SSC CHSL Tier-1 2023: Official Paper (Held On: 14 Aug, 2023 Shift 4) (Previous Year Paper)

Given: 22 July 1969 is Tuesday.

Now, 1969 to 1985 = 16 Years.

In 16 years, 4 Leap year and 12 ordinary years.

Total odd days from 22 July 1969 to 22 July 1985 = (4 × 2) + (12 × 1) = 8 + 12 = 20 days.

And, 20 days = 20/7 = 2 week and 6 odd days.

So, 22 July 1985 was = Tuesday + 6 = Monday.

Now, 22 July 1985 to 6 August 1985 = 15 days, 15/7 = 2week and 1 odd day.

Therefore, 6 August 1985 = Monday + 1 = Tuesday.

Hence, the correct option is "Option 1".

Given word: KINGDOM 

Now, arranging the word in alphabetical order:

Now, after arranged in alphabetical order the letter which is fourth from the left is: 'K',

and, the one which is second from the right is: N.

In the English alphabetical series 'Two' letters between 'K' and 'N' i.e: 'L', 'M'.

Hence, the correct answer is "Option 3".

The logic followed here is:

thus, "228" will replace the question mark in the given series.

Hence, the correct option is "Option 3".

The logic followed here is:

For, 'DGJH is related to LORP'

For, 'JMPN is related to RUXV'

Similarly, for 'ILOM'

So, 'ILOM' will be related to 'QTWU'

Hence, the correct answer is "Option 2".

The logic followed here is:

For, 'SFBV is related to HUYE'

For, 'JQEF is related to QJVU'

Similarly, for 'CKSW'

So, 'CKSW' will be related to 'XPHD'

Hence, the correct answer is "Option 3".

The logic followed here is:

So, 'KCBEG' will be the correct alternative that will complete the series.

Hence, the correct answer is "Option 1".

BODMAS Table: 

Given equation: 63 ÷ 3 + 14 × 7 - 16 = ?

Now, if ‘+’ and ‘-‘ and ‘×' and '÷’ are interchanged, then:

⇒ 63 × 3 - 14 ÷ 7 + 16 = ?

⇒ 63 × 3 - 2 + 16 = ?

⇒ 189 - 2 + 16 = ?

⇒ 205 - 2 = 203.

Hence, the correct answer is "Option 3".

The paper when unfolded will appear as shown below:

Hence, 'option 4' is the correct answer.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 2".

The logic followed here is:

‘like the way' is written as 'pl zs kq' 

'on my way' is written as 'kq mk In’,

So, 'way' will be written as 'kq'. 

Hence, the correct answer is "Option 2".

BODMAS Table: 

Given equation: 11 ÷ 4 + 8 × 2 - 1 = ?

Now, if ‘+’ and ‘-‘ and ‘×' and '÷’ are interchanged, then:

⇒ 11 × 4 - 8 ÷ 2 + 1 = ?

⇒ 11 × 4 - 4 + 1 = ?

⇒ 44 - 4 + 1 = ?

⇒ 45 - 4 = 41.

Hence, the correct answer is "Option 1".

The logic followed here is:

For, ‘LRUP is written as RXAV’,

For, 'CILG is written as IORM',

Similarly, for 'HNQL'

So, 'HNQL' will be written as 'NTWR'.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (1st number + 2nd number) ÷ 4 = 3rd number.

Given,

13 - 15 - 7

⇒ (13 + 15) ÷ 4

⇒  28 ÷ 4 = 7.

And, 9 - 11 - 5

⇒ (9 + 11) ÷ 4

⇒  20 ÷ 4 = 5.

Similarly, Option 1) 16 - 24 - 10

⇒ (16 + 24) ÷ 4

⇒  40 ÷ 4 = 10.

 Hence, the correct option is "Option 1".

The logic followed here is:

Logic: The 'curve' part of the image is getting increase one place to the next images.

So, option 2 will complete the series.

Hence, the correct answer is "Option 2".

The logic followed here is:

Option 1) SUT

Option 2) DGE

Option 3) WYX

Option 4) FHG

Here, 'DGE' is odd among the given options.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (1st number)² × 3 = 2nd number.

20 ∶ 1200

⇒ (20)² × 3 

⇒ 400 × 3 = 1200.

28 ∶ 2352

⇒ (28)2 × 3 

⇒ 784 × 3 = 2352.

Similarly, for 50 ∶ ?  

⇒ (50)2 × 3 

⇒ 2500 × 3 = 7500.

Hence, the correct option is "Option 2"

The logic followed here is:

thus, "180" will replace the question mark in the given series.

Hence, the correct option is "Option 1".

Family Chart:

Decoding the Symbols:

Given: S × T + U - V ÷ W

It means: S is the Sister of T, T is the Husband of U, U is the Mother of V, V is the Brother of W.

So, S is the 'Father's sister' of W.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: 1st number - 1 = n²

2nd number - 1 = (n + 1)2 

10 is related to 17

⇒ 10 - 1 = 9 → 3² 

⇒ 17 - 1 = 16 → 42 

50 is related to 65

⇒ 50 - 1 = 49 → 72 

⇒ 65 - 1 = 64 → 82 

Similarly, 26 is related to

⇒ 26 - 1 = 25 → 52 

⇒ 37 - 1 = 36 → 62 

So, 26 will be related to 37.

Hence, the correct option is "Option 2"

Given Statements:

All Eagles are Predators.

All Tigers are Predators.

Some Tigers are Cats.

The least possible Venn diagram for the given statement is:

Conclusions:

I. All Cats are Predators - False (Because, only those part of cat which is tigers will predators, but All Cats are Predators can be possible only).

II. All Eagles are Tigers - False (Because, No definite relation given between eagles and tigers, so All Eagles are Tigers can be possible only).

So, Both conclusions (I) and (II) do not follow.

Hence, the correct answer is "Option 1".

The Rectangles are:

So, there are '11' Rectangles in the given figure.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: **(**1st number × 3) - 3 = 2nd number

Now,

1) 7 - 19

→ (7 × 3) - 3 

→ 21 - 3 = 18  ≠ 19.

2. 11 - 30

→ (11 × 3) - 3 

→ 33 - 3 = 30.

3. 14 - 39

→ (14 × 3) - 3 

→ 42 - 3 = 39.

4. 17 - 48

→ (17 × 3) - 3 

→ 51 - 3 = 48.

So, odd number pair is '7 - 19'.

Hence, the correct option is "Option 3".

The logic followed here is:

So, 'SQR' will replace the question mark in the given series.

Hence, the correct answer is "Option 2".

Family Chart:

Decoding the Symbols:

Given: V ÷ P - F + G × C

It means: V is the Father of P, P is the Husband of F, F is the Daughter of G, G is the Brother of C.

So, P is the 'Daughter's husband' of G.

Hence, the correct answer is "Option 3".

The logic followed here is:

‘stars moon sun satellite planet' is written as 'pit rit kit sit nit' 

'moon mars venus mercury' is written as 'mit cit git sit’

'venus stars mercury' is written as 'cit git rit'

'mercury satellite planet' is written as 'pit cit nit'

So, 'sun' will be written as 'kit'. 

Hence, the correct answer is "Option 1".

The correct answer is Hemant Gupta.

Key Points

• In 2022, former Supreme Court judge Hemant Gupta has been appointed as the chairperson of the New Delhi International Arbitration Centre (NDIAC).
• The Appointments Committee of the Cabinet has approved the appointment of Justice Hemant Gupta (retired) as NDIAC chairperson and that of Ganesh Chandru and Anant Vijay Palli as its part-time members.
• Justice Gupta, who left the position on October 14, 2022, was a member of the bench that rendered a divided decision in a number of cases contesting the Karnataka High Court's decision from March 15 to uphold the state's prohibition on the hijab in educational institutions.
• The petitions against the high court ruling upholding the prohibition on the headscarf had been dismissed by Justice Gupta.
• He was elevated as a top court judge on **November 2, 2018.**​

Additional Information

• New Delhi International Arbitration Centre (NDIAC):
• The New Delhi International Arbitration Centre (NDIAC), which replaced the International Centre for Alternative Dispute Resolution (ICADR), is a self-governing organization situated in New Delhi that carries out conciliation, mediation, and arbitration procedures.
• It was renamed, the India International Arbitration Centre in 2022.
• It was founded in 2019 and designated by a parliamentary act as an Institute of National Importance.
• Composition:
• The NDIAC consists of seven members, including:
• (i) a Chairperson who may be a Judge of the Supreme Court or a High Court, or an eminent person with special knowledge and experience in the conduct or administration of arbitration;
• (ii) two eminent persons having substantial knowledge and experience in institutional arbitration;
• (iii) three ex-officio members, including a nominee from the Ministry of Finance and a Chief Executive Officer (responsible for the day-to-day administration of the NDIAC); and
• (iv) a representative from a recognised body of commerce and industry, appointed as a part-time member, on a rotational basis.

The correct answer is Somnath.

Key Points

• Somnath was the last invasion by Mahmud Ghazni outside Punjab.
• The Turkish invader Mahmud Ghazni, attacked and raided the temple of Somnath in 1025 AD.
• Mahmud of Ghazni:
• He, also known as Sultan Mahmud, ruled the Ghaznavid Empire from 998 to 1030 AD.
• He was the son of Sebüktigin, the founder of the Ghaznavid dynasty, and ascended the throne in 998 AD at the age of 27.
• Mahmud Ghazni did raid Mathura in 1018 AD, the city which falls within the historical region of Doab, located between the Ganges and Yamuna rivers.
• Kalinjar was conquered in 1023 AD, and Kanauj fell to Mahmud Ghazni in 1021 AD.

Additional Information

• Somnath temple: 
• The first of India's twelve sacred jyotirlingas is said to have arisen at the elaborately carved honey-colored Somnath temple or Deo Patan, located in Prabhas Patan, Veraval in Gujarat, India.
• It is said that Shiva manifested there as a blazing column of light.
• The temples are situated where the Sarasvati, Hiran, and Kapila rivers converge, and the shoreline where they are built is touched by the ebb and flow of the Arabian Sea.
• Although the timeline of the ancient temple starts in 649 BC, it is thought to be older.
• Though it's difficult to see them through the foggy glass, vibrant dioramas depicting the Shiva narrative border the north side of the temple grounds.
• The temple was reconstructed several times in the past after repeated destruction by multiple Muslim invaders and rulers, notably starting with an attack by Mahmud Ghazni in the 11th century.
• The Pran-Pratistha at the existing temple was done on May 11, 1951, by the then President of India, Dr. Rajendra Prasad.

The correct answer is 1975.

Key Points

• India won its first Hockey World Cup for Men's in 1975, defeating arch-rivals Pakistan in the final held in Kuala Lumpur, Malaysia.
• 1975 Men's Hockey World Cup:
• The men's field hockey competition held annually at the Hockey World Cup was in its third iteration in 1975.
• Malaysia's Kuala Lumpur hosted the event.
• India won the match against Pakistan with a 2-1 goal differential.
• Ashok Kumar scored the game-winning goal after Surjit Singh had scored the first important goal.
• For both countries, it was their second World Cup final participation; India finished second in the 1973 tournament while Pakistan won the first World Cup in 1971.
• For third place, Germany defeated the hosts, Malaysia, 4-0 on goal differential.

Additional Information

• Men's Hockey World Cup:
• The International Hockey Federation (FIH) is the organization that oversees the Men's FIH Hockey World Cup, an international field hockey championship.
• The competition got underway in 1971.
• Every four years, it serves as a bridge event between the Summer Olympics every four years.
• With four tournament victories, Pakistan is the most successful squad.
• Germany, Australia, and the Netherlands have each taken home three championships.
• The competition has been won once each by Belgium and India.
• The 2023 competition took place in Bhubaneswar, India, between January 13 and 29.
• Germany won their third World Cup title, defeating Belgium 5–4 in a penalty shootout after the game finished in a 3–3 draw.
• In 2018, the World Cup was extended to sixteen teams.

The correct answer is Violet.

Key Points

• White light is split into seven colors when passing through a triangular prism.
• The colors that are visible to the human eye are Red, Orange, Yellow, Green, Blue, Indigo, and Violet.
• These colors are commonly remembered using the acronym VIBGYOR.
• Typically, the human eye can detect wavelengths from 380 to 700 nanometers.
• Violet has the minimum wavelength among all, and it deflects the most when passed through a prism.
• Shorter wavelengths correspond to higher frequencies and higher energy in the visible spectrum.
• The wavelength of the colour components of white light:
• | Colour | Wavelength (in nanometers (nm)) | | --- | --- | | Violet | 380-450 | | Indigo | 450-480 | | Blue | 480-500 | | Green | 500-570 | | Yellow | 570-590 | | Orange | 590-620 | | Red | 620-750 |

Additional Information

• In the 1660s, English physicist and mathematician Isaac Newton began a series of experiments with sunlight and prisms.
• He demonstrated that clear white light was composed of seven visible colors.
• One of the greatest scientific books ever written, Opticks, details Newton's findings from his experiments using prisms to bend light.
• The phenomenon of splitting light into its constituent colors is called dispersion.​
• The bending of light as it moves from one transparent substance into another is known as refraction.
• The bending caused by refraction allows us to create rainbows, prisms, magnifying glasses, and lenses.
• Our eyes are dependent on this light bending as well.

The correct answer is Punjab.

Key Points

• The first wave of the Green Revolution package was received by more prosperous states of Haryana, Punjab, Andhra Pradesh, Tamil Nadu and Western Uttar Pradesh.
• The Green Revolution in India:
• The Green Revolution, which refers to the large-scale introduction of high-yielding varieties of seeds, fertilizers, and pesticides in agriculture, has been criticized for its negative impact on small farmers.
• The Government of India launched the Green Revolution in 1965 under the Third Five-Year Plan(1961-66).
• MS Swaminathan is considered the father of the Green Revolution in India.
• Norman Borlaug is known as the 'Father of Green Revolution' in the world.
• In India, the aim of this revolution was to increase the productivity of agricultural crops, particularly wheat and rice.
• The main focused crops were Wheat, Rice, Jowar, Bajra and Maize.
• In the first phase of the Green Revolution, the use of HYV seeds was limited to the more prosperous states of Haryana, Punjab, Andhra Pradesh, Tamil Nadu and Western Uttar Pradesh.
• HYV seeds refer to high-yielding varieties of seeds that were developed during the Green Revolution to increase crop yields.
• These are resistant to insects and diseases and have a high yield capacity.​

Additional Information

• The Green Revolution was a period of agricultural transformation that took place in the 1960s and 1970s in India.
• The goal of the Green Revolution was to increase agricultural productivity and food security by introducing high-yielding crop varieties (HYV seeds), modern irrigation systems, and chemical fertilizers and pesticides.
• It was a significant success in India, as it helped to increase agricultural output (especially wheat and rice) and reduce food shortages.
• However, it also had some negative impacts, such as environmental degradation, soil erosion, and the loss of traditional farming practices.

The correct answer is Mission Amrit Sarovar.

Key Points

• The Government of India initiated Mission Amrit Sarovar, aimed at developing and rejuvenating 75 water bodies in each district of the country, as a part of the celebration of Azadi ka Amrit Mahotsav.
• The Prime Minister of India, Mr. Modi, has launched it on April 24, 2022.
• The mission is actively carried out by eight Central ministries and departments: the Department of Rural Development, the Department of Land Resources, the Department of Drinking Water and Sanitation, the Department of Water Resources, the Ministry of Panchayati Raj, the Ministry of Forest, the Ministry of Environment and Climate Changes, the Ministry of Railway, and the Ministry of Road, Transport & Highways.
• It has enlisted the Bhaskaracharya National Institute for Space Application and Geo-informatics (BISAG-N) as a technical partner.

Additional Information

• Azadi Ka Amrit Mahotsav (AZAM):
• It is an initiative of the Government of India to celebrate and commemorate 75 years of independence and the glorious history of its people, culture and achievements.
• It commenced on March 12, 2021, which started a 75-week countdown to our 75th anniversary of independence and ended on August 15, 2023.
• The Mahotsav is being celebrated on the basis of its 5 pillars:

1. Struggle for independence,
2. Ideas of 75 years,
3. Achievements of 75 years,
4. Actions of 75 years and
5. Resolutions of 75 years.

The correct answer is 2.9%.

Key Points

• The prevalence of self-reported goitre or thyroid disorder in the National Family Health Survey V {NFHS-V (2019-2021)} was 2.9%.
• While in NFHS IV (2015-2016), it was 2.2%.
• It is believed that iodine supplementation can cause a spurt in autoimmune thyroid dysfunction and hypothyroidism by making the thyroid gland more susceptible to damage by the body’s own immune system.

Additional Information

• The NFHS (National Family Health Survey) is a multi-round, extensive survey that is carried out in a representative sample of Indian households.
• The International Institute for Population Sciences (IIPS) in Mumbai has been tasked by the Ministry of Health and Family Welfare (MoHFW) as the focal institution for coordinating and providing technical guidance for the survey.
• The survey provides state and national data for India on : Fertility, Infant and child mortality, The practice of family planning, Maternal and child health, Reproductive health, Nutrition, Anaemia, Utilization and quality of health and family planning services.
• The first NFHS-1 was conducted in 1992-93.
• NFHS-5 captured the data during 2019-21 and was conducted in 2 phases.
• It includes some new topics, such as preschool education, disability, access to a toilet facility, death registration, bathing practices during menstruation, and methods and reasons for abortion.
• Key findings of National Family Health Survey (NFHS)-V (2019-21):
• According to NFHS-5 data, the country's sex ratio in India in 2019–2021 was 1,020 women for every 1000 men.
• Total Fertility Rate (TFR) was 2 in 2019-2021, just below the replacement fertility rate of 2.1.
• Just five states in India have fertility levels over the replacement threshold of 2.1: Bihar (2.98), Meghalaya (2.91), Uttar Pradesh (2.35), Jharkhand (2.26) and Manipur (2.17).
• Total Fertility Rate (TFR) shows the expected number of children that a woman can have between the ages of 15 and 49 throughout her reproductive years.
• Child nutrition statistics indicate a little improvement across the board in India, with stunting falling from 38% to 36%, wasting from 21% to 19%, and underweight falling from 36% to 32%.
• At the national level, the percentage of institutional births has significantly grown from 79% to 89%.
• The percentage of children under six months old who receive exclusive breastfeeding improved across India from 55% in 2015-16 to 64% in 2019-21.

The correct answer is Commercial banks priority sector lending.

Key Points

• Commercial banks priority sector lending (PSL):
• This refers to mandatory lending requirements imposed by regulatory authorities like the Reserve Bank of India (RBI) on commercial banks.
• These banks must allocate a specific portion of their loans to specific categories considered "weaker sections," including small and marginal farmers, micro and small enterprises, and weaker sections of society like scheduled castes and scheduled tribes.
• This makes it the most conventional and widespread form of formal sector lending reaching these groups.
• Rather of financing only successful industries or locations that are crucial to economic growth, the aim of a PSL project is to give credit to the less fortunate segments of society.
• Financial assistance is readily available to all key sectors, allowing them to apply for loans that banks are obligated to provide at a reduced interest rate.

Additional Information

• Money lenders: Traditionally, money lenders operate outside the formal financial system, often charging high interest rates and lacking transparency.
• While they reach some weaker sections, they are not considered formal sector lending.
• Self-help group (SHG) bank linkage model: This model connects self-help groups formed by underprivileged individuals with banks, facilitating access to formal credit.
• Microfinance institutions (MFIs): Although MFIs cater to low-income populations, they are specialized institutions separate from the mainstream banking system.

The correct answer is assets (reserves + loans) - liabilities.

Key Points

• To determine a bank's net worth, you subtract its liabilities from its assets.
• i.e. Total assets minus total liabilities.
• Assets: Everything the bank owns (loans, cash, investments, buildings, etc.)
• Liabilities: Everything the bank owes (customer deposits, loans payable, etc.)
• Net worth: The difference between assets and liabilities (what the bank truly owns after accounting for all its debts)

Additional Information

• Reserve Bank of India (RBI) is India’s central bank.
• In compliance with the terms of the Reserve Bank of India Act, 1934, it was founded on April 1, 1935 in Calcutta.
• It was permanently moved to Mumbai in 1937.
• Though originally privately owned, since nationalisation in 1949, the Reserve Bank is fully owned by the Government of India.
• As a qualitative instrument of monetary policy, the Reserve Bank of India (RBI) employs moral suasion.
• It regulates the issue of Bank notes and keeping of reserves with a view to securing monetary stability in India and generally to operate the currency and credit system of the country to its advantage.
• It also monitors the monetary policies through its Monetary Policy Committee (MPC).

The correct answer is Ustad Amjad Ali Khan.

Key Points

• Ustad Amjad Ali Khan:
• He is a traditional Indian sarod player best recognized for his quick and fluid ekhara taans.
• Khan has been performing all around the world since the 1960s and was raised in a classical music family.
• He received the Padma Vibhushan, India's second-highest civilian medal, in 2001; the Padma Bhushan, India's third-highest civilian honor, in 1991; and the Padma Shree in 1975.

Additional Information

• Ustad Bismillah Khan was an Indian musician credited with popularizing the shehnai, a reeded woodwind instrument.
• Ustad Zakir Hussain is a globally renowned Tabla player.
• Hariprasad Chaurasia is a celebrated Bansuri player.
• ​Some other famous instrumentalists:

The correct answer is CaCl₂

Key Points

• CaCl2 (calcium chloride) is responsible for permanent hardness in water.
• Hard water has a high mineral content.
• It is formed when water percolates through the deposits of chalk and limestone, which are made up of magnesium and calcium carbonates.
• It does not lather with soap, so it is not suitable for laundry purposes.
• It can damage boilers because it causes salt to build and lowers the boiler's performance.
• Although hard water is safe to drink, consuming it frequently can cause a number of issues, including:
• skin strain
• Water appliances have to work harder, which raises the cost of water.
• Spots show up on linens and clothing.

Additional Information

• There are two categories of water hardness:
• 1. Temporary Hardness of Water:
• Water becomes momentarily hard due to the carbonates of calcium and magnesium present.
• In this instance, boiling the water will eliminate the hardness.
• The soluble salts of Mg(HCO₃)₂ are changed into the insoluble Mg(OH)₂ when water is boiled; this precipitates and is eliminated.
• We obtain soft water as a result of filtration.
• 2. Permanent Hardness of Water:
• The presence of soluble compounds of calcium and magnesium in water in the form of chlorides and sulfides is referred to as permanent hardness because boiling cannot eliminate this hardness.
• By using washing soda to treat the water, we may get rid of this hardness.
• When washing soda combines with the calcium and magnesium sulfide and chloride salts, insoluble carbonates are created, turning hard water into soft water.

The correct answer is Kabichandra Kalicharan Patnaik.

Key Points

• Odisha's classical dance style was named "Odissi" by Oriya poet, dramatist, and researcher Kavichandra Kalicharan Pattanayak.
• Kavichandra Kalicharan Pattanayak:
• He, was often called Kabichandra, was a renowned Odishan writer and artist.
• He made contributions to the fields of Odissi theater, dance, and music.
• Additionally, he made a substantial contribution to the early development of the Odia film.
• On December 23, 1898, he was born in Badamba, a princely kingdom at the time.
• The Odissi music and dance community frequently performs his pieces in a variety of traditional ragas.

Additional Information

• Raja Ram Mohan Roy:
• ​In Radhanagar, Bengal, on May 22, 1772, Raja Ram Mohan Roy was born into an orthodox Brahman household.
• He is regarded as the "Father of Modern India" and ‘Father of Indian Renaissance’.
• In Patna, he studied Persian and Arabic in his early schooling. There, he read the Quran, the writings of Sufi mystic poets, and the Arabic translations of Plato and Aristotle.
• He read the Vedas and Upnishads and studied Sanskrit in Benaras.
• When he was sixteen, he penned a logical criticism of Hindu idolatry after returning to his village.
• He served as Woodforde's and Digby's personal diwan for the East India Company from 1803 until 1814.
• He left his position in 1814 and relocated to Calcutta to dedicate his life to religious, social, and political reforms.
• He founded the Atmiya Sabha in 1815, the Calcutta Unitarian Association in 1821, and the Brahmo Sabha in 1828 which later became the Brahmo Samaj.
• Rabindranath Tagore:
• Bengali polymath Rabindranath Tagore (7 May 1861 – 7 August 1941) was involved in the Bengal Renaissance.
• He was a poet, novelist, playwright, composer, philosopher, social reformer, educator, and painter.
• Using Contextual Modernism in the late 19th and early 20th centuries, he transformed Indian art and music as well as Bengali literature.
• In 1913, he became the first non-European and the first lyricist to win the Nobel Prize in Literature.
• He was awarded the Nobel Prize for Literature in recognition of his work Geetanjali.
• In the 1915, King George V bestowed upon Tagore a knighthood, which he later renounced following the 1919 Jallianwala Bagh massacre.
• While Tagore's graceful prose and enchanted poetry were immensely well-liked throughout the Indian subcontinent, his poetic songs were perceived as mystical and mercurial.
• He was a fellow of the Royal Asiatic Society.
• Tagore was referred as "the Bard of Bengal" and went by the monikers Gurudeb, Kobiguru, and Biswokobi.
• Geetanjali, Sadhana, Ghare-Baire, Gora and Rabindra Sangeet are among his important works.
• His works, "Jana Gana Mana" in India and "Amar Shonar Bangla" in Bangladesh, were selected as national anthems by two countries. West Bengal has made "Banglar Mati Banglar Jol" into its official state anthem.
• In 1901 he founded the famous Shantiniketan which later came to be known as Vishwabharati University.

The correct answer is Kartika.

Key Points

• Kartik (October-November):
• The Hindu calendar's eighth month, Kartik, is linked to the celebration of Deepavali (Diwali), the festival of lights.
• The month is also linked to the observance of Karva Chauth, a festival honoring the marriage union of husband and wife.
• It is also linked with festival of Bhai Dooj.​

Additional Information

• Chaitra (March-April): 
• In the Hindu calendar, the first month is Chaitra and is highly fortunate.
• Occurs in March or April on the Gregorian calendar.
• The Hindu New Year, known in Maharashtra as Gudi Padwa, in Andhra Pradesh and Telangana as Ugadi, and in other parts of India as Chaitra Navratri, ushers in the month.
• The month is linked to fresh starts, development, and wealth as well as the start of the spring season.
• Ashwin (September-October): 
• According to the Hindu calendar, Ashwin, the seventh month, is connected to the celebration of Navratri, a holiday honoring the divine feminine force.
• Additionally, the month is linked to the celebration of Dussehra, a festival honoring Lord Rama's victory over the demon king Ravana.

The correct answer is Bihar.

Key Points

• The highest population density (person per square kilometre), as per the 2011 Census, is in Bihar, with 1106
• The population density of West Bengal is 1028, Kerala is 860, and Uttar Pradesh is 829.
• The overall population density of India is 382.
• Census of India 2011:
• It started on April 1, 2010.
• "Our Census, Our Future" was the 2011 census's slogan.
• India's population, according to the 2011 Census, is estimated to be 1.21 billion.
• The population density was 382 persons per square kilometer in 2011.
• India's sex ratio, as per the 2011 census, is 940.
• India's child sex ratio is 918, the lowest since the country's independence, as per Census 2011.
• This marked the commencement of the 15th Census of India and the 7th Census of Independent India (2011).
• The Indian Census Commissioner for 2011 was C. Chandramouli.
• The 2011 India Census was carried out in two phases:
• House listing and Housing Census (April to September 2010).
• Population Enumeration (9th to 28 February 2011).

Additional Information

• Population density is the number of people per unit of area, usually transcribed as "per square kilometer" or square mile.
• The 1948 Census Act governs how the census is carried out.
• The Indian Home Minister at the time, Sardar Vallabhbhai Patel, spearheaded the bill for this Act.
• The Indian Constitution's Article 246 declares the population census to be a Union subject.
• It is mentioned in the Seventh Schedule of the Constitution under serial number 69.
• The Ministry of Home Affairs' Office of the Registrar General and Census Commissioner oversees the decennial census.
• The first census of India was conducted by Lord Mayo in 1872.
• The first official census was started by Lord Ripon in 1881.

The correct answer is Concurrent list.

Key Points

• India's Constitution establishes a crucial framework that defines the nature of the political system, the authorities' responsibilities, and the people's basic rights and obligations to the nation.
• The protection of peoples' fundamental rights is the primary goal of the constitution.
• The Indian Constituent Assembly enacted the constitution on November 26, 1949 and became operative on January 26, 1950.
• Some features of Indian constitution were borrowed from constitutions of different countries of the world.
• Important provisions adopted from the Constitution of Canada:
• Centrifugal form of federalism where the centre is stronger than the states.
• Residuary powers vest with the centre
• Centre appoints the Governors at the states
• Advisory jurisdiction of the Supreme Court .
• Concurrent list was adopted from Australian Constitution.

Additional Information

• List of Borrowed Features of Indian Constitution:

The correct answer is Microbial gum.

Key Points

• Xanthan gum is a microbial gum produced by the bacterium Xanthomonas campestris.
• This polysaccharide finds numerous industrial applications, one of which is as a prevalent food additive.
• It works well as a stabilizer and thickening agent to keep ingredients from separating.
• It can be made through fermentation from simple sugars or carbohydrates.
• It was first identified by US Department of Agriculture researcher Allene Rosalind Jeanes and her team, and in the early 1960s, CP Kelco commercialized it under the brand name Kelzan.

Additional Information

• Seed gum: This type of gum is extracted from the seeds of various plants like guar beans and locust beans.
• Examples include guar gum and tara gum.
• Seaweed gum: This type of gum is extracted from different types of seaweeds.
• Examples include agar-agar, alginate, and carrageenan.
• Exudate gum: This type of gum is naturally exuded from trees and other plants as a protective measure.
• Examples include gum arabic and gum tragacanth.

The correct answer is Nawab Abdul Latif.

Key Points

• Muhammedan Literary Society:

• Muslim writers in British India formed the Mohammedan Literary Society.

• It was founded in Calcutta in 1863 by Nawab Abdul Latif, and the Muslim Institute of Calcutta took its place in 1930.

• Latif served as the society's secretary, and Mysore's Prince Mahomed Ruheemoodin served as president.

• The society used Arabic, English, Persian, and Urdu languages.

• Nawab Bahadur Qazi Abdul Latif:

• He was a social worker, professor, and nobleman of Bengali Muslim descent.

• In 1880, the British bestowed upon him the title Nawab.

• He was among the first Muslims in India during the 1800s to accept modernity.

Additional Information

• Sir Syed Ahmed Khan:
• He was born into a wealthy, aristocratic family with intimate ties to the Mughal court in Delhi, the capital of the Mughal Empire.
• He received instruction in both science and the Quran.
• In his insightful pamphlet "Asbab-e-Baghawat-e-Hind" (Reasons for the Indian Revolt of 1857), he identified the main causes of the uprising as British ignorance and aggressive expansionist policies.
• He supported interfaith harmony as well. In addition, he wrote a book titled "Commentary on the Holy Bible" and was a Christian scholar.
• In order to further education, he founded a number of educational institutions, the most notable of which was the Muhammadan Anglo-Oriental College (MAOC), founded in 1875.
• It subsequently evolved into the Aligarh Muslim University.
• Mirza Ghulam Ahmad:
• The Ahmadiyya Movement, which he founded, got its start in Punjab, British India, in 1889.
• It was a movement of modern messianism.
• It was established on liberal ideas, the belief that religion should be accessible to all people, opposition to jihad, etc.

The correct answer is Maharastra.

Key Points

• Maharastra is the top producer of jowar in India.
• Jowar:
• It is a crop that is mostly grown in moist areas and is rainfed; irrigation is rarely necessary.
• In terms of both production and area, it ranks as the third-most significant food crop.
• Rainfall: 30-100 cm of moderate rain.
• Temperatures: high temperatures ranging from 20 to 32°C.
• Vulnerability of Jowar: Both excessive moisture and prolonged drought are harmful.
• Soil: Light soils with good drainage are ideal.
• It is cultivated as the major food crop in semi-arid areas of central and south India.
• In north India, Jowar is mainly a Kharif crop whereas it is sown as both Kharif and Rabi in the southern states.
• Maharashtra, Karnataka, Andhra Pradesh, and Madhya Pradesh are the top producers.
• India is the largest producer of jowar in the world.

Additional InformationList of major millet producing state as of 2024:

The correct answer is 1935.

Key Points

• The structural part of the Indian Constitution is, to a large extent, derived from the Government of India Act, 1935.
• Government of India Act, 1935:
• There was a growing demand for constitutional reforms in India by Indian leaders.
• India’s support to Britain in the First World War also aided in British acknowledgment of the need for the inclusion of more Indians in the administration of their own country.
• The Act was based on
• Simon Commission Report
• The recommendations of the Round Table Conferences
• The White Paper published by the British government in 1933 (based on the Third Round Table Conference)
• Report of the Joint Select Committees.
• Features of the Government of India Act 1935: 
• It provided for the establishment of an All-India Federation consisting of provinces and princely states as units.
• The Act divided the powers between the Centre and units in terms of three lists - Federal List (for Centre, with 59 items), Provincial List (for provinces, with 54 items) and the Concurrent List (for both, with 36 items).
• Residuary powers were given to the Viceroy. However, the federation never came into being as the princely states did not join it.
• It abolished dyarchy in the provinces and introduced ‘provincial autonomy’ in its place.
• It provided for the establishment of a Reserve Bank of India to control the currency and credit of the country.
• It provided for the establishment of not only a Federal Public Service Commission but also a Provincial Public Service Commission and Joint Public Service Commission for two or more provinces.
• It provided for the establishment of a Federal Court.

Additional Information

• Government of India Act, 1919:
• It is also known as Montagu-Chelmsford reform or Montford reform.
• The matters, which were of National importance or related to more than one province were governed at the central level, such as Foreign Affairs, Defence, Political Relations, Communication, Public Debt, Civil and Criminal Laws, Wire services, etc.
• The Central Legislature was made more powerful and more representative by this Act.
• The Act introduced a bicameral legislature; the Lower House or Central Legislative Assembly and the Upper House or Council of State.
• The legislators, under the new reforms, could now ask questions and supplementary, pass adjournment motions, and vote a part of the budget, but 75% of the budget was still not votable.
• The legislature had virtually no control over the Governor-General and his Executive Council.
• Indian Councils Act of 1909:
• It is also called the Morley-Minto Reforms.
• Important reform measures enacted under it are:
• The legislative councils at the Centre and the provinces increased in size.
• Central Legislative Council – from 16 to 60 members.
• Legislative Councils of Bengal, Madras, Bombay, and United Provinces – 50 members each.
• Legislative Councils of Punjab, Burma, and Assam – 30 members each.
• The legislative councils at the Centre and the provinces were to have four categories of members as follows:
• Ex officio members: Governor-General and members of the executive council.
• Nominated official members: Government officials who were nominated by the Governor-General.
• Nominated non-official members: nominated by the Governor-General but were not government officials.
• Elected members: elected by different categories of Indians.​
• Indian Independence Act, 1947:
• India was proclaimed an independent and sovereign state by the Act.
• On the basis of religious disagreements, it also included provisions for the division of the Indian state into the independent dominions of India and Pakistan.
• The Secretary of States for India post was eliminated.
• Along with the elimination of the Viceroy's position, the Act provided for the appointment of two distinct Governors-General—one for each of the dominions of India and Pakistan—on the recommendation of the British Cabinet.
• Both the dominions' Constituent Assemblies had the authority to draft their own constitutions and to override any British Parliament legislation created for the Indian state, including the Independence Act itself.
• The Constituent Assemblies were empowered to act as legislative bodies for their respective dominions till the time they could formulate a constitution for their state.
• It granted authority to the princely states to join either of the dominions or remain independent.
• The British Monarch no longer had the authority to veto or ask for the bills of the Indian state.

The correct answer is Alpine.

Key Points

• Alpine is a type of vegetation found in the Himalayan region.
• Alpine:
• This type of vegetation is characterized by low-growing plants, grasses, mosses, and lichens adapted to harsh cold and windy conditions at high altitudes.
• The Himalayas, being a vast mountain range, have extensive alpine zones with diverse flora perfectly suited to this environment.

Additional Information

• Mangrove: These are salt-tolerant trees and shrubs found in coastal areas and tidal wetlands, mainly in tropical and subtropical regions. The Himalayas are far from the coast and lack the necessary conditions for mangroves to thrive.
• Pampas: These are tall grasses native to South America, primarily Argentina and Uruguay.
• Savannah: These are grasslands with scattered trees and shrubs, typically found in Africa.

The correct answer is Anahat Singh.

Key Points

• Anahat Singh:
• She is an Indian squash player who was born on March 13, 2008.
• She was the youngest athlete to represent India at the 2022 Commonwealth Games, having turned 14 years old.
• She took home the Asian Junior Squash Individual Championships Girls U15 championship in June 2022.
• She emerged victorious at the August 2023 Asian Junior Squash Individual Championships in Dalian, China, winning the Girls U17 division.
• Subsequently, she won two bronze medals in the women's team event and mixed doubles alongside Abhay Singh in Asian Games, 2022.

Additional Information

• Squash:
• It is a racquet and ball sports, but squash's dynamics are very different from other racquet and ball sports like tennis etc.
• It was created in England in the early 1800s and has quickly become well-liked by players of all skill levels.
• It is a part of the Asian Games since 1986 and the Commonwealth Games since 1998, although not yet being an Olympic sport.
• Since the mid-1970s, there have also been high-profile, specialised competitions such as the World Squash Championships.
• Asians Games:
• The Asian Games, also known as Asiad, is a multi-sport event held every four years among athletes from across Asia.
• They were regulated by the Asian Games Federation (AGF) till 1978.
• The first games were in New Delhi, India, in 1951.
• Since the breakup of the Asian Games Federation in 1982, the Olympic Council of Asia (OCA) has organized the Games.
• The Games are recognized by the International Olympic Committee (IOC) and are described as the second largest multi-sport event after the Olympic Games.
• The next edition is expected to be held in Aichi-Nagoya, Japan in 2026.

The correct answer is Kathak.

Key Points

• Kumari Kamala was an exceptional Indian classical Kathak dancer who was born on June 16th, 1934.
• She made appearances in over 100 Tamil, Kannada, Telegu, and Hindi films as a kid dancer.
• With the aid of Shankar Rao Vyas, she became well-versed in Hindustani classical music, and Lachhu Maharaj in Bombay trained her in Kathak.
• With "Nam Iruvar," her film, she achieved great success.
• She starred in the lead role of "Jagathalaprathapan," a Tamil film.
• She was asked to play for Queen Elizabeth II's coronation celebrations in 1953, and during the 1950s, she went on tour through China and Japan.
• Even after receiving the Branta Professorship in 1975, she attended Colgate University for two terms.
• In 1970, she received the Padma Bhushan.

Additional Information

• Kathak:
• The well-known ancient Indian classical dance known as Kathak is said to have originated with the nomadic storytellers from North India known as Kathakars.
• These Kathakars traveled and told tales using songs, dances, and music that were reminiscent of classical Greek theatre.
• The foundations of Kathak are rooted in the Natya Shastra, an ancient Sanskrit text written by Bharata Muni.
• The three chief sections of a Kathak dance are:
• Invocation: The act of an artist offering a prayer or salutation to God and their guru is known as an invocation.
• Hindu performers employ mudras, or hand gestures, to convey the same message.
• On Muslim holidays, the artist presents a "salami."
• Nritta: The artist's portrayal of pure dancing.
• He or she begins by moving the neck, wrists, and eyebrows slowly and elegantly.
• The quick sequences according to "bols" come next. A bol is a brief rhythmic pattern sequence. Here, the artist also demonstrates lively footwork.
• Nritya: In this piece, the performer uses facial expressions, slow body motions, and vocal and instrumental music to tell a tale or explore a theme.
• 8 important Classical Dance forms of India:

The correct answer is Kalaripayattu.

Key Points

• SRD Prasad:
• Padma Shri 2023 has been given to Kerala's Kalaripayattu Acharya SRD Prasad in recognition of his services to sports.
• The martial technique that SRD Prasad Gurukkal learned from his father, Chirakkal T. Sreedharan Nair, a legendary figure in Kalaripayattu, has been a lifelong study and teaching endeavour for him.
• Respected and experienced in the world of kalarippayattu, Prasad is also a skilled author and orator with mastery over the martial artform.
• He is the recipient of the Sangeet Natak Akademy award.
• He operates the well-known SRD Prasad Gurukul to educate interested parties about the specialised art form.
• Kalaripayattu:
• The words "Kalari" (meaning gym or training area) and "payattu" (meaning to battle or exercise) are the origin of the phrase Kalaripayattu.
• Kerala is where Kalaripayattu, one of the world's oldest and most scientific martial arts, originated.
• Praised as Kerala's pride, it enjoys international recognition and esteem.
• The first step of the training is to massage the body with oil until it is supple and agile.
• Other essential elements of the art form are feats like marichil (somersault), ottam (running), and chattom (jumping).
• Additionally, there are instruction in the use of weapons such as maces, swords, daggers, spears, and bows and arrows.
• The ultimate goal is complete mental-body synergy. Kalaripayattu also emphasises specialising in traditional medical methods.

Additional Information

• Padma Shri:
• The Padma Shri, which is also written Padma Shree, is the fourth-highest civilian honor granted by the Indian Republic, ranking behind the Bharat Ratna, Padma Vibhushan, and Padma Bhushan.
• Awardees are chosen for their "distinguished contribution in various spheres of activity including the arts, education, industry, literature, science, acting, medicine, social service and public affairs."
• The award was established on January 2, 1954.
• Every year on India's Republic Day, the Indian government bestows this honour.

The correct answer is Adjustments for congestion of urban life.

Key Points

• Net Economic Welfare (NEW):
• A suggested national income metric called net economic welfare aims to quantify the expenses associated with crime, pollution, traffic, and other "negative" spillovers in an effort to determine the genuine national income.
• To date, it has not been widely adopted.
• It is an adjusted assessment of the entire production of the country that only includes investments and consumption that directly enhance economic well-being.
• It is computed as deductions for things like environmental harm, adjustments for congestions and other negative externalities from gross national product (GNP) and additions of value of leisure and the black market to the gross national product (GNP).

Additional Information

• Gross National Product (GNP):
• It is an estimate of the total value of all the final products and services turned out in a given period by the means of production owned by a country's residents.
• GNP is commonly calculated by taking the sum of personal consumption expenditures, private domestic investment, government expenditure, net exports, and any income earned by residents from overseas investments, then subtracting income earned by foreign residents.
• Net exports represent the difference between what a country exports minus any imports of goods and services.
• ​​Gross National Product (GNP) at Factor Cost or GNPFC :It is referred to as the gross money value of all the final goods and services that are produced by the residents living within the boundaries of a nation during one accounting year excluding the net indirect taxes.
• It is shown as: GNPFC = GNPMP - Net Indirect Taxes.

The correct answer is Reserve Bank of India.

Key Points

• In India, the Reserve Bank of India (RBI) fixes the CRR for the banks in the economy.
• Cash Reserve Ratio (CRR) is an important tool used by the RBI to manage liquidity in the banking system and control inflation.
• Cash reserve ratio (CRR): 
• It is a monetary policy tool used by central banks, including the Reserve Bank of India (RBI), to regulate and control the money supply in the economy.
• CRR is the percentage of total deposits that commercial banks are required to keep as reserves with the central bank.
• It is a portion of the bank's demand and time liabilities.
• The primary objective of implementing CRR is to ensure the liquidity and stability of the banking system while controlling inflation and managing credit growth.
• When the central bank increases the CRR, it reduces the amount of money available for lending by commercial banks.
• This helps reduce excess liquidity in the economy by controlling inflationary pressures and curbing excessive credit expansion.
• On the other hand, when the central bank decreases the CRR, it increases the amount of money available for lending by commercial banks.
• This can stimulate credit growth, promote economic activity, and ease liquidity conditions in the economy.

Additional Information

• Reserve Bank of India (RBI):
• It is India’s central bank.
• In compliance with the terms of the Reserve Bank of India Act, 1934, it was founded on April 1, 1935 in Calcutta.
• It was permanently moved to Mumbai in 1937.
• Though originally privately owned, since nationalisation in 1949, the Reserve Bank is fully owned by the Government of India.
• It also functions as the "lender of last resort" and is considered Banker to Banks.
• It regulates the issue of Bank notes and keeping of reserves with a view to securing monetary stability in India and generally to operate the currency and credit system of the country to its advantage.
• It also monitors the monetary policies through its Monetary Policy Committee (MPC).

GIVEN:

A number is first increased = 16%

A number is second increased = 20%

The number so obtained is now decreased = 40%

CALCULATION:

Let, the original number = N

⇒The first increased = N × (116/100) = 29N/25

⇒The second increased = (29N/25) × 120/100 = (29N/25) × (30/25) = 870N/625 = 174N/125

⇒The number so obtained is now decreased = (174N/125) × 60/100 = 522N/625

⇒The net decreased percentage in the original number = (N - 522N/625) × 100 =  $625N - 522N \over 625$ × 100 = $103N\over 625$ × 100 = $412N\over 25$  = 16$12\over25$%

∴ Option 1 is the correct.

Shortcut Trick Let, original number = 100

Now,

⇒100 × $116\over 100$ × $120\over 100$ × $60 \over 100$ = $8352 \over 100$ = $2088\over 25$

⇒100 - $2088\over 25$ = $412\over 25$ = 16$12\over25$%.

Option 1 is the correct

Given:

Angle θ = 60° 

Radius (r) = 21 cm

Formula used:

The length of arc = $2\pi r\over 360$× θ 

Calculation:

Length of arc (l) = (2× $22\over7$ × 21) / 360 × 60° = 22 cm.

∴ The length of arc CD is 22 cm.

Calculation:

According to the given data,

Number of boys whose height is less than 170 = 82

∴ The correct answer is 82.

Given:

∠Q = 50^°

∠P = 70^°

ΔPQR similar to ΔSTR

Concept used:

If two triangles are similar then the ratio of their sides and their corresponding angle will be equal.

Calculation:

⇒ ∠R = 180 - (∠P + ∠Q) = 180 - 120 = 60° 

According to the concept,

∠S = 70°      [∵ ∠P = 70° ]

Similarly, ∠T = 50°      [∵ ∠Q = 50° ]

Also,

PQ = ST, QR = TR, PR = SR, and  ∠PRQ = 60°

But, ∠TSR = 70° 

So ∠TSR = 80° will be not correct. 

∴ The option 1 is NOT correct.

Given:

Time taken by Ram  to complete a work = 18 days

Time taken by Reena to complete a work = 12 days

Time taken by Ram, Reena and Shyam together to complete a work = 6 days

Concept used:

Time taken to complete a work is inversely proportional to efficiency

Calculation:

Total work = 36 (LCM of 18, 12 and 6 = 36)

⇒ Efficiency of Ram = 36 / 18 = 2

⇒ Efficiency of Reena = 36 / 12 = 3

⇒ Efficiency of Ram, Reena and Shyam together = 36 / 6 = 6

⇒ Efficiency of Shyam (alone) = 6 - (2 + 3) = 1

⇒ Time taken by Shyam (alone) to complete a work = Total work / Efficiency of Shyam

⇒ Time taken by Shyam = 36 / 1 = 36 days

∴ The correct answer is 36 days.

Given: 

Curved surface area of the cone = 990 cm²

Diameter of the cone = 42 cm.

Formula Used: 

Curved surface area of a right circular cone =   $\pi r l$

Where, r is the radius and l is the slant height.

Calculation:

Radius of the cone = 42 / 2 = 21 cm

According to the question,

⇒  $\frac{22}{7}\times 21\times l$ = 990 

⇒ 15 cm

∴ Slant height of the cone is 15 cm.

Given:

MP = 35% above CP

Profit = 14%

Formula used:

MP(100 - discount%) = CP ( 100 + Profit%)

Calculation:

Let the CP be 100

So, MP = (100 +35)/100 × 100 = 135

⇒ 135(100 - Discount%) = 100 (100 + 14)

⇒ 135(100 - discount%) = 100 × 114

⇒ 135 (100 - Discount%) = 11400

⇒ 100 - Discount% = 84.44

⇒ Discount% = 15.55%

∴ The rate of discount is 15.55%

Given:

a = 12

b = 6√5

Formula Used:

Third proportional = $\frac{b^2}{a}$

Calculation:

Third proportional = $\frac{(6√{5})^2}{12}$

⇒ 15

∴ Third proportional of 12 and 6√ 5 is 15.

Given :

Quantity of the old mixture = 70 litres

Water in old mixture = 10 %

Calculation:

Amount of water in the old mixture = 10% of 70 = 7 litres

Amount of wine in the old mixture = 70 - 7 = 63 litres

So, Amount of wine in the resulting mixture = 63 litres     [∵ No addition of wine]

Let X litres of water be added to the mixture 

According to the question 

⇒ 7 + X = 9      ------(1)

Now,

⇒ (100 - 12.5)% = 63    

⇒ 87.5 % = 63    

⇒ 1 % = $\frac{63}{87.5\%}$

So, Water in resulting mixture = 12.5 % = $\frac{63}{87.5\%}\times12.5$ = 9 litres

Putting the value of X in equation (1),

⇒ 7 + X = 9

⇒ X = 2 

∴ 2 litres of water must be added.

Formula Used:

1. sin θ/cos θ = tan θ
2. cot θ = 1/tan θ
3. sin²θ + cos²θ = 1

Calculation :

According to question 

⇒ ( cot B - tan B ) × sin B · cos B

Put the value in the formula

⇒ $(\frac{cosB}{sinB} -\frac{sinB}{cosB}) × sinB.cosB$

⇒ $\frac{cos^2B-sin^2B}{sinB.cosB} \times sinB.cosB$

⇒ $\frac{cos^2B-(1-cos^2B)}{sinB.cosB}$ × sin B.cos B

⇒ cos²B - 1 + cos²B

⇒ 2 cos² - 1

Hence, the correct option (3).

Given : 

 $\triangle$TUV is similar to  $\triangle$PQR and areas are 18 cm2 and 32 cm2,  TU = 6 cm,

Concept used : 

In this type of question. If two triangles are similar then their corresponding angles are congruent and corresponding areas as in proportion of square of their respective sides.

Formula used :

Area $\triangle$ XYZ: Area $\triangle$ ABC = (XY)² : (AB)²

Calculation : 

Using the above formulas, We get

⇒ (TU)² : (PQ)² = 18 : 32

⇒ TU : PQ = √ 9 : √ 16

⇒ 6 : PQ = 3 : 4

⇒ PQ = (4×6)/3

⇒ PQ = 8

Hence, the correct option (2).

Calculation:

Difference between truck Q in year 2023 to 2022 is given by,

⇒ (20% of 375000) - (15% of 350000)

⇒ 75000 - 52500 = 22500

∴ Truck Q in 2023 as compared to 2022 is 22500 more.

Given:

a - b = 5 and ab = 24

Formula Used:

a³ - b³ = (a - b) (a² + ab + b²)

Calculation:

a - b = 5

Squaring both side,

(a - b)² = 5²

⇒ a² + b² - 2ab = 25

⇒ a2 + b² = 25 + 2(24) = 73

a³ - b³ = (a - b) (a2 + ab + b2)

Putting all the values from above,

⇒ a3 - b³ = 5 × (73 + 24) = 5 × 97 = 485

∴ The correct answer is 485.

Given:

Cost price of 11 oranges is Rs.10 

Selling price of 10 oranges is Rs.11 

Formula used:

Gain = Selling price – Cost price 

Gain% = (Gain/CP) × 100

Where CP is the cost price.

Calculations:

Cost price of an orange = 10/11

Selling price of an orange = 11/10 

Gain = (11/10) – (10/11) = 21/110  

Gain% = ((21/110)/(10/11)) × 100

⇒ 21%

∴ The gain percentage is 21%

Given: 

The length of the circular track = 2575 m

Anil's speed = 72 km/h

Arun's speed = 90 km/h

Concept used:

When A and B are moving with x km/h and y km/h, respectively in the same direction,

Relative speed = (x - y) km/h

Formula used:

1 km/h = (5/18) m/s

Speed = Distance / Time

Calculation:

Anil and Anuj are running in the same direction,

Relative speed = (90 - 72) km/h = 18 km/h

⇒ Relative speed = 18 x (5/18) m/s = 5 m/s

Time = Distance / Speed

⇒ Time = 2575 / 5 = 515 s

∴ They will meet again for the first time after 515 seconds.

Concept Used:

Divisibility rule of 8 = Number formed by the last 3 digits should be divisible by 8

Divisibility rule of 3 = Sum of the digits of the number must be divisible by 3

Calculation:

The number 24 can be expressed as 24 = 3 × 8

A number will be divisible by 24 when it is divisible by both 3 and 8

Option 1: 35751 = 3 + 5 + 7 + 5 + 1 = 21 is divisible by 3

The number formed by the last 3 digits is 751, which is not divisible by 8

So, 35751 is not divisible by 24

Option 2: 48168 = 4 + 8 + 1 + 6 + 8 = 27 is divisible by 3

The number formed by the last 3 digits is 168, which is divisible by 8

So, 48168 is divisible by 24

Option 3: 25560 = 2 + 5 + 5 + 6 + 0 = 18 is divisible by 3

The number formed by its last 3 digits is 560, which is divisible by 8

So, 25560 is divisible by 24

Option 4: 49608 = 4 + 9 + 6 + 0 + 8 = 27 is divisible by 3

The number formed by its last 3 digits is 608, which is divisible by 8

So, 49608 is divisible by 24

∴ The correct answer is option 1

Given:

Marked Price = Rs. 2500

Selling Price = Rs. 1800

Formula Used:

$\rm Discount\ Percentage = \frac{Discount}{Marked\ Price} \times 100\%$

Calculation:

⇒ Discount = Marked Price - Selling Price

⇒ Discount = 2500 - 1800

⇒ Discount = 700

⇒ Discount Percentage = (700 / 2500) × 100

⇒ Discount Percentage = 28%

∴ The discount percentage is 28%.

Given:

The amount spent on the Printing is Rs. 1,40,000

Calculation:

According to the information,

12.5% = 140000

⇒ 1% = 11200

Now, Expenditure on Paper cost = (11200 × 15) = Rs. 168000

So, option 1 is correct

Expenditure on Editing = (11200 × 7.5) = Rs. 84000

So, option 2 is correct

Expenditure on Retailer's margin = (11200 × 22.5) = Rs. 252000

So, option 3 is incorrect

Expenditure on transportation = (11200 × 10) = Rs. 112000

So, option 4 is correct

∴ The correct answer is option 3

Given:

$\sin \theta = \frac{43}{47}$

Formula Used:

$\cot \theta = \frac{\cos \theta}{\sin \theta}$

$\cos \theta = \sqrt{1 - \sin^2 \theta}$

Calculation:

⇒ $\sin \theta = \frac{43}{47}$

⇒ $\cos \theta = \sqrt{1 - \left(\frac{43}{47}\right)^2}$

⇒ $\cos \theta = \sqrt{1 - \frac{1849}{2209}}$

⇒ $\cos \theta = \sqrt{\frac{2209 - 1849}{2209}}$

⇒ $\cos \theta = \sqrt{\frac{360}{2209}}$

⇒ $\cos \theta = \frac{6\sqrt{10}}{47}$

⇒ $\cot \theta = \frac{\frac{6\sqrt{10}}{47}}{\frac{43}{47}}$

⇒ $\cot \theta = \frac{6 \sqrt{10}}{43}$

∴ The value of cot θ is $\frac{6 \sqrt{10}}{43}$.

Concept Used:

a² - b² = (a + b) (a - b)

Calculation:

$\frac{1}{8}\left[\frac{1}{b-1}-\frac{1}{b+1}-\frac{2}{b^2+1}-\frac{4}{b^4+1}\right]$

⇒ $\frac{1}{8}[\frac{(b+1-b+1)}{b^2-1}-\frac{2}{b^2+1}-\frac{4}{b^4+1}]$

⇒ $\frac{1}{8}[\frac{2}{b^2-1}-\frac{2}{b^2+1}-\frac{4}{b^4+1}]$

⇒ $\frac{1}{8}[\frac{2b^2+2-2b^2+2}{b^4-1}-\frac{4}{b^4-1}]$

⇒ $\frac{1}{8}[\frac{4}{b^4-1}-\frac{4}{b^4+1}]$

⇒ $\frac{1}{8}[\frac{4b^4+4-4b^4+4}{b^8-1}]$

⇒ $\frac{1}{8}[\frac{8}{b^8-1}]$

⇒ $\frac{1}{b^8-1}$

∴ The correct answer is option 1

Given:

cosec θ =$\frac{17}{15}$

Formula used:

cosec θ = $\frac{Hypotenuse}{Perpendicular}$

cos θ = $\frac{Base}{Hypotenuse}$

Pythagoras theorem says,

Hypotenuse2 = Base2 + Perpendicular2

Calculation:

According to the question,   

cosec θ =$\frac{17}{15}$

As we know,

cosec θ = $\frac{Hypotenuse}{Perpendicular}$

⇒cosec θ =$\frac{Hypotenuse}{Perpendicular}$=$\frac{17}{15}$

Then,

Hypotenuse = 17

Perpendicular = 15

Applying the Pythagoras theorem to find the Base,

Hypotenuse2 = Base2 + Perpendicular2

⇒ 17² = Base² + 15²

⇒ Base² = 17² - 15²

⇒ Base² = 289 - 225

⇒ Base² = 64

⇒ Base = $\sqrt{64}$

⇒ Base = 8 

As we know,

cos θ = $\frac{Base}{Hypotenuse}$

⇒cos θ = $\frac{Base}{Hypotenuse}$ = $\frac{8}{17}$

∴ The value of cos θ is $\frac{8}{17}$

Given:

a² + b²  + c² = 160

a + b + c = 16

Formula Used:

(a + b + c)² = a² + b² + c²  + 2(ab + bc + ca)

Calculation:

(a + b + c)2 = a2 + b2 + c2  + 2(ab + bc + ca)

⇒ 16² = 160 + 2(ab + bc + ca)

⇒ 2(ab + bc + ca) = 256 - 160 = 96

⇒  ab + bc + ca = 96

∴ The value of (ab + bc + ca) is 48.

Given:

The rate of Interest is 10% and in 't' years received interest is 5/8^th of the principal amount

Concept Used:

Simple Interest (SI) = (P × R × t) / 100

Where, P = Principal, R = rate of interest and, t = time

Calculation:

Let, the principal = 8a and the interest received = 5a

Now, if the rate of interest is 3/4^th of 10% then R = 10% × 3/4 = 7.5%

According to the formula,

Required time (t) = (5a × 100) / (8a × 7.5) = 25/3 = 8$\frac{1}{3}$ years

∴ The correct answer is option 3

Given : 

 An equilateral triangle each side = 18 cm 

Formula used : 

inradius of equilateral triangle = Side/2√3

circumradius of equilateral  triangle =  Side/√3

Calculation :

inradius of equilateral triangle = Side/2√3

⇒ Inradius = 18/2√3 

 circumradius of equilateral  triangle =  Side/√3

⇒ circumradius = 18/√3

The ratio of the inradius to circumradius of the triangle 

⇒ 18/2√3 : 18/√3 = 1 : 2