DSSSB Jail Warder : (25 Nov 2025) Memory-Based Paper (Previous Year Paper)

The least possible venn diagram for the above statements is shown below.

Conclusion:

I. Some flowers are not sweet → True (It is true as **“**No sweet is flowers ” is given in statement hence it is true.)

II. All sweet are fruits is a possibility → True (As there is no negative relation given between sweet and fruits, all sweet can be definitely fruits.)

III. No fruits are Sweet → False (It is possible but not defined hence, false)

Hence, the “both conclusions I and II follow” is the correct answer.

The pattern followed here is:

Given: - and × , 7 and 2

I. 11 + 2 - 8 × 16 ÷ 7 = 56

After interchanging the sign and numbers we get the;

Given: - and × , 7 and 2

⇒ 11 + 7 × 8 - 16 ÷ 2 = 56

⇒ 11 + 7 × 8 - 8 = 56

⇒ 11 + 56 - 8 = 56

⇒ 67 - 8 = 56

⇒ 59 ≠ 56 (Not correct)

II. 7 - 16 × 28 ÷ 2 + 9 = 37

After interchanging the sign and numbers we get the;

Given: - and × , 7 and 2

⇒ 2 × 16 - 28 ÷ 7 + 9 = 37

⇒ 2 × 16 - 4 + 9 = 37

⇒ 32 - 4 + 9 = 37

⇒ 41 - 4 = 37

⇒ 37 = 37. (Correct)

So, only I is not correct.

Hence, the correct answer is "Option 3".

The logic followed here is:

Identify a common feature among - Trot, Cackle, Bray, and Croak

Explanation:

1. "Trot" is a sound made by a horse, but not from the throat.
2. Cackle refers to the sound made by a hen from the throat.
3. Bray to a donkey from the throat.
4. Croak to a frog from the throat.

Hence, the odd word is "Trot".

The logic followed here is:

Logic: (1st number + 2nd number) × 2 = 3rd number

Check all options:

Option (1): 8, 40, 96

⇒ 8 + 40 = 48 × 2 = 96 [True]

Option (2): 3, 15, 36

⇒ 3 + 15 = 18 × 2 = 36 [True]

Option (3): 6, 30, 72

⇒ 6 + 30 = 36 × 2 = 72 [True]

Option (4): 9, 45, 110

⇒ 9 + 45 = 54 × 2 = 108 ≠ 110 [False]

Hence, "9, 45, 110" is odd.

The path covered by Kumar is traced below:

If the final direction is west, the direction diagram should be rotated by 180º in the clockwise direction as shown below:

Considering the updated direction diagram, Kumar started walking in the west direction.

Therefore, the correct answer is west.

The logic followed here is:

• 

Similarly,

• 

Hence, 'DKUSRZ' is the correct answer.

The paper when unfolded will appear as follows:

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

The least possible venn diagram for the above statements is shown below

Conclusion:

I. No sky is rain → False

II. All rain is sky is possibility → True

III. Some cloud can be rain → True

Hence, If both conclusions II and III follow is correct answer.

Six friends:  Ch, Do, Ka, Ra, Te and Zu

i) Zu sits fourth to the left of Ch.

ii) Ka sits to the right of Ch.

iii) Ra sits to the immediate right of Do.

iv) Do is not an immediate neighbour of Zu.

Hence, two persons are sitting to the left of Do.

The correct mirror image of the given figure when the mirror is placed at line AB will be: 

Hence, the correct answer is 'Option 4'.

The logic follows here:

All option letter is arranged in random sequence except "ACE"

Option (1): ACE → A(1), C(3), E(5) → Word are arranged in ascending order.

Option (2): ICE → I(9), C(3), E(5) → Word are arranged in random sequence.

Option (3): EAR → E(5), A(1), R(18) → Word are arranged in random sequence.

Option (4): OUT → O(15), U(21), T(20) → Word are arranged in random sequence.

Hence "ACE" is an odd one.

The logic followed here is :

Alphabet positional values are arranged in increasing order.

ZOMBIE is written as BEIMOZ.

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And

FLEX is written as EFLX.

Similarly,

PRODUCT will be written as :

Hence, the correct answer is "CDOPRTU".

Given equation: 36 * 120 * 4 * 46 * 20

Let's check each option:

Option 1: =, ×, ÷, -

After replacing the symbols and Using BODMAS rule,:

36 = 120 × 4 ÷ 46 - 20

⇒ 36 = 120 × 0.086 - 20

⇒ 36 = 10.43 - 20

⇒ 36 = -9.57 (LHS ≠ RHS)

Option 2: +, ÷, -, =

After replacing the symbols and Using BODMAS rule,:

36 + 120 ÷ 4 - 46 = 20

⇒ 36 + 30 - 46 = 20

⇒ 66 - 46 = 20

⇒ 20 = 20 (LHS = RHS)

Option 3: ×, ÷, +, =

After replacing the symbols and Using BODMAS rule,:

36 × 120 ÷ 4 + 46 = 20

⇒ 36 × 30 + 46 = 20

⇒ 1080 + 46 = 20

⇒ 1126 = 24 (LHS ≠ RHS)

Option 4: +, ÷, =, ×

After replacing the symbols and Using BODMAS rule,:

36 + 120 ÷ 4 = 46 × 20

⇒ 36 + 30 = 46 × 20

⇒ 66 = 920 (LHS ≠ RHS)

Hence, the correct answer is "Option 2".

Despair is the synonym of Desperation.

Similarly,

Hideous is the synonym of Ugly.

Hence, "Hideous : Ugly" is the correct answer.

Nurses who are either Surgeon or Patients represented by shaded part i.e. M and R.

Hence, MR is the correct answer.

Predictions:

I. People can move out of their houses only from the next week onwards. → There is nothing mentioned in the given statement about when people are allowed to leave their houses. So, we can't decide anything about this prediction.

II. People are safer inside their houses. → As the administration has instructed people to stay inside just to protect them from the deadly virus. This means that they are more secured inside their houses.

Thus, only prediction II is implicit.

According to given conditions, 

Clearly, Ram is 2 km to the West from his starting point.

Hence, '2 km West' is the correct answer.

The logic followed here is:

Logic: Sum of positional value of alphabet × number alphabet given = Code

'USE' is coded as '135'

→ U(21) + S(19) + E(5) = 45 × number of alphabet is 3

→ 45 × 3 = "135"

And,

'BY' is coded as '54'

→ B(2) + Y(25) = 27 × number of alphabet is 2

→ 27 × 2 = "54"

Similarly,

'PART' is coded as '?'

→ P(16) + A(1) + R(18) + T(20) = 55 × number of alphabet is 4

→ 55 × 4 = "220"

Hence, the correct answer is "220".

From the given statement it can be implied that the sale of electric vehicles has risen due to its lower environmental impact since it is gaining influence. Thus it can be assumed that people are getting aware of environmental benefits of electric vehicles.

The given statement does not talk about the servicing of electric vehicles.Therefore assumption II is not implicit.

Hence the correct answer is Option 1.

The pattern followed is,

Similarly,

Hence, FJDO is the correct answer.

Brass is an alloy.

Similarly, Silicon is a metalloid.

Hence, “Metalloid” is the correct answer.

Alloy - Metal made by mixing two types of metal together.

Metalloid - an element whose properties are intermediate between those of metals and solid non-metals or semiconductors.

Given,

Mistake Points

Shubham's house faces North.

He leaves from the back gate of his house which means he starts the journey in the south direction.

Now,

He leaves from the back gate of his house it means he starts the journeying south direction and walks 14 m.

Then he turns left and walks 30 m.

Then he turns left and walks 50 m.

Then he turns left and walks 10 m.

He then turns left and walks 36 m.

Here, we see Shubham is 20 m away in East direction from his home.

The logic followed here is:

 

'K @ L % M # W – Z' means K is father of L, L is Son of M, M is Sister of W, W is mother of Z.

Hence, L is cousin of Z.

Preparing the family tree using the following symbol:

According to the given data:

The blood-relation diagram of the given 'P - A ÷ S × F ÷ H' is:

Here, P the maternal grandfather of H is correct as per the blood-relation diagram.

Hence, the correct answer is "maternal grandfather".

The logic is as follows:

9² - 1 = 81 - 1 = 80

9³ + 1 = 729 + 1 = 730

Similarly,

7² - 1 = 49 - 1 = 48

7³ + 1 = 343 + 1 = 344.

Hence, the answer is 48.

A woman can be a politician as well as an officer.

The correct Venn diagram is,

Hence, "Option 1" is the correct answer.

The least possible venn diagram for the above statements is shown below.

Conclusion:

I. Some words are test is a possibility → True

II. No test is word is a possibility → True

Hence, the “both conclusions I and II follow” is the correct answer.

Given entities: Building, Shop, Customer, Salesman.

CONCEPT:

Shop is a building. Thus shop should be represented within the building.

Customer and salesman are different entities within the shop, but they don't have any specific connection.

Hence they should be put seperately within the shop.

Then the relation between them can be represented as below:

Hence this is the correct representation of the above entities.

The figure that will replace the question mark (?) in the following figure series is shown below:

    

Hence, ‘option 3’ is the correct answer.

Given :

• Seven boxes - J, K, L, M, N, O, and P
• They are kept in a stack from top to bottom.

​Explanation :

1) Box P is kept the fourth position from the top. There are only 2 boxes above box J. 

2) There are three boxes between box O and box L which is kept at the second position from the bottom.

3) Box M is neither adjacent to box P nor is kept at the top position.

4) There are minimum two boxes between box O and box K.

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

Thus, according to final arrangement there are two boxes kept between box N and box K.

Hence, "Three" is the correct answer.

Preparing the family tree using the following symbols:

Hence, brother of Shalini is Maternal Uncle of the girl.

Logic : 

• Vowels - (3) is subtracted from each position value.
• Consonants - (3) is added to each position value.

So,

• NERDS is written as :

• CARING is written as :

 

Simila

rly,

• CLOSET is written as :

Hence, "FOLVBW" is the correct answer.

A, B, C, D, E and F are sitting around a circle facing the centre.

1. D is third to the left of A, who is second to the left of F.
2. E is not a neighbour of either F or D.
3. C is third to the left of B, who is not an immediate neighbour of D.

Condition to be checked: First person sitting to the immediate right of the second person.

Option 1 → A and E (It is clear A is sitting immediate right of the E, thus satisfying the condition).

Option 2 → C and E (It is clear C is immediate left of E, thus not satisfying the given condition).

Option 3 → A and B (It is clear A is immediate left of the B, thus not satisfying the given condition).

Option 4 → F and C (It is clear F is second left of C, thus not satisfying the given condition).

Thus only Option 1 satisfy the given condition.

Hence, the correct answer is "A and E".

1. D is third to the left of A, who is second to the left of F means:

• D is sitting third to the left of A.
• A is sitting second to the left of F. 2. C is third to the left of B, who is not an immediate neighbour of D means:
• C is sitting third to the left of B.
• B is not the immediate neighbour of D.

Confusion Points

Use of the word "Who" / "AND". 

Suppose for an example 

1. In a circular seating arrangement facing center, P is fourth to the left of Q, (WHILE / AND / BUT) 2nd to the left of R.

2. In a circle seating arrangement facing center Pis 3rd to the right of Q (WHILE / WHOM / WHO) is 2nd to the left of R.

The logic follows here is:

12² - 1 = 143

10² - 1 = 99

8² - 1 = 63

62 - 1 = 35

42 - 1 = 15

22 - 1 = 3

Hence, "3" is the correct answer.

Explanation :

• Seven-storied building, having floors numbered 1 to 7
• Six persons - Amy, Ben, Carl, Dev, Avy, and Glen
• Ground floor is numbered as 1 → to → top floor is numbered as 7
• One of the floors in the building is vacant.

​1) Amy lives on the fifth floor

2) No floor below the fifth floor is vacant and no odd numbered floor is vacant. 

3) Only Dev lives between Glen and Avy, who does not live in an odd-numbered floor. 

4) Ben does not live on the bottom-most floor and there is two floors between ben and Avy - As in case -(2) there are four floors between ben and Avy, thus this case is eliminated.

⇒ Thus, according to the final arrangement Carl is positioned one floor below Dev.

Hence, "Carl" is the correct answer.

The pattern followed here is:

Hence, "VCDF" is the correct answer.

The Logic here is as follows:

I. Now, more foreign tourists might visit the country: True. (We clearly see that the Government of India is taking steps to attract more tourism. So, it is possible)

II. The Government of India seems to be serious about attracting tourists: True. ( Again, we clearly see that the Government of India is taking steps to attract more tourism)

Hence**,** The correct answer is "Both I and II follows".

The pattern followed is,

Hence, ‘293’ is the correct answer.

The pattern follows here is:

2³ + 2 = 10

3³ + 3 = 30

4³ + 4 = 68

5³ + 5 = 130

6³ + 6 = 222

Hence, the correct answer is "222".

The pattern here is,

Hence, "FHJ" is the correct answer.

The correct answer is Onam.

Key Points

• Onam is related to Kerala state.
• Onam is the largest and official festival in Kerala, an Indian state known as God’s Own Country.
• Malayali people celebrate the Onam festivals as annual harvesting.
• The Onam festival is celebrated in Kerala between August and September. ​

Additional Information

The Correct Answer is Australia.

In News

• WTC Final 2025: South Africa beat Australia by 5-wickets; end 27-year ICC trophy drought.

Key Points

• South Africa won the ICC World Test Championship (WTC) Final 2025, beating Australia by five wickets.
• This is South Africa’s first ICC title in 27 years, and second overall, after the 1998 ICC Knockout Trophy.
• Aiden Markram was named Player of the Match for his century.
• Kagiso Rabada took 9 wickets in the match, starring with the ball.
• Temba Bavuma became the second South African captain to lift an ICC Trophy, and the first to win a World Championship.
• Bavuma remains unbeaten as Test captain, with 9 wins and 1 draw.
• South Africa is now the third team to win the WTC mace, after New Zealand and Australia.
• Both Markram and Rabada were part of the 2014 U-19 World Cup-winning team.

The correct answer is 448

• As of January 2019, there were 448 articles in the Indian Constitution.

Key Points 

• The original text of the Constitution contained 395 articles in 22 parts and eight schedules. It came into effect on January 26, 1950, the day that India celebrates each year as the Republic Day. The number of articles has since increased to 448 due to 100 amendments.
• The constitution is the topmost law of India.
• It is a document that provides laws for political structures, powers, and duties of the government.
• It includes fundamental rights, directive principles, and duties of a citizen.
• India's constitution is the largest constitution in the world.
• It was adopted on 26 November 1949 by the Constituent Assembly of India and became effective on 26 January 1950.

The correct answer is Vijayanagara.

Key Points

• The Mahanavami Dibba was the King’s palace in Vijayanagara Empire though there is no definite evidence.
• Mahanavami Dibba is a massive platform rising from a base of about 11,000 sq. ft to a height of 40 ft.
• The Mahanavami Dibba was located on one of the highest points in the city.
• There is evidence that it supported a wooden structure.
• The base of the platform is covered with relief carvings
• Many rituals were associated with the Mahanavami Dibba.
• Here the Hindu Festival Mahanavami or Navaratri was celebrated with great pomp and show in the months of September-October.
• This festival continued for 9 days.
• On this occasion several ceremonies were performed this including:
• Worship of the different gods and goddesses.
• Worship of the state horse.
• The sacrifice of buffaloes and other animals.
• The main attraction of this occasion were dance, Wrestling matches processions of horses, elephants, chariots, and soldiers.

Additional Information​ 

• In the Vijayanagara Empire The “king’s palace” is the largest of the enclosures.
• It has two of the most impressive platforms, usually called the Audience hall and the Mahanavami Dibba.
• The Audience Hall is a high platform with slots for wooden pillars at close and regular intervals.
• It had a staircase going up to the second floor, which rested on these pillars.
• The pillars being closely spaced would have left little free space, and thus it is not clear what the hall was used for.

The correct answer is Only II.

Key Points 

• I. Mars – 2 moons:
• Mars has two known moons: Phobos and Deimos.
• These moons were discovered in 1877 and have been the subject of much scientific study and interest.

Hence statement I is correct. 

• II. Venus – 1 moon:
• Venus is known to have no moons.
• There is no known natural satellite orbiting Venus.
• This lack of moons is one of the distinguishing characteristics of Venus in our solar system.

Hence statement II is incorrect. 

Shortcut Trick

 

• My Very Excited Mother Just Served Us Nachos
• M →  Mercury, V → Venus, E → Earth, M → Mars, J → Jupiter, S → Saturn, U → Uranus, N → Neptune
• The Solar System contains 8 planets:

The correct answer is Fa-Hien.

Key Points

• Fa-Hien:
• He was a Chinese Buddhist monk, who visited India in around 405 A.D.
• He visited India during the region of Chandragupta II.
• Fa-Hein travelled to many cities associated with the life of the Buddha such as Sravasti, Sarnath, Bodh Gaya, Vaishali, Rajgir, etc.
• The Fa-Hien account suggests that during Guptas there was peace and security within the empire.
• Hiuen-Tsang:
• He visited India in 630 A.D during the reign of Harsha Vardhana.
• He was a Chinese traveller.
• Hiuen-Tsang was impressed by King Harsha’s patronage of both scholarship and Buddhism.
• Harsha Vardhana invited Hiuen Tsang to Kumbh Mela in Prayag.
• As per Hiuen-Tsang, the burden of taxation in Harsha's reign was less and the main source of income was land revenue.
• Al-Masudi :
• He was an Arab traveller.
• He visited India in 957 A.D.
• He explained his journey in his book Muruj-ul-Zehab.
• Ibn Battuta :
• He was a Moroccan traveller, who visited India in around 1333 A.D, during the rule of Mohammed Bin Tughlaq.
• He wrote a book called Rihla.

The Correct Answer is ​Talisman Sabre.

In News

• India joins bilateral military exercise in Australia.

Key Points

• India has participated for the first time in Exercise Talisman Sabre, Australia’s largest bilateral military drill.
• The exercise was launched in 2005 as a biennial joint military exercise between the United States and Australia.
• In 2025, it involves over 35,000 personnel from 19 countries.
• Participating nations include: United States, Australia, India, Canada, Fiji, France, Germany, Indonesia, Japan, Netherlands, New Zealand, Norway, Papua New Guinea, Philippines, South Korea, Singapore, Thailand, Tonga, and the United Kingdom.
• Malaysia and Vietnam are attending as observers.
• The exercise will be held over three weeks, covering joint operations across land, sea, and air domains.
• India’s participation marks a step forward in strengthening Indo-Pacific defence ties and interoperability.

The correct answer is Option 2. 

Key Points

• The Industrial Policy Resolution of 1956 was an important policy document in India's economic history and played a key role in shaping the country's economic development trajectory.
• It was adopted by the Indian government under the leadership of Prime Minister Jawaharlal Nehru with the aim of promoting industrialization and economic growth in the country.
• The policy was closely linked to India's Second Five Year Plan (1956-61), which was the country's second major economic development plan after independence.
• The Second Five Year Plan was heavily influenced by the principles laid out in the Industrial Policy Resolution of 1956, which emphasized the importance of state-led development and the establishment of a mixed economy in which the private sector and public sector would both have a role to play.
• The Second Five Year Plan focused on promoting industrialization, particularly in key sectors such as steel, power, and heavy engineering, and on developing the country's infrastructure.
• The plan was also aimed at promoting social welfare and reducing poverty by creating employment opportunities and improving access to essential goods and services for the people of India.

Additional Information

• A Five Year Plan is a strategic planning framework used by organizations, governments, and individuals to set long-term goals and objectives over a five-year period. The plan typically includes specific targets and timelines for achieving those goals.
• The Fifth Five Year Plan was a period of economic planning in India that covered the period from 1974 to 1979.
• The plan was introduced during a period of economic crisis, marked by high inflation and slow economic growth.
• The main focus of the Fifth Five Year Plan was on increasing agricultural production, promoting rural development, and reducing poverty.
• The plan also emphasized the need to increase industrial production and promote exports to earn foreign exchange.
• The Fourth Five-Year Plan was a period of economic planning in India that covered the period from 1969 to 1974.
• The main focus of the Fourth Five-Year Plan was on achieving self-sufficiency in food production and reducing poverty.
• The plan also emphasized the need to increase industrial production and to promote exports to earn foreign exchange.
• The Third Five-Year Plan was a period of economic planning in India that covered the period from 1961 to 1966.
• The main objective of the Third Five-Year Plan was to achieve self-sustaining growth and to reduce poverty.
• This plan was introduced after a brief period of stability following the Indo-China war in 1962.

The correct answer is Cold desert​.

Key Points 

• Cold Desert is one of India's most fascinating biosphere reserves, known for its snow leopard conservation efforts.
• It stretches over the Western Himalayas from Ladakh to Kinnaur in Himachal Pradesh.
• It was declared a biosphere reserve in 2009 and includes the Pin Valley National Park and its surrounds, as well as the Kibber Wildlife Sanctuary, Sarchu, and Chandratal.
• Some of the common wildlife found here are the Himalayan black bear, Himalayan blue sheep, Himalayan ibex, snow pigeon, Tibetan gazelle, woolly hare, red fox, and others.
• Nanda Devi Biosphere Reserve, located in the Himalayan Mountains in the northern part of the country(Uttarakhand, CM: Pushkar Singh Dhami), includes as core areas the Nanda Devi and Valley of Flowers National Parks, which are one World Heritage site.
• The Nanda Devi Biosphere Reserve is famous for its being a habitat for many rare species of animals and plants. Animals such as Himalayan Musk Deer, Himalayan Tahr, Snow leopard Himalayan Black Bear,  Himalayan Brown Bear, and Langurs are commonly spotted in the area.
• Fir, Birch, Rhododendron, and Juniper consist of the flora in this region.

Additional Information 

The correct answer is Babur.

Key Points

• Babur defeated Ibrahim Lodi at Panipat in 1526.
• Babur was the founder of the Mughal Empire.
• He was the first Emperor of the Mughal dynasty who ruled between 1526 to 1530.
• He defeated Ibrahim Lodhi in the first battle of Panipat in 1526.
• He defeated Mahmud Lodi in the battle of Ghaghra in 1529. Babur died in 1530 in Agra.
• He was first buried in Agra, later his mortal remains were moved to Kabul and reburied in Bagh-e Babur in Kabul.
• Autobiography of Babur: Baburnama.

Additional Information

• Jahangir was born in 1569 at Fatehpur Sikri, present Uttar Pradesh.
• In 1605, Prince Salim succeeded with the title Jahangir (Conqueror of World) after the death of Akbar.
• Jahangir issued coins jointly in Nurjahan's name and his own.
• Jahangir also married Manbai in 1585 AD and Jodhbai in 1587 AD.
• He defeated and imprisoned his son, Khusrau Mirza.
• He also beheaded Guru Arjun, the 5th Sikh Guru and one of the supporters of Khusrau Mirza.
• Captain Hawkins (1608-1611) and Sir Thomas Roe (1615-1616) visited Jahangir's court.
• Humayun (1530 to 1540 and again from 1555 to 1556)
• He was Babur's son.
• He ascended the throne of India three days after Babur's death in 1530.
• Six months after his accession, Humayun besieged the fortress of Kalinjar in Bundelkhand.
• Humayun forces were defeated by Afghan ruler Sher Shah Suri at Chausa near Buxar in June 1539.
• On May 17, 1540, the Mughals and the Afghans met again opposite Kannauj.
• His hopelessly demoralised army was defeated at the battle commonly known as the Battle of Kannauj.
• In February 1555, he captured Lahore, and after a few months captured also.
• Akbar (1556 AD-1605 AD)
• He undertook the title of Jalaluddin Muhammad Akbar Badshah Ghazi at the young age of 14.
• The Second Battle of Panipat,1556 was fought between Hemu, the Hindu General of Muhammad Adil Shah and Bairam Khan, the regent of Akbar.
• He divided his empire into 12 subbas. The word 'subba' means the province.
• He built Buland Darwaza at Fatehpur Sikri.
• He also built Fatehpur Sikri, Agra Fort, Lahore Fort, Allahabad Fort and Humayun’s Tomb in Delhi.
• He proclaimed a new religion, Din‑i‑Ilahi, in 1581 AD.
• Birbal was the only Hindu who followed Din-i-Ilahi.

The correct answer is '29'.

Key Points Ajanta Caves

• The Ajanta Caves are about 29 rock-cut Buddhist monumental caves.
• They are located in Maharashtra, India, dating back to the 2nd century BC.
• Here excellent specimens of depiction and craftsmanship related to Buddhism are found.
• Along with these, living illustrations are also found.
• These caves are located near a village called Ajanta, which is in the Aurangabad district of Maharashtra.
• The Ajanta Caves have been declared a UNESCO World Heritage Site since 1983.

Thus, the correct answer is 29.

The correct answer is Right to Constitutional Remedies.

Key Points

• It is one of the fundamental rights listed in the Constitution that each citizen is entitled to.
• It entitles the citizens of India to move the Supreme Court or High Courts for the enforcement of these rights.
• In the Constituent Assembly debate, Dr. B.R Ambedkar said that Article 32 is the heart and soul of the Constitution.
• Article 32 falls under Part III of the Constitution which includes the fundamental rights of individuals.

Additional Information

• Article 32 of the UCMJ requires any service member accused of violating any Punitive Article of the UCMJ to undergo a preliminary hearing.
• An article 32 hearing is required before a defendant can be referred to a general court-martial, in order to determine whether there is enough evidence to merit a general court-martial.
• An Article 32 hearing is a proceeding under the united States Uniform Code of Military justice, similar to that of a preliminary hearing in civilian law.
• The Right against Exploitation is enshrined in Articles 23 and 24 of the Indian Constitution.

The correct answer is 6 years or up to the age of 65 years, whichever is earlier.

• Chief Election Commissioner has a tenure of 6 years, or up to the age of 65 years, whichever is earlier.

Key Points

• The President appoints the Chief Election Commissioner, who has a tenure of 6 years, or up to the age of 65 years, whichever is earlier.
• The Chief Election Commissioner enjoys the same status and receives the same salary and perks as available to Judges of the Supreme Court.
• The Chief Election Commissioner can be removed from his office only in a manner and on the grounds prescribed for removal of Judge of the Supreme Court.
• Other Election Commissioners can be removed by the President on the recommendation of the Chief Election Commissioner.

Additional Information

• The Election Commission has the power of superintendence, direction, and conduct of all elections to Parliament and the State Legislatures.
• It also conducts elections in the offices of the President and Vice-President.

The correct answer is North Indian.

Key Points

• 'Nagara' temples typically have a North Indian style of architecture.
• Nagara or North Indian Temple Style:
• Nagara (in North India) is associated with the land between the Himalayas and Vindhyas.
• The Nagara style is associated with the land between the Himalayas and Vindhyas, the Dravida style with the land between the Krishna and Kaveri rivers, while the Vesara style is sometimes associated with the area between the Vindhyas and the Krishna river.
• In North India, it is common for an entire temple to be built on a stone platform with steps leading up to it.
• It does not usually have elaborate boundary walls or gateways.
• While the earliest temples had just one tower or shikhara, later temples had several.
• The garbhagriha is always located directly under the tallest tower.
• There are many subdivisions of nagara temples depending on the shape of the shikhara.
• The second major type of architectural form in the nagara order is the phamsana, which tends to be broader and shorter than the Latina ones.
• Their roofs are composed of several slabs that gently rise to a single point over the centre of the building, unlike the Latina ones which look like sharply rising tall towers.
• The third main sub-type of the nagara building is generally called the valabhi type.
• These are rectangular buildings with a roof that rises into a vaulted chamber.

Additional Information

• Three main styles of temple architecture are the Nagara or the Northern style, the Dravida or the Southern style, and the Vesara or Mixed style. But at the same time, there are also some regional styles.
• A number of architectural texts known as the Shilpashastras were written in early medieval times. These refer to three major styles of temple architecture, Nagara, Dravida, and Vesara.
• Dravida Or South Indian Temple Style:
• Unlike the nagara temple, the Dravida temple is enclosed by a compound wall.
• The front wall has an entrance gateway in its centre, which is known as a gopuram.
• The shape of the main temple tower known as vimana in Tamil Nadu is like a stepped pyramid that rises up geometrically rather than the curving shikhara of North India.
• It is common to find a large water reservoir, or a temple tank, enclosed within the complex.
• Subsidiary shrines are either incorporated within the main temple tower or located as distinct, separate small shrines beside the main temple.
• Kanchipuram, Thanjavur or Tanjore, Madurai, and Kumbakonam are the most famous temple towns of Tamil Nadu, where, during the 8th-12th centuries, the role of the temple was not limited to religious matters alone.

The correct answer is 22.

Key Points

• The nuclear energy programme in India was launched around the time of independence under the leadership of Homi J. Bhabha.
• Nuclear power is the fifth-largest source of electricity in India after coal, gas, hydroelectricity and wind power.
• As of November 2020, India has 22 reactors with a total capacity of 6780 MW in operation and one reactor.
• KAPP-3 (700 MW) has been connected to the grid on January 10, 2021.
• Operational nuclear power plants in India-
• Kaiga-Karnataka
• Kakrapar-Gujarat
• Kudankulam-Tamil Nadu
• Kalpakkam-Tamil Nadu
• Narora-Uttar Pradesh
• Tarapur-Maharastra
• Rajasthan Atomic Power Project-Rajasthan

The Correct Answer is 27.

In News

• 19th Ramnath Goenka Awards for Excellence in Journalism awarded by President.

Key Points

• President Droupadi Murmu was the chief guest at the 19th Ramnath Goenka Award for Excellence in Journalism 2025.
• The winners were presented with a citation, a trophy, and a cash prize of ₹1 lakh.
• The award honors journalists in Print/Digital & Broadcast journalism.
• Mridulika Jha of Aaj Tak won the award for her coverage of the “Dunki route”, a method used by youths from Haryana to illegally enter the United States.
• A total of 27 journalists were felicitated in 20 categories at the ceremony held in New Delhi on 19 March 2025.
• The Ramnath Goenka Award was instituted by the Indian Express Group in honor of its founder’s birth centenary.
• The award, first given in 2005, recognizes journalists who display courage and excellence in their work, often in the face of significant political and economic pressures.

The Correct Answer is ​Thanh Tam Monastery.

In News

• Lord Buddha’s Holy Relics Arrive in Vietnam for Vesak Celebrations.

Key Points

• The Holy Relics of Lord Buddha arrived in Ho Chi Minh City with Indian Union Minister Kiren Rijiju, Andhra Pradesh Minister Kandula Durgesh, monks, and officials.
• The visit is part of the United Nations Day of Vesak celebrations in Vietnam from May 6-8.
• The Relics were received with reverence by Vietnamese leaders and monks.
• The Relics were enshrined at Thanh Tam Monastery after ceremonial prayers.
• A Sacred Bodhi tree sapling from India was planted at the Vietnam Buddhist University.
• The Relics were brought from Sarnath, supported by the Mahabodhi Society, National Museum of India, and International Buddha Confederation.
• The Relics will be displayed in Ho Chi Minh City until May 7, then travel to Tay Ninh, Ha Noi, and Ha Nam until May 21.

The Correct Answer is 103 minutes.

In News

• 79th Independence Day: At 103 minutes, PM Modi delivers longest Independence Day speech.

Key Points

• Date & Occasion: August 15, 2025, 79th Independence Day.
• Location: Red Fort, Delhi.
• Duration: 103 minutes – longest I-Day address by any Indian PM.
• Surpassed his own 2024 record of 98 minutes.
• 12th consecutive speech since 2014.
• Second-longest consecutive streak after Nehru (17 speeches).
• Speech Durations (select years):
• 2014: 65 mins (first)
• 2015: 88 mins
• 2016: 96 mins
• 2017: 56 mins (shortest)
• 2018: 83 mins
• 2019: 92 mins
• 2020: 90 mins (pandemic year)
• 2021: 88 mins
• 2022: 74 mins
• 2023: 90 mins
• 2024: 98 mins (previous record)
• 2025: 103 mins (new record)

The correct answer is Ashok Chakra.

Key Points

• Ashok Chakra
• ​The Ashok Chakra is the top honour for valour during peacetime, followed by the Kirti Chakra and the Shaurya Chakra.
• It is given in recognition of bravery, selflessness, or other acts of valour off the battlefield.
• The first recipient was flying lieutenant Suhas Biswas in 1952.
• It is Param Vir Chakra's counterpart during peacetime.

Additional Information

• Vir Chakra
• ​In terms of precedence among wartime gallantry decorations, the Vir Chakra is in third place behind the Param Vir Chakra and the Mahavir Chakra.
• It is given out for bravery displayed when fighting the enemy on land, at sea, or in the air.
• Brigadier Harbaksh Singh received it for the first time in 1948.
• Param Vir Chakra
• ​India's highest military honour, the Param Vir Chakra, is given to individuals who exhibit exceptional deeds of valour while fighting.
• That is the biggest and most obvious display of bravery when the enemy is there.
• Major Somnath Sharma received it for the first time in 1947.
• ​​Mahavir Chakra
• ​The Maha Vir Chakra (MVC), often known as the "great warrior medal," is the second-highest military decoration in India, behind the Param Vir Chakra.
• It is given for acts of remarkable bravery against the enemy, whether they take place on land, at sea, or in the air.
• The British Distinguished Service Order was replaced (DSO).

The correct answer is Blue Nile River.

In News

• The Grand Ethiopian Renaissance Dam (GERD) is located on the Blue Nile River in Ethiopia, about 30 km upstream from Sudan.

Key Points

• The GERD is Africa’s largest hydroelectric project, built for power generation and regional energy trade.
• It is located on the Blue Nile River, which contributes around 85% of the water to the Nile River, making the project geopolitically sensitive.
• The dam has a height of about 170 meters and a length of approximately 2 km, with a reservoir capacity of 74 billion cubic meters.
• The dam’s power capacity ranges from 5,150 MW to 6,450 MW, making it the largest hydroelectric project in Africa.

Additional Information

• Blue Nile River
• One of the two major headstreams of the Nile River, providing around 70% of its floodwaters at Khartoum.
• It rises from a spring near Lake Tana in Ethiopia, flowing through rapids and gorges before joining the White Nile at Khartoum in Sudan.
• GERD Features
• Reservoir capacity: 74 billion cubic meters, flooding around 1,874 km².
• The dam aims to trap sediment inflow, ensuring sustainable power generation for decades.
• Nile River
• The Nile River, formed by the confluence of the Blue Nile and White Nile, is crucial to the water security of Egypt and Sudan.

Concept:

• Symbiotic denotes “living together” of two or more organisms. Symbiosis is the biological interaction between two different biological organisms

Explanation:

• Lichens are symbiotic associations i.e. mutually useful associations, between algae and fungi.
• The algal partner is known as phycobiont, which is autotrophic and fungal partner is know as mycobiont, which is heterotrophic.
• Algae prepare food for fungi and fungi provide shelter and absorb mineral nutrients and water for its partner.
• The symbiotic association between fungi and roots of higher plants is called as Mycorrhizae.

Additional Information

The symbiotic association may be mutualistic, commensalism or parasitism.

• Mutualisms are a form of association in which both partners benefit from the interaction with each other.
• Commensalism is a form of association in which one organism benefits from others. One partner is completely dependent on the other for food, shelter and locomotion, but there is no harmful effect on the other partner.
• Parasitism is the non-mutualistic form of the symbiotic association. In this type of association when one of the organisms benefits and the other organism get harmed.

Concept:

Photosynthesis:

• Photosynthesis is the process by which green plants and certain other organisms transform light energy into chemical energy.
• During photosynthesis in green plants, light energy is captured and used to convert water, carbon dioxide, and minerals into oxygen and energy-rich organic compounds.

​

• Oxygenic photosynthesis is written as follows:

(\rm \underset{(Carbon\ dioxide)}{6CO_2} + \underset{(Water)}{6H_2 O} \xrightarrow[Chlorophyll]{Sunlight} \underset{(Carbohydrates)}{C_6H_{12}O_6} + \underset{(Oxygen)}{6O_2})

Explanation:​

• Photosynthesis takes place in only those parts of the plants which have chlorophyll, the green plant parts. Photosynthesis is so evident that at times it seems to mask the respiratory process in plants.
• Respiration must not be mistaken for photosynthesis. Respiration occurs all through the day, but the photosynthesis process occurs in the daytime, in the presence of sunlight only.
• Consequently, respiration becomes evident at night time in plants.

The correct answer is ​Kerala.

• Theyyam is a popular dance form of North Kerala (Malabar region).

Key Points

• It has been practiced since thousands of years.
• It is a ritual dance done for impressing Goddess Kali and is a Dravidian art form.
• It got its name from the word ‘Devam’ (Malayalam word) which means ‘God’.
• The people of Kerala consider it as a road to take blessings from God.
• It is generally performed by males and it belongs to the lower caste community.
• There are approximately 400 types of Theyyam.
• Theyyam, Chakyar Koothu, and Thiruvathirakali are the art-forms of Kerala.

The correct answer is Limestone.

Key Points

• Limestone is the main ingredient of cement.
• Limestone is a sedimentary type of rock naturally found on earth.
• Limestone rock primarily contains calcium carbonate i.e CaCO3.
• Quartz, clay minerals, pyrite, siderite and feldspar etc. are other minerals found in limestone.
• It is known by other names like- chalk, coquina, travertine, tufa, lithographic limestone. oolithic limestone etc.

The main ingredients of cement are as follows-

Additional Information 

Other uses of limestone-

The correct answer is 1972.

Key Points

• In order to maintain and protect the nation's wildlife (flora and fauna), the Indian Parliament passed the Wildlife (Protection) Act in 1972.
• The Act imposes prohibitions on a variety of animal species' hunting, among other things.
• The Act was last modified in 2006.
• Wildlife Act Constitutional Provisions:
• The State is required by Article 48A of the Indian Constitution to maintain the environment, preserve animals, and protect forests. The 42nd Amendment to the Constitution, passed in 1976, included this provision.
• The Indian people are subject to a number of fundamental obligations under Article 51A.
• One of them is to have compassion for all living things and to maintain and enhance the natural environment, which includes woods, lakes, rivers, and wildlife.
• Important Elements of the Wildlife Protection Act:
• The Act outlines how to establish wildlife advisory boards and wildlife wardens as well as their responsibilities.
• India was aided in joining the Convention on International Trade in Endangered Species of Wild Fauna and Flora as a result (CITES).
• A thorough list of the nation's endangered wildlife was created for the first time. The Act made it illegal to hunt endangered species.
• The provisions of the Act restrict the trading of animals that have been scheduled. For the purchase, transfer, and possession of some wildlife species, the Act establishes licence requirements.
• The Act established six schedules with differing levels of protection for various flora and wildlife classes.
• Under the terms of this Act, the National Board for Wildlife was established as a statutory institution.
• The National Tiger Conservation Authority was to be established under the Act.

Additional Information

• India's legislative history relating to wildlife conservation:
• The Wild Birds Protection Act, of 1887, was the first of its kind, and it was enacted by the British Indian Government in 1887.
• The intention of the law was to make it illegal to own or sell certain wild birds that were either shot or caught during a nesting season.
• The Wild Birds and Animals Preservation Act, a second piece of legislation, was passed in 1912.
• The Wild Birds and Animals Protection (Amendment) Act 1935, which was approved, changed this. The preservation of animals was not a top priority during the British Raj.
• The concern about protecting wildlife and averting the extinction of specific species didn't really take off until 1960.

The correct answer is Kirana.

Key Points

• Pandit Bhimsen Joshi is a renowned figure in the world of Indian classical music, celebrated for his contributions to the Khayal genre.
• He belonged to the Kirana Gharana, which is known for its emphasis on the emotional expression in music, detailed alap (improvisation), and slow tempo renditions.
• The Kirana Gharana, to which Pandit Bhimsen Joshi belonged, has produced several other legendary musicians and is considered one of the most influential schools of music in India.
• His music was marked by his powerful voice, brilliant technique, and soulful renditions, making him one of the most respected and loved classical singers of India.

Additional Information

the correct answer is  Ex-Ayutthaya

In News

• Ex-Ayutthaya was the name of the maiden bilateral maritime exercise between the Indian Navy and Royal Thai Navy.

Key Points

• Date of Exercise: 20 to 23 December 2023.
• Indian Naval Ships: Kulish and IN LCU 56.
• Royal Thai Navy Ship: His Thai Majesty's Ship (HTMS) Prachuap Khiri Khan.
• 36th Edition of Indo-Thai CORPAT: Conducted alongside the bilateral exercise.
• Sea Phase Participation: Maritime Patrol Aircraft from both navies.
• Exercise Components: Surface and anti-air exercises, weapon firing, seamanship evolutions, and tactical maneuvers.
• Operational Synergy: Strengthening operational synergy between the Indian Navy and Royal Thai Navy.
• Bilateral Relations: Reflects the growing bilateral relations between India and Thailand in the maritime domain.
• Interoperability: Aims to enhance interoperability between the two navies.
• Symbolic Name: The bilateral exercise is named 'Ex-Ayutthaya,' symbolizing the historic ties between Ayodhya in India and Ayutthaya in Thailand.

The correct answer is Factories.

Key Points

• The seventh schedule of the Indian constitution deals with the division of powers between the central government and the state governments through three lists: the Union List, the State List, and the Concurrent List.
• The Concurrent List consists of subjects on which both the central government and state governments have the power to legislate, such as criminal law, marriage and divorce, bankruptcy and insolvency, factories, education, forests, and more. Hence option c is correct.
• Both the central and state governments can make laws, regulate, and govern the subjects mentioned in the Concurrent List simultaneously, subject to certain limitations and guidelines.
• In case of a conflict between central and state laws on Concurrent List subjects, the law made by the central government prevails, provided it receives the President's assent.
• Any amendment to the Concurrent List requires the approval of the Parliament, and state legislatures can also make laws on these subjects unless they conflict with existing central laws.

Additional Information

• Union List:
• The Union List consists of around 100 items over which the central government has exclusive legislative authority, including defence, foreign affairs, atomic energy, banking, and telecommunications.
• The central government has the power to make laws, regulate, and govern the subjects mentioned in the Union List uniformly across all states and union territories in India.
• Items in the Union List ensure the central government's authority in critical areas such as national security, inter-state trade and commerce, currency, copyright, air and water pollution, and more.
• Any amendment to the Union List requires the approval of the Parliament through a prescribed legislative process, ensuring that changes to these subjects are made at the national level.
• State List:
• The State List consists of subjects over which state governments have exclusive legislative authority, including public order, police, public health, local government, agriculture, state taxation, and more.
• State governments exercise their legislative and executive powers to make laws, regulate, and govern the subjects mentioned in the State List within their respective states.
• Subjects in the State List allow state governments to address regional and local concerns, implement policies specific to their states, and ensure effective governance at the state level.
• Any amendment to the State List requires the approval of the state legislature concerned and does not require the consent of the Parliament, providing states with autonomy in making changes to these subjects.

The correct answer is Lumen.

 Key Points

• Luminous flux is the measure of the brightness of a light source in terms of energy being emitted.
• In other words, it is the measure of the perceived power of light.
• The S.I unit of Luminous Flux is Lumen.

 Additional Information

The correct answer is Option 3.

Key PointsAdenosine Triphosphate:

• The energy released during cellular respiration is used to synthesize a molecule called ATP.
• Adenosine triphosphate fuels all activities in the cell.
• When ATP is broken down, it gives rise to the energy that can drive the endothermic reactions in the cell.
• ATP is the energy currency for most cellular processes.
• The energy released during respiration is used to make an ATP molecule from ADP and inorganic phosphate.
• When the terminal phosphate linkage in ATP is broken, the energy equivalent to 30.5 kJ/mol is released.

The correct answer is Narasimhavarman II

Important Points

• Narasimhavarman II (695 – 722 CE)  was an eminent ruler of the Pallava Dynasty.
• He had the title "Rajasimha‟.
• He enjoyed a peaceful reign and is credited with the construction of large and beautiful temples like the Shore temple at Mamallapuram and the Kailasanatha temple at Kanchi. Hence, option 3 is the correct answer.
• He had the titles like Shankara Bhakta and Agamapriya.
• He was also a great patron of Art and letters.
• The famous Sanskrit scholar Dandin is said to have adorned his court.
• He sent embassies to China and the maritime trade flourished during his reign.

The correct answer is  option 2

Key PointsSports Honours in India:

• Major Dhyan Chand Khel Ratna Award: 
• The recipient(s) is/are selected by a committee constituted by the Ministry and is honoured for their "spectacular and most outstanding performance in the field of sports over a period of four years" at international level.
• Hence pair 1 is correctly matched.
• Arjun Award:
• The Arjuna Award, officially known as Arjuna Awards for Outstanding Performance in Sports and Games,is the second-highest sporting honour of India.
• Dhyan chand award is the lifetime achievement sporting honour of India.
• Hence pair 2 is not correctly matched.
• Dronacharya Award:
• ​It is given to coaches for doing outstanding and meritorious work on a consistent basis and enabling sportspersons to excel in International events.
• Hence, pair 3 is correctly matched.
• ‘Rashtriya Khel Protsahan Puruskar’:
• It is given to corporate entities (both in private and public sector), Sports Control Boards, NGOs, including sports bodies at the State and National level, who have played a visible role in the area of sports promotion and development.
• Hence pair 4 is not correctly matched.

The correct answer is Ribosomes.

Key Points

• Ribosomes are the cellular structures responsible for protein synthesis.
• Polyribosomes are clusters of ribosomes may sit on an mRNA and make proteins, each making a strand of polypeptides.
• These clusters are called polyribosomes. When they are free in the cytoplasm, they are called free polyribosomes (linked by the mRNA).
• Ribosomes are the protein factories of the cell.
• Ribosomes link amino acids together to form polypeptide chains, which are further modified before becoming functional proteins.

Additional Information

• The Golgi apparatus is responsible for transporting, modifying, and packaging proteins and lipids into vesicles for delivery to targeted destinations.
• Vesicle is an important term used to describe the appearance of many rashes that typically consist of or begin with tiny-to-small fluid-filled blisters.
• Pemphigus is classified as one of the blistering diseases.
• Vesicles are small structures within a cell, consisting of fluid enclosed by a lipid bilayer involved in transport, buoyancy control, and enzyme storage.
• Peroxisomes are organelles that sequester diverse oxidative reactions and play important roles in metabolism, reactive oxygen species detoxification, and signalling.
• Oxidative pathways housed in peroxisomes include fatty acid β-oxidation, which contributes to embryogenesis, seedling growth, and stomatal opening.

The correct answer is Only I.

Key Points 

Article 14 

• The Right to Equality is one of the Fundamental Rights enshrined in the Constitution of India.
• The right to equality provides for the equal treatment of everyone before the law, prevents discrimination on various grounds, treats everybody as equals in matters of public employment, and abolishes untouchability, and titles
• Article 14 treats all people the same in the eyes of the law.
• ​This provision states that all citizens will be treated equally before the law
• The law of the country protects everybody equally
• Under the same circumstances, the law will treat people in the same manner.
• ​Therefore 1st statement is correct.​

RIGHT TO FREEDOM OF RELIGION - Article 25

• Freedom of Conscience and Free Profession, Practice and Propagation of Religion :
• Article 25 says that all persons are equally entitled to freedom of conscience and the right to freely profess, practice and propagate religion.
• It covers not only religious beliefs (doctrines) but also religious practices (rituals).
• These rights are available to all persons–citizens as well as non-citizens.
• However, these rights are subject to public order, morality, health and other provisions relating to fundamental rights.
• Therefore 2nd statement is incorrect.
• Article 21 deals with the protection of life and personal liberty.

Additional Information

• Six fundamental rights are recognized by the Indian constitution.
• Under Part-III (article 12 - 35) of the constitution, every citizen has provided 6 fundamental rights.
• A total of seven rights were originally provided by the Constitution.
• 44th amendment (1978 A.D.) removed the right to property and made a legal right (300A).
• The fundamental rights secure the natural rights of all citizens and it was taken from the constitution of the U.S.A.

The Correct answer is Shane Watson.

Key Points

• Shane Watson, former Australian cricketer, is the author of the book “The Winner’s Mindset.”
• The book was released in 2024 and focuses on the mental aspects of sports and life, emphasizing resilience, positivity, and focus.
• Watson shares his personal experiences as a professional cricketer, especially how he overcame setbacks, injuries, and performance pressures.
• The book provides insights into the importance of mental health, discipline, and mindset in achieving success, not just in cricket but also in life and leadership.
• He retired from international cricket in 2016 and later from franchise cricket in 2020, making him one of the last active players from Australia’s golden era of cricket.
• Watson was known as one of the world’s best all-rounders, excelling in both batting and bowling, and played key roles in ICC tournaments for Australia.
• Through this book, he highlights how a strong mindset can transform challenges into opportunities and separate winners from others.

 Additional Information

• Ricky Ponting
• Former Australian cricket captain and one of the most successful captains in cricket history.
• He has authored books like “At the Close of Play” and “Ponting: At the Close of Play.”
• Ponting is known for leading Australia to victories in two ICC World Cups (2003, 2007).

The correct answer is Kidney → ureter → urinary bladder → urethra.

Explanation:

• The human excretory system consists of a pair of kidneys, two ureters, a urinary bladder, and a urethra.
• The kidney initiates the formation of urine, and the urethra facilitates urine excretion.
• Humans are ureotelic, and excretion occurs in the form of urea, resulting in less loss of body water.
• Kidneys are reddish brown, bean-shaped structures. An adult human kidney measures 10-12cm in length, 5-7cm in width, and 2-3cm in thickness, with an average weight of 120-170gm.
• Through nephrons (tiny filtering units), the kidneys remove waste products called urea, as well as extra water and ions from the blood to form urine.
• The nephron is the functional unit of kidney.
• The pelvis of kidney is continued as a ureter. Ureter is a long and muscular tube.
• Ureter carries urine from the kidneys to the bladder.
• In the pelvic cavity, there is a thin-walled, pear-shaped, white transparent sac called the urinary bladder.
• It temporarily stores the urine.
• The urethra is a membranous tube that arises from the urinary bladder. It conducts urine to the exterior.
• The actual path of urine in the human body is Kidney → ureter → urinary bladder → urethra.

The correct answer is Information sharing, submarine search and rescue, and joint staff talks.

In News

• India and Australia signed three key agreements to enhance military cooperation, including pacts on information sharing, submarine search and rescue, and joint staff talks.

Key Points

• The agreements were signed in Canberra after talks between Indian Defence Minister Rajnath Singh and Australian Deputy Prime Minister Richard Marles.
• The leaders reaffirmed their shared commitment to enhancing defence cooperation in areas such as military exercises, maritime security, and defence industry collaboration.
• The meeting marked the fifth anniversary of the India-Australia comprehensive strategic partnership, highlighting the deepening bilateral ties between the two countries.
• The agreements aim to strengthen defence cooperation and enable both countries to address emerging security challenges more effectively.

Additional Information

• India-Australia Comprehensive Strategic Partnership
• A strategic relationship that has grown significantly over the years, focusing on areas such as defence, trade, technology, and research collaboration.
• Joint Staff Talks
• Mechanism to facilitate communication and cooperation between the armed forces of both countries, strengthening their ability to coordinate on defence issues.
• Submarine Search and Rescue Cooperation
• An agreement to enhance both nations' capabilities in responding to submarine emergencies, ensuring greater maritime security.

The correct option is CO (Carbon Monoxide).

Explanation:

Greenhouse Effect: 

• Solar energy is trapped by the earth atmosphere and radiate slowly so to cover our earth with a warm blanket.
• This is the natural process of the greenhouse effect on earth to maintain its temperature and makes the earth perfect for life.

Greenhouse gases are carbon dioxide, other greenhouse gases are methane, water vapour, nitrous oxide, CFCs and ozone. 

Values of radiation absorbed by the greenhouse gases are as follow:

 

From the above table, it is clear that carbon dioxide absorbs the maximum radiation in the earth’s atmosphere

Hence the correct option is Carbon Monoxide (CO) which is not a greenhouse gas.

The major greenhouse gases are

• Water vapour - causes about 36% - 70% of the greenhouse effect
• Carbon dioxide (CO2) causes 9 - 26%
• Methane (CH4) causes 4 - 9%
• Ozone (O3)
• Nitrous Oxide
• Chlorofluorocarbons (CFCs)

Important Points

Global warming: If the amount of greenhouse gases cross by delicate proportion, the natural greenhouse balance may get disturbed and there is a continuous rise in temperature of the earth by trapping the solar heat continuously. This creates the overall effect of Global warming.

The correct answer is Amit Shah

In News

• On 2nd January 2025, Union Minister for Home Affairs and Cooperation, Shri Amit Shah will preside over the release of the book ‘Jammu Kashmir and Ladakh: Through the Ages’ in New Delhi, with Union Minister for Education, Shri Dharmendra Pradhan as the Guest of Honour.

Key Points

• Book Overview: The book ‘Jammu Kashmir and Ladakh: Through the Ages’ provides a comprehensive history of the regions, spanning over three thousand years. It presents the story of Jammu Kashmir and Ladakh from an accessible perspective, catering to both experts and general readers.
• The book was authored by the Indian Council of Historical Research (ICHR), with Prof. Raghuvendra Tanwar serving as its editor.
• Structure: The book is divided into seven sections, each illustrating key periods and historical contributions of the regions. The illustrations included are carefully selected to represent significant ages and their relevance in the larger historical context of Indian history.
• Collaborative Effort: The book is a collaborative publication by National Book Trust, India and the Indian Council of Historical Research, and is available in both Hindi and English.

The Correct Answer is 25.

In News

• India achieve record high of renewable energy capacity addition of 25 gigawatts in the last financial year.

Key Points

• 25 gigawatts of renewable energy capacity was added, setting a record for the highest-ever addition.
• 35% increase in renewable energy capacity compared to 18.57 gigawatts in FY 2023-24.
• Solar energy capacity grew from 15 to nearly 21 gigawatts, a 38% growth.
• BioCNG will be mandated for blending with compressed natural gas and piped natural gas to decarbonize transportation and households.
• Solar PV cell manufacturing capacity nearly tripled, from 9 gigawatts.
• PM KUSUM Scheme showed good progress both physically and financially.
• PM Surya Ghar Muft Bijli Yojana benefited more than 1.1 lakh households.
• The sector generated nearly 7 lakh employment opportunities in the last financial year.

Given:

Price increase of honey = 15%

Formula Used:

Let the original price be P and the reduced consumption be C.

New price = P + 0.15P = 1.15P

To keep the expense the same: P × C = 1.15P × (1 - x)

where x is the percentage reduction in consumption.

Calculation:

P × C = 1.15P × (1 - x)

⇒ C = 1.15 × (1 - x)

Since expense is not increased, C = 1

⇒ 1 = 1.15 × (1 - x)

⇒ 1 = 1.15 - 1.15x

⇒ 1.15x = 1.15 - 1

⇒ 1.15x = 0.15

⇒ x = 0.15 / 1.15

⇒ x = 0.1304

⇒ x ≈ 13%

The correct answer is option 2.

Given:

Saving = Rs 8,000

Calculation:

Saving % = 60° =Rs 8,000

Then, 1° = 8000/60 = Rs 800/6

Then, portion spent on food = 120° 

Portion spend on housing = 105° 

Difference in amount spent (in degree) in food and housing =  120° - 105° = 15° 

Then, required difference = 15 × 800/6 = Rs 2,000.

∴ The required difference is Rs 2,000.

Given:

C.P = Rs. 5400

C.P = Cost Price

Calculation:

According to the question,

(5400 × (\dfrac{2}{3}) × 8%) + (1800 × x%) = (5400 × 18%) 

⇒ (3600 × 8%) + (1800 × x%) = (5400 × 18%)

⇒ 288 + 18x = 54 × 18

⇒ 288 + 18x = 972

⇒ 18x = 972 - 288

⇒ x = 684/18

⇒ x = 38

∴ The correct answer is 38%.

Shortcut Trick

Simplify given eq: x(3 − 2/x) = 3/x ⇒ 3x − 2 = 3/x ⇒ x − 1/x = 2/3

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

Here k = 2/3, so x³ − 1/x³ = (2/3)³ + 3 × (2/3)

⇒ 8/27 + 2 = (8 + 54) / 27 = 62/27

∴ The correct answer is 62/27.

Alternate Method

Given equation: x(3 − 2/x) = 3/x

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

⇒ 3x − 2 = 3/x

⇒ 3x − 3/x = 2

⇒ 3(x − 1/x) = 2

⇒ x − 1/x = 2/3

Cubing both sides of the equation:

⇒ (x − 1/x)³ = (2/3)³

⇒ x³ − 1/x³ − 3 × x × (1/x) × (x − 1/x) = 8/27

⇒ x³ − 1/x³ − 3 × (2/3) = 8/27

⇒ x³ − 1/x³ − 2 = 8/27

⇒ x³ − 1/x³ = 8/27 + 2

⇒ x³ − 1/x³ = (8 + 54) / 27

⇒ x³ − 1/x³ = 62/27

∴ The correct answer is 62/27.

Additional Information

Algebraic Identity for Addition

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

Square Identity

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

Relation between Sum and Difference

(x + 1/x)² − (x − 1/x)² = 4. This is used to convert between addition and subtraction forms.

Given:

The expression to simplify is √((1191-√(1250-√(599+√676))))

Formula Used:

√a means the square root of a.

Calculation:

Start with the innermost square root: √676

⇒ √676 = 26

Then, 599 + 26 = 625

⇒ √(599 + √676) = √625 = 25

Next, 1250 - 25 = 1225

⇒ √(1250 - √(599 + √676)) = √1225 = 35

Finally, 1191 - 35 = 1156

⇒ √(1191 - √(1250 - √(599 + √676))) = √1156 = 34

∴ The simplified result of the given expression is 34.

Given:

Average of four consecutive odd numbers = 42

Formula used:

Average of n consecutive numbers = Sum of numbers ÷ n

Calculations:

Let the four consecutive odd numbers be (x - 3), (x - 1), (x + 1), and (x + 3).

Average = (Sum of numbers) ÷ 4

⇒ 42 = [(x - 3) + (x - 1) + (x + 1) + (x + 3)] ÷ 4

⇒ 42 = (4x) ÷ 4

⇒ x = 42

Largest number = x + 3 = 42 + 3 = 45

Sum of digits of 45 = 4 + 5 = 9

∴ The sum of the digits of the largest number is 9.

Given:

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

Time is taken by both pipe and leak to fill the tank = (12 + 8) = 20 hours

Formula used:

Time is taken = Total work/Efficiency

Calculation:

Part of the tank filled by the pipe in 1 hour = 1/12

Part of the tank filled by pipe and leak in 1 hour = 1/20

Part of the tank empty by a leak in 1 hour = 1/12 - 1/20 = 1/30

Total time is taken by the leak to empty full tank = 30 hours

∴ The time is taken by the leak to empty the full tank in 30 hours

Shortcut Trick

The efficiency of leak = 3 – 5 = - 2     (Here negative sign indicating that it is removing water from the tank)

Time = 60/2 = 30 hours

∴ The time taken by the leak to empty the full tank is 30 hours.

Given:

A table showing the number of trees of 3 different fruits, planted during 2018- 2022.

Formula used:

Percentage increase = (Mango in 2020 - Mango in 2018) / Mango in 2018 × 100

Calculation:

Percentage increase = (52000 - 40000) / 40000 × 100 

⇒ 12000 / 40000 × 100

⇒ 30%

∴ The correct answer is 30%.

Given :

Radius of cone(r) = 11 cm

The slant height of cone (l) = 24 cm

Formula used :

Total surface area of the cone = πr(r + l) 

Calculation:

Total surface area of the cone = πr(r + l) 

⇒  (\dfrac{22}{7}× 11× (11+24) ) 

⇒ ({\dfrac{22}{7}}× 11× 35)

⇒ 22 × 11 × 5 = 1210 cm²

∴ The answer is 1210 cm² .

Shortcut TrickTotal surface area of the cone is the multiple of π. Which is the multiple of 11 and only one option is the multiple of 11 that is 1210.

Given:

Let ABCD be a quadrilateral and AC, BD be diagonals.

The length of BD = 20 cm and the heights of the triangles ABD and BCD are, respectively, 6 cm, 8 cm.

Calculation:

According to the question,

Area of Quadrilateral = Sum of Area (Triangle ABD + Triangle BCD)

⇒ (1/2)× 20 × 6 + (1/2)× 20 × 8

⇒ 60 + 80 

⇒ 140

∴ The area of the quadrilateral ABCD is 140 cm².

Given:

1st Proportional(a) = 2; 6

2nd Proportional(b) = 5; 8

3rd Proportional(c) = 6; 9

Formula Used:

4th Proportional(d) = (b x c)/a

Calculation:

According to the formula,

(5 x 6)/2 = 15

The fourth proportion is 15

Again,

(8 x 9)/6 = 12

The fourth proportion is 12

Ratio = 15 : 12

⇒ 5 : 4

∴ The ratio is 5 : 4

Given:

The given cubic sum is as follows,

 13 + 23 + ......... 103

Concept:

The sum of the cube of the first n natural number is ({[\frac{n(n+1)}{2}]}^2)

Solution:

As per the given cubic sum n = 10

Substituting the value of n in ({[\frac{n(n+1)}{2}]}^2) we will get,

({[\frac{n(n+1)}{2}]}^2={[\frac{10\times 11}{2}]}^2)

(55^2=3025)

Hence, option 1 is correct.

Shortcut Trick

Recognize the Pythagorean triplet: 5, 12, 13.

Given hypotenuse = 13 cm and one side = 5 cm, the other side (height) must be 12 cm.

Area = (1 ÷ 2) × base × height = (1 ÷ 2) × 5 × 12 = 30 cm².

∴ The correct answer is 30 cm².

Alternate Method

Given: Hypotenuse (h) = 13 cm, Base (b) = 5 cm.

Formula Used: Pythagoras Theorem: h² = b² + p² | Area = (1 ÷ 2) × b × p

⇒ p² = 13² − 5²

⇒ p² = 169 − 25 = 144

⇒ p = √144 = 12 cm

⇒ Area = (1 ÷ 2) × 5 × 12

⇒ Area = 5 × 6 = 30 cm²

∴ The correct answer is 30 cm².

Additional Information

Pythagorean Triplets

Common sets of integers that satisfy a² + b² = c² include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Area of Triangle (Heron's Formula)

For any triangle with sides a, b, and c, Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c) ÷ 2.

Circumradius of Right Triangle

The radius of the circumcircle of a right-angled triangle is always half of the hypotenuse (R = h ÷ 2).

Shortcut Trick

For 1 year compounded half-yearly, the number of periods (n) = 2 and rate (r) = 25 ÷ 2 = 12.5% = 1/8.

The difference between CI and SI for 2 periods is given by: Difference = P × (r/100)².

⇒ 4375 = P × (1/8)²

⇒ 4375 = P × (1/64)

⇒ P = 4375 × 64 = 280000.

∴ The correct answer is ₹ 280000.

Alternate Method

Given: Rate (R) = 25% per annum, Time (T) = 1 year, Difference (CI − SI) = ₹ 4375.

Formula Used: SI = PRT/100 | CI = P[(1 + r/100)ⁿ − 1]

⇒ Simple Interest (SI) = (P × 25 × 1) ÷ 100 = 0.25P

⇒ For Compound Interest (half-yearly), Rate (r) = 25 ÷ 2 = 12.5% and n = 2.

⇒ CI = P[(1 + 12.5/100)² − 1] = P[(1 + 1/8)² − 1]

⇒ CI = P[(9/8)² − 1] = P[81/64 − 1] = 17P/64

⇒ Difference = CI − SI = 17P/64 − 0.25P

⇒ 4375 = (17P − 16P) ÷ 64 = P/64

⇒ P = 4375 × 64 = 280000

∴ The correct answer is ₹ 280000.

Additional Information

Compound Interest Half-Yearly

When interest is compounded half-yearly, the annual rate is divided by 2 (R/2) and the time period is multiplied by 2 (2T).

SI vs CI Difference Formula

For 2 years (or 2 compounding periods), the difference is P(r/100)². For 3 periods, it is P(r/100)² × (3 + r/100).

Effective Rate of Interest

The effective rate for two successive periods of r% is calculated as (r + r + r²/100)%.

Shortcut Trick

Initial Ratio of Rida and Riya = 3 : 5

New Ratio after Rs. 5,000 increment = 5 : 7

Both ratios increased by 2 parts (5 − 3 = 2 and 7 − 5 = 2).

2 parts = Rs. 5,000 ⇒ 1 part = Rs. 2,500

Riya's present salary = 5 parts × 2,500 = Rs. 12,500

∴ The correct answer is Rs. 12,500.

Alternate Method

Given:

Initial ratio of salaries of Rida and Riya = 3 : 5

Increment in the salary of each = Rs. 5,000

New ratio of salaries = 5 : 7

Rida = 3 parts

Riya = 5 parts

• 2 parts

• 2 parts

Rida = 5 parts

Riya = 7 parts

2 parts = Rs. 5,000

Calculations:

⇒ Let the present salaries of Rida and Riya be 3x and 5x, respectively.

⇒ After adding Rs. 5,000 to each, the new salaries become (3x + 5000) and (5x + 5000).

⇒ According to the question, (3x + 5000) ÷ (5x + 5000) = 5 ÷ 7

⇒ By cross-multiplying, we get:

⇒ 7 × (3x + 5000) = 5 × (5x + 5000)

⇒ 21x + 35000 = 25x + 25000

⇒ 25x − 21x = 35000 − 25000

⇒ 4x = 10000

⇒ x = 2500

⇒ Riya's present salary = 5x = 5 × 2500 = 12500

∴ The correct answer is Rs. 12,500.

Additional Information

Constant Difference in Ratios

When a constant value is added to or subtracted from both terms of a ratio, the difference between the terms stays constant. If the initial part difference is unequal, multiply by cross differences to balance them.

Cross-Multiplication Method

For two numbers a and b, if x is added to both to form a new ratio c : d, then (a + x) ÷ (b + x) = c ÷ d. This is solved by directly equating d(a + x) = c(b + x).

Age Problems Relation

This specific ratio change shortcut is heavily used in Age problems, where the gap in ages between two people remains strictly constant regardless of the time elapsed.

Given:

The ratio of the speed of a boat to that of the current water is 35 : 8.

The boat goes along with the current in 5 hours 10 minutes.

Formula used:

Speed of boat in still water (B) / Speed of current (C) = 35 / 8

Time = Distance / Speed

Calculation:

Let speed of current be 8x, then speed of boat in still water = 35x

Speed downstream = 35x + 8x = 43x

Speed upstream = 35x - 8x = 27x

Time taken to go along with the current = 5 hours 10 minutes = 5 + 10/60 = 31/6 hours

⇒ Distance = Speed × Time

⇒ Distance = 43x × 31/6

Time taken to come back = Distance / Speed upstream

⇒ Time = (43x × 31/6) / 27x

⇒ Time = (43 × 31) / (6 × 27)

⇒ Time = 1333 / 162

⇒ Time = 8.2284 hours

⇒ Time = 8 hours 13 minutes 48 seconds

∴ The correct answer is option (4).

Formula used:

Perimeter of Square = 4a where, a is the side of Square.

Area of Square = a² where, a is the side of Square.

Perimeter of Rectangle = 2(L + B) where, L and B are the

Length and Breadth of Rectangle 

Area of Rectangle = L × B 

Calculations:

Perimeter of Square = 4a = 120 cm 

a = 30 cm

Area of Square = a2 = 900cm²

 The length of a rectangle is two times the side of the square. = 60cm

Perimeter of Rectangle = 2(L + B)  = 2(60 + B) = 156 cm 

60 + B = 156/2 = 78cm 

B = 78 - 60 = 18 

Area of Rectangle = L × B = 60 × 18 = 1080cm²

The difference between the areas is:

A_rectangle - A_square = 1080 - 900 = 180 cm²

Hence, the difference between the areas of the rectangle and the square is 180 cm².

Given:

A sold a mobile phone to B at a gain of 25%

B sold the mobile to C at a loss of 10%

Total money paid by C = Rs. 5625

Calculation:

Let, the A paid for the mobile phone = x

So, x × (125/100) × (90/100) = 5625

⇒ x = 5625 × (100/125) × (100/90)

⇒ x = 5000

∴ A paid Rs. 5000 (in Rs.) for the phone

Given:

Which of the following number is divisible by 11?

Options: 1) 6589, 2) 9164, 3) 8962, 4) 4857

Formula used:

A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11.

Calculation:

1. 6589

Odd positions: 6 + 8 = 14

Even positions: 5 + 9 = 14

⇒ 14 - 14 = 0

∴ 6589 is divisible by 11

2. 9164

Odd positions: 9 + 6 = 15

Even positions: 1 + 4 = 5

⇒ 15 - 5 = 10

∴ 9164 is not divisible by 11

3. 8962

Odd positions: 8 + 6 = 14

Even positions: 9 + 2 = 11

⇒ 14 - 11 = 3

∴ 8962 is not divisible by 11

4. 4857

Odd positions: 4 + 5 = 9

Even positions: 8 + 7 = 15

⇒ 9 - 15 = -6

∴ 4857 is not divisible by 11

∴ The correct answer is 6589.

Given:

Speed of Mohit from his home to office = 10 m/s

Speed of Mohit from his office to home = x km/hr

Average speed of Mohit for the whole journey = 12 m/s

Concept:

Unit conversion from Km/hr to m/s, then multiply from 5/18.

Unit conversion from m/s to Km/hr, then multiply from 18/5.

Formula used:

Distance = Speed × Time

Average speed = 2 × v₁ × v₂/(v₁ + v₂)

Where v₁ and v₂ are the speeds of journey for equal distance

Calculation:

Average speed of Mohit = 12 × 18/5 Km/hr

Speed of Mohit from his home to office = 10 × 18/5 = 36 Km/hr

⇒ Average speed = 2 × 36 × x/(36 + x)

⇒ 12 × 18/5 = 2 × 36 × x/(36 + x)

⇒ 6 × 18 = 180 × x/(36 + x)

⇒ 6 × (36 + x) = 10x

⇒ 216 = 4x

⇒ x = 54 km/hr

∴ Speed of Mohit from his office to home is 54 km/hr.

Given:

Height of cone = 8 cm

Radius of cone = 2 cm

Formula used:

Volume of sphere = (\frac{4}{{3}})πR³

Volume of cone = (\frac{1}{{3}})πr²h

Calculation:

According to the question

The volume of a sphere = Volume of a cone

⇒  (\frac{4}{{3}})πR³ = (\frac{1}{{3}})πr2h

⇒ (\frac{4}{{3}}) × π × R³ = (\frac{1}{{3}}) × π × 2 × 2 × 8

⇒ R³ = 8

⇒ R = 2 cm

∴ The radius of the sphere is 2 cm.

Given:

(81)-1 × 3-5 × 39 × (64)5/6 ×((\sqrt[3]{3})^6=?)

Calculation:

Let the unknown number be x.

(81)-1 × 3-5 × 39 × (64)5/6 × ((\sqrt[3]{3})^6) = x

⇒ (3⁴)-1 × 3-5 × 39 × (2⁶)5/6 × (3^1/3)⁶ = x

⇒ 3^-4× 3^-5 ×  39 × 2^(6 × 5/6) × 3 ^6/3 = x

⇒ 3-4× 3-5 ×  39 × 2(6 × 5/6) × 3² = x

⇒ 3^{(- 4 - 5 + 9 + 2)} × 2⁵ = x

⇒ 3² × 32 = x 

⇒ x = 288

∴ The correct answer is option 2 i.e. 288

Shortcut Trick

Volume of material in a hemispherical bowl = 2/3 × π × (R³ − r³)

Inner radius (r) = 5 cm, Outer radius (R) = 5 + 0.25 = 5.25 cm

Volume = 2/3 × 22/7 × (5.25³ − 5³) ≈ 2.095 × (144.703 − 125) ≈ 2.095 × 19.703

Volume ≈ 41.28 cm³

∴ The correct answer is 41.28 cm³.

Alternate Method

Given:

Inner radius (r) = 5 cm

Thickness (t) = 0.25 cm

Outer radius (R) = Inner radius + Thickness = 5 + 0.25 = 5.25 cm

Formula Used:

Volume of material = (\frac{2}{3}) × π × (R³ − r³)

Calculations:

⇒ Volume = 2/3 × 22/7 × (5.25³ − 5³)

⇒ Volume = 44/21 × (144.703125 − 125)

⇒ Volume = 44/21 × 19.703125

⇒ Volume = 866.9375 / 21

⇒ Volume ≈ 41.2827... cm³

∴ The correct answer is 41.28 cm³.

Additional Information

Volume of Hemisphere

The volume of a solid hemisphere is given by V = 2/3 × π × r³.

Surface Area of Hemispherical Bowl

Inner Curved Surface Area = 2πr²; Outer Curved Surface Area = 2πR².

Total Surface Area of Bowl

TSA = Outer CSA + Inner CSA + Area of Ring = 2πR² + 2πr² + π(R² − r²).

Shortcut Trick

Radius (r) = 42 cm.

Curved Surface Area (CSA) of a hemisphere = 2πr².

Half of CSA = (1/2) × 2πr² = πr².

Calculation: (22/7) × 42 × 42 = 22 × 6 × 42 = 132 × 42 = 5544 cm².

∴ The correct answer is 5544 cm².

Alternate Method

Given:

Radius (r) of the hemisphere = 42 cm.

Value of π = 22/7.

Formula Used:

Curved Surface Area (CSA) of a hemisphere = 2πr²

Required Value = (1/2) × CSA = πr²

Calculations:

⇒ Required Area = π × r × r

⇒ Required Area = (22/7) × 42 × 42

⇒ Required Area = 22 × (42 ÷ 7) × 42

⇒ Required Area = 22 × 6 × 42

⇒ Required Area = 132 × 42

⇒ Required Area = 5544 cm²

∴ The correct answer is 5544 cm².

Additional Information

Total Surface Area of Hemisphere

The Total Surface Area (TSA) includes the curved part and the flat circular base: TSA = 3πr².

Volume of Hemisphere

The Volume of a hemisphere is exactly half the volume of a sphere: V = (2/3)πr³.

Sphere Properties

For a complete Sphere, the Surface Area is 4πr² and the Volume is (4/3)πr³.

Interest rate for first 2 years = 8%

Interest rate for 5/8 year = 5/8 × 8 = 5%

P = 12,000

As we know,

A = P (1 + r/100)³

⇒ A = 12,000 × (108/100) × (108/100) × (105/100)

⇒ A = 12,000 × (27/25) × (27/25) × (21/20)

⇒ A = 14697

∴ CI = 14697 – 12000 = 2697

Short Trick:

12500 unit = 12000

15309 – 12500 = 2809 unit

∴ 2809 unit = 12000/12500 × 2809 = 2697

Shortcut Trick

We know that, Profit Ratio = Ratio of Equivalent Capital (Investment × Time).

Profit of P / Profit of Q = (P's Capital × P's Time) / (Q's Capital × Q's Time)

3 / 5 = (4 × 21) / (7 × Q's Time)

3 / 5 = 12 / Q's Time ⇒ Q's Time = (12 × 5) / 3 = 20

∴ The correct answer is 20 months.

Alternate Method

Given:

Investment ratio of P : Q = 4 : 7

P's investment period = 21 months

Profit ratio of P : Q = 3 : 5

Formula Used:

Profit Ratio = (Capital of A × Time of A) : (Capital of B × Time of B)

Calculation:

Let the investments of P and Q be 4x and 7x respectively.

Let Q's investment period be t months.

⇒ Profit of P / Profit of Q = (4x × 21) / (7x × t)

⇒ 3 / 5 = 84x / 7xt

⇒ 3 / 5 = 12 / t

⇒ 3 × t = 12 × 5

⇒ 3t = 60

⇒ t = 20

∴ The correct answer is 20 months.

Additional Information

Basic Principle of Partnership

In a partnership, the profit is distributed in proportion to the product of capital invested and the time period of investment. Hence, Profit = Capital × Time.

Active and Sleeping Partners

An active partner actively manages the business and usually receives a fixed salary or a specific percentage of profit for their effort, while the remaining profit is distributed according to capital investments.

Joining Mid-Way

If a business runs for a specific period (e.g., 12 months) and a partner joins after 'x' months, their capital is considered invested only for the remaining time, i.e., (12 − x) months.

Given:

P : Q : R = 3 : 7 : 12

Q - P = Rs. X

R - Q = Rs. 30000

Solution:

Let, k = constant

R - Q = 12k - 7k = 30000

⇒k = 30000/5 = 6000

Q - P = 7k - 3k = 4k = X

X = 4 x 6000 = 24000

Total money = 3k + 7k + 12k = 22k = 22 x 6000 = Rs. 132000

Hence, the correct option is 3.

Shortcut Trick

Ratio of Father to Son Today = 3 : 1 (Difference = 2 units)

Ratio after 5 years = 2.5 : 1 = 5 : 2 (Difference = 3 units)

To equate difference, multiply Today by 3 and Future by 2:

Today = 9 : 3 | After 5 years = 10 : 4

Growth of 1 unit = 5 years. Son age today = 3 units = 3 × 5 = 15 years.

∴ The correct option is B.

Alternate Method

Given:

Let Son age today = S years

Father age today = 3S years

After 5 years: Son = S + 5 | Father = 3S + 5

Present F = 3S S = S After 5 Yrs F + 5 = 2.5(S+5)

• 5 years

Ratio change: 3:1 → 2.5:1

Calculation:

⇒ Father_future = 2.5 × Son_future

⇒ 3S + 5 = 2.5(S + 5)

⇒ 3S + 5 = 2.5S + 12.5

⇒ 3S − 2.5S = 12.5 − 5

⇒ 0.5S = 7.5

⇒ S = 7.5 ÷ 0.5

⇒ S = 15 years

∴ The correct option is B.

Additional Information

Constant Age Difference

The difference between the ages of two persons always remains constant regardless of the number of years passed.

Ratio Balancing Method

If A:B is the current ratio and C:D is the ratio after n years, equate (B−A) and (D−C) by multiplying with suitable constants to find the value of 1 unit.

Ages n years ago

If current age is X, then age n years ago was (X − n) and age n years hence will be (X + n).

Given:

A number when increased by 50% gives 2430.

Formula used:

If a number is increased by x%, the new value = original number × (1 + x/100).

Calculation:

Let the number be N.

According to the problem:

⇒ N × (1 + 50/100) = 2430

⇒ N × 1.5 = 2430

⇒ N = 2430 ÷ 1.5

⇒ N = 1620

∴ The correct answer is option (1).

Given:

SI = Rs. 862.50

Rate = 7(2/3)%

Time = 2(1/2) years

Formula Used:

SI = PRT/100

Where, P = Principal, R = Rate, T = Time(in years)

Calculation:

According to the question,

862.50 = (\frac{x\times7\frac{2}{3}\times2\frac{1}{2}}{100})

⇒ 862.50 = (\frac{x\times23\times5}{3\times2\times100})

⇒ x = (\frac{862.5\times3\times2}{23\times5}) = 4500

∴ The value of x is Rs. 4500.

Shortcut Trick

Sum of ratio parts = 2 + 3 + 5 = 10 units.

Each variable appears twice in the sum, so 2 × (a + b + c) = 10 units.

Since a + b + c = 20, then 2 × 20 = 40 = 10 units ⇒ 1 unit = 4.

Therefore, a + b = 2 units = 2 × 4 = 8.

Value of c = (a + b + c) − (a + b) = 20 − 8 = 12.

∴ The correct answer is 12.

Alternate Method

Given: (a + b) : (b + c) : (c + a) = 2 : 3 : 5 and a + b + c = 20.

⇒ Let a + b = 2k, b + c = 3k, and c + a = 5k.

⇒ Adding the ratios: (a + b) + (b + c) + (c + a) = 2k + 3k + 5k.

⇒ 2(a + b + c) = 10k.

⇒ Given a + b + c = 20, substitute: 2(20) = 10k.

⇒ 40 = 10k ⇒ k = 4.

⇒ Now, a + b = 2k = 2 × 4 = 8.

⇒ We know c = (a + b + c) − (a + b).

⇒ c = 20 − 8 = 12.

∴ The correct answer is 12.

Additional Information

Constant of Proportionality

When terms are given in a ratio (x : y = m : n), they can be expressed as x = mk and y = nk, where k is the common multiplier.

Cyclic Ratio Sums

For expressions involving pairs like (a+b), (b+c), and (c+a), the sum of all pairs is always equal to 2(a + b + c).

Finding Individual Variables

To find a single variable like c from the total sum S = a+b+c, subtract the sum of the other two variables: c = S − (a+b).

Given:

A completes work in 15 days.

B completes work in 10 days.

Concept Used:

Share of wages is distributed as the ratio of effciency

Calculations:

We know that amount must be shared as the ratio of their efficiencies.

So efficiencies of A : B = 1/15 : 1/10 

⇒ 10 : 15 = 2 : 3

Sum of efficiencies = 2 + 3 = 5

So A share in the total = (2/5) × 30,000

⇒ Rs.12000

∴ The share of A in the contracted money will be Rs.12000

Shortcut Trick

For finding the HCF of prime factorised numbers, multiply the lowest powers of all common prime factors.

For base 2 → minimum power is 2 → 2²

For bases 3 and 5 → minimum powers are 2 and 1 → 3² and 5

HCF = 2² × 3² × 5

∴ The correct answer is 2² × 3² × 5.

Alternate Method

Given:

First number = 2² × 3⁵ × 5³

Second number = 2⁴ × 3² × 5

Formula Used:

HCF = Product of the lowest power of each common prime factor.

Calculations:

⇒ Compare the powers of the common base 2: the lowest power is 2².

⇒ Compare the powers of the common base 3: the lowest power is 3².

⇒ Compare the powers of the common base 5: the lowest power is 5.

⇒ Multiplying these lowest powers together gives the Highest Common Factor.

⇒ HCF = 2² × 3² × 5

∴ The correct answer is 2² × 3² × 5.

Additional Information

LCM of Prime Factors

To find the LCM of numbers in prime factorised form, multiply the highest powers of all prime factors present in the given numbers.

Co-prime Numbers

Two numbers are considered co-prime if their HCF is 1, meaning they do not share any common prime factors.

HCF and LCM Relation

For any two numbers, the product of the numbers is always equal to the product of their HCF and LCM.

Given:

15 males or 20 females can complete a project in 26 days.

Formula used:

(M1 × D1)/W1 = (M2 × D2)/W2

Calculation:

15 males × 26 days = 20 females × 26 days 

∵ 15 males = 20 females 

∴  30 males = 40 females 

Total work in terms of females  = 20 females × 26 days = 520 units 

No of days taken by 30 males and 12 females:

⇒ (40 females + 12 females) = 52 females 

∴ No of days taken = 520 units /52 females = 10

Given:

The ratio of the radius to the height of the cylinder = 6 : 7

Volume of the cylinder = 792 cm³

Formula used:

Volume of a cylinder = πr²h

Curved surface area of a cylinder = 2πrh

Calculation:

Let the common ratio be x.

Then, the radius r = 6x and the height h = 7x.

Using the volume formula:

π(6x)²(7x) = 792

⇒ π × 36x² × 7x = 792

⇒ 252πx³ = 792

Take π as 22/7:

⇒ 252 × 22/7 × x³ = 792

⇒ 792x³ = 792

⇒ x³ = 1

⇒ x = 1

Thus, radius r = 6x = 6 × 1 = 6 cm

And height h = 7x = 7 × 1 = 7 cm

Now, calculate the curved surface area:

Curved surface area = 2πrh = 2 × 22/7 × 6 × 7

= 2 × 22 × 6

= 264 cm²

∴ The curved surface area of the cylinder is 264 cm².

Side of triangle a = 8 cm

Area of triangle = √3/4 × a²

⇒ Area of triangle ABC = √3/4 × 8 × 8 = 16√3

As we know, If P,Q and R are the mid points of sides AB, BC and CA, then

Area of ΔPQR = 1/4 × Area of ABC

⇒ Area of ΔPQR = 1/4 × 16√3 = 4√3

Shortcut Trick

Difference in Selling Prices = 1,498 − 1,300 = ₹198.

Ratio of Gain to Loss = 125 : 100 = 5 : 4.

Value of 1 unit = 198 ÷ (5 + 4) = 198 ÷ 9 = ₹22.

Cost Price (CP) = 1,300 + (4 × 22) = 1,300 + 88 = ₹1,388.

New SP for 25% gain = 1,388 × 1.25 = ₹1,735.

∴ The correct answer is ₹1,735.

Alternate Method

Given: SP₁ = ₹1,498, SP₂ = ₹1,300, Gain = 1.25 × Loss.

Formula: CP = SP − Gain = SP + Loss

⇒ Let Loss = L

⇒ Gain = 1.25L

⇒ 1,498 − CP = 1.25L and CP − 1,300 = L

⇒ (1,498 − CP) ÷ (CP − 1,300) = 1.25 ÷ 1 = 5 ÷ 4

⇒ 4 × (1,498 − CP) = 5 × (CP − 1,300)

⇒ 5,992 − 4CP = 5CP − 6,500

⇒ 9CP = 12,492

⇒ CP = ₹1,388

⇒ New SP = 1,388 × (125/100) = 1,388 × (5/4)

⇒ New SP = 347 × 5 = ₹1,735

∴ The correct answer is ₹1,735.

Additional Information

Profit and Loss Basic Relations

Profit = SP − CP and Loss = CP − SP. CP is always considered as the 100% base for calculations.

Marked Price and Discount

Discount is always calculated on Marked Price (MP). SP = MP × (100 − Discount%)/100.

Successive Profit/Loss

If there are successive percentage changes a and b, the effective change is [a + b + (ab/100)]%.

Given:

Length of the train = 80 meters

Length of the platform = 120 meters

Speed of the train = 72 km/hr

Formula Used:

Time = Distance / Speed

Calculation:

Convert speed from km/hr to m/s:

Speed = 72 × (1000/3600) = 72 × (10/36) = 72 / 3.6 = 20 m/s

Total distance to be covered = Length of the train + Length of the platform

Total distance = 80 + 120 = 200 meters

Time taken to cross the platform:

Time = Distance / Speed

Time = 200 / 20

Time = 10 seconds

The train will take 10 seconds to cross the platform.