SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 2) (Previous Year Paper)

By using the symbols in the table given below, we can draw the following family tree:

Given: 

‘X × Y’ means ‘X is the father of Y’.

‘X ÷ B’ means ‘X is the mother of B’.

‘X - Y’ means ‘X is the Brother of Y’.

Find:- expression shows that A is the father of C?

Let's check each option one by one.

Option 1) A – B × C

(A is the brother of B, and B is the father of C)

Here, A is the Paternal uncle of C. (Incorrect)

Option 2) A ÷ C – B

(A is the mother of C, and C is the brother of B)

Here, A is the mother of C. (Incorrect)

Option 3) A × B ÷ C

(A is the father of B, and B is the mother of C)

Here, A is the maternal grandfather of C. (Incorrect)

Option 4) A × B – C

(A is the father of B, and B is the brother of C)

Here, A is the father of C. (Correct)

Hence, the correct answer is "Option 4".

The correct mirror image of the given figure when the mirror is held on the AB side.

Hence, the correct answer is "Option 2".

Additional Information

1. In the mirror image left side and right side changed vice-versa where the top and bottom remain the same.

2. In a real given mirror image the farthest number or alphabet appears closest in the mirror image.

The pattern followed here is:

Octagon: Eight → In geometry, an octagon is a polygon that has Eight sides and Eight angles.

Similarly,

Heptagon: Seven → A heptagon is a polygon that has seven sides. 

Hence, the correct answer is "Seven".

Additional Information

The pattern followed here is:

Logic: (First number + Third number)³ = Second number.

1. (2, 125, 3)

⇒ (2 + 3)³ ⇒ (5)³ = 125

And,

2. (1, 64, 3)

⇒ (1 + 3)3 ⇒ (4)3 = 64

Let's check each option one by one:

Option 1) (2, 100, 8)

⇒ (2 + 8) 3 ⇒ (10)3 = 1000 ≠ 100 (Incorrect)

Option 2) (5, 512, 3)

⇒ (5 + 3)3 ⇒ (8)3 = 512 (Correct)

Option 3) (12, 50, 13)

⇒ (12 + 13)3 ⇒ (25)3 = 15625 ≠ 50 (Incorrect)

Option 4) (4, 341, 3)

⇒ (4 + 3)3 ⇒ (7)3 = 343 ≠ 341 (Incorrect)

Hence, the correct answer is "(5, 512, 3)"

Logic: (First number ÷ 2) × (First number - 1) = Second number

10 : 45 →

⇒ (10/2) × (10 -1) = 5 × 9 = 45

And, 

11 : 55 →

⇒ (11/2) × (11 -1) = (11/2) × 10 = 11 × 5 = 55

Similarly,

? : 28 →

⇒ (x/2) × (x -1) = 28

⇒ x(x - 1) = 56

⇒ x² - x - 56 = 0 

⇒ (x - 8)(x + 7) = 0

⇒ x = either 8 or -7

As value can not be negative here. So, the correct value will be 8.

Hence, the correct answer is "8".

The pattern followed here is:

Interchanging the given two signs so that the given equation will be correct.

Given: + and ÷ 

Let's check each option one by one:

Option 1) 9 × 18 + 27 ÷ 36 – 30 = 18

After interchanging the mathematical signs we get the:

⇒ 9 × 18 ÷  27 + 36 – 30 = 18

⇒ 9 × 0.666 + 36 - 30 = 18

⇒ 5.994 + 36 - 30 = 18

⇒ 41.994 - 30 = 18

⇒ 11.994 ≠ 18

⇒ LHS ≠ RHS

Option 2) 9 + 3 × 2 – 8 ÷ 1 = –1

After interchanging the mathematical signs we get the:

⇒ 9 ÷ 3 × 2 – 8 + 1 = –1

⇒ 3 × 2 - 8 + 1 = - 1

⇒ 6 - 8 + 1 = - 1

⇒ 7 - 8 = -1

⇒ - 1 = - 1

⇒ LHS = RHS

Option 3) 16 + 8 × 2 ÷ 6 – 9 = 10

After interchanging the mathematical signs we get the:

⇒ 16 ÷ 8 × 2 + 6 – 9 = 10

⇒ 2 × 2 + 6 - 9 = 10

⇒ 4 + 6 - 9 = 10

⇒ 10 - 9 = 10

⇒ 1 ≠ 10 

⇒ LHS ≠ RHS

Option 4) 16 + 2 × 6 ÷ 3 – 7 = 50

After interchanging the mathematical signs we get the:

⇒ 16 ÷ 2 × 6 + 3 – 7 = 50

⇒ 8 × 6 + 3 - 7 = 50

⇒ 48 +3 - 7 = 50

⇒ 51 - 7 = 50

⇒ 44 ≠ 50

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 2".

The pattern followed here is:

Logic: √(First number - Second number) = Third number.

First row: 243, 162, 9

⇒ √(243 - 162)

⇒ √81 = 9

And,

Second row: 108, 72, 6

⇒ √(108 - 72)

⇒ √36 = 6

Similarly,

Third row: 48 : ? : 4

⇒ √(48 - X) = (4)²

⇒ √(48 - X) = 16

⇒ 48 - 16 = 32

Hence, the correct answer is "32".

The pattern followed here is:

Logic: (First number)² - 3 =  Second number.

Let's check each option one by one.

Option 1) 8 - 60

⇒ (8)² - 3 = 64 - 3 = 61 ≠  60 (Incorrect)

Option 2) 6 - 33

⇒ (6)2 - 3 = 36 - 3 = 33 (Correct)

Option 3) 12 - 141

⇒ (12)2 - 3 = 144 - 3 = 141 (Correct)

Option 4) 10 - 97

⇒ (10)2 - 3 = 100 - 3 = 97 (Correct)

Hence, the correct answer is "8 - 60".

The pattern followed here is:

We have to interchange the given numbers in the options and find which option is correct.

Given: 14 + 39 - ( $\sqrt{144}$ ÷  4 ) + ( 5 × 3 ) - 6 = 63

Let's check each option one by one:

Option 1) 14 and 6

After interchanging the numbers we get the:

⇒ 6 + 39 - ( $\sqrt{144}$ ÷  4 ) + ( 5 × 3 ) - 14 = 63

⇒ 6 + 39 - (12 ÷ 4) + (5 × 3) - 14 = 63

⇒ 6 + 39 - 3 + 15 - 14 = 63

⇒ 60 - 3 - 14 = 63

⇒ 43 ≠ 63

⇒ LHS ≠ RHS

Option 2) 5 and 39

After interchanging the numbers we get the:

⇒ 14 + 5 - ( $\sqrt{144}$ ÷  4) + (39 × 3) - 6 = 63

⇒ 14 + 5 - (12 ÷ 4) + (39 × 3) - 6 = 63

⇒ 14 + 5 - 3 + 117 - 6 = 63

⇒ 136 - 3 - 6 = 63

⇒ 127 ≠ 63

⇒ LHS ≠ RHS

Option 3) 4 and 3

After interchanging the numbers we get the:

⇒ 14 + 39 - ( $\sqrt{144}$ ÷  3) + ( 5 × 4) - 6 = 63

⇒ 14 + 39 - (12 ÷ 3) + (5 × 4) - 6 = 63

⇒ 14 + 39 - 4 + 20 - 6 = 63

⇒ 73 - 4 - 6 = 63

⇒ 63 = 63

⇒ LHS = RHS

Option 4) 4 and 6

After interchanging the numbers we get the:

⇒ 14 + 39 - ($\sqrt{144}$ ÷  6) + (5 × 3 ) - 4 = 63

⇒ 14 + 39 - (12 ÷ 6) + (5 × 3) - 4 = 63

⇒ 14 + 39 - 2 + 15 - 4 = 63

⇒ 68 - 2 - 4 = 63

⇒ 62 ≠ 63

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 3".

The pattern followed here is:

Two types of movement are followed.

1. The first two elements and the last two elements are interchanged in their position mutually.

2) The first two elements and the last two elements are interchanged in their position simultaneously.

This movement occurs alternatively and so on.

Hence, the correct answer is "Option 2".

The position of the English alphabet series is given below:

Option 1) MNG

Option 2) STM

Option 3) ABU

Option 4) HED

Hence, the correct answer is "HED".

The position of the English alphabet is given below:

Logic: Letters are coded as their opposite positional value.

‘NULLIFY’ is written as ‘MFOLRUB’ 

And,

‘SKYWALK’ is written as ‘HPBWZOP’

Similarly,

‘FLAGGER’ be written as '?'

Hence, the correct answer is "UOZGTVI".

The pattern followed here is:

The series is the square of a prime number that starts from 11.

Given: 121, 169, 289, ?, 529, 841

Hence, the correct answer is "361".

The pattern followed here is:

Logic: The pair of Male and Female animals is given.

Dog: Bitch → Dog is the male Dog and Bitch is the adult female Dog.

Similarly,

Stallion: Mare → Stallion is the male horse and Mare is the adult female horse.

Hence, the correct answer is "Mare".

Additional Information

The pattern followed here is:

Given:

Detailed Explanation:

= 4 commons in both the dice and rotate clockwise from number 4.

Opposite pairs:

⇒ 3 - 5

⇒ 1 - 2

⇒ 6 - 4

So, the number '6' is at the top when '4' is at the bottom.

Hence, the correct answer is "4".

The pattern followed here is:

Given:

  

Hence, the correct answer is "Option 1".

The logic here followed is :

1. Two different series are followed below. The letter placed in the left upper corner is increased by +1 and the letter placed in the right lower corner is increased by +3.

2) Two different series are followed below. The letter placed in the right upper corner is increased by +2 and the letter placed in the left lower corner is increased by +4.

 

Hence, the correct answer is "option 2".

The pattern followed here is:

The least possible Venn diagram is shown below according to the given information.

Statements:

Some mice are keyboards.

All keyboards are CPUs.

All mice are webcams.

Conclusions:

I. Some CPUs are mice → Follow → As some mice are keyboards and all keyboards are CPUs. So some CPUs are mice is definitely followed.

II. Some webcams are keyboards → Follow → As Some mice are keyboards and all mice are webcams. So some webcams are keyboards definitely followed.

III. Some webcams are CPUs → Follow → As Some mice are keyboards, all keyboards are CPUs and All mice are webcams. So some webcams are CPUs is definitely followed.

So, All conclusions are follows.

Hence, the correct answer is "Option 1".

The pattern followed here is:

Here in this question interchanging the given two numbers and two signs in the given equation.

Given: × and –, 4 and 5

I. 9 ÷ 3 × 6 + 5 – 4

After interchanging the two numbers and two signs we get the;

⇒ 9 ÷ 3 - 6 + 4 × 5

⇒ 3 - 6 + 4 × 5

⇒ 3 - 6 + 20

⇒ 23 - 6

⇒ 17

II. 5 – 4 × 3 + 6 ÷ 2 

After interchanging the two numbers and two signs we get the;

⇒ 4 × 5 - 3 + 6 ÷ 2  

⇒ 4 × 5 - 3 + 3

⇒ 20 - 3 + 3

⇒ 23 - 3

⇒ 20

Hence, the correct answer is "17 , 20".

The pattern followed here is:

Given words are arranged as per appears in the English dictionary.

2. Miscalculate 4. Miscall 5. Miscasting 1. Miscellaneous 3. Mischance

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

By using the symbols in the table given below, we can draw the following family tree:

Given: 

A – B means ‘A is the mother of B’

A % B means ‘A is the brother of B’

A $ B means ‘A is the sister of B’

A @ B means ‘A is the son of B’

Find how is L related to P.

Given:- L @ M – N $ O % P

Clearly, L is the brother of P.

Hence, the correct answer is "Brother".$

The position of the English alphabet is given below:

Hence, the correct answer is "IFQE".

The position of the English alphabet is given below:

Logic: Addition of the positional place value of letters = Code

BELOVED is coded as 65

​

And,

FLOWER is coded as 79

Similarly,

QUIVER be coded as '?'

Hence, the correct answer is "92".

The pattern followed here is:

The least possible Venn diagram is given below according to the given information.

Statements:

I. All Q are M.

II. All O are M.

Conclusion:

I. Some O are not Q → Does not follow → As All Q are M and All O are M. So some O are not Q is a possibility but not definitely true.

II. All M are Q → Does not follow ​→ As All Q are M and All O are M. So All M are Q is a possibility but not definitely true.

So, Neither conclusion follows.

Hence, the correct answer is "Option 4".

The position of the English alphabet is given below:

Hence, the correct answer is "NNLJ".

The correct answer is April.

Key Points

• In India, Baisakhi marks the beginning of spring.
• Traditionally, Baisakhi marks the end of the harvest season and is a time of great joy and festivity for farmers.
• Punjab and Haryana are the states where the celebrations are concentrated.
• There are many names for this festival, including Pohela Baishakhi in West Bengal, Bohag Bihu in Assam, Puthandu in Tamil Nadu, Phool Dei in Uttarakhand, Ugadi in Andhra Pradesh and Karnataka, Pooram Vishu in Kerala and Mahavishuva Sankranti in Odisha.

Additional Information

• Gangaur
• It is a festival in Rajasthan. There is a celebration of spring and harvest.
• Ganesh Chaturthi
• Traditionally held in Maharashtra. God Ganesh is revered during this ten-day festival.
• Yaosang
• People from diverse communities gather in Manipur to celebrate this festival.
• It is a five-day event on a full moon day. It is generally at the same time as Holi.
• Khasi Festival
• The majority tribe of Meghalaya observes this festival with music.

The correct answer is Devadana.

Key Points

Chola inscriptions

• The funds from the revenues were used to keep the king's army afloat as well as to build temples and forts. The authority of collecting revenue was from powerful families.
• The Brahmanas were often honoured by kings with land gifts. These grants were written down on copper plates and distributed to the people who were given the land.
• The Chola inscriptions cited various types of land:
• Brahmadeya - The lands gifted to Brahamanas.
• Vellanvagai -  Land of non-Brahamana peasant owners.
• Shalabhoga - The lands for the maintenance of a school.
• Devadana - Land gifted to temples
• Pallichchhandam - Land donated to Jaina organisations.

Additional Information

• Vijayalaya (850–871 CE) overthrew the Kaveri delta from Muttaraiyar. He built the city of Thanjavur and established the Chola kingdom in 850.
• Rajaraja I was regarded as the most powerful Chola ruler.
• The well-known dancing figure of Shiva as Nataraja fully developed during the Chola Period
• The Grand Temple of Tanjavur, known as Rajarajisvaram and Brihadishvarar Temple, were some of the outstanding examples of Chola architecture, painting, sculpture and iconography.

The correct answer is Suresh N. Patel.

Key Points

• President Droupadi Murmu on Wednesday (August 3, 2022) administered the Oath of Office to the Central Vigilance Commissioner (CVC) Suresh N Patel at Rashtrapati Bhavan in Delhi.
• The ceremony was also attended by the Prime Minister and the Vice President.
• A three-member selection panel headed by the prime minister had met in July to decide on the CVC and vigilance commissioners.
• The other two members on the panel are the Union home minister and the Leader of the Opposition in Lok Sabha.
• During the meeting, the panel approved Patel's appointment as the CVC, besides approving the appointments of former Intelligence Bureau chief Arvind Kumar and ex-bureaucrat Praveen Kumar Srivastava as the vigilance commissioners.

Important Points

• Praveen Kumar Srivastava was appointed Central Vigilance Commissioner on May 29, 2023, by President Droupadi Murmu.

 Additional Information 

• Central Vigilance Commission (CVC) is an apex Indian governmental body created in 1964 to address governmental corruption.
• In 2003, the Parliament enacted a law conferring statutory status on the CVC.
• It was created on the recommendations of the Committee on Prevention of Corruption, headed by K. Santhanam, to advise and guide Central Government agencies in the field of vigilance.
• Nittoor Srinivasa Rau was selected as the first Chief Vigilance Commissioner of India.
• The Commission consists of: A Central Vigilance Commissioner – Chairperson; Not more than two Vigilance Commissioners – Members

The correct answer is Samant Kumar Goel.

Key Points

• Samant Kumar Goel, a 1984-batch IPS officer of the Punjab cadre, had completed his two-year tenure as RAW secretary last year but was given a year’s extension.
• This is the second extension of service for Samant Kumar Goel
• He was instrumental in India’s planning for the Balakot strikes in February 2019

Additional Information

• RAW
• It was founded in 1968
• RAW is the foreign intelligence agency of India. Its preliminary function is to gather foreign intelligence, counter-proliferation, and counter-terrorism, advancing India’s foreign strategic interests and advising Indian policymakers.
• The objective of RAW is to observe the political, military, scientific and economic developments in countries having a direct bearing on the national security of India and the formulation of its foreign policy.
• Rameshwar Nath Kao was the 1^st chief of India's  Research and Analysis Wing.

The correct answer is Once.

Key Points

• Delhi in India organized the Commonwealth Games in 2010, only once.
• Australia hosted the Commonwealth Games the most (5) times.

Additional Information

• The first commonwealth Games were held in 1930 in Hamilton, Canada.
• In the Games,  11 countries sent 400 athletes to take part in six sports and 59 events.
• Since then, the Games have been conducted every four years (except for 1942 and 1946 due to World War II) and the event has seen many changes, not least in its name.
• The Commonwealth Games are overseen by the Commonwealth Games Federation (GCF), which also controls the sporting program and selects the host cities.
• The Commonwealth Games of Nations is an association of independent sovereign states, most of which are former colonies of the United Kingdom.
• The British Monarch remains the head of theCommonwealth Games
• The 2022 Commonwealth Games officially known as the XXII Commonwealth Games and commonly known as Birmingham 2022, took place in Birmingham, England.

The correct option is Humus.

Key Points

• Humus is an amorphous dark-coloured and colloidal substance which is highly resistant to microbial action.
• It undergoes decomposition at an extremely slow rate.
• It can also act as a bank for nutrients.
• The process that leads to the formation of humus is known as humification.
• Humus is further degraded by some microbes and the release of inorganic nutrients occurs through the process known as mineralisation.

Additional Information

• Chitin
• Chitin is the most abundant amino polysaccharide polymer occurring in nature and is the building material that gives strength to the exoskeletons of crustaceans, insects, and the cell walls of fungi.
• Carotenoids
• They are pigments in plants, algae, and photosynthetic bacteria. These pigments produce bright yellow, red, and orange colours in plants, vegetables, and fruits.
• Carotenoids act as a type of antioxidant for humans.
• Colloids
• A colloid is one of the three primary types of mixtures, with the other two being a solution and suspension. A colloid is a mixture that has particles ranging between 1 and 1000 nanometers in diameter, yet are still able to remain evenly distributed throughout the solution.

The correct answer is Five.

Key Points

• Indian states that share borders with Bangladesh are Assam, West Bengal, Mizoram, Meghalaya, and Tripura.

Important Points

• India shares borders with Bangladesh, China, Pakistan, Nepal, Myanmar, Bhutan, and Afghanistan.
• The longest border is shared by Bangladesh which is 4096.70 Km (2,545 miles).
• Arunachal Pradesh, Nagaland, Manipur, and Mizoram share the border with Myanmar.
• Assam shares the international border with Bhutan and Bangladesh.

The correct answer is Prarthana Samaj.

Key Points

Prarthana Samaj:

• The Prarthana Samaj was founded in 1867 in Bombay by Dr. Atmaram Pandurang.
• It was an off-shoot of Brahmo Samaj.
• It was a reform movement within Hinduism and Justice M.G. Ranade and R.G. Bhandarkar joined it in 1870 and infused new strength into it.
• Mahadev Govind Ranade also ran the Deccan Education Society.
• Several members of the Prarthana Samaj had earlier been active in the Paramhansa Mandali.
• This Samaj denounced idolatry, priestly domination, caste rigidities, and preferred monotheism.
• It also concentrated on social reforms like inter-dining, inter-marriage, widow remarriage, and the uplift of women and depressed classes.
• Apart from Hindu sects, it also drew upon Christianity and Buddhism.
• It sought truth in all religions.
• Drawing inspiration from the Maratha Bhakti saints of the medieval period, Ranade sought to establish the concept of one compassionate God.
• Veeresalingam Pantulu was the Telugu reformer who encouraged the Prarthana Samaj in South India.​

The correct answer is Thaipusam.

Key Points

• Thaipusam is an important festival celebrated by the Hindus of southern India during the Tamil month of Thai (January - February). Outside of India, it is observed mainly by the Tamil-speaking community settled in Malaysia, Singapore, South Africa, Sri Lanka and elsewhere around the world.
• Thaipusam is devoted to the Hindu god Murugan, the son of Shiva and Parvati.
• Murugan is also known as Karttikeya, Subrahmanya, Shadanana, Skanda and Guha.
• It is believed that on this day, Goddess Parvati offered a lance to Lord Murugan to defeat the demon army of Tarakasura and combat their evil deeds. Therefore, Thaipusam is a celebration of the victory of good over evil.
• In Singapore, the festival is celebrated with a chariot procession that begins at the Sri Srinivasa Perumal Temple at 397 Serangoon Road in the Little India district.

Additional Information

• Karaga
• The Karaga festival is held at the Dharmaraya Swamy Temple in Bangalore.
• During Mahabharata, Draupadi, wife of five Pandavas made several Veera Kumaras (brave sons) to form a mini army and conquer the demon Timirasura. At the time of her death, these Veera Kumaras begged Draupadi not to leave them. Draupadi instead promised to return each year during the full moon day of Chaitra masa (month). Karaga festival is celebrated each year to mark the return of Draupadi in the form of Adishakti.
• Bihu
• It is the soul of Assam and is celebrated across the state with enormous zeal and enthusiasm.
• There are three Bihu festivals namely ‘Bohag Bihu’ celebrated in the month of ‘Bohag’ (Baisakh, the middle of April), ‘Magh Bihu’ observed in the month of ‘Magh’ (the middle of January), and ‘Kati Bihu’ celebrated in the month of ‘Kati’ (Kartik, the middle of October).
• Onam
• The festival of Onam is celebrated all over the state of Kerala. Kerala during Onam is marked by happiness, excitement and enjoyment among all sections of people.
• Onam is marked as an outcome of reasons that have to do with mythology as well as old agrarian practices.

The correct answer is 1 July 2017.

Key Points

• ​GST was passed as the 101^st Amendment Act of 2016.
• GST (Goods and Services Tax): is a comprehensive indirect tax on the manufacture, sale and consumption of goods and services throughout India.
• The four basic rate structures of GST are 5%. 12%, 18% and 28%.

Additional Information

• The motto of GST - is "One Nation, One Tax, One Market".
• Three types of taxes in Indian GST are State GST(SGST)/ Union Territory GST(UTGST), Central GST(CGST) and Integrated GST(IGST).
• GST bill was passed by Rajya Sabha on 3^rd August 2016.
• GST bill was passed by Lok Sabha on 8^th August 2016.
• GST bill was signed by President on 8^th September 2016.
• GST came into effect from 1^st July 2017.
• Articles deals with the formation of the GST council is 279A.
• The Chairman of the GST council is Union Finance Minister.
• The first Chairman of the GST council is Arun Jaitley.
• The concept of GST was first presented in Parliament by P. Chidambaram in 2005.
• India has chosen the Canadian model of dual GST.
• The first country to introduce GST: France in 1954.

The correct answer is Nagaram.

 Key Points

• The inscriptions of the Pallavas mention a number of local assemblies.
• These assemblies functioned through subcommittees, which looked after irrigation, agricultural operations, making roads, local temples, etc.
• The Nagaram was an organisation of merchants.
• It is likely that these assemblies were controlled by rich and powerful landowners and merchants.
• There were three types of places during this time:
• Ur - This is the place where the peasants lived and were headed by a headman who collected and paid the taxes.
• Sabha - Land granted to Brahmins and was also called Agrahara villages.
• Nagaram - Where merchants and traders resided

Additional Information

• The founder of the Pallava Dynasty was Simha Vishnu.
• The Pallava kings were great patrons of art and architecture and this society was based on Aryan culture.
• The Pallava kings  worshipped Shiva and Vishnu.
• The Pallava capital was Kanchipuram.

The correct answer is Veena.

Key Points

• Sundaram Balachander was an Indian veena player and filmmaker
• Balachander was honoured with the Padma Bhushan in 1982.
• In 1948 he directed the film En Kanavar. In 1954 he directed Andha Naal.

Additional Information

• Some of the famous artists of different Musical instrument
• Flute -  Hari Prasad Chaurasia,  Pannalal Ghosh, T.R. Mahalingam
• Shehnai - Ustad Bismillah Khan, Ali Ahmad Hussein, Krishna Ram Chaudhary.
• Santoor - Pandit Shiv Kumar Sharma, Pandit Ulhas Bapat, Pandit Tarun Bhattacharya
• Sarod - Allauddin Khan, Amjad Ali Khan(known as Sarod Samrat), Ali Akbar Khan
• Mridangam - Palghat Mani Iyer, Pudukkottai Dakshinamurthy Pillai, Umayalpuram K. Sivaraman

The correct answer is N Rangaswamy.

Key Points

• The All India NR Congress (AINRC) founder leader N Rangasamy is the Chief Minister of Puducherry.
• This is the fourth term of Mr N Rangswamy serving the post of chief minister of Puducherry.
• The Governor of Puducherry is Dr Tamilisai Soundararajan.

Additional Information

• On November 1, 1954, the French possessions in India were de facto transferred to the Indian Union and Puducherry became a Union Territory
• “Puducherry” is the French interpretation of the original name “Puducheri” meaning “new settlement”.
• The areas of Puducherry district and Karaikal district are bound by the state of Tamil Nadu, while Yanam district and Mahe district is enclosed by the states of Andhra Pradesh and Kerala, respectively.

The correct answer is 13 km.

Key Points

Troposphere

• The lowermost layer of the atmosphere with an average height of 13 km (18 km over the equator and 8 km over the poles).
• The air we breathe exists here. Almost all the weather phenomena (like rainfall, fog, clouds, dew, frost and hailstorm) occur in this layer.
• Temperature decreases with increasing height at the rate of 6.5℃ per 1000m. This is called normal lapse rate.
• The height of the troposphere varies from the equator towards the pole (decreases towards the poles) and from one season to another (increases during summer while decreases during winter) during a year.
• The upper limit is called the tropopause which is 1.5 km thick. (The word “troposphere” literally means “zone/region of mixing” and tropopause means “where the mixing stops”).

Additional Information

Stratosphere

• Above the troposphere lies the stratosphere. It extends up to a height of 50 km.
• This layer is almost free from clouds and associated weather phenomenon, making conditions most ideal for flying aeroplanes.
• One important feature of the stratosphere is that it contains a layer of ozone gas between the height of 15 to 30 km (also called Ozonosphere).
• Temperature increases with height due to the absorption of UV rays by the ozone layer.
• The upper limit of the stratosphere is known as stratopause.

Mesosphere

• Lying above the stratosphere this is the third layer of the atmosphere and extends between 50 km and 80 km.
• Meteorites burn up in this layer on entering from space.
• Temperature decreases with increasing height again.
• The uppermost limit is the mesopause where the temperature becomes -80℃.

Thermosphere

• Temperature here rises very rapidly with increasing height.
• The International Space Station is situated in this layer.
• It is further divided into two layers:

Ionosphere:

• It extends between 80 - 400 km.
• This layer helps in radio transmission. In fact, radio waves transmitted from the earth are reflected back to the earth by this layer.
• Includes a number of ionic layers with increasing heights like the D layer, E layer, F layer and G layer.

Exosphere:

• This is the upper most layer of the atmosphere.
• This layer has very thin air.
• Light gases like helium and hydrogen float into space from here.
• The density here is very low and the atmosphere resembles a nebula because it is highly rarefied.

The correct answer is 10.

Key Points

• Milk of Magnesia is the magnesium compound which acts as an antacid.
• The term milk of magnesia was first used by English pharmacist Charles Henry Phillips in 1872.
• Milk of Magnesia is basic in nature.
• The pH value of the Milk of Magnesia is 10.

Additional Information

• The scale used to express the acidic or alkaline nature of a substance based on the concentration of hydrogen ions in its solution is called a pH scale.
• pH scale was discovered by Soren Sorensen.
• The pH value of the acids are less than 7 (0 to 7)
• Acid substances usually produce a sour taste.
• The pH value of the Bases are greater than 7 (7 to 14)
• Base substances usually produce a bitter taste.
• The pH value of the neutral substance is equal to 7.
• The pH value of the pure water is 7.
• The pH value of the blood is close to 7.4.

The correct answer is Prime Minister.

Key Points

• Real executive power vests in a Council of Minister with the Prime Minister as the head.
• Article 74(1) of the Constitution provides that there shall be a Council of Ministers headed by the Prime Minister to aid and advise the President who shall, in the exercise of his functions, act in accordance with such advice.
• The Council of Ministers is collectively responsible to the Lok Sabha, the House of the People.
• Thus, it is clear that the real executive power under the Constitution of India rests with the Prime Minister and his council.

Additional Information

• In the states, the Governor, as the representative of the President, is the head of the Executive, but real executive power rests with the Chief Minister who heads the Council of Ministers.
• The Council of Ministers of a state is collectively responsible to the elected legislative assembly of the state.
• The Constitution governs the sharing of legislative power between Parliament and the State Legislatures and provides for the vesting of residual powers in Parliament.
• The power to amend the Constitution also vests in Parliament.
• The Union Executive consists of the President, the Vice-President and Council of Ministers with the Prime Minister at the head to aid and advise the President.

The correct answer is Sonu Nigam.

Key Points

• Singer, composer and actor Sonu Nigam is from India.
• He received the Padma Shri award from the Indian government in 2022 for his contributions to the arts.
• He is called the "Modern Rafi," a moniker inspired by his musical hero Muhammad Rafi.

Additional Information

• Kumar Sanu:
• The playback singer Kumar Sanu is from India.
• In Bollywood, he is referred to as the King of Melody.
• From 1990 to 1994, he set a record by winning the Best Male Playback Singer Filmfare Award five times in a row.
• In 2009, the Indian government honoured him with the Padma Shri.
• Udit Narayan:
• Indian playback singer Udit Narayan has primarily had songs featured in Hindi movies.
• The Indian government honoured him with the Padma Shri in 2009 and the Padma Bhushan in 2016.
• Abhijeet Bhattacharya:
• Bollywood playback singer Abhijeet Bhattacharya is well known.
• In more than 1000 films, Abhijeet has performed 6034 songs.
• The Uttar Pradesh Gaurav Samman was given to him.

The correct answer is Magnitude.

Key Points

• The measurement or absolute value of a quantity is its magnitude.
• A magnitude is represented by a positive real number.
• The magnitude of positive numbers is equal to their own magnitude.
• The magnitude of a negative number is its absolute value or the negative number without the minus sign.
• The magnitude of a complex number is its modulus.
• A scalar quantity's numerical measure in some unit is referred to as its magnitude.

Additional Information

• Reference:
• A relationship between objects known as a reference occurs when one object designates, provides a connection to, or links to, another object.
• Direction:
• ​The term "direction" is frequently used to describe the way something is travelling or pointing.
• Distance:
• ​Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.

The correct answer is 33 percent.

Key Points

• For all state government jobs and admission to higher education institutions, the Tripura government has decided to grant a 33% reservation to all women.
• All female applicants to Institutes of National Importance will receive 3% off of whatever loans they take out.
• Women will be given a 50% reservation to run businesses in government marketplaces or retail centers.
• 50% of the venture capital fund is set aside to support female-led enterprises.

Additional Information

• According to Amit Shah, farmer earnings have more than doubled, and the per capita income has increased to Rs 1.3 lakh.
• Rail has been used to connect Agartala with the rest of the nation.
• The length of the nation's highways is 542 km.
• The Union Home Minister claims that there has been a 30% drop in heinous crimes in Tripura and an improvement in the conviction rate from 5% to 53%.

The correct answer is Bombay.

Key Points

• In 1849, a covert socio-religious organization called the Paramhans Mandali was founded in Bombay.
• It shared a close relationship with Manav Dharma Sabha, which was established in Surat in 1844.
• Dadoba Pandurang, Durgaram Mehtaji, and several of his friends founded it
• It served as a covert organization, and it's thought that when its existence was made public in 1860, it quickly disintegrated.
• It was the first socioreligious institution in Maharashtra.
• This Mandli's founders held a monotheistic belief.
• They were mostly concerned with disobeying caste laws.
• The members consumed food prepared by members of lower castes during their sessions.
• Also, the Mandala advocated women's education and widow remarriage.

Additional Information

• Manav Dharma Sabha:
• One of the oldest organizations for socio-religious change in Gujarat and British India was the Manav Dharma Sabha.
• Durgaram Manchharam Mehta, Dadoba Pandurang Tarkhadkar, and a few others founded it on June 22, 1844 in Surat.
• Exposing the hypocritical practices seen in the Christian, Muslim, and Hindu religions was one of the Sabha's main objectives.
• As Dadoba and Durgaram departed for Bombay in 1846 and Rajkot in 1852, respectively, it ceased to exist.​

The correct answer is still in play.

Key Points

• If, for any reason, the ball strikes the frame of the goal or the referee and remains within the goal and touch lines, it is still in play. A goal is scored when the entire ball has crossed the goal line within the frame of the goal.
• A challenge or tackle that threatens an opponent's safety or makes use of excessive force or brutality must be penalized as serious foul play.
• Serious foul play is committed by any player who lunges at an opponent while vying for the ball from the front, the side, or the back, using one or both legs, with excessive force, or while putting the opponent's safety in peril.

Additional Information

• The ball is out of play when it has wholly passed over the goal line or touchline on the ground or in the air play has been stopped by the referee it touches a match official, remains on the field of play and a team starts a promising attack or the ball goes directly into the goal or the team in possession of the ball changes in all these cases, play is restarted with a dropped ball.
• Ball in play
• The ball is in play at all other times when it touches a match official and when it rebounds off a goalpost, crossbar or corner flagpost and remains on the field of play.
• Trophies related to Football:
• Euro Cup
• UEFA Champions League
• Santosh Trophy
• EFL Cup
• Durand Cup
• FIFA World Cup
• FA Cup

The correct answer is Dehradun.

Key Points

• The Indian Institute of Remote Sensing is a leading institution for research, advanced study, and training in
• remote sensing,
• geoinformatics, and
• GPS technology for managing natural resources,
• the environment, and
• natural disasters.
• It falls within the purview of the 1966-founded Indian Department of Space.
• It is situated in the Uttarakhand city of Dehradun.

Additional Information

• On February 27, the NASA Kenedy Space Center in Cape Canaveral will launch the Crew-6 mission.
• It is a cooperative effort between SpaceX and NASA.
• The SpaceX Falcon 9 rocket will transport the Crew Dragon spacecraft.
• It is being sent to the International Space Station in a capsule.
• Two American astronauts, a Russian cosmonaut, and an astronaut from the UAE will be launched on this mission.
• The mission's landing zone is in the Atlantic Ocean.
• It is a component of NASA's Commercial Crew Program.
• The program offers crew transportation services, which include moving astronauts and cargo to and from the ISS.

The correct answer is adopting a Western lifestyle.

Key Points

• Modernization is the adoption of cutting-edge technology in the production sector and a shift in social values.
• Modernization, therefore, involves two main components:
• Adoption of new technology:
• It boosts efficiency and productivity.
• For instance**, utilizing HYV (high-yielding variety) seeds** and new agricultural tools instead of outdated ones can boost agricultural production.
• Similar to this, an industry can boost production by installing additional machines in its manufacturing facility.
• Changes in social attitudes also have a significant impact.
• For instance, acceptance of contraceptive methods aids in reducing population increase.
• Equal rights and pay for men and women will also promote the best possible use of women's talent.

Additional Information

• An economic plan allots a country's resources to accomplish the broad and detailed objectives that the government has set for it over a given time period.
• These plans are called as "five-year plans" in India since they are developed for a period of five years.
• In 1950, the Planning Commission was established with Jawaharlal Nehru as its chairman.
• It identified the kind of plan best suited for accelerating economic growth.
• The Prime Minister of India serves as the Planning Commission's chair.
• Functions:
• Evaluation of the material, financial, and human
• creation of a strategy to maximize their effectiveness and balance
• distribution of resources and the setting of priorities.

The correct answer is Robert Hooke.

Key Points

• Englishman Robert Hooke was a polymath who worked as an architect, scientist, and natural philosopher.
• He is recognized with being one of two scientists to use a compound microscope he created himself to discover microbes in 1665.
• Hooke devoted a lot of time to unraveling the universe's secrets.
• The Big Red Spot of Jupiter was first noted by Hooke, who also confirmed the planet's rotation.
• The fifth star in the Trapezium, an asterism in the constellation Orion, was found by Hooke in 1664.
• Hooke's meticulous depictions of Mars from 1666 made it possible to determine the planet's rotational period more than 200 years later.

Additional Information

• George Willis Ritchey:
• American astronomer, telescope manufacturer, and optician George Willis Ritchey was born in Tuppers Plains, Ohio.
• Along with Henri Chrétien, he designed the Ritchey-Chrétien reflecting telescope.
• Giordano Bruno:
• Italian philosopher Giordano Bruno was also a mathematician, poet, cosmological thinker, and practitioner of the Hermetic esoteric.
• His cosmological theories, which conceptually included the then**-novel Copernican paradigm,** are well recognized.
• Johannes Kepler:
• German astronomer, mathematician, astrologer, natural philosopher, and composer Johannes Kepler also wrote about music.
• He played a significant role in the Scientific Revolution of the 17^th century and is best remembered for his laws of planetary motion.

The correct answer is (i) (d), (ii) (c), (iii) (b), (iv) (a).

Key Points

Additional Information

Kwashiorkor

• ​It is caused due to deficiency of protein unaccompanied by calorie deficiency.
• It is caused due to replacement of mother's milk with a low-protein high-calorie diet in children below one year of age.
• The affected individuals show retarded brain development, thinning of limbs, wasting of muscles, swelling of body parts, etc.

Weak bones and muscles

• The deficiency of Calcium and Phosphorus are the elements responsible for the weakening of bones.
• Calcium and Phosphorus help to build bones.
• The bone stores 99 per cent of the body's calcium and 85 per cent of the phosphorus.
• Dairy products, leafy vegetables and meat are good sources of these elements.

Anaemia:

• A nutritional deficiency of iron causes anaemia.
• Anaemia is a condition in which the number of red blood cells decreases in the blood.
• Anaemia decreases the ability of blood to transport oxygen to different organs of the body.
• Symptoms of Anaemia include shortness of breath, dizziness, and fatigue.
• For treatment, iron supplements can be used.
• For lower vitamin levels Vitamin B supplements can be used.

Goitre:

• Deficiency of proper Iodine in the diet causes Goitre.
• Swelling in the neck due to enlarged thyroid gland is a major symptom of Goitre.

Calculation:

Infinitely many circles can be drawn passing through two points.

∴ Infinitely many circles can be drawn passing through two points.

Shortcut Trick

For mean proportional x between a and b, x = √(a × b).

x = √(12.8 × 64.8) = √(1.28 × 6.48 × 100) / 10 is not needed, simply write:

x = √(128/10 × 648/10) = √(64 × 2 × 324 × 2) / 10 = (8 × 18 × 2) / 10 = 28.8

∴ The correct answer is 28.8.

Alternate Method

Given: First number (a) = 12.8, Second number (b) = 64.8

Formula Used: Mean Proportional (x) = √(a × b)

⇒ x² = 12.8 × 64.8

⇒ x² = (128/10) × (648/10)

⇒ x² = (64 × 2 × 324 × 2) / 100

⇒ x = √((64 × 324 × 4) / 100)

⇒ x = (8 × 18 × 2) / 10

⇒ x = 288 / 10 = 28.8

∴ The correct answer is 28.8.

Additional Information

Third Proportional

The third proportional of two numbers a and b is defined as the value c such that a : b :: b : c, which implies c = b²/a.

Fourth Proportional

The fourth proportional of three numbers a, b, and c is the value d such that a : b :: c : d, which implies d = (b × c) / a.

Invertendo and Alternendo

If a : b = c : d, then Invertendo gives b : a = d : c and Alternendo gives a : c = b : d.

Given:

cot A = 15/8

Concept used:

1. tan 2α = $\frac {2 \times tan α}{(1 - tan^2 α)}$
2. tan α = 1/cot α 

Calculation:

cot A = 15/8

⇒ tan A = 8/15

Now, tan 2 A

⇒ $\frac {2 \times tan A}{(1 - tan^2 A)}$

⇒ $\frac {2 \times \frac {8}{15}}{(1 - (\frac {8}{15})^2)}$

⇒ $\frac {\frac {16}{15}}{\frac {161}{225}}$

⇒ ${\frac {16 \times 225}{15 \times 161}}$

⇒ 240/161

∴ The value of tan 2A is 240/161.

Calculation:

Now, the required percentage = $\frac {500}{200} \times 100\%$ = 250%

∴ Number of persons participating in the survey from L is 250% of the number of persons participating in the survey from J.

Calculation:

Now, the difference between the temperature recorded on Monday and Tuesday together and the temperature recorded on Friday and Saturday together

⇒ (25 + 55) - (20 + 45)

⇒ 15°

∴ The difference between the temperature recorded on Monday and Tuesday together and the temperature recorded on Friday and Saturday together is 15°.

Given:

350 + 926 + 2718 + 928 + 929 

Calculation:

350 + 926 + 2718 + 928 + 929

⇒ 3⁵⁰ + 3⁵² + 3⁵⁴ + 3⁵⁶ + 3⁵⁸

⇒ 3⁵⁰(1 + 3² + 3⁴ + 3⁶ + 3⁸)

⇒ 350(1 + 9 + 81 + 729 + 6561)

⇒ 350 × 7381

⇒ 350 × (11² × 61)

Hence, the given number is divisible by 11.

∴ 350 + 926 + 2718 + 928 + 929 is divisible by 11.

Given:

A car with a price of ₹6,50,000 is bought by making some down payment. On the balance, a simple interest of 10% is charged in lump sum and the money is to be paid in 20 equal annual instalments of ₹25,000. 

Concept used:

Amount becomes in lump sum = P(1 + R%)

P = Principal

R = Rate of interest

Calculation:

Let the downpayment be of Rs. X.

​According to the question,

(650000 - X) × (1 + 10%) = 25000 × 20

⇒ (650000 - X) × (1 + 10%) = 500000

⇒ (650000 - X) = 500000 ÷ (1 + 10%)

⇒ (650000 - X) ≈ 454545.45

⇒ X ≈ 650000 - 454545

⇒ X ≈ 195455

∴ The downpayment was Rs. 195455.

Given:

A shopkeeper has 2220 kg of rice. A part of which he sells at a 20% profit and the rest at a 12% profit. He gains 18% on the whole. 

Calculation:

Using mixture and alligation,

So, the ratio of the quantity of rice that is sold at 20% profit to the quantity of rice that is sold at 12% = 3 : 1

Now, the quantity of rice that is sold at 12% profit = 2220 × 1/(3 + 1) = 555 kg

∴ The quantity sold at a 12% profit is 555 kg.

Concept used:

HCF of two or more numbers is the greatest factor that divides the numbers.

Calculation:

HCF of two or more numbers is the highest number that perfectly divides all the given numbers.

∴ Option 2 is the correct answer.

Calculation:

So,

J1 = ((30 + 12)/2)% × 12000 = 2520

J2 = ((20 + 15)/2)% × 12000 = 2100

Now, J1 - J2 = 2520 - 2100 = 420

∴ The value of (J1 – J2) is 420.

Shortcut Trick

Given a/b + b/a = 1, simplifying gives a² + b² = ab or a² − ab + b² = 0.

The sum of cubes identity is a³ + b³ = (a + b)(a² − ab + b²).

Substituting the derived value: a³ + b³ = (2) × (0) = 0.

∴ The correct answer is 0.

Alternate Method

Given: a/b + b/a = 1 and a + b = 2

Formula Used: a³ + b³ = (a + b)(a² − ab + b²)

⇒ a/b + b/a = 1

⇒ (a² + b²) / ab = 1

⇒ a² + b² = ab

⇒ a² − ab + b² = 0

⇒ a³ + b³ = (a + b)(a² − ab + b²)

⇒ a³ + b³ = 2 × 0

⇒ a³ + b³ = 0

∴ The correct answer is 0.

Additional Information

Sum of Cubes Identity

The formula for the sum of two cubes is a³ + b³ = (a + b)(a² − ab + b²).

Difference of Cubes Identity

The formula for the difference of two cubes is a³ − b³ = (a − b)(a² + ab + b²).

Cubic Expansion

The expansion of (a + b)³ is a³ + b³ + 3ab(a + b), which relates the sum of cubes to the cube of the sum.

Standard Algebraic Property

If a/b + b/a = −1, then a² + ab + b² = 0, which implies that a³ − b³ = 0, or a³ = b³.

Shortcut Trick

Discount % = [Free Items ÷ Total Items] × 100

Free coconuts = 3, Purchased coconuts = 12

Total coconuts = 12 + 3 = 15

Discount % = [3 ÷ 15] × 100 = 1/5 × 100 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Price per coconut = ₹25

Number of coconuts paid for = 12

Number of free coconuts = 3

Calculations:

⇒ Total Marked Price (MP) of 15 coconuts = 15 × 25 = ₹375

⇒ Selling Price (SP) of 15 coconuts = Price of 12 coconuts = 12 × 25 = ₹300

⇒ Total Discount = MP − SP = 375 − 300 = ₹75

⇒ Discount % = (Discount ÷ MP) × 100

⇒ Discount % = (75 ÷ 375) × 100 = 1/5 × 100 = 20%

∴ The correct answer is 20%.

Additional Information

Buy X Get Y Free Formula

Discount % = [Y ÷ (X + Y)] × 100, where Y is the number of free items and X is the number of paid items.

Successive Discount

If two successive discounts of a% and b% are given, total discount = [a + b − (ab/100)]%.

Marked Price and SP Relationship

SP = MP × [100 − Discount%]/100. Discount is always calculated on the Marked Price.

Given:

The population of country A decreased by p% and the population of country B decreased by q% from the year 2020 to 2021. Here 'p' is greater than ‘q’. Let 'x' be the ratio of the population of country A to the population of country B in the given year.

Calculation:

Let the initial population of Country A and B be J and K respectively.

Hence, x = J/K

Let the ratio of the population of country A to the population of country B for the next year be x₁.

​According to the question,

(J × (1 - p%)) : (K × (1 - q%)) = x₁

⇒ $\frac {J}{K} \times \frac {100 - p}{100 - q} = x_1$

Now, % decrease

⇒ $\frac {x - x_1}{x} \times 100\%$

⇒ $\frac {\frac {J}{K} - \frac {J}{K} \times \frac {100 - p}{100 - q}}{\frac {J}{K} } \times 100\%$

⇒ $\frac {(p - q)}{(100 - q)} \times 100\%$

⇒ $\frac{100(p - q)}{(100 - q)} \%$

∴ The percentage decrease in 'x' from 2020 to 2021 is $\frac{100(p - q)}{(100 - q)} \%$.

Shortcut Trick

Assume,

The population of A in 2020 be 200 and B in 2020 be 100,

and p = 20% & q = 10% (as per the question)

hence according to the question,

So now,

x = 2 and x' = 16/9

now as per the question,

⇒ ${{2} - {16\over 9}}\over 2$ × 100 ⇒ (100/9)

Now substituting the values in the given options,

Only 1 option satisfies the value.

Given:

A chord of length 40 cm is drawn in a circle having a diameter of 50 cm.

Length of another chord = 30 cm

Concept used:

1. The perpendicular from the centre of a circle to a chord bisects the chord. 2. Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. 3. Diameter = Radius × 2

Calculation:

Let C be the centre of the circle and AB and CD be the shorter and longer chord respectively.

Since the minimum distance is required, the chords must be on the same side of the centre of the circle.

AB = 30 and CD = 40

OF is the perpendicular distance between O and AB. 

Since AB and CD are parallel, OF is also perpendicular to CD at E.

Radius of the circle = 50/2 = 25 cm

OC = OD = OA = OB = 25 cm = Radii

​According to the concept,

AF = FB = 30/2 = 15 cm

CE = ED = 40/2 = 20 cm

ΔOEC is a right-angle triangle at E.

So, OE = $\sqrt {25^2 - 20^2}$ = 15 cm

Likewise, OF = $\sqrt {25^2 - 15^2}$ = 20 cm

Distance between AB and CD, EF = 20 - 15 = 5 cm

∴ The minimum distance is 5 cm.

Given:

4x2 + y2 = 40 and xy = 6

Concept used:

(a + b)² - 2ab = a² + b²

Calculation:

4x2 + y2 = 40

⇒ (2x + y)² - 4xy = 40

⇒ (2x + y)2 - 4 × 6 = 40

⇒ (2x + y)2 = 64

⇒ (2x + y) = 8

∴ The positive value of 2x + y is 8.

Given:

Piyush sold a guitar to Anuj at a 16% gain and Anuj sold it to Mayank at a 32% gain.

Mayank paid Rs.3,828 for the guitar.

Concept used:

1. Selling Price = Cost Price × (1 + Gain%) 2. Final percentage change after two successive increments of A% and B% = $(A + B + {AB \over 100})\%$

Calculation:

The net percentage profit from Piyush to Mayank

⇒ 16 + 32 + (16 × 32)/100 = 53.12%

Now, the cost price of the guitar to Piyush = 3828 ÷ (1 + 53.12%) = Rs. 2500

∴ Piyush paid Rs. 2500 for the guitar.

Given:

The external diameter of an iron pipe is 20 cm and its length is 12 cm. 

Its length is 12 cm and the thickness of the pipe is 1 cm.

Concept used:

1. Curved surface of a cylinder = 2πrh (where r = Radius of the base, h = height) 2. Total surface area of the pipe = Outside surface area + inside surface area + Top Base Area + bottom base area 3. Area of a circle = πR² (R = Radius)

Calculation:

External radius of the iron pipe, R = 20/2 = 10 cm

Internal radius of the iron pipe, r = 10 - 1 = 9 cm

Height, h = 12 cm

​According to the concept,

2πRh + 2πrh + π(R²−r²) + π(R²−r²)

⇒ 2πh(R + r) + 2π(R2−r2)

⇒ 2π {12 × (10 + 9) + (10² - 9²)} 

⇒ 1552.5714 ≈ 1,552.57 cm2

∴ The total surface area of the pipe is 1,552.57 cm2.

Given:

A group of men decided to do a job in 6 days, but 18 men dropped out every day.

The job was completed in 8 days.

Concept used:

Total work = Efficiency of each worker × Number of days to finish × Number of total workers

Calculation:

Let there be Q men initially with the efficiency of 1 unit per day.

Total work = Q × 1 × 6 = 6Q units

​According to the question,

Q + (Q - 18) + (Q - 18 × 2) + .... + (Q - 18 × 7) = 6Q

⇒ 8Q - (18 + 36 + .... + 126) = 6Q

⇒ 2Q = 504

⇒ Q = 252

∴ There were 252 men initially.

Given:

$\frac{cos37^\circ}{sin53^\circ}$

Concept used:

sin θ = cos (90° - θ)

Calculation: 

$\frac{cos37^\circ}{sin53^\circ}$

⇒ $\frac{cos(90 - 53)^\circ}{sin53^\circ}$

⇒ $\frac{sin 53^\circ}{sin53^\circ}$

⇒ 1

∴ The simplified value is 1.

Given:

Cos ( - $\frac{17\pi}{3}$ )

Concept used:

1. cos (- θ) = cos θ
2. cos is always positive in the fourth quadrant.
3. sin 30° = 1/2

Calculation:

Cos ( - $\frac{17\pi}{3}$ )

⇒ Cos $\frac{17\pi}{3}$

⇒ Cos $\frac{17\times 180^\circ}{3}$

⇒ Cos ${17\times 60^\circ}$

⇒ Cos 1020°

⇒ Cos $({90^\circ \times 11 + 30^\circ})$

⇒ Sin 30°

⇒ $\frac{1}{2}$

∴ The value of Cos ( - $\frac{17\pi}{3}$ ) is $\frac{1}{2}$.

Shortcut Trick

Relative Speed in same direction = 24 − 10 = 14 km/h.

Convert Relative Speed to m/s: 14 × (5/18) = 35/9 m/s.

Time Taken = Initial Distance ÷ Relative Speed = 280 ÷ (35/9) = 72 seconds.

Convert seconds to minutes: 72 ÷ 60 = 1.2 min.

∴ The correct answer is 1.2 min.

Alternate Method

Given:

Initial distance = 280 m

Speed of Cat (S_c) = 10 km/h

Speed of Dog (S_d) = 24 km/h

Formula Used:

Time = Distance ÷ Relative Speed

Calculations:

⇒ Relative Speed = S_d − S_c = 24 − 10 = 14 km/h

⇒ Relative Speed in m/min = 14 × (1000 ÷ 60) = 1400/6 m/min

⇒ Time = Distance ÷ Relative Speed = 280 ÷ (1400/6)

⇒ Time = (280 × 6) ÷ 1400

⇒ Time = 1680 ÷ 1400 = 1.2 min

∴ The correct answer is 1.2 min.

Additional Information

Relative Speed Concept

When two objects move in the same direction, relative speed is the difference (u − v). In opposite directions, it is the sum (u + v).

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert km/h to m/min, multiply by 1000/60 (or 50/3).

Catching Problems

The time required for a faster object to catch a slower one is always Initial Gap ÷ Relative Speed.

Given:

A tangent is drawn from point M to a circle, which meets the circle at T such that MT = 12 cm.

A secant MAB intersects the circle at points A and B.

MA = 8 cm

Concept used:

If SUV and SW are a secant and a tangent respectively drawn from an external point S on a circle whose center is at C, then SU × SV = SW2

Calculation:

​According to the concept,

MA × MB = MT2

⇒ 8 × MB = 122

⇒ MB = 144/8

⇒ MB = 18

⇒ MA + AB = 18

⇒ 8 + AB = 18

⇒ AB = 18 - 8

⇒ AB = 10

∴ The measure of AB is 10 cm.

Given:

p = 7 + 4$\sqrt{3}$

Concept used:

1. a² - b² = (a + b)(a - b)
2. a³ + b³ = (a + b)³ - 3ab(a + b)

Calculation:

p = 7 + 4$\sqrt{3}$

⇒ 1/p = 1/(7 + 4$\sqrt{3}$)

⇒ $\frac {1}{p} = \frac {(7 - 4\sqrt3)}{(7 - 4\sqrt3)(7 + 4\sqrt3)}$

⇒ $\frac {1}{p} = \frac {(7 - 4\sqrt3)}{49 - 48}$

⇒ $\frac {1}{p} = \frac {(7 - 4\sqrt3)}{1}$

⇒ $\frac {1}{p} = {(7 - 4\sqrt3)}$

So, p + 1/p

⇒ 7 + 4$\sqrt{3}$ + 7 - 4$\sqrt{3}$

⇒ 14

Now, $\frac{p^6 + p^4 + p^2 + 1 }{p^3}$

⇒ $(p^3 + \frac {1}{p^3}) + (p + \frac {1}{p})$

⇒ $(p + \frac {1}{p})^3 - 3(p + \frac {1}{p}) + (p + \frac {1}{p})$

⇒ 14³ - 2 × 14

⇒ 2716

∴ The value of $\frac{p^6 + p^4 + p^2 + 1 }{p^3}$ is 2716.

Given:

The height of an equilateral triangle is 7$\sqrt{3}$ cm. 

Concept used:

Height of an equilateral triangle = $\frac {\sqrt3}{2} \times Side$

Area of an equilateral triangle = $\frac {\sqrt3}{4} \times Side^2$

Calculation:

Each side of the triangle = ${7\sqrt3} \div \frac {\sqrt3}{2}$ = 14 cm

Area of the triangle = $\frac {\sqrt3}{4} \times 14^2$ = 49 $\sqrt{3}$ cm2

∴ The area of this equilateral triangle is 49 $\sqrt{3}$ cm2.