SSC GD Constable Previous Year Paper (Held on: 15th December 2021 Shift 2)

Given :

• Six friends - A, B, C, D, E and F
• They are sitting around a circular table facing the center.

Explanation :

1) D is third to the right of B. 

2) F is to the immediate right of D.

3) C is between D and E. - After positioning C and E only one position is left which will be occupied by the only person left i.e A.

Thus, according to the final arrangement A is sitting between F and B.

Hence, "A" is the correct answer.

Logic : [Square of (Second number - 1)] + 1 = First number

So,

• 26 : 6

⇒$(6 - 1)^2$ + 1 = 26

⇒$(5)^2$ + 1 = 26

⇒25 + 1 = 26

⇒26 = 26 (LHS = RHS)

• 37 : 7

​⇒$(7 - 1)^2$ + 1 = 37

⇒$(6)^2$ + 1 = 37

⇒36 + 1 = 37

⇒37 = 37 (LHS = RHS)

Similarly,

• ? : 11

​⇒$(11 - 1)^2$ + 1 = ?

⇒$(10)^2$ + 1 = ?

⇒100 + 1 = ?

⇒? = 101

Hence, "101" is the correct answer.

Logic : The pattern followed here is row wise.

(First number + Third number) ÷ 2 = Second number 

So,

• First row :

​(26 + 12 ) ÷ 2 = 19

38 ÷ 2 = 19

19 = 19 (LHS = RHS)

• Third row :

(23 + 17) ÷ 2 = 20

40 ÷ 2 = 20

20 = 20 (LHS = RHS)

Similarly,

• Second row :

​(32 + 16) ÷ 2 = ?

48 ÷ 2 = ?

? = 24

Hence, "24" is the correct answer.

So,

• Pointing to a photograph of a boy, Aditya said, “He is the only son of my mother-in-law’s only daughter.” - It means Aditya's mother-in-law has only one daughter, thus Aditya is the husband of her daughter. And Aditya is the father of the boy as he is the son of his mother-in-law's daughter, who is his wife.

​

As, it is clear from the family tree that the boy is the son of Aditya.

Hence, "Son" is the correct answer.

According to given figure:

The figure will appear when it is opened as follows:

Hence, "Option - (2)" is the correct answer.

Logic : Opposite letter's position value is written against each letter according the English alphabetic series.

So,

• GLARE is written as :

​

• DUST is written as :

​

Similarly,

• HYPER is written as :

​

Hence, "19211229" is the correct answer.

The image embedded in given figure is as shown below :

∴ Here, Option figure 4 is embedded in given figure.

Hence, the correct answer is "Option-(4)".

Logic : The pattern followed here is alternately.

Hence, "51" is the correct answer.

Logic : 

• (+6) is added the first letter's position value.
• (+7) is added the second letter's position value.
• (+8) is added the third letter's position value.

So,

• BGL : HNT

​

Similarly,

• EIM : ?​

Hence, "KPU" is the correct answer.

According to the sequence in the dictionary.

5. Patella
6. Patent
7. Paternalism
8. Patience
9. Patient

Hence, the correct answer is "4, 5, 2, 3, 1"

Logic : Square of consecutive odd numbers are added.

Hence, "90" is the correct answer.

The pattern followed here is : 

• (2) is subtracted from the position value of the first letter.
• (3) is subtracted from the position value of the second letter.
• (4) is subtracted from the position value of the third letter.

So,

Hence, "HBM" is the correct answer.

The logic followed here is:

• Pharmacy is a place where medicines are compounded or dispensed.

Similarly,

• Museum is a place where historical objects are kept.

Hence, the correct answer is "Museum".

Additional Information 

Logic : 

• Consonants - (2) is added to the position value.
• Vowels - (2) is subtracted from the position value .​

So, 

• LOTUS is written as :

Similarly,

• TULIP is written as :

Hence, "VSNGR" is the correct answer.

The logic followed here is :-

1) DSE - There is at least one vowel i.e 'E'.

2. MMV - There is no vowel.

3. LPU - There is at least one vowel i.e 'U'.

4. AMU - There are two vowels i.e 'A' and 'U'.

Thus, Out of the four letter clusters only second option doesn't have a vowel in it.

Hence, "MMV" is the correct answer.

Let the number be = X

Now, according to the question :-

• Twice of a number :

⇒X = 2x

• Added to 3 :​

⇒2x + 3

• Multiplied by 5

⇒(2x + 3) 5

• Added to the number itself

⇒[(2x + 3) 5] + X

• It gives 158​

⇒[(2x + 3) 5] + X = 158

⇒10X + 15 + X = 158

⇒11X = 158 - 15

⇒11X = 143

⇒X = 143/11

⇒X = 13

So, the square of the number will be :-

⇒$(13)^2$ = 169

Hence, "169" is the correct answer.

Given : 

• Eight girls - K, L, M, N, O, P, Q and R
• They are sitting in two lines, with four girls in each line.
• Both the lines are facing the same direction.
• One line is behind the other line.

​Explanation :

1) K is at a corner and to the immediate left of P. 

2) Two persons are sitting between K and R.

3) L is just behind P.

As  L is just behind P, therefore P is sitting in the first row.

4) O is between L and M. 

5) O is to the immediate left of M.

6) N is not in the front line.

As after positioning N only one position is left which will be occupied by the only person left i.e Q.

Thus, according to the final arrangement Q  is sitting between P and R.

Hence, "Q" is the correct answer.

The correct mirror image of the given combination when mirror is placed at PQ is as shown below:

Detailed Explanation:

• The line PQ is the mirror
• The word "NUMERICAL" the fourth letter is "E". So, the mirror image should be "

" ⇒ Option 2 is eliminated.

• The word "NUMERICAL" the mirror is placed vertically instead of horizontally ⇒ Option 3 is eliminated..
• The word "NUMERICAL" the mirror is placed vertically instead of horizontally ⇒ Option 4 is eliminated.

Hence, the correct answer is "Option - 1".

Given : K U _ _ N K _ Q P _ _ U _ P N

By checking options :

1. QPUNKQ → K U Q P N K U Q P N K U Q P N → (It follows the pattern of : KUQPN - KUQPN - KUQPN)
2. QPUNQK → K U Q P N K U Q P N Q U K P N → (It doesn't Follows the pattern)
3. QQPUNK → K U Q Q N K P Q P U N U K P N → (It doesn't Follows the pattern)
4. QUPQNK → K U Q U N K P Q P Q N U K P N → (It doesn't Follows the pattern)

⇒Option - (1) gives the pattern of " K U Q P N - K U Q P N - K U Q P N "

Hence, "QPUNKQ" is the correct answer.

Logic : 

• (1) is added to each letter's position value.
• last letter's one additional code is added i.e (1) is also subtracted from the position value of the last letter.

So, 

• TONIC is coded as :

​

• PRINT is written as :

Similarly,

• SUPER is written as :

Hence, "TVQFSQ" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some roses are lilies → Does not follow (As some roses are pansies, some lilies are pansies. So, some roses are lilies is possible but not definitely true)

II. All pansies are daisies → Does not follow (As some roses are pansies, all roses are daisies. So, all pansies are daisies is possible but not definitely true)

∴ Here, Neither conclusion I nor II follows.

Hence, the correct answer is "Neither conclusion I nor II follows".

Logic : The pattern followed followed here is diagonally.

• The shaded triangle is shifting diagonally alternately.
• After shifting diagonally , the shaded area shifts after one gap in the clockwise direction.
• The pervious shaded triangle is eliminated simultaneously.

​

Hence, "Option - (4)" is the correct answer.

The faces opposite to each other are shown below:

⇒ As the alternate positions becomes opposite to each other and the remaining two faces becomes opposite to each other.

So, opposite pairs are:

• D → F
• E → H
• C → G

Therefore,

• Option(1) → E and D ⇒ Not opposite (As E is opposite to H and D is opposite to F)
• Option(2) → E and H ⇒ Opposite
• Option(3) → C and F ⇒ Not opposite (As C is opposite to G and F is opposite to D)
• Option(4) → C and H ⇒ Not opposite (As C is opposite to G and H is opposite to F)

Hence, "E and H" is the correct answer.

The correct Venn diagram the best illustrates the relation between Mothers, Daughters, Females is shown below:

As,

• Mothers are someone's daughter , therefore mother will be inside the daughter.
• Mothers and daughters are female , therefore they will be inside the female.

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

Given : 45 + 35 × 7 – 81 ÷ 9 = 321

So, by interchanging the number according to question :

• Option - (1) : 45 and 35

35 + 45 × 7 – 81 ÷ 9 = 321

35 + 45 × 7 – 9 = 321

35 + 315 - 9 = 321

350 - 9 = 321

341 ≠ 321 (LHS ≠ RHS)

• Option - (2) : 45 and 7

7 + 35 × 45 – 81 ÷ 9 = 321

7 + 35 × 45 – 9 = 321

7 + 1575 - 9 = 321

1582 - 9 = 321

1573 ≠ 321 (LHS ≠ RHS)

• Option - (3) : 7 and 9

45 + 35 × 9 – 81 ÷ 7 = 321

45 + 35 × 9 – 11.57 = 321

45 + 315 - 11.57 = 321

360 - 11.57 = 321

348.43 ≠ 321 (LHS ≠ RHS)

• Option - (4) : 45 and 81

81 + 35 × 7 – 45 ÷ 9 = 321

81 + 35 × 7 – 5 = 321

81 + 245 - 5 = 321

326 - 5 = 321

321 = 321 (LHS = RHS)

Hence, "45 and 81" is the correct answer.

The correct answer is the Constitutional amendment.

Key Points

• Article 368 of the Constitution of India mentions two types of amendments to the Indian Constitution.
• One type of amendment is by a special majority of Parliament (Lok sabha and Rajya sabha) and the second type of amendment is by a special majority of the Parliament with the ratification by half of the total states.
• But, some other articles provide for the amendment of certain provisions of the Constitution by a simple majority of the members of each House present and voting (Similar to the ordinary legislative process).
• Notably, these amendments are not deemed to be amendments to the Constitution for the purposes of Article 368.

Additional Information

• Agricultural Procedures:
• Article 48 in the Constitution of India is related to agriculture and animal husbandry.
• This article come under Part 4 which is the Directive Principle of State Policy.
• Parliament:
• It comes between Articles 79 and 122 of the Indian Constitution.
• It consists of the President, Lok Sabha, and Rajya Sabha.
• ​Center-state relation:
• Articles 264 to 293 of Part Xii of the Constitution deal with financial relations between the Centre and the state.
• Since India is a federal country, it follows the separation of powers relating to taxes and it is the duty of the centre to allocate funds to the states.

The correct answer is Article 51A.

Key Points

• 42^nd Amendment Act of 1976 added to Fundamental Duties to the Indian Constitution 86th Amendment Act 2002 later added 11^th Fundamental duty to the list.
• Swaran singh committee in 1976 recommended fundamental duties, the necessity of which was felt during the internal emergency of 1975-77.
• The Fundamental Duties are dealt with Article 51A under Part-IV a of the Indian Constitution.

Additional Information

• Article 18:
• It talks about the abolition of titles.
• It says: No title, not being a military or academic distinction, shall be conferred by the state.
• Article 81:
• It defines the composition of the House of the people or Lok Sabha.
• It states that the House shall not consist of more than 550 elected members of whom not more than 20 will represent Union Territories.
• Article 21A:
• The constitution (Eighty-sixth Amendment) Act, 2002 inserted Article 21 A in the constitution of India to provide free and compulsory education of all children in the age group of six to fourteen years as a fundamental right in such a manner as the state may, by law.

The correct answer is Iqta.

Key Points

• Like the earlier sultans, the Khalji and Tughluq monarchs appointed military commanders as the governors of territories of varying sizes.
• These lands were called iqta and their holder was called iqtadar or muqti.
• The duty of the muqtis was to lead military campaigns and maintain law and order in their iqtas.
• In exchange for their military services, the muqtis collected the revenues of their assignments as salary.
• They also paid their soldiers from these revenues.
• Control over muqtis was most effective if their office was not inheritable and if they were assigned Iqtas for a short period before being shifted.

Additional Information

• Khalji dynasty:
• It was founded by Jalal-ud-din Khalji who ruled from 1290 to 1296.
• The Khilji dynasty succeeded the Mamluk Dynasty or the slave dynasty (1206-1290) which was ruled by the early Turkish rulers.
• Tughluq:
• Ghiyas-ud-din Tughluq or Ghazi Malik was the founder of the Tughluq dynasty.
• Tughluq's policy was harsh against Mongols.

The correct answer is Murshidabad.

Key Points

• Hazarduari Palace is a landmark of sizable importance in Murshidabad, West Bengal.
• The palace was given to the Archaeological Survey of India (ASI) for preservation in 1985 and sprawls over a huge area.
• Hazarduari Palace was earlier called Bara Kothi and lies within the Kila Nizamat campus.
• It lies near the Ganga River's bank and was built in the 19th century by the famous architect Duncan Macleod, during the reign of Nawab Nazim Humayun Jah who ruled Bengal, Orissa, and Bihar from 1824 to 1838.

Additional Information

• Archaeological Survey of India:
• It is an attached agency of the Ministry of Culture of the Government of India.
• It engages in archaeological research and conservation, and protection and preservation of ancient monuments and archaeological sites in the country.
• ASI regulates all archaeological activities conducted in the country through the provisions of the Ancient Monuments and Archaeological Sites and Remains Act (AMASR Act), 1958.
• It also regulates the Antiquities and Art Treasure Act, 1972.

The correct answer is 2009.

Key Points

• Project Snow Leopard was launched in 2009 to promote an inclusive and participatory approach to conserving snow leopards and their habitat.
• Snow Leopard is on the list of 21 critically endangered species for the recovery program of the Ministry of Environment Forest and Climate Change.
• Snow Leopard conservation breeding program is undertaken at Padmaja Naidu Himalayan Zoological Park, Darjeeling, West Bengal.

Additional Information

• Global Snow Leopard and Ecosystem Protection (GSLEP) Programme:
• The GSLEP is a high-level inter-governmental alliance of all the 12 snow leopard range countries.
• The snow leopard countries namely, India, Nepal Bhutan, China, Mongolia, Russia, Pakistan, Afghanistan, Kyrgyzstan, Kazakhstan, Tajikistan, and Uzbekistan.
• It majorly focuses on the need for awareness and understanding of the value of Snow Leopard for the ecosystem.

The correct answer is Arunachal Pradesh.

Key Points

• The India state of forest report 2021 has vindicated what activists, lawyers and academicians have been saying all along**- Arunachal Pradesh, Which is second-largest forested state in India, is losing its primary forests and that too at a large scale every passing year.**
• As per the ISFR 2021- brought out by the Forest Survey of India (FSI) and released on January 13- Arunachal Pradesh has a geographical area (GA of  83,743 sq km with its 16 hill districts, has witnessed a loss of 257 sq km of forest cover compared to the 2019 asssessment.
• Increasing in Arunachal Pradesh is the dumping of muck and road-building debris on the slopes by the contractors.
• Not just in the area where Krong lives but in other district .

Additional Information

• Arunachal Pradesh:
• Chief Minister - Pema Khandu
• Governor - B.D. Mishra
• Legislature - Unicameral (60 seats)
• Lok Sabha - 2 seats
• Rajya Sabha - 1 seats

The correct answer is Laterite.

Key Points

• Laterite soils are very suitable for tea, espresso and cashew cultivation.
• Laterite soils lack fertility due to intensive leaching.
• When manured and irrigated, some Laterite are fantastic for developing the plantation floras like tea,coffee, rubber, cinchona, coconut, areca nut, etc,
• Tea and coffee crops demand evenly distributed rainfall and no problems of water logging.
• The hill slopes provide an easy drainage for rain water and helps to prevent water logging.
• The tea and coffee plantations grow well in loamy soil that is found in large quantities on the hill slopes.

Additional Information

• Alluvial Soil:
• It is widespread in the northern plains and river valleys.
• It covers about 40% of the total land area of the country.
• Black Soil:
• It is also known as 'Regur Soil' or the Black cotton Soil.
• It covers most of the Deccan Plateau.
• Arid Soil:
• It is also known as desert soil.
• It is primarily found in the parts of Haryana, Western Rajasthan, and Punjab, and elongates up to the Rann of Kutch in Gujarat.

The correct answer is Eight.

Key Points

• Eight Indian beaches have been awarded the prestigious 'Blue Flag certification by an International jury comprising members of the following organizations:
• The International Union for Conservation of Nature (IUCN)
• World Tourism Organization (UNWTO)
• United Nations Environment Programme (UNEP)
• Foundation for Environment Education (FEE).

Important Points

• The Blue Flag certification:
• It is a certification that is given to a beach, marina, or sustainable boating tourism operator.
• It also serves as an eco-label.
• The certification indicates their high environmental and quality standards.
• It is awarded by the foundation for Environmental Education, an NGO based in Denmark.
• It was instituted in France in 1985 and for nations out of Europe in 2001.

The correct answer is Anthrax.

Key Points

• Anthrax causes a fatal blood disease known as sorter's disease.
• It is a rare infectious disease caused by the bacterium Bacillus anthracis.
• It occurs naturally around the world in wild and domestic hoofed animals, especially cattle, sheep, goats, camels, and antelopes.
• It can also occur in humans when they are exposed to the bacterium, usually through handling animals or animals' hides.
• There are 3 forms of anthrax infection: cutaneous (skin), inhalation (lungs), and gastrointestinal (stomach and intestine).

Additional Information

• Acetobacter pasteurianus:
• It is an acetic acid-producing bacterium commonly found associated with plants and plant products.
• This organism is used in the production of fermented foods, such as kefir, and vinegar.
• Edwardsiella:
• It is a genus of gram-negative, fermentation bacteria of the family Hafniaceae.
• It was first discovered in snakes in 1962.
• Melittangium boletus:
• ​It is a mesophilic proteobacterium that builds a fruiting body and was isolated from soil with rotting wood.

The correct answer is Assam.

Key Points

• Orundoi or Arunodoi Scheme:
• It is a new scheme of the Government of Assam launched on 2nd October 2020.
• Under this scheme, Monetary benefits have been envisaged for more than 24 lac poor households in the state.
• The schematic benefit has been enhanced from 830/- to Rs. 1000/ Women.
• This is the biggest ever scheme in Assam post-independence.
• It will strengthen the role of the women as the money will be deposited in the bank accounts of the women of the families.

Important Points

• Assam:
• Chief Minister - Hemant Biswa Sarma
• Governor - Jagdish Mukhi
• Number of districts - 33
• Lok Sabha seats - 14.
• Rajya Sabha Seats - 7.

The correct answer is Sambad Kumudi.

Key Points

• Raja Rammohan Roy was one of the founders of the Brahmo Sabha, the precursor of the Brahmo Samaj, which was a social-religious reform movement in the Indian subcontinent.
• He had started two newspapers- one in Bangali, which was known as the Sambad kumudi, and another in Persian, which was called the Mirat-ul-Akbar.
• Given below refers to a brief description of the two newspapers:
• Sambad Kumudi:
• It referred to a Bengali weekly newspaper that was published in Kolkata during the first half of the 19th century by Ram Mohan Roy.
• It mentioned a noted pro-reformist publication that had actively campaigned for the abolition (stop) of the Sati Pratha.
• Mirat-ul-Akhbar (Mirror of News):
• It referred to a Persian language journal rant that was founded as well as edited by Raja Rammohan Roy.

Additional Information

• Amrita Bazar Patrika:
• It was published on 20 February 1868 by two brothers in the undivided Bengal's Jessore district.
• It shut down in 1991.
• Karmayogin:
• It was originally published in the nationalist newspaper Karmayogin between June 1909 and February 1910.
• It was published by Sri Aurobindo.
• Ananda Bazar Patrika:
• It is an Indian Bengali-language daily newspaper owned by the ABP Group.
• It was published on 1922.

The correct answer is Calcium Carbonate.

Key Points

• The chief component of the nacre that constitutes the pearl is aragonite (Calcium Carbonate).
• Nacre also contains a small amount of conchiolin, a hornlike organic substance (albuminoid) that is the main constituent of the mollusk's outer shell.
• Pearl also contains Magnesium carbonate along with Calcium carbonate.

Additional Information

• Calcium Carbonate:
• It is a common substance found in rocks as the minerals calcite and aragonite and is the main component of eggshells, snail shell, seashells, and pearls.
• The Molar Mass of Calcium Carbonate is 100.0869 g/mol.
• Melting point: 825-degree celsius.

The correct answer is Kerala.

Key Points

• Kerala became the first state to fix the floor price for vegetables, which would be 20 percent above the production cost.
• The scheme would come into effect from November 1, 2020.
• This was the first time the floor price was fixed for 16 varieties of vegetables produced in Kerala.
• This was also the first such initiative by any state which would provide relief and support to farmers.
• Even if the market price went below this, the produce would be procured at the floor price from farmers.
• Local Self Government (LSG) bodies would play an important role in this scheme as they would be coordinating the procurement and distribution of vegetables.

Important Points

• Kerala:
• Chief Minister - Pinarayi Vijayan
• Governor - Arif Mohammad Khan
• Legislature - Unicameral (141 seats)
• Lok Sabha - 20 seats
• Rajya Sabha - 9 seats

The correct answer is 2022.

Key Points

• India is all set to host AFC Women's football Asian Cup India 2022 from 20th January 2022 in Mumbai, Navi Mumbai, and Pune.
• The tournament will witness 12 teams competing for the trophy.
• AFC Women's Asian Cup India will also be the final stage of Asian qualification for the 2023 FIFA Women's World Cup in Australia and New Zealand.
• Five teams will qualify for the main event directly while two of them will progress to the inter-confederation play-offs.
• Japan is the defending champions of the Women's Asian Cup, having won it in 2018.

Additional Information

• Football Women Asian Cup:
• It is a quadrennial competition in women's football for national teams which belongs to the Asian football conderation.
• It is the oldest women's international football competition and the premier women's football competition in the AFC region for national teams.
• It was founded in 1975.

The correct answer is 24.

Key Points

• Ashoka Chakra is also known as Samay chakra in which the 24 spokes represent 24 hours of the day and is the symbol of the movement of the time.
• The Ashoka chakra is rendered in navy blue on a white background replacing the symbol of the charkha of the pre-independence version of the flag.
• Chakra signifies that there is life in movement and death in stagnation.
• It represents the dynamism of a peaceful change.

Additional Information

• National Flag:
• Our National Flag called Tiranga meaning tricolor was adopted on July 22, 1947, by the constituent assembly on July 22, 1947, by the constituent assembly.
• It is made from Khadi which is domestically spun Indian cotton as a symbol of nationalism and freedom.
• It has three equal horizontal bands.
• The top band consists is saffron which represents strength and courage.
• The middle part is white which denotes honesty, purity, and peace of the nation.
• The bottom is green indicating prosperity, fertility, and growth.

The correct answer is Poshan Abhiyaan.

Key Points

• Union finance minister Nirmala sitharaman announced the plan to merge the existing Supplementary Nutrition Programme (SNP) and the Poshan Abhiyan to strengthen nutritional content, delivery, outreach, and outcome during her Budget 2021-22 speech on February 1, 2021.
• The New scheme would now be called Mission Poshan 2.0.
• However, the budget document also reveals that the budget estimate on nutrition has gone down to Rs. 2700 crore in 2021-22, from Rs. 3700 crores in 2020-21.

Additional Information

• Poshan Abhiyan:
• The government has approved the Centrally Sponsored Scheme 'Pradhan Mantri Poshan Shakti Nirman (PM POSHAN) for providing one hot cooked meal in Government and Government-aided schools from 2021-22 to 2025-26.
• This scheme is being implemented by the Ministry of Education.
• The tagline of Poshan Abhiyaan is Sahi Poshan Desh Roshan.
• The program aims to provide adequate nutrition to infants, pregnant ladies, and lactating mothers.

The correct answer is Gyanendro Ningombam.

Key Points

• On being elected unopposed, Ningobam becomes the first President from the North East region to spearhead Hockey India.
• He formerly held the position of officiating President after Mohd Mushtaque Ahmed had tendered his resignation in July this year.
• On 6 November 2020, Manipur's Gyanendra Ningombam was elected unopposed as the President of Hockey India.
• He was elected for a term of two years.
• He served as the Chief Executive Officer of Manipur Hockey between 2009-2014 and has been associated with Manipur Hockey for over a decade.

Additional Information

• About Hockey India:
• It is the apex body of the country which has the sole mandate to govern and conduct all activities for both men and women hockey in India.
• Formed on May 20, 2009, it is also affiliated with the International Hockey Federation (FIH), the Indian Olympic Association (IOA), and Asian Hockey Federation (AHF).
• It is recognised as National Sports Federation by the Ministry of Youth Affairs and Sports, Government of India, and since 28 February 2014, it is acting as the sole body responsible for promoting Hockey in India.

The correct answer is Tuluva dynasty.

Key Points

• Sri Krishnadeva Raya was the most illustrious king of the Vijayanagar Empire.
• He belonged to the Taluva dynasty.
• When he ascended the throne in 1509, the affair of the Empire was in a gloomy state.
• The sultan of Bijapur and the rulers of Orissa were a constant threat to the empire.
• He defeated the combined Muslim forces of Deccan Sultanates and captured Raichur Doab in 1512 AD.
• He maintained friendly relations with the Portuguese.
• Besides being a great warrior, he was an able administrator and a liberal patron of art and literature.

Additional Information

• Saluva Dynasty:
• This dynasty's rulers were the rulers of northern Karnataka in modern India.
• This dynasty was ruled by three kings from 1485 to 1505.
• Saluva Narasimha
• Thimma Bhupala
• Narasimha Raya II
• Sangama Dynasty:
• The Sangama dynasty was a dynasty of the Vijayanagara Empire founded in the 14th century by two brothers: Harihara I and Bukka Raya I.
• Aravidu Dynasty:
• It was the fourth and last Hindu dynasty, of Telugu language and origin, which ruled the Vijayanagar Empire in South India.

The correct answer is West Bengal.

Key Points

• Swapna Barman became the first Indian female heptathlete to win gold in the Asiad event.
• She overcame an immense amount of pain to script the record in Jakarta.
• She finished with her personal best score of 6026 which included her personal best throw in Javelin.
• She hails from the Jalpaiguri district of West Bengal.
• In August 2019, she was honoured with the Arjuna Award.

Important Points

• Heptathlon:
• It is a seven-event contest that covers a range of track and field events and is spread over two days.
• The first day comprises 100m hurdles, a high jump, a shot put, and 200m, while day two has a long jump, javelin, and 800m.

Additional Information

• Asian Games:
• It is the oldest and most prestigious event on the Olympic Council of Asia (OCA) calendar, dating back to the inaugural edition in 1951.
• Like the Olympic games, they are held every four years.
• The 2018 Asian Games in Jakarta and Palembang, Indonesia will be the 18th edition.

The correct answer is Dushyanta.

Key Points

• Abhigyan Shakuntalam is an excellent drama by Mahakavi Kalidas.
• It has been acclaimed internationally.
• It consists of seven acts that deal with the well-known love story of king Dushyant and the maiden Shakuntala.
• This love story has been presented artistically.
• It is a pictorial presentation of human feelings.
• It is an excellent presentation of human love and natural love.

Additional Information

• Kalidas:
• He was a Sanskrit author who is often considered ancient India's greatest poet and playwright.
• His plays and poetry are primarily based on the Vedas, the Mahabharata, and the Purana.
• He is still remembered because as Kalidas was a writer, he also wrote many moral poems, also the most popular in most of the region.

The correct answer is The Deccan.

Key Points

• Aurangzeb had depleted his empire's military and financial resources by fighting a long war in Deccan.
• Under his successors, the efficiency of the imperial administration broke down.
• It became increasingly difficult for the later Mughal emperors to keep a check on their powerful mansabdars.
• Nobles appointed as governors (subadars) often controlled the offices of revenue and military administration (Diwani and faujdari) as well.
• This gives them extraordinary political, economic, and military powers over vast regions of the Mughal Empire
• As the governors consolidated their control over the provinces, the periodic remission of revenue to the capital declined.

Additional Information

• Hyderabad:
• Nizam-ul-Mulk Asaf Jah, the founder of Hyderabad state, was one of the most powerful members of the court of the Mughal Emperor Farrukh Siyar.
• The state of Hyderabad was constantly engaged in a struggle against the Marathas to the west and with independent Telugu warrior chiefs (nayakas) of the plateau.
• Awadh:
• Burhan-ul-Mulk Saadat Khan was appointed subadar of Awadh in 1722 and founded a state which was one of the most important to emerge out of the break-up of the Mughal Empire.
• Bengal:
• It gradually broke away from Mughal control under Murshid Quli Khan who was appointed as the naib, deputy to the governor of the province.
• He quickly seized all the power that went with that office.

The correct answer is Bajra.

Key Points

• The cabinet committee on Economic Affairs (CCEA) chaired by prime minister Shri Narendra Modi, has approved the increase in the MSP for all mandated Kharif Crops for Marketing season 2022-23.
• The increase in MSP for Kharif Crops for marketing season 2021-22 is in line with the union budget 2018-19 announcement of fixing the MSPs at a level of at least 1.5 times the All-India weighted average Cost of Production (CoP), aiming at reasonably fair remuneration for the farmers.
• The expected returns to farmers over their cost of production are estimated to be highest in the case of Bajra (85%) followed by urad (65%) and tur (62%).
• For the rest of the crops, the return to farmers over their cost of production is estimated to be at least 50%.

Additional Information

• Minimum Support Price:
• It is the rate at which the government purchases crops from farmers, and is based on a calculation of at least one-and-a-half times the cost of production incurred by the farmers.
• MSP is a "minimum price" for any crop that the government considers as remunerative for farmers and hence deserving of "support".
• Based on the recommendations of the Commission for Agricultural costs and prices, the department of Agriculture and Co-operation, the Government of India declares Minimum Support Price for 22 crops before their sowing seasons.

The correct answer is Punjab.

Key Points

• Catchment Area:
• A river drains the water collected from a specific area, which is called its catchment area.
• The catchment area of the Yamuna river system covers parts of Uttar Pradesh, Uttarakhand, Himachal Pradesh, Haryana, Rajasthan, Madhya Pradesh, and Delhi states.
• The tributaries contribute 70.9% of the catchment area and the balance of 29.1% accounted for direct drainage into the Yamuna river or to the smaller tributaries.
• On the basis of Yamuna amounts to 40.2% of the Ganga Basin and 10.7% of the total land mass of the country.

Important Points

• Yamuna River:
• The river Yamuna, a major tributary of the river Ganges, originates from the Yamunotri glacier near Banderpoonch peaks in the Mussourie range of the lower Himalayas at an elevation of about 6387 meters above mean sea level in district Uttarkashi.
• It is the largest tributary of the Ganga in the northern Plains.

The correct answer is Srigaverapura.

Key Points

• At Sringaverapura near Allahabad in Uttar Pradesh, India, there exists an extraordinary example of hydraulic engineering dating back to the end of the 1st century BC.
• It comprises three percolation-cum-storage tanks, fed by an 11 m wide and 5 m deep canal that is used to skim the floodwaters off the monsoon-swollen Ganga.
• During the reign of Chandragupta Maurya, dams, irrigation systems, and harvesting systems were extensively built throughout his kingdom.

Additional Information

• Water Harvesting System:
• It is a collection and storage of rain, rather than allowing it to run off.
• Rainwater is collected from a roof-like surface and re-directed to a tank, cistern, deep pit, aquifer, or reservoir with percolation so that it seeps down and restores the ground water.

The correct answer is Raghuram Rajan.

Key Points

• Raghuram Rajan is the author of the book "The Third Pillar: How Markets and The State Leave the Community Behind".
• This book is a reflection on the present state of our world seen through the prism of the triad of markets, state, and community, constituting the three pillars of society as it were.
• Raghuram Rajan was the Chief Economist of the International Monetary Fund Between 2003 and 2006.
• He was an Indian economist and 23^rd Governor of the RBI and also the author of the book 'I Do What I Do'.

Additional Information

Given:

CP of 21 articles = SP of 15 articles

Formula Used:

1. Profit = SP - CP

2. Profit% = (Profit/CP) × 100

Calculation:

21 × CP = 15 × SP

⇒ CP/SP = 15/21

Profit = 21 - 15 = 6

⇒ Profit% = (6/15) × 100 = 40%

∴ There is a profit of 40%.

Shortcut Trick

The divisibility rule of 9: The sum of digits should be divisible by 9.

By using the divisibility rule of 9, in the given options, only Option (2) satisfies the divisibility of 9.

So the correct answer is 18.

Alternate Method

Given:

A number when divided by 12, 16 and 20 leaves remainder 6

The number is divisible by 9

Concept used:

The divisibility rule of 9: The sum of digits should be divisible by 9

Calculation:

LCM(12, 16, 20) = 240

⇒ The required number is (240k + 6)

⇒ (240k + 6) is divisible by 9

By hit and trial method, k = 2

⇒ (240 × 2) + 6 = 480 + 6 = 486

Thus, the required number is 486

∴ The sum of the digits of 486 is 18.

Concept Used:

Follow the BODMAS rule according to the table given below:

⇒ 5 × [6 × 2{3 × 7 ÷ (5 × 3)}

⇒ 5 × [6 × 2{3 × 7 ÷ 15}]

⇒ 5 × [6 × 2{3 × 7 × $\frac{1}{15}$}]

⇒ 5 × [6 × $\frac{14}{5}$]

⇒ 5 × $84\over5$

⇒ 84

∴ The value 5 × [6 × 2{3 × 7 ÷ (5 × 3)} is 84.

Given:

The average age of 10 members of a family is 29 years

Formula used:

Average =  $\frac{Sum\ of\ all\ Observations}{Total\ Number\ of\ Observations}$

Calculation:

The average age of 10 members of a family is 29 years

⇒ Sum of ages of all family members = 10 × 29 = 290

The youngest members are twins and each is 5 years old

⇒ Sum of ages of the remaining members = 290 – (10 × 5)

⇒ Sum of ages of the remaining members = 290 – 50 = 240

The average age of family members at the time of birth of twins

⇒ 240/8 = 30 years

∴ The average age of family members at the time of birth of twins is 30 years.

Given:

Sum = 10000

Amount = 13225

Time = 2 years

Formula used:

A = P$(1+ \frac{r}{100})^{nt}$

Where, A = Amount, P = Principal, r = Rate, t = Time

n = Number of times interest is compounded annually

Calculation:

According to the question,

Interest is compounded annually

⇒ 13225 = 10000 × ${(\frac{100 + r}{100})^2}$

⇒ 1.3225 = ${(\frac{100 + r}{100})^2}$

⇒ ​$\sqrt{1.3225}$ = ${\frac{100 + r}{100}}$​

⇒ 1.15 × 100 = 100 + r

⇒ r = 15%

Again, according to the question,

Interest is compounded 8 monthly

⇒ n = 12/8 = 3/2

⇒ r = $\large{\frac{15×8}{12}}$ = 10%

A = 10000 × ${(1 + \frac{10}{100})^{(\frac{3}{2}\times 2)}}$

⇒ A = 10000 × ${(1 + \frac{10}{100})^3}$

⇒ A = 10000 × $\frac{110}{100}$ × $\frac{110}{100}$ × $\frac{110}{100}$ = 13310

CI = 13310 - 10000 = 3310

∴ The interest on 10000 for 2 years at the rate of 15%, interest compounded 8 monthly will be Rs 3310.

Shortcut Trick

Speed of train = Total Distance ÷ Time = (250 + 200) ÷ 45 = 10 m/s.

Speed of man = 6 × (5 ÷ 18) = 5/3 m/s.

Relative speed in same direction = 10 − 5/3 = 25/3 m/s.

Time to pass the man = Train Length ÷ Relative Speed = 250 ÷ (25/3).

Time = 250 × (3 ÷ 25) = 30 seconds.

∴ The correct answer is 30 s.

Alternate Method

Given:

Length of train = 250 m

Length of platform = 200 m

Time taken to cross platform = 45 s

Speed of man = 6 km/h

Formula Used:

Speed = Distance ÷ Time

Relative Speed (Same Direction) = Speed of Train − Speed of Object

Time to cross a moving object = Train Length ÷ Relative Speed

Case 1: Train crossing platform

Train (250 m)

Platform (200 m)

Total Distance = 450 m | Time = 45 s

Case 2: Train crossing man (Same Direction)

Train (250 m)

10 m/s

5/3 m/s Man

Time = ?

Calculations:

⇒ Total distance covered to cross the platform = Length of train + Length of platform

⇒ Total distance = 250 + 200 = 450 m

⇒ Speed of train = 450 ÷ 45 = 10 m/s

⇒ Speed of man in m/s = 6 × (5 ÷ 18) = 5/3 m/s

⇒ Relative speed = 10 − 5/3 = (30 − 5) ÷ 3 = 25/3 m/s

⇒ Time taken to cross the man = Length of train ÷ Relative speed

⇒ Time = 250 ÷ (25/3) = (250 × 3) ÷ 25

⇒ Time = 10 × 3 = 30 s

∴ The correct answer is 30 s.

Additional Information

Relative Speed

When two objects move in the same direction, Relative Speed = S₁ − S₂. When they move in opposite directions, Relative Speed = S₁ + S₂.

Unit Conversion

To convert speed from km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Train Crossing Rules

When a train crosses a stationary object with length (platform, bridge), distance = L_train + L_object. When it crosses a point object (man, pole), distance = L_train.

Given:

Ratio of efficiency of machine and man is 2 : 1

Formula:

Total Work = Efficiency × Time

Calculation:

Total Work = (10 machine + 5 men) × 60

⇒ Total Work = (10 × 2 + 5 × 1) × 60

⇒ Total Work = 25 × 60 = 1500 units

Efficiency of 10 men and 5 machines = (10 × 1) + (5 × 2)

⇒ Efficiency of 10 men and 5 machines = 20 units

Time taken by 10 men and 5 machines to complete the work

⇒ 1500/20 = 75 days

∴ The time taken by 10 men and 5 machines to complete the work is 75 days.

Shortcut Trick Ratio of efficiency of machine and man is 2 : 1

⇒ (10 Mach + 5 Men ) × 60 = (5 Mach + 10 Men ) × D

⇒ (10 × 2 + 5 × 1) × 60 = (5 × 2 + 10 × 1) × D

⇒ 25 × 60 = 20 × D

⇒ Number of days required = (25 × 60)/20 = 75 days 

∴ The time taken by 10 men and 5 machines to complete the work is 75 days.

Given:

Radius of cylinder = 10.5 cm

Volume of cylinder = 5197.5 cm³

Formula Used:

1. Volume of Cylinder = πR²h

2. Total Surface Area of Cylinder = 2πR(R + h)

Where, R = Radius, h = Height

Calculation:

According to the question

5197.5 = 22/7 × 10.5 × 10.5 × h

⇒ h = (495 × 7)/(22 × 10.5)

⇒ h = 15 cm

Total Surface Area of Cylinder = 2 × 22/7 × 10.5 (10.5 + 15)

⇒ Total Surface Area of Cylinder = 2 × 22/7 × 10.5 × 25.5 

⇒ Total Surface Area of Cylinder = 25.5 × 1.5 × 44

⇒ Total Surface Area of Cylinder = 1683 cm²

∴ The total surface area of the cylinder is 1683 cm2.

Shortcut Trick

Speed of the car = 990 ÷ 15 = 66 km/h.

Speed of the train = 180% of 66 = 1.8 × 66 = 118.8 km/h.

Time taken by train = Distance ÷ Speed = 891 ÷ 118.8 = 7.5 hours.

7.5 hours is equal to 7½ hours.

∴ The correct answer is 7½ hours.

Alternate Method

Given:

Distance covered by car = 990 km

Time taken by car = 15 hours

Average speed of train = 180% of average speed of car

Distance to be covered by train = 891 km

Formula Used:

Speed = Distance ÷ Time

Calculations:

⇒ Speed of the car = 990 ÷ 15

⇒ Speed of the car = 66 km/h

⇒ Speed of the train = 180% of 66

⇒ Speed of the train = (180 ÷ 100) × 66 = 1.8 × 66 = 118.8 km/h

⇒ Time taken by the train = 891 ÷ 118.8

⇒ Time taken by the train = 8910 ÷ 1188

⇒ Time taken by the train = 7.5 hours

⇒ 7.5 hours = 7½ hours

∴ The correct answer is 7½ hours.

Additional Information

Average Speed

Average speed is the total distance traveled divided by the total time taken. Formula: Average Speed = Total Distance ÷ Total Time.

Relative Speed

When two objects move in the same direction, their relative speed is the difference of their individual speeds (S₁ − S₂). In opposite directions, it is the sum (S₁ + S₂).

Conversion of Units

To convert speed from km/h to m/s, multiply by 5 ÷ 18. To convert from m/s to km/h, multiply by 18 ÷ 5.

Given:

LCM = 1920

HCF = 4

N₁ = 60

Formula Used:

LCM × HCF = Product of Two Numbers 

Calculation:

1920 × 4 = 60 × N₂

⇒ N₂ =1920 × 4/60 

⇒ N₂ = 128

∴ The second number is 128.

Shortcut Trick

Value of x can be found using the cross-difference formula: x = (ad − bc) ÷ ((a + d) − (b + c))

Given numbers: a = 22, b = 39, c = 56, d = 107

⇒ x = (22 × 107 − 39 × 56) ÷ ((22 + 107) − (39 + 56))

⇒ x = (2354 − 2184) ÷ (129 − 95) = 170 ÷ 34 = 5

Mean proportional between (5 + 3) and (3 × 5 − 7) = √(8 × 8) = 8

∴ The correct answer is 8.

Alternate Method

Given: Numbers are 22, 39, 56, and 107. After subtracting x, they are in proportion.

Formula: If a, b, c, d are in proportion, then a/b = c/d.

⇒ (22 − x) ÷ (39 − x) = (56 − x) ÷ (107 − x)

⇒ (22 − x)(107 − x) = (56 − x)(39 − x)

⇒ 2354 − 22x − 107x + x² = 2184 − 56x − 39x + x²

⇒ 2354 − 129x = 2184 − 95x

⇒ 129x − 95x = 2354 − 2184

⇒ 34x = 170

⇒ x = 5

Now, calculate Mean Proportional (M) between (x + 3) and (3x − 7):

⇒ M = √((x + 3) × (3x − 7))

⇒ M = √((5 + 3) × (3 × 5 − 7))

⇒ M = √(8 × 8) = 8

∴ The correct answer is 8.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is defined as √(a × b).

Third Proportional

If a, b, and c are in continued proportion, then c is the third proportional to a and b, where c = b²/a.

Fourth Proportional

If a, b, c, and d are in proportion, then d is the fourth proportional to a, b, and c, where d = (b × c)/a.

Componendo and Dividendo

If a/b = c/d, then (a + b)/(a − b) = (c + d)/(c − d). This rule is often used to simplify ratio-based equations.

Given:

Anuj completed a double century = 200 Runs

Total number of sixes = 15

Total number of four = 18

Calculation:

Total runs by sixes = 15 × 6 = 90

Total runs by four = 18 × 4 = 72

Total runs by sixes and fours = 90 + 72 = 162 runs 

Runs made by Anuj running between the wickets = 200 - 162 = 38

Percentage of runs made by Anuj running between the wickets

⇒ 38/200 × 100 = 19%

∴ 19% of runs were made by Anuj running between the wickets.

Shortcut Trick  200 - (15 × 6 + 18 × 4) = 200 - (90 + 72) = 38

⇒ Runs % = 38/200 × 100 = 19%

∴ 19% of runs were made by Anuj running between the wickets.

Given:

A₁ = 7920, T₁ = 2 years

A₂ = 11220, T₂= 7 years

Formula used:

1. SI = $\frac{PRT}{100}$

2. Amount = P + SI

Concept Used:

Amount = P + $\frac{PRT}{100}$ = P(1 + $\frac{RT}{100}$)

Calculation:

According to the question,

7920 = P${(1+ \frac{2R}{100})}$       -----(1)

11220 = P${(1+ \frac{7R}{100})}$     -----(2)

Equation(1) ÷ Equation(2)

⇒ 792 + ${\frac{7 ×792 × R}{100}}$ = 1122 + ${\frac{2 × 1122 × R}{100}}$

⇒ ${\frac{R}{100}}$ (5544 - 2244) = 330

⇒ R =  ${\frac{33000}{3300}}$ 

⇒ R = 10%

Shortcut Trick

SI of 5 years = Rs 3300

⇒ SI of 1 year = Rs 660

⇒ SI of 2 years = Rs 1320

P = A - SI

⇒ P = 7920 - 1320 = Rs 6600

SI = (P × R × T)/100

⇒ R = $1320 \times 100\over 6600 \times 2$ = 10%

∴ The rate of interest per annum is 10%.

Given:

Bought an item at Rs 4500

Sold it at a loss of 5%

Bought another item and sold it at a profit of 10%

Formula used:

1. SP = CP × (100 - Loss)/100

2. SP = CP × (100 + Profit)/100

Calculation:

SP of item = 4500 × (100 - 5)/100

⇒ SP of item = 4500 × (95/100) = 4275

He bought another item for Rs 4275 and sold it at a profit of 10%

SP of another item = 4275 × (100 + 10)/100

⇒ SP of another item = 4275 × (110/100) = 4702.5

Overall profit = 427.5 - 225 = 202.5

∴ The overall profit is Rs 202.50.

Shortcut TrickBy successive method,

Final SP = 4500 × $\frac{95}{100}$ × $\frac{110}{100}$ = 4702.5

Overall profit = 427.5 - 225 = 202.5

∴ The overall profit is Rs 202.50.

Shortcut Trick

Using the Alligation method on average weights:

Ratio of original to new students = (58 − 56.5) : (56.5 − 56) = 1.5 : 0.5 = 3 : 1

Given that 1 unit corresponds to 5 new students,

The original number of students (3 units) = 3 × 5 = 15.

∴ The correct answer is 15 students.

Alternate Method

Given:

Average weight of original students = 56 kg

Number of new students = 5

Average weight of new students = 58 kg

Increase in average weight = 0.5 kg (New average = 56.5 kg)

Formula Used:

Average = Sum of observations ÷ Total number of observations

Original (56) New (58)

56.5

58 − 56.5 = 1.5 56.5 − 56 = 0.5

Ratio = 1.5 : 0.5 = 3 : 1

Calculations:

Let the original number of students be x.

⇒ Total weight of original students = 56x

⇒ Total weight of new students = 5 × 58 = 290 kg

⇒ Total number of students = x + 5

⇒ New average = (56x + 290) ÷ (x + 5)

⇒ 56.5 = (56x + 290) ÷ (x + 5)

⇒ 56.5 × (x + 5) = 56x + 290

⇒ 56.5x + 282.5 = 56x + 290

⇒ 56.5x − 56x = 290 − 282.5

⇒ 0.5x = 7.5

⇒ x = 7.5 ÷ 0.5 = 15

∴ The correct answer is 15 students.

Additional Information

Combined Average

When two groups of sizes n₁ and n₂ with averages A₁ and A₂ are mixed, the combined average is given by: A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Alligation Method

It is a quick method to find the ratio of quantities in a mixture. The ratio of the quantity of group 1 to group 2 is (A₂ − A_mix) : (A_mix − A₁).

Deviation Method

The net change in an average is distributed equally among all observations. Net deviation = (New group average − Old average) × Number of new members.

Shortcut Trick

Equate the work done by both groups: (4M + 4W) × 5 = (2M + 5W) × 6

20M + 20W = 12M + 30W ⇒ 8M = 10W ⇒ 4M = 5W (Efficiency ratio M:W = 5:4)

Total Work = (4 × 5 + 4 × 4) × 5 = 36 × 5 = 180 units

Time for 1 Woman = 180 ÷ 4 = 45 days; Time for 1 Man = 180 ÷ 5 = 36 days.

∴ The correct answer is 45 and 36.

Alternate Method

Given:

Group 1: 4 Men and 4 Women finish in 5 days.

Group 2: 2 Men and 5 Women finish in 6 days.

Formula Used:

Total Work = (Number of people × Efficiency) × Time

Calculations:

⇒ (4M + 4W) × 5 = (2M + 5W) × 6

⇒ 20M + 20W = 12M + 30W

⇒ 20M − 12M = 30W − 20W

⇒ 8M = 10W ⇒ M/W = 5/4

⇒ Total Work = (4 × 5 + 4 × 4) × 5 = 180 units

⇒ Time taken by 1 Woman = 180 ÷ 4 = 45 days

⇒ Time taken by 1 Man = 180 ÷ 5 = 36 days

∴ The correct answer is 45 and 36.

Additional Information

Efficiency and Time Relationship

The time taken to complete a task is inversely proportional to the efficiency of the worker. Time = Total Work ÷ Efficiency.

Work Equation for Groups

When different groups complete the same work, use the relation M₁D₁ = M₂D₂ to find the ratio of efficiencies between different types of workers.

Pipes and Cisterns Analogy

This problem follows the same logic as Pipes and Cisterns, where man/woman efficiency acts as the rate of flow and total work acts as the capacity of the tank.

Given:

A : B : C = 2 : 3 : 5

The sum of the squares of these numbers = 3800

Calculation:

Let the A, B, and C be 2X, 3X, and 5X

According to the question,

⇒ (2X)² + (3X)² + (5X)² = 3800

⇒ 4X² + 9X² + 25X² = 3800

⇒ 38X² = 3800

⇒ X²  = 100

⇒ X = 10

⇒ C = 5X = 5 × 10 = 50

∴ The value of C is 50.

Given:

CP = 960

Discount = 20%

Profit = 20%

Formula used:

1. SP = CP × (100 + P)/100

2. MP = SP × 100/(100 - D)

Calculation:

SP = 960 × (100 + 20)/100

⇒ SP = = 960 × 120/100 = 1152

MP = 1152 × 100/(100 - 20)

⇒ MP = 1152 × 100/80 = 1440

∴ MP of the article is Rs 1440.

Shortcut Trick MP/CP = (100 + P)/(100 - D)

⇒ MP/960 = 120/80

⇒ MP = Rs 1440

∴ MP of the article is Rs 1440.

Given:

The diagonal of a cube = $\sqrt{108}$ cm

Formula used:

1. Diagonal of Cube = $\sqrt{3}$ × Side of the Cube

2. Volume of Cube = (side)³

Calculation:

Let the length of the sides of the cube be x cm

⇒ $\sqrt{3}$x = $\sqrt{108}$

Squaring both sides, we get

⇒ 3x² = 108

⇒ x² = 36

⇒ x = 6 cm

Volume of the cube = (6)³ = 216 cm³

∴ The volume of the cube is 216 cm3.

Given:

${5{5\over8}\over6{3\over7}}$ of ${6{7\over11}\over9{1\over8}} ÷{8\over9}(2{3\over11}+{13\over22})$ of ${9\over5}$

Concept:

Follow the BODMAS rule according to the table given below:

Calculation:

${5{5\over8}\over6{3\over7}}$ of ${6{7\over11}\over9{1\over8}} ÷{8\over9}(2{3\over11}+{13\over22})$ of ${9\over5}$ 

⇒ ${45\over8}×{7\over45}$ of ${73\over11}×{8\over73}$(÷{8\over9}({25\over11}+{13\over22}) \) of ${9\over5}$

⇒ ${7\over8}×{8\over11}$(÷{8\over9}({{50+13}\over22}) \) of ${9\over5}$

⇒ $7\over11$ ÷  ${8\over9}×{63\over22}×{9\over5}$

⇒ $7\over11$ × $55\over252$

⇒ $5\over36$

∴ The correct answer is $5\over36$

Shortcut Trick

Interest for 9 months is 12% of the principal (since 0.12 = 12/100).

Convert 9 months to 1 year (12 months) to find the annual rate.

Rate per year = (12% ÷ 9) × 12 = 16%.

∴ The correct answer is 16%.

Alternate Method

Given:

Let the money borrowed (Principal) be P.

Simple Interest (SI) = 0.12 × P

Time (T) = 9 months = 9 ÷ 12 years = 3/4 years = 0.75 years

Formula Used:

Rate (R) = (Simple Interest × 100) ÷ (Principal × Time)

Calculations:

⇒ R = (0.12 × P × 100) ÷ (P × 0.75)

⇒ R = (12 × P) ÷ (P × 0.75)

⇒ R = 12 ÷ 0.75

⇒ R = 1200 ÷ 75

⇒ R = 16%

∴ The correct answer is 16%.

Additional Information

Simple Interest Formula

SI = (P × R × T) ÷ 100, where P is Principal, R is Rate per annum, and T is Time in years.

Relationship between SI and Amount

Total Amount (A) = Principal (P) + Simple Interest (SI). It represents the total money returned.

Time Conversion Rule

Always ensure Time (T) is in years. For months, divide by 12; for days, divide by 365.

Shortcut Trick

Ratio of A : C = 8 : 5 and B gets 75% of A.

If A = 8 units, then B = 75% of 8 = 6 units.

Ratio A : B : C = 8 : 6 : 5. Total units = 8 + 6 + 5 = 19 units.

19 units = ₹9,500 ⇒ 1 unit = ₹500.

B share = 6 × 500 = ₹3,000.

∴ The correct answer is ₹3,000.

Alternate Method

Given: Total amount = ₹9,500. B = 75% of A. A : C = 8 : 5.

Calculations:

⇒ Let A = 8x and C = 5x.

⇒ B = 75% of 8x = (3/4) × 8x = 6x.

⇒ Total = A + B + C = 8x + 6x + 5x = 19x.

⇒ 19x = 9500

⇒ x = 9500 ÷ 19 = 500.

⇒ B share = 6x = 6 × 500 = 3000.

∴ The correct answer is ₹3,000.

Additional Information

Ratio Balancing

When multiple ratios like A:B and B:C are given, make the common term (B) equal by multiplying with suitable factors to get A:B:C.

Percentage to Fraction Conversion

Converting percentages to fractions (e.g., 75% = 3/4, 25% = 1/4) simplifies ratio calculations significantly.

Proportional Division

To divide a total amount S in ratio a:b:c, the share of the first person is [a / (a+b+c)] × S.

Given:

SP = Rs 3750 

Profit = 25%

Formula used:

1. SP = CP × $\frac{100+Profit}{100}$

2. Profit % = $\frac{SP-CP}{CP}$ × 100

Calculation:

According to the question,

3750 = CP ×  $\frac{100+25}{100}$

⇒ CP = (3750 × 100)/125

⇒ CP = 3000

The item is sold for Rs 300 more

⇒ New SP = 3750 + 300 = Rs 4050

Profit % = $\frac{4050-3000}{3000}$ × 100

⇒ Profit % = 105/3 = 35%

∴ The profit percentage of the shopkeeper is 35%.

Given:

Shopkeeper marks his goods 40% above CP

He sells 60% of the goods at MP and remaining at 65% discount on MP

Formula used:

Profit = $\frac{SP-CP}{CP}$ × 100

Calculation:

Let CP be ₹100

Let the total number of goods be 100

Total CP = 100 × 100 = ₹10000

According to the question,

MP = 100 × (140/100) = ₹140

Total SP = $[100×\frac{60}{100}×140]$ + $[100×\frac{40}{100}×140×\frac{35}{100}]$

⇒ Total SP = 8400 + 1960 = ₹10360

Profit% = $\frac{10360-10000}{10000}$ × 100 = 3.6%

∴ The shopkeeper gains 3.6% profit in the whole transaction.

Shortcut TrickMP = ₹140 and SP (at 65% discount) = ₹49

Ratio of goods sold at MP to sold at 65% is 60:40 = 3:2

Here, 140 - 49 = 91, thus 91/(3+2) = 18.2

By mixture and allegation method,

⇒ Profit % = 103.6 - 100 = 3.6%

Shortcut Trick

Required percentage = (Value of First Number / Value of Second Number) × 100

Required percentage = (12 / 48) × 100

Required percentage = 1/4 × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given:

Let the Third Number be 100.

First Number = 12% of 100 = 12

Second Number = 48% of 100 = 48

Calculations:

⇒ Let the numbers be A, B, and C.

⇒ Let C = 100.

⇒ A = 0.12 × 100 = 12

⇒ B = 0.48 × 100 = 48

⇒ Required Percentage = (A / B) × 100

⇒ Required Percentage = (12 / 48) × 100

⇒ Required Percentage = 0.25 × 100

⇒ Required Percentage = 25%

∴ The correct answer is 25%.

Additional Information

Percentage Comparison

To find what percentage X is of Y, use the formula: (X / Y) × 100.

Base Change

When comparing two numbers relative to a third, the third number acts as a common base, allowing direct ratio comparison between the first two.

Fraction to Percentage

Common conversions: 1/4 = 25%, 1/2 = 50%, 3/4 = 75%, 1/5 = 20%.

The correct answer is "support". 

Key Points

• Sustain means keeping something alive for a long period of time. 
• Example: Ron sustained despite his peer pressure.
• Support means to endure something with bravery.
• Example: Luke endured his family's financial needs despite his meagre salary.
• Therefore, support is the most appropriate synonym for sustain.

Additional Information

• Believe - to have faith in something or somebody.
• Example: Harry believed his mother's stories to be true as a child.
• Weaken - to become less strong. 
• Example: Fever weakened Ted's body.
• Suspect - to doubt someone.
• Example: The police suspect William's gang for the burglary.

The correct answer is "corrupt". 

Key Points

• Just means being honest and truthful.
• Example: The ruling party looks just.
• Corrupt means being dishonest and immoral.
• Example: The parent is corrupting the child by gifting her.
• Therefore, the antonym of Just is Corrupt.

Additional Information

• Blur - unclear.
• Example: The path seems blurred because of the fog.
• Fail - unsuccessful in doing something.
• Example: Jim failed to keep up his word.
• Conclude - to bring to an end.
• Example: Sam concluded his speech with a message.

The correct answer is "Distasteful".

Key Points

• Delicious means something that tastes very good.
• Example: My mother cooks deliciously.
• Distasteful means something that tastes very bad.
• Example: I felt that the food from the newly opened restaurant was distasteful.
• Therefore, the antonym of Delicious is Distasteful.

Additional Information

• Satisfactory - upholds the required level.
• Example: Jerry's team managing skills were just satisfactory.
• Sweet - containing a lot of sugar.
• Example: My grandfather was not allowed to eat sweets because of his diabetes.
• Tasteful - something that is very pleasant.
• Example: Rita's designing ideas look tasteful.