanation:

Cause of tooth decay:

• Bacteria in the mouth feed on sugary, starchy foods and drinks (fruit, candy, bread, cereal, sodas, juice, and milk).
• The bacteria convert these carbohydrates into acids.
• Tooth decay starts when the pH of the mouth becomes lower than 5.5.
• Enamel which is composed of calcium phosphate, arranged in a crystal structure called hydroxyapatite, starts to dissolve at such low pH.
• Tooth decay can lead to cavities (dental caries), which are holes in your teeth.
• If tooth decay is not treated, it can cause pain, infection, and even tooth loss.

Prevention of tooth decay: Tooth decay can be prevented by 

• eating a healthy diet,
• drinking plenty of tap water instead of sugary drinks
• brushing your teeth twice a day
• using a fluoride toothpaste
• flossing once a day.

The correct answer is Coal.

Concept:

Source of energy:

• A source of energy is that which is capable of providing enough useful energy at a steady rate over a long period of time.
• A good source of energy should be :
• Safe and convenient to use
• For example; nuclear energy can be used only by highly trained engineers with the help of nuclear power plants. It cannot be used for our household purpose.
• Easy to transport
• For example; coal, petrol, diesel, LPG, etc. have to be transported from the places of their production to the consumers.
• Easy to store
• For example; huge storage tanks are required to store petrol, diesel, LPG, etc.

Explanation:

Types of sources on the basis of their renewability: 

Renewable sources of energy:

• These sources of energy are inexhaustible, i.e., they can be replaced as we use them and can be used to produce energy again and again.
• These are available in an unlimited amount in nature and develop within a relatively short period of time.
• Example of Renewable Sources of Energy :
• Solar energy.
• Wind energy.
• Water energy (hydro-energy).
• Geothermal energy.
• Ocean energy.
• Biomass energy (firewood, animal dung, and biodegradable waste from cities and crop residues constitute biomass).

Non-renewable sources of energy:

• These sources of energy are exhaustible and cannot be replaced once they have been used.
• These sources have been accumulated in nature over a very long period of millions of years.
• Examples of Non-renewable Sources of Energy :
• Coal
• Oil
• Natural gas
• All these fuels are called fossil fuels.

Explanation:

From 0s to 10s the current is increasing at the same rate and induces the current i₁ in the coil B.

From 20s to 30s the current is decreasing at the same rate and induces the current i3 in the coil B.

In both cases, the time period is the same and the rate is also the same, so i₁ = i₃.

As the i₁ current is increasing and i₃ is decreasing so, their direction will be opposite.

The correct answer is Pb and Sn.

Concept:

Alloy:

• An alloy is a homogeneous mixture of two or more metals, or a metal and a non-metal.
• Properties of alloys are different from the constituent elements. 
• They are harder than their constituent metals.
• They are more resistant to corrosion than pure metals.
• They are more durable than the metals they are made from.
• They have less electrical conductivity and melting point than the constituent metals.
• Some of the properties of constituent elements are retained in the alloy.

Explanation:

List of some important alloys:

Brass

• It is composed of copper and zinc (Cu + Zn).
• It is used in making utensils.

Bronze

• It is composed of copper and tin (Cu + Sn).
• It is used in making coins, bells, and utensils.

Solder

• It is composed of lead and tin (Pb + Sn).
• It is used for soldering (welding electrical wires together).

Stainless steel

• It is composed of iron, chromium, nickel, and carbon (Fe + Cr + Ni + C).
• It is used for making utensils and surgical cutlery.

The correct answer is Iris.

Concept:

Human Eye: It is a specialized sense organ capable of receiving visual images, which are then carried to the brain.

Explanation:

Structure of the human eye:

The correct answer is 0.96; away from.

Concept:

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

• The refraction of light takes place on going from one medium to another because the speed of light is different in the two media.

• The greater the difference in the speeds of light in the two media, the greater will be the amount of refraction.

• A medium in which the speed of light is more is known as an optically rarer medium and a medium in which the speed of light is less is known as an optically denser medium.

Refractive Index (n):

• It is the measure of the bending of a ray of light when passing from one medium into another.
• If 'i' is the angle of incidence of a ray in a vacuum and 'r' is the angle of refraction, then the refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction; i.e., n = sin i / sin r.
• It is also equal to the velocity of light (c) of a given wavelength in empty space divided by its velocity v in a substance, or n = c/v.

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 ice with respect to alcohol = refractive index of ice / refractive index of alcohol = \(\frac{1.31}{1.36}\) = 0.96
• Greater the refractive index, the denser the medium. Thus, alcohol (1.36) is denser than ice (1.31).
• The refracted ray moves away from the normal when it travels from a denser to a rarer medium.
• Hence, when the light ray travels from alcohol to ice, the refracted ray will move away from the normal.

The refractive index of ice with respect to alcohol is 0.96 and the light ray bends away from the normal in ice.

The correct answer is blood stream.

Concept:

Pancreas:

• It is an elongated organ that is located between the stomach and the small intestine.
• It contains both exocrine cells that excrete digestive enzymes and endocrine cells that release hormones.
• It is sometimes referred to as a heterocrine gland because it has both endocrine and exocrine functions.

Explanation:

The endocrine part of the Pancreas:

• The endocrine cells of the pancreas form clusters called pancreatic islets or the islets of Langerhans.
• The pancreatic islets contain two primary cell types: alpha cells, which produce the hormone glucagon, and beta cells, which produce the hormone insulin.
• These hormones regulate blood glucose levels and are released directly into the bloodstream.
• Glucagon raises blood glucose levels while insulin lower blood glucose levels.

Exocrine part of the Pancreas:

• Functioning as an exocrine gland, the pancreas excretes enzymes into the small intestine via a duct.
• These enzymes include trypsin and chymotrypsin to digest proteins; amylase for the digestion of carbohydrates; and lipase to break down fats.

The correct answer is Calcium sulphate hemihydrate.

Concept:

Calcium Sulphate hemihydrate: 

• It is popularly known as the Plaster of Paris.
• Its chemical formula is CaSO₄.\(\frac{1}{2}\)H₂O

​Properties:

• It is a white powder.
• It has a remarkable property of setting into a hard mass on wetting with water.

Calcium Sulphate Dihydrate:

• It is also known as Gypsum.
• Its chemical formula is CaSO4.2H2O.

Explanation:

Preparation of Calcium Sulphate hemihydrate**:**

• It is manufactured by heating gypsum at 373 – 393 K or 150° C/300° F.
• CaSO₄·2H₂O + Heat → CaSO₄·\(\frac{1}{2}\)H₂O + \(1\frac{1}{2}\)H₂O
• On heating gypsum at 373 – 393 K, it loses water molecules and becomes calcium sulphate hemihydrate.

Uses of Calcium Sulphate hemihydrate: It is used in 

• chemical laboratories for sealing air gaps in apparatus where the air-tight arrangement is required
• in making smooth surfaces before painting
• hospitals for setting fractured bones
• making toys, decorative materials, cheap ornaments, blackboards, cosmetics, casts for statues, etc.

Hence, the substance which is used for making toys, making surfaces smooth and for supporting fractured bones is Calcium Sulphate hemihydrate.

The correct answer is that the soil becomes barren of life forms.

Concept:

Fertilizers: 

• Fertilizers are chemical substances that are usually rich in selective nutrients like nitrogen, potassium, and phosphorus.
• These are used by the farmers daily to increase the crop yield

Pesticides:

• A pesticide is any substance used to kill, repel, or control certain forms of plant or animal life that are considered to be pests.
• Pesticides include
• Herbicides for destroying weeds and other unwanted vegetation,
• Insecticides for controlling a wide variety of insects,
• Fungicides used to prevent the growth of moulds and mildew,
• Disinfectants for preventing the spread of bacteria, and
• Compounds used to control mice and rats.

Explanation:

**Harmful effects of prolonged use of fertilizers and pesticides:**​

• The synthetic chemicals in fertilizers change soil pH, which adversely affects the health of naturally found soil microorganisms.
• These altered levels of acidity in the soil eliminate the microorganisms that are beneficial to plants.
• Pesticides can linger in the soil for years or decades after they are applied, continuing to harm soil health.
• The studies have shown that prolonged use of pesticides impacts soil organisms in many ways, from increased mortality to reduced reproduction, growth, cellular functions and even reduced overall species diversity.

Thus, we can say that the soil becomes barren of life forms after the prolonged application of fertilizers and pesticides.

The correct answer is 1.08 m.

Concept:

• Lens: The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
• The lens whose refracting surface is upside is called a convex lens and the lens whose refracting surface is inside is called a concave lens or diverging lens.
• The convex lens is also called a converging lens.

When two or more lenses are in contact with each other then, the equivalent focal length is given by:

\(\frac{1}{F} = \frac{1}{{{f_1}}} + \frac{1}{{{f_2}}}\)

Where f1 and f2 are focal lengths of the two lenses

• 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) = 1/f

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

• The unit of power of a lens is Dioptre when the focal length of the lens is taken in meter (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 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 = \(\frac{1}{f}\)

f = \(\frac{1}{p}\) = \(\frac{100}{5}\) = 20 cm

Given: Object distance, u = -30 cm, Focal length, f = 20 cm

 v=?

\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)

\(\frac{1}{20} = \frac{1}{v} - \frac{1}{-30}\)

\(\frac{1}{20} = \frac{1}{v} + \frac{1}{30}\)

\(\frac{1}{20} - \frac{1}{30} = \frac{1}{v} \)

\(\frac{1}{v} = \frac{3-2}{60}\)

\(\frac{1}{v} = \frac{1}{60}\)

v = 60 cm

For concave lens

f = \(\frac{1}{p}\) = \(\frac{100}{-5}\) = -20 cm

Object distance, u = -90-(-60)= -90 + 60 = -30cm, focal length, f = -20cm

v = ?

\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)

\(\frac{1}{-20} = \frac{1}{v} - \frac{1}{-30}\)

\(\frac{1}{-20} = \frac{1}{v} + \frac{1}{30}\)

\(\frac{1}{-20} + \frac{1}{-30} = \frac{1}{v} \)

\(\frac{1}{-20} - \frac{1}{30} = \frac{1}{v} \)

\(\frac{1}{v} = \frac{-3-2}{60} = \frac{-5}{60} = \frac{-1}{12}\)

v= -12 cm 

Distance between original object and final image = 30 + (90-12) = 30 + 78 = 108 cm = 1.08 m.

The correct answer is ovule.

Concept:

Flower:

• A flower can be defined as a specialized structure that bears reproductive organs and takes part in the process of reproduction.
• It is involved in the formation of fruits and seeds.

Explanation:

Structure of flower:

• Each flower is supported by a stalk called a pedicle.
• This stalk leads to a broad basal region of the flower. This part is called the thalamus. Also called the receptacle.
• A typical flower has four main parts—or whorls—known as the calyx, corolla, androecium, and gynoecium.

​Calyx:

• The outermost whorl of the flower has green, leafy structures known as sepals.
• The sepals, collectively called the calyx, help to protect the unopened bud.

​Corolla

• The second whorl is comprised of petals usually, brightly colored collectively called the corolla.
• They help in pollination by attracting insects.

Androecium

• The third whorl contains the male reproductive structures and is known as the androecium.
• The androecium has stamens. Each stamen has an anther and a filament.

​Gynoecium

• The innermost group of structures in the flower is the gynoecium or the female reproductive part.
• The carpel is the individual unit of the gynoecium and has a stigma, style, and ovary.
• Inside the ovary, there are ovules.

The ovule develops into a seed and the ovary develops into fruit after fertilization.​

Per capita income is national income divided by population size.

• Per capita income is often used to measure a sector's average income and compare the wealth of different populations.
• Per capita income is also often used to measure a country's standard of living.
• The Ministry of Statistics and Programme Implementation (MoSPI) is a ministry of the Government of India concerned with coverage and quality aspects of statistics released.
• The surveys conducted by the Ministry are based on scientific sampling methods.
• Ministry of Statistics and Programme Implementation published the report on National and per Capita Income.

Additional Information

• The Ministry of Home Affairs is a ministry of the Government of India. As an interior ministry of India, it is mainly responsible for the maintenance of internal security and domestic policy. The Home Ministry is headed by the Union Minister of Home Affairs Amit Shah.
• Ministry of planning: Preparation of Plan and Budget Link, Plan Supplement, etc. Monitoring and review of the implementation of Plan Schemes. Coordination in the matter of planning and development in the State. Overseeing the execution of plan schemes.
• Ministry of Human Resource Resource Development: Formulating the National Policy on Education and ensuring that it is implemented in letter and spirit. Planned development, includes expanding access and improving the quality of the educational institutions throughout the country, including in the regions where people do not have easy access to education.

The six fundamental rights enshrined in the Constitution are considered essential for the functioning of Indian democracy.

• The right to freedom gives citizens basic freedom with respect to speech and expression, form associations, freedom of personal liberty, freedom to live a life of dignity, etc.

Important Points The right to freedom guarantees freedom for citizens to live a life of dignity among other things. These are given in Articles 19, 20, 21A, and 22 of the Indian Constitution. Article 19 guarantees six freedoms. They are:

• Freedom of speech and expression: 
• The State guarantees freedom of speech and expression to every person in India.
• However, the State can impose restrictions on the freedom of speech and expression in the interests of the integrity, security, and sovereignty of the country, friendly relations with foreign nations, public order, with respect to defamation, incitement to offense, or contempt of court.
• Freedom to assemble: The State guarantees every person the freedom to assemble peacefully without arms.
• However, as above, reasonable restrictions can be imposed in the interests of the sovereignty and integrity of the country and public order.
• Freedom to form associations/unions/cooperative societies:
• Again, the State can impose restrictions in the interests of the integrity, security, and sovereignty of the country, friendly relations with foreign nations, for public order, with respect to defamation, incitement to offense or contempt of court.
• This freedom gives workers the right to form trade unions, which is thus a fundamental right. 
• The Police Forces (Restriction of Rights) Act, 1966 prohibits police personnel from forming trade unions.
• The Constitution also allows the Parliament to pass a law restricting the right to form a political association with members of the armed forces, intelligence bureaus, persons employed with telecommunication systems.
• Freedom to move freely: A citizen of India can move freely throughout the territory of India. But this right can also be restricted on the grounds of security, public order or for protecting the interests of the Scheduled Tribes.
• Freedom of residence: Citizens of India have the right to reside in any part of the country. Although restrictions can be imposed on the grounds of security, public order or for protecting the interests of the Scheduled Tribes.
• Freedom of profession: All citizens have the right to carry on any trade or profession/occupation, provided the trade or occupation is not illegal or immoral. Also, the law does not prevent the State from making laws related to technical or professional qualifications required for practising the occupation or trade.

Thus, we can conclude that the Freedom to keep slaves is NOT included in the Right to Freedom as per the Constitution of India.