MP Police Constable : (6 Nov 2025, Shift 1) Memory-Based Paper (Previous Year Paper)

The correct answer is Option 3.

Key Points

• Fundamental rights available to citizens not to foreigners:
• Prohibition of discrimination on grounds of religion, race, caste, sex or place of birth (article 15).
• Equality of opportunity in matters of public employment (article 16).
• Protection of six rights regarding freedom of (speech and expression, (ii) assembly (iii) association, (iv) movement (v) residence and profession (article 19).
• Protection of language, script and culture of minorities (article 29).
• Right of minorities to establish and administer educational institutions (article 30).

Additional Information 

• Fundamental rights are enshrined in part III of the constitution from article 12 to 35.
• These rights are taken from the constitution of USA.
• These rights are provided to all the citizens of the country without any discrimination.
• These rights made the part III of the Indian constitution as the Magna-Carta of India.

The correct answer is Oriental Bank of Commerce.

Key Points

• Global Trust Bank (GTB) was merged with Oriental Bank of Commerce (OBC) on July 24, 2004, under the directive of the Reserve Bank of India (RBI).
• This merger was prompted due to financial instability and irregularities in GTB's operations, which caused a decline in depositor confidence.
• Oriental Bank of Commerce took over the assets and liabilities of Global Trust Bank, ensuring continuity for customers and stakeholders.
• The merger was undertaken to protect the interests of depositors, ensure stability in the banking sector, and strengthen the financial system.
• Post-merger, OBC became one of the stronger banks in India, benefiting from GTB’s branch network and customer base.

Additional Information

• Global Trust Bank:
• GTB was established in 1994 as a private sector bank in India.
• It was known for its aggressive growth strategy but faced issues due to non-performing assets (NPAs) and financial mismanagement.
• By 2004, the bank faced a severe liquidity crisis, leading to its merger with OBC.
• Oriental Bank of Commerce (OBC):
• OBC was founded in 1943 and became one of India’s leading public sector banks.
• It played a critical role in ensuring depositor safety during the merger with GTB.
• In April 2020, OBC itself merged with Punjab National Bank (PNB) as part of the Indian government’s banking consolidation plan.
• Role of the Reserve Bank of India (RBI):
• RBI played a pivotal role in orchestrating the GTB-OBC merger to maintain stability in India’s banking sector.
• The RBI’s intervention aimed to safeguard depositors’ interests and restore public confidence in the banking system.
• Banking Consolidation in India:
• The merger of GTB and OBC was one of the early steps in India’s broader banking sector reforms.
• In recent years, the Indian government has consolidated several public sector banks to enhance their financial strength and operational efficiency.

The correct answer is Troposphere.

• Almost all the clouds are found in the Troposphere.

Key Points

• Troposphere
• The troposphere is the lowest portion of Earth’s atmosphere and contains approximately 80% of the atmosphere’s mass and 99% of its water vapour and aerosols.
• The average depth of the troposphere is approximately 17 km in the middle latitudes.
• The characteristic features of the Troposphere are its great density.
• In addition to nitrogen and oxygen, carbon dioxide, and water vapour (nearly all of the water vapour contained in the atmosphere is concentrated in the troposphere) and numerous particles of various origin
• It thickness of the Troposphere is maximum at the equator, deeper in the tropics, up to 20 km, and shallower near the polar regions, at 7 km in summer, and indistinct in winter.
• In India, it is taken to be around 16 Kilometers.
• The thickness of the troposphere and consequently the atmosphere is maximum at the equator.
• Almost all the clouds are found in the troposphere.

Additional Information

• Stratosphere
• It is the second layer of the atmosphere found above the troposphere.
• It extends up to 50 km in height.
• This layer is very dry as it contains little water vapour.
• This layer provides some advantages for flight because it is above stormy weather and has steady, strong, horizontal winds.
• The ozone layer is found in this layer.
• The ozone layer absorbs UV rays and safeguards the earth from harmful radiation.
• Stratopause separates Stratosphere and Mesosphere.
• Mesosphere
• It is the coldest of the atmospheric layers.
• The mesosphere starts at 50 km above the surface of Earth and goes up to 85 km.
• The temperature drops with altitude in this layer.
• By 80 km it reaches -100 degrees Celsius.
• Meteors burn up in this layer.
• Mesopause separates Mesosphere and Thermosphere.
• Thermosphere
• This layer is found above Mesopause from 80 to 400 km.
• Radio waves that are transmitted from the earth are reflected by this layer.
• The temperature increases with height.
• Satellites occur in this layer.
• Exosphere
• It is the outermost layer of the atmosphere.
• The zone where molecules and atoms escape into space is mentioned as the exosphere.
• It extends from the top of the thermosphere up to 10,000 km.

The correct answer is Madhya Pradesh.

Key Points

• Matki dance is a traditional folk dance form from Madhya Pradesh, India.
• This dance is performed primarily by the womenfolk of the Malwa region of Madhya Pradesh.
• The dance is characterized by the intricate balancing of earthen pots (Matkis) on the head.
• It is generally performed on festive occasions and social gatherings.

Additional Information

• Folk Dances of Other States:
• Punjab: Punjab is famous for its energetic dance forms like Bhangra and Gidda. Bhangra is a vibrant dance performed by men, while Gidda is performed by women.
• Gujarat: Gujarat is renowned for its colorful dance forms such as Garba and Dandiya Raas. These dances are performed during the Navratri festival.
• Maharashtra: Lavani is a popular folk dance of Maharashtra known for its powerful rhythm and sensuous movements. It is performed to the beats of traditional music.
• Matki Dance:
• Matki dance involves women dressing in traditional attire and performing graceful movements while balancing earthen pots on their heads.
• The performance often includes multiple participants and may involve the stacking of pots to showcase skill and balance.
• The dance is a celebration of femininity, grace, and the cultural heritage of the Malwa region.
• It is an integral part of various cultural and social events, including weddings and festivals.

The correct answer is Banihal Pass.

Key Points

• Banihal Pass has been created by the Indus River. It is a narrow pass between two mountains generated by a water body. It is located in the Pirpanjal ranges of Jammu and Kashmir.
• The Indus River is located in three countries: China, India, and Pakistan.
• The river flows for about 3180.14 km.
• It is fed by many smaller tributaries during its course.
• The Indus River Basin covers nearly 1,165,495.5 square kilometers.
• The Indus is a transboundary river of Asia and a trans-Himalayan river of South and Central Asia. The 3,120 km river rises in mountain springs northeast of Mount Kailash in Western Tibet,

Additional Information

• Bara-lacha la also known as Bara-lacha Pass, or Bārā Lācha La, is a high mountain pass in the Zanskar range of Northern India, connecting the Lahaul district in Himachal Pradesh to Leh district in Ladakh.
• Nathu La is a mountain pass in the Dongkya Range of the Himalayas between China's Yadong County in Tibet, and the Indian states of Sikkim and West Bengal in Bengal, South Asia. The pass, at 4,310 m, connects the towns of Kalimpong and Gangtok to the villages and towns of the lower Chumbi Valley.
• Rohtang Pass is a high mountain pass on the eastern end of the Pir Panjal Range of the Himalayas around 51 km from Manali in the Indian state of Himachal Pradesh. It connects the Kullu Valley with the Lahaul and Spiti Valleys of Himachal Pradesh, India.

Thus, Banihal Pass has been created by the Indus river.

The correct answer is Narmada.

Key Points

• Rani Avantibai Lodhi Sagar Project (Bargi dam) has been built on Naramda river in Jabalpur district.
• The total installed capacity of the Bargi hydroelectric project: 100 MW.
• It was commissioned in 1990.
• It was the first major reservoir to be built on the Narmada river in Madhya Pradesh.
• It irrigated 4.37 lakh hectares of land.
• **It is one of the first completed dams out of the chain of 30 major dams to be constructed on the Narmada River in Madhya Pradesh.**​

Additional Information

• Narmada is the largest river in Madhya Pradesh, flowing towards the west and falling in the Arabian Sea.
• Its total length is 1312 km of which it covers 1077 km in Madhya Pradesh.

The correct answer is Diana Edulji.

Key Points

• Diana Edulji became the first Indian woman to be inducted into the prestigious ICC Hall of Fame.
• She was a pioneering figure in Indian women's cricket and captained the Indian women's team during her career.
• Diana Edulji played for India from 1976 to 1993, establishing herself as one of the most successful Indian cricketers of her time.
• She was widely known for her left-arm spin bowling and her immense contribution to popularizing women's cricket in India.
• Edulji has also been recognized with the Padma Shri, one of India's highest civilian honors, for her contribution to sports.

Additional Information

• ICC Hall of Fame
• The ICC Hall of Fame was launched in 2009 by the International Cricket Council to recognize the greatest cricket players in history.
• It honors players who have made significant contributions to the game of cricket at the international level.
• Inductees are selected by a special committee of cricket experts and historians.
• It includes players from all cricket-playing nations, highlighting their achievements and legacy in the sport.
• Diana Edulji's Career Stats
• Edulji played 20 Test matches for India, taking 63 wickets at an average of 25.77.
• In 34 ODIs, she took 46 wickets and was instrumental in many of India's victories.
• She was also known for her leadership, captaining India in multiple international matches.
• Women's Cricket Milestones
• India's women's cricket team played their first Test match in 1976, with Diana Edulji as a key player.
• The team has since grown significantly, making notable achievements such as reaching the finals of the ICC Women's World Cup in 2005 and 2017.
• Other Indian ICC Hall of Fame Inductees
• Other Indian cricketers in the ICC Hall of Fame include Sunil Gavaskar, Kapil Dev, Anil Kumble, Rahul Dravid, and Sachin Tendulkar.
• These players have been recognized for their outstanding contributions to Indian and world cricket.

The correct answer is Narmada. 

Key Points

• Narmada river flows in Rift Valley.
• Narmada is the largest west-flowing river in peninsular India.
• Narmada flows westwards through a rift valley between the Vindhyan Range on the north and the Satpura Range on the south.
• It rises from the Maikala range near Amarkantak in Madhya Pradesh.

Additional Information

• Rift Valley
• A rift valley is a lowland region that forms where Earth’s tectonic plates move apart or rift.
• Rift valleys are found both on land and at the bottom of the ocean and are created by the process of seafloor spreading.
• The Tapti River and Mahi River also flow through rift valleys, but between different ranges.

The correct answer is 6.9%.

In News

• ICRA projects India’s GDP growth rate to be 6.9% in Q4 of FY2025, an increase from 6.2% in Q3 FY2025.

Key Points

• India’s GDP is expected to grow by 6.9% in Q4 FY2025 according to ICRA.
• This growth is higher than the 6.2% recorded in Q3 FY2025.
• Earlier quarters’ GDP growth were 6.7% (Q1) and 5.6% (Q2) of FY2025.
• The National Statistical Office (NSO) estimates a higher growth rate of 7.6% for Q4 FY2025.
• Full-year GDP growth for FY2025 is projected at 6.3%, significantly lower than 9.2% in FY2024.

Additional Information

• ICRA
• Indian credit rating agency providing economic forecasts and analysis.
• Offers projections on GDP, inflation, and market trends.
• National Statistical Office (NSO)
• Government agency responsible for official statistics on GDP and economy.
• Estimates a Q4 FY2025 growth rate of 7.6%, higher than ICRA’s projection.
• GDP Growth Trends FY2025
• Q1 (April-June): 6.7%
• Q2 (July-September): 5.6%
• Q3 (October-December): 6.2%
• Q4 (January-March): 6.9% (ICRA projection)
• Full Year Projections
• FY2025 expected GDP growth: 6.3%
• FY2024 recorded GDP growth: 9.2%

The correct answer is Manipur.

Key Points

• The Lai Haraoba Festival is a traditional festival celebrated primarily in the Indian state of Manipur.
• It is one of the oldest and most important festivals of the Meitei community in Manipur.
• The festival is celebrated to honor the deities known as Umang Lai, the local forest gods.
• Lai Haraoba, meaning "merry making of the gods," reflects the rich cultural heritage and history of the Manipuri people.

Additional Information

• Lai Haraoba Festival
• This festival is a ritualistic celebration that involves various cultural performances, including traditional dances, music, and enactments of myths and legends.
• The festival usually extends for several days, sometimes up to a month, with different activities scheduled for each day.
• The primary performers in the festival are the Maibas (priests) and Maibis (priestesses) who perform rituals and dance sequences narrating the creation stories and legends of the gods.
• The festival is also marked by the participation of the local community, who come together to celebrate and preserve their cultural identity.
• Meitei Community
• The Meitei people are the predominant ethnic group in Manipur, with a rich cultural and historical background.
• They have their own language, Meiteilon (Manipuri), which is one of the 22 scheduled languages of India.
• Besides Lai Haraoba, the Meitei community celebrates other significant festivals such as Yaoshang (Holi), Ningol Chakouba, and Cheiraoba.
• Their traditional art forms include Manipuri dance, which is one of the classical dance forms of India, and Thang Ta, an ancient martial art.

The correct answer is 1 November 1956.

Key Points

• Madhya Pradesh came into existence on 1 November 1956.
• Madhya Pradesh is the second-largest Indian State in size.
• In 1950, Madhya Bharat was created from former British Central Provinces.
• The new states of Madhya Pradesh, Vindhya Pradesh, and Bhopal were formed from central Indian agency,
• In 1956, the states of Madhya Bharat, Vindhya Pradesh, and Bhopal were merged into Madhya Pradesh, and Bhopal became the capital.
• In November 2000, the southeastern portion of the state was split off after as the 26^th state Chhatisgarh, a new state with the capital Raipur.

Important Points

• ​​As of February 2022:

Concept:

• Olympic is an international multi-sportings event.
• It is held once every four years.
• It includes several countries' selected players as participants.

Explanation:

Olympic History:

• In the year, 1920 at the Games in Antwerp, the Olympic flag was hoisted for the first time in an Olympic stadium.
• It was the idea of Pierre de Coubertin.
• He presented it to the Olympic Congress in the year 1916 but due to the First world war, it was suspended.

Thus, the Olympic Flag was first hoisted at Antwerp(1920).

Additional InformationOlympic logo:             

• It consists of five rings and one icon of the place where it is held
• Blue, yellow, black, green, and red is the order of the color of  the Olympic logo rings
• It represents five continents: Asia, Africa, America, Australia, and Europe.

The correct answer is Option 2: 4, 3, 1, and 2.

Key Points

• Delhi Sultanate: The Delhi Sultanate was established in the early 13^th century and lasted until the 16^th century. It consisted of five major dynasties: the Khalji Dynasty, Tughluq Dynasty, Sayyid Dynasty, and Lodi Dynasty.
• Order of Dynasties: The ruling dynasties of Delhi followed this sequence:
• Khalji Dynasty (1290-1320): This dynasty was founded by Jalal-ud-din Khalji and is known for expanding the Sultanate's territory and implementing military reforms.
• Tughluq Dynasty (1320-1414): Established by Ghiyas-ud-din Tughluq, this dynasty is notable for its administrative innovations and ambitious projects, such as shifting the capital to Daulatabad.
• Sayyid Dynasty (1414-1451): The Sayyid Dynasty ruled during a politically fragmented period and is considered relatively weaker compared to the previous dynasties.
• Lodi Dynasty (1451-1526): The last ruling dynasty of the Delhi Sultanate, the Lodis were eventually defeated by Babur at the Battle of Panipat, marking the beginning of the Mughal Empire.

Hence, the sequence is Option 2: Khalji, Tughluq, Sayyid, and Lodi.

• This historical order reflects the chronological progression of the dynasties that ruled over Delhi. Hence, the answer is correct.

Additional Information

• Khalji Dynasty:
• Founder: Jalal-ud-din Khalji in 1290.
• Key Ruler: Alauddin Khalji, known for his military conquests and market reforms.
• Significant Events: Expansion of the Sultanate into southern India and implementation of economic reforms.
• Tughluq Dynasty:
• Founder: Ghiyas-ud-din Tughluq in 1320.
• Key Ruler: Muhammad bin Tughluq, known for his ambitious but often unsuccessful projects like shifting the capital to Daulatabad.
• Notable Achievements: Administrative innovations and territorial expansion.
• Sayyid Dynasty:
• Founder: Khizr Khan in 1414.
• Key Characteristics: Weak central authority and limited territorial control.
• Lodi Dynasty:
• Founder: Bahlul Lodi in 1451.
• Key Ruler: Sikandar Lodi, known for his administrative capabilities and urban development.
• End of Dynasty: Defeated by Babur at the Battle of Panipat in 1526, leading to the establishment of the Mughal Empire.

Important Points

• Impact on Indian History:
• The Delhi Sultanate laid the foundation for centralized administration and the integration of northern India under Islamic rule.
• The Sultanate's rulers introduced architectural and cultural developments that significantly influenced Indian civilization.
• Transition to Mughal Empire:
• The defeat of the Lodis at the Battle of Panipat marked the end of the Delhi Sultanate and the beginning of Mughal rule in India.

The correct answer is Silchar and Porbander.

Key Points

• The East-West Corridor is a part of the larger Golden Quadrilateral project aimed at connecting the eastern and western parts of India through a high-speed road network.
• This corridor specifically links Silchar in Assam in the East to Porbandar in Gujarat in the West.
• The project is one of the most ambitious infrastructure projects in India, intended to facilitate faster transportation and contribute to the economic development of the regions it connects.
• The total length of the East-West Corridor is approximately 3,300 kilometers, making it one of the longest road projects in India.
• It is implemented by the National Highways Authority of India (NHAI) under the Ministry of Road Transport and Highways.

Additional Information

• The Golden Quadrilateral is a highway network connecting most of the major industrial, agricultural, and cultural centers of India.
• It forms a quadrilateral linking the four major metropolitan cities of India: Delhi, Mumbai, Chennai, and Kolkata.
• Overall, the Golden Quadrilateral covers a distance of about 5,846 kilometers, making it one of the largest highway projects in the world.
• The project aims to reduce travel times, improve cargo movement, and connect rural and urban areas for economic growth.

The correct answer is Viswanathan Anand.

• Viswanathan Anand was the first recipient of the award.
• He was honoured for the performance in the year 1991–92

Important Points

About Rajiv Gandhi Khel Ratna Award

• It is the highest sporting honour of India.
• The recipient(s) is/are honoured for their outstanding performance in the field of sports over a period of four years at an international level.
• It was instituted in 1991–92.
• The award comprises a medallion, a certificate, and a cash prize of Rs 25 lakh.
• Abhinav Bindra is the youngest recipient of the award.

Additional Information

• For the year 2020 five sportspersons received the Rajiv Gandhi Khel Ratna on the occasion of the National Sports Day on 29^th August.

The correct answer is A and B only

In-situ Conservation

• It is the method of conserving all the species, especially the wild and endangered species in their natural habitats and environment.
• In-situ conservation of Biodiversity includes biosphere reserves, national parks, wildlife sanctuaries, etc. Hence option A and B is correct.

Ex-situ Conservation

• In this method of conserving the species, the artificial habitats are created which reflect their natural living habitats.
• Ex-situ Conservation of Biodiversity comprises of aquariums, botanical gardens, Cryopreservation, DNA banks, zoos, etc.

The correct answer is 1958.

Key Points

• The Madhya Pradesh Public Service Commission conducted the examination for the first time in 1958.
• Madhya Pradesh Public Service Commission was formed on 1^st November 1956 as per section 118(3) of the State Reorganization Act.
• DV Rege was the first Chairman of the Madhya Pradesh State Public Service Commission (MPPSC).
• Headquarters: Indore.
• The present Chairman of MPPSC is Rajesh Lal Mehra.

Additional Information

• State Public Service Commission:
• Part XIV of the Indian Constitution mentions the independence, power, formation and appointment, and dismissal of members of the State Public Service Commission from Articles 315 to 323.
• State Public Service Commission recruits second and third-class officers.
• The composition of the State Public Service Commission includes Chairman + other members.
• The number of members is not determined. It is determined by the Governor.
• Members are appointed by the Governor.
• There is no mention of eligibility for the appointment of members of the State Public Service Commission.
• However, half of the members of the commission will be those who have at least 10 years of experience working under the Government of India or the State Government.
• The chairman and members of the State Public Service Commission hold office for the term of 6 years or 62 years, whichever is earlier.
• In the absence of the Chairman, the work is done by the Acting Chairman appointed by the Governor.
• Salary and allowances of the members and the chairman are charged on the Consolidated Fund of the State.
• The Chairman and members of the Commission are appointed by the Governor, but only the President has the power to remove them.
• The President removes the Chairman and the members from the post in the same manner as the Chairman and members of the Union Public Service Commission.
• The President seeks advice from the Supreme Court in case of removal from office on the grounds of misconduct, which is binding.
• The Commission submits its annual report to the Governor under Article 323.

Important Points 

• The provision for the establishment of the Joint Public Service Commission (JPSC) for two or more states is also mentioned in the constitution.
• JPSC is a statutory body as it will be formed after a Parliamentary Act.
• The Chairman and members of the Joint Public Service Commission are appointed and removed by the President.

The Correct Answer is only I.

Key Points

• The foreign exchange rate is the price of one currency in terms of another. Because the foreign exchange rate compares the currencies of 2 countries, the rate depends on the value of each currency and, thus, on the economies of both countries.
• There are 3 primary economic factors that affect the foreign exchange rate:
• the relative purchasing power of each currency;
• the investment opportunities and risks of each country, and
• the desirability of the goods and services of each country.

Important Points

• Key Factors that Affect Foreign Exchange Rates:
• Inflation Rates
• Interest Rates
• Country’s Current Account / Balance of Payments
• Government Debt
• Terms of Trade
• Political Stability & Performance
• Recession
• Speculation

Additional Information

• Exchange Rate
• The price of one currency in terms of the other is known as the exchange rate. A currency’s exchange rate vis-a-vis another currency reflects the relative demand among the holders of the two currencies.
• Gross Domestic Product (GDP): is a measure of economic activity in a country. It is the total value of a country’s annual output of goods and services. It gives the economic output from the consumers’ side.
• Gross Value Added (GVA): is the sum of a country’s GDP and net of subsidies and taxes in the economy. It provides the rupee value for the number of goods and services produced in an economy after deducting the cost of inputs and raw materials that have gone into the production of those goods and services.

The correct answer is Chandrashekhar Azad Sagar Project.

Key Points

• The Shahid Chandar Shekhar Azad sagar (Jobat)
• This project is in Madhya Pradesh, and it is an irrigation project envisaging the construction of a composite dam across river Hatni, a tributary of river Narmada, which is near village Waskal, 24 km from Kukshi town.
• It was started in the year 1974.
• It is also known as the Jobat project. Hence, Option 4 is correct.
• Under this project, the dam is being built on the Hathni river in Jhabua district which aims to irrigate the 9,848 hectares of Dhar district.
• The beneficiaries constitute 85% of the tribal population.
• This project is planned to benefit the drought-prone areas declared by the Government of India.
• The Jobat Irrigation Project is planned to benefit the drought-prone area declared by the Government of India and tribal areas of Kukshi Tehsil in Dhar District of Madhya Pradesh.
• The dam is in Jhabua District, while the command is located in Dhar District.

Additional Information

• Halali River Project
• This project has been developed over the tributary of Betwa river i.e. the Halali river.
• It was constructed in the year 1973-76.
• Through this project, around 16,000 hectares of cropped areas of Raisen and Vidisha district are irrigated.
• This project is renamed as Samarat Ashok Sagar Project.
• Bansagar Project
• This project is a multipurpose river valley project on Son river situated in the Ganga basin of Madhya Pradesh near Shahdol district.
• There was an agreement in 1973 between the state governments of Madhya Pradesh, Bihar, and Uttar Pradesh for the construction of the dam, in which the states shared the expenditure in 2:1:1 proportion.
• This project irrigates land in Madhya Pradesh, Uttar Pradesh, and Bihar.
• Its power capacity is 405 MW and it irrigates 1.53 lakh hectares of land.
• Thawar Dam Project
• It was constructed in 1977 in Jhulpur village of Mandla district. It irrigates 18,212 hectares of land.​

The correct answer is Maharashtra.

• Khetial village is located on the border of Maharashtra and Madhya Pradesh.
• It is located in the Nandurbar district.

Key Points

• Nandurbar district was formed in 1998 by partitioning the Dhule district.
• Nandurbar district has two border boundaries. Gujarat is on the northwestern border of the state, while on the northeast border of the state of Madhya Pradesh.
• Khetia village is located in the Barwani district of Madhya Pradesh.

Concept:

• The cell is the fundamental structural and functional unit of all living organisms.
• Anton Von Leeuwenhoek first saw and described a live cell.
• A cell may be defined as a unit of protoplasm bound by plasma or cell membrane and possessing a nucleus.
• Protoplasm is a life-giving substance and includes the

cytoplasm and the nucleus.

• The cytoplasm has in it organelles such as ribosomes,

mitochondria, Golgi bodies, plastids, lysosomes, and endoplasmic reticulum.​

Explanation:

Mitochondria:

• Mitochondria are not easily visible under the microscope.
• The number of mitochondria per cell is variable depending on the physiological activity of the cells.
• Mitochondria are the sites of aerobic respiration.
• They produce cellular energy in the form of ATP, hence they are called ‘power houses’ of the cell.

​

Thus, the active site of energy production in a cell is the mitochondria.

Additional Information

Other cell organelles are:

Nucleus:

• The nucleus is the largest organelle seen clearly when the cell is not dividing.
• The functions of the nucleus are:
• Maintains the cell in working order.
• Coordinates the activities of other cell organelles.
• Participates directly in cell division.

Chloroplast:

• They are found in all green plant cells in the cytoplasm.
• They contain the pigment chlorophyll.
• Chloroplasts are the site of photosynthesis.
• Photosynthesis is the production of sugar, from carbon dioxide and water in the presence of sunlight.

Golgi apparatus:

• Golgi bodies are a stack of membranous sacs of the same thickness as ER.
• Functions of Golgi bodies are:
• Synthesis and secretion such as enzymes.
• Participates in the transformation of membranes to give rise to other membrane structures such as
• lysosome,
• acrosome, and
• dictyosomes,
• Synthesize wall element like pectin, mucilage.

Concept:

• Isotones are atoms or nuclei which have an equal number of neutrons.
• ₁₇Cl³⁷ and ₁₉K³⁹ both have the same number of neutrons.
• Isobars are Atoms of a chemical element that have the same atomic mass but a different atomic number.
• Isotopes are Atoms of a chemical element that have the same atomic number but a different atomic mass.

Explanation:

In 6C13, 7N14

For 6C13

No of proton = 6

No of proton + No of neutron = 13

No of neutron = 13 - 6 = 7

For 7N14**:**

No of proton = 7

No of proton + No of neutron = 14

No of neutron = 14 - 7 = 7

Thus, we conclude that 6C13, 7N14 are isotones.

Additional Information

The correct answer is because adding water to acid can cause the mixture to heat up and splash concentrated acid.

 Key Points

• When water is added to a concentrated acid, an exothermic reaction occurs that can cause the mixture to heat rapidly and boil.
• This can result in the splashing of the concentrated acid, which poses a safety risk.
• By adding acid to water, the heat of the reaction is dispersed in the larger volume of water, reducing the risk of the mixture boiling and splashing.
• Always remember the phrase "add acid to water, like you oughta" for safety in the lab.

 Additional Information

• Acids are corrosive substances that can cause burns or other injuries if they come into contact with skin or eyes.
• Therefore, safety precautions, like using protective equipment and following proper procedures for handling acids, are crucial in a laboratory environment.

The correct answer is Fatty tissue.

Key Points

Fatty tissue/Adipose tissue:

• Adipose tissue, body fat, or simply fat is a loose connective tissue composed mostly of adipocytes.
• Adipose tissue is made up of adipocytes that are embedded in a structural mesh of collagen fibers.
• Adipose tissue is a type of loose connective tissue located mainly beneath the skin.
• The adipose tissue can be found under our skin (subcutaneous tissue), around our organs (visceral fat), in bone marrow (marrow fat), and in breast tissues.
• The cells of this tissue are specialized to store fats.
• Adipose tissue is oval and filled with fat droplets.
• The excess nutrients which are not used immediately are converted into fats and are stored in this tissue.
• Adipose tissue helps in maintaining body temperature.
• It acts as an insulator. It reduces the loss of fat from the body, that is, it regulates body temperature. Hence, option 3 is correct.
• Recently, the adipose tissue has been acknowledged as an endocrine gland because it produces hormones, such as oestrogen, leptin, resistin, and cytokines.
• Adipose tissue is also associated with the release of pro-inflammatory markers called adipokines in the development of metabolic syndromes, such as type-2 diabetes, atherosclerosis, and cardiovascular diseases.
• The adipocytes can be classified into three different cell types based on their function, origin, and location.
• The three types are white, beige, and brown adipocytes.

The correct answer is Aristotle.

Key Points

• Aristotle -
• The 'father of biology' is called the Greek philosopher Aristotle (384–322 BCE).
• Aristotle arranged it with his ideas and concepts about biology.
• Aristotle is also called the 'Father of Zoology' which is the branch of biology.
• He was a disciple of Plato and a master of Alexander.
• Aristotle's famous book on politics is **"Politics".**​

Additional Information

• ​Theophrastus -
• Theophrastus is the father of Botany.
• Plants are studied in botany.
• Carl Linnaeus-
• He was a Swedish Botanist, Physician, and Zoologist.
• Linnaeus made the first systematic attempt to classify Flora and Fauna.
• Carl Linnaeus conceptualized the binomial nomenclature of classification.
• ​Gregor John Mendel-
• He was a German-speaking Austrian Augustinian pastor and scientist.
• He is called the 'Father of Genetics.
• He set the rules of genetics by experimenting on the seeds of peas.

Important Points

• Mendel's three rules of genetics-

1. Law of Dominance
2. Law of Segregation
3. Law of Independent Assortment

• Georg Simon Ohmis the discoverer of the ‘Law of Electric Resistance’.
• He was a physicist and mathematician from Germany.
• According to the Ohm’s Law, ‘the current flowing through a conductor is directly proportional to the potential difference (voltage)across the ideal conductor.’ The constant of proportionality is termed as ‘resistence’(R).
• The unit of ‘resitence’ is named after him. (Ohm Ω)

• Metalloids are term given to those physical elements that exhibit the physical and chemical properties of both the metals and non-metals in them.
• They have a metallic appearance with the brittle property of non-metals. They show average conductance and most of their chemical properties resemble the non-metals.

The pancreas is the second largest gland in the human body and plays an important part in the digestive process. It is responsible for the production of insulin and it secretes pancreatic juice into duodenum. The liver is the largest gland in the human body.

The human eye works like a photographic camera, the rays that move from the object we see fall through the cornea and the ophthalmic fluid into the lens through the pupil. The retina makes it focus. Where a small and inverted reflection of the object is formed.

CONCEPT:

Ammeter:

• It is a device used to measure current and is always connected in series with the ‘element’ through which current is to be measured.
• The reading of an ammeter is always lesser than the actual current in the circuit.
• Smaller the resistance of an ammeter more accurate will be its reading.

EXPLANATION:

• DC ammeter measures the average value over a cycle.
• And in case of AC, the average value of the current over a cycle is zero. Hence we cannot measure AC current using DC ammeter. Therefore option 2 is correct.

Concept:

• A stain is an unwanted mark or colouration on a fabric.
• It is caused by contact and absorption of foreign matter, which cannot be removed by the normal washing process and requires special treatment.
• Stains (dyes) are used to colour parts of the cell to study the detailed structure.
• A base is a substance that furnishes hydroxide ions (OH– ) when dissolved in water.
• **Bases that are soluble in water are called alkalis.**​

Explanation:

The stains can be classified as:

• Vegetable/botanical stains: tea, coffee, fruits, and vegetables.
• Animal stains: blood, milk, meat, eggs, etc.
• Oil stains: oils, ghee, butter, etc.
• Mineral stains: ink, rust, coal tar, medicine, etc.
• Dye bleeding: colour from other fabrics.

Important Points

• Soaps and detergents are sodium and potassium salts of long-chain fatty acids.
• They are majorly alkaline in nature.
• Vegetable stains are acidic by nature and can be removed by an alkaline medium.
• Some alkaline stains are ammonia, borax, and baking soda.

​Thus, an alkaline agent should be used to remove botanical stains.

Additional Information

• Mineral stains should be washed first in an acidic medium and then in an alkaline medium.
• Stains from dye bleeding can be removed either by dilute alkalies or acids depending on the fabric type.
• Oil stains are removed by the use of grease solvents and absorbents.
• Animal stains are proteins in nature and are removed by detergents in cold water only.

The correct answer is Non-metals.

Key Points

CONCEPT:

• Elements on the left side of the periodic table are metals.
• Transition metals are placed in between metals and non-metals.

EXPLANATION:

• Elements on the right side of the periodic table are mostly non-metals.

Image of the Periodic Table:

The correct answer is Jonas Salk.

Explanation:

• Polio is a viral disease.
• It causes paralysis by affecting the nervous system.
• It spreads through direct contact with infected individuals.
• An inactivated (killed) polio vaccine (IPV) was developed by Dr. Jonas Salk and was first used in 1955.
• A live attenuated (weakened) oral polio vaccine (OPV) was developed by Dr. Albert Sabin and first used in 1961.

Thus, Polio vaccine was first developed by Jonas Salk.

Additional InformationAlbert Sabin:

• Albert Sabin developed a live attenuated (weakened) oral polio vaccine (OPV) and first used in 1961.

Thomas Francis:

• Thomas Francis was an American physician, virologist, and epidemiologist who guided the discovery and development of Jonas Salk's polio vaccine.

The correct answer is Delta decay.

Concept:

• The disintegration of an unstable nucleus of an atom is identified as the radioactive decay of the nucleus.
• The radioactive decay owes its name to the radiation emitted by the nucleus upon breakdown.
• The disintegration of the nucleus concludes into energy and matter.
• Depending upon the manner in which the nucleus is decomposed, radioactive decay is distinguished into three types, alpha \((\alpha)\), beta \((\beta)\), and gamma \((\gamma)\).

Explanation:

The correct answer is Option 3.

Key Points

Carbon black is obtained by burning hydrocarbons in limited supply of air.

CH₄ + 2O₂ →CO₂ + 2H₂O

• It is used as a black pigment in black ink.
• It is also used as a filler in automobile tyres.
• Heating wood at high temperature in absence of air releases charcoal and volatile tars.
• Heating coal at high temperature in absence of air results in destructive distillation of coal.
• Heating coal at high temperature in the presence of air would produce Carbon dioxide.

Based on information given direction diagram can be traced as,

Let both X and Y start from point S.

X travels 17 m west and reaches T, then takes right turn and reaches point U by traveling 13 m.

Similarly, Y travels north for 9 m and reaches R, then turns east for 7 m and finally stops at point P.

Thus, UP = 17 + 7 = 24 m

∴ Y is 24 m to the east of X.

The pattern followed here is:

Every letter is coded by its positional value.

Similarly,

Hence, “1693202118519” is the correct answer.

• The correct answer is option(1)

• Qualities Projected in this situation:​

Key Points 

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Additional Information Officer qualities:

We have check all the options,

(1): b a a b / b a b b / b a a b / a a a b

(2): a a a a / b a a b / b b a b / b a a b

(3): b a a a / b a b b / b a a b / b a a b

(4): b a a b / b a a b / b a a b / b a a b 

Hence, the correct answer is "bbaab".

The least possible Venn diagram is given below-

Conclusion:

I) Some volumes are Forces – True (Definite case)

II) Some volumes are currents – True (Definite case)

So, both conclusion I and conclusion II follows.

Considering today is Tuesday,

A week consists of 7 days.

63 days is equal to 9 weeks.

Exactly after 63 days, that is 9 weeks, it will be a Tuesday.

Hence, “Tuesday” is the correct answer.

The logic followed here is:

Given word 'BILLIONAIRE'

Reverse of 'BILLIONAIRE' is ERIANOILLIB

Replacing each letter of 'ERIANOILLIB' with the succeeding letter in the alphabet,

Therefore, the 10^th letter is 'J'.

Hence, the correct answer is "Option (3)".

Hint succeeding = Given letter place value + 1 place value

The logic followed is:

Both the conclusions follow.

Since the option is available from next year, it implies that this option was not available earlier. Secondly, students, who are weak in Mathematics and Science, will be benefited.

Hence, the correct answer is "If both I and II follow". 

Additional Information

• If there are two or more sentences that are used to frame a statement, then, the sentences must be interrelated, and mutual contradiction should be there.
• Do not look for truthful notions. The information provided in the statement is the only requirement for a student to answer the question.

No assumptions must be made.

• Read the statement carefully and look for keywords that are common between the statement and the conclusions
• If there is more than one conclusion that is applicable to the statement, students must ensure that the conclusions they opt for have some relation with each other.

The pattern followed is,

Option 1 → 64 - 100 → 8² - 10²

Option 2 → 25 - 36 → 5² - 6²

Option 3 → 16 - 49 → 4² - 7²

Option 4 → 48 - 81 → 48 is not a square of any number and 81 is 9².

All follow the same pattern, except ’48 - 81’.

Hence, “48 - 81” is the odd pair.

The least possible Venn diagram is:

Conclusions:

I. Some fan are mop → True (As some mop are whipper and all whipper are fan)

II. Some mop are hanky → True (As some hanky are mop. So, Some mop are definitely hanky)

III. Some mop are fan → True (As some mop are whipper and all whipper are fan)

Hence, All conclusions are follows.

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

1. The product of floors on which E and F live is 10.

The possible pairs of floor numbers (from 1 to 6) whose product is 10 are (2, 5) or (5, 2). So, E and F live on floors 2 and 5.

2. The sum of floors on which B and E live is 11.​

4. A lives immediately above C. The last remaining person is D, and the only remaining floor is 1. So D lives on Floor 1.

Now, we need to find the sum of floors on which C and D live.

C lives on Floor 3.

D lives on Floor 1.

Sum of floors = 3 + 1 = 4.

Hence, the correct answer is "Option 1".

• The correct answer is Option 3: along with the remaining friends, repairs the rope bridge, holds hands off each other for maintaining balance, and crosses the river safely. later, he informed the authorities about the bridge to avert any future misadventures.

• Qualities Projected in this situation:  (Effective intelligence, Speed of decision making, Strong reasoning ability, and Cooperation).

Key Points

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Additional Information

Officer qualities:

Given:

Raju ranked sixteenth from the top and forty-ninth from the bottom among those who passed an examination

Total number of students who passed the examination = 16 + 49 - 1 = 65 -1 = 64

Seven students did not appear in the examination and two failed.

Therefore, the total number of students in the class = 64 + 7 + 2 = 73

Hence, the correct answer is 73.

The logic follows here is:

The statement asks a question that should the use of animals for research be banned.

The argument I agree with the statement and suggests an illogical reason stating that researchers end up wasting resources on animals. But saving resources does not benefit study or research and no conclusion can be reached.

Therefore, argument I is not strong.

Argument II disagrees and points out the benefit that conducting research on animals improves scientists' understanding of the study, therefore the use of animals should not be banned.

Therefore, argument II is strong.

Hence, the correct answer is "Only II is strong". 

Additional Information

1. The agreement which is the reconstruing part of the statement is a strong agreement.
2. The argument should not be imagined.
3. The relationship of the agreement should be direct from the statement.
4. The argument should be simple and clear.
5. The agreement should be based on scientific facts.
6. The statement in the argument should receive a logical answer.

The logic is here,

In given series 23, 29, 31, 37, 43, 47 all are prime number except 42.

41 is prime number not 42.

Hence, “42” is correct answer.

Decoding the codes for words:

So, the code for 'again' is 'ka'.

Hence, the correct answer is option 4.

The diagram shown below shows the path followed by the man:

In right triangle ADF

Using pythagoras theorem,

(AF)² = (AD)² + (DF)²

(AF)² = 6² + 8²

(AF)² = 36 + 64

(AF)² = 100

AF = \( { \ \sqrt{100} }\)

AF = 10km

So, he is '10 km' far from the starting point.

Hence, "10 km" is the correct answer.

The logic followed here is:

Hence, "Option 2" is the correct answer.

The pattern followed is:

Logic: (First Number × Last Number) ÷ 4 = Middle Number

(26 × 8) ÷ 4 = 52

(48 × 16) ÷ 4 = 192

Similarly,

(A × 14) ÷ 4 = 175

A × 14 = 175 × 4 

A = (175 × 4) ÷ 14 

∴ A = 50

Hence, 50 is correct.

Logic: (FIrst number ÷ 2) × (Third number ÷ 2) = Second Number

• The correct answer is Option 2: will give him first aid, call the ambulance and take him to the hospital.

• Qualities Projected in this situation:  (courage, speed of decision, and sense of responsibility)

Key Points

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Additional Information

Officer qualities:

Shortcut Trick

Directly substitute the standard trigonometric values.

sin 60° = √3/2, cos 30° = √3/2, cot 45° = 1, sec 60° = 2.

(√3/2)² + (√3/2)² + 1² + 2² = 3/4 + 3/4 + 1 + 4 = 6/4 + 5 = 1.5 + 5 = 6.5.

6.5 = 13/2.

∴ The correct answer is 13/2.

Alternate Method

Given: sin² 60° + cos² 30° + cot² 45° + sec² 60°

Formula Used: Standard trigonometric ratios at specific angles.

⇒ sin 60° = √3/2

⇒ cos 30° = √3/2

⇒ cot 45° = 1

⇒ sec 60° = 2

Calculations:

⇒ (√3/2)² + (√3/2)² + (1)² + (2)²

⇒ (3/4) + (3/4) + 1 + 4

⇒ 6/4 + 5

⇒ 3/2 + 5

⇒ (3 + 10) / 2

⇒ 13/2

∴ The correct answer is 13/2.

Additional Information

Trigonometric Identities

sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

Complementary Angles

sin(90°−θ) = cosθ and cot(90°−θ) = tanθ. This explains why sin 60° = cos 30°.

Reciprocal Relations

secθ = 1/cosθ; cosecθ = 1/sinθ; cotθ = 1/tanθ.

Expression: \(\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{42 + \sqrt{49}}}}}\)

Calculation:

\(\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{42 + \sqrt{49}}}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{42 + 7}}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + \sqrt{74 + \sqrt{49}}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + \sqrt{74 + 7}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + \sqrt{81}}}\)

⇒ \(\sqrt{42 + \sqrt{40 + 9}}\)

⇒ \(\sqrt{42 + \sqrt{49}}\)

⇒ \(\sqrt{42 + 7}\)

⇒ \(\sqrt{49} = 7\)

The value of the expression is 7.

Given:

Isha and Anshu's total investment = ₹44,000

Total profit = ₹8,800

Isha's share of profit = ₹1,100

Formula used:

Let Isha's investment be I and Anshu's investment be A.

I + A = ₹44,000

Profit ratio = Investment ratio

Isha's share of profit / Total profit = Isha's investment / Total investment

Calculation:

Isha's share of profit / Total profit = Isha's investment / Total investment

⇒ 1100 / 8800 = I / 44000

⇒ I = 44000 × (1100 / 8800)

⇒ I = 44000 × (1 / 8)

⇒ I = 5500

Anshu's investment = Total investment - Isha's investment

⇒ A = 44000 - 5500

⇒ A = 38500

∴ The correct answer is option 3.

Shortcut Trick

Present Ratio (Woman : Daughter) = 4 : 1 (Difference = 3 units)

Ratio after 6 years = 3 : 1 (Difference = 2 units)

Equalize differences: Present (8 : 2) and Future (9 : 3). Ratio increase = 1 unit = 6 years.

Sum of present ratios = 8 + 2 = 10 units ⇒ 10 × 6 = 60 years.

∴ The correct answer is 60 years.

Alternate Method

Given: Woman age = 4 × Daughter age. After 6 years, Woman = 3 × Daughter.

Let the present age of the daughter be x and woman be 4x.

⇒ (4x + 6) = 3(x + 6)

⇒ 4x + 6 = 3x + 18

⇒ 4x − 3x = 18 − 6

⇒ x = 12 years

⇒ Woman present age = 4 × 12 = 48 years

⇒ Sum of present ages = 48 + 12 = 60 years

∴ The correct answer is 60 years.

Additional Information

Ratio Difference Constant

The age difference between two people remains constant throughout their lives. Always multiply ratios to keep the difference parts equal.

Age Sum Property

When calculating the sum after 'n' years for 'k' people, the total sum increases by n × k years.

Shortcut Trick
Use the direct empirical relationship between mean, median, and mode:
Mode = 3 × Median − 2 × Mean
Mode = 3 × 6 − 2 × 7 = 18 − 14 = 4
∴ The correct answer is 4.

Alternate Method
Given:
⇒ Median = 6
⇒ Mean = 7

Formula Used:
⇒ Mode = 3 × Median − 2 × Mean

Calculations:
Substitute the given values of mean and median into the formula:
⇒ Mode = 3 × 6 − 2 × 7
⇒ Mode = 18 − 14
⇒ Mode = 4
∴ The correct answer is 4.

Additional Information
Karl Pearson's Empirical Formula
For moderately asymmetrical distributions, the distance between the mean and the mode is approximately three times the distance between the mean and the median: (Mean − Mode) = 3 × (Mean − Median).
Symmetric Distribution
In a perfectly symmetrical distribution, the values of mean, median, and mode are identical: Mean = Median = Mode.
Positively Skewed Distribution
In a distribution skewed to the right, the values follow the order: Mean > Median > Mode.
Negatively Skewed Distribution
In a distribution skewed to the left, the values follow the order: Mean < Median < Mode.

Given:

Radius of circle = 21 cm.

Formula used:

Area of circle = πr²

Area of semi - circle (when the radius is given) = πr²/2

Area of triangle = (Base × height)/2

Calculation:

Area of circle = 22/7 × 21 × 21 = 1386 cm²

Area of semi - circle = 1386/2 = 693 cm²

To find out enclosed area of semi circle but exterior to triangle.

We can first find the area of semi circle & then subtract the area of right angled isosceles triangle.

Base of the triangle will 42 cm (21 × 2) which is diameter and height = 21 cm.

⇒ Area of triangle = (42 × 21) / 2 = 441 cm².

Area of  semi circle -  Area of triangle

⇒ 693 - 441 = 252 cm².

∴ The area in the semi circle excluding the triangle is 252 cm2.

Shortcut Trick

Fourth proportional of a, b, c is (b × c) ÷ a.

First fourth proportional (x) = (56 × 63) ÷ 42 = 84.

Second fourth proportional (y) = (273 × 153) ÷ 189 = 221.

Required Ratio = 84 : 221.

∴ The correct answer is 84 : 221.

Alternate Method

Given: Two sets of numbers for finding the fourth proportional.

Formula Used: If a, b, c, d are in proportion, then a/b = c/d ⇒ d = (b × c) / a.

Calculations:

⇒ For the first set (42, 56, 63):

⇒ 42 / 56 = 63 / x

⇒ x = (56 × 63) / 42

⇒ x = (4 × 14 × 63) / (3 × 14) = (4 × 63) / 3 = 4 × 21 = 84

⇒ For the second set (189, 273, 153):

⇒ 189 / 273 = 153 / y

⇒ y = (273 × 153) / 189

⇒ y = (273 × 17 × 9) / (21 × 9) = (273 × 17) / 21

⇒ y = 13 × 17 = 221

⇒ Required Ratio = x : y = 84 : 221

∴ The correct answer is 84 : 221.

Additional Information

Mean Proportional

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

Third Proportional

The third proportional of two numbers a and b is c such that a : b = b : c, which means c = b² / a.

Continued Proportion

Three quantities a, b, c are in continued proportion if a : b = b : c.

Given:

The area of the square piece of glass = 225 cm²

The width between the glass piece and one side of the table = 9 cm

Formula Used:

Area of a square = side²

Calculation:

Let the side length of the square piece of glass be S cm.

Area of the square piece of glass:

S² = 225

S = √225

S = 15 cm

Width between the glass piece and one side of the table = 9 cm

So, the total width added on both sides = 9 cm × 2 = 18 cm

The length of the table:

Length of the table = Side length of glass piece + Total width added on both sides

Length of the table = 15 cm + 18 cm

Length of the table = 33 cm

The length of the table is 33 cm.

Given:

A shopkeeper offers a "buy three, get one free" scheme.

Formula Used:

Percentage Discount = (Discounted Quantity / Total Quantity) × 100

Calculation:

In this scheme, for every 4 items, 1 item is free.

Discounted Quantity = 1 item

Total Quantity = 4 items (3 paid + 1 free)

Percentage Discount = (1 / 4) × 100

⇒ Percentage Discount = 0.25 × 100

⇒ Percentage Discount = 25%

The correct answer is option 4.

Calculation:

∠A = ∠B = 90° & ∠O = 120°

So, ∠A + ∠B + ∠O + ∠P = 360°

⇒ 90° + 90° + 120° + ∠P = 360°

⇒ ∠P = 360° - 300°

∴ ∠P = 60°

Given:

The ages of Ritika and Animesh are in the ratio 7:9 respectively.

After 6 years, the ratio of their ages will be 4:5.

Calculation:

Let the present ages of Ritika and Animesh be 7x and 9x respectively.

After 6 years:

\(\dfrac{7x+6}{9x+6} = \dfrac{4}{5}\)

⇒ 5(7x + 6) = 4(9x + 6)

⇒ 35x + 30 = 36x + 24

⇒ 36x - 35x = 30 - 24

⇒ x = 6

Present age of Ritika = 7x = 7 × 6 = 42 years

Present age of Animesh = 9x = 9 × 6 = 54 years

Difference in their ages = 54 - 42 = 12 years

∴ The correct answer is option (3).

Given:

A sum of money doubles itself in 20 years.

Formula used:

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

Calculation:

According to the question, the sum of money doubles itself in 20 years.

⇒ 2P = P + P × r × 20 (For the Amount to double)

⇒ P = P × r × 20

⇒ 1 = 20r 

⇒ r = 0.05

Now, 3P = P + P × r × t.

⇒ 3 = 1 + 0.05 × t

⇒ t =\( \dfrac{ 3-1 }{0.05} \) = 40 years

∴ It will take 40 years for the money to triple at the same rate as simple interest.

Concept use:

When the Number of Observation is odd then median will be the middle value 

When the Number of observation is even then median will be middle value + next to the middle value divide by 2.

Explanation:

To find the median, we need to arrange the data in ascending order.

Given data: 5, 7, 9, 11, 13, x, 17, 19, 21

Arranged data: 5, 7, 9, 11, 13, x, 17, 19, 21

Since there are 9 data points, the median will be the middle value, which is the 5^th value. We are given that the median is 13.

Therefore, the 5^th value in the arranged data should be 13, which means x = 13.

Hence, The correct answer is 3) 13.

Given:

x + y = 7

xy = 4

Concept used:

x³ + y³ = (x + y) (x² - xy + y²)

(x + y)² = x² + 2xy + y²

Calculations:

x + y = 7

⇒ x² + 2xy + y² = 49

⇒ x² - xy + y² = 49 - (3 × 4)

⇒ x² - xy + y² = 37

⇒ (x + y) (x² - xy + y²) = 37 × 7

⇒ (x + y) (x2 - xy + y2) = 259

⇒ x³ + y³ = 259

∴ The value of x³ + y³ is 259.

Shortcut Trick

If an equation is in the form a + 1/a = 2, then the value of a is always 1.

Here, replacing a with x³, we get x³ + 1/x³ = 2.

So, x³ = 1 ⇒ x = 1.

Substitute x = 1 in the required expression x² − 2x.

⇒ 1² − 2(1) = 1 − 2 = −1

∴ The correct answer is -1.

Alternate Method

Given:

x³ + 1/x³ = 2

Calculations:

⇒ (x⁶ + 1) ÷ x³ = 2

⇒ x⁶ + 1 = 2x³

⇒ x⁶ − 2x³ + 1 = 0

Using the algebraic identity (a − b)² = a² − 2ab + b²:

⇒ (x³)² − 2(x³)(1) + (1)² = 0

⇒ (x³ − 1)² = 0

Taking square root on both sides:

⇒ x³ − 1 = 0

⇒ x³ = 1

⇒ x = 1

Now, we need to find the value of x² − 2x.

⇒ (1)² − 2(1)

⇒ 1 − 2 = −1

∴ The correct answer is -1.

Additional Information

Standard Algebraic Case 1

If x + 1/x = 2, then the only possible real value is x = 1.

Standard Algebraic Case 2

If x + 1/x = −2, then the only possible real value is x = −1.

Sum of Squares Identity

If x + 1/x = k, then the square values follow the pattern x² + 1/x² = k² − 2.

Sum of Cubes Identity

If x + 1/x = k, then the cube values follow the pattern x³ + 1/x³ = k³ − 3k.

The family tree diagram is shown below:

Hence, the boy plying cricket is brother of Gaurav.