DSSSB Jail Warder : (4 Dec 2025) Memory-Based Paper (Previous Year Paper)

The least possible Venn diagram is as follows:

Conclusions:

I. Some Cruz are Black. → True (Some Cruz are Eon and All Eon are Black)

II. No Black is Creta.→ False (it is possible but not definite)

III. Some Creta are Eon.→ False (it is possible but not definite)

Hence, only conclusion I follows.

Here, plastic is the repeating word.

plastic/ plastic/ plastic

Hence, the correct answer is ‘l t p s c a i’.

• It is given in the question that the man is blind and elderly. It is therefore important that you help the man. So options 3 and 4 are eliminated.
• You need to tell the man that the dog has run away so that he could tell you if the dog keeps doing so or can guide you on where to find it.
• Hence the correct answer is option 1.

According to the given information-

1. A lives on 4th floor

2. Two persons live between A and F. F does not live on top floor.

3. Q lives on 2^nd floor.

4. M lives just above E.

Case 1:

Case 2:-

5. L is not an immediate neighbour of Q and does not live on the top floor. Therefore, case 1 is eliminated

The final arrangement is given below-

Hence, M lives on the top floor.

Let the number of students appeared for examination be x.

40% students passed in Algebra = 40% of x = 0.4x

30% students passed in Geometry = 30% of x = 0.3x

20% students passed in both Algebra and Geometry = 20% of x = 0.2x

Those who failed in both are 50.

Number of students passed only in Algebra = 0.4x – 0.2x = 0.2x

Number of students passed only in Geometry = 0.3x – 0.2x = 0.1x

Total number of students passed = 0.2x + 0.1x + 0.2 x = 0.5x

Number of students who failed both = x – 0.5x = 0.5x

According to given information,

0.5x = 50

x = 100

Number of students passed only in Geometry = 0.1x = 0.1 × 100 = 10

Number of students failed only in geometry = 100 – (50 + 10) = 40

Hence, 40 is the correct answer.

The pattern followed is:

Hence, the correct answer is "217".

• There are multiple ways of solving the given question.
• Two more methods are shown below:

1st Method:

Hence,  the correct answer is "217".

2nd Method:

Hence, the correct answer is "217".

1. Car M is at the immediate right of car O and the immediate left of car L.

2. . Neither car O nor car L is at any of the extreme ends.

So, we have two cases.

2. Car J is the third to the left of car L

3. Car N is between car L and car K.

Therefore, case 2 is not possible.

The final arrangement is as follows.

Hence, three cars M, L, and N are parked between car O and car K.

According to the given information, we get the following figure,

Hence, point P is in the south-east of point Q.

Both the arguments are weak.

Globalization is the process of sharing and spreading of products, technology, information, and jobs across nations and cultures.

Hence, it need not lead to people leaving their countries and serving the other country, as one could be involved in the process of globalization without doing so.

Similarly, striving to improve one's life, need not lead people to abandon their countries.

The logic followed here is :-

1. Consonants - Immediate next alphabet is written.
2. Vowels - position value + 2
3. After vowel and consonant arrangement all the alphabets are arranged is descending order according to the English alphabetic series.​

So,

• ‘FINE’ is written as ‘OKGG’.

And

• 'HATE' is written as 'UIGC’.

Similarly,

• ‘RISE’ will be written as :

Hence, the correct answer is "TSKG".

From the information above, we can easily conclude that Disha publication is a renowned publishing company because of the huge number and the popularity of the books mentioned in the statement.

Therefore, conclusion I follows.

Similarly, we can also conclude that Disha publication has published a variety of books as it is mentioned in the statement “10000 different books”.

Therefore, conclusion II also follows.

Hence, Both I and II follow.

Given :

• Seven boxes - P, Q, R, S, T, U, and V
• They are kept in a stack from top to bottom.

​Explanation :

1) Box P is kept at the fifth position from the top.

2. There are two boxes between box P and box S.

2) Box Q is four boxes above box T. 

• This means there are 3 boxes between Q and T.

3) Box U is neither adjacent to box S nor box T.

4) There are minimum two boxes between box Q and box V.

After positioning box V only one position is left which will be occupied by the only box left i.e box R.

Thus, according to final arrangement there are five boxes kept above box V.

Hence, "More than three" is the correct answer.

The pattern followed is, 

Logic: For all the other option sum of place value is 14 except “DJA”

Hence, “DJA” is the correct answer.

Persons: Pritham, Quincy, Rasagna, Sanam, Teja, Uha, Vanitha and Warren.

1. Pritham is second to the right of Teja.

2. Teja is the neighbour of Rasagna and Vanitha and Vanitha is the neighbour of Uha. So Vanitha is immediate left of Teja and Rasagna is immediate right of Teja.

3. Uha is neighbor of Vanitha. Sanam is not the neighbour of Pritham.

4. Warren is not between Uha and Sanam. Quincy is not between Sanam and Warren. Sanam is not the neighbour of Pritham.

To satisfy the above conditions the positions should be as follows

Sanam is immediate left of Uha

Warren is immediate left of Sanam

Quincy is immediate left of Warren

The final arrangement will be as shown:

Hence, Sanam is immediate right of Warren.

The logic followed here is :-

1. Consonants - Written as it is diagonally with same consonant.
2. Vowels - Opposite alphabet is written as code.​

So,

• ‘SOLE’ is written as ‘LLSV’.

And

• 'YEAR' is written as 'RVZY’.

Similarly,

• ‘USED’ will be written as :

Hence, the correct answer is "FDVS".

The logic is:

1) 32 - 19 → (3³ - 2³) = 19

2) 42 - 56 → (43 - 23) = 56

3) 54 - 61 → (53 - 43) = 61

4) 74 - 33 → (73 - 43) ≠ 33

Hence, '74 - 33' is the odd one.

N + M & O & P → N is the wife of M, who is the father of O, who is the father of P.

Q # O → Q is the son of O.

The family tree diagram is shown below:

Hence, Q is the grandson of N.

The logic followed here is :-

Second number = First number² 

Third number = First number² - (First number - 1)² 

(19, 361, 37) → (19, 19², (19² - (19 - 1)²)) → (19, 361, (361 - 324)) → (19, 361, 37)

And

(13, 169, 25) → (13, 13², (13² - (13 - 1)²)) → (13, 169, (169 - 144)) → (13, 169, 25)

Similarly,

(17, 289, 33) → (17, 17², (17² - (17 - 1)²)) → (17, 289, (289 - 256)) → (17, 289, 33)

Hence, the correct answer is "(17, 289, 33)".

The logic is:

Hence, 'TWD' is the correct answer.

Hence sister is correct answer

The logic followed here is :-

1. In the given word consonant's position value is multiplied by 3 .
2. In the given word vowel's position value are added by 3​

So,

• ‘CODE’ is written as ‘IRLH’.

And

• 'HIDE' is written as "XLLH’.

Similarly,

• ‘AGED’ will be written as :

Hence, the correct answer is "DUHL".

Given,

Given expression: 21 ÷ 2 – 12 + 4 × 3 ÷ 7 – 20

According to question:

= 21 × 2 + 12 ÷ 4 – 3 × 7 + 20

Using BODMAS rule,

= 21 × 2 + 3 – 3 × 7 + 20

= 42 + 3 – 21 + 20

= 65 – 21

= 44

Hence, the correct answer is 44.

This paper would be unfolded as-

Hence, 'option 2' is the correct answer.

The logic followed here is :-

1. Consonants - Immediate next alphabet is written.
2. Vowels - Immediate previous alphabet is written.
3. After vowel and consonant arrangement all the alphabets are arranged is ascending order according to the English alphabetic series.​

So,

• ‘EAST’ is written as ‘DTUZ’.

And

• 'DOSE' is written as 'DENT’.

Similarly,

• ‘FUEL’ will be written as :

Hence, the correct answer is "DGMT".

The pattern followed is:

The given series is an example of fibonacci series.

Hence, the correct answer is "47".

The logic followed is:

The Assertion is correct because hot air is light and remain upper than cool air. So, hot air can be easily flow out through the ventilators. Thus they are provided near the roof but the Reason is not the correct explanation of the Assertion.

Hence, the correct answer is "Option 1". 

Additional Information

When warm air rises up and cold air from the surrounding areas rushes in to fill its place then this sets up convection in air.

• When warm air rises, the air pressure at that place gets lowered. The cold air from the surrounding areas rushes in to fill its place. This sets up convection currents in the air.
• Wind currents are generated due to uneven heating on the earth.
• Convection is the process by which the transmission of heat takes place through a substance from one point to another due to actual bodily movement of heated particles of the substance.

The pattern followed is:

Hence, the correct answer is "69".

• Option 1 is incorrect: Immediate arrest without an investigation is a misuse of authority. You are currently in the village on a specific investigative assignment, and you must gather preliminary facts before initiating formal penal charges.
• Option 2 is incorrect: A father paying a salary to a "hardly a teenager" child does not make forced labor legal. Child labor protection laws focus on safety, wellbeing, and education, not wage distribution within a family.
• Option 3 is incorrect: Checking the legal license of the commercial kiosk does not address the immediate, humanitarian issue of a child being forcefully overworked right in front of you.
• Option 4 is correct: This is the most balanced and tactical first response. Speaking to the child allows you to assess the situation directly, determine if he is being denied an education, and gather necessary statements to report the issue to local child welfare authorities or the village council (Panchayat) properly.

Hence the correct answer is option 4.

Table show alphabet serial number –

The logic is shown below –

Here A, E, I, O and U are Vowels.

Hence, “TUV” is the missing term which completes the series.

The least possible Venn diagram for the given statement is as follows,

Conclusions:

I. All stars are white → definitely true.

II. Some stars are not white → definitely false.

Hence, only conclusion I follows.

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

Detailed Explanation :- 

• The line PQ is the mirror.
• The word "

" ends with "

". So, the mirror image will start with "

" → Options 1, 2 are eliminated.

• The 5th letter in the given word is "

". So, the 5th last letter of the word in the mirror image will be "

"→ Options 3 is eliminated.

Hence, Option 4) is the correct answer.

Additional Information

• In a mirror image Left changes to rightand theright changes to leftwheretop and bottom remains the same.
• When placement of mirror not given, by default we will assume it in vertical direction.
• The starting letter word will be at last after the mirror image drawn with left changes to right and right changes to left.

Here, we use the table given below:

​

The logic followed in the given pairs:

In DRH : IXM →

In PIR : UOW →

Now, check all the options:

(1) MSP : RXV →

(2) GSM : MXS →

(3) THL : YNQ →

Similar logic followed.

(4) APS : FVW →

Here, in 'THL : YNQ' similar logic followed as given.

Hence, the correct answer is "THL : YNQ".

According to the given information, we get the following figure, 

Shortest distance between point A and point H = FG – (ED + CB) = 9m – (2m + 4m) = 3m

Hence, ‘3m’ is the correct answer.

The logic followed here is;

Sphygmomanometer →

An instrument for measuring blood pressure.

Similarly;

Barometer → 

An instrument for measuring Atmospheric Pressure.

Hence, the correct answer is " Atmospheric Pressure ".

1) 8 and 5

72 ÷ 14 + 6 × 5 - 8 = 25

Interchanging the numbers and using BODMAS rule:

72 ÷ 14 + 6 × 8 - 5 

= 5.14 + 6 × 8 - 5

= 5.14 + 48 - 5

= 53.14 - 5

= 48.14 ≠ 25

2. 6 and 14

72 ÷ 14 + 6 × 5 - 8 = 25

Interchanging the numbers and using BODMAS rule:

72 ÷ 6 + 14 × 5 - 8 

= 12 + 14 × 5 - 8

= 12 + 90 - 8

= 102 - 8

= 194 ≠ 25

3. 14 and 5

72 ÷ 14 + 6 × 5 - 8 = 25

Interchanging the numbers and using BODMAS rule:

72 ÷ 5 + 6 × 14 - 8

= 14.4 + 6 × 14 - 8

= 14.4 + 84 - 8

= 98.4 - 8

= 90.4 ≠ 25

4) 14 and 8

72 ÷ 14 + 6 × 5 - 8 = 25

Interchanging the numbers and using BODMAS rule:

72 ÷ 8 + 6 × 5 - 14

= 9 + 6 × 5 - 14

= 9 + 30 - 14

= 39 - 14

= 25 = 25

Hence, the correct answer is "14 and 8".

The logic followed here is:

All except 'Monarchy' are the different forms of art, while monarchy is a form of government in which a person, the monarch, is head of state for life or until abdication.

Hence, "Monarchy" is the correct answer.

Additional Information

Monarchy, political system based upon the undivided sovereignty or rule of a single person. The term applies to states in which supreme authority is vested in the monarch, an individual ruler who functions as the head of state and who achieves his or her position through heredity.

The first conclusion is completely contradicting the given statement, therefore it does not follow.

The second conclusion is the direct implication of the statement mentioned above. It is directly emphasizing the fact that due to the population increase, the resources will deplete and the Government will be unable to help its people.

Therefore, conclusion II follows.

Hence, only conclusion II follows.

Snacks: Pasta, Pizza, Burger, Lasagne, Nachos, Tortilla and Falafel.

Days: Monday to Sunday.

According to the question,

1. Pasta is made on the last day.

2. Nachos are made in middle of the week.

3. Lasagne is made on Tuesday.

4. Tortilla is made just 2 days after Falafel.

Important Points

• This means that there is a gap of 1 day between Tortilla and Falafel.

5. Tortilla and Pizza are made between Thursday and Sunday.

(This means that Falafel is made on Wednesday and Tortilla is made 2 days after Falafel i.e. Friday).

Only burger is left now, so it must be made on Monday.

Hence, Burger is made on Monday.

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

Conclusions:

I. Some animals are tigers → It is possible but not definite, hence false.

II. No tiger is elephants → It is not possible as some elephants are tigers, hence false

Hence, neither conclusion I nor II follows.

Preparing the family tree using the following symbols:

Hence, lady in portrait is the wife of Mr. Suman.

The correct answer is Kochi.

Key Points

• The High Court of Kerala and the Union Territory of Lakshadweep is located in Kochi, Ernakulam district.
• Thiruvananthapuram is the capital of Kerala.
• Pinarayi Vijayan is the Chief Minister of Kerala.
• Kavaratti is the capital of Lakshadweep.

The correct answer is Why I am an Atheist.

Key Points

• When Bhagat Singh was in prison in 1930-1931 his inmate Randhir Singh tried to convince him of the existence of God and when he failed to do so, he said to Bhagat Singh you have developed an ego which is standing between you and God.
• In his defense, he wrote an essay titled "Why I am an Atheist” to address whether his atheism was born out of vanity.
• In his essay, he defended his own beliefs and said he was a firm believer of God but could not understand people’s beliefs and myths.
• He said that religion made death easier, but also believed that unproven philosophy was a sign of weakness.

Additional Information

• Bhagat Singh was born in September 1907 in Banga, Punjab.
• In December 1928, he along with his Rajguru shot a British police officer John Saunders in Lahore who was on probation for British superintendent James Scott, who was responsible for the murder of Lala Lajpat Rai.
• In April 1929, he and his other associate Batukeshwar Dutt exploded two bombs inside the Central Legislative Assembly in Delhi.
• They threw leaflets, shouted slogans, and allowed the higher authorities to arrest them.
• In prison, he started a hunger strike demanding better conditions for Indian prisoners he was convicted and hanged on 23rd March 1931 at the age of 23.

The correct answer is option 4 i.e. Gateway of India,

The correct answer is Buddha, dhamma(dharma), sangha.

Key Points

Triratna in Sanskrit means 'Three Jewels'

• The Buddha
• Dhamma(dharma): his teaching
• Sangha: the community of all those who follow his teachings.

​Buddhism

• It is faith that was founded by Siddhartha Gautama("the Buddha").
• Siddhartha Gautam, the Lord Buddha was born in 563 B.C at Lumbini in Nepal.
• Attained Nirvana under a Pipal tree at Bodh Gaya & henceforth known as Buddha(The enlightened one).
• Delivered his first sermon at Sarnath (Banaras) know called the Dhammacakkappavattana.
• Died at the age of 80 at Kushinagar (U.P).

Noble truth by Buddha

• The world is full of sorrow.
• People suffer on account of desires
• If desires are conqueredNirvana can be achieved i.e., free from the cycle of birth and death can be achieved by following 8 fold path(ashtangika marga)
• Right View
• Right Resolve
• Right Speech
• Right Action
• Right Livelihood
• Right Effort
• Right Mindfulness
• Right Concentration

Teaching by Buddha

• Buddha was a practical reformer and did not believe in the soul or God or the metaphysical world and concerned himself with worldly problems.
• Suggested that a person should avoid an excess of both luxury & austerity and prescribed a middle path.
• Laid great emphasis on Karma(Varna based on action not on birth) & Ahimsa.
• Opposed the varna system and laid down the principle of social equality.
• Buddhist Text
• Tripitaka's: All written in Pali Language
• Sutta-Pitaka
• Vinaya-Pitaka
• Abhidhamma-Pitaka
• Buddhist Councils

The correct answer is Protein synthesis.

Key Points

• Ribosomes are non-membranous granular structures present in the cytoplasm.
• They were first observed under an electron microscope as dense particles by George Palade in the year 1953.
• Ribosomes are the site for ''protein synthesis'' so they are also called the ''protein factory'' of the cell.
• There are two types of ribosomes

1. Eukaryotic ribosomes - 80s - occurs in the cytoplasm of eukaryotic cell
2. Prokaryotic ribosomes - 70s - occur in the cytoplasm as well as are associated with the cell membrane of prokaryotic cell.

• The subunits of the ribosomes are:
• 80s ribosomes - are made of 60s and 40s subunits.
• 70s ribosomes - are made of 50s and 30s subunits.

Important Points

• Composition of the structure of ribosome:
• They are composed of ribonucleic acid (RNA) and proteins

Additional Information

• Photosynthesis: It is the process by which green plants and some other organisms use sunlight to synthesize nutrients from carbon dioxide and water. In this process, plant the chlorophyll, carbon dioxide, water, sunlight, and release oxygen.
• Synthesis of Fatty acids occurs in the cytoplasm.

The correct answer is Three.

Key Points 

• India is a peninsula because it is surrounded by water on three sides.
• The Indian Peninsula is surrounded by water in the Southwest, South, and Southeast.
• The Indian Ocean on the south, the Arabian Sea on the west, and the Bay of Bengal on the east.
• In the north, India is attached to the landmass.
• A peninsula is a piece of land that is bordered by water on three sides but connected to the mainland.

Additional Information 

• The length of the coastline in India is 7516.6 km Mainland.
• Indian coastline touches nine states Gujarat, Maharashtra, Goa, Karnataka, Kerala, Tamil Nadu, Andhra Pradesh, Odisha, West Bengal, and two union territories Daman and Diu and Puducherry.

The correct answer is Article 40.

Key Points

• Article 40- It talks about the Organisation of village panchayats.
• The State shall take steps to organise village panchayats and endow them with such powers and authority as may be necessary to enable them to function as units of self-government.​

Important Points 

• The Directive Principles of State Policy are contained in Part IV from Article 36 to Article 51 of the Constitution.
• DPSPs are borrowed from the Constitution of Ireland, which had copied from the Spanish Constitution.
• Features of DPSP
• It denotes the ideals that the State should keep in mind while formulating policies and enacting laws.
• It resembles the ‘Instrument of Instructions’ enumerated in the Government of India Act of 1935.
• It constitutes a very comprehensive economic, social and political programme for a modern democratic State.
• They promote social and economic democracy.
• They embody the concept of a ‘welfare state’ DPSP is non-justiciable.

Additional Information

• Article 48- It deals with the Organisation of agriculture and animal husbandry.
• Article 43- It deals with the topic of Living wage and employment generation for workers.
• Article 46- It deals with Promotion of educational and economic interests of Scheduled Castes, Scheduled Tribes and other weaker sections.

The correct answer is Basketball.

Key Points

• The term 'dribble' is used in Basketball.
• In basketball, dribbling is bouncing the ball on the floor continuously with one hand at a time.
• It is the only legal way that a player may maintain possession of the ball while walking or running.
• The dribble allows for much faster advancement and thus more opportunities for scoring.
• It also provides an opportunity for a crafty player on the opposing team to "steal" the ball in mid-bounce.
• Dribbling should be done with finger pads and the fingers should be relaxed and spread.
• The wrist should be pushing the basketball, and the forearm should be moving up and down.

Additional Information

• Basketball is a team sport in which there are two teams of five players each.
• Players advance the ball by bouncing it while walking or running (dribbling) or by passing it to a teammate.
• On offense, players may use a variety of shots – the layup, the jump shot, or a dunk; on defense.
• They may steal the ball from a dribbler, intercept passes, or block shots; either offense or defense may collect a rebound.
• It is a violation to lift or drag one's pivot foot without dribbling the ball, to carry it, or to hold the ball with both hands and then resume dribbling.

The correct answer is Catenation.

Key Points

• The property of self-linkage among identical atoms to form long-chain compounds is known as catenation.
• Carbon is the most common element that exhibits catenation.
• It can form long hydrocarbon chains and rings like benzene (C6H6).

Additional Information 

• Isomerization is the process in which a molecule is transformed into an isomer with a different chemical structure.
• Halogenation is a chemical reaction that involves the addition of one or more halogens to a compound or material.
• Halogens - fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At).

The correct answer is Bharatanatyam

Key Points

• Deepak Mazumdar is a renowned exponent of Bharatanatyam, one of the classical dance forms of India.
• He has been honored with the Sangeet Natak Akademi Award for his contributions to this dance form.
• Bharatanatyam is known for its fixed upper torso, bent legs, and intricate footwork, along with sophisticated hand and facial gestures.
• It originated in the temples of Tamil Nadu and is one of the oldest classical dance traditions in India.

Additional Information

• The Sangeet Natak Akademi is India's national academy for music, dance, and drama. It was established in 1952 by the Indian government.
• The Akademi Awards are the highest national recognition given to practicing artists.
• Bharatanatyam has its roots in the Natya Shastra, an ancient treatise on performing arts written by Bharata Muni.
• This dance form is traditionally performed by women, but in contemporary times, it is also performed by men.
• The themes of Bharatanatyam performances are usually derived from Hindu mythology and epics.

The correct answer is Vishakhadatta.

• Mudrarakshasa is a historical play in Sanskrit by Vishakhadatta that narrates the ascent of the king Chandragupta Maurya to power in India.
• The historical authenticity of the Mudrarakshasa is somewhat supported by the description of this period of history in Classical Hellenistic sources: the violent rule of the Nanda, the usurpation of Chandragupta, the formation of the Maurya Empire, and the various battles with the kingdoms of the Northwest resulting from the conquests of Alexander the Great.

The correct answer is Odometer.

Key Points

• An odometer is used to measure the distance travelled in an automobile.
• An odometer or odograph is an instrument used for measuring the distance travelled by a vehicle, such as a bicycle or a car.
• The device may be electronic, mechanical, or a combination of the two (electromechanical).

Additional Information

• A speedometer or a speed meter is a gauge that measures and displays the instantaneous speed of a vehicle.
• Now universally fitted to motor vehicles, they started to be available as options in the early 20th century, and as standard equipment from about 1910 onwards.
• A tachometer refers to any device that produces a signal proportional to the speed of rotation of a joint.
• There are many different types of tachometers, some based on measuring the frequency of, or the time between, pulses generated by the rotating shaft.
• Pedometers are designed to detect vertical movement at the hip and so measure the number of steps and provide an estimate of the distance walked.
• They cannot provide information on the temporal pattern of physical activity or the time spent in different activities at different intensities.

The correct answer is Ghatam.

Key Points

• Ghatam
• A Ghatam is a large, narrow-mouthed earthenware pot used as a percussion instrument.
• The ghatam is a percussion instrument that is utilized in several Indian repertoires.
• The ghatam is an Indian percussion instrument that dates back thousands of years. It's a narrow-mouthed clay pot.
• A small amount of plasticine clay or water can be used to change the pitch significantly.

Additional Information

• Mridangam​​​
• The mridangam is a percussion instrument of ancient origin.
• One of the most ancient drums of India, the mridangam, which literally means 'body of clay,' originated in South India.

• Sarod
• Sarod is a stringed instrument made of coconut shell, tun wood, drone, shikri, and ivory.
• This is a traditional instrument that is found in various parts of North India.
• A popular plucked instrument, it is used in North Indian classical music for solo concerts.

• Tabla
• Tabla is a small drum or  Pair of Drums tuned to different pitches playing with hands.
• It was invented by Amir khusru in 1738.
• The right side is called the Tabla and the left, the Bayan or Dagga.
• It is a type of Avanaddha vadya or Membranophone.

​

The Correct answer is 1906, Calcutta.

• The word swaraj was first used by Dadabhai Naoroji in the congress session held at Calcutta in 1906.

Key Points

• Swarāj means self-governance or "self-rule".
• Swaraj warrants a stateless society.
• Word 'swaraj' was used synonymously with "home-rule" by Dayanand Saraswati.
• Dadabhai Navroji said that he had learnt the word swaraj from the Satyarth Prakash of Dayanand Saraswati.

Additional Information

Important INC Sessions

The correct answer is Sikkim.

Key Points

• Sikkim has a population of 6.11 Lakhs.
• The Sikkim census of 2011 says the population of Sikkim is the least in all of India.

Additional Information

• According to a 2011 census, in that year Mizoram's population was 1,091,014.
• It is the 2nd least populous state in the country.
• As per details from Census 2011, Tripura has a population of 36.74 Lakhs.
• According to the 2011 Census of India, Uttarakhand has a population of 10,086,292.

Important Points

The highest population as per the 2011 census is observed in UP.

The correct answer is Rabbit.

Key Points

• Cold-blooded Animals- are animals that cannot regulate their internal body temperature with the change in the environment.
• Warm-blooded animal-A warm-blooded animal, for example, a bird or a mammal, has a fairly high body temperature which does not change much and is not affected by the surrounding temperature.
• About Rabbit:
• Oryctolagus cuniculus, scientfic name of rabbit.
• A baby rabbit is called a kit, a female is called a doe and a male is called a buck.
• A rabbit's teeth never stop growing.
• It belongs to the class Mammalia, so they are warm-blooded animals.
• Rabbits’ eyes are on the sides of their head, meaning they can see almost all the way around them.

Additional Information

• Sharks.
• Sharks don't have bones.
• Scientists hypothesize sharks first appeared in the ocean around 455 million years ago.
• Not all sharks have the same teeth.
• There are more than 500 species of sharks and range in different sizes.
• Sharks have six highly refined senses: smell, hearing, touch, taste, sight, and electromagnetism.
• Crocodile.
• Crocodiles are reptiles.
• Crocodiles have the strongest bite of any animal in the world.​
• Most crocodiles live in freshwater rivers and lakes but some live in salt water.
• Crocodiles can hold their breath underwater for at least one hour.
• The saltwater crocodile has an average lifespan of 70 years, The Nile crocodile can live up to 100 years.
• The saltwater crocodile is the largest aquatic reptile on Earth.
• ​Frog.
• There are 6,000 species of frogs across the world.​
• Frogs actually drink water through their skin by absorbing it.
• Each frog species has its own special call.
• In natural populations, this frog lives for a maximum of 5 years; the reproductive age ranges between 3–5 years.​

The Correct Answer is Navi Mumbai.

In News

• Seema wins gold in women’s discus at Indian Open Throws Competition 2025.

Key Points

• Seema won the gold medal in the women’s discus throw event at the Indian Open Throws Competition 2025 in Navi Mumbai with a throw of 56.39 metres.
• Neetika Verma secured the silver medal with a throw of 50.23 metres, and Priya won the bronze with a throw of 48.88 metres.
• The opening day also featured qualifying rounds for the men’s javelin and discus throw events.

The correct answer is Messe Frankfurt

In News

• The Minister of Textiles inaugurated the India Pavilion at Heimtextil 2025.

Key Points

• The event was held at Messe Frankfurt.
• India showcased its growing strength in the textile industry at the event.
• The Minister addressed global home textile exporters, importers, and manufacturers.
• Highlighted India's growing competitiveness and the need for collaboration for sustainable growth.

Additional Information

• Heimtextil
• The largest international trade fair for home and contract textiles.
• Held annually at Messe Frankfurt in Frankfurt, Germany.
• Attracts exhibitors and visitors from all over the world.
• India Pavilion
• Showcases India's strength and innovation in the textile industry.
• Provides a platform for Indian manufacturers and exporters to connect with global buyers.

The correct answer is Layman.

Key Points

• Layman  are basically love songs that originated in Himachal Pradesh.
• Laman is the regional music of Himachal Pradesh.
• It is famous in kullu valley.
• This song form is highly romantic in nature and symbolizes the emotion of love.
• This is the reason that band has been named laman which is synonymous of love.

Additional Information Himachal Pradesh

• The capital of Himachal Pradesh is Shimla.
• The Chief Minister of Himachal Pradesh is Sukhvinder Singh Sukhu and the Governor is Shiv Pratap Shukla.
• Hindi is the official language in Himachal Pradesh.
• The state flower of Himachal Pradesh is Pink Rhododendron; the state animal is snow leopards and the state tree is the Deodar cedar.

The Correct Answer is ​Dr. Ajay Kumar.

In News

• Former Defence Secretary Ajay Kumar appointed as UPSC Chairman

Key Points

• President Droupadi Murmu has appointed Dr. Ajay Kumar as the new Chairman of the Union Public Service Commission (UPSC).
• The appointment was announced by the Department of Personnel and Training (DoPT).
• Dr. Kumar’s tenure will begin from the day he assumes charge.
• He is a retired IAS officer from the 1985 batch, Kerala cadre.
• Dr. Ajay Kumar served as Defence Secretary from August 2019 to October 2022.

The correct answer is Nepal.

Key Points

• Indian states that shares border with Nepal are - Uttrakhand, Uttar Pradesh, Sikkim, West Bengal, and Bihar.
• The border was formed after the Sugauly Treaty of 1816 between Nepal and the British Raj.
• The state-wise length of borders are given below :
• ​ Uttrakhand: 251 km
• Uttar Pradesh: 551 km
• Sikkim: 99 km
• West Bengal: 100 km
• Bihar: 726 km

Additional Information

Some of the International borders with the Indian states are:

Explanation:

• Metal salts commonly used in firework displays include calcium chloride, sodium nitrate, barium chloride, copper chloride, etc.
• The green flame produced in fireworks is due to the presence of Barium.
• The blue flame is due to the presence of Copper.
• The orange flame is due to the presence of Calcium.
• A yellow flame is due to the presence of Sodium.
• Lithium /Strontium are used to impart a red colour to fireworks.

So,  Sodium metal is used for yellow colour In fireworks.

The correct answer is In New Delhi.

Key Points

• The Bahai House of Worship, popularly known as the Lotus Temple is not only a symbol of excellence in modern Indian architecture but also one of the most visited religious buildings in the world.
• The Temple located on a 9.7-hectare site near Nehru Place in South Delhi is a place of worship open to all races, religions, and castes.
• The form of this House of Worship takes the shape of the lotus, a flower considered sacred by most Indians.
• It is designed to reflect the simplicity, clarity, and freshness of the Baha'i Faith and to act as a symbol of the unity of mankind and religions.
• The structure is composed of three ranks of nine petals each, springing from a podium that elevates the building above the surrounding plain.
• The reinforced-concrete petals are clad by white marble panels, done to fit the surface profiles and to patterns related to the structure's geometry.

The correct answer is Tungabhadra.

Key PointsTungabhadra River:

• The river Tungabhadra derives its name from the Tunga, and  the Bhadra, and confluence of the two streams at Koodli in Shimoga.
• The Tungabhadra River does not flow into the Arabian Sea.
• Tungabhadra River is a major tributary of Krishna River.
• It's Major tributaries are the Bhadra, the Haridra, the Vedavati, the Tunga, the Varda and the Kumdavathi.

Additional InformationNarmada River:

• The Narmada rises in the Amarkantak hills in Madhya Pradesh.
• It flows towards the west in a rift valley formed due to faulting.
• On its way to the sea, the Narmada creates many picturesque locations.
• The ‘Marble rocks’, near Jabalpur, where the Narmada flows through a deep gorge, and the ‘Dhuadhar falls, where the river plunges over steep rocks, are some of the notable ones.
• All tributaries of the Narmada are very short and most of these join the main stream at right angles.
• The Narmada basin covers parts of Madhya Pradesh and Gujarat.
• The Narmada river conservation mission has been undertaken by the government of Madhya Pradesh by a scheme named Namami Devi Narmade.

Mandovi River:

• The Mandovi river is also known as the Mahadayi in Karnataka.
• This river is Goa's lifeline.
• Mahadayi river rises in the Western Ghats, from the Bhimgad Wildlife Sanctuary in Khanapur taluk of Karnataka’s Belagavi district.
• Flowing westward, it enters Goa from Sattari taluk of North Goa districts.
• A number of streams join the flow of the river to form the Mandovi which is one of two major rivers that flow through Goa.
• It joins the Arabian Sea at Panaji.

​Sabarmati River:

• Sabarmati river originates from Aravalli Hills, Rajasthan and meets in Bay of Khambhat in Arabian sea.
• This is one of the major west flowing river in India
• Its length is 371 km. and total catchment area is 21,674 sq. km.
• Sei, Siri and Dhamni are the right bank’s tributaries.
• **Wakal, Harnav, Hathmati, Khari, Watrak are left bank’s tributaries.**​

The correct answer is Odissi.

Key Points

• Odissi is one of the 8 classical dances of India recognized by the Sangeet Natak Academy.
• Odissi is a major ancient classical dance that originated in the Indian state of Orissa.
• The famous dancers of Odissi are -
• Sujata Mohapatra, Kelucharan Mohapatra, Ratikant Mohapatra, Gangadhar Pradhan, etc.
• Kelucharan Mohapatra is the first person to receive the Padma Vibhusan from Orissa.

Additional Information

The correct answer is Ira Jadhav.

In News

• In the Women’s Under-19 One Day Trophy, Ira Jadhav scored an unbeaten 346 runs off 157 balls, including 42 fours and 16 sixes, against Meghalaya.
• This record-breaking performance surpassed the previous record set by Smriti Mandhana, who scored 224 runs in 2013.

Key Points

• Ira Jadhav, a 14-year-old cricketer from Mumbai, achieved this milestone at the Alur Cricket Stadium, Bengaluru.
• Her innings helped Mumbai post a massive total of 563 for 3 in 50 overs.

Additional Information

• About the Record:
• The previous record of 224 runs was held by Smriti Mandhana in the Women’s Under-19 One Day Trophy in 2013.
• About Ira Jadhav:
• At just 14 years old, Ira’s innings demonstrates her exceptional talent and potential in Indian domestic cricket.

The correct answer is Sardar Vallabhai Patel.

Key Points

• The Constituent Assembly appointed a number of committees to deal with different tasks of constitution-making.
• Out of these eight were major committees and the others were minor committees.

Additional Information

• The idea of a Constituent Assembly for India was for the first time put forward by M.N.Roy in 1934.
• In 1935 the Indian National Congress (INC) officially demanded a Constituent Assembly to frame the Constitution of India.
• The demand was finally accepted in principle by the British Government in what is known as the 'August Offer' of 1940.
• The Constituent Assembly was constituted in November 1946 under the scheme formulated by the Cabinet Mission Plan (1946).
• The Constituent Assembly held its first meeting on December 9, 1946.
• Dr Sachidananda Sinha, the oldest member, was elected as the temporary President of the assembly, following the French practice.
• Later, Dr Rajendra Prasad was elected as the President of the assembly
• Similarly, both H.C. Mukherjee and V.T Krishnamachari were elected as the Vice Presidents of the Assembly. In other words, the assembly had two Vice Presidents.

The correct answer is Devika Rani.

• Devika Rani was the first winner of the Dadasaheb Phalke Award which she won in the year 1969.
• Devika Rani was an Indian film actress hailing from the city of Vishakhapatnam.
• She had won one of the highest civilian awards Padma Shri and was the first recipient of the Dada Saheb Phalke Award for Lifetime Achievement.
• She is also known as the 'First Lady of Indian Cinema'.

Key Points

• Dadasaheb Phalke Award is given in remembrance of the man who made the first Indian Feature film Raja Harishchandra in 1913.
• The Dadasaheb Phalke Award was introduced in 1969 by the government to recognise the contribution of film personalities towards the development of Indian Cinema.
• The award comprises a Swarna Kamal, a Cash Prize of Rs. 10,00,000/- (Rupees Ten Lakhs) certificate, a silk scroll and a shawl.
• The most recent awardee of the Dadasaheb Phalke award is Waheeda Rahman who won the award in 2023.
• Durga Khote was awarded the Dadasaheb Phalke Award in the year 1983.

The correct answer is Laws of Photoelectric Effect.

Key Points

• Albert Einstein was awarded Nobel Prize for the Photoelectric effect in the field of theoretical physics on 9 November 1921.
• He was a German Scientist known as one of the greatest physicists ever existed.
• He is widely known for developing the iconic Theory of Relativity, but surprisingly not won the Noble prize for that.

Additional Information

• Apart from Physics he also made a significant contribution to developing the theory of Quantum Mechanics.
• His formula of mass-energy equivalence **E=mc² **is titled the world's most famous equation.

The correct answer is Sarod.

Key Points

• Buddhadev Dasgupta was a renowned Sarod player.
• He was a disciple of the legendary Ustad Ali Akbar Khan and part of the Maihar gharana.
• The Sarod is a prominent stringed instrument used in Hindustani classical music.
• It is known for its deep, weighty, and introspective sound, typically played with a plectrum called the jaba.
• Buddhadev Dasgupta received several prestigious awards including the Padma Bhushan and the Sangeet Natak Akademi Award.
• His contribution to Indian classical music significantly enhanced the popularity and technique of the Sarod.

 Additional Information

• Sarangi
• The Sarangi is a bowed, short-necked string instrument used in Hindustani classical music.
• It is known for its vocal quality and ability to imitate the human voice.
• It has three main playing strings and a number of sympathetic strings.
• Bansuri
• The Bansuri is a transverse flute made from bamboo.
• It is associated with the Hindustani classical music and is known for its soothing sound.
• Lord Krishna is often depicted playing the Bansuri.
• Mridangam
• The Mridangam is a percussion instrument from South India.
• It is an essential part of Carnatic music concerts.
• It is a double-headed drum, traditionally made from jackfruit wood.

The correct answer is Spain.

Key Points

• The Indian men’s hockey team defeated Spain 2-1 to win the bronze medal at the Paris 2024 Olympics.
• This victory marked the first time since 1972 that India has won consecutive Olympic medals in men’s hockey.
• India had previously won a bronze medal at the Tokyo 2020 Olympics by defeating Germany.
• The match against Spain was held at the Yves de Manoir Stadium in Paris.

Important Points

• The last time India won consecutive medals in men’s hockey was at the Mexico City 1968 and Munich 1972 Olympics, both bronze.
• India's pursuit of a gold medal in Paris 2024 ended after a 2-3 loss to Germany in the semifinals.
• This achievement highlights the consistency and resilience of the Indian men’s hockey team on the global stage.
• Harmanpreet Singh was a key player in the victory against Spain, contributing to India’s success in the tournament.

Additional Information

• Germany: India lost to Germany in the semifinals of the Paris 2024 Olympics men’s hockey event.
• Belgium: India lost to Belgium in the semifinals of the Tokyo 2020 Olympics before winning bronze.
• Argentina: Argentina did not face India in the bronze medal match at Paris 2024.
• Spain: India defeated Spain to secure the bronze medal at the Paris 2024 Olympics.

The correct answer is Dominica Award of Honour.

In News

• PM Modi was awarded the 'Dominica Award of Honour' by the Dominican Republic for his support during the COVID-19 pandemic.
• In 2021, PM Modi provided 70,000 doses of the AstraZeneca vaccine to Dominica.

Key Points

• The 'Dominica Award of Honour' recognizes PM Modi's support during the COVID-19 pandemic, especially for providing vaccines to Dominica.
• The Dominican Republic is a Caribbean nation, sharing the Hispaniola island with Haiti.
• Dominica's capital is Santo Domingo, and its official language is Spanish.
• The award reflects India’s strong diplomatic ties with the Caribbean nations, especially during the pandemic.

Additional Information

• Dominican Republic
• Located in the Caribbean, the Dominican Republic shares the Hispaniola island with Haiti to the west.
• The capital city is Santo Domingo, and the official language is Spanish.
• AstraZeneca Vaccine
• AstraZeneca's COVID-19 vaccine was developed by AstraZeneca and Oxford University, widely used during the global pandemic for mass vaccination drives.
• The vaccine was offered as part of global assistance programs, especially to countries with limited access to vaccines.
• India's Foreign Relations
• India has strengthened its diplomatic relations with several Caribbean nations through humanitarian efforts, such as vaccine distribution and disaster relief.

The correct answer is Muhammad Shah.

• Muhammad Shah was an ineffective, pleasure-seeking Mughal emperor of India.
• Due to his pleasure-loving attitude, he was also called Rangila.
• His name was Roshan Akhtar.

Key Points

• During his reign, Maratha under Baji Rao for the first in Mughal history raided Delhi.
• Nadir Shah of Persia invaded Delhi with the help of Sadat Khan who defeated the Mughal army at the Battle of Karnal during his reign.

Additional Information

• Rafi-Ud-Daula was popularly known as ‘Shah Jahn II’.
• Rafi-Ud-Darajat was one of the Mughal rulers who ruled a very short period of merely a few months. During the course of the Revolt of Nikusiyyar, he captures the fort of Agra and declared himself as a ruler.
• Farrukhsiyar was also known as ‘Sahid-i-Mazlum’ and son of Azim-us-Shah. He ascended himself to the throne with help of the Sayyid brothers- Abdullah Khan and Hussain Ali.
• Farrukhsiyar assigned the duty of Deccan’s governor to Chin Quilch Khan who was better known as ‘Nizam-ul-Mulk’, later who laid the foundation of the independent state of Hyderabad.

The correct answer is 8.

Key Points

• The latitude approximately 23°27′ N of the terrestrial equator is called tropic of cancer.
• There are 16 countries through which the tropic of cancer passes.
• The tropic of cancer is the only latitude pass through India.
• The tropic of cancer passes through 8 Indian states.
• The 8 Indian states through which tropic of cancer passes through are:

1. Gujarat.
2. Rajasthan.
3. Madhya Pradesh.
4. Chhatisgarh.
5. Jharkhand.
6. West Bengal.
7. Tripura.
8. Mizoram.

Important Points

• Mahi River is the only river in India that cuts the Tropic of Cancer twice.
• "Bhopal (capital of Madhya Pradesh)” and “Gandhinagar (capital of Gujarat)” is also located fairly close to the “Tropic of Cancer”.
• The only state capital in India situated on the Tropic of Cancer is Ranchi, the capital of Jharkhand.
• Tropic of Cancer passes through 16 countries, 3 Continents, 6 water bodies.​

The correct answer is Washington D.C.

• The World Bank Group (WBG) is a specialized agency of the United Nations and its headquartered in Washington D.C.

Key PointsThe World Bank Group include five groups which are:

• International Bank for Reconstruction and Development (IBRD)
• International Development Association (IDA)
• International Finance Corporation (IFC)
• Multilateral Guarantee Agency (MIGA)
• International Centre for the Settlement of Investment Disputes (ICSID)
• To become members of the IDA, IFC, and MIGA, the countries must first become members of IBRD.

Additional Information

• World Bank approved 1 billion US$ aid to India to accelerate 'India's Covid 19 special protection response programme'.
• There are 2 goals for the world to achieve by 2030 –
• End extreme poverty by decreasing the percentage of people living on less than $1.90 a day to no more than 3%.
• Promote shared prosperity by fostering the income growth of the bottom 40% for every country.

The correct answer is Vitamin K.

Key Points 

Vitamin K

• Vitamin K is called antihemorrhagic.
• It is found in the green leaves of plants, as well as in those parts of plants that contain chlorophyll, a lot of it in berries of mountain ash, as well as in the liver.
• Vitamin K is needed for the posttranslational modification of proteins required for blood coagulation.
• Vitamin K is involved in metabolism pathways, bone mineralization, cell growth, and metabolism of the blood vessel wall.

Vitamin K injection:

• It is used to treat bleeding (hemorrhage or threatened hemorrhage) associated with a low blood level of prothrombin or factor VII.
• It is recommended that vitamin K be given IV, and not IM until coagulation parameters normalize to minimize the risk of hematoma at the injection site.
• 1 mg IM/subcutaneous is the FDA-approved dosage.
• Neonate has low plasma concentrations and low levels of vitamin K-dependent clotting factors.
• Therefore, immediately after the birth, Vitamin K will be administered to the newborn in order to prevent bleeding.

Additional Information

Vitamins :

• Vitamins are organic substances that are required for the proper functioning of the body.
• Vitamins are divided into two groups:
• Fat-soluble (Vit. A, D, E, and K)
• Water-soluble ( Vitamins of B group and Vit. C).

The correct answer is 4G.

Key Points

• In Telecommunications, LTE Technology stands for Long-Term Evolution.
• LTE is a standard for wireless broadband communication and is the primary technology used in 4G networks.
• It provides faster data transfer rates, lower latency, and improved spectral efficiency compared to previous generations.
• It allows us to download many things such as music, videos, websites etc.
• It is known for being developed by the 3GPP.
• 4G has the more stability and faster speed when compares to the LTE.
• It is because LTE is a half point between 3G and 4G.
• Its capability is 3.95G which has been marketed as 4G LTE.

Additional Information3G (Third Generation):

• 3G refers to the third generation of wireless technology.
• Common 3G technologies include UMTS (Universal Mobile Telecommunications System) and CDMA2000 (Code Division Multiple Access 2000).
• 3G networks provided faster data speeds compared to 2G but were slower than 4G.

2G (Second Generation):

• 2G refers to the second generation of wireless technology.
• Common 2G technologies include GSM (Global System for Mobile Communications) and CDMA (Code Division Multiple Access).
• 2G networks primarily focused on voice calls and provided limited data capabilities.

1G (First Generation):

• 1G refers to the first generation of wireless technology.
• 1G networks were analog-based and primarily supported voice calls.
• 1G networks had limited data capabilities and slower transmission speeds compared to subsequent generations.

Key PointsLala Lajpat Rai:

• Lala Lajpat Rai is also known as Punjab Kesari.
• He was a prominent Freedom fighter.
• He was also one the founder member of Punjab National Bank.
• He was one-third of the Lal Bal Pal triumvirate.
• He was elected as the President of the Indin National Congress in 1920 in Calcutta Session.​

Important Points

Sobriquets of some Eminent Persons:

Thus, Lala Lajpat Rai is known as 'Punjab Kesari'.

Additional Information

Bhagat Singh:

• He was an Indian Socialist Revolutionary who was born in Banga, Pakistan in 1907.
• In the year 1926, Bhagat Singh founded the Naujawan Bharat Sabha whose aim was to encourage revolution against British Rule by rallying the peasants and the workers.
• He was hanged till death on 23rd March 1931 in the Lahore Jail. He was just 23 years old.

Sukhdev:

• Bhagat Singh along with his associates Sukhdev Thapar and Shivaram Rajguru were charged for the assassination of 21-year-old British police officer John Saunders.
• Bhagat Singh, Sukhdev, and Rajguru were sentenced to death on 7th October 1930, while they were hanged on 23rd March 1931.
• The day Bhagat Singh, Sukhdev, and Rajguru lay down their lives for Freedom is called Martyrs' Day.

C. Azad:

• Azad was born in a small Madhya Pradesh village of Bhavra in Jhabua district.
• on July 23, 1906, Young Azad was terribly moved by the Britishers killing thousands of innocent Indians at Jhalianwala Baug in Punjab.
• He wholeheartedly plunged into the freedom struggle. He was arrested for his protests against the British rulers.

The correct answer is Kabul.

Key Points

• Kabul:-
• It is the capital and largest city of Afghanistan.
• It is located in the eastern part of the country, at an altitude of 1,790 meters (5,873 ft), in a narrow valley surrounded by the Hindu Kush mountains along the Kabul River.
• Kabul has been inhabited for over 3,500 years and has been the capital of many different empires and kingdoms throughout its history.

Additional Information

• Kandahar:-
• It is the second largest city in Afghanistan, located in the south of the country on the Arghandab River.
• It is the capital of Kandahar Province and the center of the larger cultural region called Loy Kandahar.
• Kathmandu:-
• It is the capital and largest city of Nepal.
• Kathmandu is a multicultural city with a population of over 4 million people.
• The majority of the population is Newari, but there are also significant Nepali, Tamang, and Sherpa minorities.
• The city is also home to a small number of Hindus, Sikhs, and Christians.
• Karachi:-
• It is the capital city of the Pakistani province of Sindh.
• It is the largest city in Pakistan and 12th largest in the world, with a population of over 20 million.
• It is situated at the southern tip of the country along the Arabian Sea coast.

The correct answer is 15

Key Points

• In tennis, the points in a game are counted as 15, 30, 40, and then game point.
• The first point in a game is referred to as 15.
• 0 points = Love
• 1 point = 15
• 2 points = 30
• 3 points = 40
• 4 points = Game point (if the player has a 2-point lead)
• To win a game, a player must win four points by a margin of at least two points.
• When both players have 40 points, it's called "deuce". T
• o win the game, one player must win two consecutive points after the score reaches deuce.
• Here are some other things to know about tennis:
• The first point of a game is served from the server's right side.
• The server alternates serving from the right and left sides of their court from point to point.
• The winner of a set is the first player to win six games, but they must also win by at least two games.
• The winner of the match is determined by the outcome of a series of sets, which can be best of three or five sets.
• The term "break point" refers to when the receiver has a chance to win the game with the next point.

Given:

150% of 0.05% of x = 75

Formula used:

a% of b = (\frac{a}{100} \times b)

Calculation:

(\frac{150}{100} \times \frac{0.05}{100} \times x = 75)

⇒ (1.5 \times 0.0005 \times x = 75)

⇒ (0.00075 \times x = 75)

⇒ (x = \frac{75}{0.00075})

⇒ x = 1,00,000

∴ The correct answer is option (1).

Shortcut Trick

From x − 4y = 0, we get x = 4y or x : y = 4 : 1.

Substitute x = 4 and y = 1 in the second equation: 4 + 2(1) = 6 units.

Given 6 units = 24 → 1 unit = 4. Thus x = 16 and y = 4.

Required Ratio = (2 × 16 + 3 × 4) ÷ (2 × 16 − 3 × 4) = 44 ÷ 20.

Simplifying 44/20 gives 11/5.

∴ The correct answer is 11/5.

Alternate Method

Given:

Equation 1: x − 4y = 0

Equation 2: x + 2y = 24

Formula Used:

Substitution method for linear equations in two variables.

Calculations:

⇒ From Equation 1: x = 4y

⇒ Substitute x = 4y in Equation 2:

⇒ 4y + 2y = 24

⇒ 6y = 24

⇒ y = 24 ÷ 6 = 4

⇒ Now, x = 4 × 4 = 16

⇒ Substitute values of x and y in (2x + 3y) ÷ (2x − 3y):

⇒ (2 × 16 + 3 × 4) ÷ (2 × 16 − 3 × 4)

⇒ (32 + 12) ÷ (32 − 12)

⇒ 44 ÷ 20

⇒ 11/5

∴ The correct answer is 11/5.

Additional Information

Substitution Method

It involves expressing one variable in terms of the other from one equation and substituting it into the second equation to solve for the variables.

Ratio Simplification

A ratio a/b is simplified by dividing both terms by their Highest Common Factor (HCF). In this case, HCF of 44 and 20 is 4, so 44/20 = 11/5.

Nature of Linear Equations

Two linear equations in two variables (x and y) represent two lines. Their intersection point gives the unique solution for x and y.

Concept used:

BODMAS rule 

calculation:

[0.08 - {3.5 - 4.9 - (12.5 - 7.8 - 4.6)}]

⇒ [0.08 - {3.5 - 4.9 - (0.1)}]

⇒ [0.08 - {3.5 - 5}]

⇒ 0.08 + 1.5

⇒ 1.58

∴ The answer is 1.58.

Given:

P and Q completed a work together and were paid ₹1,080 and ₹1,440

P can complete the work in 20 days

Concept used:

Total work = Efficiency of the worker × time taken by them

Efficiency is directly proportional to the amount gets

Calculation:

Ratio of amount paid to P and Q = 1080 : 1440

⇒ 3 : 4

Now,

Total work = 20 × 3

⇒ 60 units

So, time taken by both of them to complete the work = 60/7

⇒ (8{4\over7}) days

∴ They take (8{4\over7}) days to complete the work together.

Radius of the circle r = 14 cm

Area of the circle = πr² = (22/7) × 14 × 14 = 616 cm²

Circumference of the circle = 2 πr = 2 × (22/7) × 14 = 88 cm

Given:

ABCD is a cyclic quadrilateral

AB = BC

'O' is the center of a circle

∠DCA = 40° 

Concept used:

In the cyclic quadrilateral, the sum of the opposite angle is 180° 

And angle made in a semi-circle through its diameter is 90° 

The sum of all angle inside a triangle = 180° 

In a triangle, if two sides are equal, it will be an isosceles triangle and also two angle opposite to the two equal sides are equal.

Calculation:

Let us assume AC be diagonal that passes through the center

From the above figure, we can see that AC is diagonal, and AC is also a diameter of circle then ∠ABC = ∠ADC = 90°  

In ΔADC,

∠CAD + ∠ADC + ∠DCA = 180°

⇒ ∠CAD + 90° + 40° = 180°

⇒ ∠CAD + 130° = 180° 

⇒ ∠CAD = 180° - 130° 

⇒ ∠CAD = 50° 

In ΔABC, it is isosceles triangle because AB is equal to BC, then ∠BAC = ∠ACB 

∠BAC + ∠ABC + ∠BCA = 180° 

⇒ 2∠BAC + 90° = 180° 

⇒ 2∠BAC = 180° - 90° 

⇒ 2∠BAC = 90° 

⇒ ∠BAC = 90°/2

⇒ ∠BAC = 45°

∠BAD = ∠BAC + ∠CAD

⇒ ∠BAD = 45° + 50° 

⇒ ∠BAD = 95° 

∴ The ∠BAD is 95°

Calculation:

The central angle corresponding to the sector indicates the expenses incurred on Health:

⇒ 50000 → 360°

⇒ 15000 → (360°/50000) × 15000

⇒ 15000 → 36 × 3

⇒ 15000 → 108°

The central angle corresponding to the sector indicates the expenses incurred on Health is 108°.

Shortcut Trick

Apply the successive percentage change formula: Net Change = a + b + (a × b) ÷ 100

Here, a = +8 (increase) and b = −18 (discount).

Net Change = 8 − 18 + (8 × −18) ÷ 100

Net Change = −10 − 1.44 = −11.44%

The negative sign indicates an actual discount of 11.44% on the original price.

∴ The correct answer is 11.44%.

Alternate Method

Given:

Initial price markup = +8%

Discount announced = 18%

Calculations:

Let the original price of the commodity be 100.

⇒ Marked Price after 8% increase = 100 + 8% of 100

⇒ Marked Price = 100 + 8 = 108

⇒ Final Selling Price after 18% discount = Marked Price − 18% of Marked Price

⇒ Final Selling Price = 108 − (18 ÷ 100) × 108

⇒ Final Selling Price = 108 − 19.44 = 88.56

⇒ Total discount amount = Original Price − Final Selling Price

⇒ Total discount amount = 100 − 88.56 = 11.44

⇒ Since the assumed original price is 100, the overall discount percentage is strictly equal to the discount amount.

∴ The correct answer is 11.44%.

Additional Information

Successive Percentage Change

When a value is sequentially changed by a% and then by b%, the effective overall percentage change is a + b + (a × b) ÷ 100. Always use a positive sign for an increase and a negative sign for a decrease or discount.

Discount vs Markup

Markup is always calculated on the Cost Price to arrive at the Marked Price (MP). A discount is invariably provided on the Marked Price to arrive at the Final Selling Price.

Effective Discount of Two Successive Discounts

For two sequential discounts of x% and y%, the net single equivalent discount magnitude is given directly by x + y − (x × y) ÷ 100.

Given:

In a 1500 m race, Anil beats Bakul by 150 m and in the same race Bakul beats Charles by 75 m.

Concept used:

Time × Speed = Distance

Calculation:

According to the question,

Anil goes 1500m while Bakul goes (1500 - 150) i.e. 1350m.

Ratio of speed of Anil and Bakul = 1500 : 1350 = 10 : 9 = 200 : 180

According to the question,

Bakul goes 1500m while Charlie goes (1500 - 75) i.e. 1425m.

Ratio of speed of Bakul and Charlie = 1500 : 1425 = 20 : 19 = 180 : 171

So, the ratio of the speeds of Anil, Bakul and Charlie = 200 : 180 : 171

Let the speeds of Anil, Bakul and Charlie be 200k, 180k and 171k m/s respectively.

Time taken by Anil to finish the race = 1500/200k = 7.5/k seconds

Now, Anil beats Charlie by = (200 - 171)k ×7.5/k = 217.5m

∴ Anil beat Charlie by 217.5m.

Shortcut Trick

In a 1500 m race, Anil beats Bakul by 150 m

When Anil completes the race, Bakul covered (1500 - 150) = 1350 m

In a 1500 m race Charles is 75 m behind Bakul

So, in 1350 m race Charles is 75/1500 × 1350 = 67.5 m behind Bakul

So, Charles is (67.5 + 150) = 217.5 m behind from Anil in 1500 m race

∴ Anil beat Charlie by 217.5m.

Given:

Number are (\frac{1}{3}, \frac{3}{5}, \frac{4}{7} ) and (\frac{9}{16})

Formula used:

LCM of fraction = (\frac{LCM of numerator}{HCF of denominatior})

Calculation:

⇒ LCM of (\frac{1}{3}, \frac{3}{5}, \frac{4}{7} ) and (\frac{9}{16}) = (\frac{LCM of 1, 3, 4, 9}{HCF of 3, 5, 7, 16})

⇒ LCM of (\frac{1}{3}, \frac{3}{5}, \frac{4}{7} ) and (\frac{9}{16}) = (\frac{36}{1})

∴ LCM = 36. The correct answer is Option 1)

Shortcut Trick

Volume = (2/3) × π × r³ = 19404

⇒ r³ = 19404 × (21/44) = 441 × 21 ⇒ r = 21 cm

TSA of solid hemisphere = 3 × π × r²

⇒ TSA = 3 × (22/7) × 21 × 21 = 66 × 63 = 4158 cm²

∴ The correct answer is 4158 cm².

Alternate Method

Given:

Volume of solid hemisphere = 19,404 cm³

π = 22/7

Formula Used:

Volume of hemisphere = (2/3)πr³

Total surface area (TSA) of solid hemisphere = 3πr²

Calculations:

⇒ (2/3) × (22/7) × r³ = 19404

⇒ (44/21) × r³ = 19404

⇒ r³ = (19404 × 21) ÷ 44

⇒ r³ = 441 × 21

⇒ r³ = 21 × 21 × 21

⇒ r = 21 cm

Now, calculate Total Surface Area (TSA):

⇒ TSA = 3 × π × r²

⇒ TSA = 3 × (22/7) × 21 × 21

⇒ TSA = 3 × 22 × 3 × 21

⇒ TSA = 66 × 63

⇒ TSA = 4158 cm²

∴ The correct answer is 4158 cm².

Additional Information

Curved Surface Area of Hemisphere

The curved surface area of a hemisphere (excluding the flat base) is given by 2πr².

Volume and Surface Area of a Sphere

For a full sphere, Volume = (4/3)πr³ and Total Surface Area = 4πr².

Relationship between Sphere and Hemisphere

A solid hemisphere has a flat circular base, which is why its TSA (3πr²) is more than half of a sphere's surface area (2πr²).

Given:

The numerical value of twice the curved surface area of a right circular cylinder is equal to the numerical value of its volume.

Concept used:

1. Curved surface of a cylinder = 2πrh 2. Volume of a cylinder = πr²h

where r = Radius of the base, h = height

Calculation:

Let the radius of the base and height be R and H respectively.

According to the question,

2πRH × 2 = πR²H

⇒ R = 4 (∵ R ≠ 0 and H ≠ 0)

∴ The numerical value of the radius of the base of the cylinder is 4.

Shortcut Trick

Selling Price (SP) can be calculated directly by multiplying the Marked Price with successive discount factors.

SP = MP × (100 − D₁)/100 × (100 − D₂)/100

SP = 1200 × (85/100) × (90/100)

SP = 1200 × 0.85 × 0.9 = 918

∴ The correct answer is ₹918.

Alternate Method

Given:

Marked Price (MP) = ₹1200

Successive discounts = 15% and 10%

Formula Used:

Selling Price = MP × (1 − D₁/100) × (1 − D₂/100)

Calculations:

⇒ Price after 1st discount = 1200 − (15/100 × 1200)

⇒ Price = 1200 − 180 = ₹1020

⇒ SP after 2nd discount = 1020 − (10/100 × 1020)

⇒ SP = 1020 − 102 = ₹918

∴ The correct answer is ₹918.

Additional Information

Effective Discount Formula

When two successive discounts of A% and B% are given, the equivalent single discount can be directly determined using: D = (A + B − A×B/100)%.

Relation between MP, CP, Profit%, and Discount%

The exact ratio of Marked Price (MP) to Cost Price (CP) when a certain profit is made after giving a discount is: MP/CP = (100 + Profit%) / (100 − Discount%).

Buy X Get Y Free Discount

In scenarios involving free items, the net percentage discount is computed as: Discount % = [Y ÷ (X + Y)] × 100.

Shortcut Trick

Rate 8% = 2/25. The ratio of Principal to Amount for 1 year is 25 : 27.

For 2 years, the ratio becomes (25)² : (27)² = 625 : 729.

729 units = ₹72,900 → 1 unit = ₹100.

Principal (625 units) = 625 × 100 = ₹62500.

∴ The correct answer is ₹62500.

Alternate Method

Given:

Amount (A) = ₹72,900

Rate (R) = 8% p.a.

Time (n) = 2 years

Formula Used:

A = P(1 + R/100)ⁿ

Calculations:

⇒ 72900 = P(1 + 8/100)²

⇒ 72900 = P(1 + 2/25)²

⇒ 72900 = P(27/25)²

⇒ 72900 = P × (729 / 625)

⇒ P = (72900 × 625) / 729

⇒ P = 100 × 625

⇒ P = 62500

∴ The correct answer is ₹62500.

Additional Information

Effective Rate for 2 Years

The effective compound interest rate for 2 years at R% is given by (2R + R²/100)%. For 8%, it is 16 + 0.64 = 16.64%.

Difference between CI and SI

For 2 years, the difference (D) between CI and SI is P(R/100)².

Compounding Periods

If interest is compounded half-yearly, the rate becomes R/2 and the time becomes 2n periods.

Given:

The average of 9 consecutive numbers = 20

Formula used:

Average = Sum of the terms/Number of the terms

Calculation:

Let, the 9 consecutive numbers are x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5), (x + 6), (x + 7), (x + 8)

So, [x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) + (x + 7) + (x + 8)]/9 = 20

⇒ (9x + 36)/9 = 20

⇒ 9x + 36 = 180

⇒ 9x = 180 - 36 = 144

⇒ x = 144/9 = 16

∴ The smallest of these numbers is 16

Alternate Method 

Average of Consecutive Numbers = 1/2 × (First Term + Last Term)

Here, in the question let the First term be x and the last term will be x + 8

According to the question,

(1/2) × (x + x + 8) = 20

⇒ 2x + 8 = 40

⇒ 2x = 32

∴ x = 16

The smallest number is 16

Given:

(30 - [40 - {56 - (25 - 13 - 12)}] = ?)

Formula used:

BODMAS Rule

Calculation:

(30 - [40 - {56 - (25 - 13 - 12)}])

⇒ (30 - [40 - {56 - (12 - 12)}])

⇒ (30 - [40 - {56 - 0}])

⇒ (30 - [40 - 56])

⇒ (30 - (-16))

⇒ (30 + 16)

⇒ 46

∴ The correct answer is option (4).

Shortcut Trick

The given percentage by which the number changes =  16(\frac{2}{3})%

The respective fraction conversion form = (\frac{50}{3} \times \frac{1}{100} = \frac{1}{6})

For increasing case: 

⇒ (\frac{\text {Increased value}}{\text {Original value}} = \frac{6+1}{6})

⇒ (\frac{49}{\text {Original value}} = \frac{7}{6})

⇒ Original value = 42

Therefore, '42' is the required answer.

Alternate MethodGiven:

The number is increased by 16(\frac{2}{3})% = (\frac{50}{3} \times \frac{1}{100} = \frac{1}{6}),

The increased value of the number = 49

Calculation:

Let 'x' be the value of the original number.

The increased value = 49

According to the question,

⇒ x of (100% + 16(\frac{2}{3})%) = 49

⇒ x of (1 + (\frac{1}{6})) = 49

⇒ x of (\frac{7}{6}) = 49

⇒ x = 49 × (\frac{6}{7})

⇒ x = 42

Therefore, '42' is the required answer.

Calculation:

Total of A in three cities = 250 + 175 + 350

⇒ 775

Average = 775/3

⇒ 258.33

Total of B in three cities = 220 + 190 + 240

⇒ 650

Average = 650/3

⇒ 216.67

Total of C in three cities = 260 + 200 + 270

⇒ 730

Average = 730/3

⇒ 243.33

Total of D in three cities = 245 + 185 + 330

⇒ 760

Average = 760/3

⇒ 253.33

So, an average of A is the highest

∴ The required answer is A.

Shortcut Trick

By observing the given bar graph, the data distribution is perfectly symmetrical around the central bar.

For any perfectly symmetrical distribution, the Mean, Median, and Mode are exactly equal.

∴ Mean = Mode

Difference between mean and mode = 0.

∴ The correct answer is 0.

Alternate Method

Given:

From the symmetrical bar graph, we can extract the representative frequencies for the ages:

Ages (x): 8, 9, 10, 11, 12

Number of children (f): 2, 4, 5, 4, 2

Formula Used:

Mean = Σ(fx) ÷ Σf

Mode = Observation with the maximum frequency

Calculations:

⇒ Total sum of ages Σ(fx) =(1 × 20) + (2 × 50) + (3 × 70) + (4 × 50) + (5 × 20)

⇒ Σ(fx) = 20 + 100 + 210 + 200 + 100 = 630

⇒ Total number of children Σf = 20 + 50 + 70 + 50 + 20 = 210

⇒ Mean = 630 ÷ 210 = 3

Since the maximum number of children is for age 3 (70 children), the mode is 3 years.

⇒ Mode = 3

⇒ Difference = Mean − Mode = 3 - 3 = 0

∴ The correct answer is 0.

Additional Information

Mean

The mean is the average of a dataset, calculated by dividing the sum of all observations by the total number of observations.

Mode

The mode is the value that appears most frequently in a data set. A set of data may have multiple modes or no mode at all.

Symmetrical Distribution

In a perfectly symmetrical distribution, the Mean, Median, and Mode are all equal and perfectly aligned at the center.

Empirical Relationship

For moderately skewed distributions, the empirical formula is: Mode ≈ 3 × Median − 2 × Mean.

Shortcut Trick

Edge of small cube = ³√64 = 4 cm.

Number of cubes = (Large Edge ÷ Small Edge)³

Number of cubes = (48 ÷ 4)³ = 12³ = 1728.

∴ The correct answer is 1728 cubes.

Alternate Method

Given:

Edge of large cube = 48 cm

Volume of each small cube = 64 cm³

Formula Used:

Volume of a cube = (Edge)³

Number of cubes = Total Volume ÷ Volume of each small cube

⇒ Volume of the large cube = 48 × 48 × 48

⇒ Volume of the large cube = 110592 cm³

⇒ Volume of one small cube = 64 cm³

⇒ Number of small cubes (n) = 110592 ÷ 64

⇒ n = 1728

∴ The correct answer is 1728 cubes.

Additional Information

Melting and Recasting Rule

When a solid is melted and recast into another shape (or multiple smaller shapes) without wastage, the total volume remains constant.

Properties of a Cube

For a cube of side 'a', Volume = a³, Total Surface Area = 6a², and Diagonal = a√3.

Scaling Factor in Volume

If the dimensions of a 3D object are scaled by a factor 'k', its volume is scaled by a factor of k³.

Using allegation method

20% - 10%

0%

10 : 20

Ratio of first book to second book = 10 : 20 = 1 : 2

1 + 2 = 3 unit

⇒ 3 unit = 300

⇒ 1 unit = 100

CP of the first book = Rs. 100

∴ SP of the first book = 100 × 120/100 = Rs. 120

Alternate Method 

Let CP of both books 100x and 100y respectively.

One is sells at 20% and other at 10% loss. There is no loss no profit means profit from one book is equal to loss from second book.

Profit from one book = 20% of 100x = 20x

Loss from other book = 10% of 100y = 10y

So

20x = 10y

⇒ x/y = 1/2

And we know total cost of both books is Rs. 300,

100x + 100y = 300

⇒ x + y = 3

So 

x = 1

y = 2

cost price of book which sells at profit = 100 * 1 = Rs. 100

SP of book which sells at profit = 120% of 100 = Rs. 120

As we know,

Difference between the compound interest and simple interest for 2 years formula,

Given, r = 12%, time = 2 years and P = x

⇒ Pr²/(100)² = difference

⇒ (P × 12 × 12)/100 × 100 = 18

⇒ P = 1250

Shortcut Trick

Since both trains start at the same time, the time taken to meet is constant.

Distance ratio = Speed ratio = 30 : 40 = 3 : 4.

Difference in ratio parts = 4 − 3 = 1 unit.

Given, 1 unit = 40 km. Total distance = (3 + 4) units = 7 units.

Total distance = 7 × 40 = 280 km.

∴ The correct answer is 280 km.

Alternate Method

Given:

Speed of Train 1 (from C) = 30 km/hr

Speed of Train 2 (from D) = 40 km/hr

Difference in distance covered = 40 km

Calculations:

Let the time taken by both trains to meet be 't' hours.

⇒ Distance covered by Train 1 = Speed × Time = 30t

⇒ Distance covered by Train 2 = Speed × Time = 40t

⇒ Difference = 40t − 30t = 40 km

⇒ 10t = 40

⇒ t = 4 hours

⇒ Total Distance = Distance(Train 1) + Distance(Train 2)

⇒ Total Distance = (30 × 4) + (40 × 4)

⇒ Total Distance = 120 + 160 = 280 km

∴ The correct answer is 280 km.

Additional Information

Relative Speed in Opposite Direction

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

Direct Proportionality of Distance and Speed

When time is constant, the distance covered is directly proportional to the speed (D ∝ S), meaning D₁/D₂ = S₁/S₂.

Total Distance Formula

Total distance between two points when moving towards each other = (S₁ + S₂) × Time of meeting.

Shortcut Trick

Combined efficiency of filling pipes A and B and emptying pipe C.

Total work (LCM of 5, 6, 15) = 30 units.

Efficiencies: A = +6, B = +5, C = −2.

Net efficiency = 6 + 5 − 2 = 9 units/hr.

Time taken = 30 ÷ 9 = 3¹/₃ hours = 3 hours 20 minutes.

∴ The correct answer is 3 hr 20 min.

Alternate Method

Given: Pipe A fills in 5 hours, Pipe B fills in 6 hours, and Pipe C empties in 15 hours.

Formula Used: Total Work = LCM of individual times; Efficiency = Total Work ÷ Time.

⇒ Total efficiency when all work together = 6 + 5 + (−2)

⇒ Total efficiency = 11 − 2 = 9 units/hr

⇒ Time required to fill the tank = Total Work ÷ Total Efficiency

⇒ Time = 30 ÷ 9 = 10/3 hours

⇒ Time = 3 hours + (1/3 × 60) minutes

⇒ Time = 3 hours 20 minutes

∴ The correct answer is 3 hr 20 min.

Additional Information

Inlet and Outlet Pipes

Inlet pipes add water (positive work) while outlet pipes remove water (negative work).

Work done formula

If two pipes fill a tank in x and y hours, net work in 1 hour = (1/x + 1/y).

Time and Work Relation

Time taken is inversely proportional to efficiency: Time = Work / Efficiency.

Shortcut Trick

Equating total work: (4M + 6W) × 8 = (3M + 7W) × 10

⇒ 32M + 48W = 30M + 70W ⇒ 2M = 22W ⇒ 1M = 11W

Total Work in terms of women: (4 × 11W + 6W) × 8 = 50W × 8 = 400 units

Time for 10 women = 400 ÷ 10 = 40 days

∴ The correct answer is 40 days.

Alternate Method

Given: Work done by 4 men and 6 women in 8 days is equal to work done by 3 men and 7 women in 10 days.

Formula Used: Total Work = (Number of persons × Efficiency) × Time

⇒ 8(4M + 6W) = 10(3M + 7W)

⇒ 32M + 48W = 30M + 70W

⇒ 32M − 30M = 70W − 48W

⇒ 2M = 22W

⇒ 1M = 11W

⇒ Total Work = (4 × 11W + 6W) × 8 = 50W × 8 = 400W

⇒ Required Days = 400W ÷ 10W = 40 days

∴ The correct answer is 40 days.

Additional Information

Work-Efficiency Relationship

Total work is the product of the number of people, their individual efficiency, and the time taken (W = M × E × D).

Pipes and Cisterns

Similar logic applies where filling pipes have positive efficiency and leakage pipes have negative efficiency.

Man-Days Concept

M₁D₁H₁/W₁ = M₂D₂H₂/W₂ is used to compare work scenarios involving different variables.

Shortcut Trick

Heights of the three cones from the vertex are h₁ = 7 cm, h₂ = 14 cm, and h₃ = 21 cm.

Ratio of heights (h₁ : h₂ : h₃) = 7 : 14 : 21 = 1 : 2 : 3.

Since CSA ∝ (height)² for similar cones, ratio of CSAs of cones = 1² : 2² : 3² = 1 : 4 : 9.

Ratio of CSA of parts (top : middle : bottom) = 1 : (4 − 1) : (9 − 4) = 1 : 3 : 5.

∴ The correct answer is 1 : 3 : 5.

Alternate Method

Given:

Total Height (H) = 21 cm, Base Radius (R) = 9 cm.

Cuts are at 7 cm and 14 cm from the base.

Formula:

Curved Surface Area (CSA) of cone = πrl

For similar cones formed by parallel cuts, CSA₁ : CSA₂ : CSA₃ = h₁² : h₂² : h₃²

Calculations:

⇒ Height of small cone (top) from vertex = 21 − 14 = 7 cm

⇒ Height of medium cone (top + middle) from vertex = 21 − 7 = 14 cm

⇒ Height of original cone (total) = 21 cm

⇒ Ratio of heights = 7 : 14 : 21 = 1 : 2 : 3

⇒ Ratio of CSA of three cones = 1² : 2² : 3² = 1 : 4 : 9

⇒ CSA of Top part = 1 unit

⇒ CSA of Middle part = CSA of medium cone − CSA of top cone = 4 − 1 = 3 units

⇒ CSA of Bottom part = CSA of total cone − CSA of medium cone = 9 − 4 = 5 units

⇒ Required Ratio = 1 : 3 : 5

∴ The correct answer is 1 : 3 : 5.

Additional Information

Volume Ratio of Similar Cones

If heights are in ratio a : b : c, then the volumes are in ratio a³ : b³ : c³.

CSA of Frustum

CSA of a frustum = π(r₁ + r₂)l, where r₁, r₂ are radii of bases and l is the slant height of the frustum.

Slant Height Relationship

For a cone, l = √(r² + h²). In similar cones, the ratio of slant heights is equal to the ratio of their vertical heights.

Shortcut Trick

Given equation: x − 1/(x − 2) = 7

Subtract 2 from both sides: (x − 2) − 1/(x − 2) = 5

Let (x − 2) = k. Then k − 1/k = 5.

The required value is k³ − 1/k³ = k³ + 3k

Shortcut: 5³ + 3 × 5 = 125 + 15 = 140

∴ The correct answer is 140.

Alternate Method

Given: x − 1/(x − 2) = 7

Formula Used: (a − b)³ = a³ − b³ − 3ab(a − b)

⇒ Let m = (x − 2)

⇒ x = m + 2

⇒ (m + 2) − 1/m = 7

⇒ m − 1/m = 7 − 2 = 5

⇒ Cubing both sides: (m − 1/m)³ = 5³

⇒ m³ − 1/m³ − 3 × m × (1/m) × (m − 1/m) = 125

⇒ m³ − 1/m³ − 3(5) = 125

⇒ m³ − 1/m³ = 125 + 15

⇒ (x − 2)³ − 1/(x − 2)³ = 140

∴ The correct answer is 140.

Additional Information

Cubic Identity (Plus)

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k.

Square Identity

If x − 1/x = k, then x² + 1/x² = k² + 2. If x + 1/x = k, then x² + 1/x² = k² − 2.

Power 4 Relation

If x + 1/x = k, then x⁴ + 1/x⁴ = (k² − 2)² − 2.

Let the sum lent be P

Simple interest after 15 years at 5% = P × 0.05 × 15 = 0.75 × P

This amount is less than P by Rs 250

Hence P - 0.75 × P = 0.25 × P = 250

∴ P = 1000

Given:

The upstream distance = 210 km

The downstream distance = 210 km

The total time is taken by the boat to travel 210 km upstream and returns to the starting point = 10 hours.

The speed of the boat = 50 kmph.

Formula used:

Upstream speed = u - v

Downstream speed = u + v

Where,

u, is the speed of the boat

v, is the speed of the stream

Time = (\frac{\text {Distance}}{\text {Speed}})

Calculation:

Let 't₁' and 't₂' is the time taken by the boat to cover upstream and downstream respectively.

Let 'v' is the speed of the river.

The time is taken by the boat to cover the upstream distance, t₁ = (\frac{210}{50-v}) hours

The time is taken by the boat to cover the downstream distance, t2 = (\frac{210}{50+v}) hours

According to the question,

⇒ (\frac{210}{50-v}+\frac{210}{50+v}) = 10

⇒ 210 × ((\frac{1}{50-v}+\frac{1}{50+v})) = 10

⇒ 21 × ((\frac{1}{50-v}+\frac{1}{50+v})) = 1

⇒ 21 × (50 + v + 50 - v) = (50 - v)(50 + v)

⇒ 21 × 100 = (50 - v)(50 + v)

The above equation can be written as:

⇒ 7 × 3 × 100 = (50 - v)(50 + v)

⇒ 30 × 70 = (50 - v)(50 + v)

On comparing L.H.S and R.H.S, we get,

⇒ 50 - v = 30

⇒ v = 20 kmph

∴ The speed of the stream is 20 kmph.