SSC CGL 2024 Tier-I Official Paper (Held On: 09 Sept, 2024 Shift 3) (Previous Year Paper)

The image embedded in the given figure is as shown below :

 

∴ Here, the given figure is embedded in option Figure - 3.

Hence, the correct answer is "Option 3".

The logic followed here is:

​'SILK' is written as 'TIML'

And,

'INSECT' is written as 'IOTEDU'

Similarly,

'CHANGE' will be written as

Hence, "Option 4" is the correct answer.

The logic followed here is:  

(19, 456, 6)

19 × 6 × 4 = 456

456 = 456 (LHS = RHS)

And,

(16, 320, 5)

16 × 5 × 4 = 320

320 = 320 (LHS = RHS)

So, checking each option one by one:

Option 1) (18, 378, 7)

18 × 7 × 4 = 378

504 ≠ 378 (LHS ≠ RHS)

Option 2)  (14, 210, 5)

14 × 5 × 4 = 210

280 ≠ 210 (LHS ≠ RHS)

Option 3) (21, 504, 8)

21 × 8 × 4 = 504

672 ≠ 504 (LHS ≠ RHS)

Option 4) (18, 648, 9)

18 × 9 × 4 = 648

648 = 648 (LHS = RHS)

Thus, out of all the options, '(18, 648, 9)' follows the same logic as given.

Hence, "Option 4" is the correct answer.

The logic followed here is:

​Option 1) BEHI

Option 2) TWYZ

Option 3) PSUV

Option 4) FIKL

Thus, out of all the options, 'BEHI' is the correct answer.

Hence, "Option 1" is the correct answer.

Given word: 'JANITOR'

After arranged in alphabetical order:

 

Now,

there are Zero alphabets that will remain unchanged if each of the letters in the word 'JANITOR' is arranged in English alphabetical order.

Hence, the correct answer is "Option 4".

The logic followed here is:

1. First box series →

All the elements shift clockwise.

Center element is replaced by new element subsequently.

2) Second box series →

2^nd column elements shift to the 3^rd column.

2^nd and 3^rd element of third column shift to the 2^nd column diagonally.

Rest of the elements interchange positions.

Thus, the final series is:

Hence, "Option 3" is the correct answer.

The logic followed here is:

(12, 145)

12² + 1 = 145

144 + 1 = 145

145 = 145 (LHS = RHS)

And,

(9, 82)

92 + 1 = 82

81 + 1 = 82

82 = 82 (LHS = RHS)

So, checking each option one by one:

Option 1) (16, 256)

162 + 1 = 256

256 + 1 = 256

257 ≠ 256 (LHS ≠ RHS)

Option 2) (14, 197)

142 + 1 = 197

196 + 1 = 197

197 = 197 (LHS = RHS)

Option 3) (22, 483)

222 + 1 = 483

484 + 1 = 483

485 ≠ 483 (LHS ≠ RHS)

Option 4) (8, 69)

82 + 1 = 69

64 + 1 = 69

65 ≠ 69 (LHS ≠ RHS)

Thus, out of all the options, '(14, 197)' follows the same logic as given.

Hence, "Option 2" is the correct answer.

The logic followed here is:

​

Hence, "Option 4" is the correct answer.

Given series: P _ A A _ _ Z A _V _ _ A _ _

Option 1) VPZZPVAP→ P V A A P Z Z A Z V P V A A P → (It doesn't follow any pattern)

Option 2) ZPVVAPVZ → P Z A A P V Z A V V A P A V Z → (It doesn't follow any pattern)

Option 3) ZVPAPZAV → P Z A A V P Z A A V P Z A A V → (It follows the pattern of: PZAAV - PZAAV - PZAAV)

Option 4) VZAAPVPZ → P V A A Z A Z A A V P V A P Z → (It doesn't follow any pattern)

Hence, "Option 3" is the correct answer.

The number of triangles in the given figure is shown below:

1) Total triangles = Number of parts × Number of diagonals

= 2 × 1 ⇒ 2

 

2) Total triangles = [Number of parts × (1 + Number of parts)] ÷ 2

= [2 × (1 + 2)] ÷ 2

= [2 × 3] ÷ 2

= 6 ÷ 2

= 3

 

3) As marked there are a total of 3 triangles.

Thus, there are total (2 + 3 + 3) = 8 triangles.

Hence, "Option 2" is the correct answer.

According to the given Venn diagram:

The shaded region represents the total number of persons who have applied for more than one post.

So, the total number of persons who have applied for more than one post = (4 + 6 + 8 + 3) = 21

Hence, the correct answer is "Option 1".

The logic followed here is:

Option 1) 36 – 84

36 × 7 ÷ 3 = 84

252 ÷ 3 = 84

84 = 84 (LHS = RHS)

Option 2)  72 – 168

72 × 7 ÷ 3 = 168

504 ÷ 3 = 168

168 = 168 (LHS = RHS)

Option 3) 66 – 154

66 × 7 ÷ 3 = 154

462 ÷ 3 = 154

154 = 154 (LHS = RHS)

Option 4) 33 – 72

33 × 7 ÷ 3 = 72

231 ÷ 3 = 72

77 ≠ 72 (LHS ≠ RHS)

Thus, out of all the options, '33 – 72' is the odd one out.

Hence, "Option 4" is the correct answer.

The logic followed here is:

​CWE : ZFX

And,

PYT : MDI

Similarly,

KIL : ?

Hence, "Option 2" is the correct answer.

According to the given Venn diagram:

The shaded region represents the total number of men who are doctors.

So, the total number of men who are doctors = (23 + 24) = 47

Hence, the correct answer is "Option 1".

The logic followed here is:

​

Hence, "Option 2" is the correct answer.

The figure which will complete the pattern is:

Hence, option 3 is the correct answer.

The logic followed here is:

(34, 47, 62)

34 + 2 = 36 ⇒ Perfect square of 6

47 + 2 = 49 ⇒ Perfect square of 7

62 + 2 = 64 ⇒ Perfect square of 8

And,

(119, 142, 167)

119 + 2 = 121 ⇒ Perfect square of 11

142 + 2 = 144 ⇒ Perfect square of 12

167 + 2 = 169 ⇒ Perfect square of 13

So, checking each option one by one:

Option 1) (27, 38, 51)

27 + 2 = 29 ⇒ Not a perfect square

38 + 2 = 40 ⇒ Not a perfect square

51 + 2 = 53 ⇒ Not a perfect square

Option 2) (48, 65, 82)

48 + 2 = 50 ⇒ Not a perfect square

65 + 2 = 67 ⇒ Not a perfect square

82 + 2 = 84 ⇒ Not a perfect square

Option 3) (64, 78, 99)

64 + 2 = 66 ⇒ Not a perfect square

78 + 2 = 80 ⇒ Not a perfect square

99 + 2 = 111 ⇒ Not a perfect square

Option 4) (79, 98, 119)

79 + 2 = 81 ⇒ Perfect square of 9

98 + 2 = 100 ⇒ Perfect square of 10

119 + 2 = 121 ⇒ Perfect square of 11

Thus, out of all the options, '(79, 98, 119)' follows the same logic as given.

Hence, "Option 4" is the correct answer.

The logic followed here is:

Hence, "Option 4" is the correct answer.

The logic followed here is :-

From the given two different cubes the adjacent sides are as shown below :

As R is common on both the dices, it is clear that M, A, Y, and S are adjacent to it, and the remaining i.e. Q will be opposite to it.

Opposite pairs:

M → Y

A → S

R → Q

So, the opposite side of "S" will be side "A".

Hence, the correct answer is "Option 4".

Given: 24 ÷ 3 – 4 × 2 + 6 × 5 +12 = 50

According to the question, after interchanging the numbers:

Option 1) 5 and 4

24 ÷ 3 – 4 × 2 + 6 × 5 +12 = 50 ⇒ 24 ÷ 3 – 5 × 2 + 6 × 4 +12 = 50

⇒ 24 ÷ 3 – 5 × 2 + 6 × 4 +12 = 50

⇒ 8 – 5 × 2 + 6 × 4 +12 = 50

⇒ 8 + 24 +12 – 10 = 50

⇒ 44 – 10 = 50

⇒ 34 ≠ 50 (LHS ≠ RHS)

Option  2) 4 and 3

24 ÷ 3 – 4 × 2 + 6 × 5 +12 = 50 ⇒ 24 ÷ 4 – 3 × 2 + 6 × 5 +12 = 50

⇒ 24 ÷ 4 – 3 × 2 + 6 × 5 +12 = 50

⇒ 6 – 3 × 2 + 6 × 5 +12 = 50

⇒ 6 + 30 +12 – 6 = 50

⇒ 48 – 6 = 50

⇒ 42 ≠ 50 (LHS ≠ RHS)

Option  3) 24 and 12

24 ÷ 3 – 4 × 2 + 6 × 5 +12 = 50 ⇒ 12 ÷ 3 – 4 × 2 + 6 × 5 +24 = 50

⇒ 12 ÷ 3 – 4 × 2 + 6 × 5 +24 = 50

⇒ 4 – 4 × 2 + 6 × 5 +24 = 50

⇒ 4 + 30 +24 – 8 = 50

⇒ 58 – 8 = 50

⇒ 50 = 50 (LHS = RHS)

Option  4) 3 and 2

24 ÷ 3 – 4 × 2 + 6 × 5 +12 = 50 ⇒ 24 ÷ 2 – 4 × 3 + 6 × 5 +12 = 50

⇒ 24 ÷ 2 – 4 × 3 + 6 × 5 +12 = 50

⇒ 12 – 4 × 3 + 6 × 5 +12 = 50

⇒ 12 + 30 +12 – 12 = 50

⇒ 54 – 12 = 50

⇒ 42 ≠ 50 (LHS ≠ RHS)

Hence, "Option 3" is the correct answer.

The logic followed here is :-

From the given two different cubes the adjacent sides are as shown below :

As R is common on both the dices, it is clear that P, T, Q, and U are adjacent to it, and the remaining i.e. S will be opposite to it.

=

Opposite pairs:

P → Q

T → U

R → S

So, the opposite side of "R" will be side "S".

Hence, the correct answer is "Option 4".

Decoding symbols:

Given: P ÷ Q × R − M + T

P ÷ Q → P is the mother of Q.

Q × R → Q is the brother of R.

R − M → R is the sister of M.

M + T → M is the son of T.

Thus, T is P's husband.

Hence, the correct answer is "Option 4"

Given: 321 – 371 ÷ 22 + 216 × 6 = ?

According to the question, after '+' and '−' are interchanged and '×' and '÷' are interchanged:

321 – 371 ÷ 22 + 216 × 6 = ? ⇒ 321 + 371 × 22 – 216 ÷ 6 = ?

⇒ 321 + 371 × 22 – 216 ÷ 6 = ?

⇒ 321 + 371 × 22 – 36 = ?

⇒ 321 + 8162 – 36 = ?

⇒ 8483 – 36 = ?

⇒ 8447 = ?

Hence, "Option 4" is the correct answer.

The logic followed here is:

1) Top left corner circle is alternately shift clockwise.

2. Top right corner circle is alternately shift clockwise.

Thus, the final series is:

Hence, "Option 3" is the correct answer.

The logic followed here is:

​'SET' is coded as '37'

And,

'MIX' is coded as '35'

Similarly,

'WAR' will be coded as

Hence, "Option 1" is the correct answer.

The correct answer is Lord Wellesley

Key Points

• The system of 'Subsidiary Alliance' was devised by Lord Wellesley.
• Lord Wellesley was the British Governor-General of India from 1798 to 1805, and he introduced this diplomatic policy to secure British control over Indian states and ensure that they remained under British influence.
• The system required Indian rulers to:
• Maintain a British subsidiary force at their own expense.
• Not engage in any foreign relations without British approval.
• Provide territory as security for the maintenance of British forces.
• This system was used effectively to expand British control over Indian territories by isolating rulers from one another and by exerting indirect control.

Additional Information

• Lord Canning (Governor-General from 1856 to 1862)
• Lord Canning is best known for his role during the Indian Rebellion of 1857 (also called the Sepoy Mutiny).
• He was the last Governor-General of the East India Company and the first Viceroy of British India after the British government took direct control from the East India Company in 1858.
• Canning managed the rebellion and its aftermath, which led to the end of the East India Company’s rule and the establishment of direct British rule in India.
• Lord William Bentinck (Governor-General from 1828 to 1835)
• Lord William Bentinck is known for his reforms aimed at modernizing India under British rule.
• He abolished Sati (the practice of widow burning) in 1829.
• He also worked towards education reforms, including the promotion of Western-style education and the founding of English as the medium of instruction.
• He is also credited with promoting the growth of the railways and civil services during his tenure.
• Lord Dalhousie (Governor-General from 1848 to 1856)
• Lord Dalhousie is known for his doctrine of lapse, a policy that allowed the British to annex any Indian state where the ruler died without a direct heir (adopted sons were not recognized as legitimate heirs).
• This led to the annexation of several states, including Satara, Jhansi, and Nagpur. His policies caused resentment and contributed to the unrest that led to the Indian Rebellion of 1857.
• He is also credited with the development of infrastructure, including the expansion of the railway network and the introduction of the telegraph and postal system.

The correct answer is 1936

Key Points

• Kho-Kho was featured in an exhibition at the main stadium during the 1936 Olympics.
• The 1936 Summer Olympics, officially known as the Games of the XI Olympiad, were held in Berlin, Germany.
• This exhibition aimed to showcase traditional sports from different countries, and Kho-Kho represented India.
• Although it was not an official Olympic sport, the exhibition provided international exposure to Kho-Kho.

Additional Information

• The 1936 Olympics are often remembered for the political context and the propaganda efforts of the Nazi regime.
• Jesse Owens, an African-American athlete, won four gold medals at these games, challenging the Nazi ideology of racial superiority.
• Kho-Kho is a traditional Indian sport that involves running and chasing and is popular in schools and colleges across the country.
• The sport is governed by the Kho-Kho Federation of India, which organizes national-level competitions and promotes the game internationally.

The correct answer is 2023

Key Points

• The "Naye Bharat Ke Sapne" campaign, also known as the Amrit Generation Movement, was launched by Meta and the Ministry of Women and Child Development on June 8, 2023.
• The campaign's goals are to:
• Empower and engage young people in India
• Encourage young people to express their dreams and aspirations
• Provide support to help young people achieve their dreams
• The campaign invites young people to create Reels on Instagram and Facebook to showcase their creativity and share their aspirations.
• The campaign will select 50 entries and invite them to New Delhi to interact with industry leaders and policymakers.
• The selected young people will also get to visit the Meta office in Gurugram to learn from industry leaders and creators.
• The Ministry of Women and Child Development is responsible for the overall development of women and children in India.

Additional Information

Organization:

• The Ministry of Women and Child Development is headed by Hon'ble Minister Smt. Annpurna Devi.
• Minister of State Sushri Debasree Chaudhuri
• Shri Rabindra Panwar is the Secretary of the Ministry of Women and Child Development

The Ministry has 6 autonomous organizations:

• National Institute of Public Cooperation and Child Development (NIPCCD)
• National Commission for women (NCW)
• National Commission for Protection of Child Rights (NCPCR)
• Central Adoption Resource Agency (CARA)
• Central Social Welfare Board (CSWB)
• Rashtriya Mahila Kosh (RMK)

The correct answer is Article 28

Key Points

• Article 28 of the Indian Constitution prohibits religious instruction in state-funded educational institutions.
• However, it does allow religious instruction in special circumstances.
• Article 28 states, "No religious instruction shall be provided in any educational institution wholly maintained out of State funds".

Additional Information

• Other articles of the Indian Constitution related to education include:
• Article 29
• Prohibits discrimination in admission to state-aided or maintained educational institutions based on religion, race, caste, or language
• Article 30
• Gives minorities the right to establish and administer educational institutions of their choice
• Article 31
• It was part of the original fundamental rights in the Constitution of India, guaranteeing the right to property.
• It protected individuals against the arbitrary acquisition of their property by the State.

The correct answer is option 1

Key Points

• The statement that is incorrect is "Fats and oils get reduced over time and smell bad".
• The correct statement is that fats and oils become rancid when they are oxidized.
• some other facts about fats and oils:
• Rancidity
• When fats and oils are oxidized, they become rancid, which means they change in smell and taste and may also discolor.
• Antioxidants
• Antioxidants are added to foods containing fats and oils to prevent oxidation.
• Nitrogen gas
• Chip manufacturers often flush bags of chips with nitrogen gas to prevent the chips from oxidizing.
• Storage
• Rancidity can be prevented by storing food in airtight containers or jars, or keeping it in the refrigerator

The correct answer is the Salk Vaccine

Key Points

• The inactivated poliovirus vaccine (IPV), or Salk vaccine, was developed in the 1950s by American physician Jonas Salk and first used in 1955:
• IPV is a mixture of three inactivated poliovirus strains, one from each serotype.
• The poliovirus strains are grown in Vero cells and inactivated with formaldehyde.
• IPV is given by intramuscular or subcutaneous injection.
• IPV reduced the number of paralytic polio cases from about 20,000 per year to around 2,000. It also eradicated polio in Scandinavia and the Netherlands.
• The initial formula developed by Salk was replaced by an enhanced potency formula in the late 1980s.
• In the 1960s, Dr. Albert Sabin developed a live attenuated (weakened) oral polio vaccine (OPV).
• OPV was shown to interrupt epidemics and break viral transmission, leading to the elimination of the virus from entire continents by the 1980s.

The Correct Answer is less than 183 days (or six months) in a year.

Key Points

• A person who works for less than 183 days (or six months) in a year.
• Marginal workers are typically engaged in seasonal, irregular, or part-time work.
• They may be involved in agriculture, labor, or other informal sectors where employment is not continuous throughout the year.
• The contrast to marginal workers are 'main workers', who work for 183 days or more during the year.

The correct answer is Odisha.

Key Points

• Nuakhai  or Navakhai is an agricultural festival mainly observed by people of Western Odisha and Southern Chhattisgarh in India.
• Nuakhai is observed to welcome the new rice of the season.
• It will be celebrated on Thursday, 1 September 2022.
• The new harvest crops are worshipped and people celebrate it by eating the first rice of the harvest together with their families.
• Nuakhai Juhar is sharing gifts with your dear ones, wishing them on the occasion, and coming together as a family to symbolize unity.

Additional Information

• some state festivals in India:
• Meghalaya
• The Wangala Festival, also known as the 100 Drums Festival, is a harvest festival that celebrates the end of a period of hard work and the good output of the fields.
• The festival honors Saljong, the Sun-god of fertility.
• Other festivals in Meghalaya include the Ahaia festival, Nongkrem Dance Festival, and Bob Dylan Festival.
• Odisha
• The Ratha Yatra, or Chariot Festival, is a well-known religious festival that takes place in June-July.
• During the festival, Lord Jagannath and his siblings ride in a chariot to their aunt's home and return after a seven-day holiday.
• Other festivals in Odisha include Durga Puja, Saraswati Puja, Ganesh Puja, Shiva Ratri, Janmashtami, Kali Puja, and Kartik Puja.
• Tamil Nadu
• Pongal is a major festival in Tamil Nadu, celebrated as a harvest festival in the Tamil month of Thai (mid-January to mid-February).
• Margazhi (Margali) is the Tamil month before Thai, spanning from mid-December to mid-January.
• Bihar
• Bihula is a prominent festival in eastern Bihar, especially in the district of Bhagalpur.
• It takes place in August, and devotees pray to Goddess Mansa for the welfare of their families

The correct answer is Government of India Act 1858

Key Points

• The GoI Act of 1858 marked the beginning of Crown Rule in the Indian subcontinent, as power was transferred from the Company to the British Crown.
• From then on, the Secretary of Indian Affairs took over the colony's administration.
• The British Parliament passed the Government of India Act on August 2, 1858.
• The act transferred the East India Company's administrative powers, territories, revenues, armed forces, and Indian possessions to the British Crown.
• It also changed the title of the Governor General of India to Viceroy of India.
• The act was passed after the British blamed the East India Company's ineptitude for the mutiny

Additional Information

• Charter Act of 1833
• Purpose: To renew the charter of the East India Company for 20 years and reform its administration in India.
• Regulating Act of 1773
• Purpose: To address the mismanagement of the East India Company in India and establish British government control over its operation
• Pitt’s India Act of 1784
• Purpose: To address the shortcomings of the Regulating Act and establish a more efficient system of dual control between the British government and the East India Company.

The correct answer is Loo

Key Points

• The hot, dry, and dusty wind that blows over north India in the summer is called the Loo:
• The Loo originates from the Iranian, Baloch, and Thar deserts.
• It's especially strong in May and June.
• The Loo can reach temperatures of 45–50 °C (115–120 °F).
• Exposure to the Loo can cause heatstroke, and its low humidity and high temperature can dry out vegetation.
• The Loo blows over the western Indo-Gangetic Plain region of North India and Pakistan, with higher intensity between Delhi and Patna.
• Other local winds include:
• Blossom Shower: A local storm that occurs mainly in Kerala, where coffee flowers bloom
• Mango Shower: A local storm that occurs mainly in Kerala and the coastal areas of Karnataka, where mangoes ripen early
• Kalbaisakhi: A local storm that occurs mainly in Bengal and Assam, where evening thunderstorms are common
• Local winds can be caused by a number of factors, including pressure difference, topography, thermal differences, and diurnal and seasonal changes

Additional Information

• Chinook
• A warm, dry wind that blows down the eastern slopes of the Rocky Mountains in North America.
• Features:
• Causes a rapid increase in temperature, often referred to as a "snow-eater" as it can quickly melt snow.
• Occurs due to the adiabatic heating of air as it descends on the leeward side of mountains.
• Beneficial for livestock grazing in winter but can lead to sudden weather changes.
• Mango Showers
• Pre-monsoon showers experienced in parts of South India, especially in Kerala, Karnataka, and Tamil Nadu.
• Features:
• These light rains occur in April and May, aiding in the ripening of mangoes (hence the name).
• Caused by the convective activity over land due to the heating of the surface.
• They also benefit crops like coffee and spices.
• Purga
• A violent snowstorm or blizzard common in the Siberian regions of Russia.
• Features:
• Accompanied by strong winds, blowing snow, and low visibility.
• Temperatures can drop drastically, making it hazardous for life and travel.
• Associated with cold Arctic air masses

The correct answer is 60:40

Key Points

• The cost of unit assistance is shared between Central and State Governments in the ratio 60:40 in plain areas and 90:10 for North Eastern and hilly states.
• The Pradhan Mantri Gramin Awaas Yojana (PMGAY), previously known as Indira Awaas Yojana, is a flagship scheme by the Government of India aimed at providing housing for all in rural areas.
• Objective: To provide a pucca house with basic amenities to all rural households living in kuccha (non-permanent) houses by 2024.Beneficiary Selection:
• Beneficiaries are identified based on the Socio-Economic and Caste Census (SECC) data.
• Priority is given to households with vulnerable members like widows, senior citizens, or persons with disabilities.
• Beneficiaries are eligible for free LPG connections under the Ujjwala Yojana and electrification under the Saubhagya scheme.

The correct answer is Option 3

Key Points

• Five-Year Plans are strategic frameworks used by the government to guide the economy's development over a fixed period (typically five years).
• In India, these plans were implemented by the Planning Commission (replaced by NITI Aayog in 2015).
• Focus on Developmental Goals:
• Poverty Alleviation: Plans aimed at reducing poverty through employment generation schemes, rural development, and welfare programs.
• For instance, the Sixth Five-Year Plan (1980–1985) emphasized poverty reduction.
• Industrialization: Plans like the Second Five-Year Plan (1956–1961), which focused on heavy industries, laid the foundation for India's industrial base.
• Agriculture: Plans like the First Five-Year Plan (1951–1956) concentrated on increasing agricultural productivity.
• Infrastructure Development: Several plans prioritized building physical and social infrastructure, including power, transportation, education, and healthcare.​
• Hence statement 3 is correct

The correct answer is Ajta Srivastava 

Key Points

• Ajita Srivastava is a renowned folk singer from Uttar Pradesh who has been awarded the Padma Shri, India's fourth-highest civilian award, for her contributions to preserving and promoting folk music.
• She has significantly contributed to the rich folk traditions of Uttar Pradesh.
• Folk music in Uttar Pradesh encompasses a variety of genres, including Kajri, Thumri, Dadra, Sohar, Chaiti, and Birha, all of which reflect the region's cultural heritage. Ajita Srivastava's contributions have been pivotal in keeping these art forms alive in the face of modernization and changing entertainment preferences.

Additional Information

• Ila Arun
• Ila Arun is a well-known Indian playback singer, actress, and television personality.
• She is particularly famous for her folk-inspired Bollywood songs and distinctive husky voice.
• Association with Folk Music:
• She has drawn from Rajasthan's rich folk traditions in her songs, often infusing them with contemporary styles.
• Some of her famous songs include Choli Ke Peeche Kya Hai and Ringa Ringa.
• Gurmeet Bawa
• Gurmeet Bawa (1944–2021) was a legendary Punjabi folk singer, known for her long breath-holding technique while singing.
• She was famous for her songs in Punjabi folk genres like Jugni and Heer.
• Association with Folk Music:
• Gurmeet Bawa played a significant role in promoting Punjabi folk music and is particularly celebrated for introducing it to international audiences.
• Teejan Bai
• Teejan Bai is a renowned exponent of Pandavani, a traditional performing art form from Chhattisgarh that narrates tales from the Mahabharata through music and storytelling.
• Association with Folk Music:
• She has been instrumental in bringing Pandavani to global audiences and was honored with multiple awards, including the Padma Shri, Padma Bhushan, and Padma Vibhushan.

The correct answer is India

Key Points

• India won the first men's Asian Hockey Champions Trophy in 2011, defeating Pakistan in the final via a penalty shootout.
• The Asian Champions Trophy is a prestigious field hockey tournament held in Asia, showcasing the talent and competitiveness of top Asian hockey nations.
• It was held in 2011
• Host: Ordos, China
• Participating Teams: India, Pakistan, Malaysia, Japan, South Korea, China
• Winner: India
• India defeated Pakistan in a thrilling penalty shootout

Additional Information

• The Asian Champions Trophy is organized by the Asian Hockey Federation (AHF).
• It was first introduced in 2011, and since then, it has become a key event in the Asian hockey calendar.
• Teams like India, Pakistan, Malaysia, and South Korea are regular participants in the tournament.
• The event helps in improving the competitive standards of Asian teams on the global stage.
• Chennai last hosted a major international hockey event in 2007, making the 2023 tournament a significant occasion for the city.

The correct answer is Intermediate goods

Key Points

• Intermediate goods need further transformation in the economic process:
• Intermediate goods:
• These are partially finished goods that are used to make other goods.
• They are also known as producer goods.
• Intermediate goods undergo further processing and transformation to become final goods.
• For example, a car component can be an intermediate good if it is incorporated into a vehicle, or a final good if it is sold to the consumer as a spare part.

Additional Information

• Consumer durable goods
• A type of consumer good that lasts for more than three years and is purchased infrequently.
• Examples include appliances, cars, and furniture.
• Finished goods
• A finished product that is purchased by consumers for personal or household use.
• Examples include food, clothing, vehicles, electronics, and appliances.
• Capital goods
• A tangible product that is used to produce goods and services, and is not typically sold to consumers.
• Examples include buildings, machinery, vehicles, large tools, and equipment

The correct answer is the Pacific plate

Key Points

• Pacific- The Pacific Plate is an oceanic tectonic plate that lies in the Pacific Ocean. The size of the plate is 102,900,000 km².
• Most of the Pacific Plate is made up of oceanic crust, except for areas around New Zealand and parts of California.
• Antarctic- Antarctica, the southernmost continent and site of the South Pole. The size of the Antarctic is approx 14 million km².
• Eurasian- Most of the continents of Europe and Asia are in the Eurasian Plate. The size of the Eurasian plate is 67,800,000 km².
• Indian Plate- The Indian tectonic plate is located in the northeast hemisphere. The size of the Plate is approx 11,900,000 km².

Additional Information

• South American plate-  The South American Plate is a major tectonic plate which includes the continent of South America as well as a sizable region of the Atlantic Ocean seabed extending eastward to the African Plate, with which it forms the southern part of the Mid-Atlantic Ridge.
• African plate- The African Plate, also known as the Nubian Plate, is a major tectonic plate that includes much of the continent of Africa and the adjacent oceanic crust to the west and south.
• Eurasian plate - The Eurasian Plate is a tectonic plate that makes up most of the continent of Eurasia, including Europe and northern Asia. It's the third-largest tectonic plate on Earth, covering an area of 67.8 million square kilometers

The correct answer is Ilango Adigal

Key Points

• Some of the best–known epics were written during the Sangam period.
• Epics are grand, long compositions, about heroic men and women, and include stories about gods.
• A famous Tamil epic, the Silappadikaram, was composed by a poet named Ilango, around 1800 years ago.
• It is the story of a merchant named Kovalan, who lived in Puhar and fell in love with a courtesan named Madhavi, neglecting his wife Kannagi.
• Later, he and Kannagi left Puhar and went to Madurai, where he was wrongly accused of theft by the court jeweller of the Pandya king.
• The king sentenced Kovalan to death.
• Kannagi, who still loved him, was full of grief and anger at this injustice, and destroyed the entire city of Madurai.
• Therefore, we can conclude that the Tamil epic, "Silappadikaram' was composed by Ilango.

Additional Information

• Tolkappiyar:
• Tolkappiyar is an ancient Tamil scholar and poet, known for writing the Tolkappiyam, one of the earliest works of Tamil literature.
• The Tolkappiyam is a treatise on grammar, poetics, and rhetoric, and it lays the foundations for the study of the Tamil language.
• It is believed to have been composed around 200 BCE to 300 BCE.
• The text covers phonetics, morphology, syntax, and semantics, providing a detailed description of the Tamil language structure and its rules for poetry.
• Tolkappiyar's work has been influential in shaping Tamil literary tradition.
• Sittalai Sattanar:
• Sittalai Sattanar was a Tamil poet and philosopher, credited with composing Patthupattu, a collection of ten poems.
• He is believed to have lived during the Sangam period, around the 3^rd century BCE.
• Sattanar is noted for his philosophical insights, especially his focus on ethics, governance, and the responsibilities of rulers.
• His work often touches upon the theme of justice, societal values, and the roles individuals play within society.
• Sattalai Sattanar's contributions to Tamil literature and philosophy have had a lasting impact on Tamil culture.
• Tirumalisai Alvar:
• Tirumalisai Alvar was one of the twelve Alvars, a group of poet-saints in Tamil Vaishnavism, who composed devotional hymns dedicated to Lord Vishnu.
• He is believed to have lived during the 8^th century CE.
• His works focus on expressing deep devotion to Vishnu, and he is known for his Prabandham (devotional hymns) which are a part of the Divya Prabandham anthology. Tirumalisai Alvar's hymns reflect the love and reverence for Lord Vishnu and advocate for the importance of surrendering to divine will.
• He is also credited with making significant contributions to the Bhakti movement in Tamil Nadu.

The correct answer is 67,956 km.

Key Points

• Indian Railways is the largest government undertaking in the country.
• The length of the Indian Railways network was 67,956 km (Railwayyearbook 2019-20).
• Its very large size puts a lot of pressure on a centralised railway management system.
• Based on the width of the track of the Indian Railways, three categories have been made:
• Broad gauge:
• The distance between rails in broad gauge is 1.676 metres.
• The total length of broad gauge lines was 63950 km (2019-20).
• Metre gauge:
• The distance between rails is one metre.
• Its total length was 2402 km(2019-20).
• Narrow gauge: ​
• The distance between the rails in this case is 0.762 metres or 0.610 metres.
• The total length of the narrow gauge was 1604 km (2019-20).
• It is generally confined to hilly areas.

The correct answer is b

Key Points

• The illustration that shows the structural details of the mitochondrion is option (b).
• This is because mitochondria are typically depicted as oval or bean-shaped organelles with an inner membrane folded into cristae, which helps in energy production within the cell.
• The mitochondrion is an essential organelle found in eukaryotic cells, often referred to as the "powerhouse of the cell" because it produces energy in the form of ATP (adenosine triphosphate).
• The structure of the mitochondrion includes the following key features:
• Outer Membrane: The outer membrane surrounds the mitochondrion and acts as a barrier, controlling the movement of ions and molecules into and out of the organelle.
• Inner Membrane: The inner membrane is highly folded into structures called cristae, which significantly increase the surface area for the chemical reactions that occur within the mitochondrion. These reactions are vital for ATP production, particularly in the electron transport chain.
• Matrix: The space inside the inner membrane is filled with a gel-like substance called the matrix. It contains enzymes that are essential for the Krebs cycle (part of cellular respiration).

The correct answer is Karnataka.

Key Points

• Nrityagram is an Odissi dance institution located near Hesaraghatta Lake in Karnataka.
• It was established by Odissi dancer Protima Gauri in 1990.
• It offers training in 7 Indian classical dance forms.
• These are- Odissi, Mohiniattam, Kathak, Bharatnatyam, Kuchipudi, Kathakali, and Manipuri.
• It is made by architect Gerard da Cunha.
• It is located near Hesaraghatta lake 30km from Bengaluru.
• Nrityagram Dance Ensemble has performed across India and in many countries abroad.
• Training is offered for a period of 6-7 years to become professional dancers and teachers.

The correct answer is Butyric acid

Key Points

• Butyric acid is a straight-chain alkyl carboxylic acid with the chemical formula CH3CH2CH2CO2H.
• It is also known as butanoic acid.
• Butyric acid is a colorless, oily liquid with an unpleasant odor.
• It is a saturated fatty acid that is generally neutral, hydrophobic, and nearly insoluble. Butyric acid is responsible for the rancid smell of spoiled fatty products.
• In the International Union of Pure and Applied Chemistry (IUPAC) nomenclature system, the parent hydrocarbon is the longest continuous chain (LCC) that contains the carboxyl group.
• The suffix "-oic" and the word "acid" replace the "-e" ending of the parent alkane

Additional Information

• Methanoic acid
• Also known as formic acid, its chemical formula is HCOOH.
• It's the simplest carboxylic acid and is found in nature, such as in bee and ant stings.
• It's also used as a preservative and antibacterial agent in livestock feed.
• Ethanoic acid
• Also known as acetic acid, its chemical formula is CH₃COOH.
• It's a colorless liquid with a strong vinegar-like odor.
• Propanoic acid
• Its chemical formula is CH₃CH₂COOH.
• It's used as an intermediate in the production of other chemicals, such as polymers, pesticides, and pharmaceuticals.
• It's a colorless, oily liquid with a slightly pungent, rancid odor and a sour, mildly cheese-like taste.

The correct answer is Ustad Zakir Hussain.

Key Points

• Zakir Hussain is the youngest percussionist to be awarded Padma Shri and Padma Bhushan awards by the Government of India.
• Zakir Hussain (born 9 March 1951) is an Indian tabla player, composer, percussionist, music producer, and film actor.
• He is the eldest son of tabla player Alla Rakha.
• He was awarded the Padma Shri in 1988, and the Padma Bhushan in 2002, by the Government of India presented by President Abdul Kalam.
• He also won the Sangeet Natak Akademi award in 1990, making him one of the youngest musicians to receive this recognition given by the Sangeet Natak Academy, India's National Academy of Music, Dance & Drama.​

Additional Information

• Pandit Ravi Shankar (1920-2012):
• He was an Indian sitar virtuoso and a composer.
• He became the world's best-known exponent of North Indian classical music, in the second half of the 20^th century and influenced many other musicians throughout the world.
• Ravi Shankar was awarded India's highest civilian honour, the Bharat Ratna in 1999 and received three Grammy Awards for his outstanding work.
• Pandit Bhimsen Joshi​
• Pt Bhimsen Joshi is known for the khayal form of singing, as well as for his popular renditions of devotional music (bhajans and abhangs).
• Joshi belongs to the Kirana gharana tradition of Hindustani Classical Music.
• He received his training in singing and harmonium from Shamacharya Joshi.
• Joshi heard Ustad Abdul Kareem Khan and decided to sing like him.
• ​Ustad Bismillah Khan​
• Ustad Bismillah Khan used to play Shehnai.
• Ustad Bismillah Khan (1916 – 2006) (Real name is Qamaruddin Khan), was an Indian musician credited with popularizing the Shehnai.
• Shehnai is a musical instrument that is similar to the oboe (common in India, Pakistan, and Bangladesh.)
• He was felicitated with several awards including:
• Padma Shri in 1961
• Padma Bhushan in 1968
• Padma Vibhushan in 1980
• Bharat Ratna in 2001
• He also played the Shehnai at the 1^st Republic Day celebration in 1950.

The correct answer is Todar Mal

Key Points

• Raja Todar Mal was the revenue minister during the reign of Mughal emperor Akbar:
• Introduced the Dahsala system
• In 1580, Todar Mal introduced the Dahsala system of taxation, which was based on the average crop production over the previous 10 years.
• The state's share was one-third of the average produce.
• Introduced the Zabt tax
• Todar Mal also introduced the Zabt tax, a land tax system based on the productive capacity of the land.
• The tax was adjusted periodically to reflect changes in the land's value.
• Other contributions
• Todar Mal also introduced standard weights and measures, a land survey and settlement system, revenue districts, and officers.
• A member of Akbar's court
• Todar Mal was one of the Navaratnas in Akbar's court.

Additional Information

• Abdul Rahim, Mulla Do-Piyaza, and Tansen were all part of the "Navaratnas" or "Nine Jewels" of Mughal emperor Akbar's court:
• Abdul Rahim Khan-I-Khana
• A poet and statesman who was one of the nine important ministers in Akbar's court.
• He was also known as Rahim and Khan-i-Khanan.
• Mulla Do-Piyaza
• An advisor and vizier to Akbar who was portrayed as witty and a rival to Birbal. However, most scholars believe he was fictional.
• Tansen
• A musician whose full name was Ramtanu.
• He died in Agra on April 26, 1589 and is buried at the Memorial of Tansen in Gwalior.

Important Points

• The other members of the Navaratnas were:
• Abu'l-Fazl
• Raja Todar Mal
• Birbal
• Faizi
• Fakir Aziao-Din
• Man Singh
• The Navaratnas were experts in different art fields and helped Akbar make important decisions.

The Correct answer is Section 5.

Key Points

• The Muslim Women (Protection of Rights on Marriage) Act, 2019 was enacted to protect the rights of married Muslim women.
• Under this act, Section 5 specifically deals with the provision for subsistence allowance.
• It mandates that a Muslim woman against whom talaq has been pronounced is entitled to receive a subsistence allowance from her husband for her and her children.
• The allowance amount and terms are determined by the First Class Magistrate upon the woman’s application.
• This provision aims to ensure the financial stability of Muslim women who are divorced through the practice of instant triple talaq.

 Additional Information

• Section 4
• This section of the act makes the pronouncement of triple talaq (talaq-e-biddat) a criminal offence.
• A husband who pronounces triple talaq can be punished with imprisonment for up to three years and a fine.
• Section 6
• This section pertains to the custody of minor children.
• It states that the determination of custody will be made by the First Class Magistrate as deemed just and proper for the welfare of the minor.
• Section 7
• This section states that an offence under this act is cognizable, compoundable, and non-bailable.
• The offence can be compounded only at the instance of the married Muslim woman upon whom talaq is pronounced.

The correct answer is the conduct of business of the Government of India

Key Points

• Article 77 of the Indian Constitution deals with the conduct of business of the Government of India.
• It includes the following provisions:
• The President makes rules to facilitate the transaction of government business.
• These rules also allocate the business among Ministers.
• All executive actions of the Government of India are to be taken in the name of the President.
• The President authenticates orders and other instruments made in their name.
• The validity of an authenticated order or instrument cannot be questioned.

Shortcut Trick

Weighted average return = Sum of (Weight × Return) ÷ Total weight

⇒ [(20 × 6) + (30 × 8) + (20 × 4) + (30 × −5)] ÷ 100

⇒ (120 + 240 + 80 − 150) ÷ 100

⇒ 290 ÷ 100 = 2.9%

∴ The correct answer is 2.9%.

Alternate Method

Given:

Weight of Stock A (W_A) = 20% = 0.20 , Return (R_A) = 6%

Weight of Stock B (W_B) = 30% = 0.30 , Return (R_B) = 8%

Weight of Stock C (W_C) = 20% = 0.20 , Return (R_C) = 4%

Weight of Stock D (W_D) = 30% = 0.30 , Return (R_D) = −5%

Portfolio Weighted Return

A (20%) B (30%) C (20%) D (30%)

6% 8% 4% −5%

Net Return = (W × R) Sum = 2.9%

Formula Used:

Average Return = (W_A × R_A) + (W_B × R_B) + (W_C × R_C) + (W_D × R_D)

Calculations:

⇒ Average Return = (0.20 × 6%) + (0.30 × 8%) + (0.20 × 4%) + (0.30 × −5%)

⇒ Average Return = 1.2% + 2.4% + 0.8% − 1.5%

⇒ Average Return = 4.4% − 1.5% = 2.9%

∴ The correct answer is 2.9%.

Additional Information

Weighted Average

A measure of central tendency where some values contribute more than others. Formula: Average = Σ(w_i × x_i) ÷ Σw_i.

Combined Average

The overall average of multiple distinct groups. Formula: A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Return on Investment (ROI)

A metric evaluating the efficiency of an investment. Formula: ROI = (Net Return ÷ Initial Cost) × 100.

Given:

Expression: 13 - [7 - (4 + 7) - {7 - (7 - 4 + 7)} + 14]

Formula used:

Use the BODMAS rule (Bracket, Order, Division, Multiplication, Addition, Subtraction).

Calculations:

Step 1: Simplify the innermost brackets.

13 - [7 - (4 + 7) - {7 - (7 - 4 + 7)} + 14]

⇒ 13 - [7 - 11 - {7 - 10} + 14]

Step 2: Simplify the curly brackets.

⇒ 13 - [7 - 11 - {7 - 10} + 14]

⇒ 13 - [7 - 11 +3 + 14]

Step 3: Simplify the square brackets.

⇒ 13 - [7 - 11 + 3 + 14]

⇒ 13 - [13]

Step 4: Perform the subtraction.

⇒ 13 - 13 = 0

∴ The value of the expression is 0.

Given:

Total pages printed on Saturday:

L = 8540

M = 11230

N = 6580

O = 7890

Total pages printed on Wednesday are 15% more than total pages printed on Saturday.

Formula used:

Total on Wednesday = Total on Saturday × (1 + 15/100)

Calculation:

Total on Saturday = 8540 + 11230 + 6580 + 7890

⇒ Total on Saturday = 34240

Total on Wednesday = 34240 × (1 + 15/100)

⇒ Total on Wednesday = 34240 × 115/100

⇒ Total on Wednesday = 34240 × 1.15

⇒ Total on Wednesday = 39376

∴ The total number of pages printed on Wednesday is 39376.

Shortcut Trick

Discount = Marked Price − Selling Price

Discount = 10490 − 9441 = 1049

Since 1049 is exactly 1/10^th of the Marked Price 10490, the discount is 10%.

∴ The correct answer is 10%.

Alternate Method

Given:

⇒ Marked Price (MP) = ₹10,490

⇒ Selling Price (SP) = ₹9,441

Formula Used:

⇒ Discount = MP − SP

⇒ Discount % = (Discount ÷ MP) × 100

Calculations:

⇒ Discount = 10,490 − 9,441 = 1,049

⇒ Discount % = (1049 ÷ 10490) × 100

⇒ Discount % = (1 ÷ 10) × 100 = 10%

∴ The correct answer is 10%.

Additional Information

Successive Discount

When two consecutive discounts of a% and b% are given, the net equivalent discount is (a + b − ab ÷ 100)%.

Selling Price Formula

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

Markup Percentage

Markup is always calculated over the Cost Price (CP). Markup % = ((MP − CP) ÷ CP) × 100.

Shortcut Trick

Time taken by the leak to empty the tank = (T₁ × T₂) ÷ (T₂ − T₁)

Here, T₁ = 12 hours (without leak) and T₂ = 18 hours (with leak).

Required time = (12 × 18) ÷ (18 − 12)

⇒ 216 ÷ 6 = 36 hours.

∴ The correct answer is 36 hours.

Alternate Method

Given:

Time taken by the pipe to fill the tank = 12 hours

Time taken to fill the tank with the leak = 18 hours

Method Used:

Total Work = LCM of times taken

Efficiency = Total Work ÷ Time

Calculations:

⇒ Let the efficiency of the leak be L.

⇒ Efficiency of Pipe + Efficiency of Leak = Overall Efficiency

⇒ 3 + L = 2

⇒ L = 2 − 3 = −1 unit/hour

⇒ The negative sign signifies that the leak empties the tank at 1 unit/hour.

⇒ Time taken by the leak to empty the full tank = Total Work ÷ Emptying Efficiency

⇒ Time = 36 ÷ 1 = 36 hours.

∴ The correct answer is 36 hours.

Additional Information

Pipes & Cisterns - Leakage Concept

If a pipe fills a tank in x hours and a leak empties it in y hours, the net part filled in 1 hour = (1/x) − (1/y).

Total Work Strategy

The total capacity of the tank is generally assumed to be the LCM of all individual times given. This helps in avoiding complex fractional calculations.

Positive and Negative Work

Filling pipes do positive work and have a positive (+) efficiency. Emptying pipes or leaks do negative work and have a negative (−) efficiency.

Shortcut Trick

Congruent triangles have exactly the same size, shape, and enclosed area.

If ΔEFG ≅ ΔHIJ, then Area of ΔHIJ = Area of ΔEFG.

Since the Area of ΔEFG is given as 124 cm².

Therefore, the Area of ΔHIJ is also 124 cm².

∴ The correct answer is 124 cm².

Alternate Method

Given:

ΔEFG and ΔHIJ are congruent triangles (ΔEFG ≅ ΔHIJ).

Area of ΔEFG = 124 cm²

Concept Used:

When two triangles are congruent, their corresponding sides and angles are perfectly equal, which means they cover the exact same region and possess equal area.

E F G 124 cm² ≅

H I J ? cm²

Calculations:

⇒ Area of ΔHIJ = Area of ΔEFG

⇒ Area of ΔHIJ = 124 cm²

∴ The correct answer is 124 cm².

Additional Information

Congruence vs Similarity

Congruent triangles have exactly the same area. In contrast, similar triangles only have the same shape, and the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Conditions for Congruence

Two triangles are strictly congruent if they satisfy any of the five standard criteria: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), or RHS (Right angle-Hypotenuse-Side).

Area of a Triangle

The general formula for the area of a triangle is Area = 1/2 × base × height. Since congruent triangles possess equal corresponding bases and equal corresponding altitudes, their areas are naturally identical.

Shortcut Trick

Let distinct values a = 1 and b = 3. Since a + b = 2c, we get 1 + 3 = 2c ⇒ c = 2.

Substitute a = 1, b = 3, and c = 2 into the given expressions to find the correct one.

Check the expression: a² + 2bc = b² + 2ac

LHS = 1² + 2 × 3 × 2 = 1 + 12 = 13

RHS = 3² + 2 × 1 × 2 = 9 + 4 = 13 (LHS = RHS)

∴ The correct answer is a² + 2bc = b² + 2ac.

Alternate Method

Given:

a + b = 2c

Formula Used:

a² − b² = (a − b)(a + b)

Calculations:

⇒ a + b = 2c

Multiplying both sides by (a − b), we get:

⇒ (a + b)(a − b) = 2c(a − b)

⇒ a² − b² = 2ac − 2bc

Rearranging the terms from both sides:

⇒ a² + 2bc = b² + 2ac

∴ The correct answer is a² + 2bc = b² + 2ac.

Additional Information

Difference of Squares Formula

The identity a² − b² = (a − b)(a + b) is commonly used to simplify algebraic equations by generating symmetrical terms on both sides of the equation.

Value Substitution Trick

For algebraic equations with unknown variables, substituting simple distinct numbers (like 1, 2, 3) into the options often reveals the correct expression rapidly without complex derivations.

Linear Equations & Averages

The relation a + b = 2c can also be interpreted as c being the arithmetic mean (average) of a and b, which mathematically means c = (a + b) ÷ 2.

Shortcut Trick For two lines to be parallel, the ratio of their x and y coefficients must be equal: a1/a2 = b1/b2. ⇒ 4 / (k − 2) = (k − 2) / 9 ⇒ (k − 2)2 = 36 ⇒ k − 2 = 6 (taking positive root since k > 0) ⇒ k = 8 ∴ The correct answer is 70. Alternate Method Given: Equation 1: 4x + (k − 2)y + 3 = 0 Equation 2: (k − 2)x + 9y − 5 = 0

x y

4x + (k - 2)y + 3 = 0

(k - 2)x + 9y - 5 = 0

Parallel: a1/a2 = b1/b2

Formula Used: For the lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 to be parallel, the required algebraic condition is: ⇒ a1/a2 = b1/b2 ≠ c1/c2 Calculations: Substitute the given coefficients into the condition: ⇒ 4 / (k − 2) = (k − 2) / 9 Cross-multiply to solve for k: ⇒ (k − 2) × (k − 2) = 4 × 9 ⇒ (k − 2)2 = 36 Taking the square root on both sides: ⇒ k − 2 = ±6 Because it is given that k > 0, we take the positive value for k − 2: ⇒ k − 2 = 6 ⇒ k = 8 Now, substitute the value of k into the target expression k2 + 6: ⇒ k2 + 6 = 82 + 6 ⇒ 64 + 6 = 70 ∴ The correct answer is 70. Additional Information Condition for Intersecting Lines Two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 intersect at a unique point if a1/a2 ≠ b1/b2. Condition for Coincident Lines Two lines are identical (coincident) and have infinitely many solutions if all ratios are equal: a1/a2 = b1/b2 = c1/c2. Slope of a Line For a linear equation ax + by + c = 0, the slope (m) is given by −a/b. Parallel lines always possess strictly equal slopes.

Given:

The table shows the production of T-shirts (in thousands) by companies C1, C2, C3, and C4 over 4 years.

Formula used:

Average production = Total production over 4 years / Number of years

Calculation:

Total production by C1 = 243 + 248 + 232 + 242

⇒ Total production by C1 = 965

Average production by C1 = 965 / 4

⇒ Average production by C1 = 241.25

Total production by C2 = 244 + 239 + 240 + 244

⇒ Total production by C2 = 967

Average production by C2 = 967 / 4

⇒ Average production by C2 = 241.75

Total production by C3 = 244 + 236 + 235 + 230

⇒ Total production by C3 = 945

Average production by C3 = 945 / 4

⇒ Average production by C3 = 236.25

Total production by C4 = 240 + 230 + 248 + 242

⇒ Total production by C4 = 960

Average production by C4 = 960 / 4

⇒ Average production by C4 = 240

Comparison:

C1: 241.25

C2: 241.75

C3: 236.25

C4: 240

∴ Company C2 had the maximum average production of T-shirts during these four years (241.75 thousand).

Shortcut Trick

For symmetric minimum value problems, the extreme value occurs when all variables are equal.

Given x + y + z = 1, we set x = y = z.

⇒ 3x = 1 ⇒ x = 1/3, y = 1/3, z = 1/3.

Substitute these values to find the least value:

⇒ 1/x + 1/y + 1/z = 1/(1/3) + 1/(1/3) + 1/(1/3) = 3 + 3 + 3 = 9

∴ The correct answer is 9.

Alternate Method

Given:

x, y, and z are positive numbers.

x + y + z = 1

Formula Used:

For any set of positive numbers, Arithmetic Mean ≥ Harmonic Mean (AM ≥ HM).

Calculations:

⇒ AM = (x + y + z) ÷ 3

⇒ HM = 3 ÷ (1/x + 1/y + 1/z)

⇒ (x + y + z) ÷ 3 ≥ 3 ÷ (1/x + 1/y + 1/z)

Substitute the given condition x + y + z = 1:

⇒ 1/3 ≥ 3 ÷ (1/x + 1/y + 1/z)

Since x, y, and z are positive numbers, cross-multiplying the inequality preserves the sign:

⇒ (1/x + 1/y + 1/z) ≥ 3 × 3

⇒ 1/x + 1/y + 1/z ≥ 9

∴ The correct answer is 9.

Additional Information

AM-GM-HM Inequality

For positive real numbers, Arithmetic Mean (AM) ≥ Geometric Mean (GM) ≥ Harmonic Mean (HM). Equality holds only when all the numbers are identical.

Cauchy-Schwarz Inequality

This algebraic theorem states that (a² + b² + c²)(d² + e² + f²) ≥ (ad + be + cf)². Applying it here gives (x + y + z)(1/x + 1/y + 1/z) ≥ (1 + 1 + 1)² = 9.

Symmetry Principle for Extrema

In symmetric algebraic functions with a symmetric constant sum constraint, the absolute minimum or maximum value typically occurs when all variables are exactly equal.

Shortcut Trick

The mean proportional between two terms x and y is calculated directly as √(x × y).

Here, the given terms are x = 8a² and y = 18/a⁴.

Mean proportional = √(8a² × 18/a⁴)

Mean proportional = √(144/a²) = 12/a.

∴ The correct answer is 12/a.

Alternate Method

Given:

First number (A) = 8a²

Second number (B) = 18/a⁴

Formula Used:

If M is the mean proportional between A and B, then M² = A × B ⇒ M = √(A × B)

Calculations:

⇒ M² = (8a²) × (18/a⁴)

⇒ M² = (8 × 18) × (a² / a⁴)

⇒ M² = 144 / a²

⇒ M = √(144 / a²)

⇒ M = 12/a

⇒ Since a is given as a positive number, its square root yields a perfectly positive 12/a.

∴ The correct answer is 12/a.

Additional Information

Mean Proportional

The mean proportional between two distinct terms A and B is defined as the geometric mean or the square root of their product. Direct Rule: √(A × B).

Third Proportional

If three numbers A, B, and C strictly exist in continued proportion (such that A:B = B:C), then C acts as the third proportional. Formula derived: C = B² / A.

Fourth Proportional

When four independent terms A, B, C, and D conform to a standard ratio format (A:B = C:D), D evaluates to the fourth proportional. Formula applied: D = (B × C) / A.

Shortcut Trick

Apply the Componendo and Dividendo rule directly to the given ratio.

⇒ sec α / tan α = (7 + 4) / (7 − 4)

⇒ (1 / cos α) / (sin α / cos α) = 11 / 3

⇒ 1 / sin α = 11 / 3

⇒ cosec α = 11 / 3

∴ The correct answer is 11/3.

Alternate Method

Given:

(sec α + tan α) / (sec α − tan α) = 7/4

Formula Used:

sec α = 1 / cos α

tan α = sin α / cos α

cosec α = 1 / sin α

Calculations:

⇒ (sec α + tan α) / (sec α − tan α) = 7/4

By cross-multiplying the terms:

⇒ 4 × (sec α + tan α) = 7 × (sec α − tan α)

⇒ 4 sec α + 4 tan α = 7 sec α − 7 tan α

Rearranging the terms to group sec α and tan α:

⇒ 4 tan α + 7 tan α = 7 sec α − 4 sec α

⇒ 11 tan α = 3 sec α

Converting sec α and tan α into sin α and cos α:

⇒ 11 × (sin α / cos α) = 3 × (1 / cos α)

⇒ 11 sin α = 3

⇒ sin α = 3 / 11

Since cosec α = 1 / sin α:

⇒ cosec α = 11 / 3

∴ The correct answer is 11/3.

Additional Information

Componendo and Dividendo Rule

If a fraction a/b = c/d, then (a + b) / (a − b) = (c + d) / (c − d). This rule is highly useful for simplifying rational algebraic and trigonometric equations quickly.

Basic Trigonometric Ratios

sec α is the reciprocal of cos α (sec α = 1/cos α), and cosec α is the reciprocal of sin α (cosec α = 1/sin α).

Pythagorean Identities

The three fundamental identities are: sin²α + cos²α = 1, sec²α − tan²α = 1, and cosec²α − cot²α = 1.

Shortcut Trick

Interest from given parts = (5% of 7000) + (6% of 6000) = 350 + 360 = ₹710

Remaining interest for the 3^rd part = 1160 − 710 = ₹450

Remaining principal = 18000 − (7000 + 6000) = ₹5000

Required rate = (Remaining interest ÷ Remaining principal) × 100

Required rate = (450 ÷ 5000) × 100 = 9%

∴ The correct answer is 9%.

Alternate Method

Given:

Total Capital = ₹18,000

Capital 1 (P₁) = ₹7,000 at Rate (R₁) = 5% per annum

Capital 2 (P₂) = ₹6,000 at Rate (R₂) = 6% per annum

Total Simple Interest (SI) = ₹1,160 for Time (T) = 1 year

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Total: ₹18,000

P = ₹7000 R = 5% I = ₹350

P = ₹6000 R = 6% I = ₹360

P = ₹5000 R = ? I = ₹450

Total Interest = ₹1160

Calculations:

⇒ Remaining Capital (P₃) = 18000 − (7000 + 6000) = ₹5,000

⇒ Interest on P₁ = (7000 × 5 × 1) ÷ 100 = ₹350

⇒ Interest on P₂ = (6000 × 6 × 1) ÷ 100 = ₹360

⇒ Let the rate of interest on P₃ be R%

⇒ Interest on P₃ = (5000 × R × 1) ÷ 100 = 50R

⇒ Total Interest = 350 + 360 + 50R

⇒ 1160 = 710 + 50R

⇒ 50R = 1160 − 710

⇒ 50R = 450

⇒ R = 450 ÷ 50 = 9%

∴ The correct answer is 9%.

Additional Information

Simple Interest (SI)

It is the interest calculated only on the principal amount for the entire period. Formula: SI = (P × R × T) ÷ 100.

Compound Interest (CI)

It is the interest calculated on both the principal and the accumulated interest. Formula: A = P(1 + R/100)^T and CI = A − P.

SI vs CI Difference

For 2 years, Difference = P × (R/100)². For 3 years, Difference = P × (R/100)² × (3 + R/100).

Shortcut Trick

The volume of a cuboid is calculated directly by multiplying its three dimensions together.

Volume = Length × Breadth × Height

Volume = 8 × 4 × 6

Volume = 192 cm³

∴ The correct answer is 192 cm³.

Alternate Method

Given:

Length of the cuboid (l) = 8 cm

Breadth of the cuboid (b) = 4 cm

Height of the cuboid (h) = 6 cm

Formula Used:

Volume of Cuboid = l × b × h

Calculations:

⇒ Volume = 8 × 4 × 6

⇒ Volume = 32 × 6

⇒ Volume = 192 cm³

∴ The correct answer is 192 cm³.

Additional Information

Total Surface Area of a Cuboid

The sum of the area of all 6 rectangular faces is calculated using the formula: TSA = 2(lb + bh + hl).

Length of the Longest Diagonal

The maximum length of a rod that can be placed entirely inside a cuboid is determined by its body diagonal: D = √(l² + b² + h²).

Lateral Surface Area

The area of the 4 standing walls (excluding the top ceiling and bottom floor) is calculated as: LSA = 2h(l + b).

Cube Properties

When the length, breadth, and height are exactly equal (l = b = h = a), the solid becomes a cube. For a cube, Volume = a³ and Total Surface Area = 6a².

Given:

Sales of Helmets C in 1999 = 54 thousand

Sales of Helmets C in 2002 = 68 thousand

Formula used:

Percentage increase = ((New value - Old value) / Old value) × 100

Calculations:

Percentage increase = ((68 - 54) / 54) × 100

⇒ Percentage increase = (14 / 54) × 100

⇒ Percentage increase = 25.93%

∴ The percentage increase in the sale of Helmets C is 25.93%.

Given:

Production by Company A in 2018 = 140 (in thousand)

Production by Company B in 2018 = 190 (in thousand)

Production by Company C in 2018 = 150 (in thousand)

Formula used:

Percentage = (Part / Total) × 100

Calculation:

Total production = 140 + 190 + 150

⇒ Total production = 480 (in thousand)

Percentage of Company C = (150 / 480) × 100

⇒ Percentage of Company C = 0.3125 × 100

⇒ Percentage of Company C = 31.25%

∴ The refrigerators produced by Company C form 31.25% of the total production.

Shortcut Trick

Perimeter of a sector = Radius × [θ × (π / 180) + 2]

⇒ Perimeter = 10 × [30 × (3.14 / 180) + 2]

⇒ Perimeter = 10 × [3.14 / 6 + 2]

⇒ Perimeter = 10 × [0.5233 + 2] = 10 × 2.5233

⇒ Perimeter = 25.233 cm ≈ 25.2 cm

∴ The correct answer is 25.2 cm.

Alternate Method

Given:

Radius of the sector (r) = 10 cm

Angle of the sector (θ) = 30°

π = 3.14

Formula Used:

Length of Arc (l) = (θ / 360°) × 2πr

Perimeter of Sector = Length of Arc + 2 × Radius

Calculations:

⇒ Length of Arc (l) = (30° / 360°) × 2 × 3.14 × 10

⇒ l = (1 / 12) × 62.8

⇒ l = 5.233 cm

⇒ Perimeter of the sector = l + 2r

⇒ Perimeter = 5.233 + 2 × 10

⇒ Perimeter = 5.233 + 20

⇒ Perimeter = 25.233 cm

⇒ Rounding off to one decimal place, we get 25.2 cm.

∴ The correct answer is 25.2 cm.

Additional Information

Area of a Sector

The area of a sector of a circle is calculated using the formula: Area = (θ / 360°) × πr².

Length of an Arc

The length of the curved arc boundary of a sector can be found using: Arc Length = (θ / 360°) × 2πr.

Area of a Segment

The area of a segment is obtained by subtracting the area of the triangle formed by the radii and the chord from the area of the corresponding sector.

Shortcut Trick

By the divisibility rule of 11, the difference between the sums of alternating digits must be 0 or a multiple of 11.

Sum of odd-placed digits = 7 + 4 + K + 5 = 16 + K

Sum of even-placed digits = 8 + 5 + 8 + 4 = 25

Equating the difference to 0: 25 − (16 + K) = 0 ⇒ 9 − K = 0 ⇒ K = 9

∴ The correct answer is 9.

Alternate Method

Given:

The number 7845K854 is perfectly divisible by 11.

Formula Used:

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or a multiple of 11.

Calculations:

⇒ Let's find the sum of the digits at the odd positions (1^st, 3^rd, 5^th, and 7^th from left):

⇒ S₁ = 7 + 4 + K + 5 = 16 + K

⇒ Let's find the sum of the digits at the even positions (2^nd, 4^th, 6^th, and 8^th from left):

⇒ S₂ = 8 + 5 + 8 + 4 = 25

⇒ Find the difference between the two alternating sums:

⇒ Difference = S₂ − S₁ = 25 − (16 + K) = 9 − K

⇒ For the whole number to be divisible by 11, the difference must be 0, 11, 22, etc.

⇒ Since K is a single-digit positive integer (from 0 to 9), the only possible valid difference is 0:

⇒ 9 − K = 0

⇒ K = 9

∴ The correct answer is 9.

Additional Information

Divisibility Rule of 3 & 9

A number is divisible by 3 or 9 if the sum of all its digits is completely divisible by 3 or 9, respectively.

Divisibility Rule of 4 & 8

A number is divisible by 4 if the last two digits form a number divisible by 4. It is divisible by 8 if the last three digits form a number divisible by 8.

Divisibility Rule of 7, 11 & 13 (Combined Block Trick)

Group the number into blocks of 3 digits moving from right to left. If the alternating difference of these blocks is divisible by 7, 11, or 13, the original number is divisible by the respective divisor.

Shortcut Trick

Put A = 60° in the given expression.

⇒ sin 60° ÷ (1 + cos 60°) = (√3/2) ÷ (1 + 1/2) = (√3/2) ÷ (3/2) = 1/√3

Now, check the given options for A = 60°:

⇒ Option 1: (1 − cos 60°) ÷ sin 60° = (1 − 1/2) ÷ (√3/2) = (1/2) ÷ (√3/2) = 1/√3

Option 1 matches the exact value of the given expression.

∴ The correct answer is (1 − cos A)/(sin A).

Alternate Method

Given:

Expression = (sin A) / (1 + cos A)

Formula Used:

sin² A + cos² A = 1 ⇒ 1 − cos² A = sin² A

Calculations:

⇒ Multiply the numerator and denominator by (1 − cos A)

⇒ [sin A × (1 − cos A)] / [(1 + cos A) × (1 − cos A)]

⇒ Using (a + b)(a − b) = a² − b² in the denominator:

⇒ [sin A × (1 − cos A)] / (1 − cos² A)

⇒ [sin A × (1 − cos A)] / sin² A

⇒ (1 − cos A) / sin A

∴ The correct answer is (1 − cos A)/(sin A).

Additional Information

Pythagorean Identities

Fundamental identities relating squared trigonometric functions: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Double Angle Formulas

Used to express trigonometric functions of double angles: sin 2θ = 2 sinθ cosθ and cos 2θ = cos²θ − sin²θ = 2 cos²θ − 1 = 1 − 2 sin²θ.

Half Angle Formulas

Used to find trigonometric values of half angles: sin(θ/2) = √[(1 − cosθ)/2] and cos(θ/2) = √[(1 + cosθ)/2] for acute angles.

Shortcut Trick

Direct property for internal angle bisectors meeting at the incentre O:

∠QOR = 90º + ∠P / 2

107º = 90º + ∠P / 2

∠P / 2 = 107º − 90º = 17º

∠P = 34º

∴ The correct answer is 34º.

Alternate Method

Given:

In ΔPQR, the bisectors of ∠Q and ∠R meet at point O inside the triangle.

∠QOR = 107º

Formula Used:

When the internal bisectors of two base angles of a triangle meet at the incentre, the angle formed is equal to 90º + (opposite angle) / 2.

∠QOR = 90º + ∠P / 2

107º

P = ? P Q R O

Calculations:

⇒ 107º = 90º + ∠P / 2

⇒ 107º − 90º = ∠P / 2

⇒ 17º = ∠P / 2

⇒ ∠P = 17º × 2

⇒ ∠P = 34º

∴ The correct answer is 34º.

Additional Information

Incentre (Internal Bisectors)

When the internal bisectors of angles B and C of a triangle ABC meet at point I, the angle formed at the incentre is given by: ∠BIC = 90º + ∠A/2.

Excentre (External Bisectors)

When the external bisectors of angles B and C of a triangle ABC meet at point E outside the triangle, the angle formed is: ∠BEC = 90º − ∠A/2.

Circumcentre (Perpendicular Bisectors)

The angle formed at the circumcentre O by the vertices B and C is always double the opposite angle: ∠BOC = 2 × ∠A.

Orthocentre (Altitudes)

The angle formed at the orthocentre H and the opposite angle A are supplementary to each other: ∠BHC = 180º − ∠A.

Shortcut Trick

Divide the given equation by cosθ to quickly find tanθ:

(7tanθ + 4) / (9tanθ − 2) = 5 / 4

Cross-multiplying gives: 28tanθ + 16 = 45tanθ − 10 ⇒ 17tanθ = 26 ⇒ tanθ = 26/17

Substitute tan²θ = (26/17)² = 676/289 in the required expression:

(676/289 + 5) / (676/289 − 5) = (676 + 1445) / (676 − 1445) = 2121 / −769 = −2121/769

∴ The correct answer is −2121/769.

Alternate Method

Given:

(7sinθ + 4cosθ) / (9sinθ − 2cosθ) = 5/4

Dividing numerator and denominator on the LHS by cosθ:

⇒ (7(sinθ/cosθ) + 4(cosθ/cosθ)) / (9(sinθ/cosθ) − 2(cosθ/cosθ)) = 5/4

⇒ (7tanθ + 4) / (9tanθ − 2) = 5/4

Cross-multiplying the equation:

⇒ 4 × (7tanθ + 4) = 5 × (9tanθ − 2)

⇒ 28tanθ + 16 = 45tanθ − 10

⇒ 45tanθ − 28tanθ = 16 + 10

⇒ 17tanθ = 26

⇒ tanθ = 26/17

Now, we need to find the value of (tan²θ + 5) / (tan²θ − 5)

Substitute tanθ = 26/17:

⇒ [(26/17)² + 5] / [(26/17)² − 5]

⇒ (676/289 + 5) / (676/289 − 5)

⇒ [(676 + 5 × 289) / 289] / [(676 − 5 × 289) / 289]

⇒ (676 + 1445) / (676 − 1445)

⇒ 2121 / −769

⇒ −2121/769

∴ The correct answer is −2121/769.

Additional Information

Trigonometric Ratios

tanθ = sinθ / cosθ and cotθ = cosθ / sinθ

Componendo and Dividendo

If a/b = c/d, then (a+b)/(a−b) = (c+d)/(c−d). This property often simplifies ratio-based equations.

Pythagorean Identities

sin²θ + cos²θ = 1, sec²θ − tan²θ = 1, and cosec²θ − cot²θ = 1.

Shortcut Trick

The net change for two successive percentage changes is: x + y + (x × y) / 100

First two increases (+12% and +23%): Net = 12 + 23 + (12 × 23) / 100 = 35 + 2.76 = +37.76%

Now, combine the new net (+37.76%) with the final decrease (−34%):

Net Change = 37.76 − 34 − (37.76 × 34) / 100 = 3.76 − 12.8384 = −9.0784%

The negative sign indicates an overall decrease, which is approximately 9%.

∴ The correct answer is 9% decrease.

Alternate Method

Given: Initial increase = 12%, Second increase = 23%, Final decrease = 34%

Formula Used:

Final Value = Initial Value × (1 + r₁/100) × (1 + r₂/100) × (1 − r₃/100)

Calculations:

⇒ Let the original number be 100.

⇒ Value after 12% increase = 100 × 1.12 = 112

⇒ Value after 23% increase = 112 × 1.23 = 137.76

⇒ Value after 34% decrease = 137.76 × 0.66 = 90.9216

⇒ Net Change = Final Value − Initial Value

⇒ Net Change = 90.9216 − 100 = −9.0784

⇒ A negative value indicates a decrease in the original number.

⇒ Decrease percentage ≈ 9% (nearest to an integer).

∴ The correct answer is 9% decrease.

Additional Information

Successive Percentage Change Formula

When a quantity undergoes two successive changes of a% and b%, the equivalent overall percentage change is given by (a + b + ab/100)%. Use a positive value for an increase and a negative value for a decrease.

Multiplying Factor Method

For multiple successive percentage variations, using decimal multipliers is highly efficient. An increase of r% uses a multiplying factor of (1 + r/100), while a decrease of r% uses (1 − r/100). The final value is found by multiplying the initial base value by all successive factors.

Shortcut Trick

When goods are sold at cost price but false weights are used, the actual price is irrelevant.

Gain % = [Error ÷ (True Weight − Error)] × 100

⇒ True Weight = 1000 gm, Error = 200 gm

⇒ False Weight = 1000 gm − 200 gm = 800 gm

⇒ Gain % = (200 ÷ 800) × 100 = 25%

∴ The correct answer is 25%.

Alternate Method

Given:

Claimed Selling Price (SP) of 1 kg (1000 gm) = ₹25

Actual Cost Price (CP) of 1 kg (1000 gm) = ₹25

Quantity removed from each kg = 200 gm

Formula Used:

Profit % = (Profit ÷ CP) × 100

Calculations:

⇒ Actual weight given by shopkeeper = 1000 gm − 200 gm = 800 gm

⇒ Cost of 1000 gm = ₹25

⇒ Actual Cost Price (CP) of 800 gm = (25 ÷ 1000) × 800 = ₹20

⇒ Selling Price (SP) charged to customer for 1 kg = ₹25

⇒ Profit = SP − CP = 25 − 20 = ₹5

⇒ Profit % = (5 ÷ 20) × 100 = 25%

∴ The correct answer is 25%.

Additional Information

Dishonest Dealer Selling at CP

When a dealer claims to sell goods at cost price but uses a false weight, Gain % = (Error ÷ False Weight) × 100.

Dishonest Dealer Selling at Profit/Loss

If goods are sold at a profit of P% but weighed incorrectly, actual Gain % = [((100 + P) × True Weight ÷ False Weight) − 100]%.

Successive Cheating

If a dealer cheats by x% while buying and y% while selling, the overall profit % can be calculated successively as x + y + (xy ÷ 100).

Shortcut Trick

Relative speed (same direction) = 15 − 12 = 3 km/h.

Initial Distance = 600 m = 0.6 km.

Time = Distance ÷ Relative speed = 0.6 ÷ 3 = 0.2 hours.

Time in minutes = 0.2 × 60 = 12 minutes.

∴ The correct answer is 12 minutes.

Alternate Method

Given:

Distance between Policeman and Thief (D) = 600 m = 0.6 km

Speed of Policeman (S_p) = 15 km/h

Speed of Thief (S_t) = 12 km/h

Formula Used:

Relative Speed (when moving in the same direction) = S_p − S_t

Time = Distance ÷ Relative Speed

Calculations:

⇒ Relative Speed = 15 km/h − 12 km/h = 3 km/h

⇒ Time required to catch the thief = 0.6 km ÷ 3 km/h

⇒ Time = 0.2 hours

⇒ Time in minutes = 0.2 × 60 = 12 minutes

∴ The correct answer is 12 minutes.

Additional Information

Relative Speed (Opposite Direction)

When two objects move towards each other, their relative speed is the sum of their individual speeds: Relative Speed = S₁ + S₂.

Average Speed

Average speed is the total distance traveled divided by the total time taken. For two equal distances covered at speeds x and y, Average Speed = 2xy ÷ (x + y).

Unit Conversion

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

Shortcut Trick

Perimeter of a sector = r(2 + πθ/180°)

Given Perimeter = 64/3 cm and central angle θ = 60°.

⇒ r(2 + (22/7) × 60/180) = 64/3 ⇒ r(2 + 22/21) = 64/3 ⇒ r(64/21) = 64/3 ⇒ r = 7 cm.

Area of sector = (θ/360°) × πr² = (60/360) × 22/7 × 7²

Area = 1/6 × 154 = 77/3 cm².

∴ The correct answer is 77/3 cm².

Alternate Method

Given:

Perimeter of the sector = 64/3 cm

Central angle (θ) = 60°

Value of π = 22/7

Formula Used:

Arc length (l) = (θ/360°) × 2πr

Perimeter of sector = 2r + l

Area of sector = (θ/360°) × πr²

Calculation:

⇒ Arc length (l) = (60/360) × 2 × (22/7) × r

⇒ l = (1/6) × (44/7) × r

⇒ l = 22r/21

⇒ Perimeter = 2r + 22r/21 = (42r + 22r)/21

⇒ Perimeter = 64r/21

Equating the formula with the given value:

⇒ 64r/21 = 64/3

⇒ r/21 = 1/3

⇒ r = 21/3 = 7 cm

Now, substitute the radius to find the area of the sector:

⇒ Area = (60/360) × (22/7) × (7)²

⇒ Area = (1/6) × (22/7) × 49

⇒ Area = (1/6) × 22 × 7

⇒ Area = 154/6

⇒ Area = 77/3 cm²

∴ The correct answer is 77/3 cm².

Additional Information

Area of a Sector

The region enclosed by two radii and the corresponding arc. The formula is A = (θ/360°) × πr² or alternatively A = 1/2 × l × r, where l is the arc length.

Length of an Arc

The continuous portion of the circumference of a circle. The length is determined by the central angle using the formula l = (θ/360°) × 2πr.

Perimeter of a Sector

The total boundary length of the sector, which is the sum of the two radii and the arc length. Formula: Perimeter = 2r + l.

The correct answer is Option 3.

Key Points

• The sentence logically begins with the subject: "R: the advantage of travelling different places and".
• Following this, "P: having the opportunity of observing people's" continues the thought, specifying what the advantage includes.
• "S: culture, custom and lifestyle, is that" completes the specifics of what can be observed.
• Finally, "Q: we respect and appreciate their point of views" wraps up the sentence by explaining the outcome of these observations.

Therefore, the correct answer is RPSQ.

Additional Information

• Option 1 (RQPS): This option starts with "we respect and appreciate their point of views," which does not start the sentence logically.
• Option 2 (PSQR): This option starts with "having the opportunity of observing people's," which lacks the initial subject.
• Option 4 (SQPR): This option starts with "culture, custom and lifestyle, is that," which does not introduce the advantage of travelling.

The correct answer is: Option 2.

Key Points

• The phrase "Each participant have" is grammatically incorrect. The correct auxiliary verb should be singular to match the singular noun "participant".
• "Each participant has" means that every individual participant has performed well. (प्रत्येक प्रतिभागी ने अच्छा प्रदर्शन किया है।)
• Example: Each participant has submitted their project on time.

Therefore, the correct answer is: Option 2.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Option 1: Each participant was (प्रत्येक प्रतिभागी था): This phrase is incorrect in the given context as it does not correctly complete the sentence.
• Example: Each participant was eager to win.
• Option 3: Each participant have been (प्रत्येक प्रतिभागी रहे हैं): This phrase is grammatically incorrect as "have" does not agree with the singular noun "participant".
• Example: Each participant have been preparing for months. (Incorrect)
• Option 4: Each participant were (प्रत्येक प्रतिभागी थे): This phrase is incorrect because "were" does not agree with the singular noun "participant".
• Example: Each participant were given a certificate. (Incorrect)

The correct answer is: Option 4.

Key Points

• The term "Morbid compulsion to consume alcohol continuously" refers to an uncontrollable and pathological urge to drink alcohol frequently. (लगातार शराब पीने की विकृत प्रवृत्ति)
• Example: Despite numerous attempts to quit, his dipsomania led him to relapse repeatedly.
• "Dipsomania" is the medical term for this condition, characterized by an insatiable craving for alcohol. (मद्यपान की उन्मत्त इच्छा)
• Example: The patient was diagnosed with dipsomania and was advised to seek immediate treatment.

Therefore, the correct answer is: Option 4.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Satyromania (व्यभिचार की उन्मत्त इच्छा): An excessive, uncontrollable sexual desire in men.
• Example: His satyromania caused numerous problems in his personal relationships.
• Maniac (उन्मादी): A person exhibiting extreme symptoms of wild behavior, especially when violent and dangerous.
• Example: The maniac was apprehended by the police after causing chaos in the neighborhood.
• Kleptomania (चोरी करने की आदत): A recurrent urge to steal, typically without regard for need or profit.
• Example: Her kleptomania led her to shoplift items she didn't even need.

The correct answer is Option 2.

 

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the passive voice, the sentence is: "The painting was admired by art enthusiasts from around the world."
• To convert to active voice: Place the subject "art enthusiasts from around the world" at the beginning.
• Change the passive verb form "was admired" to the active verb form "admired."
• Place the object "the painting" after the verb.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "Art enthusiasts from around the world admired the painting."

 

Additional Information

• Option 1: "The painting was being admired by art enthusiasts from around the world." – Incorrect as it is still in passive voice and uses the past continuous tense.
• Option 3: "Art enthusiasts from around the world have admired the painting." – Incorrect tense; uses present perfect which is not needed for this sentence.
• Option 4: "The painting has been admired by art enthusiasts from around the world." – Incorrect as it is still in passive voice and uses present perfect tense.

The correct answer is: Option 1.

Key Points

• The idiom "at her wits' end" means being so worried, confused, or annoyed that one does not know what to do next. (इतना चिंतित, भ्रमित या परेशान होना कि अगले कदम का पता न हो।)
• Example: She was at her wits' end trying to manage the unruly children.
• Worried refers to feeling anxious or concerned about something. (चिंतित)
• Example: He was worried about his upcoming exams.
• Hence, we can infer that the idiom 'at her wits' end' means being in a state of extreme worry or confusion.

Therefore, the correct answer is: Option 1.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Option 2: So worried, confused or annoyed that she became unconscious (इतना चिंतित, भ्रमित या परेशान होना कि वह बेहोश हो गई)
• Example: She was so stressed that she almost fainted.
• Option 3: So calm and composed that she knows what to do next (इतनी शांत और संयमित कि उसे पता है कि आगे क्या करना है)
• Example: Despite the chaos, she remained calm and composed.
• Option 4: So worried, confused or annoyed that she insulted others for no reason (इतना चिंतित, भ्रमित या परेशान होना कि उसने बिना किसी कारण दूसरों का अपमान किया)
• Example: His frustration led him to snap at his colleagues.

The correct answer is Option 4.

 

Key Points

• The primary issue in the sentence is the incorrect use of the verb "are" with the subject "I."
• The correct verb to use with the subject "I" is "am."
• The correct phrase should be "I am dancing," ensuring grammatical correctness and clarity.
• Thus, the error is located in Option 4 of the sentence.

Therefore, the correct answer is Option 4.

 

Correct Sentence: "I am dancing with my husband at my sister's wedding."

 

Additional Information

• 1: "husband at my" – This part of the sentence is grammatically correct and does not require any changes.
• 2: "sister's wedding" – This part of the sentence is grammatically correct and does not require any changes.
• 3: "with my" – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is: Option 2.

Key Points

• The word "Mischeivious" is incorrectly spelt. The correct spelling is "Mischievous".
• English Meaning: Causing or showing a fondness for causing trouble in a playful way. (शरारती)
• Example: The mischievous child hid his sister's shoes as a prank.
• "Mischievous" refers to causing or showing a fondness for causing trouble in a playful way. (शरारती)
• Example: The mischievous kitten knocked over the vase while playing.

Therefore, the correct answer is: Option 2.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Accommodate (समायोजित करना): The correct spelling is "Accommodate", which means to provide lodging or sufficient space for.
• Example: The hotel can accommodate up to 500 guests.
• Millennium (सहस्राब्दी): The correct spelling is "Millennium", which refers to a period of a thousand years.
• Example: The year 2000 was celebrated as the beginning of a new millennium.
• Privilege (विशेषाधिकार): A special right, advantage, or immunity granted or available only to a particular person or group.
• Example: It is a privilege to have access to quality education.

The correct answer is Option 2.

 

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the passive voice, the sentence is: "He will be made President by the people."
• To convert to active voice: Place the subject "the people" at the beginning.
• Change the passive verb form "will be made" to the active verb form "will make."
• Place the object "him" after the verb.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "The people will make him President."

 

Additional Information

• Option 1: "People will be making him the President." – Incorrect tense; uses future continuous which is not needed for this sentence.
• Option 3: "By the people, he shall be made the President." – Incorrect word order; remains passive.
• Option 4: "He will be made President by the people." – This is the original passive voice sentence.

The correct answer is: Tight.

Key Points

• The word "taut" means something that is stretched or pulled tight; not slack. (कसावदार)
• Example: The rope was taut, ready to bear the weight of the climber.
• "Tight" refers to something that is firmly or closely fixed in place; not loose or slack. (कस हुआ)
• Example: She pulled the knot tight to ensure it wouldn't come undone.
• Hence, we can infer that the synonym of 'taut' is 'tight'.

Therefore, the correct answer is: Tight.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Slack (ढीला): Not tight; loose.
• Example: The rope went slack after the load was removed.
• Torn (फटा हुआ): Damaged by having been pulled apart or ripped.
• Example: He wore a torn shirt to the party, which looked quite out of place.
• Flaccid (ढीला): Soft and hanging loosely or limply.
• Example: The patient's muscles became flaccid after the surgery.