ICAR Technician 28 Feb 2022 Shift 2 (Previous Year Paper)

The correct answer is Indiagold.

Key Points

• Shivalik Small Finance Bank and India gold collaborated with each other to launch India's first loan against Digital Gold.
• It offers instant loans up to Rs 60,000.
• It starts with a monthly interest rate of only 1%.

Additional Information

• The Headquarters of Shivalik Small Finance Bank is in Noida (Uttar Pradesh).
• MD and CEO of Shivalik Small Finance Bank are Suveer Kumar Gupta.

The correct answer is Sukhoi 30 MK-I.

Key Points

• DRDO on 8 april 2022 successfully flight-tests Solid Fuel Ducted Ramjet (SFDR) technology at the Integrated Test Range (ITR), Chandipur off the coast of Odisha.
• DRDO on 27 March 2022 successfully flight-tests India Army version of Medium Range Air to Surface missile at the Integrated Test Range (ITR), Chandipur off the coast of Odisha.
• DRDO on 23 December 2021 successfully conducted a second flight - test of the indigenously developed conventional Surface to Surface missile ‘Pralay’ from Abdul Kalam Island off the coast of Odisha.

Additional Information

• BrahMos
• The name of the BrahMos missile was taken from the Indian Brahmaputra river and the Russian Moscow river.
• In 2017 Brahmos was first time successfully flight-tested.
• BrahMos missile is a supersonic cruise missile that can be launched from Land, Aircraft, Ship or Submarine.
• Sukhoi 30 MK
• It is a twinjet fighter developed by Russia under the licence of HAL

Important Points

• 1 Mach = Sound speed.
• Supersonic means equal to 3.5 Mach.
• Hypersonic > 5 Mach
• It is based on the Ramjet engine.​
• A cruise missile means it can change its path after launching.

The correct answer is He used to wear British-made clothes.

Key Points

• Chitranjan Das also known as Deshbandhu.
• Motilal Nehru and Chitranjan Das, established the Swaraj Party in January 1923.​

Additional Information

• The Non-Cooperation Movement was launched by Mahatma Gandhi in 1920.
• It was started due to the Jallianwala Bagh Massacre on 13 April 1919.
• On 4 february 1922, a group of peasants set fire to a police station in chauri chaura (Uttar Pradesh).
• Due to which Non Cooperation was ended.

The correct answer is Antibiotics.

Key Points

• Antibiotics are substances that are derived from one microorganism in order to kill another microorganism. Antibiotics are effective against bacterial, fungal and parasitic infections.

Important Points

• Types of Antibiotics:
• Penicillins - phenoxymethylpenicillin, flucloxacillin and amoxicillin.
• Cephalosporins - cefaclor, cefadroxil and cefalexin.
• Tetracyclines - tetracycline, doxycycline and lymecycline.
• Aminoglycosides - gentamicin and tobramycin.

The correct answer is Shajapur, Agar and Neemuch.

Key Points

• Aiming to meet the 50% power demand of Madhya Pradesh through renewable energy, CM Shivraj Singh Chouhan laid the foundation stones for setting up three solar power plants of 1500-megawatt capacity in Shajapur, Agar and Neemuch at a cost of Rs 5,250 crore.

Additional Information

• 2 units of 550 Megawatt in Agar.
• 3 units of 450 megawatts in Shajapur.
• 3 units of 500 megawatts in Neemuch.
• Power generation will start in March 2023.

The correct answer is Noida.

Key Points

• The Union Minister of Heavy Industries Mahendra Nath Pandey has inaugurated the first air pollution control tower of the state of Uttar Pradesh in Noida.
• The Air Pollution Control Tower (APCT) prototype has been developed by state-run Bharat Heavy Electricals Ltd (BHEL).
• The indigenously developed APCT is set up between the DND flyway and the slip road to Noida Expressway.
• The tower will help to mitigate the rising air pollution problem in the city.

Important Points

• The tower will clean the polluted air around it and release purified air.
• Equipped with intake and exhaust fans, the tower will initially run with the help of electricity.
• The authority, however, plans to run the tower with the help of solar energy later.

Additional Information

• About Uttar Pradesh:
• Capital: Lucknow
• Governor: Anandiben Patel
• UP Chief minister: Yogi Adityanath

The correct answer is Nitrogen.

Key Points

• Table sugar is the common name for a sugar known as sucrose.
• It is a type of disaccharide made from the combination of the monosaccharides glucose and fructose.
• The chemical or molecular formula for sucrose is C₁₂H₂₂O_11.
• That means each molecule of sugar contains 12 carbon atoms, 22 hydrogen atoms and 11 oxygen atoms.​

Important Points

• The type of sugar called sucrose is also known as saccharose.
• It is a saccharide that is made in many different plants.
• Most table sugar comes from sugar beets or sugarcane.
• The purification process involves bleaching and crystallization to produce a sweet, odourless powder.
• The English chemist William Miller coined the name sucrose in 1857 by combining the French word sucre, which means "sugar", with the -ose chemical suffix that is used for all sugars.
• Formulas for Different Sugars:
• Arabinose - C₅H₁₀O₅
• Fructose - C₆H₁₂O₆
• Galactose - C₆H₁₂O₆
• Glucose - C₆H₁₂O₆
• Lactose - C₁₂H₂₂O₁₁

The correct answer is Uday Shankar.

Key Points

• The Federation of Indian Chambers of Commerce and Industry (FICCI) announced that Sanjiv Mehta was appointed as its President.
• Mehta succeeded media industry veteran Uday Shankar.
• Mehta was also the President of Unilever South Asia (India, Pakistan, Bangladesh, Sri Lanka & Nepal).
• And is a member of the ‘Unilever Leadership Executive’ which is Unilever’s Global Executive Board.

Important Points

• FICCI is the largest and oldest apex business organisation in India.
• It is a non-government, not-for-profit organization. FICCI provides a platform for networking and consensus building within and across sectors.
• FICCI Founded: 1927
  

FICCI Headquarters: New Delhi

Additional Information

• Mr Mehta has done his Bachelors in Commerce (India), and Chartered Accountancy (India) and has also completed his Advanced Management Program (Harvard Business School).
• Mr Mehta is married to Mona Mehta who too is a Chartered Accountant, and they have twin daughters Naina and Roshni who have studied at MIT, Cornell, and Harvard Universities.
• A firm believer that ‘doing well’ and ‘doing good’ are two sides of the same coin, he propagates the cause of compassionate capitalism.
• Mr Mehta was conferred an honorary ‘Doctorate degree in Business Management by Xavier University, Bhubaneswar.

The correct answer is Shabir Hussein Shekhadam Khandwawala.

Key Points

• Shabir Hussein Shekhadam Khandwawala has become the head of BCCI Anti-Corruption Unit 2021.
• Shabir Hussein Shekhhdam Khandwawala, a 1973 batch IPS officer.
• He retired as Gujarat DGP in December 2010, After that he was an advisor of Essar Group for 10 years.
• The BCCI Anti-Corruption Unit is effective from March 2019.
• This Unit ensures that every event must be fair and **without any corruption.**​

Additional Information

• Chetan Sharma is the Chairman of the selection committee of the Indian cricket team.
• Jay Shah is the secretary of BCCI (Board of Control for Cricket in India).
• Sourav Ganguly is the President of BCCI.
• BCCI (Board of Control for Cricket in India) is the national governing body for all cricket in India.
• ​Formed - 1928
• Headquarter - Mumbai

The correct answer is Australia.

Key Points

• Australia is the winner of the ICC Men's T20 World Cup 2021.
• The T20 World Cup 2021 was started on 17th October in UAE and Oman.
• The final match was played between Australia and New Zealand.
• That was the first time when the Australian cricket team won the T20 World Cup 2021.
• Australian cricketer Mitchell Marsh was the player of the match in the T20 World Cup 2021.

Additional Information

• ICC headquarter is located in Dubai, United Arab Emirates.
• It was established in 1909 by the representatives of Australia, England, and South Africa as Imperial Cricket Conference.
• The ICC is the global governing body for cricket which is also responsible for all ICC events.

The correct answer is Piyush Goyal.

Key Points

• In November 2021, Union Minister Piyush Goyal virtually launched India's first digital food museum in Thanjavur, Tamil Nadu.
• Thanjavur is the birthplace of the FCI that's why Thanjavur was chosen as the site for India's first digital food Museum.
• This museum has 1,860 square feet co-developed by the Food Corporation of India (FCI) and Technological Museums, Bengaluru and Visvesvaraya Industrial with an estimated outlay of Rs 1.1 crore.

Additional Information

• Narendra Modi is the 14th Prime Minister of India.
• Nitin Gadkari is Union Minister for Road Transport and Highways.
• Nirmala Sitaraman is an Indian economist and currently, she is the Minister of Finance and Corporate Affairs of India.

The correct answer is It is an RNA plasmid-based COVID-19 vaccine.

Key Points

• ZyCoV-D vaccine for 2022 is India's first indigenously developed plasma DNA vaccine against COVID-19.
• ZyCoV-D is also the world's first Plasmid DNA vaccine authorized for COVID-19.
• The vaccine is developed by Zydus Cadila using a non-replicating and non-integrating plasmid carrying the novel coronavirus.
• This vaccine is fully authorized by the DCGI (Drug Controller General of India).
• It will be started in 7 Indian states.
• ​Bihar
• Jharkhand
• Maharashtra
• Punjab
• Tamil Nadu
• Uttar Pradesh
• West Bengal
• It will be applied to the 12-18 years age group.
• It is 66.6% effective, Hence options 1,2, and 3 are correct.
• It is a DNA plasmid-based Vaccine, Hence 4th option is incorrect. ​

The correct answer is Lodi.

Key Points

• Bahlul Khan Lodi was the chief of the Pashtun Lodi tribe.
• Bahlul Lodi was the founder of the Lodi dynasty of the Delhi Sultanate upon the abdication of the last claimant from the Sayyid rule.
• Bahlul became the Sultan of the **dynasty on 19 April 1451.**​
• He retained Delhi as his capital.
• He extended his territory to Jaunpur in 1479, Gwalior, and upper Uttar Pradesh.

Additional Information

• Khilji Dynasty (1290 - 1320) founder was Jalaluddin Khilji. Alauddin Khilji was the first sultan who introduced the system of Daag and the Huliya in the army.
• Sayyid Dynasty (1414 -1444) Khizar khan was the founder and previous was governor of Punjab on the behalf of Timur, during Sayyid Dynasty the narrow horseshoe arch was replaced by the true arch, an idea imported directly from Persia.
• Tomar Dynasty's founder was Anangapal Tomar in 736 CE.

The correct answer is Antyodaya Programme.

Key Points

• Antyodaya Anna Yojana
• Antyodaya Anna Yojana was launched on 25^th December 2000.
• ‘Micro Plan for Sustainable livelihood for every deprived household’ is the major objective of this Programme.
• It was launched to help the poorest of the poor.
• It provided rice and wheat at a low rate through the public distribution system.
• It was launched by former Indian Prime Minister A.B. Vajpayee during the 9^th five-year plan in India.
• The scheme was first implemented in Rajasthan.

  

Additional Information

• Prime Minister’s Rozgar Yojana (PMRY)
• Prime Minister Rozgar Yojana was started in 1993 with the aim of creating self-employment opportunities for educated but unemployed youths in rural areas and small towns.
• Under this scheme, youths are provided support so that they can set up small businesses and industries.
• National Food for Work Programme (NFFWP)
• National Food for Work Programme was launched in February 2001.
• Under this programme, the government provided work to poor people related to the construction of kutcha roads, clearing debris, etc and gave foodgrains instead of wages.
• Rural Employment Generation Programme (REGP)
• The Khadi & Village Industries Commission (KVIC) launched and initiated the Rural Employment Generation Programme scheme on 1st April 1995.
• The programme aims at the generation and expansion of sustainable and continuous employment opportunities in rural and urban areas across the country.
• Giving a provision to establish and generate micro-enterprises for employment generation.
• Smooth and easy flow of credit to the micro sector by facilitating the participation of financial institutions.
• Increase the need for raw materials generated by small scale industries to high scale industries.

The correct answer is Option 1.

Key Points

• Delhi is the highest urbanized state/union territory in India with a 97.50 percent urban population, followed by Chandigarh.
• Himachal Pradesh is the least urbanized state/union territory, followed by Bihar.
• Uttar Pradesh is the state/ union territory with the highest child population, followed by Bihar.

Hence, Options 2,3, and 4 are CORRECT.

• Sikkim is the state/union territory with the least child population in Census 2011.

Hence, Option 1 is INCORRECT.

Important Points 

• Child Population in regard to the Census of India is described as the population of children in the age group 0-6 years.
• Even though the population of this age group is included in the total population of the country and the states, it is very important to have accurate statistical data in respect of the population of this age group for framing policies and programmes in the education sector, health sector, etc.

Additional Information

• Top three literate states/union territories are Kerala - 94.00 %, Lakshadweep - 91.85 %, Mizoram - 91.33 %.
• Highest sex ratio top states/ union territories are Kerala - 1084, Puducherry - 1037, Tamil Nadu  - 996.
• Lowest sex ratio states/ union territories are Daman and Diu - 618,  Dadra & Nagar Haveli - 774, Chandigarh - 818.
• Top three highly populated states are Uttar Pradesh - 199,281,477 (16.49%), Maharashtra - 112,372,972 (9.28%), Bihar - 103,804,637 (8.58%).

The correct answer is Karsten Warholm.

Key Points

• 400m hurdler Karsten Warholm from Norway was named men's World Athlete of the Year.
• Warholm won the men's Athlete of the Year Award for a season in which he broke the men's 400m hurdles world record twice.
• Warholm also became the first man to run the race in under 46 seconds, achieving that feat in the Tokyo 2020 Olympic final.

Important Points 

• Thompson-Herah from Jamaica took the women's World Athlete of the Year Award.
• She also came close to breaking Florence Griffith Joyner's long-standing women's 100m world record.
• She won three gold medals in Tokyo Olympics including the 100m and 200m gold in the women's category.

Additional Information

• Lionel Messi
• Lionel Messi is an Argentine professional footballer who plays as a forward for Ligue 1 club Paris Saint-Germain.
• He also captains the Argentina national team.
• Messi has a record of  winning seven Ballon d'Or awards
• He also has a record of winning six European Golden Shoes.
• Cristiano Ronaldo
• Cristiano Ronaldo is a Portuguese professional footballer who plays as a forward for Premier League club Manchester United.
• He also captains the Portugal national team.
• He is currently the top scorer in the history of men's football with 807 goals.
• He holds the record for the most UEFA Champions League titles (five), and the most goals scored in the competition’s history (141).
• Roger Federer
• Roger Federer is a Swiss professional tennis player.
• He has won 103 Association of Tennis Professionals (ATP) singles titles, the second-most of all time after Jimmy Connors.
• He has won 20 Grand Slam titles, including a record eight men's singles Wimbledon titles.
• Roger Federer was the first living person in Switzerland to have a coin minted in his honour in 2019.

The correct answer is Nitin Chug.

Key Points

• Ittira Davis has been appointed as the MD and CEO in December 2021 for a period of 3 years.
• Davis has been appointed as MD and CEO to fill the vacancy caused by the resignation of former MD and CEO Nitin Chugh.
• Ujjivan Small Finance Bank witnessed a large-scale exodus of its directors, with as many as eight board members, including Chugh, making a hasty exit over the last year.

Additional Information

• Ujjivan Small Finance Bank headquarters: Bengaluru

The correct answer is Vishnu.

Key Points

• The Lakshmana temple is dedicated to Vaikuntha Vishnu - an aspect of Vishnu.
• Main image is of a three-headed & four-armed sculpture of Vaikuntha Vishnu.
• The central head is of a human, and two sides of boar (depicting Varaha) and lion (depicting Narashima).

Additional Information

• The Lakshmana temple was the first of several temples built by the Chandella kings in their newly-created capital of Khajuraho. Between the 10th and 13th centuries, the Chandellas patronized artists, poets, and performers, and built irrigation systems, palaces, and numerous temples out of sandstone.
• At one time over 80 temples existed at this site, including several Hindu temples dedicated to the gods Shiva, Vishnu, and Surya. There were also temples built to honor the divine teachers of Jainism.
• Approximately 30 temples remain at Khajuraho today.
• The original patron of the Lakshmana temple was a leader of the Chandella clan, Yashovarman, who gained control over territories in the Bundelkhand region of central India that was once part of the larger Pratihara Dynasty.
• Yashovarman sought to build a temple to legitimize his rule over these territories, though he died before it was finished.
• His son Dhanga completed the work in 954 C.E.

The correct answer is Kalasha – The lower part of the temple.

Key Points

• Shikhara 
• Shikhara is a mountain-like spire on top of a temple.
• Shikhara is found in North Indian temples.
• Shikhara has a curving shape.
• Mandapa
• It is the entrance to the temple.
• It may be a portico or colonnaded (series of columns placed at regular intervals) hall that incorporates space for a large number of worshippers.
• Dances and other entertainments are practiced here.
• Some temples have multiple mandapas in different sizes named Ardhamandapa, Mandapa, and Mahamandapa.
• Amalaka
• It is a stone disc-like structure at the top of the temple.
• they are common in North Indian temples.

Hence, Option 1, 3 and 4 are correct 

• Kalasha
• The Kalash is a pointed dome at the top of a temple
• It is commonly seen in North Indian temples.

Hence, Option 2 is incorrect.

The correct answer is an Oxidation reaction.

Key Points

• Rancidity refers to the spoilage of food in such a way that it becomes undesirable for consumption.
• It is caused by the oxidation of fats and oils present in food.
• It causes changes in the taste and smell of food.

Additional Information

• Rancidity can be controlled by
• Adding antioxidants to foods.
• Keeping food items in a closed container.
• Refrigerating food.
• Replacing oxygen in the containers with another gas.

The correct answer is Garba.

Key Points

• Garba
• Garba is a form of dance that originates from the state of Gujarat in India.
• It is commonly performed at festivals and on other special occasions.
• It is a joyful style of dance, based on a circular pattern and characterized by a sweeping action from side to side.

Additional Information

• Bhangra
• Bhangra is a type of traditional dance originating in the Majha area of Punjab.
• The dance is associated primarily with the spring harvest festival, Baisakhi.
• Kathak
• Kathak dance originated in Uttar Pradesh in North India.
• The Kathak dancers communicate stories through rhythmic foot movements, hand gestures, facial expressions, and eye work.
• Rouf
• Rouf dance is a traditional and rhythmic folk dance of Jammu and Kashmir.
• This dance is performed by women wearing colourful clothes during the time of Eid and Ramzan.

The correct answer is Arunachal Himalayas.

Key Points

• Namcha Barwa is a mountain in Arunachal Himalayas.
• It is considered the Eastern point of the Himalayas.
• It is located in the extreme east of the Indian state of Arunachal Pradesh.
• The height of Namcha Barwa is about 7782m.
• Brahmaputra river takes a U-turn on reaching Namcha Barwa.

Additional Information

• Himalayas
• The Himalayas are known as young fold mountains. These were formed during the past 10-25 million years ago.
• These mountains are characterized by faulting, volcanic activities, erosion, and weathering caused by running water, ice, winds, etc.
• They have deeper and steeper slopes with glacier-capped high peaks.

The correct answer is Khilafat Movement.

Key Points

• Khilafat Movement
• Launched in 1919 with the support of Mahatma Gandhi.
• In First World War, Turkey fought against the British.
• After Turkey’s defeat, the Ottoman caliphate was proposed to be dissolved.
• Muslims regarded the Sultan of Turkey as their Caliph (religious head of the Muslims).
• The Khilafat movement was launched under the leadership of the Ali Brothers (Maulana Mohammed Ali and Maulana Shaukat Ali) to persuade the British government not to abolish the caliphate.
• Mahatma Gandhi supported the movement.
• 

Confusion PointsThe Khilafat Movement, (1919-1922) was a movement of Indian Muslims, led by Muhammad Ali and Shaukat Ali

• That demanded the following: The Turkish Sultan or Khalifa must retain control over the Muslim sacred places in the erstwhile Ottoman empire; the jazirat-ul-Arab (Arabia, Syria, Iraq, Palestine) must remain under Muslim sovereignty; and the Khalifa must be left with sufficient territory to enable him to defend the Islamic faith.

• The Congress supported the movement and Mahatma Gandhi sought to conjoin it to the Non-cooperation Movement

Additional Information

• Non-Cooperation Movement
• Launched on 5th September 1920 by the Indian National Congress under the leadership of Mahatma Gandhi.
• Demanded Swaraj or self-rule.
• Anti-Rowlatt agitation, the Jallianwala Bagh tragedy, Khilafat Movement were the reasons for Non-Cooperation  Movement.
• On 4^th February 1922, an angry mob attacked a police station at Chauri Chau      ra in Gorakhpur district of Uttar Pradesh
• Gandhiji was compelled to withdraw from the Non-Cooperation Movement.
• Civil Disobedience Movement
• Started by Gandhiji on 12th March 1930 with Dandi March.
• Together with 78 chosen followers, Gandhi walked nearly 375 km from Sabarmati Ashram to Dandi, a village on the Gujarat sea coast.
• On 6th April 1930, Gandhiji broke the salt law by making salt.
• This movement resulted in Gandhi-Irwin Pact on 5 March 1931.
• Quit India Movement
• Also known as the August Movement or August Kranti.
• Congress Working Committee passed the Quit India Resolution on 8 August 1942 in Bombay.
• Gandhiji was the movement’s leader. He gave the slogan – ‘Do or die’.
• The Movement demanded an immediate end to British rule over India.

The correct answer is Bhasha Sangam.

Key Points

• Bhasha Sangam is an initiative of the Ministry of Education under Ek Bharat Shreshtha Bharat.
• This app consists of daily used conversations in various languages.
• It is designed to teach basic sentences of everyday usage in 22 Indian languages.
• The idea is to make people acquire basic conversational skills in an Indian language other than their mother tongue.
• Language learning is also promoted as a skill with a formal credit-earning system.
• It also facilitates students to embrace the linguistic diversity of our nation and sensitizes them about the richness of our culture, heritage and diversity.
• It is also in tune with the NEP(National Educational Policy) 2020 emphasis on the promotion of Indian languages.

The correct answer is Emma Raducanu.

Key Points

• Emma Raducanu is a professional Woman Tennis player from the United Kingdom.
• She is among the few youngest women players to win a US Open.
• She won the women’s Singles US Open 2021 title at the age of 19 years.
• She was voted as WTA Newcomer of the year 2021.
• She also won the BBC Sports Personality of the Year 2021.

Additional Information

• Ashleigh Barty
• ​She is a professional women's Tennis player from Australia.
• She was at top of the rankings(till March 2022) from 2019 to 2022.
• She won the women’s Singles Australian Open 2022 & Wimbledon 2021 titles.
• She is among the youngest players to announce her retirement from tennis in March 2022.
• Barbora Krejčíková
• She is a Czech professional tennis player.
• She is known for her Grand Slam victories in women’s Doubles.
• She recently won the women's Singles French 2021 title.
• Carla Suarez Navarro
• She is a former woman tennis player from Spain.
• She announced retirement in 2021 from professional tennis after a cancer diagnosis.

Given:

A, B, and C can complete the work together = 15 days

Formula used:

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

Calculation:

Let the B alone can complete the remaining work be in B days

According to the question

The total work = 15 × (3 + 5 + 6) = 15 × 14 = 210

The 7 days work of A and C = 7 × (3 + 6) = 7 × 9 = 63

The remaining work = 210 - 63 = 147

The B can complete the work = ${147\over 5}\ =\ {29{2\over 5}}\ days$

∴ The required result will be ${29{2\over 5}}\ days.$

Given:

The total profit of A = Rs. 2.5 lakhs

Calculation:

Let the difference in the profit of C and B be X

The ratio of investment = ${{1} \over 3} : {{1} \over 6} : {{3} \over 4}$

After simplifying, the ratio of investment = 8 : 4 : 18

According to the question

Total ratio of capital of A = I_A

IA = 8 × 3 + 4 × 3 + 2 × 3 + 1 × 3 

IA = 45

Total ratio of capital of B = IB

IB = 4 × 3 + 8 × 3 + 16 × 3 + 32 × 3

IB = 180

Total ratio of capital of C = IC

IC = 18 × 12 = 216

Now, IA : IB : IC = 5 : 20 : 24

Protit ratio of A : B : C = 5 : 20 : 24

According to the question 

5 unit → 2.5 lakhs

1 unit → 0.5 lakhs

Difference between the profit of C and B = 4 unit 

So, 4 unit = 0.5 × 4 = 2 lakhs

∴ The required result will be 2 lakh.

Given:

4a - 3b = 2 and ab = ${{1} \over 4}$,

Formula used:

a³ - b³ = (a - b)³ + 3ab(a - b)

Calculation:

64a³  -  27b³

⇒ (4a)3 - (3b)3

⇒ (4a - 3b)³ + 3 × 4a × 3b (4a - 3b)

⇒ (4a - 3b)3 + 36ab (4a - 3b)

⇒ (2)³ + 36 × 1/4 × 2

⇒ 8 + 18 = 26

∴ The required result will be 26.

Given:

The case price = ₹ 1800

Calculation:

Let the rate of interest be R

Interest charged = 800 + 1050 - 1800 = 50

Now principle for the first month = 1800 - 800 = 1000

The principle for second month = 1000 - 350 = 650

The third month principle = 650 - 350 = 300

The total principle = 1000 + 650  + 300 = 1950

The rate of interest on 1950 rupees = 100 × 12 × ${50\over 1950}\ =\ 30.76\%\ \approx 30.80\%$

∴ The required result will be 30.80%.

Given:

The surface area increased by ${ {4840} \over 7}$  cm² by the increase of the radius 5 cm

Formula used:

V = ${4\over 3}\ × π × R^3$     

A = 4 × π × R²     Where, V = Volume of the sphere, A = Surface area of the sphere and R = Radius of the sphere 

Calculation:

Let the radius of the sphere be R

According to the question

⇒ 4 × π × (R + 5)² - 4 × π × R² = ${ {4840} \over 7}$

⇒ 4 × ($22\over 7$) × [R² + 25 + 10R - R²] = ${ {4840} \over 7}$

⇒ 25 + 10R = 55

⇒ 10R = 30

⇒ R = 3 cm

The volume of the sphere = ${4\over 3}\ × π × R^3$ = ${4\over 3}\ × π × 3^3\ =\ {4\over 3}\ \times {22\over 7}\ \times 3^3$ = 113.14 ≈ 113 cm³

∴ The required result will be 113 cm³.

Given:

Speed of A = 25% more than the speed of B

Formula used:

${S\ =\ {D\over T}}$     Where, S = Speed, D = Distance, and T = Time

Calculation:

Let the distance between X and Y be D and the speed of B and A be 4s and 5s respectively

According to the question

Time is taken by them to meet each other = ${D\over (4s\ +\ 5s)}\ =\ {D\over 9s}$

The distance covered by A in ${D\over 9s}$ hours = ${D\over 9s}\ × 5s\ =\ {5D\over 9}$

The distance covered by B in ${D\over 9s}$ hours = ${D\over 9s}\ × 4s\ =\ {4D\over 9}$

The remaining distance for A = ${D\ -\ {5D\over 9}}\ =\ {4D\over 9}$

The remaining distance for B = ${D\ -\ {4D\over 9}}\ =\ {5D\over 9}$

For A 

⇒ $({3\ +\ {12\over 60})\ × 5s\ =\ {4D\over 9}}$

⇒ 3.2 × 5s × 9 = 4D

⇒ 144 = 4D

⇒ D = 36s     ----(1)

For B

⇒ x × 4s= ${5D\over 9}$

⇒ 36sx = 5D

By putting the value of D from equation (1)

⇒ 36sx = 5 × 36s

⇒ x = 5

The is taken by B = x = 5 hours

∴ The required result will be 5 hours.

Shortcut Trick We know (Speed of A)/(Speed of B) = √(time taken by B after meeting)/(time taken by A after meeting)

⇒ 5/4 = √x/(16/5)

Squaring both sides we get

⇒ 25/16 = 5x/16

⇒ x = 5

∴ The required result will be 5 hours.

Shortcut Trick

Slant height (l) = Curved Surface Area ÷ (π × r) = 2145π ÷ (33π) = 65 cm.

Vertical height (h) = √(l² − r²) = √(65² − 33²) = 56 cm.

Volume = (1/3) × π × r² × h = (1/3) × π × 33 × 33 × 56.

Volume = 11 × 33 × 56 × π = 20328π cm³.

∴ The correct answer is 20328 π cm³.

Alternate Method

Given:

Curved Surface Area (CSA) of the cone = 2145π cm²

Radius (r) of the base = 33 cm

Formula Used:

1. CSA = π × r × l (where l is the slant height)
2. l² = r² + h² (where h is the vertical height)
3. Volume (V) = (1/3) × π × r² × h

Calculations:

⇒ 2145π = π × 33 × l

⇒ l = 2145 ÷ 33

⇒ l = 65 cm

⇒ h² = l² − r²

⇒ h² = 65² − 33²

⇒ h² = (65 + 33)(65 − 33) = 98 × 32

⇒ h = √(3136) = 56 cm

⇒ Volume = (1/3) × π × 33 × 33 × 56

⇒ Volume = π × 11 × 33 × 56

⇒ Volume = 20328π cm³

∴ The correct answer is 20328 π cm³.

Additional Information

Total Surface Area (TSA) of a Cone

The TSA includes both the curved surface area and the base area: TSA = πrl + πr² = πr(l + r).

Relationship with Cylinder

For the same radius and height, the volume of a cone is exactly 1/3^rd the volume of a cylinder: V_cone = (1/3)V_cylinder.

Slant Height and Pythagoras

The radius, vertical height, and slant height of a right circular cone always form a right-angled triangle: l = √(h² + r²).

Given:

AB = 12 cm and AC = 35 cm

Concept:

Sum of all angles of the triangle = 180° 

Calculation:

Let the right-angle triangle ΔABC and ED be x

⇒ AD is the angle bisector of ∠CAB

⇒ ∠ EAD = 45° 

In ΔEAD

⇒ ∠EAD + ∠DEA + ∠EDA = 180° 

⇒ 45° + 90° + ∠EDA = 180° 

⇒ ∠EDA = 45° 

⇒ EA = ED

⇒ EC = 35 - x

In ΔCED and ΔCAB

⇒ ∠C = ∠ C     (Common)

⇒ ∠CED = ∠CAB = 90° 

⇒ ΔCED ~ ΔCAB

⇒ ${ED\over AB}\ =\ {CE\over CA}$

⇒ ${x\over 12}\ =\ {35\ -\ x\over 35}$

⇒ 35x = 420 - 12x

⇒ x = ${420\over 47}$

The length of the DE = ${420\over 47}$ cm

∴ The required result will be ${420\over 47}$ cm.

Given:

The number of apples is 75% more than the number of oranges

Formula used:

${More \ or \ less\%\ =\ {More \ or \ less \ Quantity\over Total \ Quantity}\ × 100\%}$     

Calculation:

Let the number of oranges be X

The number of apples = $({1\ +\ {75\over 100}})\ \times X\$

⇒ $\ {175X\over 100}\ =\ {7X\over 4}$

The numbers of bananas = (${7X\over 4}$ + X) × (1 - ${60\over 100}$)

⇒ $({7X\ +\ 4X\over 4})\ \times {40\over 100}\ =\ {11X\over 4}\ \times {4\over 10}\ =\ 1.1X$

The required percentage = ${{7X\over 4}\ -\ 1.1X\over \frac{7x}{4}}\ \times\ 100\$

⇒ $\ {2.6\over 7}\ \times 100\ =\ 37.14\%\ \approx 37.1\%$

∴ The required result will be 37.1%.

Shortcut Trick(A + B) can do 80% of work in 20 days 

(A + B) can do 100% of work in 20 × 5/4 = 25 days 

Let the total work by 450 units 

Efficiency of A = 450 ÷ 45 = 10 unit/day

Efficiency of (B + C) = 450 ÷ 30 = 15 unit/day

Efficiency of (A + B) = 450 ÷ 25 = 18 unit/day

So, Efficiency of B = 8 unit/day

Efficiency of C = 7 unit/day

Since, A + B completed 80% work 

So, Remaining work = 20%

Now, 70% of remaining total work = 450 × (1/5) × (7/10) = 9 × 7 

∴ Required time taken by C = (9 × 7)/7 = 9 days.

 

Alternate Method 

Given:

A can do a piece of work = 45 days

B and C together can do a piece of work = 30 days

Formula used:

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

Calculation:

Let the C alone can complete the work in C days and B alone can complete the work in B days

The efficiency of A = ${1\over 45}$

A and B together can complete the 100% work together = 25 days

⇒ ${1\over 45}\ +\ {1\over B}\ =\ {1\over 25}$

⇒ ${1\over B}\ =\ {1\over 25}\ -\ {1\over 45}$

⇒ ${1\over B}\ =\ {9\ -\ 5\over 225}$

B can complete the work = ${225\over 4}$ days

⇒ ${4\over 225}\ +\ {1\over C}\ =\ {1\over 30}$

⇒ ${1\over C}\ =\ {1\over30}\ -\ {4\over 225}$

⇒ ${1\over C}\ =\ {15\ -\ 8\over 450}$

C can complete the work = ${450\over 7}$ days

The 20 days work of for A and B = ${20\over 45}\ +\ {80\over 225}\ =\ {100\ +\ 80\over 225}\ =\ {180\over 225}$

The remaining work = ${45\over 225}\ =\ {1\over 5}$

The 70% of the work = ${7\over 10}\ × {1\over 5}\ =\ {7\over 50}$

C will complete the 70% of the remaining work = ${7\over 50} × {450\over 7}\ =\ 9\ days$

∴ The required result will be 9 days.

Given:

The height of the helicopter = 360 metres

Formula used:

tanθ = ${Perpendicular\over Base}$

Calculation:

Let the helicopter be at point B and the two ships be at C and D such that their angles of depression from B are 60° and 30° respectively

⇒ AB = 360 metres, AC = x and DC = y

In ΔCAB

⇒ tan60° = ${AB\over CA}$

⇒ √3 = ${360\over x}$

⇒ x = ${360\over √{3}}\ =\ {120√{3}}$     ----(1)

In ΔABD

⇒ tan30° = ${AB\over AD}$

⇒ ${1\over √{3}}\ =\ {360\over x\ +\ y}$

⇒ x + y = 360√3

By equation (1)

⇒ 120√3 + y = 360√3

⇒ y = 360√3 - 120√3 = 240√3 m

∴ The required result will be 240√3.

Shortcut Trick

Net deviation from the given parts = 8 × (45 − 54) + 14 × (60 − 54) = −72 + 84 = +12

To balance the total average, the remaining 3 numbers must have a reverse deviation of −12.

Sum of 9^th, 10^th, and 11^th numbers = (3 × 54) − 12 = 162 − 12 = 150

Let the 10^th number be x. Then (x − 3) + x + (x + 3) = 150 ⇒ 3x = 150 ⇒ x = 50

The 9^th number = 50 − 3 = 47. Average of 9^th and 10^th = (47 + 50) ÷ 2 = 48.5

∴ The correct answer is 48.5.

Alternate Method

Given:

Total numbers = 25, Average = 54

Average of first 8 numbers = 45

Average of last 14 numbers = 60

9^th number = 10^th number − 3

11^th number = 10^th number + 3

Formula Used:

Sum of observations = Average × Number of observations

Total 25 numbers (Average = 54)

8 numbers Avg = 45

14 numbers Avg = 60

3

9th, 10th, 11th Sum = 150 (x − 3) + x + (x + 3)

Calculations:

⇒ Total sum of 25 numbers = 25 × 54 = 1350

⇒ Sum of first 8 numbers = 8 × 45 = 360

⇒ Sum of last 14 numbers = 14 × 60 = 840

⇒ Sum of remaining 3 numbers (9^th, 10^th, and 11^th) = 1350 − (360 + 840) = 1350 − 1200 = 150

⇒ Let the 10^th number be x.

⇒ The 9^th number = x − 3 and the 11^th number = x + 3

⇒ (x − 3) + x + (x + 3) = 150

⇒ 3x = 150

⇒ x = 50

⇒ The 10^th number = 50

⇒ The 9^th number = 50 − 3 = 47

⇒ Average of 9^th and 10^th numbers = (47 + 50) ÷ 2 = 97 ÷ 2 = 48.5

∴ The correct answer is 48.5.

Additional Information

Basic Average Formula

The arithmetic average is calculated by adding up all the numerical values in a dataset and then dividing by the total count of numbers.

Net Deviation Method

The sum of deviations of all observations from their actual arithmetic mean is exactly zero. This principle is extremely useful to find missing elements rapidly without calculating large multiplications.

Combined Average

When a main group is split into sub-groups, the sum of the combined totals of the sub-groups will always equate back to the total sum of the main parent group.

Given:

A varies directly as B and inversely as C

Formula used:

A ∝ ${B\over C}$

Calculation:

Let the value of C be X

According to the question

⇒ ${4\over 3}\ =\ {k} \ \times\ {{3\over 7}\over{9\over 14}}$

⇒ ${36\over 42}\ =\ {3k\over 7}$

⇒ k = 2

When, A = 4√3 and B = 30 then,

⇒ 4√3 = ${}30k\over X$

⇒ X = ${60\over 4√ {3}}$ = ${15\over √{3}}\ =\ {5\ \times √{3}\ \times √{3}\over √{3}}\ =\ 5√{3}$

∴ The required result will be 5√3.

Given:

The revenue in 2016, 2017, 2018, 2019, and 2020 = 250, 200, 280, 300, and 350 respectively

The expenditure in 2016, 2018, and 2019 = 175, 250, and 275 respectively

Formula used:

${GM\% =\ {GM\over TM}}\ × 100$     Where, GM = Gain marks, and TM = Total marks

Calculation:

According to the question

The total revenue of all the years = 250 + 200 + 280 + 300 + 350 = 1380

The 70% of the revenue = 1380 × 0.7 = 966

The total expediture = 175 + 250 + 275 =  700

The required percentage = ${966\ -\ 700\over 966}\ \times 100\ =\ 27.53\%$

∴ The required result will be 27.53%.

Given:

The total students = 72

Formula used:

${Average\ =\ {The\ sum\ of\ all\ the\ items\over The\ total\ number\ of\ items}}$

Calculation:

Let the number of girls be G

The number of boys = 1.4G

The total students = G + 1.4G = 2.4G

⇒ 2.4G = 72

⇒ G = 30

The number of boys = 72 - 30 = 42

The sum of the numbers of all the students = 58 × 72 = 4176

The sum of the numbers of all boys scored = 42 × A     Where A = Average numbers scored by boys

The sum of the numbers of all girls scored = 30 × 1.5A = 45A

⇒ 42A + 45A = 4176

⇒ 87A = 4176

The average number of boys = A = 48

The average numbers of girls = 48 × 1.5 = 72

∴ The required result will be 72.

Given:

The required expression: ${\sqrt[4]{24-16\sqrt{2}} } × {\sqrt{4+2\sqrt{2}} }$ 

Formula used:

(a - b)2 = a2 + b2 - 2ab

$\sqrt[n]{x^m} = x^{\frac{m}{n}}$

(a + b)(a - b) = a² - b²

Calculation:

The required expression can be written as:

⇒ ${\sqrt[4]{24-2\sqrt{8 \times 8 \times 2}} } × {\sqrt{4+2\sqrt{2}} }$

 

⇒ ${\sqrt[4]{24-2\sqrt{8 \times 16}} } × {\sqrt{4+2\sqrt{2}} }$

⇒${\sqrt[4]{16 + 8 -2\sqrt{8 \times 16}} } × {\sqrt{4+2\sqrt{2}} }$

⇒ ${\sqrt[4]{\sqrt{16}^2 + \sqrt{8}^2 -2\sqrt{8 \times 16}} } × {\sqrt{4+2\sqrt{2}} }$

⇒ ${\sqrt[4]{(\sqrt{16 } - \sqrt{8})^2 } } × {\sqrt{4+2\sqrt{2}} }$

⇒ ${\sqrt[4]{(4 - 2\sqrt{2})^2 } } × {\sqrt{4+2\sqrt{2}} }$

⇒ ${\sqrt{(4 - 2\sqrt{2}) } } × {\sqrt{4+2\sqrt{2}} }$

⇒ ${\sqrt{(4- (2\sqrt{2}))(4 + (2\sqrt{2})) } }$

⇒ ${\sqrt{(4^2- (2\sqrt{2})^2) } }$

⇒ ${\sqrt{(16 - 8) } }$

⇒ ${\sqrt{(8) } } = 2 \sqrt{2}$

∴ $2 \sqrt{2}$ is the required answer.

Given:

Reena sells an article at a profit = 28%

Formula used:

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

L = CP - SP     Where, L = Loss, SP = Selling price, and CP = Cost price

Calculation:

Let the cost price of the article be C

According to the question

The selling price of the article = 1.28C

If the cost price is 30% less = 0.7C

The new selling price = 1.28C - 20.10

The new profit = 1.35 × (0.7C)

⇒ 1.28C - 20.10 = 1.35 × (0.7C)

⇒ 1.28C - 20.10 = 0.945C

⇒ 1.28C - 0.945C = 20.10

⇒ 0.335C = 20.10

⇒ C = 60

The cost price = Rs. 60

The new selling price = Rs. 62.70

New profit percentage = ${62.70\ -\ 60\over 60}\ \times 100\ =\ 0.045\ \times 100\ =\ 4.5\%\ profit$

∴ The required result will be "4.5% profit".

Given:

The total number of toys manufactured = 1500

Formula used:

${GM\%\ =\ {GM\over TM}}\ × 100$     Where, GM = Gain marks, and TM = Total marks

Calculation:

The total E type of toys = 16 × ${1500\over 100}$ = 240

The cost price of the all toys type E = 240 × 260 = 62400

The revenue received on selling the toys E = 22 × ${400000\over 100}$ = 88000

The profit on selling the type E toys = 88000 - 62400 = 25600

The total number of toys A type = 20% of 1500 = 300

The total cost price of toys A type = 300 × 240 = 72000

The total number of toys D type = 25% of 1500 = 375

The total cost price of the toys type D = 375 × 210 = 78750

The total cost price of type A and type D toys = 72000 + 78750 = 150750

The required percentage = ${25600\over 150750} \times 100\ =\ 16.98\%\ \approx 17\%$

∴ The required result will be 17%.

Shortcut Trick

Let Marked Price (MP) = 100 units.

Initial SP = 100 − 36% = 64 units.

Initial CP = 64 ÷ 1.25 = 51.2 units.

New SP = (0.8 × Initial CP) × 1.25 = Initial CP = 51.2 units.

New Discount % = 100 − 51.2 = 48.8%.

∴ The correct answer is 48.8%.

Alternate Method

Given:

Initial Discount = 36%

Initial Profit = 25%

New Cost Price = Reduced by 20%

New Profit = 25% (same as before)

Formula Used:

Selling Price (SP) = Marked Price (MP) × (100 − Discount%) ÷ 100

Cost Price (CP) = SP × 100 ÷ (100 + Profit%)

Calculations:

⇒ Let the Marked Price (MP) be 100 units.

⇒ Initial Selling Price (SP) = 100 × (100 − 36) ÷ 100 = 64 units.

⇒ Initial Cost Price (CP) = 64 × 100 ÷ 125 = 51.2 units.

⇒ The new Cost Price is reduced by 20%, so New CP = 51.2 × 0.8 = 40.96 units.

⇒ The dealer earns the same profit of 25%, so New SP = 40.96 × 1.25 = 51.2 units.

⇒ (Notice that New SP = Initial CP, because reducing by 20% and increasing by 25% cancel out exactly: 0.8 × 1.25 = 1).

⇒ New Discount = Marked Price − New Selling Price = 100 − 51.2 = 48.8 units.

⇒ Required Discount Percentage = (48.8 ÷ 100) × 100 = 48.8%.

∴ The correct answer is 48.8%.

Additional Information

Relation between CP and MP

A direct relationship formula connects Cost Price and Marked Price: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Successive Discounts

When two consecutive discounts of a% and b% are offered, the effective single discount is calculated as (a + b − a×b ÷ 100)%. It always results in a lower effective discount than their straightforward arithmetic sum.

Mark Up Percentage

Mark up percentage is the percentage by which the Marked Price is set above the Cost Price. Mark Up % = (MP − CP) ÷ CP × 100.

Given:

The rate of interest = x% per annum

The sum = Rs. 18500

Formula used:

${SI\ =\ {P\ ×\ T\ ×\ R\over 100}}$     Where, SI = Simple interest, P = Principle, T = Time, and R = Rate

Calculation:

Let the rate of interest on the second sum be R

The second sum = 2 × 18500 = 37000

According to the question

⇒ $25900\ =\ {18500\ ×\ x\ × 3.5\over 100}\ +\ {37000\ ×\ (x\ +\ 2)\ ×\ 3.5\over 100}$

⇒ ${25900\ =\ {18500\ ×\ 3.5\over 100}\ ×\ (x\ +\ 2x\ +\ 4)}$

⇒ 25900 = (185 × 3.5) × (3x + 4)

⇒ 25900 = 647.5 × (3x + 4)

⇒ 25900 = 1942.5x + 2590

⇒ 1942.5x = 25900 - 2590

⇒ 1942.5x = 23310

⇒ x = ${23310\over 1942.5}\ =\ 12\%$

The rate of interest for the second sum = 12 + 2 = 14%

∴ The required result will be 14%.

Given:

The numbers = 5758, 6610, and 8101

Concept:

HCF is the highest common factor of two or more numbers.

if three no's are divided by the same no the remainder will be the same. It is a concept

Let's take three numbers N1, N2, and N3

N1 = ax + r

N2 = ay + r

N3 = az + r

Where a is a divisor (This will be the HCF), x, y and z are quotients and r is a remainder.

By subtracting the equations we will get-

N1 - N2 = a(x-y)

N2 -N3 = a(y-z)

N3 - N1 = a (z-x)

Calculation:

According to the question

Taking difference

⇒ 6610 - 5758 = 852

⇒ 8101 - 6610 = 1491

⇒ 8101 - 5758 = 2343

The HCF of the (852, 1491, and 2343) = 213

The greatest number = x = HCF = 213

The remainder is obtained when 5758, 6610, and 8101 are divided by x leaving y = 7 as the remainder.

The value of (x - 5y) = 213 - (5 × 7) = 213 - 35 = 178

∴ The required result will be 178.

Given:

The ∠B = 104°

Formula used:

Opposite angles of the cyclic quadrilateral = 180° 

Calculation:

In given cyclic quadrilateral ABCD

⇒ ∠ABC + ∠ADC = 180° 

⇒ ∠ADC = 180° - 104° = 76° 

Since PA is tangent on the circle at point A and AC is the cord which is subtending the angle ∠D = 76°

 

The angle between a tangent and a chord of a circle is equal to the angle subtended by the chord in the alternate segment of the circle.

In this case, the tangent at point A (line segment PA) and chord AC subtend ∠PAC in the alternate segment, which is equal to the angle ∠D subtended by the same chord AC. Therefore, ∠PAC = ∠D = 76°.

⇒ ∠PAC = ∠D = 76°

Also,

⇒ ∠PAC  =  ∠PCA, (As PA and PC are the tangents of A and C) 

⇒ ∠PAC = ∠PCA = ∠ADC = 76°    

In ΔPAC

⇒ ∠PAC + ∠PCA + ∠APC = 180° 

⇒ 76° + 76° + ∠APC = 180° 

⇒ ∠APC = 180° - 152° = 28° 

∴ The required result will be 28°.

Given:

The cost of a notebook is 80% more than the cost of a pen

Therefore the ratio of CP of notebook and pen will be,

${Notebook\over Pen } = {180\over100} = {9\over5}$

Therefore cost of 1 Notebook = 9x

Cost of 1 Pen = 5x

Now as per the question, the cost of 5 notebooks and 8 pens is ₹6 more than the cost of 13 pens and 2 notebooks,

Therefore,

(9x * 5) + (5x * 8) = 85x - 6 = (5x * 13) + (9x * 2) 

85x - 6 = 83x

2x = 6

x = 3

Therefore cost of 3 pens and 4 notebooks will be -

15x + 36x = 51x 

Where x = 3

Therefore cost of 3 pens and 4 notebooks will be (51 * 3) = ₹153.

Given:

The number = 760x93y

Concept:

A number is divisible by 8 if last 3 digits of the number divisible by 8

A number is divisible by 9 if the sum of the digit of the number divisible by 9

Calculation:

For divisibility rule of 8

The last three digits of the number = 93y

The possible value of y = 6

For divisibility rule of 9

The sum of the digit of the number = 7 + 6 + 0 + x + 9 + 3 + 6 = 31 + x

The possible value of x = 5,

Then,

⇒ (3x - 2y) = (3 × 5) - (2 × 6) = 15 - 12 = 3

∴ The required result will be 3.

Shortcut Trick

Ratio of Time Upstream (T_u) to Time Downstream (T_d) = 2.5 : 1 = 5 : 2.

Since Distance is constant, Speed is inversely proportional to Time.

Ratio of Speed Downstream (S_d) to Speed Upstream (S_u) = 5 : 2.

Speed of Boat in Still Water (u) = (S_d + S_u) ÷ 2 = (5 + 2) ÷ 2 = 3.5 units.

Required Ratio (u : S_d) = 3.5 : 5 = 7 : 10.

∴ The correct answer is 7 : 10.

Alternate Method

Given:

Let Speed of Boat in Still Water be u and Speed of Stream be v.

Speed Downstream (S_d) = u + v | Speed Upstream (S_u) = u − v.

Time Upstream (T_u) = 2.5 × Time Downstream (T_d).

Calculations:

⇒ Distance = Speed × Time

⇒ (u − v) × T_u = (u + v) × T_d

⇒ (u − v) × 2.5 × T_d = (u + v) × T_d

⇒ 2.5u − 2.5v = u + v

⇒ 1.5u = 3.5v ⇒ u/v = 3.5/1.5 = 7/3

⇒ Let u = 7k and v = 3k.

⇒ Speed Downstream (S_d) = u + v = 7k + 3k = 10k.

⇒ Ratio of u : S_d = 7k : 10k = 7 : 10.

∴ The correct answer is 7 : 10.

Additional Information

Relative Speed in Water

Downstream speed is the sum of boat speed and stream speed (u + v), while upstream speed is the difference (u − v).

Speed of Boat and Stream

Speed of boat in still water (u) = (S_d + S_u) ÷ 2 and Speed of stream (v) = (S_d − S_u) ÷ 2.

Inverse Proportion Rule

When distance is constant, the ratio of speeds is the inverse of the ratio of times taken: S₁/S₂ = T₂/T₁.

The correct answer is 19%.

Concept:

Resistance (R): 

• Resistance is a measure of the opposition to current flow in an electrical circuit.
• It is measured in ohms (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 decrease in length, let us take new length = L', radius of wire = r' and new resistance = R'

L' = 90 L/ 100 = 9L/10( since there is 10% 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 = 10 r2 / 9  

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

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

= $\rm \frac{\frac{\rho L}{\pi r^2}-\frac{\rho 9 L \times 9}{10\times10\pi r^2}}{\frac{\rho L}{\pi r^2}}\times 100$

= $\rm \frac{\frac{\rho L}{\pi r^2}-\frac{81\rho L}{100\pi r^2}}{\frac{\rho L}{\pi r^2}}\times 100$

= $\rm \frac{\frac{100 \rho L-81 \rho L}{100 \pi r^2}}{\frac{\rho L}{\pi r ^2}}\times 100$

= $\rm \frac{19 \rho L}{\pi r^2}\times \frac{\pi r^2}{\rho L}\times 100$

= 19%

Thus, the decrease in length is 19%.

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.

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 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 kerosene with respect to glass:

• n = refractive index of glass / refractive index of kerosene = $\frac{1.44}{1.50}$ = 0.96
• Greater the refractive index, the denser the medium.
• Thus, glass (1.50) is denser than kerosene (1.40).
• 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 glass to kerosene, it will move away from the normal.

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

The correct answer is Element 'A' is a metal: gas evolved is hydrogen.

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:

Metals react with dilute acids to give salt and hydrogen gas. 

When element 'A' reacts with dilute hydrochloric acid, bubbles of a colourless gas evolve that burn with a pop sound.

The gas is hydrogen, which is inflammable because it will burn on bringing a lit matchstick near it.

So, element A is a metal.

Additional Information Chemical properties of metals:

• The metal reacts with oxygen to form metal oxide.
• The metal reacts with an acid to form a salt and hydrogen gas.
• Metals react with water to form oxides or hydroxides.
• Metals do not react with alkalis.

The correct answer is 1.80m.

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 centimetres.
• 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 = $\frac{1}{p}$ = $\frac{100}{5}$ = 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 second convex  lens, L2

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

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

v = ?

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

$\frac{1}{20} = \frac{1}{v} - \frac{1}{-30}$

$\frac{1}{20} = \frac{1}{v} + \frac{1}{30}$

$\frac{1}{20} - \frac{1}{30} = \frac{1}{v}$

$\frac{1}{v} = \frac{3-2}{60} = \frac{1}{60}$

v= 60 cm 

Distance between original object and final image = 30 + 90 + 60 = 190 cm = 1.80 m.

The correct answer is On river Narmada.

Concept:

Dam:

• A dam is a structure built across a river or stream to hold backwater.
• Ancient dam builders used natural materials such as rocks or clay.
• Modern-day dam builders often use concrete.

Importance of dams:

• Manmade dams create artificial lakes called reservoirs.
• Reservoirs can be used to store water for farming, industry, and household use.
• They also can be used for fishing, boating, and other leisure activities. People have used dams for many centuries to help prevent flooding.

Explanation:

Sardar Sarovar Project:

• Sardar Sarovar Dam (SSD), on the Indian Narmada river, is located in the village of Kevadia in the state of Gujarat.
• The Sardar Sarovar Project is one of the largest water resources projects in India covering four major states - Maharashtra, Madhya Pradesh, Gujarat, and Rajasthan.
• The dam will be the third-highest concrete dam (163 meters) in India, the first two being Bhakra (226 meters) in Himachal Pradesh and Lakhwar (192 meters) in Uttarakhand.
• The reservoir would occupy an area of 37,000 ha. and would have a linear stretch of 214 kilometres of water and an average width of 1.77 kilometres.

Additional Information

The correct answer is inter-cropping.

Concept:

• Agriculture: It is the practice of growing crops and rearing animals.
• Crop: A crop is a plant that can be grown and harvested extensively for profit or subsistence.

Explanation:

Inter-cropping:

• Intercropping is defined as the agricultural practice of growing two or more crops on the same field at the same time in a specific pattern.
• Crops selected for intercropping normally have different abilities to use the resources available for growth.
• This leads to yield advantages and increased stability compared to a single crop in a low input system.

Additional InformationSustainable farming: 

• It is farming that meets the needs of existing and future generations, while also ensuring profitability, environmental health, and social and economic equity.
• It favours techniques that emulate nature–to preserve soil fertility, prevent water pollution and protect biodiversity.

Mixed cropping:

• It involves the growing of two or more species or cultivars of the same species simultaneously in the same field but not in a fixed pattern.
• It is done to reduce the risk of crop failure due to unfavourable conditions.

Crop rotation:

• It is the successive cultivation of different crops in a specified order on the same fields.
• Usually, leguminous plants are grown in between cereals to replenish the nutrients in the soil.

The correct answer is 'X' is aluminium hydroxide; 'Y' is sulphuric acid.

Concept:

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:

• Substance 'X' turns red litmus blue: It is a base.
• Substance 'Y' turns blue litmus red: It is an acid.

Given: 'X' and 'Y' react with each other to form water and aluminium sulphate. 

X + Y → H₂O + Aluminium sulphate. 

Acid and base react together to form salt and water. 

The correct answer is 1.0 m; 1.0 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 = hi / ho 

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 = -3 m, focal length, f = 1.5 m, height of object, ho = 3 cm

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

$\frac{1}{1.5} = \frac{1}{v} + \frac{1}{-3}$

$\frac{1}{1.5} = \frac{1}{v} - \frac{1}{3}$

v = 1 m

m = $\frac{hi}{ho} = \frac{-v}{u}$

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

hi = 1 cm

The image is formed at v = 1 m and its height hI = 1 cm.

The correct answer is It is a salt of strong acid and a weak base.

Concept:

• Acid: The substances sour in taste that turn blue litmus red.
• Base: The substances are bitter in taste, soapy to touch, and turn red litmus blue.
• Salt: The substances formed by the reaction between an acid and a base.

Explanation:

Strong Acids: 

• An acid that ionizes completely to give H⁺ ions in its aqueous solution.
• Examples: Hydrochloric acid, sulphuric acid, etc.

Weak acid:  

• An acid that ionizes partially in a solution and gives off only a few of its H⁺ ions.
• Examples: acetic acid, citric acid, etc.

Strong Base:

• A base that ionizes completely to give OH^- ions in its aqueous solution.
• Examples: Sodium hydroxide, potassium hydroxide, etc

Weak base:

• A base that ionizes partially in a solution and gives off only a few of its OH^- ions.
• Examples: magnesium hydroxide, ammonium hydroxide, etc.

Ammonium chloride is formed when ammonium hydroxide (a weak base) reacts with hydrochloric acid (a strong acid). 

Thus, it is a salt of strong acid and a weak base.

The correct answer is ductile and an electrical conductor.

Concept:

Metals: Elements that have a tendency to lose electrons are called metals.

Physical Properties of metals:

• State: Metals are solids at room temperature with the exception of mercury, which is liquid at room temperature.
• Luster: Metals have the quality of reflecting light from their surface and can be polished e.g., gold, silver, and copper.
• Malleability: Metals have the ability to withstand hammering and can be made into thin sheets known as foils.
• Ductility: Metals can be drawn into wires.
• Conduction: Metals are good conductors because they have free electrons. Silver and copper are the two best conductors of heat and electricity.
• Density: Metals have high density and are very heavy. Iridium and osmium have the highest densities whereas lithium has the lowest density.
• Melting and Boiling Points: Metals have high melting and boiling points. Tungsten has the highest melting and boiling points whereas mercury has the lowest.

Explanation:

Copper is metal that can be drawn into wires and conduct electricity. 

Thus, it is used to make wires for electrical connections. 

Additional Information Physical properties of non-metals:

• State: They are solids or gases at room temperature with exception of Bromine which is a liquid.
• Dullness: They are dull and do not possess any kind of lustre.
• Malleability: They are non-malleable.
• Ductility: They are non-ductile.
• Conduction: They are bad conductors of heat and electricity.
• Density: They have low density.
• Melting and Boiling Points: They have low melting and boiling point.

The correct answer is V1 ∶ V2 ∶ V3 = 225 ∶ 25 ∶ 9.

Concept:

Ohm's Law:

• It states that the potential difference between two points is directly proportional to the current passing through the conductor, provided the temperature remains the same.
• V = IR, where V = potential difference between two points, I = current, R = Resistance.

Resistance:

• The property of a substance to resist the flow of current through it.
• R = ρ L / A, where ρ = resistivity, L = length of conductor, and A = area of cross section.

Explanation:

The current remains the same in series combination. 

Let the current flowing through the wire be I ampere. 

For Wire AC

Length = L, Radius = r, Area of cross- section = π r2

Resistance, R1 =  $\frac{\rho L}{\pi r^2}$

Voltage, V1 = I R1 = $\frac{I\rho L}{\pi r^2}$

For Wire CD

Length = L, Radius = 3r, Area of cross- section = 9π r2

Resistance, R2 =  $\frac{\rho L}{9\pi r^2}$

Voltage, V2 = I R2 = $\frac{I\rho L}{9\pi r^2}$

For Wire BD

Length = L, Radius = 5r, Area of cross- section = 25π r2

Resistance, R1 =  $\frac{\rho L}{25\pi r^2}$

Voltage, V3 = I R3 = $\frac{I\rho L}{25\pi r^2}$

The ratio V1: V2 : V3 = $\frac{I\rho L}{\pi r^2}$ :  $\frac{I\rho L}{9\pi r^2}$  :  $\frac{I\rho L}{25\pi r^2}$ = 1 : 1/9 : 1/25 = 225 : 25 : 9. 

V1 ∶ V2 ∶ V3 = 225 ∶ 25 ∶ 9.

The correct statements are All (i), (ii), and (iii) are correct.

Concept:

Magnetic field:

• The area around a magnet where a magnetic force is experienced is called the magnetic field.
• It is a quantity that has both direction and magnitude, (i.e., Vector quantity).

Explanation:

Magnetic field around a straight wire:

• The nature of the magnetic field lines around a straight current-carrying conductor is concentric circles with the center at the axis of the conductor.
• The strength of the magnetic field is directly proportional to the current (I) through the conductor. B ∝ I
• The strength of the magnetic field is inversely proportional to the distance (r). B ∝ 1/r
• The direction of the magnetic field lines of force around a conductor is given by Maxwell’s right-hand rule.​

​

Maxwell’s right-hand rule:

• ​Imagine that you are holding a current-carrying straight conductor in your right hand such that the thumb points towards the direction of the current.
• Then your fingers will wrap around the conductor in the direction of the field lines of the magnetic field.

The correct answer is 16/49.

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 (r Ω), B (2r Ω), and C (4r Ω) are connected in parallel.

Equivalent resistance, 1/R1 = 1/r + 1/2r +1/4r = 4+2+1/ 4r = 7/4 r 

R₁= 4r/7

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

R₂ = 4r/7 + r + 2r + 4r = (4r + 7r + 14r + 28r) / 7 = 53r / 7

Equivalent current, I in the circuit = V/R₂ = $\frac{7E}{53r}$

The potential difference across C, V' = IR₁ = $\frac{7E}{53r}$  ×  $\frac{4r}{7}$ = 4E / 53

P_D = I2D =

 $\rm (\frac{7E}{53r})^2 \times r = \rm \frac{49E^2 × r}{53r ×53r}$  = 49E2/ 53 × 53r  (since current remains same in series combination)

P_A = V'2/A =  $\frac{(\frac{4E}{53})^2}{r}$  =  16E2/ 53 × 53 × r (since voltage remains same in parallel combination)

P_A/ P_D = $\rm \frac{\frac{16E^2}{53 × 53 × r}}{\frac{49 E^2}{53 × 53 × r}}$ = $\frac{16E^2 × 53r × 53}{49 E^2× 53 × 53r}$ = 16 / 49

The ratio (P_A/P_D) = 16/49.

The correct answer is A mass of undifferentiated cells.

Concept:

**Tissue culture:**​

• It is the cultivation of plant cells, tissues, or organs on specially formulated nutrient media.
• Under the right conditions, an entire plant can be regenerated from a single cell.

Explanation:

The process of tissue culture:

• The explant is removed from the parent plant.
• Then, the totipotent cells are extracted from the explant.
• These cells are given nourishment, consisting of sucrose, vitamins, and micronutrients with the plant hormones like auxins, cytokinin, etc.
• The cells divide and develop as a callus, and the callus further divides and grows as small plantlets.
• Once the plantlets are grown, they are moved to the nurseries for further growth.

Important terms: