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Given:

Median = 18.43

Mean = 37.64

Formula used:

Mode = 3Median – 2Mean

Calculation:

Mode = 3 × 18.43 – 2 × 19.145

⇒ Mode = 55.29 – 38.29 = 17

∴ The mode is 17.

Given;

Mean of a data set = 22

Ratio of Mode and Median = 1 : 3

Formula Used:

Mode = 3(Median) - 2(Mean)

Calculation:

Ratio of mode and Median be 1x : 3x

x = 3 × (3x) - (2 × 22)

⇒ 8x = 44

⇒ x = 44/8

⇒ x = 5.5

Since Mode is x so Mode of the data is 5.5

Median = 3x = 3 × 5.5

Median = 16.5

Mean = 22

Mode = 5.5

∴ The Correct relation is Mean > Median > Mode

Given:

We have to find the average of mean and median of 15, 17, 17, 17, 17, 16, 16, 22, 32, 45

Concept Used:

First, we have to arrange the given data as ascending number then we have to see how many numbers of data (n) are given and calculate their position.

If n is odd then, Median = {(n + 1)/2} th term

If n is even then, Median = [(n/2) th term + {(n/2) + 1} th term]/2

Mode: Maximum time repeated data is the median of the given data.

Average = Sum of all data/Total number of data

Calculation:

Arranging the given numbers in ascending order get, 15, 16, 16, 17, 17, 17, 17, 22, 32, 45

Here the total number of data (n) is 10, which is an even number

Median = [(n/2) th term + {(n/2) + 1} th term]/2

⇒ (5th term + 6th term)/2

⇒ (17 + 17)/2

⇒ 17

Here, maximum time repeated data is 17

Average of median and mode is (17 + 17)/2 = 17

∴ The average of median and mode of the given data is 17.

Given:

11, 13, 19, 20, 22

Concept used:

First, we have to arrange the given data as ascending order then we have to see how many numbers of data (n) is given

If n is odd then, Median = [(n+1)/2]th term

If n is even then, Median = [(n/2)th term + {(n/2) + 1}th term]/2

Mean = (Sum of observation)/(Total number of observation)

Calculation:

11, 13, 19, 20, 22

Median = [(n+1)/2]th term

⇒ Median = (6/2)th term

⇒ Median = 3rd term

⇒ Median = 19

Mean = (Sum of observation)/(Total number of observation)

⇒ Mean = (11 + 13 + 19 + 20 + 22)/5

⇒ Mean = 85/5

⇒ Mean = 17

Required difference = Median - Mean

⇒ Required difference = 19 - 17

⇒ Required difference = 2

∴ The difference between median and mean of given observation is 2.

Given:

Data = {7, 6, 7, 9, 8, 8, 10, 8}

Number of terms = 8

Concept used:

Mode is the most repeated value in a data

If the total number of observations (n) is an odd number,

Median = (n +1)/2th term

If the total number of observations (n) is an even number,

Median = {(n/2)th term + [(n/2) + 1]th term}/2

Mean = (Median + Mode)/2

Calculations:

Arranging the terms in ascending order,

6, 7, 7, 8, 8, 8, 9, 10

Most repeated term in the data = 8 (3 times)

Mode = 8

Median = (4^th term + 5^th term)/2

⇒ (8 + 8)/2

⇒ 8

Mean = (8 + 8)/2

⇒ 8

∴ The mean of mode and median is 8

Given:

Variance of 5 values = 16

Concept used:

If every value is multiplied or divided by the same number, the standard deviation changes by that number, i.e. the standard deviation also gets multiplied or divided by the number.

Formula used:

Standard deviation = √(Variance)

Calculations:

Standard deviation = √(Variance)

⇒ Standard deviation = √16

⇒ 4

∵ Each value is multiplied by 2 , then the standard deviation will also get multiplied by 2.

So, The new standard deviation = 2 × 4 = 8

∴ The standard deviation of the new value is 8.

Given:

Standard deviation(σ )= 4

Formula used:

Variance = σ²

Calculation:

Variance = (4)²

⇒ Variance = 16

∴ The value of variance is 16.

The correct answer is Only (1) and (2).

• The mode is the most frequently occurring observation or value.
  • The mode can be computed by the histogram. Hence, statement 1 is correct.
• The median is the middle value in the list of numbers.
  • Median will be changed if data's are changed. Hence, statement 2 is correct. 
• The variance is a measure of variability and is calculated by taking the average of squared deviations from the mean.
  • The variance depends on the change of scale. Hence, statement 3 is not correct.

Given:

Variance = 81

Concept used:

The positive square root of the variance is called Standard deviation

S.D = √Variance

Calculation:

S.D = √Variance

⇒ S.D = √81

⇒ S.D = 9

∴ The standard deviation of the data is 9.

Chlorobenzene on reaction with CH₃Cl  in presence of AlCl₃ give mixture of o- and p-chlorotoulene

The Wolff-Kishner reduction is an organic reaction used to convert an aldehyde or ketone to an alkane using hydrazine, base, and heat (~200 °C). The driving force for the reaction is the conversion of hydrazine to nitrogen gas. This reaction is used for the reduction of aldehydes and ketones.

(a) they used chariots driven by horses

In the early Vedic-period, Varna system was based on Occupation.

(d) Chalcolithic

(c) Age of the Buddha

(d) Not definitely known factors

(d) All the above

(d) Radio Carbon-14 dating

(d) Daya Ram Sahani

(c) sanitation and public health

(d) All the three

The Harappan Civilisation achieved far greater advancement than Sumer, Elam etc. on account of its town planning.

The correct answer is Alamgirpur.

• Alamgirpur is the eastern extents of Harappan civilization located in Meerut District of Uttar Pradesh.
• Manda is the Northern extent of Harappan civilization located in Akhnoor District of Jammu and Kashmir.  
• Sutkagandor is the Western extent of Harappan civilization located in Baluchistan, Pakistan.
• Daimabad is the Southern extent of Harappan civilization located in the Ahmadnagar district of Maharashtra.

• Alamgirpur is located on the bank of the Hindon river excavated by Yagyadatt Sharma. 
• Manda is located on the Right bank of the Chenab river excavated by J. P. Joshi.
• Sutkagandor is located on the bank of the Dask river excavated by R. L. Staine.
• Daimabad is located on the bank of the Pravara river excavated by B. P. Bopardikar.

The correct answer is C.

• Palwal - Ghafur Ali and Har Sukh Rai.

The table below is correctly matched:

• ​Sadruddin Khan:
  • Sadruddin Khan Azurda Dehlawi (1804 -1868) was an Islamic scholar.
  • Leader of the Indian Rebellion of 1857, and poet during the British era.
  • He was Grand Mufti Delhi and worked for the rebellion against the British government.
• Raja Nahar Singh:
  • Raja Nahar Singh was a Jat king of the princely state of Ballabhgarh in Faridabad District of Haryana, India.
  • His forefathers were Jats from Tewatia Gotra who had built a fort in Faridabad around 1739.
  • He was involved in the Indian Rebellion of 1857.
  • The small kingdom of Ballabhgarh is only 20 miles from Delhi.
• Nawab Ahmed Ali Khan:
  • Nawab Ahmed Ali Khan of Farrukhnagar took part in the Indian Rebellion of 1857.
  • Along with the Nawabs of Jhajjar, Rao Tula Ram of Rewari and Raja Nahar Singh of Ballabgarh, Bhatti chieftains of Hissar and Sirsa, and the Meo tribesmen.

The correct answer is Australia.

• Asia is the biggest and Australia is the smallest continent.
• Listed in order of size are Asia, Africa, North America, South America, Antarctica, Europe, and Australia.

• There are seven continents in the world and Asia is the largest, and according to land-mass, Australia is the smallest at almost one-fifth of the size of Asia, but Europe is not far behind as it has just over a million more square miles than Australia.
• Earth's oldest known piece of continental crust dates to the era of the moon's formation.
  • Australia holds the oldest continental crust on Earth, researchers have confirmed, hills some 4.4 billion years old.
• Africa is the hottest continent on the planet.
• Antarctica is the only continent that does not have an indigenous human population.
  • It is also the least populous of all the countries.
• Antarctica is the largest desert in the world.
  • Although most of the deserts in Europe are classed as "semi- deserts" and was known as the only continent without deserts. 

The correct answer is C, A, B, D.

• Battle of Singoli (1336):
  • It was fought in 1336 A.D.
  • Rana Hammir Singh defeated Muhammad bin Tughluq and annexed Ajmer, Ranthambhore, Nagor and Shivapuri.
  • The Tughlaq dynasty was forced to pay 5,000,000 Tankas for the safe passage of their sultan.
• Battle of Khatoli (1517):
  • In 1517, Ibrahim Lodi became the Sultan of Delhi after the death of his father Sikander Lodi.
  • Rana Sanga had extended his kingdom of Mewar right up to western Uttar Pradesh and threatened to attack Agra.
  • Rana Sanga defeated Ibrahim Lodhi.
• Battle of Gagron (1519):
  • The Battle of Gagron was fought between Rajput army led by Rana Sanga (Maharana Sangram Singh) and Sultanate army led by Sultan Mahmud (Shihab-ud-Din Mahmud Shah II or Sultan Mahmud Khilji II) of Malwa.
  • The battle was fought in the year 1519 A.D.
  • ​Rana Sanga defeated Mahmud Khalji of Malwa.
• Battle of Sammel (1544):
  • In 1544, near the villages, Giri and Sumel of the Jaitaran in the Pali district of Rajasthan, the armies of Sher Shah Suri and Hindu Rajputs led by Rao Maldeo Rathore, king of Marwar fought the Battle of Sammel, also known as the Battle of Giri-Sumel.
  • Sher Shah Suri won the battle and his general Khawas Khan Marwat took possession of Jodhpur and occupied the territory of Marwar from Ajmer to Mount Abu.

The correct answer is C.

• The leader in Mathura during the 1857 Revolt is Devi Singh.
• Kadam Singh was the leader of Meerut during the 1857 Revolt. Hence option C is not correctly matched.

•  Other Places of Revolt of 1857 and Leaders

The correct answer is Tamil.

• The Ramayana in Tamil known as Ramavataram was written by the Tamil poet Kamban during the 12th century.

• The Sri Ranganatha Ramayanam was adapted by Gona Budda Reddy and is the Telugu version of the Ramayana.
• Adhyathmaramayanam Kilippattu is the most popular Malayalam version of the Sanskrit epic Ramayana.
• It is believed to have been written by Thunchaththu Ramanujan Ezhuthachan in the early 17th century.
• Kannada versions of the Ramayana – the Kumudendu Ramayana(a Jain version), written in the 13th century and the Kumara-Valmiki Torave Ramayana, written in the 16th century. 

The correct answer is Valmiki.

• Ramayana is an ancient Indian epic that was composed in the 5^th century BCE.

• This poem narrates the exile and return of Rama, prince of Ayodhya.
• It is one of the two most important Sanskrit epics of ancient India, the other one is Mahabharata.
• It was composed in Sanskrit by Valmiki.
• It is one of the largest ancient epics in world literature and in its present form it consists of 24,000 verses divided into seven books.
• This poem has an important influence on later Sanskrit poetry and Hindu life and culture.

The correct answer is Sunil Gangopadhyay.

• 'Those Days' was originally written as Sei Samoy.
• Sunil Gangopadhyay won the Sahitya Akademi award for Those Days in 1982.
• Important Novels: 
  • Atma Prakash (1966)
  • Purba Paschim (1989)
  • Prothom Alo (1996) 

•  Sumitranandan Pant
  • Won Jnanpith Award Winner in 1968 for Novel ​Chidambara.
  • Kala Aur Bhooda Chand.
  • Pallav
• Nandita Das
  • ​Issac Newton - Scientists of The World.
  • Colors of delight.
  • Hedge Funds.
• Bhartendu Harishchandra
  • ​Satya Harishchandra.
  • Andher Nagari.
  • Bharat Durdasha.

The correct answer is Thiruvananthapuram.

• The Vikram Sarabhai Space Centre (VSSC) is a major space research centre of the Indian Space Research Organisation (ISRO), focusing on rocket and space vehicles for India's satellite programme.
• It is located in Thiruvananthapuram, in the Indian state of Kerala.

• The centre had its beginnings as the Thumba Equatorial Rocket Launching Station (TERLS) in 1962.
• It was renamed in honour of Dr Vikram Sarabhai, often regarded as the father of the Indian space program. 
• The Vikram Sarabhai Space Centre is one of the main research and development establishments within ISRO.
• VSSC is an entirely indigenous facility working on the development of sounding rockets, the Rohini and Menaka launchers, and SLV, ASLV, PSLV, GSLV and GSLV Mk III families of launch vehicles.

The correct answer is Uttarakhand.

• Kedarnath is located in Uttarakhand.
• Kedarnath is dedicated to Lord Shiva.

• Kedarnath is not a part of Chaar Dham yatra.
• The Chaar Dhams are Badrinath, Puri, Dwarka and Rameswaram.
• The Chaar Dhams are located in 4 directions of India.
  • Dwarka in the west,
  • Puri in East,
  • Badrinath in north and
  • Rameswaram in South.

The correct answer is Delhi.

• Election Museum is located in Delhi.
• It also has an important section in Gandhiji's engagement with democracy, set up by the National Gandhi Museum.

• Archaeological Survey of India:
  • The Archaeological Survey of India, established in 1861 is an attached office under the Ministry of Culture dedicated to the protection, preservation, and conservation of the national monuments.

The correct answer is Iran.

• Lotus Temple was designed by an architect Furiburz Sabha who belongs to Iran.
• It is the last of seven Major Bahai temples built around the world.
• Shape- Lotus Flower.
• Lotus Temple was Built in 1986.
• Its structure made up of pure white marble.
• The architect Furiburz Sabha chose the lotus as the symbol common to Hinduism, Buddhism, Bhai Temple Jainism, and Islam.

The correct answer is d and e.

• "Norwegian Wood" and "Kafka On The Shore", both novels are creations of Haruki Murakami.
• The remaining 3 novels are written by Kazuo Ishiguro.
• Kazuo Ishiguro was awarded the Nobel Prize in literature.
  • He is from Nagasaki, Japan.
  • He is best known for his novel “The Remains of the Day”,(published in 1989) about a butler serving an English lord in the years leading up to World War II.

• The 2020 Nobel Laureate in Literature, poet Louise Glück, has written both poetry and essays about poetry.
  • She was awarded "for her unmistakable poetic voice that with austere beauty makes individual existence universal."
• Austrian author Peter Handke has won the 2019 Nobel Prize in Literature.
  • He was awarded "for an influential work that with linguistic ingenuity has explored the periphery and the specificity of human experience."

The Correct Answer is None of the above.

• The Nobel Prize in Literature 2005 was awarded to Harold Pinter.

• The Nobel Prize in Literature is a Swedish literature prize that is awarded annually, since 1901.
• It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895. 
• Nobel Prizes are awarded in the fields of Physics, Chemistry, Physiology or Medicine, Literature, and Peace.
   

• Alfred Nobel was a Swedish chemist, engineer, and industrialist most famously known for the invention of dynamite.
• Malala Yousuafzai became the Youngest person to receive a Nobel Prize at the age of 17, Nobel Peace Prize (2014).
• John B. Goodenough; at the age of 97, received Nobel Prize in Chemistry (2019) is the Oldest person to receive a Nobel Prize.
• Rabindranath Tagore was the first Indian to receive a Nobel Prize.
  • He was awarded the Nobel Prize for Literature in recognition of his work Geetanjali, a collection of poems, in 1913.

The correct answer is Ghiyasuddin Mahmud Shah.

• Ghiyasuddin Mahmud Shah was the last sultan of the Husain Shah dynasty of Bengal.
  • Permitted Portuguese to establish factories at Chittagong and Hooghly.
  • Ghiyasuddin and his Portuguese allies were defeated by Sher Shah Suri in 1538.