DSSSB Jail Warder : (8 Dec 2025) Memory-Based Paper (Previous Year Paper)

The logic followed here is :-

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

(26, 100, 24) → (26 + 24) × (26 - 24) = 50 × 2 = 100

And

(36, 272, 32) → (36 + 32) × (36 - 32) = 68 × 4 = 272

Similarly,

(19, 72, 17) → (19 + 17) × (19 - 17) = 36 × 2 = 72

Hence, the correct answer is "(19, 72, 17)".

The table is alphabets place value:

The pattern followed here is:                                

(Sum of the vowels positional values) × (number of vowels) + (sum of consonants alphabet place value) = number.

NEARLY → Total number of vowels (E, A) in the word is 2.         

=>  (Sum of the vowels positional values) × (number of vowels) + (sum of consonants alphabet place value) = number. 

=> (5 + 1) × 2 + (14 + 18 + 12 + 25) = 6 × 2 + 69 = 12 + 69 = 81

And,

BABY → Total number of vowels (A) in the word is 1.         

=> (Sum of the vowels positional values) × (number of vowels) + (sum of consonants alphabet place value) = number.

=> (1) × 1 + (2 + 2 + 25) = 1 + 29 = 30

Similarly,

EXPENSE → Total number of vowels (E, E, E) in the word is 2.         

=> (Sum of the vowels positional values) × (number of vowels) + (sum of consonants alphabet place value) = number.

=> (5 + 5 + 5) × 3 + (24 + 16 + 14 + 19) = 15 × 3 + 73 = 45 + 73 = 118

Hence, EXPENSE will be written as “118”.

The given statement clearly specifies that the source of information is not reliable. Hence the first thing to be done is to verify whether or not it is true.

Hence the correct answer is Option 1.

The pattern in the given series is:

GROUND : EIQSWA  ⇒

At first, GROUND is arranged in alphabetical order ⇒ DGNORU

Then,

And,

PLANET : BGORUZ ⇒

At first, PLANET  is arranged in alphabetical order ⇒ AELNPT

Then,

Similarly,

SATURN:? ⇒

At first, SATURN is arranged in alphabetical order ⇒ ANRSTU

Then,

Hence, the correct answer is BPUWYA.

The pattern followed is:

Hence, the correct answer is "122".

Riya is going to Mumbai in July but she has decided to reserve the railway seat in May itself, two months earlier to her commencement of the journey.

This implies that the department of railways issue the reservations two months earlier.

Hence, the assumption I is implicit.

As the information about various trains going to Mumbai has not been mentioned or suggested in the given statement, we cannot determine whether there one or more trains for Mumbai.

Hence, assumption II is not implicit.

Thus, only assumption I is implicit.

From the above statement, we can easily conclude that lemons and oranges can prevent scurvy as it is already mentioned in the statement that they are sources of citric acid.

Therefore, conclusion II follows.

On the other hand, the information provided is not sufficient enough to conclude that exactly 2 lemons should be taken after lunch to prevent scurvy.

Therefore, conclusion I does not follow.

Hence, Only conclusion II follows.

The table is alphabets place value:

The pattern followed here is:

 'GLIMPS' is written as 'NMOOUV'

Similarly,

'POTATO' = ?

Hence, '​POTATO' is coded as "WPZCYR".

Logic:  

Second Number = (Difference of both digits of First Number )² – ( Difference of both digits of First Number )

In 71 : 30  →

(7 - 1)² – (7 - 1) = (6)² – 6 = 36 – 6 = 30

In 94 : 20 →

(9 - 4)² – (9 - 4) = (5)² – 5 = 25 – 5 = 20

Similarly:

In 62 :   →

(6 - 2)² – (6 - 2) = (4)² – 4 = 16 – 4 = 12

Here, 62: 12 is the correct pair as per the logic.

Hence, the correct answer is "12".

Let us first decode the given symbols and then draw a family tree.

‘B & R % I # N # G’ means B is brother of R, R is sister of I, I is father of N, N is father of G.

Now draw family tree using following notations:

 

Hence, R is aunt of N.

According to the given information :

Six boxes of different ARTICLES–A, B, C, D, E and F - are to be placed in six display racks of a shop numbered 1-6.

• A has to be placed at the bottom most rack.
• F is preferred to be kept between B and C but away from A by three racks.

• C and E should be displayed next to each other, but A should be at least four racks away from D.
• A cannot be displayed next to C for the reason of mixed-product identity.

Now, if the positions of box of soaps C and E are interchanged, then how many 

then the new arrangement will be:

Clearly, 'three" soap boxes were placed above E.

Hence, the correct answer is "Three".

The table is alphabets place value:

The pattern followed here is:

Step 1: Consonants alphabets coded as the opposite alphabet.

• Consonants = Opposite alphabet

Step 2: Vowels alphabets coded as second next alphabet,

• Vowel + 2 = new alphabet.

'BEDROOM' is written as 'YGWIQQN'.

And,

'ELITE' is written as 'GOKGG'

Similarly,

'CONTEXT' = ?

Hence, 'CONTEXT' is coded as "XQMGGCG".

The logic follows here is:

There are eight friends Amit, Varsha, Suyog, Pooja, Shubham, Suhas, Nitin, and Pankaj sitting around a circular table facing inside not necessarily in the same order.

1) Pooja is third to the left of Nitin

2) There are two-person sitting between Pooja and Suhas

3) The person who faces Suhas sits third to the right of Amit

4) There are three-person sitting between Amit and Suyog

5) Varsha is not an immediate neighbor of Amit and Suyog. 

6) The person facing Nitin is not Pankaj

Therefore, the final sitting arrangement is 

From the above sitting arrangement. it is clear that Pooja is sitting between Pankaj and Shubham.

Hence, the correct answer is Pooja.

The pattern followed is:

Hence, the correct answer is "127".

Alternate Method

The pattern followed is:

3 = 2² - 1

7 = 2³ - 1

15 = 2⁴ - 1

31 = 2⁵ - 1

63 = 2⁶ - 1

127 = 2⁷ - 1

Hence, the correct answer is "127".

The logic follows here is:

When the mirror is held downside or horizontally at the bottom of the figure then the reflection of the figure in the mirror appears by inverting the figure vertically i.e. upside down.

Thus the correct mirror image of the given figure when the mirror is placed on the line AB is :

Hence, the correct answer is "Option 1".

Additional Information

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

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

According to the given information we have to check the options one by one:

Option 1) P A T T E R N P A T T E R N P A T T E R N

Option 2) P A T T E R N P A R R E R N P A T T E R N

Option 3) P T T T E R N P A T T E R N P A T T E R N

Option 4) P A T T E R N P A T T E R N P A T N E R T

Option (1) is giving a pattern of **PATTERN/**PATTERN/PATTERN.

No other option is giving any particular pattern.

Hence, the correct answer is "AERTTRPTN".

The sitting arrangement is as follows:

Apple and Mango are placed at the extreme ends.

Orange is placed second to the right of Apple and is the neighbour of Pear and Grapes. Case 2 is incorrect. But again there are two cases.

 

 

Banana is the neighbour of Mango and Pomegranate.

Grapes is placed immediate left of Pomegranate.

Hence Case 1.2 is incorrect.

 

Hence, Banana is placed second from the extreme right.

The above given relation can be shown using a family tree with the help of following symbols:

Family tree,

So, according to the family tree, the person in the photograph is kriti's husband

Hence, "Husband" is the correct answer.

The least possible Venn diagram:

Conclusions:

I. Some Clouds are Small → True (Some Clouds are Big and All Big are Small, so the part of Clouds which is Big is also Small).

II. Some Tiny can be Clouds → True (The possibility is true, as no direct relationship between the two is given).

III. All Small being Tiny is a possibility → False (The possibility is False, as Some Small are not Tiny is already given, so All Small will never be Tiny).

Hence, Both Conclusion I and II follows.

The logic followed here is :-

By using BODMAS RULE :

Option 1) : +, ×, ÷, -, =

Given equation : 63 * 7 * 4 * 34 * 119 * 49

After inserting the symbols in given equation the equation is as follows : 63 + 7 × 4 ÷ 34 - 119 = 49

⇒ 63 + 7 × 4 ÷ 34 - 119 = 49

⇒ 63 + 7 × 0.117 - 119 = 49

⇒ 63 + 0.819 - 119 = 49

⇒ 63.819 - 119 = 49

⇒ -55.181 ≠ 49

LHS ≠ RHS

Option 2) : -, ×, ÷, =, +

Given equation : 63 * 7 * 4 * 34 * 119 * 49

After inserting the symbols in given equation the equation is as follows : 63 - 7 × 4 ÷ 34 = 119 + 49

⇒ 63 - 7 × 4 ÷ 34 = 119 + 49

⇒ 63 - 7 × 0.117 = 119 + 49

⇒ 63 - 0.819 = 119 + 49

⇒ 63 - 0.819 = 168

⇒ 62.181 ≠ 168

LHS ≠ RHS

Option 3) : ÷, ×, =, +, -

Given equation : 63 * 7 * 4 * 34 * 119 * 49

After inserting the symbols in given equation the equation is as follows : 63 ÷ 7 × 4 = 34 + 119 - 49

⇒ 63 ÷ 7 × 4 = 34 + 119 - 49

⇒ 9 × 4 = 34 + 119 - 49

⇒ 36 = 34 + 119 - 49

⇒ 36 = 152 - 49

⇒ 36 ≠ 103

LHS ≠ RHS

Option 4) : ÷, ×, +, =, -

Given equation : 63 * 7 * 4 * 34 * 119 * 49

After inserting the symbols in given equation the equation is as follows : 63 ÷ 7 × 4 + 34 = 119 - 49

⇒ 63 ÷ 7 × 4 + 34 = 119 - 49

⇒ 9 × 4 + 34 = 119 - 49

⇒ 36 + 34 = 119 - 49

⇒ 70 = 119 - 49

⇒ 70 = 70

LHS = RHS

Hence, the correct answer is "÷, ×, +, =, -".

At 12:00 noon, the rays are vertically downward hence there will be no shadow.

Hence, no shadow formation will take place.

The pattern followed here is,

Option 1 → 125 - 36 → 5³ - 6²

Option 2 → 729 - 81 → 9³ - 9²

Option 3 → 343 - 49 → 7³ - 7²

Option 4 → 512 - 64 → 8³ - 8²

All option follows the same pattern, except ‘125 - 36’

Hence, 125 - 36 is the correct answer.

According to the given information:

Students A, B, C, D and E will be reading the NEWS headlines in their school assembly on a different day of a week starting from Monday and ending on Friday of the same week.

1. Student C will be reading the NEWS on the starting day.

2. Three students will be reading NEWS between C and D.

3. Student E will be reading the NEWS just before student B and just after student A. 

Thus, the order in which the students will be reading the NEWS is 'C, A, E, B, D'.

Hence, the correct answer is "C, A, E, B, D".

Ghoomar: Rajasthan → Ghoomar is probably the most popular folk dance in India. This dance form was introduced by the Bhil tribe and later adopted by the royal communities of Rajasthan, including Rajputs. 

Similarly,

Kathakali: _________ → kathakali is one of the famous classical dances of India that developed and remained popular in the state of Kerala. 

Hence, Kathakali is related to Kerala same as the Ghoomar related to Rajasthan.

The logic follows here is:

1st word is "country" and 2nd word is "country's capital".

On checking each option :

1) Finland : Kosovo

→ Here, Finland and Kosovo both are the name of country. It does not follow the logic so it is different.

2. Germany : Berlin

→ Germany is the country and Berlin is its capital

3. Austria : Vienna

→ Austria is the country and Vienna is its capital.

4. Belgium : Brussels

→ Belgium is the country and Brussels is its capital.

Hence, the correct answer is "Finland : Kosovo".

Additional Information

All laptops are Personal Computers. All personal Computers are a form of Electronics. Thus, the three concentric circles.

The correct Venn diagram representation is,

Hence, Option 1 is the correct answer.

We are going to solve the puzzle statement by statement,

Statement 1: P lives two floors above the floor of M, who lives three floors above the floor of Q: we have

Statemen**t 2: R does not live above or below the floor of M: We have the final solution shown below:

So, R lives on the 2^nd floor.

Hence, the correct answer is "Option(1)".

The diagram for the given direction problem is as follows:

Hence, Krishika is facing South direction after taking turns.

The logic follows here is :-

• is common symbol in two dice so, now if we rotate the dice from + in anticlockwise or clockwise directions. From the above diagram is clear that "@ is opposite to $",

"! is opposite to *", we cannot determine which symbol is opposite of +.

Hence, "! is opposite to *".

Thus, the correct answer is "Only *".

The table is alphabets place value:

The pattern followed here is:

 'DIAMOND' is written as 'ZRWRWML'

Similarly,

'KINGDOM' = ?

Hence, '​KINGDOM' is coded as "MRPLNLW".

The least possible Venn diagram from the given statement can be draw as:

Conclusion:

I. Some mobiles are sticks → Doesn't Follows (No direct relation establish between mobile and stick).

II. Some shoes are books → Doesn't Follows (No direct relation establish between shoes and book).

III. Some mobiles are books → Doesn't Follows (No direct relation establish between mobile and book).

Hence, the correct answer is "None of the conclusions follow".

The logic is:

QUY

LPT

JNR

EHK

MQU

Hence, ‘EHK’ is the odd one out.

The logic follows here is:

1) KXOB

2) DAHF

3) NVRZ

4) BNFR

Therefore, 'DAHF' does not follow the same logic that is being followed by the other options thus this is the odd letter series.

Hence, the correct answer is "DAHF".

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘SV’ is the correct answer.

The logic follows here is:

Given expression :

17 # 19 $ 23 % 18 @ 3

The given expression is decoded as:

17 + 19 - 23 × 18 ÷ 3 

⇒ 17 + 19 - 23 × 6 

⇒ 17 + 19 - 138 

⇒ 36 - 138 

⇒ -102

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

The least possible Venn diagram for the given statements is as follows-

Conclusions:

I. Some bicycle can be plane → True (The possibility is true as shown below, as no direct relationship between the two is given).

II. Atleast some jeeps are bicycle → True (As ‘All bicycles are jeeps, So some part of jeep is definitely bicycle).

Hence, Both I and II follow.

The performance of the individual has to be tested over a span of time as the statement mentions. So, it can be assumed that it is not possible to judge the performance of an individual before he is appointed. Therefore, I is implicit.

The statement mentions that the individual's worth shall be reviewed (during the probation period) before confirmation. So, we can assume that an individual tries to prove his worth in the probation period.

Hence, II is also implicit.

Additional Information

Probation period means the “trial period” that you serve as a new employee in an organization. It lets both the employee and the employer get to know each other better before the organization can offer him/her a regular or permanent position.

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘OTB’ is the correct answer.

Number of person: 6

There are two married couples.

Preparing the family tree using the following symbols:

There are two married couples. Qr is mother of Ab and is married to Mn. Sv is sister of Ab. Ab is father of Kw. Hd is married to grandson of Mn.

Hence, Kw is husband of Hd.

The pattern follows here is;

Hence, "222" is the correct answer.

Confusion PointsWe have added the prime numbers in each term.

Prime Numbers: 

Prime numbers are numbers that have only 2 factors: 1 and themselves.

For example, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 etc.

Composite Numbers:

Numbers with more than 2 factors are called composite numbers.

The correct answer is Cell wall is present in animals. 

Key Points

• Cell Wall:-
• Cell walls are rigid, protective outer coverings that surround the cells of plants, fungi, algae, and some bacteria.
• They provide structural support and protection to these organisms, help maintain cell shape, and prevent the cells from bursting due to osmotic pressure.
• Cell walls are not present in animals.
• In animals, on the other hand, cells are surrounded by a flexible and selectively permeable plasma membrane.
• This membrane controls the movement of substances in and out of the cell and serves similar functions to a cell wall, but it is not rigid like a cell wall.

Additional Information

• Mitochondria are often referred to as the "powerhouse of the cell."
• This nickname comes from their role in cellular respiration, a process that generates energy in the form of adenosine triphosphate (ATP).
• ATP is the primary energy currency that powers various cellular processes within the cell.
• Chromosomes are composed of a combination of DNA (deoxyribonucleic acid) and proteins.
• They are structures within the nucleus of eukaryotic cells that carry genetic information in the form of genes.
• The cell membrane is also commonly referred to as the plasma membrane.
• Both terms are used interchangeably to describe the same structure that surrounds and encloses the contents of a cell.

The Correct Answer is June 22.

In News

• World Rainforest Day: 22 June.

Key Points

• World Rainforest Day is celebrated on June 22 every year.
• It was founded in 2017 by the Rainforest Partnership.
• Rainforests are called the "lungs of the Earth" because they absorb carbon dioxide and release oxygen.
• The Amazon Rainforest is one of the largest and most important rainforests on the planet.

The correct answer is Mudumalai Tiger Reserve.

Key Points

• Mudumalai Tiger Reserve is among the Tiger Reserves which was granted the  'Conservation Assured Tiger Standards' status in July 2021.
• Total of 14 tiger reserves in India had received the 'Conservation Assured Tiger Standards' status.
• The accreditation was given on the occasion of International Tigers day 29 July 2021.
• The Baghrakshaks were recognized for their **remarkable efforts in saving tigers.**​

Additional Information

• Conservation Assured | Tiger Standards (CA|TS) is a global association of Tiger Range countries, which provides entrustment after the assessment of tiger conservation of facilities all over the world.
• It also sets the standards to encourage and guide tiger conservation.
• India has now 53 Tiger Reserves expanded in 18 States.
• The 14 tiger reserves which received Conservation Assured Tiger Standards' status are

1. ​Manas Tiger Reserve,
2. Kaziranga Tiger Reserve
3. Orang Tiger Reserve
4. Satpura Tiger Reserve
5. Kanha Tiger Reserve
6. Panna Tiger Reserve
7. Pench Tiger Reserve
8. Valmiki Tiger Reserve
9. Dudhwa Tiger Reserve
10. Parambikulam Tiger Reserve
11. Mudumalai Tiger Reserve
12. Anamalai Tiger Reserve
13. Bandipur Tiger Reserve
14. Sundarbans Tiger Reserve

The correct answer is July.

Key Points

• Dree festival:-
• It is a three-day event that is marked by a number of rituals and traditions.
• The Apatani people offer prayers to their four main gods - Tamu, Harniang, Metii, and Danyi - and sacrifice animals to them.
• They also perform traditional dances and songs, and feast on delicious food and drinks.
• It is celebrated on the 5th of July every year by the Apatani tribe.
• The festival is held to mark the end of the rice planting season and to pray for a bountiful harvest.
• The Dree festival is a vibrant and colorful celebration that is a must-see for anyone visiting Arunachal Pradesh in the month of July.

Additional Information

Some other festivals celebrated in Arunachal Pradesh are:-

• Nyokum (February):
• This festival is celebrated by the Nyishi tribe to promote peace and prosperity in the community.
• It is a two-day event that features singing, dancing, and socializing.
• Losar (February-March):
• This festival is celebrated by the Monpa and Sherdukpen tribes to mark the Tibetan New Year.
• It is a seven-day event that is marked by traditional rituals, dances, and songs.
• Solung (January-February)::-
• This festival is celebrated by the Adi tribe to mark the end of the harvest season.
• It is a four-day event that is marked by traditional dances, songs, and games.

The Correct Answer is 87th.

In News

• Harikrishnan A Ra becomes India’s 87th Grandmaster

Key Points

• Harikrishnan A. Ra, a chess player from Chennai, has become India’s 87th Grandmaster.
• Achieved his final GM norm on July 11, 2025, at the La Plagne Chess Festival in France.
• The milestone marks the end of a 7-year journey that began when he became an International Master.
• Harikrishnan is 23 years old.
• His achievement adds to India’s growing list of elite players in international chess.

Concept:

Digestion: 

• ​it is the complex process of turning the food we eat into nutrients, which the body uses for energy, growth and cell repair needed to survive.
• It also involves creating water to be excreted.

Human Digestive system:​

• Human Digestive system consists of the alimentary canal which can be further divided into various components. a) The buccal cavity b) food pipe or oesophagus c) stomach d) small intestine e) large intestine ending in the rectum f) the anus

Mouth or Buccal cavity:

• Food is taken into the body through the mouth. The process of taking food into the body is called ingestion.
• our mouth has the salivary glands which secrete saliva.
• When we chew the food, saliva secreted from the salivary gland and mixes with food.
• Food becomes moisten by getting mixed with saliva.
• Partial digestion of food starts here.

Food pipe:

• ​The swallowed food then passes into the food pipe or oesophagus.
• Food is pushed down by the movement of the wall of the food pipe.

The stomach: 

• The stomach is a thick-walled bag. Its shape is like a flattened U and it is the widest part of the alimentary canal.
• The inner lining of the stomach secretes mucous, hydrochloric acid, and digestive juices.
• The mucous protects the lining of the stomach.
• The acid kills many bacteria that enter along with the food and makes the medium in the stomach acidic, which helps digestive juices to break down the proteins into simpler substances.

The Small Intestine:

• It is highly coiled and is about 6-8 meters long. It receives secretions from the liver and the pancreas.
• The digested food can now pass into the blood vessels in the wall of the intestine. This process is called absorption.
• The inner walls of the small intestine have thousands of finger-like outgrowths.
• These are called villi. (It increases the surface area of absorption of the digested food).

Large intestine: 

• ​It is wider and shorter than the small intestine.
• It is about 1.5 meters in length.
• Its function is to absorb water and some salts from the undigested food material.

Conclusion:

So, the correct sequence through which food goes under the complete process of digestion is

Mouth → oesophagus → stomach → small intestine → large intestine

The correct answer is option 4. i.e. Financial.

Key Points

• The Supreme Court of India has Original, Appellate, writ and Advisory jurisdiction.
• Original Jurisdiction: As per Article 32 Supreme Court is the guardian/protector of fundamental right and any person whose fundamental rights are violated can directly approach the Supreme Court for a remedy and any matter regarding the enforcement of fundamental rights comes under the original jurisdiction of the supreme court.
• The Supreme Court has original jurisdiction in a matter related between any dispute - 
• Government of India vs and one or more states
• Government of India and states on one side and states on another side
• States vs states
• Appellate Jurisdiction - 
• ​Supreme Court is the highest court of appeal from all courts in the territory of India.
• For example - Article 134: Provides the Supreme Court with appellate jurisdiction in the criminal matters from any judgment, final order, or sentence of the high court.
• Advisory Jurisdiction - 
• Article 143 (Power of President to consult supreme court)
• If the President feels that a question of law or fact has arisen or is likely to arise and the question is of such a nature of such public importance that it is expedient to obtain the opinion of the Supreme Court.
• The Supreme Court is free to advise the President or not.
• Such an opinion is not binding on the President.

Concept:

• R.H. Whittaker gave the Five Kingdom classification for living organisms.
• The five kingdoms were Monera, Protista, Fungi, Plantae, and Animalia.
• Kingdom Plantae includes all the plants.
• They are eukaryotic, multicellular, and autotrophic organisms.
• The plant cell contains a rigid cell wall.
• The plant kingdom has been classified into five subgroups namely-
• Thallophyta
• Bryophyta
• Pteridophyta
• Gymnosperms
• Angiosperms

Explanation:

Bryophytes:

• Bryophytes do not have vascular tissues.
• The plant body has root-like, stem-like, and leaf-like structures.
• Bryophytes are terrestrial plants but are known as “amphibians of the plant kingdom” as they require water for sexual reproduction.
• They are present in moist and shady places.
• They include mosses, hornworts, and liverworts.
• Examples are Marchantia, Funaria, Sphagnum, etc.

Thus, Bryophytes are called “Amphibians of the plant kingdom”.

Additional InformationPteridophyta:

• Pteridophytes have a well-differentiated plant body into roots, stems, and leaves.
• They have a vascular system for the conduction of water and other substances.
• Examples are Selaginella, Equisetum, Pteris, etc.

Gymnosperms:

• Gymnosperms have a well-differentiated plant body and vascular tissues.
• They bear naked seeds, i.e. seeds are not enclosed within a fruit.
• Examples of gymnosperms are Cycas, Pinus, Ephedra, etc.

Angiosperms:

• Angiosperms are seed-bearing vascular plants with a well-differentiated plant body.
• The seeds of angiosperms are enclosed within the fruits.
• Examples are mango, rose, tomato, onion, wheat, maize, etc.

The correct answer is Only 1.

Key Points

• Money Bill​
• ​Article 110 of the Constitution deals with Money Bills.
• It can be introduced only in Lok Sabha with prior approval from the president.
• Rajya Sabha can only suggest amendments but Lok Sabha is not bounded to accept them.
• A Bill is said to be a Money Bill if it only contains provisions related to-
• taxation
• borrowing of money by the government
• expenditure from or receipt to the Consolidated Fund of India

Additional Information

• A Bill shall not be deemed to be a Money Bill by reason only that it provides for the imposition of fines or other pecuniary penalties, etc.
• If any question arises whether a Bill is a Money Bill or not, the decision of the Speaker of the House of the People thereon shall be final.
• There shall be endorsed on every Money Bill when it is transmitted to the Council of States under article 109.
• When it is presented to the President for assent under article 111, the certificate of the Speaker of the House of the People signed by him that it is a Money Bill.

the correct option is seafloor spreading

The term that is not related to the Continental Drift Theory is "the concept of seafloor spreading." which is a separate theory. The other three terms are all related to the theory.

Important Points

Continental Drift Theory (Alfred Wegener in 1912):

• Continental drift theory was proposed by Alfred Wegener in 1912.
• It was first put forward by Abraham Ortelius in 1596 before fully being developed by Albert Wegener.
• The theory deals with the distribution of the oceans and the continents*.*
• According to Wegener’s Continental Drift theory, all the continents were one single continental mass (called a Supercontinent) – Pangaea and a Mega Ocean surrounded this supercontinent. The Mega Ocean is known by the name Panthalassa.
• Although Wegener's initial theory did not cover mantle convection until Arthur Holmes later proposed the theory.
• According to this theory, the supercontinent, Pangaea, began to split some two hundred million years back.
• Pangaea first split into 2 big continental masses known as Gondwanaland and Laurasia forming the southern and northern modules respectively.
• Later, Gondwanaland and Laurasia continued to break into several smaller continents that exist today.

Jigsaw fit: 

• According to Wegener, there is geographical similarity along both the coasts of the Atlantic Ocean.
• Both the opposing coasts of the Atlantic can be fitted together in the same way as two cut-off pieces of wood can be refitted (jig-saw fit)

panthalasa

• The size of the panthalasa (primitive Pacific Ocean) was remarkably reduced because of the movement of continental blocks from all sides toward the Panthalasa.
• Thus, the remaining portion of Panthalasa became the Pacific Ocean.

Paleoclimate

• Paleoclimate data provides important evidence for this theory by showing how the positions of continents have influenced global climate patterns in the past.
• For example, the study of ancient climate zones can help infer how continents were positioned and how this influenced ocean currents, atmospheric circulation, and other climate-related phenomena.

Additional Information 

• Harry Hess proposed the theory of SeaFloor Spreading in 1961.
• He stated that new lava pushes out the plates from the mid-oceanic ridge.
• Paleomagnetic studies of the ocean floor reveal that there is an intense volcanic eruption and a huge amount of lava coming out along the mid-Atlantic ridges.
• The equidistant rock formation has similar age, magnetic properties, and chemical compositions.
• Rocks which are closer to the mid-oceanic ridges are young having normal polarity.
• The oceanic crust is much younger than the continental crust.
• The ocean floor is very thin.
• He said that the new plate is created at the divergent boundary and the older plate is destroyed at the convergent boundary.

The Correct Answer is 2026.

In News

• Empowering women in agriculture for food security.

Key Points

• 2026 is declared as the International Year of the Woman Farmer.
• The declaration was made by the United Nations General Assembly (UNGA).
• Supported by over 100 co-sponsoring countries.
• The goal is to recognise women's role in agriculture and raise awareness about their challenges.
• Women face barriers such as limited property rights and restricted market access.
• It promotes resilient agricultural development and gender equality.
• Aims to ensure food security through women’s empowerment in agriculture.

The correct answer is "Punjab"

Key Points  Ghiyas-ud-din Tughlaq: 

• He crushed the revolts in the unfriendly provinces with sturdy influence and resorted to harmony, law, and order
• He structured an improved postal system
• He encouraged agriculture in his Era.

Additional Information

Ala-ud-din Khilji:

• The system of administration as set up by him was thorough and efficient.
• Sultan Alauddin maintained peace and order throughout the vast empire.
• He employed a large number of spies and they kept him informed of the activities of the people and their reactions to the measures of the Government.
• He fixed the price of commodities at a low level and his regulation of the market is one of the marvels of medieval statesmanship.
• He was also a patron of architecture and arts. He caused a new town to be built near Delhi.
• He also constructed a fairly large number of schools, inns, and mosques in different parts of his Empire.
• Amir Khusrau, the famous poet, was one of the many literary artists who enjoyed his patronage.

Important Points   Chronology of the Delhi Sultanate

The correct answer is Golden Girl.

Key Points

• The author of the book ‘Golden Girl’ is P.T Usha and Lokesh Sharma.
• This book is an autobiography of P.T. Usha.

Important Points

• P.T. Usha is known for her stellar performance at the 1984 Los Angeles Olympics.
• PT Usha won 200m, 400m, 400m hurdles at the 1986 Asian Games in Seoul. She is known as ‘Payyoli Express.
• She also won five gold medals in the 1985 Asian Games in Jakarta.
• She received the Arjuna Award in 1983 and Padma Shri in 1985.
• She has been appointed as a member of the Athletes Commission of the Asian Athletics Association (AAA).
• She has been awarded the prestigious International International Association of Athletics Federation (IAAF) Veteran Pin Award.

Additional Information

• Autobiography of Sports personalities​

The correct answer is Chronic.

Key Points

• Chronic Unemployment:
• Chronic unemployment refers to long-term unemployment typically caused by structural problems in the economy.
• It is not due to the usual ups and downs of the business cycle but rather persists even in good economic times.
• Those who suffer from chronic unemployment lack the skills or education needed for new jobs or live in parts of the country where jobs are scarce.
• This type of unemployment can lead to a vicious cycle of joblessness, poverty, and social issues.
• It requires concerted policy efforts to resolve, such as retraining programs, education reform, and economic development initiatives.

Additional Information

• Casual Unemployment:
• This refers to temporary unemployment which occurs when workers are laid off or lose their jobs due to seasonal changes in demand or supply in certain industries.
• Technological Unemployment:
• This type of unemployment is caused by technological changes or automation that render certain jobs obsolete.
• Workers displaced by technology need to acquire new skills to find employment in other sectors.
• Frictional Unemployment:
• This is a type of short-term unemployment that occurs when people are between jobs or are looking for their first job.
• It's a natural part of the job market as people move between roles and careers.

The correct answer is Division of land.

Key Points

• The right of inheritance, specifically in the context of land or property, often leads to the division of land among heirs.
• Inheritance laws differ across countries and cultures, but the common principle is the passing of property, rights, obligations, debts, and even titles upon the death of an individual.
• The division of land can sometimes lead to fragmentation, creating smaller and potentially less productive plots.
• This can have significant implications for agricultural practices and rural development.

Additional Information

• There are various forms of inheritance, including primogeniture (where the eldest son inherits everything), ultimogeniture (where the youngest son inherits everything), and partible inheritance (where the property is divided among heirs).
• In some cases, laws have been enacted to prevent excessive fragmentation of agricultural land.
• For example, in India, the Land Ceiling Act sets a maximum size for agricultural holdings and prohibits their further subdivision. While the division of land is the most direct outcome of inheritance, it can indirectly contribute to other issues such as land disputes and, in some cases, may influence land use and contribute to environmental concerns.

The Correct Answer is Wheat.

Key Points

• Kharif Season:
• Kharif crops also are known as monsoon crops as they are cultivated in the monsoon season.
• These crops are sown at the beginning of the rainy season.
• Rice, maize, bajra, ragi, paddy, sorghum, soybean, groundnut, cotton, etc are all Kharif types of crops.
• Zaid Season:
• It is a short season between Kharif and Rabi seasons.
• The crops grown during this season are known as Zaid crops.
• Pumpkin, cucumber, watermelon, bitter gourd etc are all zaid types of crops.
• Rabi Season:
• These are the crops that are sown at the end of the monsoon season or at the beginning of the winter season.
• These crops also are known as winter crops.
• Wheat, Mustard, Pulses, Barley, etc. are all Rabi types of crops.

The correct answer is Nana Sahib.

• Nana Sahib was believed to be the leader of the Sanyasis and Fakirs conspiring against the British in 1857.

Key Points

• Nana Sahib was believed to be the leader of the Sanyasis and Fakirs in the 1857 Revolt.
• Sanyasi Revolt or uprising engulfed the area of Bengal {including modern Bangladesh}, Bihar, and Uttar Pradesh.
• Anandamath, written by India’s first modern novelist Bankim Chandra Chatterjee is the best reminder of the Sanyasi/Fakir Rebellion.
• Vande Mataram, India’s National Song has been taken from this novel.
• The sanyasis, with a tradition of fighting against oppression, espoused the popular causes and organized raids on the company’s factories, state treasuries, and valiantly fought against the Company’s armed forces.

Additional Information

• Mangal Pandey belonged to the 34 Native Infantry.
• Bahadur Shah II was the last Mughal Emperor.
• Queen Zeenat Mahal was the wife of Bahadur Shah Zafar.

The Correct Answer is ​Ministry of Electronics and IT (MeitY).

In News

• MeitY Launches 'Tec-Verse 2025' To Accelerate Indigenous Tech Innovation.

Key Points

• Tec-Verse 2025 is the inaugural technology showcase event by the Ministry of Electronics and Information Technology (MeitY).
• Supports the broader vision of Viksit Bharat 2047.
• Features R&D contributions from premier MeitY institutions:
• C-DAC (Centre for Development of Advanced Computing)
• SAMEER (Society for Applied Microwave Electronics Engineering & Research)
• C-MET (Centre for Materials for Electronics Technology)
• Aims to highlight indigenous innovations that solve real-world societal challenges.
• Represents a shift toward a product-driven economy.
• Will be held annually to promote research, development, and commercialization of cutting-edge technologies.

The correct answer is Acharya Vinoba Bhave

Key Points

• Acharya Vinoba Bhave:-
• He was the first individual Satyagrahi of India.
• He was chosen by Mahatma Gandhi to launch the Individual Satyagraha movement in October 1940.
• Bhave was a close associate of Gandhi and a leading figure in the Indian independence movement.
• He was also a renowned scholar, social reformer, and advocate of nonviolence.
• As the first individual Satyagrahi, Bhave was arrested for giving a speech against the British government's participation in World War II.
• He was followed by thousands of other Satyagrahis who were also arrested for peacefully protesting against British rule.
• The Individual Satyagraha movement was an important step in the Indian independence struggle, and it helped to galvanize public support for the Indian National Congress.

Additional Information

• Jawaharlal Nehru:-
• He was the first Prime Minister of India and a leading figure in the Indian independence movement.
• He was a close associate of Mahatma Gandhi and a member of the Indian National Congress.
• Nehru was a socialist and a secularist, and he played a key role in shaping India's post-independence foreign policy.
• Jai Prakash Narayan:-
• He was a socialist leader and a prominent figure in the Indian independence movement.
• He was a member of the Indian National Congress and the Socialist Party of India.
• JP was a strong advocate of nonviolence and civil disobedience, and he played a key role in the Quit India Movement of 1942.
• Mahatma Gandhi:-
• He was the pre-eminent leader of Indian nationalism in British-ruled India. Employing nonviolent civil disobedience, Gandhi led India to independence and inspired movements for civil rights and freedom across the world.
• The honorific title Mahatma—meaning "high-souled"—was bestowed on him first in 1914 in South Africa, and became widely used in India in the 1920s.
• He is internationally honored as the Father of India.

The correct option is Protons and Neutrons.

Key Points

• Atom is the smallest tiny particle or unit of any compound or molecule.
• Atom is composed of electrons, protons, and neutrons called subatomic particles**.**
• The middle or center of an atom is known as the nucleus.
• The nucleus of the atom consists of protons and neutrons.
• Atom and its structure are discovered by scientist John Dalton.
• All the elements and materials consist of small atomic particles.
• Every element has an atomic particle with a different character than the other element.
• Atom is a neutral species as the number of protons in the nucleus of an atom is equivalent to the number of electrons around it.

Additional Information Electrons

• The subatomic particle of an atom containing a negative charge is called electrons.
• It is denoted as e-.
• Electrons are present around the nucleus of an atom rotating in an orbit.
• The negative charge of an electron is equivalent to -1.602 x 10 ^-19 coulomb.
• Sir J. J. Thomson was a physicist who discovered electrons.

​Protons

• The subatomic particles of an atom containing a positive charge are called protons.
• It is denoted as H+.
• Protons are present inside the centrally placed nucleus of an atom.
• The charge of a proton is equivalent to +1.602 x 10 ^-19 coulomb.
• The scientist Ernest Rutherford discovered the protons.​

Neutrons

• The subatomic particle of atoms containing no charge or neutral is called neutrons.
• It is denoted by n⁰ or n.
• Neutrons are present inside the nucleus of an atom with protons.
• The neutrons have zero charges on them.
• The mass of neutrons is quite more than the mass of protons.
• The scientist James Chadwick discovered the neutrons.

Nucleus

• The central area or middle portion of an atom is called the nucleus of an atom.
• The mass of an atom depends on the mass of its nucleus.
• The nucleus of an atom is filled with tightly packed protons and neutrons.
• The nucleus shows a positive charge due to the net positive charge of protons in it.

The correct answer is option 4.

Key Points

• B.R. Ambedkar is known as the sculptor of the Indian constitution.
• He was the chairman of the drafting committee.

Additional Information

• V.V. Giri
• He served as the 4th president of India.
• He is the only person to be elected as president as an independent candidate.
• Received Bharat Ratna in 1975.
• Rajendra Prasad
• He was the first president of the Republic of India.
• He was the President of the constituent assembly.
• Dr. S. Radhakrishnan
• He was the 2nd president of India.
• He was the 1st Vice president of India.

The correct answer is Tamil Nadu.

Key Points

• Brihadeeswara Temple is located in Thanjavur, Tamil Nadu.
• The temple is also known as Rajarajeswaram Temple.
• It is a Hindu temple dedicated to Lord Shiva.
• It is located on the south bank of river Kaveri.
• The temple is in Dravidian style.
• The temple was built by Chola emperor Raja Raja Chola I.

Additional Information

The correct answer is option 4 i.e. Papikonda National Park

The correct answer is Firefly.

In News

• Pixxel Space launched Firefly, India’s first private satellite constellation, marking a significant milestone in hyper-spectral imaging.

Key Points

• Firefly satellites provide the world’s highest-resolution hyperspectral images.
• They can observe the Earth in over 150 spectral bands.
• The satellites benefit diverse sectors, including agriculture and defense.
• Launched via SpaceX, showcasing India's private sector capabilities in space technology.

Additional Information

• Hyper-spectral Imaging
• A technology that captures detailed spectral information across numerous bands.
• Useful in areas like resource mapping, environmental monitoring, and defense applications.
• SpaceX
• An American aerospace company facilitating satellite launches for global clients.
• Pixxel Space
• An Indian space-tech startup specializing in satellite imaging and data analytics.

The revolt of 1857 was the conscious beginning of the Independence struggle against the colonial tyranny of the British.

• There are various names for the revolt of 1857 – India’s First War of Independence, Sepoy Mutiny, etc.
• It was initiated by sepoys in the Bengal Presidency against the British officers.
• This war of Independence marked the end of rule by the British East India company.

Important Points

Mangal Pandey was the first soldier to be hanged for the 1857 revolt.

• He was an Indian soldier in the British army and is believed to be one of the key figures behind Sepoy Mutiny or India’s First War of Independence in 1857.
• Due to his attack on two British soldiers, Mangal Pandey was hanged to death on April 8, 1857, at the age of 29.
• On 29 March 1857, Mangal Pandey, a sepoy of the 34th Bengal Native Infantry (BNI) mutinied against his commanding officers of the East India Company.
• This event and Pandey’s subsequent punishment led to more resentment among the sepoys of the Bengal Army ultimately aiding in the Revolt of 1857.
• Mangal Pandey’s mutiny did not directly cause the Revolt of 1857 but it did intensify the feeling of anger and frustration that Indian sepoys harboured against their English masters.

Additional Information

• Srimanth Mahadji Shinde (also spelt as Mahadji Scindia) was a Maratha statesman known for his crucial role in resurrecting Maratha power following the disastrous Third Battle of Panipat in 1761.
• Batukeshwar Dutt, also known as B K Dutt, was a Revolutionary Freedom Fighter. He, who was involved in the Central Legislative Assembly Bombing Case of 1929, passed away on 20th July 1965 after an illness at the age of 54.

The correct answer is Panipat.

• The First Battle of Panipat was fought between the Babur and the Lodi Empire, which took place on 21^st April 1526 in the small village of Panipat of the present-day Indian state of Haryana in North India.
• It marked the beginning of the Mughal Empire. This was one of the earliest battles involving gun powder firearms and field artillery.

Additional Information

Some of the battles fought are: 

The Correct Answer is ​Switzerland.

In News

• The U.K. House of Commons passed the Assisted Dying Bill to allow terminally ill people in England and Wales to end their lives.

Key Points

• The U.K. House of Commons has passed the Assisted Dying Bill for England and Wales.
• It allows terminally ill patients with less than 6 months to live to choose to end their lives.
• Patients must be:
• Of sound mind
• Approved by 2 doctors, a psychiatrist, a senior lawyer, and a social worker.
• Supporters see the bill as humane, offering dignity and relief from suffering.
• Critics worry it may pressure vulnerable or disabled people to choose death to avoid burdening family.
• Switzerland was the first country to legalise assisted dying in 1942.

The correct answer is Seventh.

Key Points

• The main objectives of the Seventh Five-Year Plan were to establish growth in areas of increasing economic productivity, production of food grains, and generating employment through "Social Justice".
• The Seventh Five-Year Plan was led by the Congress Party with Rajiv Gandhi as the prime minister.
• The plan laid stress on improving the productivity level of industries by upgrading technology.
• The Seventh Plan had strived toward socialism and energy production at large.
• The thrust areas of the Seventh Five-Year Plan were:
• Social justice, removal of oppression of the weak, using modern technology, agricultural development, anti-poverty programmes, a full supply of food, clothing, and shelter, increasing the productivity of small- and large-scale farmers, and making India an independent economy.
• The target growth rate was 5.0% and the actual growth rate was 6.01% and the growth rate of per capita income was 3.7%.

Majority of the members of the Rajya Sabha are elected by the elected members of the legislative Assemblies of various states.

Key Points

• The Rajya Sabha is the upper house of the Indian Parliament, and it is composed of 250 members.
• Of these members, 238 are elected by the elected members of the legislative assemblies of the various states.
• The remaining 12 members are nominated by the President of India.
• The method of election for the Rajya Sabha is proportional representation by means of the single transferable vote.
• This means that each voter has a number of votes equal to the number of seats that are being contested in their state.
• They can cast their votes for as many candidates as they like, but they cannot give more than one vote to any one candidate.
• The votes are then counted, and the candidates who receive the most votes are elected.
• If no candidate receives the majority of the votes, then the votes are transferred to the other candidates according to the preferences of the voters.
• This process continues until all of the seats have been filled.
• The Rajya Sabha is a very important part of the Indian Parliament.
• It has the power to pass laws, approve the appointment of the Prime Minister, and impeach the President.
• It also has the power to review laws passed by the Lok Sabha, the lower house of Parliament.
• The Rajya Sabha is designed to represent the interests of the states in the Indian Parliament.
• The fact that the majority of its members are elected by the elected members of the legislative assemblies of the various states ensures that the states have a strong voice in the national decision-making process.

The correct answer is Geneva.

Key Points

• International Labour Organization (ILO):
• It is a specialized agency of the United Nations (UN) dedicated to improving labour conditions and living standards throughout the world.
• Established in 1919 by the Treaty of Versailles as an affiliated agency of the League of Nations, the ILO became the first affiliated specialized agency of the United Nations in 1946. In recognition of its activities, the ILO was awarded the Nobel Prize for Peace in 1969.
• The functions of the ILO include the development and promotion of standards for national legislation to protect and improve working conditions and standards of living.
• India is a founding member of the ILO and it has been a permanent member of the ILO Governing Body since 1922.
• In India, the first ILO Office was started in 1928.
• Headquarters: Geneva, Switzerland
• Current Director-General: Gilbert Houngbo

Important Points

The correct answer is Cash reserve ratio.

Key Points

The correct answer is Captain Mohan Singh at Singapore in 1942.

Important Points

• In December 1941, Captain Mohan Singh, a young officer of the Punjab Regiment of the British Indian Army who had surrendered to the Japanese in the jungles of Malaya, agreed to cooperate with Fujiwara to raise an Indian army with Prisoners of Wars(POWs) to march alongside the Japanese to liberate India.
• After the fall of Singapore, several POWs were ready to join Mohan Singh. By the end of 1942, 40,000 men were ready to join the INA.
• In June 1942, a united Indian Independence League, representing all Indians in Southeast Asia was born as a civilian political body having controlling authority over the army.
• To chair this body, Rash Behari Bose, a veteran Bengali revolutionary then living in Japan was flown in.
• As Mohan Singh insisted on autonomy and allied status, he was removed from command and put under arrest.
• Rash Behari Bose tried to hold the banner for some time, but he was then too aged for the task. By the beginning of 1943, the first INA experiment virtually collapsed.
• As Mohan Singh had often mentioned to the Japanese, the INA movement needed a new leader and outside India, only one person could provide that leadership, and that was Subhas Chandra Bose.
• On an invitation from Ras Bihari Bose, Subhash Chandra Bose came to East Asia on June 13, 1943.
• Subhas Chandra Bose was made president of the Indian Independence League and the leader of the INA popularly called ‘Azad Hind Fauz’.
• Subhas Chandra Bose gave the famous battle cry ‘Chalo Dilli’. He promised independence to Indians saying, ‘tum mujhe khoon do, main tumhe Azadi dunga’ (You give me blood, I will give you freedom).

The correct answer is State election commission.

Key Points

• The Panchayati Raj System
• The Panchayati Raj System relates to the local self-government in India.
• It was adopted to decentralize the power of democracy.
• Democratic decentralization means that governmental power is divided at the local levels rather than concentrated in one place.
• So that citizens can participate and contribute to governance as per their interests and needs.
• According to Gandhiji - By improving the condition of villages, the country can be made unbeatable in all respects.
• That is why the organization of Gram Panchayats was arranged according to Gandhiji's imagination under Article 40 in the Constitution.
• The Panchayati Raj Institute was given constitutional status through the 73rd Constitutional Amendment Act, 1992 to establish democracy at the grassroots level and was entrusted with the task of rural development in the country.​

Additional Information

• State election commission 
• In Article 243 K, it is mentioned that a State Election Commission consisting of a State Election Commissioner is to be appointed by the Governor.
• Under Part IX of the Indian Constitution, Article 243 K tells about State Election Commissioner.
• State Election Commissioner shall only be removed from his office on the like ground as a Judge of a High Court.
• Tenure of State Election Commissioner is 6 years or up to the age of 65 years.

The correct answer is Anodising.

Key Points

• Anodising is the process in which a thick oxide layer of aluminium is developed over the aluminium articles that is dyed to give an attractive finish.
• Aluminium anodising is a process that creates a layer of aluminium oxide to protect the base metal from environmental impacts.
• What is Anodising?
• It is an electrochemical process that develops an aluminium oxide coat on the surface of the part or product.
• This protects the product from wear and tear while improving the aesthetics. In this process, the product to be coated acts as an anode in an electrolytic cell, hence the name.
• On an industrial scale, anodising made its first appearance in 1923.

Additional Information 

• Aluminium is the second most widely used metal in the world.
• Engineers prefer aluminium for its light weight, corrosion resistance and reasonable price.
• However, untreated aluminium has low wear resistance.

The correct answer is option 1.

Key Points

Ken River:

• Geographical Significance:
• The Ken river is the main river of the Bundelkhand plateau, located in the northeastern part of Madhya Pradesh.
• Lifeline of Panna National Park:
• Recognized as the lifeline of Panna National Park.
• Flows south to north for about 55 km within the park. Hence, option 1 is correct.
• Pandava Waterfall:
• The Pandava waterfall is formed by the Ken river and its tributaries within the Panna National Park.

The Correct Answer is 12.

In News

• 'Maratha Military Landscapes' inscribed on UNESCO World Heritage List.

Key Points

• The ‘Maratha Military Landscapes’ have been inscribed on the UNESCO World Heritage List.
• This was decided during the 47th session of the World Heritage Committee (WHC) held in Paris.
• The nomination was submitted under the 2024–25 cycle.
• The site represents extraordinary fortifications and military systems envisioned by the Maratha rulers.
• The landscapes were developed between the 17th and 19th centuries.
• The listing includes 12 components, showcasing strategic military power across varied geographical and physiographic regions.
• The 12 forts included are:
• In Maharashtra: Salher, Shivneri, Lohgad, Khanderi, Raigad, Rajgad, Pratapgad, Suvarnadurg, Panhala, Vijay Durg, Sindhudurg
• In Tamil Nadu: Gingee Fort

The correct answer is Tamil Nadu, Kerala, Karnataka.

Key Points

• The Nilgiri Biosphere Reserve is India's first biosphere reserve, established in 1986.
• It spans across three Indian states: Tamil Nadu, Kerala, and Karnataka.
• The reserve covers an area of approximately 5,520 square kilometers.
• It is part of the Western Ghats, a UNESCO World Heritage Site known for its rich biodiversity.
• The Nilgiri Biosphere Reserve is home to several endemic species, including the Nilgiri Tahr and the Lion-tailed Macaque.

Additional Information

• Biosphere Reserve:
• A biosphere reserve is an area designated to protect biodiversity and promote sustainable development.
• It comprises three zones: the core area (protected region), buffer zone (activities promoting conservation), and transition area (sustainable resource use).
• Western Ghats:
• The Western Ghats is one of the eight "hottest hotspots" of biological diversity in the world.
• It is recognized as a UNESCO World Heritage Site for its unique ecosystems.
• Flora and Fauna:
• The Nilgiri Biosphere Reserve hosts over 3,000 species of flowering plants and a variety of mammals, birds, reptiles, and insects.
• Endangered species like the Tiger, Elephant, and Nilgiri Langur are found here.
• UNESCO Program:
• The Nilgiri Biosphere Reserve is part of UNESCO’s Man and Biosphere (MAB) Program, which promotes conservation and sustainable development.
• It aims to balance environmental conservation with human activity.

The correct answer is 1993.

Key Points

• Qutb Minar:
• The Qutb Minar is five stories high.
• It is a 73 m-high tower of victory and the world's largest brick minaret in the world.
• Qutab-ud-din Aibak started the construction of Qutb Minar in 1193.
• The band of inscriptions you see is under its first balcony.
• Iltutmish completed the construction of Qutb Minar.
• Over the years it was damaged by lightning and earthquakes and repaired by Alauddin Khalji, Muhammad Tughluq, Firuz Shah Tughluq, and Ibrahim Lodi.
• Qutab Minar is a minaret and "victory tower" that forms part of the Qutb complex.
• It was added to the list of UNESCO World Heritage Site in 1993.
• It is one of the most visited tourist spots in the city due to it being one of the earliest that survives in the Indian subcontinent.

The correct answer is Noma

In News

• On December 15, 2023, the World Health Organization (WHO) officially added ‘noma’ to its list of neglected tropical diseases (NTDs).

Key Points

• Noma is a gangrenous disease that affects the mouth and face, with a 90% mortality rate.
• The disease is linked to extreme poverty, malnutrition, poor sanitation, and weak immunity.
• It mostly affects children aged 2–6 in poor communities, especially in sub-Saharan Africa.
• The name "noma" is derived from the Greek word “nomē,” meaning “to devour.”

Additional Information

• Noma
• Also known as cancrum oris or gangrenous stomatitis.
• Begins with gum inflammation, possibly triggered by bacteria after illnesses like measles.
• Prevention and early treatment involve antibiotics, rehydration, and nutritional rehabilitation.
• Survivors often suffer from disfigurement, jaw muscle spasm, and speech problems.
• Now recognized as an NTD, it will receive global attention, research, and funding support.

The correct answer is Reservation for Economically Weaker Section.

Key Points

• 103rd Constitutional Amendment Act is related to a 10% quota for Economically Weaker Sections.

Additional Information

• 102nd Constitutional Amendment Act provides constitutional status to the National Commission for Backward Classes (NCBC).
• 101st Constitutional Amendment Act is related to the Goods and Service Tax (GST).
• 104^th Amendment Act, 2020 - Extended the deadline for the cessation of seats for SCs and STs in the Lok Sabha and states assemblies from Seventy years to Eighty. Removed the reserved seats for the Anglo-Indian community in the Lok Sabha and state assemblies.

Given:

In the table, Store A, B, C, D, E sold the cars 199, 175, 123, 110, 99

Formula used

Total number of cars sold in March = Store A sold cars + Store B sold cars + Store C sold cars + Store D sold cars + Store E sold cars

Calculation

Total number of cars sold in March months = 199 + 175 + 123 + 110 + 99

The total number of cars sold in March = 706

Given:

A = 9075

P = 7500

R = 10%

Formula used:

A = P(1 + r/100)ⁿ

SI = (P × R × T)/100

where,

A = Amount

P = Principal

r = Rate of Interest

n = number of years

SI = Simple Interest

Calculation:

A = P (1 + r/100)ⁿ

⇒ 9075 = 7500( 1 + 10/100)^T

⇒ 9075/7500 = (1 + 1/10)^T

⇒ 121/100 = (11/10)^T

⇒ (11/10)² = (11/10)^T

⇒T = 2 years

Now, 

P = 7500

R = 10%

T = 2 years

SI = P × R × T/100

⇒ (7500 × 10 × 2)/100

⇒ 1500

∴ The simple interest is 1500

If 8 digit number 2074x4y2 is divisible by 88, the number will also be divisible by 8 and 11 both.

A number will be divisible by 8 if the last three digits of a number is divisible by 8.

The divisibility rule of 11 is that you must subtract and then add the digits in an alternating pattern from left to right. If your answer is 0 or 11 then it is divisible by 11.

⇒ 4y2 is divisible by 8 if y = 3 or 7

If y = 3, then

⇒ 2074x432 will be divisible by 11 if x = 9

If y = 7, then

⇒ 2074x472 is divisible by 11 if x = 5

Now we can say, if y = 3 then x = 9 and if y = 7, then x = 5

⇒ (4x + 3y)

⇒ (4 × 9 + 3 × 3) = 36 + 9 = 45

⇒ (4 × 5 + 3 × 7) = 20 + 21 = 41

Shortcut Trick

Net percentage change formula = x + y + (xy/100)

Here, length reduction (x) = −15% and breadth increment (y) = +10%

Net change = −15 + 10 + [(−15 × 10) / 100]

Net change = −5 − 1.5 = −6.5%

Negative sign indicates a decrement.

∴ The correct answer is 6.5% decrement.

Alternate Method

Given:

Reduction in length = 15%

Increase in breadth = 10%

Formula:

Area of Rectangle = Length × Breadth

Calculations:

⇒ Let original Length (L) = 100 and original Breadth (B) = 100

⇒ Original Area = 100 × 100 = 10000

⇒ New Length = 100 − 15% of 100 = 85

⇒ New Breadth = 100 + 10% of 100 = 110

⇒ New Area = 85 × 110 = 9350

⇒ Change in Area = 10000 − 9350 = 650

⇒ Percentage Change = (650 / 10000) × 100 = 6.5%

⇒ Since New Area < Original Area, it is a decrement.

∴ The correct answer is 6.5% decrement.

Additional Information

Successive Percentage Change

When a value is changed by a% and then by b%, the net change is given by [a + b + (ab/100)]%.

Area and Perimeter Relations

If the side of a square is increased by x%, the area increases by [2x + (x²/100)]%.

Base Value Concept

Percentage changes are always calculated on the initial/base value unless specified otherwise.

Shortcut Trick

Total percentage gap = Gain% − (−Loss%) = 20% + 2% = 22%.

According to the question, this 22% gap represents Rs. 44.

1% of Cost Price = 44 ÷ 22 = Rs. 2.

Cost Price (100%) = 2 × 100 = Rs. 200.

∴ The correct answer is Rs. 200.

Alternate Method

Given:

Initial Loss% = 2%

New Gain% = 20%

Difference in Selling Price (SP) = Rs. 44

Formula:

Cost Price (CP) = [Difference in SP ÷ (Gain% + Loss%)] × 100

Calculations:

⇒ Let the Cost Price (CP) of the article be Rs. x.

⇒ Initial Selling Price (SP₁) = x − 2% of x = 0.98x

⇒ New Selling Price (SP₂) = x + 20% of x = 1.20x

⇒ Difference between SP₂ and SP₁ = 1.20x − 0.98x = 0.22x

⇒ Given: 0.22x = 44

⇒ x = 44 ÷ 0.22

⇒ x = 4400 ÷ 22

⇒ x = 200

∴ The correct answer is Rs. 200.

Additional Information

Profit and Loss on CP

Profit and Loss percentages are always calculated on the Cost Price (CP) unless the question specifically mentions the Selling Price (SP).

Marked Price and Discount

Marked Price (MP) is the listed price. Discount is always calculated on MP. SP = MP × (100 − Discount%) ÷ 100.

Successive Changes

If an article is sold through multiple dealers with profit/loss percentages a and b, the net result is given by [a + b + (ab ÷ 100)]%.

Given :

22 − [9 − {6 − (10 − 4 + 3)}] ÷ 2 × 3

BODMAS Rule:

Calculation :

22 − [9 − (6 − (10 − 4 + 3)}] ÷ 2 × 3

⇒ 22 - [9 - {6 - (13 - 4)}] ÷ 2 × 3

⇒ 22 - [9 - {6 - 9}] ÷ 2 × 3

⇒ 22 - [9 - {-3}] ÷ 2 × 3

⇒ 22 - [9 + 3] ÷ 2 × 3

⇒ 22 - [12] ÷ 2 × 3

⇒22 - 6 × 3

⇒ 22 - 18

⇒ 4

∴ The answer is 4.

Shortcut Trick

Identify the form of the expression: a² + b² + ab, where a = 1.55 and b = 0.55.

Using the standard algebraic identity: a³ − b³ = (a − b)(a² + b² + ab).

Here, a − b = 1.55 − 0.55 = 1.

Therefore, a² + b² + ab = a³ − b³ directly.

∴ The correct answer is 1.55³ − 0.55³.

Alternate Method

Given:

The expression: 1.55² + 0.55² + 1.55 × 0.55

Formula Used:

a³ − b³ = (a − b)(a² + ab + b²)

Calculation:

⇒ Let a = 1.55 and b = 0.55

⇒ The given expression takes the form: a² + b² + ab

⇒ Rearranging the formula for the difference of cubes, we get: a² + ab + b² = (a³ − b³) ÷ (a − b)

⇒ Find the value of the denominator: a − b = 1.55 − 0.55 = 1

⇒ Substitute the numerical values back into the rearranged formula:

⇒ 1.55² + 1.55 × 0.55 + 0.55² = (1.55³ − 0.55³) ÷ 1

⇒ 1.55² + 1.55 × 0.55 + 0.55² = 1.55³ − 0.55³

∴ The correct answer is 1.55³ − 0.55³.

Additional Information

Sum of Cubes Identity

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

Difference of Squares

A fundamental algebraic identity is a² − b² = (a + b)(a − b).

Perfect Square Trinomials

The expansion of squared binomials follows the identities (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Shortcut Trick

Test the options to satisfy the condition: Fraction + 3 × (Reciprocal) = 73/20.

Checking option 5/4:

Reciprocal = 4/5

Thrice reciprocal = 3 × (4/5) = 12/5

Sum = 5/4 + 12/5 = (25 + 48) / 20 = 73/20. This matches the given condition.

∴ The correct answer is 5/4.

Alternate Method

Given:

Let the fraction be x.

Sum of x and 3 × (1/x) = 73/20

Formula Used:

Quadratic equation: ax² + bx + c = 0

Calculations:

⇒ x + 3/x = 73/20

⇒ (x² + 3) / x = 73/20

⇒ 20(x² + 3) = 73x

⇒ 20x² − 73x + 60 = 0

⇒ 20x² − 48x − 25x + 60 = 0

⇒ 4x(5x − 12) − 5(5x − 12) = 0

⇒ (4x − 5)(5x − 12) = 0

⇒ 4x − 5 = 0 or 5x − 12 = 0

⇒ x = 5/4 or x = 12/5

Comparing with options, the fraction is 5/4.

∴ The correct answer is 5/4.

Additional Information

Reciprocal Property

For any non-zero fraction a/b, its reciprocal is b/a. The product of a fraction and its reciprocal is always 1.

Quadratic Roots

A quadratic equation ax² + bx + c = 0 can be solved using the discriminant D = b² − 4ac. If D is a perfect square, roots are rational.

Proper vs Improper Fractions

A proper fraction has a numerator smaller than the denominator (e.g., 4/5), while an improper fraction has a numerator equal to or larger than the denominator (e.g., 5/4).

Calculation:

Let c be "a".

B = 0.65a

A = 1.2 × 0.65a = 0.78a

According to the question-

⇒ 0.78a + 0.65a + a = 121.5

⇒ 2.43a = 121.5

⇒ a = 50       (∴ C = 50)

⇒ B = 0.65 × 50 = 32.5

⇒ A = 0.78 × 50 = 39.0

Substituting the value of A, B, and C in the expression-

⇒ (50 - 2 × 32.5 + 39) 

⇒ 24

The answer is 24.

Alternate MethodA = 120% of B, & B = 65% of C

⇒ A = 120/100 B & B = 65/100 C

⇒ A = 6/5 B & B = 13/20

⇒ A : B = 6 : 5 & B : C = 13 : 20 

⇒ A + B + C = 78 + 65 + 100 = 243

According to the question, 

⇒ 243 = 121.5

⇒ 1 = 121.5/243 = 1/2

C - 2B + A = 100 - 2(65) + 78 = 48

⇒ 48 × 1/2 = 24

The answer is 24.

Given:

Total number of employees = 2400

Concept used:

A circle has a total angle = 360°

Calculation:

Required number of employees = 600

600 employees will make the angle = (600/2400) × 360 = 90°

In the pie chart, the angle of employees of office D = 90°

∴ The number of 600 employees are in office D

Given:

A chord of a circle of radius 22 cm is a tangent to another circle of radius 14 cm

Concept used:

A tangent makes an angle of 90° with the radius of the circle at the point of contact.

Calculation:

In the given figure above

AB be the chord of the larger circle

OD is the radius of the smaller circle and OB is the radius of the larger circle

∠ODB = 90°   [According to the concept]

Also AD = DB = AB/2

So,

DB = √(22² - 14²)

⇒ DB = √(484 - 196)

⇒ DB = √288

⇒ DB = 12√2

So, AB = 24√2

∴ The length of the chord is 24√2 cm.

Given:

The side of an equilateral triangle is 24 cm.

Concept used:

Area of an equilateral triangle = (\frac {\sqrt3a^2}{4}) (a = measure of each side)

Calculation:

Area of the equilateral triangle

⇒ (\frac {\sqrt3 \times 24^2}{4})

⇒ 144 (\sqrt3) cm2

∴ The area of the equilateral triangle is 144 (\sqrt3) cm2.

Given:

Bar diagram

Concept used: 

Average = Sum of observation / Number of observations

Calculation:

Sum of observation = (20 + 15 + 25) + (25 + 20 + 15) + (15 + 10 + 20) + (10 + 25 + 5)

⇒ 205

Total Number of observations = 4

Average = 205/4 = 51.25

∴ The average of sim-card sold in the four States/UT in lakhs is 51.25

Shortcut Trick

To compare surds ³√11, √7, and ⁴√45, find the LCM of their root indices (3, 2, 4), which is 12.

Raise each value to the power of 12 to eliminate the roots:

(11^1/3)¹² = 11⁴ = 14641

(7^1/2)¹² = 7⁶ = 117649

(45^1/4)¹² = 45³ = 91125

Order of values: 117649 (√7) > 91125 (⁴√45) > 14641 (³√11).

∴ The correct answer is Only III.

Alternate Method

Given:

Surds: ³√11, √7, ⁴√45

Formula Used:

For any positive numbers a and b, if aⁿ > bⁿ then a > b. To compare ⁿ√x and ^m√y, raise both to the power of LCM(n, m).

Calculations:

⇒ Convert surds to exponential form: 11^1/3, 7^1/2, 45^1/4

⇒ Indices are 1/3, 1/2, 1/4. LCM of denominators (3, 2, 4) = 12

⇒ Raise each term to the power of 12:

⇒ (11^1/3)¹² = 11⁴ = 11 × 11 × 11 × 11 = 121 × 121 = 14641

⇒ (7^1/2)¹² = 7⁶ = 7 × 7 × 7 × 7 × 7 × 7 = 343 × 343 = 117649

⇒ (45^1/4)¹² = 45³ = 45 × 45 × 45 = 2025 × 45 = 91125

⇒ Comparing the calculated values: 117649 > 91125 > 14641

⇒ Therefore: √7 > ⁴√45 > ³√11

∴ The correct answer is Only III.

Additional Information

LCM of Surd Indices

To compare surds with different indices, find the LCM of the indices and convert each surd to that common index.

Power Rule for Comparison

If x > y > 0 and n > 0, then xⁿ > yⁿ. This property is fundamental in comparing roots by raising them to a common power.

Exponent Laws

The expression ⁿ√a is equivalent to a^1/n. According to the laws of indices, (a^m)^p = a^m×p.

Given: average runs scored by 7 players = 53

⇒ Total runs scored by players = 53 × 7 = 371

⇒ Sum of runs scored by 6 players = 121 + 40 + 26 + 56 + 37 + 48 = 328

⇒ Runs scored by 7^th player = 371 – 328 = 43

∴ the correct option is 3)

Concept used:

Mean proportion of a and b = (\sqrt {ab} )

Calculation:

(\sqrt{\left( {6 + \sqrt 8 } \right)\left( {3 - \sqrt 2 } \right)})

⇒ (\sqrt{18-6\sqrt2+3\sqrt8-\sqrt{16}})

⇒ (\sqrt{18-6\sqrt2+6\sqrt2-4})

⇒ (\sqrt{18-4})

⇒ (\sqrt {14} )

∴ The required answer is (\sqrt {14} ).

Given:

a + b + c = 6 and

a3 + b3 + c3 - 3abc = 126

Formula used:

a3 + b3 + c3 - 3abc = (a + b +c) [(a + b + c)2 - 3(ab + bc + ca)]

Calculation:

As we know,

⇒ a³ + b³ + c³ - 3abc = (a + b +c) [(a + b + c)² - 3(ab + bc + ca)]

⇒ 126 = 6 [6² - 3 × (ab + bc + ca)]

⇒ 126 = 6 [36 - 3 × (ab + bc + ca)]

⇒ 3 × (ab + bc + ca) = 36 -21

∴  (ab + bc + ca) = 5

Additional Information(a³ + b³ + c³ - 3abc) = (a + b + c)[a² + b² + c² - (ab + bc + ca)]

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

Given:

Let x = (2.1\overline{36}-1.3\overline{16})

Concept:

The vinculum indicates that the digit over it repeats infinitely. 

For instance: (x.a \overline{bc}) = x.abcbcbcbc...

Calculation:

According to the question,

⇒ x = (2.1\overline{36}-1.3\overline{16})

⇒ x = 2.1363636... - 1.3161616...

⇒ x = 0.8202020...    ---(i)

Now, multiply it by 100.

⇒ 100x = 82.0202020...   ---(ii)

Now, subtract equation (i) from (ii), we get,

⇒ 99x = 81.2

⇒ x = (\frac{81.2}{99} = \frac{812}{990}=\frac{406}{495})

Therefore, "(\frac{406}{495})" is the required answer.

Given:

558 lts of mixture containing milk : water = 15 : 16.

Calculations:

Amount of milk in the mixture = 558 × (\dfrac{15}{15 + 16})

= 558 × (\dfrac{15}{31})

= 15 × 18

= 270 lts

Amount of water in the mixture = 558 × (\dfrac{16}{31})

= 16 × 18

= 288 lts

Let the amount of milk added be x to make the ratio 3 : 2.

Now, (\dfrac{270 + x}{288}) = (\dfrac{3}{2})

=> 2(270 + x) = 288 × 3

=> 540 + 2x = 864

=> 2x = 864 - 540

=> 2x = 324

=> x = (\dfrac{324}{2})

=> x = 162

∴ The answer is 162.

Given:

Expenditure incurred on binding = 30%

Expenditure incurred on printing = 25%

Calculation:

From the pie chart,

Total expenses = 100%

Total Central angle of circle = 360°

⇒ 100% → 360°

The difference between the angle of the pie-chart showing the expenditure incurred on binding and printing = 30 - 25 = 5%

⇒ 5% ≡ (360/100) × 5 = 18°  

∴  The central angle corresponding to the difference between the angle of pie-chart showing the expenditure incurred on binding and printing is 18°.

Given:

Rate of pouring water = 50 litres per minute.

Volume of the reservoir = 120 m³ = 120,000 litres. (Since 1m³ = 1000 litres)

Formula Used:

Time = Volume / Rate

Calculation:

Volume of the reservoir = 120,000 litres

Rate of pouring = 50 litres/minute

⇒ Time in minutes = 120,000 / 50

⇒ Time in minutes = 2400 minutes

Since there are 60 minutes in an hour,

⇒ Time in hours = 2400 / 60

⇒ Time in hours = 40

It will take 40 hours to fill the reservoir.

Let the speed of B be 5 unit

Speed of A = 5 × (6/5) = 6 unit

Time taken by A after meeting = 5/2 hrs

Time taken by B after meeting = x hrs

As we know,

(Speed of A/Speed of B)² = Time taken by B/Time taken by A

⇒ (6/5)² = x/(5/2)

⇒ 36/25 = 2x/5

⇒ x = 18/5

⇒ x = (3\frac{3}{5})

Shortcut Trick

Simple Interest for 8 years = 3725 − 2500 = 1225

Interest for 1 year = 1225 ÷ 8 = 153.125

Rate % = (153.125 ÷ 2500) × 100 = 6.125%

∴ The correct answer is 6.125%.

Alternate Method

Given:

Principal (P) = ₹2500

Amount (A) = ₹3725

Time (T) = 8 years

Formula Used:

Simple Interest (SI) = A − P

SI = (P × R × T) ÷ 100

T = 0 Years P = ₹2500 T = 8 Years A = ₹3725 SI = ₹1225 Rate = R%

Calculations:

⇒ SI = 3725 − 2500 = 1225

⇒ 1225 = (2500 × R × 8) ÷ 100

⇒ 1225 = 200 × R

⇒ R = 1225 ÷ 200

⇒ R = 6.125%

∴ The correct answer is 6.125%.

Additional Information

Sum Becoming 'n' Times at SI

When a certain sum of money becomes 'n' times of itself in 'T' years at Simple Interest, the rate of interest is given by R = 100 × (n − 1) ÷ T.

Compound Interest Formula

Amount under Compound Interest is calculated as A = P × (1 + R ÷ 100)^T, where interest is compounded annually.

Difference Between CI and SI

For 2 years, the difference between Compound Interest and Simple Interest is calculated directly using the formula D = P × (R ÷ 100)².

Shortcut Trick

Speed in m/s = 36 × 5/18 = 10 m/s.

Length of Train = Speed × Time = 10 × 25 = 250 m.

Total Distance to cross bridge = Train length + Bridge length = 250 + 250 = 500 m.

Required Time = Total Distance ÷ Speed = 500 ÷ 10 = 50 seconds.

∴ The correct answer is 50 seconds.

Alternate Method

Given:

Speed of train = 36 km/h

Time to cross pole (t₁) = 25 seconds

Length of bridge (L_b) = 250 m

Formula Used:

Speed (m/s) = Speed (km/h) × 5/18

Distance = Speed × Time

Calculations:

⇒ Speed of train = 36 × (5/18) = 10 m/s

⇒ Length of train (L_t) = Speed × Time to cross pole

⇒ L_t = 10 × 25 = 250 m

⇒ Total distance to cross bridge = L_t + L_b

⇒ Total distance = 250 + 250 = 500 m

⇒ Time to cross bridge = Total distance ÷ Speed

⇒ Time = 500 ÷ 10 = 50 seconds

∴ The correct answer is 50 seconds.

Additional Information

Unit Conversion

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

Relative Speed

When two objects move in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Crossing Stationary Objects

Total distance = Length of train + Length of object (If object is a point like a pole or man, its length is taken as 0).

Shortcut Trick

Net change in sum = (Correct values) − (Incorrect values)

Net change = [(25 × 2) + 38] − [(35 × 2) + 32] = 88 − 102 = −14

Change in average = Net change ÷ Total students = −14 ÷ 40 = −0.35

Actual average = Original average + Change = 45 − 0.35 = 44.65

∴ The correct answer is 44.65.

Alternate Method

Given:

Total students = 40

Initial average = 45

Incorrect readings: 35 (twice), 32 (once)

Correct readings: 25 (twice), 38 (once)

Calculations:

⇒ Total sum = Average × Number of students = 45 × 40 = 1800

⇒ Sum of incorrect values = (35 × 2) + 32 = 70 + 32 = 102

⇒ Sum of correct values = (25 × 2) + 38 = 50 + 38 = 88

⇒ Corrected total sum = 1800 − 102 + 88

⇒ Corrected total sum = 1800 − 14 = 1786

⇒ Actual average = 1786 ÷ 40

⇒ Actual average = 44.65

∴ The correct answer is 44.65.

Additional Information

Average Correction Formula

Correct Average = Observed Average + [(Total Correct Value − Total Incorrect Value) ÷ Number of Items].

Effect of Constant on Average

If every observation is increased or decreased by a constant value 'k', the average also increases or decreases by 'k'.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Formula used:

Sum of geometric progression (S_n) = {a × (rⁿ - 1)}/(r - 1)

Where, a = first term ; r = common ratio ; n = number of term

Calculation:

3 +32 + 33 +...+ 38.

Here, a = 3 ; r = 3 ; n = 8

Sum of the series (S₈) = {a × (r8 - 1)}/(r - 1)

⇒ {3 × (3⁸ - 1)}/(3 - 1)

⇒ (3 × 6560)/2 = 3280 × 3 

⇒ 9840

∴ The correct answer is 9840.

Shortcut Trick

Present ratio of Ram and Ramesh = 3 : 5 (Difference = 2 units).

Ratio after 7 years = 4 : 5 (Difference = 1 unit).

To equate differences, multiply the future ratio by 2: (4 : 5) × 2 = 8 : 10.

Change in Ramesh’s age units = 10 − 5 = 5 units.

Given that 5 units = 7 years, then Ramesh’s present age (5 units) is 7 years.

∴ The correct answer is 7 years.

Alternate Method

Given:

Present age ratio of Ram and Ramesh = 3 : 5

Ratio after 7 years = 4 : 5

Calculations:

⇒ Let the present ages of Ram and Ramesh be 3x and 5x respectively.

⇒ After 7 years, their ages will be (3x + 7) and (5x + 7).

⇒ According to the problem: (3x + 7) ÷ (5x + 7) = 4 ÷ 5

⇒ 5 × (3x + 7) = 4 × (5x + 7)

⇒ 15x + 35 = 20x + 28

⇒ 20x − 15x = 35 − 28

⇒ 5x = 7

⇒ Ramesh’s present age = 5x = 7 years.

∴ The correct answer is 7 years.

Additional Information

Age Difference Consistency

The difference between the ages of two individuals remains constant throughout their lives. If the difference is 'd' now, it will remain 'd' after any number of years.

Ratio Adjustment Method

When the time gap is the same for both people, adjust the ratios such that the numerical difference between the terms of each ratio is identical.

Cross-Multiplication in Ratios

For a ratio a : b changing to c : d after 'n' years, the value of one part x = [n × (d − c)] ÷ [ad − bc].

Given:

A can do a piece of work = 5 days

B can do a piece of work = 10 days.

Formula used:

Total work = efficiency × time

Calculation:

Let the number of days work together by (A + B) = D

According to the question:

⇒ (A + B) × D + B × 8 = 10

⇒ (2 + 1) × D + 1 × 8 = 10

⇒  3 × D = (10 - 8)

⇒ D = 2/3 days

∴ The correct answer is 2/3 days.

Shortcut Trick 

Shortcut Trick

Let the third number be 100.

First number = 50 (100 − 50) and Second number = 25 (100 − 75).

To make 25 equal to 50, we need to add 25.

Required % = (Amount to increase ÷ Second number) × 100 = (25 ÷ 25) × 100 = 100%.

∴ The correct answer is 100%.

Alternate Method

Given:

1st Number = 3rd Number − 50% of 3rd Number

2nd Number = 3rd Number − 75% of 3rd Number

Formula:

Percentage Increase = [(Difference) ÷ (Initial Value)] × 100

Calculations:

⇒ Let the third number be x = 100.

⇒ First number (A) = 100 − 50 = 50.

⇒ Second number (B) = 100 − 75 = 25.

⇒ Target is to make B = A, so we need to increase B by (A − B).

⇒ Required Increase = 50 − 25 = 25.

⇒ Percentage enhancement = (25 ÷ 25) × 100.

⇒ Percentage enhancement = 1 × 100 = 100%.

∴ The correct answer is 100%.

Additional Information

Base of Comparison

The denominator in a percentage calculation always represents the value we are comparing from. Here, we compare the increase with the second number, so 25 is the base.

Fractional Conversions

Quick calculations can be done using fractions: 50% = 1/2 and 75% = 3/4. If the third number is 4 units, the first is 2 units and the second is 1 unit.

Percentage Change Formula

% Change = [(New Value − Old Value) ÷ Old Value] × 100. A 100% increase means the value has doubled.

Shortcut Trick

Simple Interest is directly proportional to the rate of interest when Principal and Time are constant.

Original Simple Interest = Rs. 13,200 − Rs. 12,000 = Rs. 1,200

If the rate of interest is doubled, the Simple Interest will also be doubled.

New Simple Interest = 2 × 1,200 = Rs. 2,400

New Amount = Principal + New Interest = 12,000 + 2,400 = Rs. 14,400

∴ The correct answer is Rs. 14,400.

Alternate Method

Given:

Principal (P) = Rs. 12,000

Amount in 2 years (A) = Rs. 13,200

Time (T) = 2 years

Formula Used:

Simple Interest (I) = A − P

I = (P × R × T) ÷ 100

Calculation:

⇒ Original Interest = 13,200 − 12,000 = Rs. 1,200

⇒ 1,200 = (12,000 × R × 2) ÷ 100

⇒ 1,200 = 240 × R

⇒ R = 1,200 ÷ 240 = 5%

⇒ New Rate = 2 × 5% = 10%

⇒ New Interest = (12,000 × 10 × 2) ÷ 100 = Rs. 2,400

⇒ New Amount = 12,000 + 2,400 = Rs. 14,400

∴ The correct answer is Rs. 14,400.

Additional Information

Proportionality in Simple Interest

Simple interest is directly proportional to Principal (P), Rate (R), and Time (T). If any one of these is multiplied by a factor while the others remain constant, the Simple Interest is simply multiplied by the same factor.

Simple Interest vs Compound Interest

In Simple Interest, the interest is calculated only on the original principal every year, meaning it remains constant per period. In Compound Interest, interest is calculated on both the original principal and the accumulated interest from previous periods.

Simple Interest Formula

The formula to calculate simple interest is I = (P × R × T) ÷ 100. The total amount at the end of the time period is the sum of the principal and the interest earned: A = P + I.

Given:

The marked price of an article is Rs. 840.

The shopkeeper gives a discount of 15% on the marked price and still makes a profit of 19%.

Concept used:

1. Selling Price = Cost Price × (1 + Gain%) 2. Selling Price = Marked Price × (1 - Discount%)

Calculation:

Selling price of the article = 840(1 - 15%) = Rs. 714

Now, the cost price of the article = 714/(1 + 19%) = Rs. 600

∴ The cost price of the article is Rs. 600.

Given:

HCF is 9 and their ratio is 14 : 19.

Concept used:

1. LCM is the smallest common multiple of two or more numbers. 2. HCF is the largest number or quantity that is a factor of each member of a group of numbers.

Calculation:

First number = 14 × 9 = 126

Second number = 19 × 9 = 171

LCM (126, 171)

⇒ 9 × 14 × 19

⇒ 2394

∴ Their LCM is 2394.

Concept use:

Surface Area of Sphere = 4πr² where r is the radius of sphere 

Volume of Sphere = 4/3 πr³ where r is the radius of sphere 

Calculations:

The surface areas of two spheres are in the ratio 1 : 2. 

4π(r₁)²/4π(r₂)² = 1/2 

⇒ r₁²/r₂²  = 1/2

⇒  r₁/r₂ = 1/√2

Volume of sphere 4/3 πr3

The Ratio of Volume of sphere = 4/3 πr₁3 / 4/3 πr₂3 

⇒  r₁³/ r₂³ = 1: 2√2 

Hence, The Correct Answer is 1: 2√2.

Shortcut Trick

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

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

Required time = (12 × 18) ÷ (18 − 12)

⇒ 216 ÷ 6 = 36 hours.

∴ The correct answer is 36 hours.

Alternate Method

Given:

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

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

Method Used:

Total Work = LCM of times taken

Efficiency = Total Work ÷ Time

Calculations:

⇒ Let the efficiency of the leak be L.

⇒ Efficiency of Pipe + Efficiency of Leak = Overall Efficiency

⇒ 3 + L = 2

⇒ L = 2 − 3 = −1 unit/hour

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

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

⇒ Time = 36 ÷ 1 = 36 hours.

∴ The correct answer is 36 hours.

Additional Information

Pipes & Cisterns - Leakage Concept

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

Total Work Strategy

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

Positive and Negative Work

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

Concept used:

Fourth proportional to number a, b and c = bc/a

Calculations:

Fourth proportional to the number 24, 192 and 27

= 27 × 192/24

= 27 × 8

= 216

Hence, The Required value is 216.

Given:

An arc on a circle, whose length is 19.25 cm, subtends an 18° angle at the centre

Concept used:

Arc Length = θ × r, Where

r = Radius, θ is in radian

Calculation:

18° = π/10 rad

So,

r = (19.25 × 10)/π

r = 192.5/π

Area of the circle is

⇒ π × (192.5 /π) × (192.5 /π) 

⇒ 11790.625 cm2

∴ The correct option is 4

Shortcut Trick

Let the total votes be 100%.

Loser's share = 40% ⇒ Winner's share = 60%.

Vote difference = 60% − 40% = 20%.

As per the question: 20% → 600 votes.

Total (100%) = 5 × 20% → 5 × 600 = 3,000 votes.

∴ The correct answer is 3,000.

Alternate Method

Given:

Candidate 1 (Loser) = 40% of total votes

Losing Margin = 600 votes

Formula:

Total Votes = (Losing Margin ÷ Difference in % share) × 100

Calculations:

⇒ Let total votes be 'x'.

⇒ Votes obtained by Loser = 0.40x

⇒ Votes obtained by Winner = x − 0.40x = 0.60x

⇒ Winning Margin = 0.60x − 0.40x = 600

⇒ 0.20x = 600

⇒ x = 600 ÷ 0.20

⇒ x = 3,000

∴ The correct answer is 3,000.

Additional Information

Election Margin Calculation

In a two-candidate election, the margin of victory is always equal to the difference between the winner's votes and the loser's votes.

Invalid Votes Concept

If a percentage of votes is invalid, then Valid Votes = Total Votes − Invalid Votes. The winner and loser percentages are usually calculated based on valid votes unless specified otherwise.

Base Value in Percentage

When a value is expressed as a percentage, the total quantity is always considered as the base of 100%.