ICAR Technician 4 March 2022 Shift 3 (Previous Year Paper)

The correct answer is 7.5%.

• According to Asian Development Bank, India’s GDP is expected to grow by 7.5% in 2022.

Key Points

• The Asian Development Bank (ADB) has forecasted India’s GDP growth to moderate to 7.5% in 2022-23 from an estimated 8.9% in 2021-22.
• It will reach up to 8% in 2023-2024.

Additional Information

• About ADB:-
• The Asian Development Bank is a regional development bank established on 19 December 1966, which is headquartered in the Ortigas Center located in the city of Mandaluyong, Metro Manila, Philippines.
• The company also maintains 31 field offices around the world to promote social and economic development in Asia.
• India was a founding member of ADB in 1966 and is now the bank's fourth-largest shareholder.

The correct answer is SBI.

• In November 2021, SBI bank partnered with Jamshedpur Football Club to promote football in the country.

Key Points

• The State Bank of India has entered into a strategic partnership with the Jamshedpur football club, which is owned by Tata Steel.
• The aim is to support and promote the sport in the country.
• This is the first of its kind of agreement done by SBI in the game of football.
• The SBI will become one of the principal sponsors of the JFC, through this agreement, thereby having the SBI logo on Jersey.
• The JRD Tata Sports Complex was set up in Jharkhand by Tata Steels.
• It conducts ISL (Indian Super League) and promotes the sport of Football in India.
• The brands(SBI and JFC) will actively engage with fans via the first team and also during the broadcast of the Indian Super League (ISL).

Additional Information

• State Bank of India:
• The Imperial Bank of India was renamed the State Bank of India in 1955.
• The Imperial Bank was formed as a joint-stock bank in January 1921 by amalgamating the Presidency Banks of Bombay, Calcutta, and Madras.
• The Imperial Bank had the status of a quasi-central bank from its inception.
• The headquarters of the State Bank of India is in Mumbai.
• The Chairperson of the State Bank of India is Dinesh Kumar Khara.

The correct answer is North-western Himalayas.

• Pangong Tso lake is situated in North-western Himalayas.

In News

• Pangong Tso lake in eastern Ladakh has often been in the news, most famously during the Doklam standoff and the recent Galwan clash.

Key Points

• Pangong Tso Lake located in Ladakh Union territory is an endorheic lake in the Himalayas situated at a height of about 4,350 m.
• It is a long narrow, deep, endorheic (landlocked) lake situated at a height of more than 14,000 ft in the Ladakh Himalayas(North-western Himalayas).
• It is geographically situated in a disputed territory, claimed both by India and China.
• This lake is about 5 km wide and about 134 km long with about 60% of the length extending into Tibet.
• Pangong Lake in Kashmir is the world's highest brackish lake at 4,350 m above sea level.
• In winter the lake freezes completely, despite being saline water.

​

The correct answer is Cristiano Ronaldo.

• In December 2021, Cristiano Ronaldo set a record by scoring 800 goals.

Key Points

• Cristiano Ronaldo became the first player to score 800 top-level goals.
• The goals were made during Manchester United's 3-2 win over Arsenal.
• Manchester United is a football club in England founded in 1878.
• Ronaldo has won five Ballon d'Or awards.
• Ronaldo has won four European Golden Shoes.

Additional Information

• Cristiano Ronaldo plays from the year 2018-to 2021 for the club Juventus FC.
• Portuguese forwarder Cristiano Ronaldo is the captain of the national team of Portugal.
• Ronaldo joined Juventus in 2018, before that he was playing for the Real Madrid CF.

The correct answer is oxygen.

• oxygen is not a product of a combustion reaction.

Key Points

Combustion Reaction:

• Combustion is a process in which substances react with oxygen to produce water and heat.
• The combustion process is an exothermic process.

​

• The process requires the presence of oxygen without which the combustion will cease.
• The substances that burn during combustion are known as fuel.
• Fuel can be solid like wood, liquid-like kerosene, and gaseous like CNG.
• Some fuels burn with flame whereas others do not.
• Examples of combustion are:

CH4 + 2O2 → CO2 + 2H2O

C2H6 + 7/2 O2 → 2CO2 + 3H2O

C +  O2 → CO2 

• The oxygen is the oxidizer whereas the fuel is the reductant.

The correct answer is Gopal krishna Gokhale.

• Gopal krishna Gokhale was not an extremist leader.

Key Points

• Gopal Krishna Gokhale was the political guru of Mahatma Gandhi.
• Gokhale was the founder of the Servants of India Society.
• In 1905, when Gokhale was elected president of the Indian National Congress.
• Notable work of Gokhale: English weekly newspaper, The Hitavada.

Additional Information

• The Congress split into two parts - Moderates and Extremists in the year 1907 at the Surat Session of Congress, which was also popularly known as 'Surat Split'.
• Extremists are not satisfied with the methods and achievements of moderates.
• They were three groups of extremists. They are the Maharashtrian group led by Bal Gangadhar Tilak, the Bengal group led by Bipin Chandra Pal and Aurobindo Ghosh, and the Punjab group led by Lala Lajpat Rai.
• The most prominent leaders of the Extremists were Bal Gangadhar Tilak, Lala Lajpat Rai, and Bipin Chandra Pal, who are known collectively as the Lal-Bal-Pal trio.

The correct answer is Lord Curzon.

• In 1905, Lord Curzon announced the partition of Bengal.

Key Points

• Bengal was partitioned by the British viceroy Lord Curzon.
• Lord Curzon announced the partition of Bengal on 20th July 1905.
• The partition came into effect on 16th October 1905.
• At that time of partition, Bengal was the biggest province of British India including Bihar and parts of Orissa.
• The British argued that the division was for administrative convenience.
• The partition of the Bengal is an example of the British policy of divide and rule.
• The main reason for the partition of Bengal was to destroy the political influence of the educated middle class among whom the Bengali intelligentsia was the most prominent.
• The swadeshi movement started to protest against the partition of Bengal.
• Bengal partition was finally cancelled by Lord Hardinge in 1911.

Additional Information

• Lord Wavell
• He was the Viceroy of India from 1944-1947.
• Lord Linlithgow
• He was the Viceroy of India from 1936-1944.

The correct answer is Mahila Mitra Plus.

• The name of the savings scheme for women started by Federal Bank in December 2021 is Mahila Mitra Plus.

Key Points

• Mahila Mitra Plus:
• It is a savings account exclusively for women, endowed with exciting features like complementary insurance, a special rate on home loans, free RTGS / NEFT facility.
• It also provides two ZERO balance kids’ accounts, and Debit Card offers.
• Eligibility: Resident Woman
• Services Provided are:
• Complimentary Insurance up to 80.75 L
• Special rates on Home Loan – 0.60% lower than Bank’s card rate.
• Free RTGS / NEFT facility.
• 50% concession on processing fee for home loans.
• Two free FedFirst SB account in the name of minor children, with no min. balance stipulation.

Additional Information

• Federal Bank Limited is a major Indian commercial bank in the private sector headquartered at Aluva Kerala.

The correct answer is Seven.

• According to December 2021,  the ZyCov-D vaccine has been included in the Corona vaccinations in 7 Indian states.

Key Points

• ZyCoV-D is a DNA plasmid-based COVID-19 vaccine developed by Indian pharmaceutical company Cadila Healthcare, with support from the Biotechnology Industry Research Assistance Council.
• ZyCoV-D is the world’s first plasmid DNA vaccine against coronavirus.
• It uses a section of genetic material from the virus that gives instructions as either DNA or RNA to make the specific protein that the immune system recognizes and responds to.
• It is a three-dose specialized needle-free vaccine, given in the interval of 4 weeks between each dose.
• It is approved for emergency use in India.
• The 7 states are **Bihar, Jharkhand, Maharashtra, Punjab, Tamil Nadu, Uttar Pradesh and West Bengal.**​

The correct answer is Sayyid dynasty.

• Khizr Khan was related to Sayyid.

Key Points

• Sayyid Dynasty (1414-1451 A.D.)
• Sayyid Dynasty was founded by Khizr Khan in 1414 A.D.
• It was the fourth dynasty of the Delhi Sultanate.
• Sultans of Sayyid Dynasty - 
• Khizr Khan (1414-1421A.D)
• Founder of the Sayyid Dynasty.
• Was the Governor of Multan.
• Died in 1421.
• Mubarak Shah(1421-1434 A.D)
• First Sultan ruler to appoint Hindu nobles in the court of Delhi.
• Constructed “Mubarakbad” City on the banks of the river Jamuna.
• Muhammad Shah (1434-1445 A.D)
• Defeated the ruler of Malwa with the help of Bahlul Lodi the Governor of Lahore.
• Conferred Bahlul Lodi with the title Khan-i-Khanan.
• Ala-ud-din Shah (1445-1451 A.D)
• Was removed from the throne by Bahlul Lodi in 1457 A.D.
• Delhi was captured by him and he was sent to Badaun.
• Died in Badaun in 1478 A.D.

The correct answer is Madhya Pradesh.

• In 2021, Walmart and Flipkart have tied up with the Madhya Pradesh state government to support MSMEs.

Key Points

• Walmart and its subsidiary Flipkart have signed an MoU with the Department of Micro, Small, and Medium Enterprises, Government of Madhya Pradesh.
• The aim is to create an ecosystem of capacity building for MSMEs in Madhya Pradesh.
• Under this MoU, Walmart, Flipkart, and MSME Department will assist MSMEs to digitize their business and enable them to sell their products through online retail.
• The initiative came under the Walmart Vriddhi Supplier Development Programme (Walmart Vriddhi).
• It is in the tie-up with the knowledge partner Swasti, which aims to train around 50000 Indian MSMEs with business skills to become successful as suppliers to Walmart, and sellers on global marketplace platforms like Flipkart.
• Walmart and Flipkart have partnered with various states including Haryana and Tamil Nadu, under this programme.

The correct answer is Bihar.

• According to NITI Aayog in 2021,  Bihar is the only state in India wherein 50% of the population is living in poverty.

Key Points

• NITI Aayog’s Multidimensional Poverty Index:
• The report is developed on the basis of the National Family Health Survey 2015-16.
• It will facilitate the formulation of sectoral policies and targeted interventions.
• It has three equally weighted dimensions namely health, education and standard of living, which are represented by twelve indicators that are nutrition, child and adolescent mortality, antenatal care, years of schooling, school attendance, cooking fuel, sanitation, drinking water, electricity, housing, assets and bank accounts
• In this index, the states of Bihar, Jharkhand, Uttar Pradesh, Madhya Pradesh and Meghalaya have emerged as the poorest states in India with over 50% of the population in Bihar classified as multidimensionally poor.
• The index revealed that 51.9% of Bihar’s population is poor.
• Kerala, Goa, Sikkim, Tamil Nadu and Punjab have registered the lowest poverty across India and are at the bottom of the index.
• The union territories of Puducherry have 1.72% of its population as poor, Lakshadweep 1.82%, Andaman & Nicobar Islands 4.30%, Delhi 4.79% and Chandigarh 5.97%.

The correct answer is Maratha – Eastern style.

Key Points

• The temple architecture in India is not the same everywhere.
• Basically, there are three styles of temple architecture in India:

1. Nagara Style (North India)
2. Dravida Style (South India)
3. Vasara style (Mix of Nagara and Dravida style)

• Nagara Style:

1. Built on a stone platform with steps leading up to it.
2. Have a tower or Shikhara.
3. Have Grabhagriha ( A place for the idols of god and goddess).
4. Examples: Kandariya Mahadeo temple at Khajuraho, Lakshamana temple

• Dravida Style:

1. Generally enclosed within a compounded wall.
2. The entrance gateway is known as Gopuram.
3. The shape of the Temple tower is known as Vimana (similar to Shikhara in Nagara style).
4. Large water tanks are common in the temple complex.
5. Examples: Brahadeeshwara temple, Rajarajeswara temple.

• Vasara style:

1. This style of temple architecture is a mix of Nagara and Dravid styles.
2. Examples: Dodda Basappa Temple, Hoysala Temple.

Hence, Maratha architecture is not a type of Indian architecture.

The correct answer is There are two fundamental states of matter.

Key Points

• The matter is made up of particles called atoms and molecules.
• Everything in the universe is made up of matter and energy.
• The matter is anything that has mass and occupies space.
• There are four natural states of matter: Solids, liquids, gases, and plasma.
• Solids:
• Molecules are arranged in repeating, regular patterns.
• Molecules are fixed in place or in another case they vibrate in a certain area.
• Types: crystalline, noncrystalline (amorphous), quasi-crystalline.
• Liquid:
• In a liquid, particles will flow or glide over one another.
• No regular pattern follows.
• They are roaming apart by a low attractive force between them.
• It gets the shape of their containers.
• Gas:
• In gases, the particles move rapidly in all directions, frequently colliding with each other.
• Molecules are so apart, therefore the attractive force is negligible.
• Plasma:
• With an exciting position (high temperature) atoms lose their electrons and that electron is mixed up with nuclei which results in plasma.
• Plasma consists of charged particles.
• The fifth state is the Bose-Einstein condensates, which are man-made.
• Scientists, Eric Cornell and Carl Weiman discover BEC matter by a combination of lasers and magnets.
• At a temperature of absolute zero (0 K, − 273.15 °C, or − 459.67 °F; K = kelvin), it separates atoms or subatomic particles.
• It is an exotic quantum phenomenon, observed in dilute atomic gases for the first time in 1995.
• BEC only exists for “bosons” – particles with a total spin that is an integer multiple of h, the Planck constant divided by 2 pi.

The correct answer is 7.1%.

Key Points

• According to Asian Development Bank poverty data, the unemployment rate of India in 2020 was 7.1%.

Additional Information

• Asian Development Bank (ADB):
• The Asian Development Bank (ADB) envisions a prosperous, inclusive, resilient, and sustainable Asia and the Pacific while sustaining its efforts to eradicate extreme poverty in the region.
• The headquarters of the Asian Development Bank is located in Manila, Philippines.
• The current president of ADB is Masatsugu Asakawa. (as of April 2022)
• ADB assists its members, and partners, by providing loans, technical assistance, grants, and equity investments to promote social and economic development.
• ADB maximizes the development impact of its assistance by facilitating policy dialogues, providing advisory services, and mobilizing financial resources through co-financing operations that tap official, commercial, and export credit sources.
• From 31 members at its establishment in 1966, ADB has grown to encompass 68 members, of which 49 are from within Asia and the Pacific and 19 outside.

The correct answer is Andhra Pradesh.

In News

• In November 2021, Andhra Pradesh has announced the repeal of the three-capital law.

Key Points

• The Andhra Pradesh legislative assembly on November 22, passed a Bill to repeal the controversial AP Decentralisation and Inclusive Development of All Regions Act, 2020, which was intended to establish three capitals for the state.
• Under the three capital law, Andhra Pradesh had three capitals:
• Amaravati as a legislative capital,
• Kurnool in the Rayalaseema region became a judicial capital city with the location of the high court,
• Visakhapatnam in the north-coastal region would become an executive capital city.

Additional Information

• Andhra Pradesh:
• Andhra Pradesh is bordered by Telangana, Chhattisgarh, Tamil Nadu, Karnataka, and Orissa.
• Y. S. Jaganmohan Reddy is the current CM of Andhra Pradesh.
• Biswabhusan Harichandan is the current governor of Andhra Pradesh.
• Amaravati is the capital of Andhra Pradesh.

The correct answer is Bajrang Punia, PV Sindhu and Ravi Kumar Dahiya.

Key Points

• PV Sindhu became the first Indian woman and only the second Indian athlete, after Sushil Kumar, to win two individual Olympic medals.
• PV Sindhu beat China’s He Bing Jiao to win the bronze medal in the women’s singles.
• Tokyo Olympics bound athletes wrestler Bajrang Punia bagged the top honour Sportsperson of the Year at the FICCI India Sports Awards 2020.
• The athlete has had an impressive 2019-20 season.
• Won the Sportsperson of the Year awards in wrestling.
• Ravi Kumar Dahiya won the silver medal in Men's 57kg wrestling.

Additional Information

• Mirabai Chanu won the silver medal in the Tokyo 2020 Olympics in the women’s 49kg.
• Neeraj Chopra became India’s second individual Olympic champion after Abhinav Bindra.
• He won the Gold medal in the javelin throw.
• It was India’s first track-and-field medal at any Olympic Games.
• Lovlina Borgohain won a Bronze medal in women’s welterweight (64-69kg).

The correct answer is Imphal.

• The Jawaharlal Nehru Manipur Dance Academy (JNMDA) is situated in Imphal, Manipur.

Key Points

• Jawaharlal Nehru Manipur Dance Academy:
• It is a constituent unit of the Sangeet Natak Akademi, New Delhi.
• The institute is a premier institution for teaching Manipuri Dance and Music and allied subjects like Thang-Ta.
• It was established in 1954.

Additional Information

• Sangeet Natak Akademi:
• ​The Sangeet Natak Akademi was founded on 31 May 1952.
• It is also known as the National Academy for Music, Dance, and Drama.
• In India, it functions as the headquarters of performing arts.
• It presents the Sangeet Natak Akademi Awards which is the highest Indian recognition given to performing/practising artists.

The correct answer is State with highest population density – Chandigarh.

Key Points

• Census of India, 2011:
• Total Population of India was 1,210,193,422.
• The Sex Ratio (females per thousand males) in India was 940.
• The population density was reported at 382 persons per sq. km.
• Total districts covered- 640.
• Crude Birth Rate- 21.8.
• Crude Death Rate 7.1 per thousand population
• Infant Mortality Rate was 44 per thousand live births
• The literacy rate of the country is 74.04 per cent. (82.14 for males and 65.46 for females).
• The state with the highest literacy is Kerala (94.0%)
• The state with the lowest literacy is Bihar (61.8%)
• state with the highest female literacy rate- Kerala (92.1%)
• The state with the lowest female literacy is Bihar(51.5%)
• The state that has the highest decadal growth is Meghalaya (27.9%)
• State having highest Population  Uttar Pradesh (19,98,12,341)
• The state has the lowest Population is Sikkim (6,10,577)
• State with Highest Population Density Bihar (1106). Hence Option 4 is incorrect.
• State with Lowest Population Density  Arunachal Pradesh (17)
• The state has the highest Sex Ratio is Kerala (1,084)
• The state has the lowest Sex Ratio  is Haryana (879)
• The highest Death Rate among states is in Odisha (98 per thousand).
• The lowest Death Rate among states is in Kerala— 16 per thousand.
• The decadal growth rate in Population is 17.7%.
• The state has the lowest population decadal growth rate in Nagaland (–0.6%).

The correct answer is Nilmani Phookan Jr.

• Nilmani Phookan Jr. was awarded the 56th Jnanpith Award for 2020.

Key Points

• Nilmani Phookan Jr’s contribution to Indian literature:
• Phookan is based out of Guwahati.
• He was awarded the Padma Shri in 1990 and received the Sahitya Akademi Fellowship in 2002.
• Written poems such as Surya Henu Nami Ahe Ei Nodiyedi, Gulapi Jamur Lagna, and Kobita.

Additional Information

• Damodar Mauzo has won the 57th Jnanpith Award for 2021.
• He is notable for his novels, such as Karmelin, and Tsunami Simon, and short stories, such as Teresa’s Man and Other Stories from Goa.
• Birendra Kumar Bhattacharya won the Jnanpith Award in 1979.
• Mamoni Raisom Goswami won the Jnanpith Award in 2000.

The correct answer is Pagoda - Temple Cone.

Key Points

• Buddhist stupa - Symbolic representation of the Buddha’s burial mound.
• A burial mound is an artificial hill of earth and stones built over the remains of the dead.
• Terms associated with the architecture of a Buddhist Stupa:
• A hemispherical mound (anda)
• Temple Peak (Shikhar).
• A square railing (harmika)
• A central pillar supporting a triple-umbrella form (chatter)
• Enclosure wall with decorated gateways (toranas) at the cardinal directions
• A circular terrace (Medhi)
• Pagoda is a tower with roofs curving upward at the division of each of several stories and erected as a temple or memorial.

The correct answer is Switzerland.

• Switzerland has approved the Sacro Capsule in December 2021.

Key Points

• Switzerland has approved the use of a suicide aid machine called Sarco Capsule.
• Sarco is a 3D printed capsule.
• It has been developed by Exit International, an international non-profit based in Australia.
• The pod helps in assisted suicide.
• Assisted suicide is legal in Switzerland.
• In this pod, death will happen 5-10 minutes after losing consciousness.

Additional Information

• Switzerland
• Capital - Bern
• Currency – Swiss Franc
• Geneva (a worldwide center for diplomacy) is located in Switzerland.

The correct answer is Gorakhpur.

• Gorakhpur in Haryana will a new  nuclear power plant be set up by 2024.

Key Points

• India will have nine nuclear reactors by 2024
• The first nuclear power plant in northern India will come up in Gorakhpur of Haryana.
• By 2024, India will have nine nuclear reactors plus 12 new additional ones which were approved with a capacity of 9000 MW.
• India is counting on its nuclear program to help meet its Paris climate commitments to reduce the emissions intensity of its economy by a third from 2005 levels by 2030.

Additional Information

• Nuclear energy: It is the energy in the nucleus of an atom.
• Nuclear energy is generated by nuclear fusion and nuclear fission reactions.
• Nuclear energy plants do not release carbon emissions but there are other disadvantages:
• Disadvantages of nuclear energy plants:

1. ​It causes thermal pollution.
2. Its wastes are radioactive materials
3. It requires a large amount of water.

The correct answer is Madhya Pradesh.

• In November 2021, Madhya Pradesh's chief minister launched three solar power projects worth Rs. 5,250 crore.

Key Points

• Madhya Pradesh's Chief Minister Shivraj Singh Chouhan and Union Minister for Power and New and Renewable Energy R.K. Singh laid the foundation stone of 1500 MW capacity solar power parks in Agar, Shajapur, and Neemuch districts.
• The project is of the cost of Rs 5250 crores.
• The ministers also signed contracts with private investors for the Pradhan Mantri Kusum yojana while Urja Saksharta Abhiyaan was also launched for the purpose of public awareness in the field of energy conservation.
• The scheme is fast-moving towards fulfilling the target of PM Narendra Modi of meeting 50 per cent of the country’s energy requirement by 2030 with solar energy.
• In these solar projects of 1500 MW, 2 units of 550 MW in Agar, 3 units of 450 MW in Shajapur and 3 units of 500 MW capacity in Neemuch districts will be installed.
• Power generation from the projects will start in March 2023.

The correct answer is antibiotic.

• ​Antibiotic is used to treat the infection.

Key Points

• ​Antibiotics are medicines used to prevent and treat bacterial infections.
• Antibiotic resistance occurs when bacteria change in response to the use of these medicines.
• The bacteria, not humans or animals, become antibiotic-resistant.
• These bacteria may infect humans and animals, and the infections they cause are harder to treat than those caused by non-resistant bacteria.
• Antibiotic resistance is one of the biggest threats to global health, food security, and development today.

Given:

$\frac{{\tanθ + \secθ - 1}}{{\tanθ - \secθ + 1}} ÷ \left( {1 + \frac{{{{\tan }^2}θ }}{{1 + \secθ }}} \right){\rm{;}}$

Concept used:

sec²θ - tan²θ = 1

Calculation:

$\frac{{\tanθ + \secθ - 1}}{{\tanθ - \secθ + 1}} ÷ \left( {1 + \frac{{{{\tan }^2}θ }}{{1 + \secθ }}} \right){\rm{;}}$

⇒ $\frac{{\tanθ + \secθ - (sec^2θ - tan^2θ)}}{{\tanθ - \secθ + 1}} ÷ \left( {\frac{{{{1+secθ + tan }^2}θ }}{{1 + \secθ }}} \right){\rm{;}}$

⇒ $\frac{{\tanθ + \secθ - (secθ - tanθ)(secθ + tanθ)}}{{\tanθ - \secθ + 1}} ÷ \left( {\frac{{{{1+secθ + sec^2θ -1}} }}{{1 + \secθ }}} \right){\rm{;}}$

⇒ $\frac{{(\tanθ + \secθ)[1 - secθ + tanθ]}}{{\tanθ - \secθ + 1}} ÷ \left( {\frac{{{{secθ(1+ + secθ)}} }}{{1 + \secθ }}} \right){\rm{;}}$

⇒ $(\tanθ + \secθ) ÷ secθ$

⇒ $(\frac{sinθ}{cosθ} + \frac{1}{cosθ}) ÷ secθ$

⇒ $(\frac{sinθ + 1}{cosθ}) ÷ secθ$

⇒ $({sinθ + 1)}\times{secθ} ÷ secθ$

⇒ 1 + sin θ

∴ Required answer is 1 + sin θ

Calculation:

Total sales of R in five cities = 480 + 540 + 520 + 460 + 550

⇒ 2550

Average = 2550/5 = 510

Total of P in city A and C = 640 + 450

⇒ 1090

Total of Q in city D and E = 680 + 620

⇒ 1300

Total of these two = 1090 + 1300

⇒ 2390

20% of 2390 = 2390 × 1/5

⇒ 478

Now, difference = 510 - 478

⇒ 32

Required % = (32/478) × 100

⇒ 6.69%

∴ Required answer is 6.69%

Given:

x be the smallest number which when divided by 12, 18, 20, 27 and 30 leaves the remainder 2 in each case

Concept used:

LCM method to get the number

Calculation:

LCM of 12, 18, 20, 27, 30 = 540

So, the required number x will be in the form of (540m + 2), where m is a natural number

Now according to the question, the number x is divisible by 47 

Now we can check one by one by putting m = 1, 2, 3, 4......... which will be the smallest number divisible by 47

Taking m = 1

We get 542 which is not divisible by 47

Taking m = 2

We get 1082 which is also not divisible by 47

Taking m = 3

We get 1622 which is also not divisible by 47

Taking m = 4

We get 2162 which is divisible by 47.

Now,

2162 = 46 × 47

1932 = 46 × 42

HCF of 2162 and 1932 is 46 i.e y

So, sum of the numbers = 4 + 6 = 10

∴ The sum of the digits of y is 10

Shortcut Trick

Ratio of Girls to Boys = 60 : 40 = 3 : 2.

Let average marks of Girls = 100 units, then Boys = 65 units (35% less).

Weighted Average = [(3 × 100) + (2 × 65)] ÷ (3 + 2) = 430 ÷ 5 = 86 units.

86 units = 129 ⇒ 1 unit = 1.5.

Average marks of Boys = 65 × 1.5 = 97.5.

∴ The correct answer is 97.5.

Alternate Method

Given: Total students = 90. Girls = 60% of 90 = 54. Boys = 40% of 90 = 36.

Formula: Total Marks = Average × Number of Students.

⇒ Let the average marks of Girls be x.

⇒ Average marks of Boys = x − 35% of x = 0.65x.

⇒ Total marks = (54 × x) + (36 × 0.65x) = 129 × 90.

⇒ 54x + 23.4x = 11610.

⇒ 77.4x = 11610.

⇒ x = 11610 ÷ 77.4 = 150.

⇒ Average marks of Boys = 0.65 × 150 = 97.5.

∴ The correct answer is 97.5.

Additional Information

Weighted Average Formula

The combined average of two groups is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂), where n is the quantity and A is the average.

Percentage to Decimal Conversion

To decrease a value by 35%, multiply the original value by (100 − 35) ÷ 100 = 0.65.

Alligation Method

The ratio of the two quantities is inversely proportional to the difference between their individual averages and the mean average.

Given:

Pipes A and B can fill a tank in 18 h and 30 h respectively

Total time = 21 hours

Concept used:

If a pipe can complete a work alone in x hour, then the efficiency (part of the work completed in one day) = 1/x

Calculation:

Pipe A can fill 1/18 in 1 hour

Pipe B can fill 1/30 in 1 hour

Pipe C can empty 1/x in 1 hour

According to the question,

3(1/18 + 1/30 - 1/x) + 3(1/18 - 1/x) + 15/18 = 1 [Here 1 is total work]

⇒ 1/6 + 1/10 - 3/x + 1/6 - 3/x + 5/6 = 1

⇒ - (6/x) + 7/6 + 1/10 = 1

⇒  - (6/x) + [(35 + 3)/30] = 1

⇒  - (6/x) + 19/15 = 1

⇒ 6/x = 19/15 - 1

⇒ 6/x = (19 - 15)/15

⇒ 4x = 6 × 15

⇒ x = 90/4 = $22\frac{1}{2}$

∴ The value of x is $22\frac{1}{2}$

Given:

Profit% = 25%

Discount% = 10%, 22%

Concept used:

SP = CP + CP × Profit%

SP = MP - MP × Discount%

Profit % = (Profit/CP) × 100

Calculation:

Let CP of the article be 36a

So, SP = 36a + 36a × 25/100

⇒ 45a

according to the question,

45a × 10/9 = MP of the article

⇒ 50a

Now,

New SP = 50a - 50a × 22/100

⇒ 39a

Profit = 39a - 36a

⇒ 3a

Profit % = (3a/36a) × 100

⇒ $8\frac{1}{3}\%$

∴ Required answer is $8\frac{1}{3}\%$

Given:

AB = 5 cm

AD = 3 cm

BD = 7 cm

Concept used:

If AD is the angle bisector of ∠A then,

AD2 = AB × AC - BD × DC

An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides

AB/AC = BD/DC

Calculation:

Let DC be x

So,

5/BC = 3/x

⇒ BC = 5x/3

According to the concept,

72 = (5x/3) × 5 - 3x

⇒ 49 = (25x/3) - 3x 

⇒ 49 = (25x - 9x)/3

⇒ 49 = 16x/3

⇒ 147 = 16x

⇒ x = 147/16

So, DC = 147/16 cm

∴ The length (in cm) of DC is 147/16 cm

Given:

X is inversely proportional to $\sqrt { Y}$ and directly proportional to W

When X = 8, W = 5, then Y = 20.25

Concept used:

If x ∝ 1/y

The general equation for inverse variation is x = k/y

If x ∝ y

The general equation for inverse variation is x/y = k

Here k is the constant of proportionality

Calculation:

x ∝ w × 1/√y

Now,

x = k × w/√y

⇒ 8 = k × 5/√20.25

⇒ 8 = k × 5/4.5

⇒ k = 36/5 = 7.2

Now,

18 = 7.2 × 3/√y

⇒ √y = 21.6/18

⇒ √y = 1.2

⇒ (√y)2 = 1.22

⇒ y = 1.44

∴ Required value of Y is 1.44

Given:

Principal = Rs. 69440

Rate = 12.5% per annum

Time = 3 years

Formula used:

For Installment at CI,

P = x/{1 + (R/100)} + x/{1 + (R/100)}2 + x/{1 + (R/100)}3...... + x/{1 + (R/100)}n

where,

P = Money borrowed or Principal.

x = value of each instalment

R = Rate (%)

n = number of years

Calculation:

Let value of one instalment be x.

x/{1 + (R/100)} + x/{1 + (R/100)}2 + x/{1 + (R/100)}3 = 69440 

⇒ x/{1 + 12.5/100) + x/(1 + 12.5/100)2 + x/(1 + 12.5/100)3 = 69440 

⇒ x/(1 + 1/8) + x/(1 + 1/8)2 + x/(1 + 1/8)3 = 69440

⇒ x/(9/8) + x/(9/8)2 + x/(9/8)3 = 69440

⇒ 8x/9 + 64x/81 + 512x/729 = 69440

⇒ (648x + 576x + 512x)/729 = 69440

⇒ 1736x/729 = 69440

⇒ x = Rs. 29160

So, annual installment is Rs. 29160

Total amount paid = 29160 × 3 = 87480

Total interest paid = 87480 - 69440

⇒ Rs. 18040

∴ Total interest paid in the scheme is Rs. 18040

Given:

5 digit number 658xy is divisible by 7 and 33

Concept used:

When a number is divisible by 3, 7, 11 then it will be divisible by 231

Calculation:

33 = 3 × 11

So we will first evaluate: LCM (3, 7, 11) = 231

The largest possible value of 658xy is 65899

When we divide 65899 by 231 we obtain 64 as the remainder.

So required number = 65899 – 64 = 65835

So, x = 3 and y = 5

Now,

(x2 - y2 + xy) = (32 - 52 + 3 × 5)

⇒ (x2 - y2 + xy) = (9 - 25 + 15)

⇒ (x2 - y2 + xy) = - 1

∴ Required answer is - 1

Given:

The cost of 3 mangoes and 4 oranges is Rs. 70.

After increase and decrease in the price of mango and orange the cost of 5 mangoes and 7 oranges is becomes Rs.124.36

Calculation:

Let price of 1 mango be 100a and 1 orange be 100b

So, 300a + 400b = Rs. 70      ----(i)

After increase and decrease in the price of mango and orange,

Mango = 120a

Orange = 88b

600a + 616b = 124.36      ----(ii)

By multiplying 2 with eq (i) we get

600a + 800b = 140      ----(iii)

By subtracting eq (ii) from eq (iii) we get

184b = 15.64

⇒ b = 15.64/184

⇒ 100b = (15.64/184) × 100 = 8.5

⇒ 400b = 8.5 × 4 = 34

Putting the value of 400b in the eq (I) we get

300a = 70 - 34

⇒ 300a = 36

⇒ 100a = 12

Now,

Price of 2 mangoes and 3 oranges = 2 × 12 + 3 × 8.5

⇒ 24 + 25.5

⇒ 49.5

∴ The initial (price) of 2 mangoes and 3 oranges is 49.5

Shortcut Trick

Initial Ratio A:B:C = 1/5 : 1/2 : 1/3 = 6 : 15 : 10 (LCM 30)

Profit ratio is based on Investment × Time (3 periods of 4 months each).

A (total units) = 6 + 9 + 13.5 = 28.5

C (total units) = 10 + 5 + 2.5 = 17.5

Profit Ratio A : C = 28.5 : 17.5 = 57 : 35

57 units = Rs. 2.85 lakh ⇒ 35 units = Rs. 1.75 lakh

∴ The correct answer is Rs. 1,75,000.

Alternate Method

Given:

Initial ratio of capitals A : B : C = 1/5 : 1/2 : 1/3

A's profit share = Rs. 2.85 lakh = Rs. 2,85,000

Changes occur every 4 months (Total 3 cycles in a year).

A 6 9 13.5

B 15 (No Change)

C 10 5 2.5

0-4 mo 4-8 mo 8-12 mo Profit Share Ratio: A (57) : B (90) : C (35)

Step 1: Simplify initial capital ratios.

⇒ LCM(5, 2, 3) = 30

⇒ A : B : C = (1/5 × 30) : (1/2 × 30) : (1/3 × 30) = 6 : 15 : 10

Step 2: Calculate effective capital for each 4-month period.

⇒ Total Capital of A = (6 × 4) + (6 + 50% of 6) × 4 + (9 + 50% of 9) × 4

⇒ Total Capital of A = (6 × 4) + (9 × 4) + (13.5 × 4) = 4 × (6 + 9 + 13.5) = 4 × 28.5 = 114 units

⇒ Total Capital of B = 15 × 12 = 180 units

⇒ Total Capital of C = (10 × 4) + (10 − 50% of 10) × 4 + (5 − 50% of 5) × 4

⇒ Total Capital of C = (10 × 4) + (5 × 4) + (2.5 × 4) = 4 × (10 + 5 + 2.5) = 4 × 17.5 = 70 units

Step 3: Find the profit sharing ratio.

⇒ Ratio A : B : C = 114 : 180 : 70

⇒ Ratio A : B : C = 57 : 90 : 35

Step 4: Calculate C's share using A's share.

⇒ A's share = 57 units = Rs. 2,85,000

⇒ 1 unit = 2,85,000 ÷ 57 = 5,000

⇒ C's share = 35 units = 35 × 5,000 = Rs. 1,75,000

∴ The correct answer is Rs. 1,75,000.

Additional Information

Profit Sharing Rule in Partnership

Profit Share = Capital × Time. If capitals change over time, Profit Ratio = ∑(Capital_i × Time_i).

Working and Sleeping Partner

A working partner handles the business and often receives a fixed percentage or salary before the remaining profit is divided.

Ratio Simplification

To convert a fractional ratio like 1/x : 1/y : 1/z into a linear ratio, multiply each term by the LCM of denominators (x, y, z).

Given:

The length, breadth, and height of a solid metal cuboid are 64 cm, 48 cm, and 36 cm respectively.

Concept used:

The volume of cuboid = lbh

Where l = length, b = breadth and h = height

The volume of cube = a3

The lateral surface area of cube = 4 × a2

Where a = side of cube

Calculation:

According to the question,

lbh = 8 × a3

⇒ 64 × 48 × 36 = 8 × a3

⇒ a3 = 13824

⇒ a = 24

The lateral surface area of the cube = 4a² 

Sum of the lateral surface areas of 3 such cubes 

⇒ 4a² + 4a² + 4a² = 12a²

⇒ 12 × 242 

⇒ 6912 cm2

∴ The sum of the lateral surface areas (in cm2) of 3 such cubes is 6912

Given:

$a = \frac{{{{\left( {5.4} \right)}^3} + {{\left( {4.5} \right)}^3}}}{{{{\left( {5.4} \right)}^2} - {{\left( {4.5} \right)}^2}}}$

$b = {(1.0\bar 3 \div 0.\overline{93}) \times 1.\overline {36} }$

Concept used:

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

$c.\overline {ab} =\frac{cab - c}{99}$

$c.a\overline {b} =\frac{cab - ca}{90}$

(a³ + b³) = (a + b)[(a - b)² + ab]

(a2 - b2) = (a + b)(a - b)

Calculation:

$a = \frac{{{{\left( {5.4} \right)}^3} + {{\left( {4.5} \right)}^3}}}{{{{\left( {5.4} \right)}^2} - {{\left( {4.5} \right)}^2}}}$

⇒ $a = \frac{{{{ {(5.4;+;{4.5})[(5.4-4.5)^2+5.4\times4.5]}}}{{}}}}{{{{\left( {5.4+4.5} \right)(5.4-4.5)}} {{}}}}$

⇒ $a = \frac{{{{ {[(5.4-4.5)^2+5.4\times4.5]}}}{{}}}}{{{{(5.4-4.5)}} {{}}}}$

⇒ $a = (5.4 - 4.5) + \frac{5.4 \times 4.5}{0.9}$

⇒ a = 0.9 + 27

⇒ a = 27.9

$b = \left[ {(1.0\bar 3 \div 0.\overline{93}) \times 1.\overline {36} } \right]$

⇒ $b = \left( {\frac{93}{90} \div \frac{93}{99} \times \frac{135}{99} } \right)$

⇒ $b = \left( {\frac{93}{90} \times \frac{99}{93} \times \frac{135}{99} } \right)$

⇒ $b = \left( { \frac{135}{90} } \right)$

⇒ b = 1.5

Now (a - b) = (27.9 - 1.5)

⇒ 26.4

∴ Required answer is 26.4.

Shortcut Trick

For a circle, when a secant passing through the center and another secant intersecting the circle meet at an external point P.

If the external segment of the intersecting secant is exactly equal to the radius of the circle (BP = r).

Then, the central angle subtended by the larger arc is always exactly three times the external angle at P.

Direct formula for this specific case: ∠AOC = 3 × ∠APC

⇒ ∠AOC = 3 × 35° = 105°

∴ The correct answer is 105°.

Alternate Method

Given:

Center of the circle is O, and its radius is r. So, OA = OB = OC = OD = r.

Secant PAB and secant PCD (passing through the center) intersect at external point P.

BP = radius of the circle = r, and ∠APC = 35°.

      105°  35°  35°  r r r         O P C D A B  ∠AOC = 3 × ∠P = 105°

Calculations:

⇒ In ΔOBP, OB = r (radius of the circle) and BP = r (given).

⇒ Since OB = BP, ΔOBP is an isosceles triangle.

⇒ Angles opposite to equal sides are equal, so ∠BOP = ∠BPO = 35°.

⇒ Using the exterior angle theorem in ΔOBP, the exterior angle at B is ∠OBA.

⇒ ∠OBA = ∠BOP + ∠BPO = 35° + 35° = 70°.

⇒ In ΔOAB, sides OA and OB are both radii, so OA = OB = r.

⇒ Since ΔOAB is an isosceles triangle, ∠OAB = ∠OBA = 70°.

⇒ Now, looking at ΔOAP, the exterior angle at O is ∠AOC.

⇒ By the exterior angle theorem, ∠AOC = ∠OAP + ∠APO.

⇒ ∠AOC = 70° + 35° = 105°.

∴ The correct answer is 105°.

Additional Information

Secant Angle Theorem

When two secants intersect outside a circle, the measure of the angle formed is half the difference of the measures of the intercepted arcs: ∠P = (m(arc AC) − m(arc BD)) ÷ 2.

Exterior Angle Theorem

The exterior angle of a triangle is exactly equal to the sum of the two opposite interior angles. Formula: ∠Ext = ∠Int₁ + ∠Int₂

Isosceles Triangle Property

If two sides of a triangle are equal, then the angles opposite to those sides are also strictly equal in measure.

Calculation:

Total employees working in the Accounts department = 1800 × 18/100

⇒ 324

Total men in Accounts department = 324 × 5/9

⇒ 180

So, 10% of the men = 180 × 10/100 = 18

Total employees working in the HR department = 1800 × 14/100

⇒ 252

Total men in Accounts department = 252 × /14

⇒ 162

After increase total men = 162 + 18 = 180

Total employees working in the Production department = 1800 × 28/100

⇒ 504

Total female in Accounts department = 504 × 3/7

⇒ 216

1/4th of the female = 216 × 1/4

⇒ 54

Total employees working in the Marketing department = 1800 × 17/100

⇒ 306

Total female in Marketing department = 306 × 9/17

⇒ 162

After increase total female = 162 + 54 = 216

Difference = 216 - 180 = 36

Required % = (36/216) × 100

⇒ 16.7%

∴ Required answer is 16.7%

Given:

Average = $34\frac{5}{6}$

Concept used:

Average = Sum of elements/No. of elements

Calculation:

$33\frac{1}{3}\%$ = 1/3

Let the average of 1st five numbers be 3x

So, the sixth number = 3x + 3x × 1/3 = 4x

According to the question,

3x × 5 + 4x = $34\frac{5}{6}$ × 6

⇒ 15x + 4x = (209/6) × 6

⇒ 19x = 209

⇒ x = 11

So, sixth number is 11 × 4 = 44

∴ Required answer is 44

Given:

Amount = Rs. 18600

Rate of Interest = 15%

Time = $3\frac{2}{3}$ Years

Formula used:

S.I = PRT/100

Amount = Principal + S.I

In C.I

Amount = P(1 + R/100)n

P = Principal

R = Rate

T = Time

Calculation:

Let the Principal be Rs. x

S.I = Rs. (18600 – x)

According to the question,

(x × 15 × 11)/(100 × 3) = 18600 – x

⇒ 55x/100 = 186000 – x

⇒ 55x = 1860000 – 100x

⇒ 155x = 186000

⇒ x = 12000

Now, for compound interest compunded 8 monthly,

Interest rate = 15 × 8/12 = 10%

n = 24/8 = 3

So,

12000(1 + 10/100)3

⇒ 12000(1 + 1/10)3

⇒ 12000(11/10)3

⇒ 12000 × 1331/1000

⇒ 15972

∴ Required amount is Rs. 15972

Given:

The time taken by a boat to cover a certain distance downstream is two-third of the time taken by the boat to cover the same distance upstream.

The speed of the boat in still water is 10 km/h more than 7 times the speed of the stream

Concept used:

v + u = downstream

v - u = upstream

v = speed of the boat

u = speed of the stream

Speed ∝ 1/time

Calculation:

According to the question,

2v = 7u + 10

⇒ 2v - 7u = 10

Let the time taken by the boat upstream be 3x

So, the time taken by the boat downstream = 2x

Upstream speed = 2x and downstream speed = 3x

So,

v + u = 3x      ----(i)

v - u = 2x      ----(ii)

By adding (ii) with (i) we get,

2v = 5x

⇒ v = 5x/2

Putting value of v in eq (i) we get,

u = x/2

Now,

2 × 5x/2 - 7 × x/2 = 10

⇒ 5x - 7x/2 = 10

⇒ (10x - 7x)/2 = 10

⇒ (3x)/2 = 10

⇒ x = 20/3

So, u = 20/3 ÷ 2

⇒ 20/3 × 1/2 = 10/3

⇒ $3\frac{1}{3}$

∴ Required speed of the stream is $3\frac{1}{3}$ km/h

Given:

$\rm 3{\rm{x}} - \frac{1}{{2{\rm{x}}}} = √ 3$

Concept used:

if (a - 1/b) = q

So, a³ - 1/b³ = q³ + 3.a.1/b(q)

Calculation:

$\rm 3{\rm{x}} - \frac{1}{{2{\rm{x}}}} = √ 3$

⇒ $\rm 2{\rm{x}} - \frac{1}{{3{\rm{x}}}} = \frac{2√ 3}{3}$ [By multiplying both sides with 2/3]

⇒ $\rm 2{\rm{x}} - \frac{1}{{3{\rm{x}}}} = \frac{2}{√ 3}$

$\rm 8{x^3} - \frac{1}{{27{x^3}}} = \rm {(2x)^3} - \frac{1}{{(3{x)^3}}}$

⇒ $\rm 8{x^3} - \frac{1}{{27{x^3}}} = \rm {(\frac{2}{√3})^3} + 3\times2x\times\frac{1}{{3{x}}}(\frac{2}{√3})$

⇒ $\rm 8{x^3} - \frac{1}{{27{x^3}}} = \rm {\frac{8}{3√3}} + \frac{4}{√3}$

⇒ $\rm 8{x^3} - \frac{1}{{27{x^3}}} = \rm {\frac{8 ;+ ;12}{3√3}}$

⇒ $\rm 8{x^3} - \frac{1}{{27{x^3}}} = \rm {\frac{20}{3√3}}$

⇒ $\rm 8{x^3} - \frac{1}{{27{x^3}}} = \rm {\frac{20√3}{9}}$ [By multiplying both sides with √3]

∴ Required answer is $\frac{{20√ 3 }}{9}$

Given:

Time taken by P after meeting = x hrs

Time taken by Q after meeting = 8 hrs

Concept used:

(Speed of T₁/Speed of T₂)2 = Time taken by T2/Time taken by T1

Here T1 and T2 = train 1 and train2

Calculation:

AB Distance cover by train Q = S₂t₂

& BC Distance cover by train P = S1t1

Let the speed of P be 4 units

Speed of Q = 4 × (5/4) = 5 units

According to the concept,

(4/5)² = 8/x 

⇒ 16/25 = 8/x 

⇒ x = 25/2 

⇒ x = $12\frac{1}{2}$

∴ The value of x is $12\frac{1}{2}$

Shortcut Trick

Let the total number of votes be 100%.

Votes of A = 35%, Remaining votes = 100% − 35% = 65%.

Votes of B = 54% of 65% = 35.1%.

Votes of C = 65% − 35.1% = 29.9%.

Given 29.9% = 5382 ⇒ 1% = 180 ⇒ 0.1% = 18.

Winning margin = Winner (B) − Nearest (A) = 35.1% − 35% = 0.1% = 18.

∴ The correct answer is 18 votes.

Alternate Method

Given:

Candidate A got 35% of the total votes.

Candidate B got 54% of the remaining votes.

Candidate C got 5382 votes.

Formula Used:

Total Votes = A's votes + B's votes + C's votes

Calculation:

⇒ Let the total votes be x.

⇒ Votes obtained by A = 35% of x = 0.35x

⇒ Remaining votes after A's share = x − 0.35x = 0.65x

⇒ Votes obtained by B = 54% of 0.65x = 0.54 × 0.65x = 0.351x

⇒ Votes obtained by C = Remaining votes − B's votes

⇒ Votes obtained by C = 0.65x − 0.351x = 0.299x

⇒ We are given that C got 5382 votes.

⇒ 0.299x = 5382

⇒ x = 5382 ÷ 0.299 = 18000

⇒ Votes obtained by A = 0.35 × 18000 = 6300

⇒ Votes obtained by B = 0.351 × 18000 = 6318

⇒ The winner is B (6318 votes) and his nearest candidate is A (6300 votes).

⇒ Winning margin = 6318 − 6300 = 18 votes

∴ The correct answer is 18 votes.

Additional Information

Winning Margin Concept

In any election problem, the winning margin or majority is calculated as the absolute difference between the votes secured by the winner and the first runner-up (the nearest candidate).

Successive Percentage Calculation

When percentages are distributed successively on the remaining amounts, the effective percentage of the final part is the product of the fractional remaining parts. E.g., y% of remaining (100−x)% = [y × (100−x)] ÷ 100.

Valid and Invalid Votes

If a certain percentage of votes are declared invalid, the valid votes become the new base (100%) for calculating the share of the candidates, unless stated otherwise.

Given:

5 men and 12 women can complete a work in 2 days

3 men and 4 women can complete it in 5 days.

Calculation:

According to question,

(5 men + 12 women) × 2 = (3 men + 4 women) × 5 

⇒ 10 men +  24 women = 15 men + 20 women

⇒ 5 men = 4 women

⇒ men/women = 4/5

So, men : women = 4 : 5 i.e ratio of efficiency 

Now, total work = (5 × 4 + 12 × 5) × 2

⇒ (20 + 60) × 2

⇒ 160 units

So, to complete 160 units in 8 days total men need = 160/(8 × 4) [Each man has an efficiency of 4 so we will multiply 4 with the time]

⇒ 5

∴ Required number of men is 5.

Given:

Diametere of the hemisphere = 10.5 cm

Height of the cylinder = 15 cm

Volume of water = 1386 cm³

Concept used:

Volume of the hemisphere = (2/3) × π × (r)3

Volume of the cylinder = πr²h

r = radius

h = height

Calculation:

The radius of the hemisphere = 5.25 cm

Volume of the hemisphere = (2/3) × π × (5.25)³

⇒ 303.1875 cm³

If we pour water into the testtube then it will fill the hemisphere completely,

So the remaining portion of the water will fill some portion of the cylinder

Remaining portion = 1386 - 303.1875

⇒ 1082.8125

Now,

Let the height of the portion of the cylinder be h

1082.8125 = 22/7 × (5.25)² × h

⇒ h = 12.5

The total height of the cylinder is 15 cm

Difference = 15 - 12.5 = 2.5 cm

∴ The water will reach 2.5 cm from the edge (top edge) of the tube?

Given:

A trader sells article A at 30% profit and article B at 20% loss and earns Rs 865. If he sells A at 20% loss and B at 26% profit, he received Rs. 64 less.

Concept used:

Profit = Sales price - Cost price

Profit% = (Profit/Cost price) × 100

Calculation:

Let the cost price of article A be 100a, and article B be 100b

So,

130a + 80b = 865      ----(i)

80a + 126b = 801      ----(ii)

By multiplying 8 with eq (i) and 13 with eq (ii) we get

1040a + 640b = 6920      ----(iii)

1040a + 1638b = 10413      ----(iv)

By subtracting (iii) from (iv) we get

998b = 3493

⇒ b = 3493/998

⇒ b = 3.5

So, 100b = 350

Now, putting the value of b in eq (i) we get

130a = 865 - 80 × 3.5

⇒ 130a = 585

⇒ a = 4.5

⇒ 100a = 450

Total cost price of the A and B = 450 + 350 = 800

Profit = 840 - 800 = 40

Profit% = (40/800) × 100 = 5%

∴ His gain percentage is 5%

The correct answer is 0.92; away from.

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 (dense flint) with respect to turpentine oil:

$n= \frac{Refractive \ index \ of \ crown\ glass \ }{Refractiev \ index\ of\ dense \ flint\ glass}= \frac{1.52}{1.65}= 0.92$

• Greater the refractive index, the denser the medium.
• Thus, flint glass (1.65) is denser than crown glass (1.52).
• 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 ice to glass, it will move towards the normal.

The refractive index of crown glass with respect to dense flint glass is 0.92 and the light ray bends away from the normal in the dense flint glass.

The correct answer is 125 %.

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).
• $R = \frac{ρ l}{A}$ 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' = 150 L/ 100 = 3L/2 ( since there is 50% increase)

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 = 2 r2  / 3

Increase in resistance = $\frac{\frac{\rho L'}{A'}-\frac{\rho L}{A}}{\frac{\rho L}{A}}$ × 100

$=\frac{\frac{\rho L'}{\pi r^2} - \frac{\rho L}{\pi r^2}}{ \frac{\rho L}{\pi r^2} } \times 100$

$=\frac{\frac{3 \times 3 \rho L}{2 \times 2 \pi r^2} - \frac{\rho L}{\pi r^2}}{ \frac{\rho L}{\pi r^2} } \times 100$

$=\frac{\frac{9}{4}\frac{\rho L}{\pi r^2} - \frac{\rho L}{\pi r^2}}{ \frac{\rho L}{\pi r^2} } \times 100$

$=\frac{\frac{9 \rho L - 4 \rho L}{4\pi r^2}}{ \frac{\rho L}{\pi r^2} } \times 100$

$= \frac{5 \rho L}{4 \pi r^2} \times \frac{\pi r^2}{ \rho L} \times 100 = 125\%$

Thus, the increase in length is 125%.

The correct answer is 9.

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).
• $R = \frac{ρ l}{A}$ where ρ is resistivity, l is length, and A is the area of the cross-section of the wire.

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 (10 Ω), B (15 Ω), and C (30 Ω) are connected in parallel. Let their equivalent resistance is R1.

Equivalent resistance, 1/R1 = 1/10 + 1/15 + 1/30 = 3+2+1/30 = 6/30 = 1/5 Ω

R1 = 5 Ω

Now, the  resistors R1, D (10 Ω), F (15 Ω ), and G (30 Ω ) are in series. Their equivalent resistance is R2.

R2 = 5 + 10 + 15 + 30 = 60 Ω 

Equivalent current, I in the circuit = V/R2 = 12/ 60 = 1/5 A

Potential difference across A = IR1 =  = 5/5 = 1 V

P_F = I2F = 15/ 5 × 5  = 15/25 Watt = 3/5 Watt (since current remains same in series combination)

P_B = V2/B = 1 × 1 /  15 = 1/15 Watt  (since voltage remains same in parallel combination)

The ratio (PF/PB) = 3 × 15 / 5   = 3 × 3 = 9.

The correct answer is Copper does not react with water at all.

Concept:

Metals:

• The elements that tend to lose electrons are called metals.
• They are rigid, hard, and usually exist in a solid-state at room temperature.
• They are lustrous, malleable, and ductile.

Explanation:

• Metals react with water to form metal oxides or hydroxides.
• Not all metals react with water in the same way. 
• Sodium metal catches fire in reaction to water.
• magnesium reacts with hot water.
• Iron reacts with steam.
• Lead and copper do not react with water.

​Iron will react with hot water and rust over time but copper does not react with water and will remain intact. 

Thus, hot water tanks in boilers are made of copper, not iron because copper does not react with water at all.

Additional Information

Chemical properties of metals:

• • Metal + Oxygen → Metal oxide
• The metal reacts with an acid to form a salt.
• Metal + Acid → Salt + Hydrogen gas
• Metals react with water to form oxides or hydroxides.
• Metal + water → Metal oxide/ hydroxide
• Metals do not react with alkalis.
• Metal + Alkali → No reaction

The correct answer is 30 cm; 2.0 cm.

Concept:

Spherical mirror:

• A spherical mirror is a mirror that has the shape of a piece cut out of a spherical surface.
• There are two types of spherical mirrors: concave, and convex.

Mirror formula:$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$, where f = focal length, v = image distance and u = object distance.

Magnification: m = $\frac{Hi}{Ho} = \frac{-v}{u}$ , where Hi = height of image, Ho = height of object, v = image distance, and u = object distance.

Concave mirror: 

• It is part of a whole spherical mirror that reflects light from the hollow part.
• It is a converging mirror because it converges the incident rays at a point.

Explanation:

Given, u = -15 cm        f = -30 cm              h = 1 cm 

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

$\frac{1}{-30} = \frac{1}{v} + \frac{1}{-15}$

$\frac{1}{-30} = \frac{1}{v} - \frac{1}{15}$

$\frac{1}{v} = \frac{1}{-30} + \frac{1}{15}$

$\frac{1}{v} = \frac{-1 + 2}{30}$

$\frac{1}{v} = \frac{1}{30}$

v = 30 cm

m = $\frac{Hi}{Ho} = \frac{-v}{u}$ =  

Hi = 2 cm

Following New Cartesian Sign Convention, the image is formed at v = 30 cm and its height HI = 2 cm.

Additional Information

Convex mirror: 

• It is part of a whole spherical mirror that reflects light from the bulged-out part.
• It diverges the incident rays.

The correct answer is Zinc carbonate.

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:

• We exhale carbon dioxide gas while breathing.
• So, the colorless, odorless gas released when the given metal compound is heated is carbon dioxide.
• Iron objects are usually electroplated with Zinc metal to protect them from corrosion.
• So, the metal compound should be Zinc carbonate.
• The following reaction takes place when zinc carbonate is heated (in the limited supply of air):
• ZnCO₃ + Heat → ZnO + CO₂

The correct answer is At the end of a nephron.

Concept:

Excretory system: 

• Excretion is the process of removing wastes and excess water from the body.
• Organs of excretion include the skin, liver, large intestine, lungs, and kidneys. Together, these organs make up the excretory system

Explanation:

Kidneys:

• The paired kidneys are often considered the main organs of excretion.
• The primary function of the kidneys is the elimination of excess water and wastes from the bloodstream by the production of the liquid waste known as urine.
• The main structural and functional units of the kidneys are tiny structures called nephrons.
• Nephrons filter materials out of the blood, return to the blood what is needed, and excrete the rest as urine.
• The kidneys are organs of the urinary system, which also includes the ureters, bladder, and urethra - organs that transport, store, and eliminate urine, respectively.

Structure of nephron:

• It is a long tubule with a series of associated blood vessels.
• The upper end of the tubule is an enlarged cuplike structure called the Bowman’s capsule.
• Below the Bowman’s capsule, the tubule coils to form the proximal tubule, and then it follows a hairpin turn called the loop of Henle.
• After the loop of Henle, the tubule coils once more as the distal tubule.
• It then enters a collecting duct, which also receives urine from other distal tubules.
• Within the Bowman’s capsule is a coiled ball of capillaries known as a glomerulus.

​

Thus, Bowman's capsule is found at the end of the nephron.

The correct answer is Thunder.

Concept:

Ecology:

• The term ecology is derived from the Greek word ‘oikos’ meaning ‘house’, combined with the word ‘logy’ meaning the ‘science of’ or ‘the study of ’.
• Ecology is the study of the earth as a ‘household’, of plants, human beings, animals, and micro-organisms.
• They all live together as interdependent components.
• The interactions of a particular group of organisms with abiotic factors within a particular habitat resulting in clearly defined energy flows and material cycles on land, water, and air, are called ecological systems.

Explanation:

Abiotic factors:

• They refer to all the non-living components like physical conditions (temperature, pH, humidity, salinity, sunlight, etc.) and chemical agents (different gases and mineral nutrients present in the air, water, soil, etc.) in an ecosystem.

Abiotic factors affecting the life of living organisms:

• Rainfall,
• Temperature,
• Sunlight,
• Wind
• Atmospheric humidity,
• Soil conditions, inorganic substances (carbon dioxide, water, nitrogen, calcium, phosphorus, potassium, etc.).

Thus, thunder is not an abiotic factor affecting animal life.

The correct answer  is 90°.

Concept:

Electromagnetic induction:

• When a conductor is set to move inside a magnetic field or a magnetic field is set to be changing around a conductor, an electric current is induced in the conductor.
• This process is called electromagnetic induction.
• Electromagnetic induction can be explained with the help of Fleming’s Right-Hand Rule.

Fleming’s Right-Hand Rule:

• If we arrange our thumb, forefinger, and middle finger of the right-hand perpendicular to each other, then the thumb points towards the direction of the magnetic force, and the forefinger points towards the direction of the magnetic field, and the middle finger points towards the induced current in the coil.

​

Explanation:

E.M.F. induced in a coil 'e' = N × B × A × w × sin ωt. 

The induced emf is affected by the following factors:

• The induced e.m.f. is directly proportional to N, the total number of turns in the coil.
• The induced e.m.f. is directly proportional to A, the area of the cross-section of the coil.
• The induced e.m.f. is directly proportional to B, the strength of the magnetic field in which the coil is rotating.
• The induced e.m.f. is directly proportional to 'ω', the angular velocity of the coil.
• The induced e.m.f. also varies with time and depends on instant 't'.
• The induced current is the highest when the direction of motion of the coil is at right angles (90 °)to the magnetic field.
• The induced current is minimum when the direction of motion of the coil is 180 ° to the magnetic field.

The correct answer is CH3COONa.

Concept:

pH scale:

• A scale developed to measure the concentration of hydrogen ions in a solution is known as the pH scale.
• pH scale ranges from 0 (highly acidic) to 14 (highly alkaline).
• The pH of a neutral solution is 7.

Acids:

• They are sour in taste.
• They turn blue litmus red.
• Its pH value ranges from 1 to 7 on the pH scale.

Bases:

• They are bitter in taste and soapy to touch.
• They turn red litmus blue.
• Its pH value ranges from 7 to 14 on the pH scale.

Explanation:

Aqueous solution of Sodium acetate (CH₃COONa):

• Sodium acetate reacts with water to form sodium hydroxide and acetic acid.
• CH₃COONa + H₂O → CH₃COOH + NaOH
• Sodium hydroxide (NaOH) is a strong base while acetic acid (CH₃COONa) is a weak acid.
• So, the aqueous solution of Sodium acetate will be basic in nature.
• It will turn red litmus blue.

CH3COONa+H2O→CH3COOH+NaO

The correct answer is 65.

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.
• A convex lens can converge a beam of parallel rays to a point on the other side of the lens

Power of lens:

• 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.
• P = $\frac{100}{f}$ where f is the focal length in centimeters.
• 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 image distance and u is object distance.

Explanation:

For first convex lens, L1

Power = $\frac{1}{f}$

f = $\frac{1}{p}$ = $\frac{ 3 × 100}{20}$ = 3 × 5 = 15 cm

Given: Object distance, u = -30 cm, Focal length, f = 15 cm

 v=?

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

$\frac{1}{15} = \frac{1}{v} - \frac{1}{-30}$

$\frac{1}{15} = \frac{1}{v} + \frac{1}{30}$

$\frac{1}{15} - \frac{1}{30} = \frac{1}{v}$

$\frac{1}{v} = \frac{2-1}{30}$

$\frac{1}{v} = \frac{1}{30}$

v = 30 cm

For second convex  lens, L2

f = $\frac{1}{p}$ = $\frac{100 \ × \ 3}{-10}$ = -10 × 3 = -30 cm

Object distance, u = -45-(-30)= -45 + 30 = -15cm, focal length, f = -30cm

v = ?

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

$\frac{1}{-30} = \frac{1}{v} - \frac{1}{-15}$

$\frac{1}{-30} = \frac{1}{v} + \frac{1}{15}$

$\frac{1}{-30} - \frac{1}{15} = \frac{1}{v}$

$\frac{1}{v} = \frac{-1-2}{30} = \frac{-3}{30}$

v= -30 / 3 = -10 cm 

Distance between original object and final image = 30 + 45 - 10 = 30 + 35  = 65.

The correct answer is Echinus (Sea urchin).

Concept:

• The animal kingdom is divided into many sub-groups called phyla.
• The basis for categorization includes:
• Arrangement of cells
• Body symmetry
• Nature of coelom (body cavity)
• Patterns of digestive, circulatory, or reproductive systems

Explanation:

Body Symmetry:

• There are 3 types of symmetry: Bilateral, Radial, and Asymmetrical.
• Bilateral Symmetry:
• Animals, whose bodies can be divided into left and right halves, are said to be bilaterally symmetrical.
• For example Platyhelminthes, Annelida, Arthropoda, Chordata, etc.
• Radial Symmetry:
• Animals whose bodies can be divided into two equal halves from any plane passing through the center of the body are said to be radially symmetrical.
• For example Coelenterates, Echinoderms, and Ctenophores.
• Asymmetrical:
• ​Few animals cannot be divided into two equivalent parts along with any plane going through the central point of the organism. They are said to be asymmetrical.
• For example Sponges.

Thus, Echinus has radial symmetry.

The correct answer is Because viruses have fewer targets for drugs.

Concept:

Infection:

• An infection occurs when a microorganism enters a person’s body and causes harm.
• The microorganism uses that person’s body to sustain itself, reproduce, and colonize.
• These infectious microscopic organisms are known as pathogens, and they can multiply quickly.
• Examples of pathogens include:
• bacteria
• viruses
• fungi

Explanation:

Treatment of bacterial infections:

• Bacteria are single-celled organisms.
• Most bacterial infections can be effectively treated with antibiotics.
• They either kill bacteria or stop them from multiplying.
• This helps the body’s immune system to fight the bacteria.

Treatment of viral infections:

• Unlike bacteria, viruses do not have a cellular structure. They are just genetic material coated by proteins.
• They enter the host body and invade the cells to multiply by overtaking their DNA replication machinery.
• So, to kill them we have to kill our cells as well.
• For most viral infections, treatments can only help with symptoms.
• Antibodies don't work on viruses. Instead, antiviral medicines are used. But they are available for a few viral infections.

Treating viral infections is more difficult than treating bacterial infections because viruses have fewer म for drugs.

The correct answer is Bos indicus is a cow and Bos bubalis is buffalo.

Concept:

Animal Husbandry:

• Animal husbandry is the scientific management of animal livestock.
• It includes various aspects such as feeding, breeding, and disease control.
• Animal-based farming has cattle, goat, sheep, poultry, and fish farming.

Explanation:

Cattle farming:

• Cattle husbandry is done for milk and draught labor for agricultural work such as tilling, irrigation, and carting.
• Indian cattle belong to two different species, Bos indicus (cows), and Bos bubalis (buffaloes).
• Milk-producing females are called milch animals (dairy animals), while those used for farm labor are called draught animals.

The correct answer is 1/27.

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 CB 

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

Area of cross-section of wire = π r2 

R2 = 3ρ L/ A = 3ρ L /  π r2

V2 = I R2 =  3ρ I L /  π r2

Ratio of V1 to V2 = V1/ V2 =  $\frac{\frac{\rho IL}{9\pi r^2}}{\frac{3\rho I L}{\pi r^2}}$ = $\frac{\rho IL}{9\pi r^2}$ × $\frac{\pi r^2}{3\rho IL}$ = 1/ 3 × 9 = 1/27 

The ratio (V1 / V2) is 1/27.

The correct answer is It will form a tri-positive ion to acquire a stable configuration.

Concept:

Electronic configuration:

• It can be defined as the distribution of electrons around the nucleus in different energy levels (shells).
• It was suggested by Bohr and Bury.

Rules for writing the electronic configuration of an atom:​

• The maximum number of electrons present in a shell is given by the formula 2n2, where ‘n’ is the orbit number or energy level index, 1,2,3, and so on.
• Hence, the maximum number of electrons in different shells is as follows:
• The First orbit or K-shell will be = 2 × 12 = 2,
• The second orbit or L-shell will be = 2 × 22 = 8,
• The Third orbit or M-shell will be = 2 × 32 = 18,
• The fourth orbit or N-shell will be= 2 × 42= 32, and so on.
• The maximum number of electrons that can be accommodated in the outermost orbit is 8.
• Electrons are not accommodated in a given shell unless the inner shells are filled. That is, the shells are filled in a step-wise manner.

Ions: 

• An atom or group of atoms that bears one or more positive or negative electrical charges, is called an ion.
• Cations: Positively charged ions formed by losing electrons.
• Anions: Negatively charged ions are formed by gaining electrons.

​Explanation:

• Element X has 3 electrons in the M shell.
• So, its electronic configuration is 2, 8, 3.
• An element having less than 4 electrons in its outermost shell tends to lose the electrons to form a cation.

Thus, It will form a tri-positive ion to acquire a stable configuration.

The correct answer is Light rays coming from a distant source will focus behind the retina. 

Concept:

• Eye helps us in visualizing objects and also helps us in light perception, color, and depth perception.
• The human eye consists of the following parts: Sclera, Retina, Cornea, Lens, Pupil, and Optic nerve.

Concave lens:

• A concave lens is a lens that diverges a straight light beam from the source to a diminished, upright, virtual image.
• It is shaped curved inwards at the center and bulges outwards through the edges.
• A concave lens is also known as a diverging lens because it makes the light diverge.

​

​

Explanation:

• Our eyes have a convex lens that converges the light rays on the retina.

​

• If a person with normal vision wears eyeglasses with a concave lens, it will diverge the light rays and the image will be formed behind the retina.

Additional Information 

Myopia:

• Myopia is also known as near-sightedness.
• A person with myopia can see nearby objects clearly but cannot see distant objects distinctly.
• In myopia, the eyeball is too long for the normal focusing power of the eye. As a result, images of distant objects appear blurred.
• A concave lens is placed in front of a myopic eye, moving the image back to the retina and clarifying the image.

Hyperopia:

• Hyperopia is also known as far-sightedness.
• A person with hyperopia can see distant objects clearly but cannot see nearby objects distinctly.
• In this condition, nearby objects appear blurry as the light from them is focused behind the retina instead of on it.
• It can be corrected by a convex lens (converging lens).

The correct answer is Sclerenchyma > Collenchyma > Parenchyma.

Concept:

Tissue: A group of similar cells that work together to perform a particular function.

Plant tissues are classified into two main categories on the basis of the ability of their cells to divide.

These are meristematic tissue and permanent tissue.

Explanation:

Permanent Tissues:

• They are a group of cells (living or dead) formed by the meristematic tissue which takes up specific roles and loses their ability to divide.
• This process of obtaining permanent shape, size, and function is called differentiation.

Simple permanent tissues

• They are composed of similar types of cells having a common origin and function.
• It is further divided into three types namely parenchyma, collenchyma, and sclerenchyma.

Order in terms of ability to provide increased stiffness to plant Sclerenchyma > Collenchyma > Parenchyma.

The correct answer is Hydrogen.

Concept:

Global warming:

• It is the increase in the earth's overall temperature over the last one or two centuries due to various human activities.
• As the human population has increased, so has the volume of fossil fuels burned.
• Fossil fuels include coal, oil, and natural gas, and burning them causes what is known as the “greenhouse effect” in the earth’s atmosphere.

Explanation:

Greenhouse effect: 

• The greenhouse effect is when the sun’s rays penetrate the atmosphere, but when that heat is reflected off the surface cannot escape back into space.
• Gases produced by the burning of fossil fuels prevent the heat from leaving the atmosphere.
• These greenhouse gasses are carbon dioxide, chlorofluorocarbons, water vapor, methane, and nitrous oxide.
• The excess heat in the atmosphere has caused the average global temperature to rise over time, otherwise known as global warming.

Thus, Hydrogen is not a greenhouse gas.

Concept:

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:

Molar mass of Hydrogen gas H₂= 2 × 1 = 2g

Molar mass of Oxygen gas O₂ = 2 × 16 = 32g

Molar mass of water H₂O = 2 + 16 = 18g 

The reaction between hydrogen and oxygen:

• Hydrogen and oxygen react to form water.
• 2H₂ (g) + O₂ (g) → 2H₂O (l)
• 4g of hydrogen reacts with 32g of oxygen to form 36 g of water.

The number of atoms in 32g of Oxygen:

• 1 mole of O₂ = molar mass of O₂ = 6.022 × 1023 molecules of oxygen
• 32g of O₂ has molecules = 6.022 × 10 ²³
• 1 Oxygen molecule has 2 atoms of oxygen.
• The number of oxygen atoms in 32g of O₂ = 2 ×  6.022 × 10 23 atoms = 12.044 × 10²³.

The correct answer is Decomposition of silver chloride.

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.

Decomposition reaction:

• It is defined as the reaction in which a single compound splits into two or more simple substances under suitable conditions.

Types of Decomposition Reactions:

• Thermal decomposition reaction
• Electrolytic decomposition reaction
• Photo decomposition reaction

Explanation:

Photo decomposition:

• It is a chemical reaction in which a substance is broken down into simple substances by exposure to light (photons)

Decomposition of silver chloride:

• When silver chloride is exposed to sunlight, it decomposes into silver and chlorine gas.
• Silver chloride is white in color and silver metal is grey.
• 2AgCl + Sunlight →  2Ag + Cl₂

    So, the cause of the change in color of Silver chloride from white to grey when kept in sunlight is the decomposition of Silver chloride.

Additional InformationThermal decomposition:

• It is a chemical reaction where a single substance breaks into two or more simple substances when heated.
• The reaction is usually endothermic because heat is required to break the bonds present in the substance.

Electrolytic decomposition reaction (Electrolysis)

• Electrolytic decomposition may result when an electric current is passed through an aqueous solution of a compound.
• A good example is the electrolysis of water.

The correct answer is It will scatter light.

Concept:

Mixtures:

• A mixture is a substance that consists of two or more elements or compounds not chemically combined together

Types of Mixtures:

• Homogeneous Mixture:
• Those mixtures, in which the substances are completely mixed together and are indistinguishable from one another, are called homogeneous mixtures.
• A true solution is a homogeneous mixture.
• For example Soda water, Soft drinks, lemonade, salt or sugar solution, etc.
• Heterogeneous Mixture:
• Those mixtures in which the substances remain separate and one substance is spread throughout the other substance as small particles, droplets, or bubbles are called heterogeneous mixtures.
• All the suspensions and colloids are heterogeneous mixtures.
• For Example: - Sugar and sand mixture, muddy river water, soap solution.

Explanation:

Colloids:

• These mixtures appear to be homogeneous but they are actually heterogeneous.
• Their particles are very small (1-to 1000 nanometers in size). They cannot be seen with naked eyes.
• They show the Tyndall effect i.e., they scatter the beam of light passing through them.
• They don’t settle down when left undisturbed for some time. They are quite stable.
• They cannot be separated by the filtration process but they can be separated by centrifugation.

The correct answer is Neutralisation reaction.

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:

Neutralization reaction:

• In a neutralization reaction, an acid reacts with a base to form salt and water.
• Acid + Base → Salt + water

​Reaction between Copper oxide and Hydrochloric acid:

• Copper oxide is a metal oxide and thus basic in nature.
• Hydrochloric acid is a strong acid.
• Copper oxide reacts with hydrochloric acid to form copper chloride and water.
• CuO + 2HCl → CuCl₂ + H₂O

So, in the case of the reaction of copper oxide and hydrochloric acid, salt which is copper chloride, and water are produced, thus it is an example of a neutralization reaction.

Additional InformationCombination 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.

Reduction reaction:

• Reduction means losing Oxygen or gaining hydrogen.
• Reduction is accompanied by oxidation i.e., the addition of oxygen.
• The reduction and oxidation reaction is termed a redox reaction.

The correct answer is virtual and diminished.

Concept:

Spherical mirror:

• A spherical mirror is a mirror that has the shape of a piece cut out of a spherical surface.
• There are two types of spherical mirrors: concave, and convex.

Concave mirror: 

• It is part of a whole spherical mirror that reflects light from the hollow part.
• It is a converging mirror because it converges the incident rays at a point.

Convex mirror: 

• It is part of a whole spherical mirror that reflects light from the bulged-out part.
• It diverges the incident rays.

Explanation:

Image formation by the convex mirror when the object is placed between infinity and pole :

Nature of image: Virtual and erect 

Size of image: Diminished 

Position of image: Behind the mirror between the pole and focus 

Additional Information

Image formed by the convex mirror when the object is at infinity:

Nature of image: Virtual and erect 

Size of image: Highly diminished 

Position of image: Behind the mirror at the focus

The correct answer is By observation of variations in related species.

Concept:

Evolution:  It is the change in the characteristics of a species over several generations and relies on the process of natural selection. 

Explanation:

Charles Darwin's theory of Evolution: 

• He made a sea voyage on a ship named HMS Beagle around South America, Australia, Africa, and many of the Atlantic and Pacific islands.
• He observed the plants and animals on his journey and gave the theory of natural selection.
• In his book, ''On the origin of species" published in 1859, he described how organisms evolve over generations through the inheritance of physical or behavioral traits.
• The theory starts with the premise that within a population, there is variation in traits, such as the beak shape in one of the Galapagos finches Darwin studied.
• According to the theory, individuals with traits that enable them to adapt to their environments will help them survive and have more offspring, which will inherit those traits.
• Individuals with less adaptive traits will less frequently survive to pass them on.
• Over time, the traits that enable species to survive and reproduce will become more frequent in the population and the population will change or evolve.

The correct answer is a new system of slavery.

Key Points

• The 19th-century indenture has been described as a new system of slavery.
• The indentured labour migration from India also illustrates the two-sided nature of the nineteenth-century world.
• It was a world of faster economic growth as well as great misery, higher incomes for some and poverty for others.
• In the nineteenth century, hundreds of thousands of Indian and Chinese labourers went to work on plantations, in mines, and in road and railway construction projects around the world.
• In India, indentured labourers were hired under contracts that promised return travel to India after they had worked five years on their employer’s plantation.
• Most Indian indentured workers came from the present-day regions of eastern Uttar Pradesh, Bihar, central India and the dry districts of Tamil Nadu.
• In the mid-nineteenth century, these regions experienced many changes – cottage industries declined, land rents rose, and lands were cleared for mines and plantations.
• All this affected the lives of the poor.

The correct answer is Socially and Educationally Backward Classes Commission.

Key Points

• The Mandal commission was set up on 1st 1979 under the prime minister Morarji Desai.
• Criteria for Reservation based on Educational, Social and Economical.
• The report was submitted by the Mandal Commission to the President on 31st December 1980.
• In August 1990 V.P Singh announced the recommendation of the Mandal Commission in Parliament.
• The SC upheld the 27% reservation for OBCs in 1992.