SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 2) (Previous Year Paper)

The logic followed here is:

Logic: First Number = (Second Number)² × (Second Number ÷ 3)

Let's check as per the logic,

243 : 9

→ 243 = (9)² × (9 ÷ 3)

→ 243 = 81 × 3

→ 243 = 243

→ LHS = RHS

72 : 6

→ 72 = (6)2 × (6 ÷ 3)

→ 72 = 36 × 2

→ 72 = 72

→ LHS = RHS

Similarly,

576 : ?

→ 576 = (?)2 × (? ÷ 3)

→ 576 × 3 = (?)³

→ 1728 = (?)³

→ ? = 12

Hence, the correct answer is "12".

The logic followed here is :-

By using BODMAS RULE :

Given equation: 14 + 16 - 14 × 9 ÷ 4 = 61

1) 16 and 14, + and ×.

After interchanging ‘6 and 14’, and '+' and '×', we get:

L.H.S = 16 × 14 - 16 + 9 ÷ 4 

= 224 - 16 + 2.25

= 210.25 ≠ R.H.S

So, this option does not provide a correct equation.

2) 16 and 9, + and -

After interchanging '16 and 9', and '+' and '-', we get:

L.H.S = 14 - 9 + 14 × 16 ÷ 4

= 5 + 56

= 61 = R.H.S

Thus, this option provides a correct equation.

3) 14 and 4, - and +

After interchanging '14 and 4', and '-' and '+', we get:

L.H.S = 4 - 16 + 4 × 9 ÷ 14 

= 4 - 16 + 2.5

= - 9.5 ≠ R.H.S

Thus, this option does not provide a correct equation.

4) 14 and 9, + and ×

After interchanging '14 and 9', and '+' and '×', we get:

L.H.S = 9 × 16 - 9 + 14 ÷ 4

= 144 - 9 + 3.5

= 138.5 ≠ R.H.S

Thus, this option does not provide a correct equation.

Hence, 16 and 9, + and - is the correct answer.

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

Conclusions:

I. Some cooks are priests → True (As Some cooks are poets and All poets are priests so, Some cooks are priests is true)

Il. Some priests are cooks → True (As Some cooks are poets and All poets are priests so, Some priests are cooks is true)

III. All doctors are priests → False (As Some priests are doctors so, All doctors are priests is false)

IV. Some doctors are priests → True (As Some priests are doctors so, Some doctors are priests is true)

∴ Here, conclusions I, II and IV are true.

Hence, the correct answer is "Only conclusions I, Il and IV follow".

The arrangement of the given words in the order in which they appear in an English dictionary is as shown below :

6. Cheaper 
7. Cheering
8. Cheese
9. Cheetah
10. Chemical
11. Chestnut

Hence, the correct answer is "6, 3, 4, 1, 2, 5".

The logic followed here is :-

First number ÷ 2 = Second number

• 284 : 142 → 284 ÷ 2 = 142

and

• 568 : 284 → 568 ÷ 2 = 284

Similarly,

• 1136 : ? → 1136 ÷ 2 = 568

Hence, the correct answer is "568".

The logic followed here is :-

By using BODMAS RULE :

Option 1) : ÷ and -

Given equation is  : 2 × 236 - 2 + 36 ÷ 72 = 200

After interchanging the two signs the equation is as follows : 2 × 236 ÷ 2 + 36 - 72 = 200

⇒ 2 × 236 ÷ 2 + 36 - 72 = 200

⇒ 2 × 118 + 36 - 72 = 200

⇒ 236 + 36 - 72 = 200

⇒ 272 - 72 = 200

⇒ 200 = 200

LHS = RHS

Option 2) : - and +

Given equation is  : 2 × 236 - 2 + 36 ÷ 72 = 200

After interchanging the two signs the equation is as follows : 2 × 236 + 2 - 36 ÷ 72 = 200

⇒ 2 × 236 + 2 - 36 ÷ 72 = 200

⇒ 2 × 236 + 2 - 0.5 = 200

⇒ 472 + 2 - 0.5 = 200

⇒ 474 - 0.5 = 200

⇒ 473.5 ≠ 200

LHS ≠ RHS

Option 3) : × and +

Given equation is  : 2 × 236 - 2 + 36 ÷ 72 = 200

After interchanging the two signs the equation is as follows : 2 + 236 - 2 × 36 ÷ 72 = 200

⇒ 2 + 236 - 2 × 36 ÷ 72 = 200

⇒ 2 + 236 - 2 × 0.5 = 200

⇒ 2 + 236 - 1 = 200

⇒ 238 - 1 = 200

⇒ 237 ≠ 200

LHS ≠ RHS

Option 4) : + and ÷ 

Given equation is  : 2 × 236 - 2 + 36 ÷ 72 = 200

After interchanging the two signs the equation is as follows : 2 × 236 - 2 ÷ 36 + 72 = 200

⇒ 2 × 236 - 2 ÷ 36 + 72 = 200

⇒ 2 × 236 - 0.055 + 72 = 200

⇒ 472 - 0.055 + 72 = 200

⇒ 544 - 0.055 = 200

⇒ 543.945 ≠ 200

LHS ≠ RHS

Hence, the correct answer is "÷ and -".

In first and second dice V and X are common in both dices.

First dice is rotated 900 clockwise vertically on the other adjacent side of V and X is 'Y'.

∴ Here, the opposite face of 'W' is 'Y'.

Hence, the correct answer is "Y".

The logic followed here is :-

Auger is a instrument used for boring holes.

Similarly,

Needle is a instrument used for Sewing.

Hence, the correct answer is "Needle : Sew ".

The logic followed here is :-

• ADOPT : DAOTP

and

• FINAL : IFNLA

Similarly,

• HUMOR : ?

Hence, the correct answer is "UHMRO".

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

Conclusions:

I. Some sweets are cookies → True (As Some sweets are chocolates and All chocolates are cookies so, Some sweets are cookies is true)

Il. Some cookies are chocolates → True (As All chocolates are cookies so, Some cookies are chocolates is true)

III. Some chocolates are sweets → True (As Some sweets are chocolates so, Some chocolates are sweets is true)

∴ Here, Conclusions I, II and III are true.

Hence, the correct answer is "All conclusions follow".

The logic followed here is :-

• CROWN : OYRVH

and

• TABLE : FNEEY

Similarly,

• UNREAL : ?

Hence, the correct answer is "MCHVSA".

After unfolding the given paper the figure formed is as shown below :

Hence, the correct answer is "Option 1".

Given :- R E U_T R_ _Q T R E W _ _R E _ _T 

By checking options and substituting accordingly.

1) Q E V Q T X Q → R E U Q T - R E V Q T - R E W Q T - R E X Q T

• Here, '

' is repeated.

2) Q F W Q T X Q → R E U Q T - R F W Q T - R E W Q T - R E X Q T

3) Q E W Q T Y R → R E U Q T - R E W Q T R E W Q T R E Y R T

4) Q F V Q T X R → R E U Q T R F V Q T R E W Q T R E X R T

• Option (1) gives the pattern of :- R E U Q T - R E V Q T - R E W Q T - R E X Q T

Hence, the correct answer is "Q E V Q T X Q".

The logic followed here is :-

(First number × 3) + 7

• 15 : 52 →(15 × 3) + 7 = 45 + 7 = 52

and

• 22 : 73 → (22 × 3) + 7 = 66 + 7 = 73

Similarly,

• 33 : ____ → (33 × 3) + 7 = 99 + 7 = 106

Hence, the correct answer is "106".

Preparing the family tree using the following symbol:

Family Tree :-

∴ Here, 'Gaurav' is brother of 'Suraj'.

Hence, the correct is "Brother".

The logic followed here is :-

Sum of alphabetical positional value of given word.

'MARS” is coded as “51”.

= 13 + 1 + 18 + 19

= 51

and

"STARS" is coded as “77”.

= 19 + 20 + 1 + 18 + 19

= 77

Similarly,

'MOON' will be coded as:

= 13 + 15 + 15 + 14

= 57

Hence, the correct answer is "57".

The logic followed here is,

Logic: Both symbols on the left side interchanges their position in the subsequent images of the series.

Symbol in the middle goes to the left side and remains there for two subsequent images of the series and then gets eliminated. A new symbol enters the image from the right side.

During this the middle symbol and the right-side symbol interchanges their position in the subsequent two images.

As per the logic in figure 4 & 5,

Hence, the correct answer is "Option 1".

The logic followed here is :-

(First number × Third number) + 1 = Second number

• (4, 25, 6) → (4 × 6) + 1 = 24 + 1 = 25

and

• (3, 28, 9) → (3 × 9) + 1 = 27 + 1 = 28

Similarly,

• (2, 17, 8) → (2 × 8) + 1 = 16 + 1 = 17

Hence, the correct answer is "(2, 17, 8)".

The logic followed here is :-

(First number × Second number) - (First number ÷ Second number) = Third number

• (100, 2, 150) → (100 × 2) - (100 ÷ 2) = 200 - 50 = 150

and

• (50, 5, 240) → (50 × 5) - (50 ÷ 5) = 250 - 10 = 240

Similarly,

• (16, 8, 126) → (16 × 8) - (16 ÷ 8) = 128 - 2 = 126

Hence, the correct answer is "(16, 8, 126)".

The figure from among the given options that can replace the question mark (?) in the following series is as shown below :

• In figure1, circle is dotted and inside of star area in not marked.
• In figure2, circle is undotted and inside area of star is marked and this process in repeated from figure to figure.

Hence, the correct answer is "Option 4".

The logic followed here is :-

Hence, the correct answer is "1440".

Preparing the family tree using the following symbols:

According to the given information,

The given expression is :  

'L + M + N - O ÷ P × Q' → L is sister of M, M is sister of N, N is wife of O, O is father of P, P is brother of Q.

1) O is the father of Q → True (As O is father of P, P is brother of Q so, O is the father of Q is true)

2) L is the daughter of N → False (As  is sister of M, M is sister of N so, L is the daughter of N is false)

3) P is the son of N → True (As N is wife of O, O is father of P so, P is the son of N is true)

4) M is the sister of the wife of O → True (As M is sister of N, N is wife of O so, M is the sister of the wife of O is true)

∴ Here, 'L is the daughter of N' is not correct statement.

Hence, the correct answer is "L is the daughter of N".

The correct mirror image from the following options, when the mirror is placed on the right side of the given figure :

Hence, the correct answer is "Option 3".

The correct mirror image of the given figure when the mirror is placed at MN as shown below :

Detailed Explanation:

• The line MN is the mirror.
• The word 'tyj829' ends with last second number as '2'. So, the mirror image should be '

' ⇒ Option 2 and 3 are eliminated.

• The word 'tyj829' starts with second letter as 'y'. So, the mirror image will be '

' ⇒ Option 1 is eliminated.

Hence, the correct answer is "Option 4".

The logic followed here is :-

Number of alphabets of given word³ 

‘DEN’ is coded as 27.

Number of letters in word DEN = 3

= 3³ 

= 27

and

‘SNAKE’ is coded as 125.

Number of letters in word SNAKE = 5

= 5³ 

= 125

Similarly,

‘CAVE’ will be coded as :

Number of letters in word CAVE = 4

= 4³ 

= 64

Hence, the correct answer is "64".

The correct answer is 18 to 50 years.

Key Points

• Pradhan Mantri Jeevan Jyoti Bima Yojana:-
• It is a great initiative taken by the Indian government, especially for the underprivileged and poor citizens.
• It provides financial and social security for the family and gives them comfort and assurance on the death of a family member.
• The Pradhan Mantri Jeevan Jyoti Bima Yojana (PMJJBY) is a one-year life insurance scheme, renewable from year to year.
• PMJJBY offers coverage for death due to any reason and is available to people in the age group of 18 to 50 years.
• Under the PMJJBY scheme, a life cover of Rs. 2 lakhs is available for a one-year period stretching from 1st June to 31st May at a premium of Rs.436/- per annum per member.

The correct answer is Hindustani Classical Music. 

Key Points

• Bhimsen Joshi:-
• He is renowned for khayal form of singing along with the devotional singing of bhajans and abhangs.
• He was born in Gadag district of Karnataka. He received his training in singing and harmonium from Shamacharya Joshi.
• ​Pandit Jasraj:-
• He was an Indian classical vocalist, belonging to the Mewati Gharana.
• Zakir Hussain Allarka Qureshi:-
• He was born on March 9, 1951, in Bombay, India.
• He is the son of the famous Indian tabla player Ustad Allah Rakha Khan.
• Ustad Zakir Hussain is an Indian tabla player.
• All of these are associated with Hindustani Classical Music.

Additional Information

• Jazz:-
• It is a genre of music that originated in the African-American communities of New Orleans, United States, in the late 19th and early 20th centuries.
• It developed from roots in blues and ragtime. Jazz is seen by many as "America's classical music".
• Pop music:-
• It is a genre that originated in its modern form during the mid-1950s in the United States and the United Kingdom.
• The terms "popular music" and "pop music" are often used interchangeably, although the former describes all music that is popular and includes many disparate styles.
• Carnatic music:-
• It is one of two main sub-genres of Indian classical music that evolved from ancient Hindu traditions.
• Primarily from the southern region of India, it is distinguished from Hindustani music (the classical music of the north) by its emphasis on vocal music, with instruments utilized more as an accompaniment.

the correct answer is Bengal.

Key Points

• Lord Curzon:-
• Lord Curzon served as the Viceroy of India from 1899 to 1905 under Queen Victoria.
• He was born on January 11, 1859, in Kedleston, Derbyshire, England.
• Curzon was a British Conservative statesman who later served as the Foreign Secretary from 1919 to 1924.
• He declared the partition of Bengal in 1905.
• The partition, was implemented for administrative reasons according to the British.
• It was a controversial action that led to widespread protests as it was seen by Indians as an attempt to "divide and rule," given that it separated the largely Muslim eastern areas from the Hindu western areas.

The correct answer is Monthly Per Capita Expenditure.

Key Points 

• Monthly Per Capita Expenditure:-
• It is used in economics and personal finance to describe the average monthly spending of each person in a defined population, such as a household, city, province, or country.
• This is calculated by taking the total monthly expenditure of the population and dividing it by the total number of people in that population.
• Formula:- Monthly Per Capita Expenditure = Total monthly expenditure / Total population.
• It can be referred to in the estimation of poverty.

Additional Information

• Marginal utility:-
• It refers to the additional satisfaction or benefit (utility) that a consumer derives from consuming an additional unit of a good or service.
• The principle of diminishing marginal utility suggests that as a person consumes more and more of a good, the incremental benefit experienced from consuming another unit declines.
• Minimum Support Price:-
• It is generally used in the context of agricultural policies.
• MSP is a form of market intervention by the government to insure agricultural producers against any sharp fall in farm prices.
• The minimum support prices are announced by the government at the beginning of the sowing season for certain crops.

The correct answer is Chhau dance. 

Key Points

• Chhau dance:-
• It is a form of tribal martial dance popular in the Indian states of Odisha, Jharkhand, and West Bengal.
• There are three subtypes of this dance, i.e., Seraikella Chhau, Mayurbhanj Chhau, and Purulia Chhau, named after the regions where they originated.
• This folk dance is unique and celebratory in spirit, often performed at festivals and religious events.
• It is famous for its masks, costumes, and high energy choreography, and it incorporates martial arts, acrobatics, and athletics.
• Guru Shashadhar Acharya:-
• He is a renowned Indian artist, primarily recognized for his contributions to Seraikella Chhau, a type of masked dance originating from the Seraikella region of Jharkhand.
• He has played a significant role in promoting and preserving the Seraikella Chhau tradition, teaching this art form to the next generations, ensuring its continuity and widespread recognition.
• He was awarded the Padma Shri in 2020 for his contribution to Chhau dance.

Additional Information

• Odissi Chaiti Ghoda dance:-
• Chaiti Ghoda, or Chhau Ghoda, is a folk dance form from the eastern state of Odisha, India — specifically, the region of Kendrapara.
• It is a part of the traditional month-long worship of the goddess Durga during the month of Chaitra (March-April), which gives the dance its name.
• Kathak:-
• It is one of the eight forms of Indian classical dance, originating from northern India.
• Its name is derived from the Sanskrit word "katha" meaning story, and "katthaka" meaning the one who tells a story.
• Kathak focuses on rhythmic foot movements, adorned with small bells (Ghungroo), and the movement harmonizes with the music.
• This dance form includes pirouettes executed at lightning speed, complemented by subtle facial expressions.

The correct answer is Chaitra-Vaisakha.

Key Points

• Indian Calendar:-
• It is also known as the "Saka calendar" or "Saka Samvat," which serves official and legislative purposes and is used alongside the Gregorian calendar.
• This calendar was introduced by the Calendar Committee in 1957, chaired by Meghnad Saha.
• The Saka calendar begins with the vernal (Spring) equinox of 78 Common Era (CE), designates its era as Saka Era, and counts years in that era.
• Chaitra is the first month of the year, and Phalguna is the last, aligning with the solar agricultural cycles.
• Vasanta Season falls in Chaitra-Vaisakha.

Additional Information

• The months of the Indian National Calendar (Saka Samvat) are as follows:
• Chaitra (March 22 to April 21)
• Vaishakha (April 21 to May 22)
• Jyaistha (May 22 to June 22)
• Ashadha (June 22 to July 23)
• Shravana (July 23 to August 23)
• Bhadra (August 23 to September 23)
• Ashwin (September 23 to October 23)
• Kartika (October 23 to November 22)
• Agrahayana (November 22 to December 22)
• Pausha (December 22 to January 21)
• Magha (January 21 to February 20)
• Phalguna (February 20 to March 21)

The correct answer is Romania.

Key Points

• Romania:-
• It is a southeastern European country known for its preserved medieval towns, rich history, stunning landscapes, and vast cultural heritage.
• It's bordered by Bulgaria, Hungary, Serbia, Ukraine, Moldova, and the Black Sea.
• Romania was one of the first countries to use iron for the manufacture of weapons In as early as 1700 BCE.

Additional Information

• Morocco:-
• It is a North African country with a rich history and culture.
• The Moroccan Sahara was a key site for dinosaur fossils, including a species named Spinosaurus aegyptiacus, one of the largest carnivorous dinosaurs ever discovered.
• India:-
• India is one of the world's most culturally diverse countries, located in South Asia.
• It's known for its significant contributions to art, science, religion, and culture over centuries.
• India shares its borders with several countries, including Pakistan, China, Nepal, Bhutan, Bangladesh, and Myanmar.
• Bulgaria:-
• Bulgaria is a country in southeastern Europe, known for its rich history, diverse landscapes, and cultural traditions.
• The country is bordered by Romania to the north, Serbia and North Macedonia to the west, Greece and Turkey to the south, and the Black Sea to the east.

The correct answer is Calotropis.

Key Points

• Calotropis:-
• It is a genus of flowering plants in the family Apocynaceae.
• It was first described as a genus in 1810.
• It is native to southern Asia and North Africa.
• They are commonly known as milkweeds because of the latex they produce.
• They are large shrubs growing to 4 m (13 ft) tall.
• It is considered a noxious weed that has a chemical defence mechanism to protect it from predators

Additional Information

• Chicory:-
• It is scientifically known as Cichorium intybus.
• It is a somewhat woody, perennial herbaceous plant that usually has bright blue flowers.
• It originates from Europe and is now also found in North America and Australia.
• It's often seen growing along roadsides and in open fields.
• The plant is known for its long taproot, which is often ground into a powder and used as a coffee substitute or coffee additive.
• Black henbane:-
• It is scientifically known as Hyoscyamus niger, is a plant that originates from Eurasia.
• It's part of the nightshade family, which includes both poisonous and nonpoisonous plants such as tomatoes, potatoes, and belladonna.
• It's a biennial or short-lived perennial plant, with a strong, unpleasant odor.
• Field bindweed:-
• It is scientifically named Convolvulus arvensis, is a plant from the morning glory family.
• It is mostly perennial and native to Europe and Asia but has become widely distributed worldwide.
• It's known for being robust and difficult to control, characteristics that have made it quite problematic in agricultural settings where it is considered a significant weed.

The correct answer is HC Brown.

Key Points

• HC Brown:-
• Herbert C. Brown was a noted British-born American chemist.
• He is best known for his work with organoboranes, a class of chemical compounds that contain a direct bond between carbon and boron.
• Brown earned a B.S. degree in 1936 from Wright Junior College and then pursued his Ph.D. in Chemistry from the University of Chicago, which he received in 1938.
• He discovered that diborane reacts with aldehydes and ketones to produce dialkoxyboranes.

Additional Information

• Hugo Rudolph Kruyt :-
• He was a Dutch chemist who significantly contributed to the field of colloid chemistry.
• Kruyt is known for his pioneering work in surface chemistry and is considered a founder of colloid science in the Netherlands.
• Arthur Stoll:-
• He was a Swiss scientist and chemist
• He is known for his significant contributions to the field of biochemistry, especially with regard to alkaloids.
• Arne Tiselius:-
• He was a notable Swedish biochemist who was awarded the Nobel Prize for Chemistry in 1948 for his groundbreaking research on electrophoresis and adsorption analysis.
• His pioneering techniques laid the foundation for later work on separation and purification methods for complex substances, especially proteins, in the biochemistry field.

The correct answer is shooting.

Key Points

• Shooting:-
• Shooting sports are a category of competitive and recreational activities involving proficiency tests of accuracy, precision, and speed in using various types of firearms, as well as archery.
• Singhraj Adhana:-
• He won silver medals at the Mixed Team 50m Pistol SH1 event in the ongoing Chateauroux Para-Shooting World Cup on 9 June 2022 in France.

Additional Information

• Badminton:-
• It is a racquet sport played by either two opposing players (singles) or two opposing pairs (doubles), who take positions on opposite halves of a rectangular court divided by a net.
• Players score points by striking a shuttlecock with their racquet so that it lands within the marked boundaries of the opponents' court.
• High jump:-
• It is a track and field event in which competitors must jump as high as they can over a horizontal bar set at measured heights without the aid of certain devices.
• It's been part of the modern Olympic Games since its inception in 1896, and it's also included in the World Athletics Championships and other international competitions.
• Discus throw:-
• It is a track and field event in which an athlete throws a heavy disc—called a discus—in an attempt to mark a farther distance than their competitors.
• It is one of the oldest recorded events in athletics history, having been a part of the ancient Greek pentathlon, and it has been a sport in the modern Summer Olympic Games since the first Olympiad in 1896.

The correct answer is Vijayanagar 

Key Points

• Vijayanagar Dynasty:-
• The Vijayanagara Empire was a South Indian dynasty based in the Deccan Plateau region.
• Established in 1336 by Harihara I and his brother Bukka Raya I of the Sangama Dynasty, the empire lasted until 1646, although its power declined after a major military defeat in 1565 by the Deccan sultanates.
• The empire is named after its capital city of Vijayanagara, whose remains surround present-day Hampi, now a World Heritage Site in Karnataka, India.
• The Vijayanagara Empire was divided into various eras based on the ruling dynasty: Sangama Dynasty (1336–1485), Saluva Dynasty (1485–1505), Tuluva Dynasty (1505–1570), and the Aravidu Dynasty (1570–1646).
• The origin of ‘Carnatic music’ is related to this Dynasty.

Additional Information

• Bahmani Sultanate:-
• It is also called the Bahmanid Empire.
• It was a Muslim state in Deccan, India that lasted from 1347 to 1527.
• The Sultanate was founded by Alauddin Bahman Shah, a rebel officer who revolted against the Delhi Sultanate ruled by Sultan Muhammad bin Tughluq.
• After gaining independence, Alauddin took the title of 'Bahman Shah', which led to the dynasty being named "Bahmani".
• Chola Dynasty:-
• It was a Tamil dynasty that ruled primarily in southern India until the 13th century.
• It was one of the longest-ruling dynasties in the world's history.
• The earliest datable references to the Chola are in inscriptions from the 3rd century BCE, left by Ashoka, of the Maurya Empire, and the dynasty continued to rule over varying territory until the 13th century CE.
• Pandya Dynasty:-
• It was also referred to as the Pandyas, an ancient Tamil dynasty that ruled extensive territories, at times including the large regions of South India, from their home base in Madurai.
• Historical records of the Pandyas trace back to the 3rd century BCE and they have been prominently referenced in the ancient Sangam Literature of the Tamil people.

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 to 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.​

Additional Information

• Atmiya Sabha:-
• It tried to initiate social and religious reforms in society.
• The association was a philosophical discussion circle in India.
• They used to conduct debate and discussion sessions on philosophical topics and also used to promote free and collective thinking and social reform.
• The foundation of Atmiya Sabha in 1815 is considered the beginning of the modern age in Kolkata.
• Theosophical Society:-
• It was founded by Madam HP Blavatsky and Col HS Olcott in New York in 1875.
• In 1882, its headquarters were shifted to  Adyar (Tamil Nadu).
• Theosophical Society of India was  founded by Annie Beasant.
• The Theosophical Society sought inspiration from Indian thought and culture.
• It advocated the  revival and strengthening of ancient  religion of Hinduism, Zoroastrianism and  Buddhism.
• Brahmo Samaj:-
• It was formed in 1828
• It prohibited all forms of idolatry and sacrifice, believed in the Upanishads, and forbade its members from criticising other religious practices.
• It critically drew upon the ideals of religions – especially of Hinduism and Christianity – looking at their negative and positive dimensions.
• Brahmo ;Samaj discarded faith in divine Avatars.

The correct answer is Shooting

Key Points

• Omprakash Mitharwal:-
• He is of village Sihori Dhani Nimdi in Sikar district of Rajasthan.
• He is the recipients of the Arjuna Award for shooting.
• ​Arjuna Awards:-
• It is India's highest sporting award bestowed by the Government of India (Ministry of youth affairs and sports) to sportspersons for their outstanding performance in international as well as national events and also holds leadership qualities with good morals.
• The award was launched in 1961.
• The award consists of a cash prize of Rs 15 lakh, a bronze statue of Arjuna, and a scroll and is presented by the President of India.
• The honour is named on Prince Arjuna, the protagonist of the Indian epic Mahabharata.
• The sportsperson should have performed consistently well for the previous 3 years at the international level with excellence for that year for which the award is recommended.
• He must have shown qualities of leadership sportsmanship and a sense of discipline.

The correct answer is 2022.

Key Points

• 73rd Republic Day:-
• The 73rd Republic Day of India would be celebrated on January 26th, 2022.
• The Republic Day of India is a national holiday celebrated each year to honor the day the Constitution of India came into effect, on January 26th, 1950, officially marking India as a republic.
• This was a significant moment, as it marked the transition of India from a British colony to an independent republic with a democratic government system.
• On this day, a grand parade is conducted in the national capital, New Delhi, at the Rajpath, in front of the President of India.
• The Republic Day Parade is a significant event and showcases India's cultural diversity and military might

The correct answer is Manipur. 

Key Points

• National Sports University:-
• It is India's first institute dedicated to the study of sports science, sports management, sports coaching, and other related fields.
• The university is located in Manipur, a northeastern state of India.
• National Sports University was established by the Ministry of Youth Affairs and Sports, Government of India in 2018.
• Its objective is to promote sports education in the country and provide specialized knowledge and skills in order to train coaches, sports scientists, and sports managers.
• It offers various programs:-
• Sports Sciences: This area of study relates to the scientific principles and techniques that can be applied to improve athletic performance.
• Sports Coaching: This relates to the strategic, leadership, communication, and motivational skills needed to effectively coach sports teams or individual athletes.
• Sports Management: This area of study covers the management of sports teams, sports events, sports marketing, and sports facilities, etc.
• Physical Education: This is the study of physical activity and its impact on health, physical competence, and overall wellbeing.

Additional Information

• Other Important Institutions of India:- 
• University of Delhi (DU): Often regarded as one of India's top universities, it offers undergraduate, postgraduate, and doctoral programs in a broad array of disciplines.
• Jawaharlal Nehru University (JNU): Located in Delhi, JNU offers programs in a variety of disciplines, focusing on postgraduate and doctoral level study.
• Banaras Hindu University (BHU): Based in Varanasi, this university offers a range of undergraduate, postgraduate, and doctoral programs.
• Visva-Bharati University: This is a Central University and an 'Institution of National Importance' located in Santiniketan, West Bengal.
• Aligarh Muslim University (AMU): Located in Aligarh, this university is notable for its diverse range of disciplines in undergraduate, postgraduate, and doctoral programs.
• Jamia Millia Islamia: Located in New Delhi, this university offers undergraduate, postgraduate, and doctoral degrees in a wide range of disciplines.
• Rajiv Gandhi National University of Law (RGNUL): One of India's top National Law Universities, located in Patiala, Punjab.

The correct answer is Crust (outermost) - mantle - core (innermost)

Key Points

• The Earth can be divided into several layers from the outermost to the innermost based on their compositional and physical properties.
• The correct sequence is Crust (outermost) - mantle - core (innermost).
• Crust:
• This is the Earth's outermost layer, and it's where we live.
• It's the thinnest layer, varying from about 5 kilometers in thickness in the oceanic crust to about 30-70 kilometers in the continental crust. The crust is largely composed of lighter rocks, such as granite and basalt.
• Mantle:
• Beneath the crust, the mantle extends up to 2900 kilometers into Earth.
• It is composed primarily of silicate rocks that are richer in iron and magnesium than the crust.
• The mantle can be divided further into the upper and lower mantle. The asthenosphere, a part of the upper mantle, behaves plastically due to the intense heat and pressure.
• Outer Core:
• The outer core, lying beneath the mantle, is mostly composed of liquid iron and nickel.
• This liquid layer is about 2200 kilometers thick and creates Earth's magnetic field due to its liquid state and its circulation movement.
• Inner Core:
• The innermost layer, the inner core, is a solid ball consisting primarily of iron and nickel.
• Despite the extremely high temperature, the enormous pressure at this depth keeps the material solid.
• The radius is around 1250 kilometers.
• Between each of these main layers, there are also transitional zones known as the lithosphere (between the crust and the mantle), the Gutenberg discontinuity (between the mantle and the outer core), and the Lehmann discontinuity (between the outer core and the inner core).

The correct answer is Bhavai.

Key Points

• Bhavai:-
• Bhavai is a traditional, popular folk theatre form of the Indian state of Gujarat.
• It is used as a medium to convey social messages and entertain audiences in villages and towns.
• Bhavai performances involve numerous acts, known as "veshas", depicting popular tales from Indian mythology, history, and contemporary social and political scenarios.

Additional Information

• Paika:- 
• The term "Paika" comes from the Odia word 'Paika', which means 'fighter' or 'warrior'.
• The Paikas were the traditional landed militia of Odisha, found in particular in the districts of Khurdha, Puri, and Cuttack.
• They served as warriors for the local kings or regional rulers, and in times of peace, they worked primarily as farmers.
• Ghumra:-
• It is a folk dance form native to the Indian state of Odisha, particularly prevalent in the Kalahandi district.
• Known for its rhythmic, energetic movements and beats, Ghumura dance draws its name from the Ghumura instrument, which is an earthen terracotta pot with both ends open, played by strapping it to the chest and beaten with two sticks.
• Dhap:-
• It is a folk dance form indigenous to the Mayurbhanj district of Odisha, India.
• This dance form was traditionally performed by the Kshatriya community (the warrior class in the traditional Indian caste structure), symbolizing the spirit of martial traditions and chivalry.

The correct answer is 75% of the total assets. 

Key Points

• NBFC-MFIs:-
• Non-Banking Financial Company-Micro Finance Institutions, are a type of non-banking financial institution in India.
• They are specifically designed to provide microfinance services, which typically target low-income individuals or groups who do not have access to traditional banking and financial services.
• Generally, NBFCs in India are regulated by the Reserve Bank of India (RBI), but NBFC-MFIs answer to a more specific set of regulations due to their unique business model.
• This is because they often deal with vulnerable sections of society, which necessitates particular safeguards.
• Microloans provided by MFIs are intended to help individuals start or expand their small businesses. Thus, they play an important role in poverty reduction and financial inclusion.
• The minimum requirement of microfinance loans for NBFC-MFls is 75% of the total assets.

The correct answer is A and D only

Key Points

• Impeachment of the President of India
• The President can be removed from office by a process of impeachment for violation of the Constitution.
• However, the Constitution does not define the meaning of the phrase violation of the Constitution.
• The impeachment charges can be initiated by either House of Parliament.
• These charges should be signed by one-fourth of members of the House (that framed the charges), and a 14 days‘ notice should be given to the President.
• The nominated members of either House of Parliament can participate in the impeachment of the President though they do not participate in his election. Hence, Statement 2 is not correct.
• The elected members of the legislative assemblies of states and the Union Territories of Delhi and Puducherry do not participate in the impeachment of the President though they participate in his election.
• In the History of the Indian Republic, no Indian President has been so far "impeached" from his post.

The correct answer is Right to vote.

Key Points

• Right to vote:-
• The right to vote in India is guaranteed by the Constitution and the Representation of the People Act, 1951, subject to certain limitations.
• Every citizen over the age of 18 has the right to vote under Article 326 of the Constitution.
• The Right to vote in India is a Constitutional Right but not a fundamental right.
• The 61st Amendment of the Constitution lowered the voting age of elections to the Lok Sabha and to the Legislative Assemblies from 21 to 18 years which was done by amending Article 326 of the Constitution.
• Article 326 of the Constitution guarantees universal adult suffrage but does not mention the right to vote.
• In India, voting is a legal right guaranteed by the Representation of People Act, 1950.

Additional Information

• The Right to Equality:-
• It is one of the six fundamental rights of the Constitution.
• It is contained in the Indian Constitution from Article 14 to 18.
• Following are the provisions under the Right to Equality- 
• Article 14- ;equality before the law as well as equal protection of the law to all people.
• Article 15- prohibits discrimination on the grounds of religion, race, caste, sex, place of birth, and also gender or any of them.
• Article 16-  guarantees equality of opportunity in matters of public employment.
• Article 17- Abolition of untouchability.
• Article 18- Abolition of all titles except military and academic.
• Right to freedom of religion:-
• India is one of the most diverse nations in terms of religion.
• Freedom of religion in India is a fundamental right guaranteed by Article 25-28 of the Constitution of India.
• This right includes freedom to change his religion or belief and freedom, either alone or in community with others and in public or private, >to manifest his religion or belief, in worship, teaching practice and observance.

The correct answer is 2015.

Key Points

• Smart Cities Mission:-
• The Smart Cities Mission is an urban renewal program launched by the Government of India with the mission to develop 100 cities across the country making them citizen friendly and sustainable.
• The Union Ministry of Urban Development is responsible for implementing the mission in collaboration with the state governments of respective cities.
• The initiative was launched by Prime Minister Narendra Modi on 25 June 2015 with the government's intention to develop 'Smart Cities', a step towards improving the quality of life in urban cities and attracting people and investments to the cities.
• The mission of the Smart Cities Mission is to drive economic growth and improve the quality of life of people in urban areas, by enabling local area development and harnessing technology, especially technology that leads to smart outcomes.
• Core infrastructure elements in a smart city would include:-
• Adequate water supply,
• Assured electricity supply,
• Sanitation, including solid waste management,
• Efficient urban mobility and public transport,
• Affordable housing, especially for the poor,
• Robust IT connectivity and digitalization,
• Good governance, particularly e-Governance and citizen participation,
• Sustainable environment,
• Safety and security of citizens, particularly women, children and the elderly,
• Health and education.

The correct answer is Hookworm. 

Key Points

• Ancylostoma:-
• Ancylostoma is a genus of hookworms, which are parasitic worms.
• Two species from this genus, Ancylostoma duodenale and Ancylostoma ceylanicum, are common parasites in humans, primarily in parts of Asia, Africa, and southern Europe.
• The life cycle of these parasites begins when their larvae penetrate human skin.
• Soil contaminated with human feces often carries these larvae, making sanitation and hygiene crucial factors in preventing infection.
• Once inside the body, the larvae reach the lungs, ascend the bronchial tree, get swallowed, and eventually settle in the small intestine, where they mature into adult worms.
• Hookworms:-
• These are parasitic nematode worms that belong to the species Ancylostoma duodenale and Necator americanus.
• They are so named because of their hook-like mouthparts, which they use to attach to the wall of the small intestine of their hosts, including humans and some animals.

Additional Information

• Tapeworms:-

• These are a type of parasitic worm that belong to the class Cestoda.

• They are flat and segmented, resembling a tape or ribbon, which explains their name. They infest the digestive tracts of vertebrates, including humans, and can grow quite long, with some reaching over 20 feet in length.

• Roundworms:-

• These are also known as nematodes, are a type of parasitic worm.

• They're called "roundworms" because of their cylindrical, thread-like bodies. Roundworms are very diverse, and they can range in size from microscopic to over a meter in length in some cases.

• Filarial worms:-

• These are a type of parasitic roundworm that causes a group of diseases collectively known as filariasis.

• They are long, thread-like worms transmitted to humans through the bite of a mosquito, which serves as an intermediate host and vector.

The correct answer is m-Xylene.

Key Points

• 1,3-Dimethylbenzene:-
• It is also known as "meta-xylene" or simply "m-xylene."
• It is a type of aromatic hydrocarbon compound with a chemical structure that consists of a benzene ring substituted with two methyl groups in the meta position, which means they are attached to carbon atoms in positions 1 and 3 on the benzene ring.

Additional Information

• BHC:-
• It stands for "Benzene Hexachloride." It's a chemical compound that exists in multiple isomeric forms, including alpha-BHC, beta-BHC, gamma-BHC, and delta-BHC.
• These isomers are also known by various other names, such as Lindane (gamma-BHC) and Kwell (a brand name for lindane).
• Toluene:-
• It is also known as methylbenzene, is a common aromatic hydrocarbon compound.
• Its chemical formula is C7H8. Toluene is a clear, colorless liquid with a distinct sweet and pungent smell.
• It is primarily used as a solvent in various industrial processes and as a precursor for the production of other chemicals.

The correct answer is Norman Borlaug.

Key Points

• Norman Borlaug:-
• The "Father of the Green Revolution" is typically attributed to an American agronomist named Norman Borlaug.
• Borlaug was awarded the Nobel Peace Prize in 1970 in recognition of his contributions to world peace through increasing food supply.
• His pioneering work introducing high-yielding and disease-resistant wheat varieties combined with modern agricultural production techniques to Mexico, Pakistan, and India led these countries to greatly increase their food production and to serve as examples for the global Green Revolution.
• His work is estimated to have saved a billion people from starvation worldwide.
• Green Revolution:-
• The Green Revolution refers to a series of research, development, and technology transfer initiatives, occurring between the 1950s and the late 1960s, that increased agricultural production worldwide, particularly in the developing world.
• The term "Green Revolution" was first used in 1968 by former United States Agency for International Development (USAID) director William Gaud, who noted the spread of the new technologies and said, "These and other developments in the field of agriculture contain the makings of a new revolution.
• It is not a violent Red Revolution like that of the Soviets, nor is it a White Revolution like that of the Shah of Iran. I call it the Green Revolution."

 Additional Information

• Ralph Bunche:-
• He was an American political scientist, diplomat, and leading U.S. civil rights activist.
• He received the 1950 Nobel Peace Prize for his late 1940s mediation in Palestine.
• He was the first African American and person of color to be so honored in the history of the prize.
• Linus Carl Pauling:-
• He was an American chemist, biochemist, peace activist, author, and educator.
• He was one of the most influential chemists in history and is considered one of the greatest scientists of the 20th century.
• His work contributed significantly to the understanding of the nature of the chemical bond and the structure of molecules and crystals.
• Dr. M.S. Swaminathan:-
• He is an Indian geneticist and international administrator, renowned for his leading role in India's "Green Revolution," a program under which high-yield varieties of wheat and rice seedlings were planted in the fields of poor farmers.

The correct answer is persons with disabilities.  

Key Points

• State of Kerala Vs Leesamma Joseph:-
• The Supreme Court of India in its judgment on 28 June 2021 in the case of "State of Kerala vs Leesamma Joseph" affirmed that persons with disabilities have a right to reservation in promotion under Article 16(4) of the Constitution of India, 1950.
• While examining the constitutionality of Section 33 of the Rights of Persons with Disabilities Act, 2016, the Court noted that 'equality of opportunity' in matters of public employment includes provision of certain reservations in favour of persons with disabilities.
• Furthermore, it held that Article 16(4) of the Constitution, empowering the State to make provisions for reservation in matters of promotion in favour of any backward class of citizens, also includes persons with disabilities within its scope, regardless of the nature of their establishments, whether they belong to the public sector or the private sector.

Additional Information

• Rights of Persons with Disabilities Act, 2016 (RPDA):
• This is the principal legislation that protects the rights of individuals with disabilities in India.
• It replaces and strengthens the Persons with Disabilities Act, 1995.
• The RPDA complies with the United Nations Convention on the Rights of Persons with Disabilities, to which India is a signatory.
• The Act expands the list of recognized disabilities from 7 to 21, and mandates the central and state governments to take measures to ensure that persons with disabilities fully enjoy all human rights and fundamental freedoms.

Concept Used :

A number will be divided by three if sum of all the digits in a number is multiple of 3.

For eg : 234 = 2 + 3 + 4 = 9, and here 9 is the multiple of 3.

Calculation :

⇒ 34623 = 3 + 4 + 6 + 2 + 3 = 18 , Multiple of 3

⇒ 34716 = 3 + 4 + 7 + 1 + 6 = 21 , Multiple of 3

⇒ 34782 = 3 + 4 + 7 + 8 + 2 = 24, Multiple of 3

⇒ 34783 = 3 + 4 + 7 + 8 + 3 = 25 , Not a multiple of 3

∴ The correct answer is 34783.

Shortcut Trick

When two circles touch each other externally, the angle subtended by the direct common tangent at the point of contact is always 90°.

∴ In ΔAPB, ∠APB = 90°.

Using the angle sum property of a triangle in ΔAPB:

∠ABP = 180° − (∠APB + ∠PAB)

∠ABP = 180° − (90° + 65°) = 25°

∴ The correct answer is 25°.

Alternate Method

Given:

Two circles touch each other externally at point P.

AB is a direct common tangent touching the circles at A and B.

∠PAB = 65°

Formula/Property Used:

1. Tangents drawn from an external point to a circle are equal in length.
2. Angles opposite to equal sides in a triangle are equal.
3. The sum of angles in a triangle is 180°.

Calculations:

⇒ Let the common tangent at the point of contact P intersect the direct common tangent AB at point T.

⇒ For the left circle, TA and TP are tangents drawn from the external point T.

∴ TA = TP

⇒ In ΔTAP, since TA = TP, the angles opposite to these sides are equal:

⇒ ∠TPA = ∠TAP = 65°

⇒ Similarly, for the right circle, TB and TP are tangents drawn from the external point T.

∴ TB = TP

⇒ Since TA = TP and TB = TP, we have:

⇒ TA = TB = TP

⇒ In ΔAPB, the median PT is equal to half of the opposite side AB (since T is the midpoint of AB and TP = AB/2).

⇒ This property holds true only in a right-angled triangle where the hypotenuse is AB.

∴ ∠APB = 90°

⇒ Now, in ΔAPB, using the angle sum property:

⇒ ∠PAB + ∠ABP + ∠APB = 180°

⇒ 65° + ∠ABP + 90° = 180°

⇒ 155° + ∠ABP = 180°

⇒ ∠ABP = 180° − 155° = 25°

∴ The correct answer is 25°.

Additional Information

Angle Subtended by Direct Common Tangent

When two circles touch each other externally, the direct common tangent always subtends a right angle (90°) at the point of contact of the two circles.

Length of Direct Common Tangent (DCT)

For two circles of radii R and r with distance d between their centers, the length of the DCT is given by √(d² − (R − r)²). When they touch externally, d = R + r, simplifying the formula to 2√(R × r).

Number of Common Tangents

When two circles touch externally, there are exactly 3 common tangents: 2 direct common tangents and 1 transverse common tangent.

Given : 

Speed of 1st person = 20 m/s

Speed of the 2nd person = 30 m/s

Circumference of the Track = 100 m

Concept used :

Speed = Distance covered / Time taken

Calculation :

The time taken by the first person to complete a full lap is 100 m / 20 m/s = 5 seconds. The time taken by the second person to complete a full lap is 100 m / 30 m/s = 10/3 seconds.

​The LCM of 5 seconds and 10/3 seconds is 10 seconds, which means they will end up in the same initial positions after 10 seconds.

​Let the two persons cross each other for the first time after x seconds.

Then, total distance covered by 1st person = 20x and the 2nd person = 30x

Now, the total distance covered by both the person = Circumference of the track

⇒ 30x + 20x = 100m ⇒ 50x = 100m ⇒ x = 2 s

∴ The two persons will cross each other for the first time after 2 seconds.

The two persons will cross each other again after 2 seconds, and then again after 2 seconds, and so on.

So in 10 seconds they will meet = 10/2 = 5 times

Therefore, the two persons will cross each other at 5 distinct points on the track.

Shortcut Trick

S₁ = 20 m/s and S₂ = 30 m/s

S₁/S₂ = 2/3

They are running in opposite directions so they will meet each other at distinct points = 2 + 3 = 5

Shortcut Trick

Use the direct relation: Value = (a + b + c) × [1.5(a² + b² + c²) − 0.5(a + b + c)²]

Substitute the given values: 12 × [1.5(50) − 0.5(12)²]

Value = 12 × [75 − 72]

Value = 12 × 3 = 36

∴ The correct answer is 36.

Alternate Method

Given: (a + b + c) = 12 and (a² + b² + c²) = 50

Formula Used:

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

2. a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − (ab + bc + ca))

Calculations:

⇒ First, find the value of (ab + bc + ca) using formula 1:

⇒ (12)² = 50 + 2(ab + bc + ca)

⇒ 144 − 50 = 2(ab + bc + ca)

⇒ 94 = 2(ab + bc + ca)

⇒ ab + bc + ca = 47

⇒ Now, substitute all known values into formula 2:

⇒ a³ + b³ + c³ − 3abc = 12 × (50 − 47)

⇒ a³ + b³ + c³ − 3abc = 12 × 3 = 36

∴ The correct answer is 36.

Additional Information

Special Case (a + b + c = 0)

If the sum of three terms is zero, the identity simplifies to a³ + b³ + c³ = 3abc.

Alternative Form of Identity

The expression can be rewritten as 0.5 × (a + b + c)[(a − b)² + (b − c)² + (c − a)²], which is useful when differences are given.

Sum of Cubes (Two Variables)

The formula for two variables is a³ + b³ = (a + b)(a² − ab + b²).

Given : 

CP = Rs.500 

Profit = 16%

Discount = x %

SP = Rs.493

Formula Used :

Discount = MP - SP

Profit = SP - CP

Calculation : 

Profit = 16% = 16/100

MP = 116 × 5 = 580

Discount = x % 

So,

⇒ 580 × (100 - x)/100 = 493

⇒ 58 × (100 - x) = 4930

⇒ 5800 - 58x = 4930

⇒ 58x = 870

⇒ x = 15

∴ The correct answer is 15.

Calculation :

⇒ 100% = 360° 

⇒ 1 % = 3.6° 

⇒ 40% = 40 × 3.6° = 144° 

∴ The correct answer is 144°.

Shortcut Trick

Decrease in average weight of remaining 28 students = 18.5 − 15.5 = 3 kg.

Total weight lost by these 28 students = 28 × 3 = 84 kg.

This means the 4 students took their own average share plus this lost weight.

Total weight of 4 students = (4 × 18.5) + 84 = 74 + 84 = 158 kg.

Average weight of these 4 students = 158 ÷ 4 = 39.5 kg.

∴ The correct answer is 39.5 kg.

Alternate Method

Given:

Initial students = 32, Initial average = 18.5 kg

Students remaining = 32 − 4 = 28, New average = 15.5 kg

Formula Used:

Total Weight = Average × Number of Students

Average of left students = Total weight of left students ÷ Number of left students

Total Weight = 32 × 18.5 = 592 kg 32 students, Average = 18.5 kg

28 students, Avg = 15.5 kg Weight = 28 × 15.5 = 434 kg

4 students W = 158 kg

∴ Average of 4 = 158 ÷ 4 = 39.5 kg

Calculations:

⇒ Total weight of 32 students = 32 × 18.5 = 592 kg

⇒ Total weight of remaining 28 students = 28 × 15.5 = 434 kg

⇒ Total weight of the 4 students who left = 592 − 434 = 158 kg

⇒ Average weight of the 4 students = 158 ÷ 4 = 39.5 kg

∴ The correct answer is 39.5 kg.

Additional Information

Weighted Average

If group A has n₁ elements with average A₁ and group B has n₂ elements with average A₂, then the combined average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Net Deviation Method

The sum of deviations of all observations from their actual average is always zero. This property is highly useful to rapidly find the value of included or excluded terms without complex multiplications.

Excluding a Member

If a member leaves and the average decreases, the leaving member's value is greater than the initial average: Left Value = Old Avg + (Decrease in Avg × Remaining Members).

Given : 

$\rm \sec θ=\frac{4}{3}$

Calculation : 

We know,

⇒ Secθ = 4/3, tanθ = √7/3

⇒ tan2 θ + tan4 θ = 7/9 + 49/81

⇒ (63 + 49)/81

⇒ 112/81

∴ The correct answer is 112/81.

Calculation : 

Average = (9500 + 9400 + 9600 + 8000 + 8500)/5 = 9000

∴ The correct answer is 9000.

Calculation :

⇒ $\frac{\left(12+5-\frac{48}{16}+71\right)+\left(\frac{\frac{72}{36}+6\times 7}{11}\right)\times[(51+4-13)+(13-12\times7)]}{232}$

⇒ $\frac{(17 - 3 + 71) + \frac{(2 + 42)}{11} \times {(42 - 71)}}{232}$

⇒ $\frac{(17 - 3 + 71) + \frac{44}{11} \times {(-29)}}{232}$

⇒ $\frac{85 + 4 \times (-29)}{232}$

⇒ $\frac{85 - 116}{232}$

⇒ -31/232

∴ The correct answer is option 4.

Calculation : 

cot (A - B) = $\rm \frac{\cot A\cot B+1}{\cot B-\cot A}$

⇒ Cot15° = Cot(45° - 30°)

⇒ Cot(45° - 30°) = Cot45°Cot30° + 1/Cot30° - Cot45° 

⇒ 1 × √3 + 1/√3 - 1

⇒ √3 + 1/√3 - 1

⇒ √3 + 1/√3 - 1 ×  √3 + 1/√3 + 1

⇒ (√3 + 1)²/2 

⇒ (3 + 1 + 2√3)/2

⇒ (2√3 + 4)/2

⇒ √3 + 2

∴ The correct answer is √3 + 2.

Concept used:

sec² θ - tan² θ = 1

Calculation:

P cos α = 3

⇒ cos α = 3/P

⇒ sec α = P/3

4 tan α = Q

⇒ tan α = Q/4

From the given concept, we get

sec2 α - tan2 α = 1

⇒ P²/9 - Q²/16 = 1

∴ The correct answer is option 3

Calculation : 

∠BAC = 72° 

By angle sum property 

⇒ ∠A + ∠B + ∠C = 180

 

⇒ ∠B + ∠C = 180 − 72 = 108

 

⇒ ∠OBC + ∠OCB = 54

 

The Angular bisectors Meet at O

 

So By Angle sum property ,

 

⇒ ∠OBC + ∠OCB + ∠BOC = 180

 

⇒ 54 + ∠BOC = 180

 

⇒ ∠BOC = 126

 

∴ The correct answer is 126°.

Given : 

Lateral Surface area of cylinder = 3168 cm²

Height = 48 cm

Formula Used : 

Voulme of Cylinder = πr²h

Curved Surface area od cylinder = 2πrh

Calculation : 

⇒ 2πrh = 3168

⇒ 2 × 22/7 × r × 48 = 3168

⇒ r = 3168 × 7/(2 × 22 × 48)

⇒ r = 22176/2112 

⇒ r = 10.5 cm

Volume = 22/7 × 10.5 × 10.5 × 48 = 16632 cm³

∴ The correct answer is 16632 cm³.

Shortcut Trick

Use the direct ratio relation between Cost Price (CP) and Printed Price (MP):

CP : MP = (100 − Discount%) : (100 + Profit%)

Given Discount = 10% and Profit = 20%

⇒ CP : MP = (100 − 10) : (100 + 20)

⇒ CP : MP = 90 : 120 = 3 : 4

∴ The correct answer is 3 : 4.

Alternate Method

Given: Discount allowed = 10% | Profit earned = 20%

Formula Used: Selling Price (SP) = CP × (100 + Profit%)/100 = MP × (100 − Discount%)/100

⇒ Let the Printed Price (MP) of the item be ₹100.

⇒ Selling Price (SP) after 10% discount = 100 − 10 = ₹90.

⇒ Since there is a 20% Profit, SP = CP × (120/100).

⇒ 90 = CP × (6/5)

⇒ Cost Price (CP) = (90 × 5) ÷ 6 = 15 × 5 = ₹75.

⇒ Ratio of CP to MP = 75 : 100

⇒ Ratio = 3 : 4

∴ The correct answer is 3 : 4.

Additional Information

Direct CP and MP Relation

The relationship is derived as CP/MP = (100 − Discount%)/(100 + Profit%). This is the fastest way to solve mark-up and discount problems.

Mark-up Percentage

Mark-up % = [(MP − CP) ÷ CP] × 100. It can also be calculated as [(Profit% + Discount%) ÷ (100 − Discount%)] × 100.

Successive Discounts

If two successive discounts d₁ and d₂ are given, the single equivalent discount is (d₁ + d₂ − d₁×d₂/100)%.

Given : 

A can do a piece of work in 4 days

B can do a piece of work in 12 days

They worked together for 2 days.

Formula Used : 

Work done = time × efficiency

Calculation : 

Total work = LCM(4,12) = 12

Efficiency of A = 3

Efficiency of B = 1

Work done in 2 days = 2 × (3 + 1) = 8

Fraction of work still left = 4/12 = 1/3

∴ The correct answer is 1/3.

Calculation:

Total work or capacity of the tank is = LCM of (1.5, 4.5, 6) = 18 unit

Efficiency of (A + B) = 18/1.5 = 12 unit

Efficiency of C = 18/4.5 = - 4 unit

Efficiency of (A - C) = 18/6 = 3

Here, C = - 4 and (A - C) = 3, then efficiency of A = (4 + 3) = 7 unit

Now, efficiency of B = (12 - 7) = 5 unit

So, B can fill the whole empty tank in = 18/5 = 3.6 hour = 3 hours 36 minutes 

∴ The correct answer is 3 hours 36 minutes

Given : 

$\rm \left(3y-\frac{3}{y}\right)=5$

Formula Used : 

(a - b)² = a² + b² - 2ab

Calculation : 

⇒ y - 1/y = 5/3

⇒ y² + 1/y² - 2 = 25/9

⇒ y² + 1/y² = 25/9 + 2

⇒ y2 + 1/y2 = (25 +18)/9

⇒ y2 + 1/y2 = 43/9

∴ The correct answer is 43/9.

Shortcut Trick

Thief's total travel time = 20 + 20 = 40 minutes.

Security guard's total travel time = 20 minutes.

Since the distance is constant, Speed is inversely proportional to Time.

Time ratio (Thief : Guard) = 40 : 20 = 2 : 1.

Speed ratio (Thief : Guard) = 1 : 2.

Given Thief's speed = 12 m/h → 1 unit = 12 m/h ∴ 2 units = 24 m/h.

∴ The correct answer is 24 m/h.

Alternate Method

Given:

Speed of Thief (S_t) = 12 m/h

Time headstart = 20 minutes

Time taken to catch (T_c) = 20 minutes

Formula Used:

Distance = Speed × Time

Relative Speed (same direction) = S_guard − S_thief

Calculations:

⇒ Total time the Thief ran = 20 + 20 = 40 minutes = 40/60 hours = 2/3 hours.

⇒ Total distance covered by Thief = 12 × (2/3) = 8 meters.

⇒ The Security guard covers this same 8 meters in 20 minutes.

⇒ Time for guard = 20/60 hours = 1/3 hours.

⇒ Speed of Security guard = Distance ÷ Time

⇒ Speed = 8 ÷ (1/3) = 8 × 3 = 24 m/h.

∴ The correct answer is 24 m/h.

Additional Information

Relative Speed

When two objects move in the same direction, the relative speed is the difference of their speeds (u − v). For chasing, the catcher's speed must be greater.

Catching Time Formula

Time to catch = (Initial Distance between them) ÷ (Relative Speed).

Distance Constant Relation

If distance is constant, Speed₁ × Time₁ = Speed₂ × Time₂.

Shortcut Trick

Let the Rate of Interest be R. Then Time T = 4R.

Using the direct relation: R² = (SI × 100) ÷ (P × 4)

R² = (11664 × 100) ÷ (32400 × 4) = 11664 ÷ 1296 = 9

R = √9 = 3%

∴ The correct answer is 3%.

Alternate Method

Given:

Principal (P) = ₹32,400

Simple Interest (SI) = ₹11,664

Rate (R) = T ÷ 4 ⇒ Time (T) = 4R years

Calculations:

⇒ SI = (P × R × T) ÷ 100

⇒ 11,664 = (32,400 × R × 4R) ÷ 100

⇒ 11,664 = 324 × 4R²

⇒ 11,664 = 1,296R²

⇒ R² = 11,664 ÷ 1,296

⇒ R² = 9

⇒ R = √9 = 3

∴ The correct answer is 3%.

Shortcut Trick

Let the initial ratio of seats be 6 : 4 : 7.

To find the new ratio, multiply each by its respective growth percentage factor.

New ratio = (6 × 120%) : (4 × 140%) : (7 × 160%)

New ratio = 7.2 : 5.6 : 11.2

Multiply by 10 and divide by 8 to get the simplest form ⇒ 9 : 7 : 14

∴ The correct answer is 9 : 7 : 14.

Alternate Method

Given:

The initial ratio of seats for Mathematics, English, and Chemistry = 6 : 4 : 7

Increase in seats = 20%, 40%, and 60% respectively.

Calculations:

Let the initial number of seats be 600, 400, and 700 to make percentage calculations easier.

⇒ Increased seats in Mathematics = 600 + (20/100 × 600) = 600 + 120 = 720

⇒ Increased seats in English = 400 + (40/100 × 400) = 400 + 160 = 560

⇒ Increased seats in Chemistry = 700 + (60/100 × 700) = 700 + 420 = 1120

⇒ New ratio of seats = 720 : 560 : 1120

⇒ Divide all terms by 80 to get the simplified equivalent ratio.

⇒ New ratio = (720 ÷ 80) : (560 ÷ 80) : (1120 ÷ 80)

⇒ New ratio = 9 : 7 : 14

∴ The correct answer is 9 : 7 : 14.

Additional Information

Compound Ratio

When two or more ratios are multiplied term by term, the resulting ratio is called a compound ratio. For a:b and c:d, the compound ratio is ac:bd.

Percentage Increase

When a value increases by R%, the new value is directly calculated as Initial Value × (100 + R)/100.

Scaling in Ratios

Multiplying or dividing all terms of a ratio by the same non-zero number does not change the proportion. This property is frequently used to clear decimals or fractions.

Concept used:

Circumference of a circle = 2 × π × r

Calculation:

The circumference of of the wheel = 2 × 22/7 × 182 = 1144 cm

Here, the lorry can go 66 km in 60 min, then the lorry can cover in 1 min is = 66/60 = 1.1 km = 110000 cm

Now the wheel of the lorry makes the number of revolutions per min is 110000/1144 = 96.15 ~ 96

∴ The correct answer is 96

Shortcut Trick

Ratio of Income : Expenditure : Savings = 80,000 : 45,000 : 35,000 = 16 : 9 : 7

Total units of Income Increase = 16 × 16% = 256

Total units of Expenditure Increase = 9 × 8% = 72

Total units of Savings Increase = 256 − 72 = 184

Percentage Increase in Savings = 184 ÷ 7 ≈ 26.29%

∴ The correct answer is 26.29%.

Alternate Method

Given: Monthly Income = ₹80,000, Monthly Expenditure = ₹45,000

Formula Used: Savings = Income − Expenditure; % Increase = (Change ÷ Original) × 100

⇒ Original Savings = 80,000 − 45,000 = ₹35,000

⇒ Increase in Income = 16% of 80,000 = ₹12,800

⇒ Increase in Expenditure = 8% of 45,000 = ₹3,600

⇒ Increase in Savings = 12,800 − 3,600 = ₹9,200

⇒ Percentage Increase in Savings = (9,200 ÷ 35,000) × 100

⇒ % Increase = 920 ÷ 35 ≈ 26.2857%

∴ The correct answer is 26.29%.

Additional Information

Fundamental Income Identity

Total Income is always the sum of Expenditure and Savings (I = E + S). Any change in Income must be balanced by changes in E and S.

Weighted Average Method

Income % change = (Exp Ratio × Exp % change + Savings Ratio × Savings % change) ÷ (Exp Ratio + Savings Ratio).

Percentage Change Formula

Percentage Change = [(Final Value − Initial Value) ÷ Initial Value] × 100.

Shortcut Trick

The age difference between two people always remains constant.

Difference = 28 years. After 3 years, Ratio of Mother : Son = 2 : 1.

Ratio difference (2 − 1) = 1 unit → 28 years.

Son's age after 3 years = 1 unit = 28 years.

Present age of Son = 28 − 3 = 25 years.

∴ The correct answer is 25 years.

Alternate Method

Given:

Difference between Woman and Son = 28 years.

Condition: In 3 years, Woman's age = 2 × Son's age.

Let the present age of the son be x years.

⇒ Present age of the woman = (x + 28) years.

After 3 years:

⇒ Son's age = (x + 3)

⇒ Woman's age = (x + 28 + 3) = (x + 31)

According to the question:

⇒ (x + 31) = 2 × (x + 3)

⇒ x + 31 = 2x + 6

⇒ 2x − x = 31 − 6

⇒ x = 25

∴ The correct answer is 25 years.

Additional Information

Constant Age Difference

The numerical difference between the ages of two persons never changes over time, regardless of how many years pass.

Ratio Method for Age

If the ratio of ages at two different times is given, equate the difference in ratio parts to the actual constant age difference to solve quickly.

Linear Equation approach

Always define the unknown (usually the younger person's age) as 'x' to keep calculation terms positive and simple.

Given : 

Anil and Bipin together can complete a work in 15 days.

Bipin alone can finish it in 20 days.

Formula Used : 

Work done = time × efficiency

Calculation : 

Total work = LCM (15, 20) = 60

Efficiency of Anil and Bipin = 4

Efficiency of Bipin = 3 

Efficiency of Anil = 4 - 3 = 1 

Time taken by Anil = 60/1 = 60 days

∴ The correct answer is 60 days.

The correct answer is: Is a car not being driven by him?

Key Points

• The subject of the Active Voice is changed into the object of the Passive Voice. Also, the object of the Active Voice is changed into the subject of the Passive Voice.
• The usage of a helping verb is necessary while changing the voice of the sentence from Active to Passive.
• The preposition “by” is used before the object made in Passive Voice. However, it is optional in some cases.
• The Active voice in this question is in Present Continuous. Thus, the Passive voice will also be in Present Continuous.
• The format of Active voice is: Am/is/are + Subject + Verb (ing) + Object.
• Thus, in Passive voice, the format will be: Am/is/are + Object of the active voice (Subjective case) + being + V3 + by + Subject of the active voice (Objective case).

Therefore, the correct answer is: Is a car not being driven by him?

The correct answer is: Retain.

Key Points

• The word 'delegate' is a verb in this context, meaning to entrust tasks or responsibilities to others (Hindi meaning: प्रतिनिधि मनोनीत करना). 
• For example, "The supervisor decided to delegate some tasks to the new intern."
• The correct antonym is 'retain', which in this context means to keep or continue to have something (Hindi meaning: बरकरार रखना).
• For example, "Despite the presence of capable staff, the boss chose to retain all the responsibilities herself."

Therefore, the correct answer is "Retain".

Additional Information

• Appoint: It refers to the act of assigning a job or position to someone (Hindi meaning: नियुक्त करना).
• Nominate: It means to formally suggest someone for a position, role, or duty (Hindi meaning: मनोनीत करना).
• Depute: This verb is another term for delegating duties or authority to someone else (Hindi meaning: प्रतिनिधि मनोनीत करना).

The correct answer is: Learned.

Key Points

• The word 'Innate' is an adjective, meaning existing in one from birth; inborn; natural (Hindi meaning: जन्मजात).
• For example: "Her innate musical talent was evident from a young age."
• The correct antonym is 'Learned', which in this context means acquired by learning (Hindi meaning: सीखा हुआ).
• For example: "His ability to play the piano is not innate; it's a learned skill."

Therefore, the correct answer is "Learned".

Additional Information

• Aquatic: This word describes something related to water (Hindi meaning: जलीय).
• Natural: This term refers to things that occur in nature without human intervention (Hindi meaning: प्राकृतिक).
• Replete: 'Replete' means filled or well-supplied with something (Hindi meaning: पूर्ण).

The correct answer is: Unbelievable.

Key Points

• The word 'Incredible' is an adjective, meaning impossible to believe, or extremely good, great or large (Hindi meaning: अविश्वसनीय).
• For example: "The magician performed some truly incredible tricks."
• The correct synonym is 'Unbelievable', which in this context means not able to be believed; unlikely to be true (Hindi meaning: अविश्वसनीय).
• For example: "He made an unbelievable catch in the baseball game."

Therefore, the correct answer is "Unbelievable".

Additional Information

• Realistic: This word describes something that is sensible and reasonably like real life (Hindi meaning: यथार्थवादी).
• Unachievable: It refers to something that cannot be achieved or completed successfully (Hindi meaning: असाध्य).
• Reasonable: 'Reasonable' indicates something that is fair, practical, and sensible (Hindi meaning: योग्य).

The correct answer is 'Option 1' i.e. looks like.

Key Points

• The sentence "Radium is a white powder that ________ table salt." is in present tense.
• This infers that we need a verb that also aligns with the present tense, while also agreeing with the singular noun "Radium".
• "Looks like" is the correct answer because it agrees with the singular subject "Radium" and is in the present tense.

Therefore, the correct answer is- "Radium is a white powder that looks like table salt".

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Additional Information

• Option 2 "look like" would be incorrect because "look" does not agree with the singular noun "Radium". "Look" should be used with a plural subject.
• Option 3 "will look like" implies a future tense, which is inconsistent with the present tense structure of the sentence.
• Option 4 "looking like" is in the present continuous tense and doesn't fit in the structure of the sentence.

The correct answer is 'Option 2' i.e. 'Disagreement'.

Key Points

• The given word 'Vendetta' refers to a prolonged bitter quarrel with or campaign against someone. It generally involves harmful actions prompted by a grievance or dispute. (प्रतिशोध)
• Example: The two families have been locked in a vendetta for decades, with acts of retaliation escalating over the years.
• The correct synonym for 'Vendetta' in the given options is 'Disagreement'.
• It refers to a lack of consensus or harmony between individuals. It implies a difference in opinion, perception, or understanding that can lead to conflict. (मतभेद)
• Example: Their disagreement over financial matters eventually caused a rift between the business partners.

Therefore, the correct answer is- 'Disagreement'.

Additional Information

• Option 1: 'Dilemma' is a situation in which a difficult choice has to be made between two or more alternatives, especially equally undesirable ones. (दुविधा)
• Option 3: 'Vacillation' refers to the inability to decide between different opinions or actions; indecision. (अनिश्चय)
• Option 4: 'Passion' is a strong and barely controllable emotion or a strong enthusiasm towards something. (जुनून)

The correct answer is 'Option 3' i.e. 'who are looking to expand'.

Key Points

• The sentence is referring to the group of people who have a certain aim to expand their horizons in the tourism industry. In English grammar, when referring to people, we use 'who' not 'which'.
• The error in the sentence lies in the usage of the relative pronoun 'which' for referring to people. The correct relative pronoun to use for people is 'who'.
• The verb form 'are looking to expand' correctly maintains agreement with the plural subject (the people).

Therefore, the corrected sentence should be "They are the people who are looking to expand their horizons in the fast growing tourism industry."

Additional Information

• Option 1: 'which looked to expand' is incorrect because 'which' is not the correct relative pronoun to refer to people. Also, the use of past tense 'looked' is not consistent with the other verbs of the sentence that are in the present tense.
• Option 2: 'who is looking to expand' is grammatically incorrect. 'Is looking' would be incorrect verb agreement for the plural subject 'people'.
• Option 4: 'that are looked to expand' is grammatically incorrect. The verb phrase 'are looked to expand' doesn't make sense in the context of the sentence.

The correct answer is "Permanent."

Key Points

• Transient means something that is not permanent or lasting.
• The antonym of transient is permanent, which means lasting or enduring.
• Other possible antonyms for transient could be enduring, persistent, or long-lasting.

Therefore, the correct answer is "Option 2".

Additional Information

• Boring: Lacking interest or excitement.
• Toxic: Harmful, dangerous, or poisonous.
• Fleeting: Something that is brief or passing quickly.

The correct answer is "No error"

Key Points

• "The sky appears blue as" – This clause essentially states that the sky looks blue because of a reason that's about to follow.
• Grammatically, it's correct and can stand as an independent sentence.
• "it absorbs all colours" – This part of the sentence is also grammatically correct as a dependent clause that explains why the sky looks blue.
• It correctly uses the pronoun "it" to refer to the sky and the verb "absorbs" to describe what the sky does with all colours.
• "and reflects only blue" – This is the final dependent clause connected to the sentence by the conjunction "and".
• Its structure is parallel to the previous clause, and it further describes the behaviour of the sky concerning colours.

Therefore, the correct answer is "option 4".

The correct answer is  "Orphan".

 Key Points

• "Orphan" is a noun that refers to a child who has lost one or both parents.
• It is derived from the Greek word "orphanos", which means "bereaved".
• The term can also be used as a verb, meaning "to deprive of parents or a parent through death".
• Example: After the earthquake, many children became orphans and had to be taken in by relatives or orphanages.

Therefore, the correct answer is Option 2. 

 Additional Information

• Option 1, "Destitute", refers to someone who is extremely poor and lacking basic necessities.
• Option 3, "Lout", refers to a rude, uncouth, or aggressive person.
• Option 4, "Desolate", means barren, empty, or deserted.