DSSSB Jail Warder : (26 Nov 2025) Memory-Based Paper (Previous Year Paper)

The pattern follows here is:

Hence, the correct answer is "900".

Eight students: A, C, D, H, K, R, S and V

1. Four people are sitting between C and V from the right of C, while two people are sitting between V and S from the left of V

2. A is sitting opposite to S, while D is sitting opposite to K

There are two possible cases:

Case I:

Case II:

3. R and D are neighbours

This statement is violated in case II, so it is eliminated

In case I, R will occupy the position to the immediate right of D and H will occupy the remaining position

Thus, the final arrangement is:

Hence, C and S is the neighbour of H

The logic followed here is → (First digit of the first number × Second digit of the first number) + (Sum of the digits of first number) = Second number

So,

Option - (1) → 68 - 62

⇒(6 × 8) + (6 + 8) = 62

⇒48 + 14 = 62

⇒62 = 62 (LHS = RHS)

Option - (2) → 72 - 23

⇒(7 × 2) + (7 + 2) = 23

⇒14 + 9 = 23

⇒23 = 23 (LHS = RHS)

Option - (3) → 35 - 22

⇒(3 × 5) + (3 + 5) = 22

⇒15 + 8 = 22

⇒23 ≠ 22 (LHS ≠ RHS)

Option - (4) → 91 - 19

⇒(9 × 1) + (9 + 1) = 19

⇒9 + 10 = 19

⇒19 = 19 (LHS = RHS)

Here, "35 - 22" is different from rest of the alternatives.

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

The teacher works in the school.

Similarly,

The doctor works in the hospital.

Hence, ‘Doctor ∶ Hospital’ is the correct answer.

1) MAD is scheduled on Thursday and on 2 days before Feeraj.

2 days before = a gap of 1 day.

2) Roadies is scheduled on the first day and immediately on the day before Maleka. Art is not scheduled after MAD.

Among the given options, MAD and Art are scheduled on adjacent days.

Hence, the correct answer is ‘MAD and Art’.

In the morning the Sun is in the East, so the shadow will fall towards the West.

In the evening the Sun is in the West, so the shadow will fall towards the East.

One day a person while walking in a ground moves towards the West and takes a right turn. That is he is facing North direction. His shadow is to his right that means Sun is to his left that is in West direction.Hence, it is evening time.

Hence, it is evening time.

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 mirror image of the given figure when the mirror is held at the right side is:

Hence, option 1 is the correct answer.

The logic is:

Hence, ‘UVF’ is the correct answer.

The least possible Venn diagram is given below:-

Conclusion:

1. No monkey is human. → False ( it is possible but not definite)
2. Some humans are apes. → True (As can be seen in the Venn diagram, some part of Human is ape)

Hence, "option 4" is the correct answer.

The pattern followed here is shown below:

Hence, "642" is the correct answer.

According to the given information-

1. R lives on second floor.

2. Two persons are live between R and E.

3. Three persons are live between Q and P. P lives below Q.

4. L lives on odd number floor.

5. 5. D is not an immediate neighbour of Q.

The final arrangement is given below

Hence, P lives on the 3^rd floor.

Total number of students who like tea = 56

Total number of students who like coffee = 46

Total number of students who like neither tea nor coffee = 4

Total number of students = 90

Let,

The number of students who like both tea and coffee = x

Number of students who like only tea = 56 - x

Number of students who like only coffee = 46 – x

Total number of students = (56 - x) + (46 – x) + x + 4 = 90

106 - x = 90

x = 16

Hence, 16 students like both tea and coffee.

So,

Number of students who like only coffee = 46 – x = 46 – 16 = 30

Hence, 30 students like only coffee.

Preparing the family tree using the following symbols:

A possible tree diagram will be:

So, the woman is the sister of the father of man's wife.

Hence, the woman is the aunt of the man's wife.

Table shows the positional value of alphabets.

The logic followed here is:

 ‘RETAIL’ is written as ‘FNQWJY’

And

‘POLICE’ is written as ‘NHJUTQ’

Similarly,

‘HARBOR’ : ?

Hence, the correct answer is "GTWMFW".

On close observation, we find that the problem figure is embedded in figure (4) as shown below.

Hence, the correct answer is figure 4.

The least possible Venn diagram is: 

Conclusion:

I. Some leaves are plant → False (As There is no direct relation between plants and leaves)

II. Some plants are not tree → False (As Some plants are trees. So, Some plants are not tree is false)

Hence, Neither conclusion I nor II follows.

Additional Information

The logic followed here is:

Hence, MLBG is the correct answer.

The image obtained when the paper is unfolded is,

Hence, "option 4" is the correct answer.

The logic is -

11 : 141 → 11² + 20 = 121 + 20 = 141

Similarly,

17 : ? → 17² + 20 = 289 + 20 = 309

Hence, '309' is the correct answer.

Similarly,

Hence, ZFOPI is the correct answer.

Putting values in the given blanks and checking each option:

Given: 27_9_12_14_7 = 43

1. 27 + 9 - 12 × 14 ÷ 7 = 43

= 27 + 9 - 12 × 14 ÷ 7 = 43

= 27 + 9 - 12 × 2

= 27 + 9 - 24

= 36 - 24

= 12

12 ≠ 43

2. 27 ÷ 9 × 12 - 14 + 7 = 43

= 27 ÷ 9 × 12 - 14 + 7 = 43

= 3 × 12 - 14 + 7

= 36 - 14 + 7

= 36 - 7

= 29

29 ≠ 43

3. 27 ÷ 9 × 12 + 14 - 7 = 43

= 27 ÷ 9 × 12 + 14 - 7 = 43

= 3 × 12 + 14 - 7 

= 36 + 14 - 7

= 50 - 7

= 43 = 43

4. 27 - 9 + 12 × 14 + 7 = 43

= 27 - 9 + 12 × 14 + 7 = 43

= 27 - 9 + 168 + 7

= 202 - 9

= 193

193 ≠ 43

Hence, the correct answer is Option 3.

Assumption I is not implicit as the statement mention the spread of rumours through media. So media provide rumours also.

Assumption II is implicit because lockdown was implemented for COVID-19 as mentioned in the statement.

Hence, Only assumption II is implicit.

Preparing the family tree using the following symbols:

A possible tree diagram will be:

Hence, E is the mother-in-law of D.

Logic:

Tulip, rose, and daisy is types of flowers.

Bud is not a flower.

Here, 'Bud' is different from all other options as per logic.

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

P Q R | P Q R S | P Q R S T | P Q R S T U

Hence, ‘QRPSRSQS’ is the correct answer.

English, latin and Greek are three different language.

So, the venn diagram is –

Although it is true that there are several words directly taken from Latin and Greek, these languages are completely different from each other.

Hence, option 2 is the answer.

The logic followed here is :- 

1. ACEG → There are two consonants i.e 'C' and 'G' and two vowels i.e 'A' and 'E'.

2. MOQS → There are three consonants i.e 'M', 'Q' and 'S' and one vowel i.e 'O'.

3. IKMO → There are two consonants i.e 'K' and 'M' and two vowels i.e 'I' and 'O'.

4. OQSU → There are two consonants i.e 'Q' and 'S' and two vowels i.e 'O' and 'U'.

∴ Here, "MOQS" is different from other three alternatives.

Hence, the correct answer is "MOQS".

Conclusion:

I. Travellers without a passport will not be allowed to enter the airport for international traveling.

Yes, Travellers without a passport will not be allowed to enter the airport for international travelling.

II. It is mandatory to carry the passport to the airport for international travel.

This conclusion is mandatory or compulsory for the travelers to carry the passport to the airport.

Hence, Both conclusions I and II follow.

The usage of "Must" in the question statement tells us that it is mandatory or compulsory.

The logic followed here is:

For, 'QUIRKY' is coded as 'TCLZNG',

For, 'MUZHIK' is coded as 'PCCPLS',

Similarly, for 'FROWZY'

So, 'FROWZY' will be coded as 'IZRECG'.

Hence, the correct answer is "Option 2".

The pattern followed here is -

2 × 3 = 6

3 × 4 = 12

4 × 5 = 20

5 × 6 = 30

6 × 7 = 42

7 × 8 = 56

Hence, “56” is the missing term

1. Green box is at the bottommost position.

2. Four boxes are kept between Blue and Yellow where blue is above yellow.

3. Only the Indigo box is between the violet and Yellow box.

4. Orange box is in the second position from the top.

The red box is in the third position from the top.

Hence, ‘Third’ is the correct answer.

Preparing the family tree using the following symbol:

According to the given information,

Expression: T × P ÷ R + Q - S

T is the mother of P, P is the wife of R, R is the father of Q, and Q is the brother of S.

Hence, Q is the grandson of T.

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

Statement:

Only a few Shirt are Jacket

Some Jackets are Coat.

All Shirt are Skirts.

Conclusion:

I) Some Jackets are Shirt → Follow → As only a few Shirt are Jacket and Some Jackets are Coat. So Some Jackets are Shirt is definitely followed.

II) All Shirt are Jackets is a Possibility → Does not follow → As Only a few Shirt are Jacket. So only specific part of Shirt is Jackets not All Shirts are Jackets. So All Shirt are Jackets is a Possibility is definitely not followed.

III) All Skirts are Jackets is a Possibility → Does not follow ​→ As Only a few shirt are JAcket, Some Jackets are Coat and All Shirts are Skirts. So All Skirts are Jackets is not possible because All Jackes have to be Skirts and it is not possible that All shirt are also Jackets. So it is definitely not followed.

So, Only conclusion I followed.

Hence, the correct answer is "Option 3".

Important Points1) "Only a few" means is the combination of "Some" and "Some not".

2. Example:- Only a few A are B means Some A are B and Some A are not B.

3. Only a few A are B means only a specific part of A is B and the remaining part of the A is not B.

The logic followed here is:

'BANYAN' is written as 'EDQBDQ',

‘LAUNCH' is written as 'ODXQFK’

Similarly, for 'STRIKER'

So, 'STRIKER' will be written as 'VWULNHU'.

Hence, the correct answer is "Option 1".

The pattern followed here is:

Let's check each option one by one.

Option 1) 7 & 8

Given: 75 ÷ 18 + 51 × 8 - 82 = 87

After interchanging the digit we get;

⇒ 85 ÷ 17 + 51 × 7 - 72 = 87

⇒ 5 + 51 × 7 - 72 = 87

⇒ 5 + 357 - 72 = 87

⇒ 362 - 72 = 87

⇒ 290 ≠ 87

⇒ LHS ≠ RHS

Option 2) 1 & 5

Given: 75 ÷ 18 + 51 × 8 - 82 = 87

After interchanging the digit we get;

⇒ 71 ÷ 58 + 15 × 8 - 82 = 87

⇒ 1.22 + 15 × 8 - 82 = 87

⇒ 1.22 + 120 - 82 = 87

⇒ 121.22 - 82 = 87

⇒ 39.22 ≠ 87

⇒ LHS ≠ RHS

Option 3) 5 & 2

Given: 75 ÷ 18 + 51 × 8 - 82 = 87

After interchanging the digit we get;

⇒ 72 ÷ 18 + 21 × 8 - 85 = 87

⇒ 4 + 21 × 8 - 85 = 87

⇒ 4 + 168 - 85 = 87

⇒ 172 - 85 = 87

⇒ 87 = 87

⇒ LHS = RHS

Option 4) 8 & 2

Given: 75 ÷ 18 + 51 × 8 - 82 = 87

After interchanging the digit we get;

⇒ 75 ÷ 12 + 51 × 2 - 28 = 87

⇒ 6.25 + 51 × 2 - 28 = 87

⇒ 6.25 + 102 - 28 = 87

⇒ 108.25 - 28 = 87

⇒ 80.25 ≠ 87

⇒ LHS ≠ RHS

Hence, the correct answer is "5 & 2".

Seven people – G, H, J, K, L, M and N

1) K is sitting fourth to the left of N.

2. G is sitting immediate left of K.

3. Two people are sitting between M and G.

4. The number of people sitting between H and J is the same as the number of people sitting between J and L.

5. H is not sitting at any of the extreme ends.

Condition (4) is not satisfying in case I, so it gets eliminated and we have the final arrangement as follows:

Hence, "J, L, N" is the correct answer.

As per the given information;

Distance between initial and final point = √(20² + 15²)

= √(400 + 225)

= √625

= 25 km

Hence, "25 km, South East" is the correct answer.

Tuberculosis is Lungs disease.

Similarly, Cataract is Eyes disease.

Thus, the correct answer is "Eyes".

I. Education Boards should examine and revise examination system to tap the real talent.

It follows as it would remove the defects of the examining system.

II. Examination system at all levels should be so designed as to discourage rote learning.

It follows as it would eliminate rote learning and encourages quality learning.

Hence, if both I and II follow.

The correct answer is Bhils.

Key Points

• Ladaladi is a folk dance of the Bhil community, performed during weddings.
• It is a unique tradition where the bride and bridegroom are lifted upon the shoulders of the dancers.
• The dance symbolizes celebration and happiness and brings the community together to mark the joyous occasion.
• The Bhils are one of the largest tribal groups in India, predominantly found in the states of Rajasthan, Madhya Pradesh, Gujarat, and Maharashtra.
• The Bhil community is known for its rich cultural heritage, including dances, songs, and storytelling.
• Their dances often depict scenes from their lives, such as agriculture, hunting, and festivals, showcasing the tribal connection to nature and tradition.
• The Ladaladi dance is performed with a lot of energy and vibrancy, accompanied by traditional music and instruments.

 Additional Information

• Garos
• The Garos are a tribal group mainly found in Meghalaya, with some presence in Assam and Bangladesh.
• They are known for their Wangala dance, which is a harvest festival dance performed to honor Sun God Saljong.
• The Garo tribe is recognized for its strong connection to nature and its unique cultural practices.
• Santal
• The Santal tribe is one of the largest tribal communities in India, primarily found in Jharkhand, Odisha, West Bengal, Bihar, and Assam.
• They are famous for their Santal dance, performed during various festivals and rituals, often accompanied by traditional instruments like the flute and drum.
• The Santals have a rich tradition of folk songs, dances, and storytelling, which reflect their close bond with nature and agricultural practices.
• Chakma
• The Chakma community is primarily found in the northeastern states of India, especially in Mizoram, Arunachal Pradesh, and Tripura, along with regions in Bangladesh.
• They are known for their Buddhist cultural practices and have dances reflecting their religious beliefs.
• The Chakma dances are often performed during festivals such as Buddha Purnima and other cultural celebrations.

The correct answer is Prime Minister.

• Jawaharlal Nehru was the first Prime Minister of India.
• He is the Prime Minister who has had the longest term in office.
• He served as the prime minister of India from 15^th August 1947 to 1964.
• He is the architect of the Preamble of the Indian constitution.
• He was the Prime Minister of India during the Indo-China war in 1962.
• He served as the first chairman of the planning commission of India.
• He was honored with the Bharat Ratna in 1955.
• The name Panchayati raj was given by Jawaharlal Nehru.
• National herald is the newspaper started by Jawaharlal Nehru.
• He is the first prime minister to die in harness.
• Shantivan is the cremation ground of Jawaharlal Nehru.

The correct answer is Rekha Gupta

In News

• Rekha Gupta to take oath as Delhi’s 4th woman Chief Minister, marking BJP’s return to power in Delhi after 27 years.

Key Points

• Won Shalimar Bagh seat by over 29,000 votes, defeating AAP’s Bandana Kumari in the February 5 Delhi Assembly elections.
• Oath ceremony at Ramlila Maidan attended by PM Modi, BJP leaders, and former CMs Arvind Kejriwal & Atishi.
• Council of Ministers includes Parvesh Verma, Ashish Sood, Pankaj Singh, Manjinder Singh Sirsa, Kapil Mishra, and Ravinder Indraj.
• Gupta, a former DUSU president & municipal councillor, was chosen as BJP’s legislative party leader on Wednesday.
• She emphasized transparency, stating that the previous government must account for every rupee spent.
• Lt. Governor VK Saxena invited her to form the government after she staked her claim at Raj Niwas.

The Correct answer is Initial velocity.

Key Points

• In the equation s = ut + 1/2 at², u stands for the initial velocity of the object.
• This equation is one of the fundamental equations of motion in classical mechanics, often referred to as the second equation of motion.
• The term s represents the displacement or position change of the object.
• The term t represents the time duration over which the motion occurs.
• The term a stands for the acceleration of the object.
• The equation combines initial velocity (u), acceleration (a), and time (t) to determine the displacement (s).
• This equation is derived from the basic principles of Newtonian mechanics.

 Additional Information

• Uniform acceleration
• Uniform acceleration refers to a constant rate of change in velocity.
• In equations of motion, acceleration (a) is often assumed to be uniform.
• Speed of the object
• Speed is a scalar quantity representing how fast an object is moving.
• Speed does not include direction, unlike velocity, which is a vector quantity.
• Change in momentum
• Momentum is the product of the mass and velocity of an object.
• The change in momentum is often described by the impulse-momentum theorem.

The correct answer is The Pacific Ocean.

Key Points

• The El Niño current is not a traditional ocean current like the Gulf Stream or the California Current. Instead, it is part of the El Niño-Southern Oscillation (ENSO) climate pattern, which involves changes in ocean and atmospheric conditions in the tropical Pacific Ocean.
• During an El Niño event, warm waters from the western Pacific Ocean move eastward and flow along the equator towards the coast of South America. This warm current can disrupt normal weather and ocean patterns, leading to various climate-related effects around the world.
• It's important to note that El Niño is just one phase of the ENSO, with La Niña being its counterpart, where cooler waters dominate the central and eastern Pacific.
• The specific path and strength of the El Niño current can vary from one event to another, but it typically flows from west to east along the equator in the tropical Pacific Ocean, affecting weather and climate patterns in different regions, including the Americas, Australia, and Asia.
• El Nino was first recognized by Peruvian fishermen off the coast of Peru as the appearance of unusually warm water.
• The Spanish immigrants called it El Nino, meaning “the little boy” in Spanish.
• El Nino soon came to describe irregular and intense climate changes rather than just the warming of coastal surface waters.
• The El Nino event is not a regular cycle, they are not predictable and occur irregularly at two- to seven-year intervals.
• The climatologists determined that El Nino occurs simultaneously with the Southern Oscillation.
• The Southern Oscillation is a change in air pressure over the tropical Pacific Ocean.
• When coastal waters become warmer in the eastern tropical Pacific (El Nino), the atmospheric pressure above the ocean decreases.
• Climatologists define these linked phenomena as El Nino-Southern Oscillation (ENSO).

Additional Information Impact of El Nino: In order to understand the concept of El Nino, it’s important to be familiar with non-El Nino conditions in the Pacific Ocean.

• Normally, strong trade winds blow westward across the tropical Pacific, the region of the Pacific Ocean located between the Tropic of Cancer and the Tropic of Capricorn.
• Impact on Ocean: El Nino also impacts ocean temperatures, the speed and strength of ocean currents, the health of coastal fisheries, and local weather from Australia to South America and beyond.
• Increased Rainfall: Convection above warmer surface waters brings increased precipitation. Rainfall increases drastically in South America, contributing to coastal flooding and erosion.
• Diseases caused by Floods and Droughts: Diseases thrive in communities devastated by natural hazards such as flood or drought.
• El Nino-related flooding is associated with increases in cholera, dengue, and malaria in some parts of the world, while drought can lead to wildfires that create respiratory problems.
• Positive impact: It can sometimes have a positive impact too, for example, El Nino reduces the instances of hurricanes in the Atlantic.
• In South America: As El Nino brings rain to South America, it brings droughts to Indonesia and Australia.

The correct answer is 2) Lizard

Key Points

• Lizard is not a mammal; it is a reptile.
• Mammals are warm-blooded vertebrates that have hair or fur and whose females have mammary glands for feeding milk to their young.
• Examples of mammals include dolphins, bats, and elephants, all of which give birth to live young and have body hair at some stage of their life.
• Reptiles, like lizards, are cold-blooded and lay eggs. They have scales and do not possess mammary glands.

Additional Information

• Dolphins are aquatic mammals known for their intelligence and social behavior.
• Bats are the only mammals capable of sustained flight and are found in almost every part of the world.
• Elephants are the largest land mammals, known for their intelligence, social structure, and long trunks.
• Lizards belong to the order Squamata and are commonly found in various habitats around the world.
• Mammals and reptiles are both classes of vertebrates but differ significantly in their physiology and reproductive methods.

The correct answer is Mridangam

Key Points

• Anantha R Krishnan is a renowned musician associated with the Mridangam.
• The Mridangam is a classical percussion instrument from South India, widely used in Carnatic music performances.
• It is a double-headed drum, with one head producing a bass sound and the other producing a treble sound.
• Anantha R Krishnan is celebrated for his skill and innovative techniques on the Mridangam, contributing to its prominence in classical music.

Additional Information

• The Mridangam has a rich history and is considered the primary rhythmic accompaniment in Carnatic concerts.
• It is traditionally made from jackfruit wood and has heads made of layers of animal skin.
• In addition to Carnatic music, the Mridangam is also used in Bharatanatyam dance performances and other South Indian classical art forms.
• Modern Mridangam players, including Anantha R Krishnan, have incorporated contemporary techniques to expand the instrument's versatility.

The correct answer is Only 1.

Key Points

• Gudi Padwa marks the beginning of the Hindu New Year, as per the lunisolar calendar followed in Maharashtra and some other regions of India.
• The festival is celebrated on the first day of the Chaitra month, which typically falls in March or April.
• The term "Gudi" refers to a flag or banner-like structure decorated with a colorful cloth, flowers, and a copper or silver pot, symbolizing victory and prosperity.
• It does not involve the recitation of a sacred scripture as implied in the question, nor does the celebration traditionally begin with the consumption of sweets for good luck.
• Gudi Padwa is also associated with the arrival of spring and the harvest season, making it a time of joy and renewal for the community.

Additional Information

• Lunisolar Calendar: The Hindu calendar combines both lunar and solar movements to determine months and years. Gudi Padwa is based on this system.
• Chaitra Navratri: Gudi Padwa also marks the beginning of Chaitra Navratri, a nine-day festival dedicated to Goddess Durga.
• Symbolism of the Gudi: The Gudi symbolizes victory and is believed to ward off evil, attract prosperity, and signify the triumph of good over evil.
• Regional Variations: While Gudi Padwa is celebrated in Maharashtra, similar festivals are observed in other parts of India, such as Ugadi in Karnataka and Andhra Pradesh, and Cheti Chand among the Sindhi community.
• Cultural Practices: The festival includes cleaning homes, decorating with rangoli, hoisting the Gudi, and preparing traditional dishes like puran poli and shrikhand.

The correct answer is Aadhaar Governance Portal​.

In News

• The Ministry of Electronics and Information Technology (MeitY) has launched the Aadhaar Governance Portal (http://swik.meity.gov.in) to streamline Aadhaar authentication approvals.

Key Points

• Aadhaar Governance Portal​ aims to simplify the approval process for Aadhaar authentication requests for both government and private entities.
• The portal was launched following amendments to the Aadhaar Authentication for Good Governance Rules, 2025, under the Aadhaar Act of 2016.
• It enables the use of Aadhaar authentication for public services like healthcare, education, e-commerce, and hospitality.
• The platform provides step-by-step guidance for Aadhaar authentication approval and onboarding.

Additional Information

• Aadhaar Authentication
• A process to verify a person’s identity using Aadhaar-based biometric or demographic data.
• Used for e-KYC verification, staff attendance, and customer onboarding.
• Unique Identification Authority of India (UIDAI)
• Established under the Aadhaar Act, 2016.
• Responsible for issuing Aadhaar numbers and managing authentication services.
• Ministry of Electronics and Information Technology (MeitY)
• Oversees digital governance initiatives in India.
• Supports Aadhaar’s integration into various sectors to improve service delivery.

The correct answer is Chatkora.

Key Points

• Chatkora is a traditional dance form performed by the Korku tribe.
• The Korku tribe is primarily found in the Indian states of Madhya Pradesh and Maharashtra.
• Chatkora dance is often performed during festivals and community gatherings, reflecting the cultural heritage of the tribe.
• This dance form is characterized by its vibrant movements and rhythmic patterns.

Additional Information

• Korku Tribe
• The Korku tribe is an indigenous tribal community in India, recognized as one of the Scheduled Tribes.
• They primarily inhabit the regions of the Satpura range in Madhya Pradesh and parts of Maharashtra.
• Their traditional occupation includes farming, hunting, and gathering forest products.
• The Korkus have their own distinct language called "Korku," which belongs to the Munda language family.
• Traditional Dances of Tribes in India
• Tribal dances in India are an integral part of their culture and are performed during festivals, rituals, and social gatherings.
• These dances often convey stories, celebrate nature, and express communal harmony.
• Examples include the Santal dance by the Santal tribe and the War dance by the Nagas.
• Preservation of Tribal Culture
• The Indian government and various non-governmental organizations are actively working towards preserving the rich cultural heritage of tribal communities.
• Efforts include documentation, promoting traditional art forms, and providing platforms for showcasing their culture.
• Tribal museums and cultural festivals are organized to exhibit their traditions and crafts.

The correct answer is Mahadevi Verma.

• "Nirja" the book is written by Mahadevi Verma.

Key Points

Some famous books by Mahadevi Verma:

• Path Ke Sathi,
• Atit Ke Chalchitra,
• Agnirekha,
• Gillu,
• Atmika,
• Sandhini.

The Correct Answer is 9^th.

• The  9th five-year plan focused on Growth with Social Justice and Equity.

Important Points

9th Five year Plan

• The Ninth five-year plan was started with an objective of “Growth with Social Justice and Equality”.
• The growth in agriculture also got importance in this plan.
• Regulation of the debt program was emphasized to improve the government’s financial position.
• The policies undertaken were pro-poor and aimed at the correction of historical inequalities.

Additional Information

Eighth Five Year Plan (1992-1997)

• The 8th Plan was a plan for managing the transition from a centrally planned economy to a market-led economy through indicative planning.
• The growth rate achieved was 6.8% against the target of 5.6%.

Tenth Five Year Plan (April 1, 2002, to March 31, 2007)

• The Tenth Plan was launched by Atal Bihari Vajpayee Government on December 21, 2002.
• The economy accelerated in the Tenth Plan period to record an average growth of 7.7%.

Eleventh Five year Plan (2007 -2012)

• India entered the Eleventh Plan period with an impressive record of economic growth.
• The growth rate of the economy averaged 8 percent in the Eleventh Plan period.

The Correct Answer is Haryana.

In News

• Khelo India Para Games 2025 concludes, 18 national records broken.

Key Points

• The Khelo India Para Games 2025 concluded at JLN Stadium, New Delhi.
• 18 national records were broken during the event.
• The second edition of the Khelo India Para Games saw more than 550 medals being secured by para-athletes.
• Haryana topped the medal tally with 34 gold, 39 silver, and 31 bronze medals.
• Tamil Nadu secured second place with 28 gold, 19 silver, and 27 bronze medals.
• Uttar Pradesh finished third with 23 gold, 21 silver, and 20 bronze medals.
• More than 1,300 para-athletes participated in the event, competing across six sports: Para Archery, Para Athletics, Para Badminton, Para Powerlifting, Para Shooting, and Para Table Tennis.

The correct answer is China.

Key Points

• China:
• The "Yuan" is the official currency of the People's Republic of China.
• It is also known as Renminbi, which means “the people's currency” in Mandarin.
• The capital of China is Beijing.

Additional Information

The correct answer is Option 1 (MayilAttam dance - Madhya Pradesh).

Key Points

• MayilAttam dance:
• The MayilAttam dance, also known as the "peacock dance," is a traditional folk dance form associated with the state of Tamil Nadu, not Madhya Pradesh.
• It is performed by dancers wearing costumes resembling peacocks, and the movements imitate the graceful actions of the peacock.
• It is closely linked to the religious and cultural traditions of Tamil Nadu, particularly in temple festivals and celebrations. Hence, Option 1 is incorrect.
• Fugdi dance:
• The Fugdi dance is a traditional folk dance performed by women in the Indian state of Goa.
• It is usually performed during festivals like Ganesh Chaturthi and other religious occasions, showcasing energetic movements and rhythmic clapping. Hence, Option 2 is correct.
• Dandiya dance:
• The Dandiya dance, or "Dandiya Raas," is a popular folk dance originating from the state of Gujarat.
• It is performed during Navratri celebrations and involves dancers using decorated sticks to create rhythmic sounds while dancing. Hence, Option 3 is correct.
• Rouff dance:
• The Rouff dance is a traditional dance form of the Indian state of Jammu and Kashmir.
• It is performed by women during festive seasons, showcasing graceful movements and vibrant costumes. Hence, Option 4 is correct.

Additional Information

• MayilAttam Dance:
• This dance form is performed mainly by young women, dressed in peacock-like costumes, including feathers and vibrant clothing.
• It is an integral part of Tamil Nadu’s folk culture and often performed during temple festivals dedicated to Lord Murugan (a deity associated with Tamil Nadu).
• The dance requires intricate and graceful movements to mimic the peacock's elegance.
• Fugdi Dance:
• Performed by women in rural areas of Goa, Fugdi dance is a representation of Goan traditions.
• Women stand in circular or linear formations while clapping and singing traditional songs.
• It is a recreational activity, often performed to celebrate the harvest or during religious festivals.
• Dandiya Dance:
• Dandiya Raas is closely associated with Navratri celebrations in Gujarat, symbolizing the playful interactions between Lord Krishna and the gopis.
• Dancers use colorful sticks, and the performance involves coordinated movements in pairs or groups.
• This dance form has gained popularity globally, with events organized in various countries during Navratri.
• Rouff Dance:
• This dance form reflects the rich cultural heritage of Jammu and Kashmir.
• The Rouff dance is performed by women, typically in groups, with synchronized movements and traditional Kashmiri attire.
• It is performed during festivals and important occasions, showcasing the region’s grace and elegance.

Important Points

• Geographical and Cultural Significance:
• Each dance form is deeply rooted in the local traditions and reflects the cultural identity of its respective region.
• These dances are not only recreational but also serve as a medium to preserve and promote regional history and values.
• National Integration:
• Folk dances like these contribute to national unity by showcasing the diversity of India's culture.
• They are celebrated and appreciated across states, fostering a sense of mutual respect for different traditions.

The correct answer is 55.

Key Points

• 55 was the estimated national mortality rate of children under the age of five in the country as per the Census of India 2011.
• In 1990 this rate was 126.
• According to World Bank's data, the mortality rate or crude death rate in India is 7.30 per 1000 persons per year.
• In India, approximately 26789 deaths are reported per day.
• Infant mortality rate
• ​Infant mortality rate (IMR) is the number of deaths per 1,000 live births of children under one year of age.
• The rate for a given region is the number of children dying under one year of age, divided by the number of live births during the year, multiplied by 1,000.

The Formula for calculating the infant mortality rate is:

• IMR = the number of infant mortality/the number of infants in mid-year × 1000

Additional Information

• Census of India, 2011:
• Total Population of India was 1,210,193,422.
• The Sex Ratio (females per thousand males) in India was 943.
• The population density was reported at 382 persons per sq. km.
• Total districts covered- 640.
• Crude Birth Rate- 21.8.
• Crude Death Rate 7.1 per thousand population
• The national mortality rate of children under the age of five is 55.
• The literacy rate of the country is 74.04 per cent. (82.14 for males and 65.46 for females).
• The state with the highest literacy is Kerala (94.0%)
• The state with the lowest literacy is Bihar (61.8%)
• state with the highest female literacy rate- Kerala (92.1%)
• The state with the lowest female literacy is Bihar(51.5%)
• The state that has the highest decadal growth is Meghalaya (27.9%)
• State having highest Population  Uttar Pradesh (19,98,12,341)
• The state has the lowest population is Sikkim (6,10,577)
• State with Highest Population Density Bihar (1106). Hence Option 4 is incorrect.
• State with Lowest Population Density  Arunachal Pradesh (17)
• The state has the highest Sex Ratio is Kerala (1,084)
• The state has the lowest Sex Ratio  is Haryana (879)
• The highest Death Rate among states is in Odisha (98 per thousand).
• The lowest Death Rate among states is in Kerala— 16 per thousand.
• The decadal growth rate in Population is 17.7%.
• The state has the lowest population decadal growth rate in Nagaland (–0.47%).

The correct answer is Mahasweta Devi.

• Mahasweta Devi is the author of the book 'The Why-Why Girl'.

Other books by Mahasweta Devi :

• Mother of 1084
• The queen of Jhansi
• Imaginary Maps
• Rudali
• Chotti Munda and his arrow.
• Aranyer Adhikar
• Titu Mir

Additional Information

The Correct Answer is ​Virat Kohli.

In News

• Virat Kohli made history with the most fifty-plus scores in IPL against Punjab.

Key Points

• Virat Kohli set a new IPL record for the most fifty-plus scores.
• Achieved the feat during a match vs Punjab Kings (PBKS) at Mullanpur.
• He surpassed David Warner, who has 66 fifty-plus scores (includes 4 centuries).
• Shikhar Dhawan is third with 53 fifty-plus scores, including 2 centuries.

Important Points

• The IPL 2025 season came to an end with Royal Challengers Bengaluru triumphing over Punjab Kings in a memorable final, with Krunal Pandya winning his second Final player of the match award for a special display of defensive spin bowling to finish with figures of 2-17.
• Winner: Royal Challengers Bengaluru
• Runner Up: Punjab Kings
• Most Valuable Player: Suryakumar Yadav (MI) – 717 runs, avg 65, SR 168
• Purple Cap: Prasidh Krishna (GT) – 25 wickets
• Emerging Player: Sai Sudharsan (GT) – 759 runs
• Super Striker: Vaibhav Suryavanshi (RR) – 206.6 SR
• Most Sixes: Nicholas Pooran (LSG) – 40 sixes
• Most Fours: Sai Sudharsan (GT) – 88 fours
• Most Dot Balls: Mohammed Siraj (GT) – 151 dot balls
• Catch of the Season: Kamindu Mendis (SRH) vs Dewald Brevis
• Fairplay Award: Chennai Super Kings
• Fantasy King: Sai Sudharsan (GT) – 1495 points

The Correct Answer is Waqf by user.

In News

• Lok Sabha Passes Waqf (Amendment) Bill 2025.

Key Points

• Amendment Purpose: The Bill amends the Waqf Act of 1995 to improve the management and transparency of Waqf properties in India.
• Removal of "Waqf by User": Properties continuously used as Waqf (e.g., mosques) now require official documentation (Waqfnama) to be recognized as Waqf.
• Survey of Properties: The District Collector or other senior officers will now oversee the survey of Waqf properties, replacing the Survey Commissioner.
• Non-Muslim Representation: Non-Muslim Chief Executive Officers and members may now be appointed to state-level Waqf Boards.
• Limitation Act (1963): The Bill makes the Limitation Act applicable to Waqf properties, allowing claims of unlawful possession after 12 years.
• Section 107 Deleted: The deletion allows the Limitation Act to apply to Waqf properties, enabling claims of adverse possession.
• Government’s Rationale: The amendments are aimed at addressing loopholes such as title disputes and illegal occupations of Waqf properties.
• Transparency Measures: The Bill mandates a unified digital listing of Waqf properties to reduce litigation and improve transparency.
• Criticism: Opposition argues the Bill gives the government too much power over Waqf properties, potentially undermining Muslim community rights.
• Disputed Properties: The government (through the District Collector) will treat disputed Waqf properties as government property until resolved.

Rani Lakshmi Bai

• She was a queen of the Maratha princely state of Jhansi in North India.
• She was one of the leading figures of the 1857 revolt.
• She led the Jhansi against Sir Hugh Ross in the Indian Rebellion of 1857.
• In 1858, General Hugh Rose came and demanded that Jhansi should surrender and bombarded Jhansi and seized the Jhansi fort.
• An army which was headed by Tantia Tope to free Jhansi was defeated by the British forces.
• The tomb of Rani Laxmi Bai is located at Phool Bagh garden, Gwalior.

The correct answer is DRDO

In News

• The HimKavach multi-layer clothing system is designed for extreme cold conditions, with a functional temperature range from +20°C to -60°C.

Key Points

• Modular Design: The system’s layers are adjustable, allowing soldiers to modify clothing based on the weather, which is crucial for high-altitude regions like the Himalayas.
• Enhanced Protection: HimKavach offers broader protection compared to the previous Extreme Cold Weather Clothing System (ECWCS), ensuring better mobility, comfort, and operational readiness.
• Successful Trials: The system has successfully cleared all user trials in actual operational settings, providing improved insulation and comfort.
• Operational Readiness: HimKavach is designed to enhance the safety and effectiveness of soldiers in high-altitude, extreme cold regions, addressing ongoing security concerns along India’s Himalayan borders.
• Deployment Expected Soon: The clothing system will soon be deployed to improve mobility, durability, and efficiency for troops stationed in harsh environments.

The correct answer is Karnataka.

• Kambala is an annual buffalo race held traditionally in the Karnataka state of India.

Key Points

• Kambala is an annual buffalo race held in the southwestern Indian state of Karnataka.
• Traditionally, it is sponsored by local Tuluva landlords and households in the coastal districts of Dakshina Kannada and Udupi of Karnataka and Kasaragod of Kerala and Kannada landlords of Kundapura region.
• Traditional Kambala was non-competitive, and the pair was run one by one.
• In modern Kambala, the contest generally takes place between two pairs of buffaloes.
• In villages such as Vandaro and Choradi, there is also a ritualistic aspect, as farmers race their buffaloes to give thanks for protecting them from diseases.

Important Points

• The event was recently in news, when after the ban on Jallikattu; the Animal Welfare Board of India (AWBI) has asked the Karnataka government to ban the race citing reasons of cruelty to animals.

The correct answer is Mandapa - ​ Place in temples where people could assemble.

Key Points

• Stupa: 
• Stupas were burial mounds prevalent in India from the Vedic period.
• Stupas consist of a cylindrical drum with a circular Anda and a Harmika and a Chhatra on the top.
• Anda: Hemispherical mound symbolic of the mound of dirt used to cover Buddha’s remains (in many stupas actual relics were used).
• Harmika: Square railing on top of the mound.
• Chhatra: Central pillar supporting a triple umbrella form.
• Material Used: The core of the stupa was made of unburnt brick while the outer surface was made by using burnt bricks, which were then covered with a thick layer of plaster and medhi and the toran were decorated with wooden sculptures.
• Shikhara
• It is a Sanskrit word that means mountain peak. It is the most prominent and visible part of a Hindu temple of North India. In south India, it is the same as Vimana.
• Shikhara is the rising tower in the Hindu temple architecture of North India.
• It is also used in Jain temples.
• Shikhara is over Garbhagriha.
• Garbhagriha is the innermost sanctuary of a Hindu and Jain temple where the primary deity of the temple is kept.
• Shikhara can be classified into three main forms - Latina, Sekhar, and Bhumija.
• Shikharas form an element in the many styles of Hindu temple architecture, the three most common styles are the Nagara, the Vesara, and the Dravidian. By at least 600 CE in Odisha the Latina form of shikhara was well established.
• Mandapa
• Indian architecture, especially Hindu temple architecture is a pillared hall or pavilion for public rituals.
• Place in temples where people could assemble.
• Mandapas are described as open or closed depending on whether they have walls. In temples, one or more mandapas very often lie between the sanctuary and the temple entrance, on the same axis.
• Garbhagriha
• The innermost sanctum of the Hindu temples where the idol or murti of the main deity is placed is called the Garbhagriha.
• It is also called the womb chamber of the temple. Only the priests are allowed to enter this chamber.
• The Garbhagriha is a single chamber with the room facing towards the east to get the rising sun.
• There are no windows and hardly any access to any lights. The room is a square one and the deity is normally placed at the center for the visitors to see.
• The Garbhagriha is the most important and sacred space where the deity is worshipped.
• All the offerings to the deity are made inside here. The Vastushastra refers to the ancient science of architecture. It deals with the building of forts, towns, and other construction too.
• It also connects the philosophy of architecture with cosmic values. For female deities, the Garbhagriha is a rectangular one.
• In Tamil, the garbhagriha is called karuvarai.
• Pradakshina Patha
• It is an important architectural feature of a Hindu Temple. It is the term used to refer to the passage around the garbha griha or the sanctum sanctorum in a Hindu temple.
• The passage is essentially provided for performing pradakshina (going around the deity).
• While walking on the Pradakshina Patha the devotee establishes divine communion with the deity seated or standing in the sanctum sanctorum.
• The various forms for the deity and other aspects carved on the outer walls of the sanctum and in some instances even on the Pradakshina Patha act as points of concentration which helps in guiding the devotee towards the main murti enshrined in the garbhagriha.

The correct answer is Jharkhand.

Key Points

• The Tusu festival is primarily observed in Assam, the Tea-producing State, Northeastern Odisha, Southwest West Bengal, and Southeast Jharkhand.
• During this occasion, the goddess Tusu is worshipped. The focus is primarily on rivers. It is a unified expression of the agrarian society's shared trust and belief in the pleasure of crop gathering.
• It is thought that the term "Tusu" derives from the word "tush" for rice bran. Both a youthful child and a cosmic deity are representations of the Goddess Tusu.
• The ceremonies carried out during the Tusu Puja center on harvest-related ceremonies and songs of ethnic dedication chanted by women folk.
• Therefore, the Tusu festival is associated with Jharkhand.

Additional Information

State-Specific Festivals of India

• In the presence of an acid, a blue litmus paper turns into red.
• Litmus is made up of weak organic acid molecule.
• Litmus acts as an indicator and it reacts with an acid (H+) and shows a different colour when it is deprotonated or protonated under acidic conditions

The correct answer is Article 249.

Key Points

• Article 249 of the Indian Constitution empowers Parliament to legislate on matters in the State List if it is deemed necessary in the national interest.
• For such legislation, a resolution must be passed by the Rajya Sabha by a majority of not less than two-thirds of the members present and voting.
• The resolution gives Parliament the authority to legislate on the specified matter for a period of one year, which may be extended by subsequent resolutions.
• This provision is primarily used in circumstances where uniformity of law across states is essential for national interest.
• Examples include situations related to national security, economic stability, or environmental concerns requiring coordinated legal measures across states.

Additional Information

• State List:
• The State List is one of the three lists under the Seventh Schedule of the Indian Constitution, detailing subjects on which states can legislate.
• Examples of subjects include police, public health, agriculture, and local government.
• Union List:
• This list includes subjects on which only the Parliament has the exclusive power to legislate.
• Examples include defense, foreign affairs, and atomic energy.
• Concurrent List:
• Subjects on this list can be legislated upon by both the Parliament and state legislatures.
• Examples include education, forest conservation, and marriage laws.
• Emergency Provisions:
• Under Article 352 (National Emergency), Parliament can legislate on State List matters without requiring a resolution from the Rajya Sabha.
• This demonstrates the flexibility of the Indian Constitution in extraordinary circumstances.
• Article 123:
• This article empowers the President of India to promulgate ordinances during the recess of Parliament.
• These ordinances have the same force and effect as laws passed by Parliament but must be ratified within six weeks of the next session.

CONCEPT:

Friction on Wet Surfaces

• Friction: The force that opposes the relative motion or tendency of such motion of two surfaces in contact.
• Effect of Water: Water can act as a lubricant, significantly reducing the friction between surfaces.

EXPLANATION:

• Walking on a dry marble floor involves sufficient friction to prevent slipping.
• When water is present on the marble floor, it creates a layer between the sole of the shoe and the marble.
• This layer of water acts as a lubricant, reducing the friction between the surfaces, making it difficult to walk without slipping.

​ 

Additional Information

• Option 1: Friction does not increase dramatically; in fact, it decreases.
• Option 3: The texture of the marble does not change when wet.
• Option 4: Water reducing friction, not increasing it, so it does not act to increase friction.

The correct option is: 2) Because the water reduces friction significantly.

The Correct Answer is ​Glacier Preservation.

In News

• World Water Day, celebrated on 22 March every year since 1993, focuses on the importance of freshwater.

Key Points

• World Water Day is celebrated on 22 March every year, focusing on the importance of freshwater.
• The core focus is to support the achievement of Sustainable Development Goal 6: water and sanitation for all by 2030.
• The theme for World Water Day 2025 is ‘Glacier Preservation’.
• The UN-Water’s flagship World Water Development Report 2025 is titled ‘Water Towers: Mountains and glaciers’.
• World Water Day was established in 1992 by the United Nations during the Conference on Environment and Development in Rio de Janeiro, Brazil.
• The first observance of World Water Day took place on 22 March 1993.

The correct answer Shooting.

Key Points 

• Avani Lekhara is from Jaipur, Rajasthan.
• As 19-year-old Avani Lekhara won the gold medal in women’s 10 m air rifle Standing event in the SH 1 category at the Tokyo Paralympics.
• She became the first Indian woman to win a gold medal at the Paralympics.
• Avani shot 249.6 points in the R2 women’s 10m air rifle SH1 category for a Paralympic Record and equal the World Record.
• In the final, she led from the start and edged out China’s Zhang C and Ukraine’s I Shchetnik in the medal series to win the gold.
• Avani has won many World Cup medals since 2017 including a Silver with a Junior World Record in R2 at the WSPS World Cup 2017, bronze at the WSPS World Cup Bangkok 2017, silver in the WSPS World Cup in Osijek, Croatia 2019 and silver in the WSPS World Cup Al-Ain 2021. She won the Tokyo Paralympics quota in February 2019 in the UAE.
• In 2012, the whole Lekhara family met with an accident on their way to Dholpur from Jaipur.
• The then 11-year-old Avani suffered a spinal cord injury and was paralysed below the waist.

The Correct answer is Registration.

Key Points

• Renunciation: A person can voluntarily renounce their Indian citizenship by making a declaration of renunciation.
• Once the renunciation is accepted by the Indian government, the person ceases to be a citizen of India.
• Termination: Termination of citizenship can occur if a person voluntarily acquires the citizenship of another country and notifies the Indian government of their intention to renounce Indian citizenship.
• The Indian government has the authority to terminate citizenship in such cases.

Additional Information

• Registration: Registration is a process by which a person who is not automatically eligible for Indian citizenship can acquire it through a specific provision of the law.
• This does not lead to the loss of citizenship but rather grants citizenship to the individual.
• Deprivation: Deprivation of citizenship can occur in certain circumstances if a person obtained Indian citizenship through fraud, false representation, or concealment of material facts.
• However, this process involves legal proceedings and does not apply automatically.
• Therefore, the correct answer is option 3) Registration.

 Important Points

• Citizenship is listed in the Union List under the Constitution.
• The Constitution does not define the term ‘citizen’ but details of various categories of persons who are entitled to citizenship are given in Part 2 (Articles 5 to 11).

The correct answer is Option 3. 

Key Points

• Maize is a versatile crop that can grow in a wide range of climatic conditions.
• It is true that maize can be grown in areas with lower rainfall and moderate temperatures, but the crop's specific requirements may vary depending on the variety and the stage of growth.
• Maize can grow in a range of temperatures from 10°C to 35°C, but optimal temperatures for growth and development are between 20°C and 30°C. While maize can tolerate some drought, it requires a minimum amount of water to grow and produce good yields.
• The amount of rainfall required for maize cultivation may vary depending on the variety, soil type, and other environmental factors. In general, maize requires at least 500-600 mm of rainfall during the growing season, with an evenly distributed pattern.

Additional Information

• Rice is a type of grain that is one of the most important staple foods in the world.
• It is a member of the grass family and is grown in many countries, particularly in Asia, Africa, and South America. Rice is a rich source of carbohydrates, which makes it an important source of energy in many diets.
• There are many different varieties of rice, but the most common types are white rice and brown rice. White rice is the most commonly consumed type of rice, and it has been milled to remove the bran and germ layers, which results in a lighter color and smoother texture.
• Brown rice, on the other hand, is a whole grain that has not been milled, so it retains its bran and germ layers, which gives it a nutty flavor and chewy texture.
• Rice can be prepared in many different ways, including boiling, steaming, frying, and baking. It is used in a wide variety of dishes, such as stir-fries, curries, sushi, and rice pudding. Rice is also a popular ingredient in many gluten-free products, such as crackers and breads.
• Jute is a long, soft, shiny vegetable fiber that is spun into coarse, strong threads.
• It is primarily grown in India and Bangladesh, and is used to make a variety of products such as bags, rope, twine, and carpet backing. Jute is also sometimes blended with other fibers, such as cotton or silk, to create a variety of textiles.
• Jute is a sustainable crop, as it requires relatively little water, pesticides, and fertilizers to grow. Additionally, jute fibers are biodegradable, making it an eco-friendly choice for many applications. However, the production of jute can also have negative environmental impacts if not managed properly, such as soil degradation and water pollution.
• Cotton is a soft, fluffy, natural fiber that is widely used in the textile industry to make a variety of products such as clothing, bedding, and towels.
• It comes from the seedpod of the cotton plant, which is native to tropical and subtropical regions around the world.
• Cotton has been cultivated for thousands of years and is one of the oldest crops used for textile production. Today, it is still one of the most widely used natural fibers in the world, although synthetic fibers have gained popularity in recent years.

The correct answer is London.

• The headquarters of the International Maritime Organization (IMO) is located in London.

Key Points

• International Maritime Organization (IMO):
• Parent organization: United Nations
• Founded: 17 March 1948
• Headquarters: London, United Kingdom.
• It is a specialized agency that is concerned with the improvement and safety of international shipping.
• It also prevents the pollution caused by the ships.

Additional Information

• United Nations:
• The UNO was formed on 24 October 1945.
• At present, 193 countries are members of the UN.
• South Sudan is the latest and the 193rd member to join the UN in 2011
• The UN Charter came into force on October 24, 1945, when the Governments of China, France, the UK, the Soviet Union, the USA and a majority of other counties had ratified it.
• The headquarters of the UN is situated in New York (USA).

The correct answer is 82.14; 65.46.

Key Points

• 2011 Census:-
• ​House listing and population enumeration were the two phases of the 15th Indian Census, which took place in 2011.
• The gathering of data regarding each and every building was part of the House listing phase, which began on April 1, 2010.
• Between February 9 and February 28, 2011, the second phase of population enumeration was carried out.
• India has had a census every year since 1872, but biometric data were only collected in 2011.
• The population of India increased to 1.21 billion as of March 31, 2011, according to preliminary reports, representing a 17.70% annual growth rate.
• With a decadal growth rate of 9.21 percent, the adult literacy rate reached 74.04%. "Our Census, Our Future" was the census's motto.

Additional Information

• Literacy Rate 
• The percentage of people who are able to read and write is measured by the literacy rate. Adult literacy rates (those over the age of 15) and youth literacy rates (those between the ages of 15 and 24) further subdivide the literacy rate.
• In addition to academic achievement, India's literacy rate is one of the most important factors for socioeconomic advancement.

The correct answer is Cell

Key Points

• The cell is the basic structural and functional unit of all living organisms.
• Cells are the smallest units of life that can replicate independently, and they are often called the "building blocks of life".
• There are two main types of cells: prokaryotic cells, which lack a nucleus, and eukaryotic cells, which have a nucleus.
• Cells carry out essential functions such as energy production, nutrient processing, and waste elimination.

Additional Information

• ATP (Adenosine Triphosphate) is a molecule that carries energy within cells.
• The mitochondria are organelles within the cell that produce ATP through cellular respiration.
• The nucleus is an organelle in eukaryotic cells that contains most of the cell's genetic material.
• Cells can be specialized to perform specific functions, such as muscle cells, nerve cells, and blood cells.

The correct answer is Parsi New Year.

Key Points

• The Parsi new year, also known as Navroz, is celebrated to mark the beginning of the Iranian calendar.
• The tradition began some 3000 years ago and is observed by the Parsi community around the world.
• The day is also known as Jamshed-i-Nouroz after the Persian King, Jamshed, who introduced the Parsi calendar.
• Balban was the first who introduced the famous Persian Festival of Nauroz.

Additional Information

• Gudi Padwa and Ugadi
• These festivals are celebrated by the people in the Deccan region including Karnataka, Andhra Pradesh, and Maharashtra.
• Cheti Chand
• Sindhis celebrate the new year as Cheti Chand.
• Navreh
• It is the lunar new year that is celebrated in Kashmir.
• Sajibu Cheiraoba
• It is a ritual festival of Meiteis which is observed on the first day of Manipur lunar month Shajibu, which falls in March/April every year.
• Chaitra Shukla Pratipada
• It marks the beginning of the new year of the Vikram Samvat also known as the Vedic calendar.

The correct answer is West Bengal.

In News

• The UDISE+ Report for 2023-24 highlighted an increase in schools with zero enrollment across India, totaling 12,954.

Key Points

• West Bengal has the largest number of schools with zero enrollment at 3,254, followed by Rajasthan (2,167) and Telangana (2,167).
• The total number of zero-enrollment schools increased by 2,660 compared to the previous year.
• Single-teacher schools in India dropped by 7,219 in 2023-24, now totaling 1,10,971, with MP having the most such schools.
• States are considering closing such schools if no new enrollments occur in the next year.
• Zero-enrollment schools often retain sanctioned teacher posts despite no active students.

Additional Information

• Unified District Information System for Education Plus (UDISE+)
• It is a government database providing insights into India's education system.
• Focuses on tracking enrollment, infrastructure, and educational trends annually.
• Zero Enrollment Schools
• Schools with no student enrollments during the academic year.
• Reasons include lack of interest, migration, or the completion of the last batch of students.

The correct answer is Rig Veda

Key Points

• The Rig-Veda is the oldest of the four collections of hymns and other sacred texts known as the Vedas.
• It contains most of the information about the religious and social life of the early Vedic period.
• These works are considered the "sacred knowledge" of the Aryans.
• The Rig-Veda also contains ideas that served as the basis for India's system of castes(Varna).
• According to Brahminic ideology, Varṇa means hierarchizing society into classes.

Additional Information

• Associated information with different Veda.

The Correct Answer is ​Tral.

In News

• Operation Nader at Tral.

Key Points

• A joint anti-terror operation was launched in Nader area of Tral, Awantipora.
• The operation was based on special intelligence input.
• Forces involved:
• Indian Army
• Jammu and Kashmir Police
• CRPF (Central Reserve Police Force)
• The action is part of India’s ongoing counter-terror efforts.
• It builds on the success of Operation Sindoor.

The correct answer is Mahanadi.

Key Points

• The Mahanadi River is a major river in East Central India, predominantly flowing through the state of Odisha.
• It covers a total drainage area of 141,600 square kilometres and has a course of 858 kilometres.
• It is the third largest river in terms of water potential and drainage area in the Indian peninsula after the Godavari and the Krishna rivers.
• In Odisha, it's the largest river and holds great economic significance for the state as it supports agriculture, industry, and the daily lives of people.
• Some of the most significant rivers in the region include the Seonath, Hasdeo, Mand, Jonk, Telen, and Ib.
• The Mahanadi river system is known for the Hirakud Dam.
• This dam is one of the longest in the world and serves a critical purpose in flood control and providing irrigation water.

Additional Information

The correct answer is S.P. Sharma.

In News

• S.P. Sharma is the author of the book "India@2047: Charts Roadmap to Global Economic Leadership."
• The book discusses India's rise as a resilient economy with 8%+ growth and highlights transformative initiatives like Make in India and digital innovation.

Key Points

• The author of the book "India@2047: Charts Roadmap to Global Economic Leadership" is S.P. Sharma.
• The book outlines India's future as a resilient, reform-driven economy with sustained 8%+ growth.
• It emphasizes key initiatives like Make in India, IMEC, and digital innovation that are seen as crucial growth catalysts for India.

Additional Information

• S.P. Sharma
• Economist and author, known for his writings on India's economic policies and growth trajectory.
• India@2047
• A vision for India's economic leadership by the time it completes 100 years of independence in 2047.

Given:

Number: 5867943256

Formula Used:

Remainder of a number when divided by 9 is the same as the remainder of the sum of its digits when divided by 9.

Calculation:

Sum of digits of 5867943256: 5 + 8 + 6 + 7 + 9 + 4 + 3 + 2 + 5 + 6

Sum = 55

⇒ 55 ÷ 9

Quotient = 6

Remainder = 55 - (9 × 6)

Remainder = 55 - 54

Remainder = 1

The remainder when 5867943256 is divided by 9 is 1.

Shortcut Trick

Total work (LCM of 5 and 18) = 90 units.

Efficiency: Jitesh = 18 units/day, Kamal = 5 units/day.

Combined work in 3 days = 3 × (18 + 5) = 69 units.

Remaining work = 90 − 69 = 21 units.

Days for Jitesh to finish = 21 ÷ 18 = 7/6 days.

∴ The correct answer is 7/6 days.

Alternate Method

Given: Jitesh completes work in 5 days, Kamal in 18 days.

Formula: Remaining Work = Total Work − Work Done

⇒ Total work = LCM(5, 18) = 90 units

⇒ Efficiency of Jitesh = 90 ÷ 5 = 18 units/day

⇒ Efficiency of Kamal = 90 ÷ 18 = 5 units/day

⇒ Work done together in 3 days = 3 × (18 + 5) = 3 × 23 = 69 units

⇒ Remaining work = 90 − 69 = 21 units

⇒ Time taken by Jitesh to finish remaining work = 21 ÷ 18

⇒ Time = 7/6 days

∴ The correct answer is 7/6 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken to complete the work. Efficiency × Time = Total Work.

Work & Wages

Wages are distributed based on the ratio of work done by each individual, which is the product of their efficiency and time spent working.

Fractional Work Method

If a person does work in 'x' days, work done in 1 day = 1/x. Sum of daily fractions of work gives the total combined efficiency.

Shortcut Trick

When a train passes two objects moving in the same direction, the length of the train remains constant.

Speed of Train = (v₂ × t₂ − v₁ × t₁) ÷ (t₂ − t₁)

Speed of Train = (15 × 11 − 10 × 10) ÷ (11 − 10)

Speed of Train = (165 − 100) ÷ 1

Speed of Train = 65 km/hr

∴ The correct answer is 65 km/hr.

Alternate Method

Given:

Speed of 1st bicycle = 10 km/hr

Speed of 2nd bicycle = 15 km/hr

Time to pass 1st bicycle (t₁) = 10 sec

Time to pass 2nd bicycle (t₂) = 11 sec

Train (v km/h)

B1

10 km/h

t&sub1; = 10 sec

Train (v km/h)

B2

15 km/h

t&sub2; = 11 sec

Length = Relative Speed × Time (Constant)

Formula Used:

Distance = Relative Speed × Time

Relative speed (same direction) = Speed of Train − Speed of Object

Calculations:

⇒ Let the speed of the train be v km/hr.

⇒ Length of the train passing B1 = (v − 10) × (5 ÷ 18) × 10

⇒ Length of the train passing B2 = (v − 15) × (5 ÷ 18) × 11

⇒ Since the length of the train is constant in both cases, we can equate them:

⇒ (v − 10) × (5 ÷ 18) × 10 = (v − 15) × (5 ÷ 18) × 11

⇒ (v − 10) × 10 = (v − 15) × 11

⇒ 10v − 100 = 11v − 165

⇒ 11v − 10v = 165 − 100

⇒ v = 65 km/hr

∴ The correct answer is 65 km/hr.

Additional Information

Relative Speed (Same Direction)

When two bodies are moving in the same direction, their relative speed is the difference of their individual speeds: Relative Speed = |V₁ − V₂|.

Relative Speed (Opposite Direction)

When two bodies are moving in opposite directions towards or away from each other, their relative speed is the sum of their individual speeds: Relative Speed = V₁ + V₂.

Unit Conversion Rule

To convert speed from km/hr to m/s, multiply the value by (5 ÷ 18). Conversely, to convert from m/s to km/hr, multiply by (18 ÷ 5).

Given:

240 donors of blood group  A, B , O and AB

Formula used:

360 degrees = Total donors 

Calculation:

As, 360 degree represents 240 donors 

Hence, blood group O has 80 degree 

Blood group O has = 240/360 × 80 donors = 160/3

Now, blood group A represents  90 degree

Blood group A has = 240/360 × 90 = 60 

Now, blood group AB represents 70 degrees

Blood group AB has = 240/360 × 70 = 140/3

Now, average of A and AB = Sum of values/Total number of values = (60 + 140/3) ÷ 2 =  160/3.

Hence, the ratio between O and the average of A and AB = 160/3 : 160/3 = 1:1.

Hence, the ratio is 1:1.

Given:

Mark-up percentage = 30%

Discount percentage = 20%

Formula Used:

Marked Price (MP) = Cost Price (CP) × (1 + Mark-up %)

Selling Price (SP) = Marked Price (MP) × (1 - Discount %)

Profit % = (\frac{(SP - CP)}{CP} \times 100)

Calculations:

Let CP = ₹100

⇒ MP = 100 × (1 + (\frac{30}{100}))

⇒ MP = ₹130

⇒ SP = 130 × (1 - (\frac{20}{100}))

⇒ SP = 130 × 0.8

⇒ SP = ₹104

⇒ Profit = SP - CP

⇒ Profit = 104 - 100 = ₹4

⇒ Profit % = (\frac{4}{100} \times 100) = 4%

The correct answer is Option (3).

Given:

A works twice as fast as B.

B can complete the work in 405 days independently.

Formula Used:

Work rate of A = 2 × Work rate of B

Combined work rate = Work rate of A + Work rate of B

Time taken to complete the work together = 1 / Combined work rate

Calculation:

Let the work done by B in 1 day be 1/405.

Work done by A in 1 day = 2 × (1/405) = 2/405

Combined work rate of A and B = (1/405) + (2/405)

Combined work rate of A and B = (1 + 2)/405

Combined work rate of A and B = 3/405

Time taken to complete the work together = 1 / (3/405)

Time taken to complete the work together = 405/3

Time taken to complete the work together = 135 days

The number of days in which A and B can together finish the work is 135 days.

Shortcut Trick

Net percentage increase in area = x + x + (x × x)/100

Here, increase in side (x) = 34%

⇒ Area increase = 34 + 34 + (34 × 34)/100

⇒ Area increase = 68 + 1156/100 = 68 + 11.56 = 79.56%

∴ The correct answer is 79.56%.

Alternate Method

Given: Increase in side of equilateral triangle = 34%

Formula Used: Area of equilateral triangle = (√3/4) × a²

⇒ Let original side (a₁) = 100 units

⇒ New side (a₂) = 100 + 34% of 100 = 134 units

⇒ Ratio of areas = (a₁)² : (a₂)²

⇒ Ratio of areas = (100)² : (134)²

⇒ Ratio of areas = 10000 : 17956

⇒ Percentage increase in area = [(17956 − 10000) ÷ 10000] × 100

⇒ Percentage increase in area = [7956 ÷ 10000] × 100 = 79.56%

∴ The correct answer is 79.56%.

Additional Information

Equilateral Triangle Properties

All three sides are equal and each internal angle is 60°. Height = (√3/2) × a.

Successive Percentage Change

When a quantity depends on the product of two variables (like Area = k × x × y), the net change is given by x + y + xy/100.

Area Scaling

If the linear dimensions of a 2D shape are scaled by a factor k, the area scales by k².

Given:

Volume of cylindrical pipe = 3564 cubic.cm

Formula:

Volume of cylinder = πr²h

Calculation:

Internal radius = 12 - 3 = 9 cm

Then,

⇒ 3564 = 22/7 × (12² - 9²) × h

⇒ h = 18

∴ Length of pipe is 18cm

Given:

A dishonest shopkeeper sells sugar at Rs. 30/kg which he has bought at Rs. 24/kg

He gives 750 gm instead of 1000 gm mentioned on the weight.

Formula used:

Profit% = (\dfrac{selling \ price - cost \ price}{cost \ price}) × 100

Profit due to wrong weight = (\dfrac{error}{true \ weight - error}) × 100

Overall profit = profit1 + profit2 + (\dfrac{profit1× profit2}{100})

Calculations:

Cost price of 1 kg sugar = Rs. 24

Selling price of 1 kg sugar = Rs. 30

Profit1% = (\dfrac{30-24}{24}) × 100

= (\dfrac{6}{24}) × 100 = 25% (This can be the total profit if he actually sold 1 kg but if he has sold by using wrong weight then,)

Profit2 due to wrong weight = (\dfrac{250}{1000 - 250}) × 100

= (\dfrac{250}{750}) × 100 = 33.3%

So, overall profit% = 25 + 33.3 + (\dfrac{25 × 33.3}{100})

= 66.6 ~ (66\dfrac{2}{3})%

∴ The answer is (66\dfrac{2}{3})%  

Shortcut Trick

⇒CP :SP = 24 × 750 : 30 × 1000 

⇒CP :SP = 3:5

Profit = 5 -3 = 2 unit profit % = (2/3) × 100 =  (200/3) % =  (66\dfrac{2}{3})%

Shortcut Trick

Interest for 3 years (8 − 5) = 776 − 660 = ₹116.

Interest for 1 year = 116/3.

Principal (P) = 660 − (5 × 116/3) = (1980 − 580) ÷ 3 = 1400/3.

Rate (R) = (Interest for 1 year ÷ Principal) × 100 = (116/3 ÷ 1400/3) × 100 = 116/14 = 8(2/7)%.

∴ The correct answer is 8(2/7)%.

Alternate Method

Given:

Amount after 5 years (A₅) = ₹660

Amount after 8 years (A₈) = ₹776

Formula Used:

Amount (A) = Principal (P) + Simple Interest (SI)

SI = (P × R × T) ÷ 100

Calculations:

⇒ Simple Interest for 3 years = 776 − 660 = ₹116

⇒ SI for 1 year = 116 ÷ 3

⇒ SI for 5 years = (116 ÷ 3) × 5 = 580 ÷ 3

⇒ Principal (P) = A₅ − SI for 5 years

⇒ P = 660 − (580/3) = (1980 − 580) ÷ 3 = 1400/3

⇒ Rate (R) = (SI for 1 year × 100) ÷ P

⇒ R = ((116/3) × 100) ÷ (1400/3)

⇒ R = (116 × 100) ÷ 1400 = 116 ÷ 14

⇒ R = 58/7 = 8(2/7)%

∴ The correct answer is 8(2/7)%.

Additional Information

Simple Interest Formula

Simple interest is calculated only on the initial principal. Formula: SI = (P × R × T) ÷ 100.

Difference in Amounts

In simple interest, the difference between any two amounts is the interest for the difference in years: A₂ − A₁ = P × R × (T₂ − T₁) ÷ 100.

Relationship between P, A and SI

The amount is always the sum of principal and interest: A = P + SI. To find P, subtract total interest from the given amount.

Calculation:

The total production by companies X = 128000 + 110000 + 102000 + 80000 + 109000 + 170000

⇒ 699000

The total production by companies Y = 141000 + 192000 + 145000 + 130000 + 122000 + 161000

⇒ 891000

The approximate difference between the total production by companies X and Z in the given years

⇒ 891000 - 699000

⇒ 192000 

∴ The approximate difference between the total production by companies X and Z in the given years is 192000.

Shortcut Trick

Difference in Percentage = 82% − 73% = 9%

Given that 9% of the number = 72

Then, 1% of the number = 72 ÷ 9 = 8

Required value (48% of the number) = 48 × 8 = 384

∴ The correct answer is 384.

Alternate Method

Given:

Difference between 82% and 73% of a number = 72

Formula Used:

Value = (Percentage ÷ 100) × Number

0%100%73%82%Difference 9% = 72Target: 48% of the total number

Calculations:

⇒ Let the number be x.

⇒ (82% × x) − (73% × x) = 72

⇒ (82 − 73)% × x = 72

⇒ 9% × x = 72

⇒ (9 ÷ 100) × x = 72

⇒ x = (72 × 100) ÷ 9

⇒ x = 800

⇒ Required value = 48% of 800

⇒ Value = (48 ÷ 100) × 800

⇒ Value = 48 × 8 = 384

∴ The correct answer is 384.

Additional Information

Percentage Difference Rule

When two percentages of the same base are subtracted, the result is equal to the difference of the percentages applied to that base: a% of x − b% of x = (a−b)% of x.

Finding the Whole Number

If p% of a number is v, then the total number is calculated as (v × 100) ÷ p.

Fractional Conversion

Converting common percentages to fractions can speed up calculations: 25% = 1/4, 50% = 1/2, 75% = 3/4, and 20% = 1/5.

Shortcut Trick

Let the HCF be x.

Numbers are 2x, 1x, and 5x.

LCM of (2, 1, 5) × HCF = LCM of numbers.

10 × x = 5380

x = 538

∴ The correct answer is 538.

Alternate Method

Given:

Ratio of three numbers = 2 : 1 : 5

LCM of the numbers = 5380

Formula Used:

If the ratio of numbers is a : b : c and their HCF is H, then the numbers are aH, bH, and cH.

LCM of (aH, bH, cH) = H × LCM(a, b, c)

Calculations:

⇒ Let the numbers be 2H, 1H, and 5H, where H is the HCF.

⇒ LCM of 2, 1, and 5 = 10 (since they are prime/co-prime to each other).

⇒ LCM of (2H, 1H, 5H) = 10 × H

⇒ 10H = 5380

⇒ H = 5380 ÷ 10

⇒ H = 538

∴ The correct answer is 538.

Additional Information

HCF and LCM Relation

For two numbers A and B, A × B = HCF(A, B) × LCM(A, B). Note: This does not directly apply to three numbers.

Ratio and Multiples

If numbers are in ratio x : y : z, then the numbers can be expressed as kx, ky, and kz, where k is their HCF.

LCM of Fractions

LCM = LCM of Numerators ÷ HCF of Denominators.

Given:

We are asked to find the largest fraction among: (\frac{2}{3}, \frac{6}{53}, \frac{79}{90}, \frac{33}{44})

Approach:

To compare these fractions, we will either:

Convert them to decimal form by dividing the numerator by the denominator, or

Find a common denominator to compare them directly.

Calculations:

1. For ( \frac{2}{3})

( \frac{2}{3} \approx 0.6667 )

2. For ( \frac{6}{53})

( \frac{6}{53} \approx 0.1132 )

3. For ( \frac{79}{90})

( \frac{79}{90} \approx 0.8778 )

4. For ( \frac{33}{44})

( \frac{33}{44} = \frac{3}{4} = 0.75 )

Conclusion:

The largest fraction is ( \frac{79}{90} ) as it has the highest value of approximately 0.8778.

Number of registration of vehicles other than bikes in January 2017 = 27,000 - 21,000 = 6,000

Number of registration of vehicles other than bikes in April 2017 = 35,000 - 20,000 = 15,000

∴ the increase in the registration of vehicles other than bikes in April 2017 in comparison of Jan 2017 = 15,000 - 6,000 = 9,000

Shortcut Trick

The average of 4 consecutive odd numbers is the middle value between the 2^nd and 3^rd numbers.

Given Average = 34, so the numbers are (34−3), (34−1), (34+1), (34+3) → 31, 33, 35, 37.

Largest number = 37 and Second smallest number = 33.

Required Average = (37 + 33) ÷ 2 = 35.

Since 35 is not divisible by 2, it is an odd number.

∴ The correct answer is An odd number.

Alternate Method

Let the four consecutive odd numbers be x, (x + 2), (x + 4), and (x + 6).

Given: Average of these numbers = 34.

⇒ [x + (x + 2) + (x + 4) + (x + 6)] ÷ 4 = 34

⇒ (4x + 12) ÷ 4 = 34

⇒ 4x + 12 = 136

⇒ 4x = 124

⇒ x = 31

⇒ The numbers are 31, 33, 35, 37.

⇒ Largest number = 37

⇒ Second smallest number = 33

⇒ Required Average = (37 + 33) ÷ 2 = 70 ÷ 2 = 35

⇒ 35 is an odd number.

∴ The correct answer is An odd number.

Additional Information

Consecutive Numbers in A.P.

For any sequence in Arithmetic Progression, the average of the entire set is equal to the average of any two terms equidistant from the center.

Average of Odd/Even Numbers

The average of n consecutive odd or even numbers is always the mid-point. If n is even, the average is an integer between the two middle terms.

Sum of First n Odd Numbers

The sum of the first n consecutive odd numbers starting from 1 is always n², and their average is n.

Shortcut Trick

Capital ratio A : B = 15000 : 30000 = 1 : 2

Profit ratio A : B = 1 : 5

Time Ratio = (Profit Ratio ÷ Capital Ratio)

Time Ratio A : B = (1 ÷ 1) : (5 ÷ 2) = 1 : 2.5

Time Ratio A : B = 2 : 5

∴ The correct answer is 2 : 5.

Alternate Method

Given:

Investment of A (C_A) = Rs. 15000

Investment of B (C_B) = Rs. 30000

Profit Ratio (P_A : P_B) = 1 : 5

Formula used: Profit = Capital × Time period

Capital A (Rs. 15000)

Capital B (Rs. 30000)

Profit Ratio (A : B) = 1 : 5 Time Ratio = (P / C) = (1/1) : (5/2) = 2 : 5

⇒ P_A / P_B = (C_A × T_A) / (C_B × T_B)

⇒ 1 / 5 = (15000 × T_A) / (30000 × T_B)

⇒ 1 / 5 = (1 × T_A) / (2 × T_B)

⇒ T_A / T_B = (1 × 2) / (5 × 1)

⇒ T_A / T_B = 2 / 5

∴ The correct answer is 2 : 5.

Additional Information

Basic Partnership Rule

When two or more people invest capital for different time periods, the profit is shared in the ratio of the product of their capital and time: P₁ : P₂ = C₁T₁ : C₂T₂.

Time Period Ratio Formula

If the profit ratio and capital ratio are known, the time period ratio is found by dividing the profit units by capital units: T₁ : T₂ = (P₁ ÷ C₁) : (P₂ ÷ C₂).

Working vs Sleeping Partner

A working partner manages the business and may receive a fixed salary or commission from the profit before the remaining profit is shared among all partners.

Given:

Number of terms = 49

First term = 51

Last term = 99

Formula used:

Average = (Sum of observations) / (Number of observations)

Sum of n terms in AP = (n/2)[a + l]

Where, AP = Arithmetic progression,

n = number of terms, a = first term

and l = last term

Calculation:

Total number b/w 50 & 100 = 49

Therefore, 

a = 51, l = 99, n = 49

Sum = (49/2)[51 + 99]

⇒ Sum = (49/2) × 150

⇒ Sum = 3675

Average = Sum / Number of terms

⇒ Average = 3675 / 49

⇒ Average = 75

∴ The average of all natural numbers lying between 50 and 100 is 75.

Shortcut Trick

Identify sides: a = 8, b = 9, c = 13.

Semi-perimeter s = (8 + 9 + 13) ÷ 2 = 15 cm.

Area = √[15 × (15 − 8) × (15 − 9) × (15 − 13)]

Area = √[15 × 7 × 6 × 2] = √1260 ≈ 35.50 cm².

∴ The correct answer is 35.50 cm².

Alternate Method

Given:

Sides of the triangle: a = 8 cm, b = 9 cm, c = 13 cm.

Formula Used:

Heron's Formula: Area = √[s(s − a)(s − b)(s − c)]

Where s is the semi-perimeter: s = (a + b + c) ÷ 2

Calculations:

⇒ s = (8 + 9 + 13) ÷ 2

⇒ s = 30 ÷ 2 = 15 cm

⇒ Area = √[15 × (15 − 8) × (15 − 9) × (15 − 13)]

⇒ Area = √[15 × 7 × 6 × 2]

⇒ Area = √[1260]

⇒ Area ≈ 35.496 cm²

⇒ Rounding to two decimal places, we get 35.50 cm².

∴ The correct answer is 35.50 cm².

Additional Information

Heron's Formula

Used to find the area of any triangle when the lengths of all three sides are known. Area = √[s(s−a)(s−b)(s−c)].

Right-Angled Triangle Area

If the triangle is right-angled, the area can be simply calculated as 1/2 × base × height.

Equilateral Triangle Area

For a triangle with all equal sides a, Area = (√3 ÷ 4) × a².

Given

The total number of children in 2016 = 7500

The total number of children in 2017 = 10500

The Percentage (%) of children who are not overweight in 2016 = (100 - 30) % = 70%

The Percentage (%) of children who are not overweight in 2017 = (100 - 28) % = 72%

Solution

The number of children who were not overweight in the year 2016:

⇒ 70% of 7500 = 5250 

The number of children who were not overweight in the year 2017:

⇒ 72% of 10500 = 7560

The total number of children who were not overweight in the year 2016 and 2017 together:

⇒ 5250 + 7560 = 12810

Given:

We need to find the smallest number which when divided by 36, 45, and 54, gives a remainder of 3 each time.

Formula used:

The required number = LCM of (36, 45, 54) + 3

Calculation:

First, find the LCM of 36, 45, and 54.

Prime factorization:

36 = 2² × 3²

45 = 3² × 5

54 = 2 × 3³

LCM = 2² × 3³ × 5

LCM = 540

⇒ Required number = 540 + 3

⇒ Required number = 543

∴ The correct answer is option (3).

Shortcut Trick

Base radius r = Circumference ÷ 2π = 62.8 ÷ 6.28 = 10 cm

Height h = Volume ÷ (πr²) = 8792 ÷ 314 = 28 cm

Curved Surface Area (CSA) = Circumference × h

CSA = 62.8 × 28 = 1758.4 cm²

∴ The correct answer is 1758.4 cm².

Alternate Method

Given:

Circumference of base = 62.8 cm

Volume of cylinder = 8792 cm³

Value of π = 3.14

Calculations:

⇒ Circumference = 2πr

⇒ 62.8 = 2 × 3.14 × r

⇒ 62.8 = 6.28 × r

⇒ r = 62.8 ÷ 6.28 = 10 cm

⇒ Volume = πr²h

⇒ 8792 = 3.14 × (10)² × h

⇒ 8792 = 3.14 × 100 × h

⇒ 8792 = 314 × h

⇒ h = 8792 ÷ 314 = 28 cm

⇒ Curved Surface Area (CSA) = 2πrh

⇒ CSA = (2πr) × h

⇒ CSA = 62.8 × 28

⇒ CSA = 1758.4 cm²

Comparing the calculated result with the options, we find it corresponds to Option (2).

∴ The correct answer is 1758.4 cm².

Additional Information

Total Surface Area of Cylinder

The total surface area (TSA) includes both the curved surface and the two circular bases: TSA = 2πr(r + h).

Volume and CSA Relation

The volume (V) can also be expressed in terms of Curved Surface Area (CSA) as V = (CSA × r) ÷ 2.

Base Area of Cylinder

The area of the circular base is given by πr². A cylinder has two such bases.

Shortcut Trick

The fourth proportional (x) to three numbers a, b, and c is given by x = (b × c) / a.

Here, a = √6, b = √8, and c = √21.

x = (√8 × √21) / √6 = √(8 × 21 / 6) = √28.

x = 2√7.

∴ The correct answer is 2√7.

Alternate Method

Given:

First term (a) = √6

Second term (b) = √8

Third term (c) = √21

Formula:

For four numbers to be in proportion, the ratio of the first two must equal the ratio of the last two: a : b = c : d.

Calculations:

⇒ √6 : √8 = √21 : x

⇒ √6 / √8 = √21 / x

⇒ x × √6 = √8 × √21

⇒ x = (√8 × √21) / √6

⇒ x = √((8 × 21) / 6)

⇒ x = √(168 / 6)

⇒ x = √28

⇒ x = √(4 × 7)

⇒ x = 2√7

∴ The correct answer is 2√7.

Additional Information

Mean Proportional

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

Third Proportional

The third proportional to two numbers a and b is given by x = b² / a.

Continued Proportion

Three numbers a, b, c are in continued proportion if a/b = b/c, which implies b² = ac.

Given:

Ratio of volumes of two cones = 3 : 2

Ratio of radii of the two cones = 3 : 4

Formula:

The volume of a cone is given by the formula:

V = (1/3)πr²h

Solution:

Let's assume the radii of the two cones are 3x and 4x, where x is a common factor.

So, the ratio of their radii is 3x : 4x.

The volume of the first cone (V1) can be expressed as:

V1 = (1/3)π(3x)²h1

V1 = (1/3)π9x²h1

The volume of the second cone (V2) can be expressed as:

V2 = (1/3)π(4x)2h1

V2 = (1/3)π16x2h1

Given that the ratio of volumes of the two cones is 3 : 2, we have:

V1/V2 = 3/2

9x​2h1/16x​2h2 = 3/2

h1 / h2 = 48x²/18x​2

h1/h2 = 8/3

Therefore, the ratio of the heights of the two cones is 8 : 3.

Shortcut Trick

Total Distance = 20 + 10 = 30 miles

Total Time = 2.5 h + 1.25 h = 3.75 h

Average Speed = 30 ÷ 3.75 = 8 mph

∴ The correct answer is 8 mph.

Alternate Method

Given:

Distance 1 = 20 miles | Time 1 = 2 h 30 min

Distance 2 = 10 miles | Time 2 = 1 h 15 min

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance = 20 + 10 = 30 miles

⇒ Time 1 = 2 + (30 ÷ 60) = 2.5 hours

⇒ Time 2 = 1 + (15 ÷ 60) = 1.25 hours

⇒ Total Time = 2.5 + 1.25 = 3.75 hours

⇒ Average Speed = 30 ÷ 3.75

⇒ Average Speed = 3000 ÷ 375 = 8 mph

∴ The correct answer is 8 mph.

Additional Information

General Average Speed Formula

Average speed is always calculated as the ratio of Total Distance covered to the Total Time taken: V_avg = (D₁ + D₂ + ... + D_n) ÷ (T₁ + T₂ + ... + T_n).

Harmonic Mean for Equal Distances

If a person covers two equal distances at speeds x and y, then the Average Speed = (2 × x × y) ÷ (x + y).

Time Conversion

To convert minutes into hours, divide the value by 60. Example: 15 min = 15/60 = 0.25 h.

Given:

Ratio of Alcohol and water 23 : 17

Quantity = 240 L

Calculation:

According to question,

Since, 8 L of water is mixed

So,

⇒ 40 unit = 240

⇒ 1 unit = 6

⇒ 23 × 6 : 17 × 6

⇒ 138 : 102

⇒ 138 : (102 + 8)

⇒ 138 : 110

⇒  69 : 55     

∴ The correct answer is 69 : 55.

Shortcut Trick

For the largest cube inside a sphere, the diagonal of the cube is equal to the diameter of the sphere.

Diagonal of cube = a√3 = 2 × radius = 2 × 15√3

⇒ Side of cube (a) = 30 cm

Total Surface Area = 6a² = 6 × (30)² = 6 × 900 = 5400 cm²

∴ The correct answer is 5,400 cm².

Alternate Method

Given:

Radius of the wooden sphere (R) = 15√3 cm

Formula Used:

⇒ Diameter of sphere = 2 × R

⇒ Diagonal of a cube = a√3 (where 'a' is the side)

⇒ Total Surface Area (TSA) of cube = 6a²

Calculations:

⇒ Diameter of the sphere = 2 × 15√3 = 30√3 cm

⇒ Since the cube is the largest possible, its body diagonal must match the sphere diameter.

⇒ a√3 = 30√3

⇒ a = 30 cm

⇒ TSA of cube = 6 × (30)²

⇒ TSA = 6 × 900

⇒ TSA = 5400 cm²

∴ The correct answer is 5,400 cm².

Additional Information

Cube in Sphere

When a cube is inscribed in a sphere, the diameter of the sphere is equal to the body diagonal of the cube: D = a√3.

Sphere in Cube

When a sphere is inscribed in a cube, the diameter of the sphere is equal to the side of the cube: D = a.

Surface Area and Volume

Surface area of sphere = 4πR² and Volume of sphere = (4/3)πR³.

Given:

Principle = Rs. 2700

Time = 8 months = 8/12 year = 2/3 year

Rate of interest = 5 paisa per month = 5 × 12 paisa per year = 60 paisa per year = 60 %

Formula used:

SI = PRT/100

Calculation:

SI = (2700 × 60 × 2) / (100 × 3)

⇒ 9 × 120

⇒ 1080

∴ The SI will be Rs. 1080.

Given:

Sum of amount in 3 year = Rs. 3,025

Sum of amount in 5 year = Rs. 4,225

Formula used:

Amount at CI = P(1 + r/100)^t

where P = Principle, r = rate per annum, and t = time

Calculation:

For 3 year,

3025 = P(1 + r/100)³      ------- (1)

For 5 year,

4225 = P(1 + r/100)⁵      ------- (2)

Dividing equation (2) from equation (1)

4225/3025 = P(1 + r/100)5 ÷ P(1 + r/100)3 

⇒ 169/121 = (1 + r/100)²

⇒ 1 + r/100 = (\sqrt{\frac{169}{121}})

⇒ r/100 = 13/11 - 1

⇒ r/100 = 2/11

⇒ r = 200/11

⇒ r = 18(2 \over 11)%

∴ Rate of interest is 18(2 \over 11)%.

Given:

([\frac{1}{8}+{\frac{1}{6} \times(\frac{36}{45} \div \frac{24}{25}) - (\frac{12}{21} \times \frac{14}{15} \div \frac{24}{45})}+\frac{27}{36}])

Formula used:

BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction)

Calculation:

([\frac{1}{8}+{\frac{1}{6} \times (\frac{36}{45} \times \frac{25}{24}) - (\frac{12}{21} \times \frac{14}{15} \times \frac{45}{24})} + \frac{27}{36}])

⇒ ([\frac{1}{8}+{\frac{1}{6} \times (\frac{4}{5} \times \frac{25}{24}) - (\frac{4}{7} \times \frac{14}{15} \times \frac{15}{8})} + \frac{3}{4}])

⇒ ([\frac{1}{8}+{\frac{1}{6} \times \frac{5}{6} - (1 \times 1 \times 1)} + \frac{3}{4}])

⇒ ([\frac{1}{8}+{\frac{5}{36} - 1} + \frac{3}{4}])

⇒ ([\frac{1}{8} - \frac{31}{36} + \frac{27}{36}])

⇒ ([\frac{1}{8} - \frac{4}{36}])

⇒ ([\frac{1}{8} - \frac{1}{9}])

⇒ (\frac{9-8}{72})

⇒ (\frac{1}{72})

∴ The correct answer is option (2).

Shortcut Trick

Ratio of Mohan to Brother present age = 2 : 1 (Difference = 1 unit)

Ratio 3 years ago = 3 : 1 (Difference = 2 units)

Equating differences: Present ratio becomes 4 : 2. Difference between 4 and 3 is 1 unit.

1 unit → 3 years.

Mohan's present age = 4 units = 4 × 3 = 12 years.

∴ The correct answer is 12 years.

Alternate Method

Let the present age of Mohan's brother be x years.

⇒ Mohan's present age = 2x years.

⇒ 3 years ago, Brother's age = x − 3

⇒ 3 years ago, Mohan's age = 2x − 3

According to the question:

⇒ 2x − 3 = 3 × (x − 3)

⇒ 2x − 3 = 3x − 9

⇒ 3x − 2x = 9 − 3

⇒ x = 6

⇒ Mohan's present age = 2 × 6 = 12 years.

∴ The correct answer is 12 years.

Additional Information

Age Difference Property

The difference between the ages of two people remains constant regardless of the number of years passed or preceding.

Ratio Balancing

To solve age problems using ratios, multiply the ratios such that the numerical difference between the parts of the two ratios becomes equal to the actual time gap.

Given:

A six-digit number is divisible by 91.

143 is added to this number.

Formula Used:

If a number is divisible by a and we add another number b, then the result is divisible by the common factors of a and b.

Calculation:

Let the six-digit number be n, which is divisible by 91.

So, n = 91k where k is an integer.