SSC CGL 2024 Tier-I Official Paper (Held On: 09 Sept, 2024 Shift 2) (Previous Year Paper)

The number of triangles in the given figure is shown below:

Thus, as marked there are a total of 4 triangles.

Hence, "Option 3" is the correct answer.

Given: 4 ÷ 6 + 91 × 7 − 5 = ?

According to the question, after ‘+’ and ‘–‘ are interchanged and ‘x’ and ‘÷’ are interchanged:

4 ÷ 6 + 91 × 7 − 5 = ? ⇒ 4 × 6 – 91 ÷ 7 + 5 = ?

⇒ 4 × 6 – 91 ÷ 7 + 5 = ?

⇒ 4 × 6 – 13 + 5 = ?

⇒ 24 + 5 – 13 = ?

⇒ 29 – 13 = ?

⇒ 16 = ?

Hence, "Option 2" is the correct answer.

The logic followed here is:

Option 1) EJ - OT

Option 2) PF - OI

Option 3) KP - UZ

Option 4) CH - MR

Thus, out of al the options 'PF - OI' is the odd one out.

Hence, "Option 2" is the correct answer.

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

Conclusions:

I. Some brown are fans → Follow (As all fans are brown. As whole fans comes in brown, therefore it is true.)

II. Some chairs are brown → Follow (As some brown are chairs. As brown has some part common with chairs, therefore it is true.)

III. No chair is plastic → Does not follow (As some chairs are plastic. As no statements restricts chairs from being plastic, therefore it is false.)

∴ Here, Only I and II conclusion follow.

Hence, "Option 3" is the correct answer.

Given: 1604 × 4 – 525 ÷ 5 + 73 = ?

According to the question, after ‘+’ and ‘–‘ are interchanged and ‘x’ and ‘÷’ are interchanged:

1604 × 4 – 525 ÷ 5 + 73 = ? ⇒ 1604 ÷ 4 + 525 × 5 – 73 = ?

⇒ 1604 ÷ 4 + 525 × 5 – 73 = ?

⇒ 401 + 525 × 5 – 73 = ?

⇒ 401 + 2625 – 73 = ?

⇒ 3026 – 73 = ?

⇒ 2953 = ?

Hence, "Option 3" is the correct answer.

Given word: 'SYSTEM'

After arranged in alphabetical order:

 

Now,

there is One alphabet "S" will remain unchanged if each of the letters in the word 'SYSTEM' is arranged in English alphabetical order.

And, 'Five' letters will change.

Hence, the correct answer is "Option 1".

The logic followed here is:

Hence, "Option 4" is the correct answer.

The logic followed here is:

Hence, "Option 2" is the correct answer.

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

Conclusions:

I. No animal is a mountain → Does not follow (As no river is a mountain and some rivers are animals. As no direct relation is given between animals and mountains, therefore it is false.)

II. No river is a bird → Does not follow (As no river is a mountain and some birds are mountains. As no direct relation is given between river and bird, therefore it is false.)

∴ Here, Neither conclusion (I) nor (II) follows.

Hence, "Option 2" is the correct answer.

The logic followed here is:

1. All the elements shift clockwise excluding the center element.

2. Center element and left bottom corner is flipped vertically subsequently.

Thus, the final series is:

Hence, "Option 3" is the correct answer.

According to the given information,

Thus, according to the given codes the code 'vc' is for the word 'it'.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: Countries and their Major Rivers.

Here,

Egypt : Nile → Nile is a major river in Egypt.

Similarly,

Myanmar : Irrawaddy → Irrawaddy is a major river in Myanmar.

Hence, the correct answer is "Option 4".

According to the given information,

Thus, according to the given codes the code 'Ba' is for the word 'food'.

Hence, the correct answer is "Option 3".

Given series: N _ B A N A _ A _ A N A N A B _ N A N A B A _ A N A

Option 1) ANANB→ N A B A N A N A A A N A N A B N N A N A B A B A N A → (It doesn't follow any pattern)

Option 2) NANAB → N N B A N A A A N A N A N A B A N A N A B A B A N A → (It doesn't follow any pattern)

Option 3) ANABN → N A B A N A N A A A N A N A B B N A N A B A N A N A → (It doesn't follow any pattern)

Option 4) ANBAN → N A B A N A N A B A N A N A B A N A N A B A N A N A → (It follows the pattern of: NA - BANANA - BANANA - BANANA - BANANA)

Hence, "Option 4" is the correct answer.

The figure which will look like the paper when unfolded is shown below:

Thus, option Figure 2 will look like the paper when unfolded.

Hence, "Option 2" is the correct answer.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 1".

The logic followed here is:

Hence, "Option 4" is the correct answer.

**The logic followed here is: (**1^st number × 3^rd number × 3) = 2^nd number 

(18, 378, 7)

18 × 7 × 3 = 378

378 = 378 (LHS = RHS)

And,

(14, 210, 5)

14 × 5 × 3 = 210

210 = 210 (LHS = RHS)

So, checking each option one by one:

Option 1) (15, 405, 9)

15 × 9 × 3 = 405

405 = 405 (LHS = RHS)

Option 2) (23, 230, 5)

23 × 5 × 3 = 230

345 ≠ 230 (LHS ≠ RHS)

Option 3) (17, 204, 6)

17 × 6 × 3 = 204

306 ≠ 204 (LHS ≠ RHS)

Option 4) (17, 272, 8)

17 × 8 × 3 = 272

408 ≠ 272 (LHS ≠ RHS)

Thus, out of all the options, '(15, 405, 9)' follows the same logic as given.

Hence, "Option 1" is the correct answer.

The logic followed here is: 

(1^st number × 2^nd number) + 11 = 3^rd number

(2, 3, 17)

2 × 3 + 11 = 17

6 + 11 = 17

17 = 17 (LHS = RHS)

And,

(5, 2, 21)

5 × 2 + 11 = 21

10 + 11 = 21

21 = 21 (LHS = RHS)

So, checking each option one by one:

Option 1) (3, 4, 23)

3 × 4 + 11 = 23

12 + 11 = 23

23 = 23 (LHS = RHS)

Option 2)  (5, 6, 72)

5 × 6 + 11 = 72

30 + 11 = 72

41 ≠ 72 (LHS ≠ RHS)

Option 3) (2, 4, 17)

2 × 4 + 11 = 17

8 + 11 = 17

19 ≠ 17 (LHS ≠ RHS)

Option 4) (2, 5, 42)

2 × 5 + 11 = 42

10 + 11 = 42

21 ≠ 42 (LHS ≠ RHS)

Thus, out of all the options, '(3, 4, 23)' follows the same logic as given.

Hence, "Option 1" is the correct answer.

Note: Due to the discrepancy of the PYP, we have changed the option.

The logic followed here is:

1. The whole element rotate 45º anticlockwise subsequently.

Thus, the final series is:

Hence, "Option 1" is the correct answer.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: 1^st number × 3 + 3

Option 1) 12 : 39

12 × 3 + 3 = 39

36 + 3 = 39

39 = 39 (LHS = RHS)

Option 2)  15 : 48

15 × 3 + 3 = 48

45 + 3 = 48

48 = 48 (LHS = RHS)

Option 3) 11 : 35

11 × 3 + 3 = 35

33 + 3 = 35

36 ≠ 35 ( LHS ≠ RHS)

Option 4) 13 : 42

13 × 3 + 3 = 42

39 + 3 = 42

42 = 42 (LHS = RHS)

Thus, out of all the options, '11 : 35' is the odd one out.

Hence, "Option 3" is the correct answer.

The figure which will look like the paper when unfolded is shown below:

Thus, option Figure 2 will look like the paper when unfolded.

Hence, "Option 2" is the correct answer.

The logic followed here is:  2^nd number - 1^st number × 4 - 1 = 3^rd number.

(16, 33, 67)

(33 - 16) × 4 - 1 = 67

17 × 4 - 1 = 67

68 - 1 = 67

67 = 67 (LHS = RHS)

And,

(19, 39, 79)

(39 - 19) × 4 - 1 = 79

20 × 4 - 1 = 79

80 - 1 = 79

79 = 79 (LHS = RHS)

So, checking each option one by one:

Option 1) (22, 45, 91)

(45 - 22) × 4 - 1 = 91

23 × 4 - 1 = 91

92 - 1 = 91

91 = 91 (LHS = RHS)

Option 2)  (21, 45, 90)

(45 - 21) × 4 - 1 = 90

24 × 4 - 1 = 90

96 - 1 = 90

95 ≠ 90 (LHS ≠ RHS)

Option 3) (18, 36, 80)

(36 - 18) × 4 - 1 = 80

18 × 4 - 1 = 80

72 - 1 = 80

71 ≠ 80 (LHS ≠ RHS)

Option 4) (14, 27, 53)

(27 - 14) × 4 - 1 = 53

13 × 4 - 1 = 53

52 - 1 = 53

51 ≠ 53 (LHS ≠ RHS)

Thus, out of all the options, '(22, 45, 91)' follows the same logic as given.

Hence, "Option 1" is the correct answer.

Decoding symbols:

Given: A + B – C ÷ D * E – F ÷ G - It means that A is sister of B, B is the father of C,C is the mother of D, D is the wife of E, E is the father of F, F is the mother of .

A + B → A is the sister of B.

B – C → B is the father of C.

C ÷ D → C is the mother of D.

D * E → D is the wife of E.

E – F → E is the father of F.

F ÷ G → F is the mother of G.

Thus, F is C's daughter’s daughter or granddaughter.

Hence, the correct answer is "Option 1"

The correct answer is jaundice

Key Points

• Jaundice (Icterus) is a condition where the skin, the whites of the eyes (sclera), and sometimes other tissues develop a yellow tint.
• This yellowing happens because of an excessive buildup of a substance called bilirubin in the blood.
• Bilirubin is a yellow pigment produced during the normal breakdown of red blood cells.
• Normally, the liver processes bilirubin and excretes it into bile, which helps digest fats.
• The bile is then eliminated from the body through stool.
• Causes of Jaundice
• Pre-hepatic (before the liver):
• Caused by increased destruction of red blood cells (hemolysis).
• Examples: Sickle cell anaemia, malaria.
• Hepatic (in the liver):
• Caused by liver diseases that impair its ability to process bilirubin.
• Examples: Hepatitis, cirrhosis, alcoholic liver disease.
• Post-hepatic (after the liver):
• Caused by an obstruction in bile ducts that prevents bilirubin from being excreted.
• Examples: Gallstones, tumors, bile duct strictures.

Additional Information

• Ichthyosis
• Ichthyosis refers to a group of skin disorders that cause dry, scaly, and thickened skin, resembling fish scales.
• It is a chronic condition, often genetic, though it can sometimes occur due to other health issues (acquired ichthyosis).
• Eczema
• Eczema (also known as atopic dermatitis) is a chronic inflammatory skin condition that causes red, itchy, and inflamed patches on the skin.
• It’s commonly triggered by allergens, irritants, or stress.
• Pemphigus
• Pemphigus is a rare autoimmune disorder that causes painful blisters on the skin and mucous membranes (such as the mouth, throat, and genitals).
• The body’s immune system mistakenly attacks the proteins that hold skin cells together.

The correct answer is Chhath Puja

Key Points

• Chhath is predominantly a Hindu festival dedicated to the Sun god and his wife Usha with the motive of thanking them for providing the bounties of life on the Earth.
• The literal meaning of the word chhath is sixth and hence, this festival is celebrated on the sixth day of the Kartika month of the Hindu calendar "Vikram Samvat".
• The festival has a duration of four days. The rituals under this festival include a holy bath, keeping the fast, remaining in water for long periods of time, along with offering prayers and food to the setting sun and the rising sun.
• The main worshipers are known as Parvaitin,(usually women). Although, it's seen that sometimes men also observe this festival as it is essentially not a gender-specific festival.
• The festival is observed primarily in Mithila Province of Nepal, Terai-Madhesh region of Nepal along with the Indian states of Bihar, Jharkhand, and UP.
• Moreover, it is also observed in areas where migrants from the above-mentioned areas have their presence.

Additional Information

• Madai Festival
• The Madai Festival is celebrated primarily by the Gond tribes of Madhya Pradesh and is a significant cultural event that showcases their rich traditions and heritage.
• It typically involves vibrant rituals, traditional dance forms, music, and communal feasting, reflecting the community's connection to nature and agriculture.
• The festival usually marks the harvesting season and is a time for the tribes to give thanks for the bounty received.
• Vishwakarma Puja
• Vishwakarma Puja is dedicated to Lord Vishwakarma, the divine architect and craftsman of the universe, celebrated by artisans, builders, and craftsmen across India.
• This festival often includes the worship of tools, machinery, and vehicles, symbolizing the reverence for craftsmanship and engineering skills.
• The Puja is marked by colorful decorations, offerings, and cultural performances, emphasizing creativity and innovation in various trades.
• Sorath Sabha
• Sorath Sabha refers to a cultural and social gathering primarily associated with the Rajput community, particularly in the Sorath region of Gujarat.
• These gatherings promote community bonding, sharing of cultural traditions, and discussions on social issues, fostering a sense of unity among members.
• The Sabha often features traditional music, dance, and storytelling, highlighting the rich history and heritage of the Rajput community.

The correct answer is Girnar

Key Points

• The Junagarh Rock Inscription of Rudradaman is the first royal inscription of early India written in chaste Sanskrit:
• The inscription is on a rock near Girnar hill in Gujarat, India.
• The inscription was written by Rudradaman, a Saka ruler who lived from 130-150 CE.
• The inscription includes information about territory expansion, foreign relationships, and welfare work, and mentions that Rudradaman defected Satakarni twice.
• It also states that Pushyagupta, a governor of Chandragupta Maurya, built a dam on Sudarshana Lake near Girnar.
• Other inscriptions: The Junagarh rock also contains inscriptions of Ashoka and Skandagupta

The correct answer is Surya Sen

Key Points

• The Chittagong Armoury Raid (1930) was a significant revolutionary act against British rule in India, planned and led by Surya Sen, also known as Masterda Surya Sen.
• He was a prominent leader of the Indian independence movement in Bengal.
• The raid took place on 18 April 1930 in Chittagong, now in Bangladesh.
• Surya Sen and his group of revolutionaries aimed to:
• Seize weapons from the British armoury.
• Cut off communication lines like telephone and telegraph.
• Destroy the railway lines to disrupt British troop movements.
• The plan was to inspire a large-scale uprising against British colonial rule.
• Along with Surya Sen, other revolutionaries like Ananta Singh, Kalpana Dutta, Pritilata Waddedar, and Badal Gupta played crucial roles in the raid.

Additional Information

• Rash Behari Bose:
• A revolutionary involved in the Ghadar Conspiracy and later in the Indian National Army movement but not associated with the Chittagong Armoury Raid.
• Badal Gupta:
• A participant in the revolutionary activities under Surya Sen but not the leader. He is known for his role in the Writers' Building attack in Kolkata.
• Hemu Kalani:
• A Sindhi freedom fighter active during the Quit India Movement, much later than the Chittagong Raid.

The correct answer is Manipur

Key Points 

• Govindji Nartanalaya is a dance school for women located in Imphal, Manipur
• It was founded in 1972 by Guru Bipin Singh, a renowned Manipuri dancer, choreographer, and teacher
• He was born on 23 August 1918 into a Bishnupriya Manipuri Family. He is regarded as the Father of Manipuri Dance.
• He choreographed many dance-dramas and solo dances and produced many students including Jhaveri Sisters (Darshana Jhaveri), Kalavati Devi, Binodini Devi, Guneswori Devi, Priti Patel, Sruti Bannerjee, Latasana Devi, Laily Basu, Indrani Devi, Manorama Devi, Poushali Chatterjee, Sohini Ray, Bimbavati Devi, Ranjini

Additional Information

• The Manipuri Dance, also referred to as the Manipuri Raas Leela (Meitei: Jagoi Raas, Raas Jagoi), is one of the eight major Indian classical dance forms, originating from the state of Manipur.
• Lai Haraoba is the earliest form of dance in Manipur, and it forms the basis of all such dances.

The correct answer is Rajasthan

Key Points

• Kunds and tankas are used for water harvesting in Rajasthan, India:
• Kunds
• These circular underground wells are shaped like an upturned cup in a saucer.
• They are found in the sandier parts of the Thar Desert in western Rajasthan and some areas of Gujarat.
• Tankas
• These are covered, underground storage tanks that are built on shallow ground.
• They are a traditional rainwater harvesting technique in the Thar Desert region of Rajasthan.
• They are meant to provide drinking water for a family or a small group of families.
• Another traditional water harvesting structure in Rajasthan is the Johad, which is used to store rainwater harvested from rooftops.
• The famous Chand Baori step well in Abhaneri is another example of a traditional water harvesting system in Rajasthan.

The correct answer is Inverse

Key Points

• Interest rates bear an inverse relationship with the demand for money.
• Opportunity costs of holding money will be high when interest rates are high;
• people are losing out on possible earnings that interest-bearing investments could have generated.
• When interest rates are high, the opportunity cost of holding money increases because people can earn more by investing their money rather than keeping it as cash.
• This leads to a lower demand for money for transactional and speculative purposes
• When interest rates are low, the opportunity cost of holding money is low.
• People prefer holding more money for transactions or precautionary needs because the benefit of investing it is minimal.
• This leads to a higher demand for money.
• The relationship can be visualized using the liquidity preference theory by John Maynard Keynes:
• The demand for money (liquidity preference) decreases as the interest rate increases, and vice versa.

The correct answer is Anand- Milind

Key Points

• The music composer duo Anand-Milind was honoured with the National Lata Mangeshkar Award for the year 2020
• The award was presented to Anand-Milind on September 28, 2020, at the birthplace of Lata Mangeshkar in Indore, Madhya Pradesh.
• The award is given annually by the Madhya Pradesh Culture Department to promote excellence in light music.
• The award includes a cash prize of Rs two lakh and a citation.

Additional Information

• Other recipients of the award include:
• Shailendra Singh: Received the award in 2019
• Kumar Sanu: Received the award in 2021
• Uttam Singh: Received the award in 2022
• K. S. Chithra: Received the award in 2023
• Narendra Modi: Received the first Lata Deenanath Mangeshkar Award in 2022
• Amitabh Bachchan: Received the Lata Deenanath Mangeshkar Award in 2024

The correct answer is Devagiri

Key Points

• The first southern campaign of Alauddin Khilji in 1307-08 AD was led to Devagiri:
• In 1306-07, Alauddin Khilji, the ruler of the Delhi Sultanate, sent his general Malik Kafur to lead a large army to Devagiri, the capital of the Yadava king Ramachandra.
• Alauddin attacked Devagiri after Ramachandra refused to pay the annual tax.
• Ramachandra was brought to Delhi and later surrendered.
• The conquest of Devagiri marked the expansion of the Delhi Sultanate into the southern lands.
• It also made Devagiri the gateway to the Deccan.
• Alauddin Khilji also conquered Warangal in 1308, Dwar Samudra in 1310, and Madura in 1311.

The correct answer is Decomposition

Key Points

• When electricity is passed through water, a decomposition reaction occurs, specifically electrolysis of water.
• What happens during electrolysis?
• Water ( H2​O) breaks down into its component gases:$2H 2 O(l) Electricity 2H 2 (g)+O 2 (g)$
• Hydrogen gas is released at the cathode (negative electrode).
• Oxygen gas is released at the anode (positive electrode).
• Why is this a decomposition reaction?
• In a decomposition reaction, a single compound splits into two or more simpler substances.
• Here, water splits into hydrogen and oxygen, making it a decomposition reaction.

Additional Information

• Displacement:
• In a displacement reaction, one element displaces another in a compound.
• Double displacement:
• This involves the exchange of ions between two compounds.
• Combination:
• In a combination reaction, two or more substances combine to form a single compound, which is the opposite of what happens here.

The correct answer is Ecosystem

Key Points

• An ecosystem is a functional unit of nature because it represents a system where living organisms (plants, animals, microorganisms) interact with one another and with their non-living environment (soil, water, air, sunlight) in a self-sustaining manner.
• Characteristics of an Ecosystem:
• Biotic Components: Living organisms such as plants, animals, and microbes.
• Abiotic Components: Non-living factors like sunlight, water, air, and soil.
• Interactions: These components interact through processes like energy flow (food chains) and nutrient cycling, making it functional.

The correct answer is Mumbai

Key Points

• The inaugural match of the Women's Premier League (WPL) 2023 was held at the Dr. DY Patil Sports Academy in Mumbai on 4^th March 2023.
• The match was played between the Mumbai Indians Women and the Gujarat Giants Women.
• This marked the beginning of the first-ever Women's Premier League, a milestone in women's cricket.
• Mumbai hosted many matches during the WPL 2023, with venues like the DY Patil Stadium and Brabourne Stadium being use

Additional Information

• Barcelona Femeni won the Women’s Champions League for the first time after a brilliant 4-0 win over Chelsea in the final in Gothenberg in May 2021.
• This victory also meant that Barcelona became the first club in history to win both the men's and the women's Champions League.
• Other Sports News:
• The Ministry of Youth Affairs and Sports has invited nominations and applications from eligible athletes, coaches, and universities for the annual National Sports Awards for 2021.
• The National Sports Federations will also nominate athletes.

The correct answer is 2-Methylpropan-2-ol

Key Points

• Tertiary butyl alcohol (also known as t-BuOH) is a type of alcohol with the molecular formula C₄H₉OH.
• It is derived from butane (C₄H₁₀) by replacing one hydrogen atom with a hydroxyl group (OH).
• In the IUPAC system, the structure of tertiary butyl alcohol is as follows:
• The butane chain has four carbon atoms.
• The hydroxyl group (OH) is attached to the second carbon atom in a way that the carbon is connected to three methyl groups (CH₃) on the other side.
• This makes it a tertiary alcohol.
• The IUPAC name for this compound is 2-Methylpropan-2-ol, where:
• "2-Methyl" refers to a methyl group (CH₃) attached to the second carbon atom.
• "Propan-2-ol" indicates that the compound is a propanol derivative with the hydroxyl group on the second carbon.

The correct answer is Himachal Pradesh

Key Points

• According to the 2011 census, Himachal Pradesh had the highest female workforce participation rate in rural India at 47.4%.
• Female workforce participation in India:
• The female workforce participation rate in India was 25.51% in 2011, compared to 53.26% for males.
• The female workforce participation rate in rural India was higher than in urban India, at 30.02% compared to 53.03% for males.
• The female workforce participation rate varies across states, with some states having wider gaps than others.
• Women's share is higher than men's in agricultural operations like weeding and transplanting.
• However, women are not considered principal producers in agriculture because they don't have ownership or control over the assets they work on

The correct answer is Article 257

Key Points

• Article 257 of the Constitution of India explains that the executive power of every state shall be exercised in a way that does not impede or prejudice the exercise of the executive power of the Union
• Article 257(1) of the Constitution of India states that the executive power of every state shall be exercised in a way that does not impede or prejudice the exercise of the executive power of the Union.
• This article is essential to ensure that the Union and the states exercise their executive power in a harmonious manner.
• It also enforces the principle of Union supremacy by giving appropriate directions in the event of irreconcilable differences on vital issues.
• Article 257 shapes the relationship between the center and states in India, addressing the principle of federalism

Additional Information

• Article 261 (Public acts, records, and judicial proceedings)
• It ensures that full faith and credit shall be given throughout the territory of India to public acts, records, and judicial proceedings of the Union and states.

Judicial Process:

• The law defines how acts, records, and judgments will be authenticated and proved for recognition across state borders.
• Article 247 (Power of Parliament to provide for the establishment of certain additional courts)
• It grants the Parliament the authority to establish additional courts for better administration of laws made by it regarding matters listed in the Union List.
• This article is used to ensure the efficient handling of cases related to Union List subjects, allowing the central government to extend judicial infrastructure.
• Article 123 (Power of the President to promulgate Ordinances during recess of Parliament)
• It allows the President to issue ordinances when Parliament is not in session, and immediate action is needed, with the same effect as a law passed by Parliament.
• These ordinances must be approved by Parliament within six weeks of reassembling, or they cease to operate.

The correct answer is They are justiciable

Key Points

• The Directive Principles of State Policy (DPSP), enshrined in Part IV of the Indian Constitution, are guidelines for the governance of the country aimed at promoting social and economic justice.
• However, they are not justiciable, meaning they cannot be enforced by the courts.
• About DPSP:
• Ensure social and economic development: The DPSPs aim to promote the welfare of the people by guiding the state in formulating policies for social and economic development.
• Provide guidelines for governance: They act as a set of principles to guide the government in making laws and policies to promote the welfare of the people.
• Morally binding: Although they cannot be enforced in courts, the government is morally obligated to implement them to ensure a just society.

The correct answer is Uttar Pradesh.

Key Points

• Prime Minister Narendra Modi  laid  the foundation stone of the Raja Mahendra Pratap Singh University in Aligarh Uttar Pradesh, on September 14, 2021.
• Amid the upcoming Assembly elections, the move to name the university after the ‘Jat Icon’ comes at a time when the farmer's protest against the farm laws has been gaining momentum in Western Uttar Pradesh which is also a Jat-dominated area and this move has been seen as an attempt by the BJP to win over the Jat farmers.
• The Jat community accounts for approximately 17 per cent of the voting population in twelve districts of the Western UP region.
• In 2020, the Uttar Pradesh government had cleared a proposal to set up a new university in Aligarh, named after Mahendra Pratap Singh.
• The construction of the university is expected to be completed within at least 24 months from the date of laying the foundation.
• The university is expected to be ready by September 2023.

Additional Information 

• Raja Mahendra Pratap Singh:
• Raja Mahendra Pratap Singh was a Jat freedom fighter, social reformist, journalist, writer.
• He was the third son of Raja Ghanshyam Singh and a Jat icon.
• Singh was born in a socio-economically influential Jat family of Mursan in Hathras district in 1886.
• He was an alumnus of Muhammadan Anglo-Oriental College, which was later renamed Aligarh Muslim University (AMU) in 1920.
• Singh had served as President in the Provisional Government of India, the Indian government that served in exile during World War I.
• Singh contributed significantly to the freedom struggle of India. Singh had set up a provisional government in exile in Afghanistan during World War I.
• He also took part in the Balkan War in 1911 along with his fellow students at MAO College.
• Singh was known as an unofficial envoy of Afghanistan. During the 1957 Lok Sabha elections.
• Singh won the election from the Mathura constituency. Singh was contesting as an independent candidate while Atal Bihari Vajpayee was contesting as a candidate for the BJP.

The correct answer is It is a new strategy in agriculture to produce food grains, especially wheat and rice

Key Points

• The Green Revolution refers to a significant transformation in agriculture that began in the 1940s and 1950s,
• aimed at increasing food production, particularly in developing countries, by using new agricultural technologies and practices.
• So this statement is correct
• Green Revolution:
• High-yielding varieties (HYVs) of seeds, especially for crops like wheat and rice, were developed and promoted.
• Increased use of chemical fertilizers and pesticides to improve crop yields.
• Mechanization of farming through the use of modern equipment like tractors, harvesters, etc.
• Irrigation systems were improved to ensure a more reliable water supply to crops.
• The Green Revolution led to a significant increase in food production, particularly in countries like India, helping to prevent famines and making countries self-sufficient in staple crops like rice and wheat.

The correct answer is **14^o**N

Key Points

• The easterly jet stream over Peninsular India during the summer months typically blows around the 14°N latitude.
• This jet stream, known as the Tropical Easterly Jet (TEJ), is a low-level jet stream that flows from the east to west during the summer and plays an important role in the monsoon dynamics.
• The easterly jet stream is located at an altitude of around 10 km above the surface, and it is stronger during the summer months when the monsoon winds are active.
• The jet stream is found mainly over Peninsular India and parts of the Bay of Bengal at around 14°N latitude.
• The position of the easterly jet can influence the intensity and onset of the Indian summer monsoon.

The correct answer is 1781C.E.

Key Points

• The Madrasa in Kolkata (formerly Calcutta) to promote the study of Arabic, Persian, and Islamic law was opened in 1781 C.E..
• It was established by Warren Hastings, the then Governor-General of Bengal.
• This madrasa was intended to promote the study of Islamic subjects, particularly to facilitate the administration of Islamic law in British-ruled India.
• It played a significant role in the educational system of the time, helping to preserve and propagate Islamic learning.
• The madrasa became a center for the study of Arabic, Persian, and Islamic law.
• It was a pioneering institution in the promotion of Muslim education in India under British rule.

The correct answer is Manna Dey

Key Points

• In the year 1952, Manna Dey lent his voice for the film 'Amar Bhupali'.
• He is renowned for his versatile singing in various Indian languages, and for this film, he sang in both Bengali and Marathi, as it was produced in two languages simultaneously.
• Manna Dey had an incredibly diverse repertoire that included classical, semi-classical, folk, and contemporary songs
• Throughout his career, Manna Dey collaborated with some of the greatest music composers in Indian cinema,
• such as S.D. Burman, R.D. Burman, and Salil Chowdhury.

Additional Information

• Kishore Kumar
• Kishore Kumar was not only a legendary playback singer but also an actor, director, and producer in Indian cinema.
• His ability to sing in various genres, from romantic to sad to comic songs, made him a unique figure in Bollywood.
• He is known for his distinctive voice and expressive singing style. Hits like "Mere Sapno Ki Rani," "Ek Ladki Bheegi Bhaagi Si," and "Khaike Paan Banaras Wala" are some of his timeless classics that showcase his versatility and creativity.
• Hemanta Mukherjee
• Hemanta Mukherjee was a prominent playback singer in Indian cinema, especially known for his work in Bengali films.
• His contributions to Hindi music were also significant, with many memorable songs in the 1950s and 60s.
• His rich and soulful voice earned him a place among the greats.
• Songs like "Tumi Robe Nirobe" and "Bajlo Tomar Alor Benu" highlight his mastery in conveying deep emotions through music.
• Debabrata Biswas
• Folk and Ghazal Singer: Debabrata Biswas was celebrated for his renditions of Bengali folk songs and ghazals.
• He was known for preserving traditional music while also introducing innovative elements.
• He contributed significantly to Bengali culture and music through his performances and recordings, promoting folk traditions and winning the hearts of many with his emotive singing style.

The correct answer is Tamil Nadu

Key Points

• The Tamil Nadu government created a draft policy for senior citizens in 2022 based on Article 41 of the Indian Constitution.
• The policy aims to improve the lives of senior citizens in the state by empowering them.
• Intergenerational bonding
• The policy aims to promote intergenerational bonding between students and elders by adopting old age homes and conducting programs in educational institutions, corporate organizations, and government institutions.
• Awareness and education
• The policy aims to uplift the quality of life of senior citizens through awareness and education.
• Recognizing senior citizens
• The policy aims to recognize the contributions of senior citizens by observing international days for senior citizens.
• The policy was created by the Social Welfare & Women Empowerment Department of the Government of Tamil Nadu.

The correct answer is North and Northwestern

Key Points

• The hot, dry wind called the Loo blows over the north and northwestern parts of India:
• The Loo originates from the deserts of the northwestern Indian subcontinent, including the Great Indian Desert, the Cholistan Desert, and the desert areas of Southern Balochistan.
• The Loo blows during the hot and dry months of summer, especially in May and June. It ends in late summer with the arrival of the Indian monsoon.
• The Loo can raise temperatures to 45–50 °C (115–120 °F) and can be fatal if you are exposed to it. It can also dry out vegetation, causing widespread browning.
• The Loo can also lead to dehydration, heatstroke, and other health problems.
• The Loo blows over the western Indo-Gangetic Plain region of North India and Pakistan, including parts of Uttar Pradesh, Bihar, and Delhi

The correct answer is 30 November 2021.

Key Points

• The High Court and Supreme Court Judges (Salaries and Conditions of Service) Amendment Bill, 2021 was introduced in Lok Sabha on 30 November 2021.
• The bill seeks to amend the salaries and conditions of service for the judges of the High Court and the Supreme Court of India.
• It aims to streamline and update provisions to reflect contemporary requirements and standards for the judiciary.
• The introduction of the bill is part of ongoing efforts to ensure the independence and efficiency of the judicial system in India.

Additional Information

• The Indian judiciary is an independent body, separate from the executive and legislative branches of the government.
• The Supreme Court is the highest judicial forum and final court of appeal under the Constitution of India.
• The High Courts operate at the state level and are below the Supreme Court in the judicial hierarchy.
• The terms and conditions of service for judges are critical to maintaining judicial independence and integrity.
• Periodic amendments ensure that the judiciary is equipped to meet modern challenges and uphold the rule of law.

The correct answer is London 2012

Key Points

• Gagan Narang, an Indian shooter, won a bronze medal in the 2012 London Olympics in the men's 10m Air Rifle event.
• The final took place on August 2, 2012
• Gagan Narang finished with a score of 701.1 in the qualification and final rounds combined, securing third place.
• This was India’s first shooting medal at the London 2012 Olympics and Narang’s first Olympic medal.
• Narang’s performance was remarkable, as he had to compete against some of the world’s top shooters.
• The gold medal went to Alin George Moldoveanu of Romania, and the silver went to Hao Zhang of China.
• Before this Olympic achievement, Narang had already built a strong reputation, having won several international titles, including gold medals at the Commonwealth Games and Asian Games.

Shortcut Trick

Successive percentage change formula: Net % Change = x + y + (x × y)/100

⇒ Net % Change = −20 + 30 + (−20 × 30)/100

⇒ Net % Change = 10 − 6 = +4% (Overall Gain)

⇒ Overall Gain = 4% of ₹42,000 = (4/100) × 42000 = ₹1680

∴ The correct answer is ₹1680.

Alternate Method

Given:

Initial Cost Price = ₹42,000

Loss on the first sale = 20%

Gain on the second sale = 30%

Calculations:

⇒ Selling Price of first item = 42000 × (100 − 20)/100

⇒ Selling Price of first item = 42000 × 0.80 = ₹33,600

⇒ Since the new item is bought with the remaining amount, New Cost Price = ₹33,600

⇒ Selling Price of second item = 33600 × (100 + 30)/100

⇒ Selling Price of second item = 33600 × 1.30 = ₹43,680

⇒ Overall Gain = Final Selling Price − Initial Cost Price

⇒ Overall Gain = 43680 − 42000 = ₹1680

∴ The correct answer is ₹1680.

Additional Information

Successive Percentage Change

When a value is sequentially changed by a% and then by b%, the net percentage change is given by: Net % = a + b + (a × b)/100. Use a positive sign for gains/increments and a negative sign for losses/decrements.

Base Value in Profit and Loss

In any business transaction, profit and loss percentages are always calculated on the initial Cost Price (CP) unless explicitly stated otherwise.

Multiplying Factor Method

To directly calculate the final amount after multiple percent changes, use multiplying factors. Final Value = Initial Value × (1 ± x/100) × (1 ± y/100).

Shortcut Trick

Since the volume formula uses π (22 ÷ 7), the final answer must be a multiple of 11.

We check the given options using the divisibility rule for 11 (difference of sums of alternating digits):

Option 1: 2686 → (6 + 2) − (8 + 6) = 8 − 14 = −6 (No)

Option 2: 2816 → (6 + 8) − (1 + 2) = 14 − 3 = 11 (Yes)

Since only 2816 is exactly divisible by 11, it is the correct volume.

∴ The correct answer is 2816 cm³.

Alternate Method

Given:

Radius of cylinder (r) = 8 cm

Height of cylinder (h) = 14 cm

Formula Used:

Volume of cylinder = π × r² × h

Calculation:

⇒ Volume = (22 ÷ 7) × 8² × 14

⇒ Volume = 22 × 64 × (14 ÷ 7)

⇒ Volume = 22 × 64 × 2

⇒ Volume = 44 × 64

⇒ Volume = 2816 cm³

∴ The correct answer is 2816 cm³.

Additional Information

Curved Surface Area of Cylinder

The curved surface area is calculated as 2 × π × r × h, representing the outer lateral surface.

Total Surface Area of Cylinder

The total surface area includes the top and bottom circular bases, calculated as 2 × π × r × (r + h).

Volume of a Cone

A cone with the same base radius and height has exactly one-third the volume of the cylinder: (1 ÷ 3) × π × r² × h.

Shortcut Trick

Ratio of ages (Prachi : Daughter) 7 years ago = 4 : 1 (Difference = 3 parts)

Ratio of ages 4 years from now = 2.5 : 1 = 5 : 2 (Difference = 3 parts)

Since differences are equal, 1 ratio part = Total time gap = 7 + 4 = 11 years.

Sum of ages 7 years ago = 4 + 1 = 5 parts = 5 × 11 = 55 years.

Sum of present ages = 55 + (7 × 2) = 69 years.

∴ The correct answer is 69 years.

Alternate Method

Given:

Let Prachi's present age be P and her daughter's present age be D.

Calculations:

⇒ Seven years ago: P − 7 = 4 × (D − 7)

⇒ P − 4D = −28 + 7

⇒ P − 4D = −21   --- (Equation 1)

⇒ Four years from now: P + 4 = 2.5 × (D + 4)

⇒ P − 2.5D = 10 − 4

⇒ P − 2.5D = 6   --- (Equation 2)

⇒ Subtracting Equation 1 from Equation 2:

⇒ (P − 2.5D) − (P − 4D) = 6 − (−21)

⇒ 1.5D = 27

⇒ D = 18 years

⇒ Substitute D = 18 in Equation 1:

⇒ P − 4 × 18 = −21

⇒ P − 72 = −21 ⇒ P = 51 years

⇒ Sum of present ages = P + D = 51 + 18 = 69 years

∴ The correct answer is 69 years.

Additional Information

Constant Age Difference

The difference between the ages of two individuals remains constant at any point in time. This is a fundamental concept used to balance ratio parts in age-related problems.

Sum of Ages Shift

If the sum of present ages of n people is S, then t years ago, their sum was S − nt, and t years later, it will be S + nt.

Ratio Balancing Method

If the difference between two quantities is unchanged, multiply the ratios by suitable integers to make the difference in ratio parts equal. Then each ratio part can be directly equated to the real-world value.

Shortcut Trick

When both the arc length and the radius of a sector are given, the area can be calculated directly without finding the central angle.

Area = ¹⁄₂ × Arc Length × Radius

⇒ Area = ¹⁄₂ × 11 × 15.75

⇒ Area = 5.5 × 15.75 = 86.625 cm²

∴ The correct answer is 86.625 cm².

Alternate Method

Given:

Radius of the circle, r = 15.75 cm

Arc length of the sector, l = 11 cm

Formula Used:

Area of a sector = ¹⁄₂ × l × r

Calculations:

⇒ Area = ¹⁄₂ × 11 × 15.75

⇒ Area = 5.5 × 15.75

⇒ Area = 86.625 cm²

∴ The correct answer is 86.625 cm².

Additional Information

Area of a Sector (When central angle is given)

Area = (θ ÷ 360°) × πr², where θ is the central angle.

Arc Length (When central angle is given)

Arc length (l) = (θ ÷ 360°) × 2πr

Perimeter of a Sector

Perimeter = l + 2r (sum of the arc length and two radii)

Area of a Segment of a Circle

Area of Segment = Area of the Corresponding Sector − Area of the Triangle formed by the radii and the chord.

Shortcut Trick

The given expression follows the direct algebraic identity:

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

Here, a = 8.3, b = 9.2, and c = 6.1

Value = 8.3 + 9.2 + 6.1 = 23.6

∴ The correct answer is 23.6.

Alternate Method

Given:

Expression: (8.3³ + 9.2³ + 6.1³ − 3 × 8.3 × 9.2 × 6.1) ÷ (8.3² + 9.2² + 6.1² − 8.3 × 9.2 − 9.2 × 6.1 − 6.1 × 8.3)

Formula Used:

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

Calculations:

⇒ Let a = 8.3, b = 9.2, and c = 6.1

⇒ Substituting these variables, the expression becomes:

⇒ (a³ + b³ + c³ − 3abc) ÷ (a² + b² + c² − ab − bc − ca)

⇒ [(a + b + c)(a² + b² + c² − ab − bc − ca)] ÷ (a² + b² + c² − ab − bc − ca)

⇒ The common polynomial terms cancel out, leaving:

⇒ a + b + c

⇒ 8.3 + 9.2 + 6.1

⇒ 23.6

∴ The correct answer is 23.6.

Additional Information

Conditional Identity

If a + b + c = 0, then the standard identity simplifies to a³ + b³ + c³ = 3abc.

Algebraic Identity for Squares

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

Algebraic Identity for Cubes

a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²)

Shortcut Trick

Using the fundamental trigonometric identity: sec²(t) = 1 + tan²(t)

⇒ sec²(t) = 1 + (1 / 3)² = 1 + 1 / 9 = 10 / 9

⇒ sec(t) = √(10 / 9) = √10 / 3

∴ The correct answer is √10 / 3.

Alternate Method

Given:

tan(t) = 1 / 3

Formula Used:

tan(t) = Perpendicular / Base

sec(t) = Hypotenuse / Base

Pythagoras Theorem: Hypotenuse² = Perpendicular² + Base²

Calculations:

⇒ By comparing the ratio, let Perpendicular = 1 and Base = 3

⇒ Hypotenuse = √(1² + 3²)

⇒ Hypotenuse = √(1 + 9) = √10

⇒ sec(t) = Hypotenuse / Base

⇒ sec(t) = √10 / 3

∴ The correct answer is √10 / 3.

Additional Information

Trigonometric Identities

The three primary Pythagorean identities are: sin²θ + cos²θ = 1, sec²θ − tan²θ = 1, and cosec²θ − cot²θ = 1.

Pythagoras Theorem

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of its base and perpendicular: Hypotenuse² = Base² + Perpendicular².

Trigonometric Ratios

For an angle t in a right triangle: tan(t) = Perpendicular ÷ Base, cos(t) = Base ÷ Hypotenuse, and sec(t) is the reciprocal of cos(t) ⇒ Hypotenuse ÷ Base.

Shortcut Trick

Identify the given matching components between the two triangles directly.

We are given two equal sides (PQ = SR) and one common side (QR = RQ).

The angle exactly between these sides is given as equal (∠PQR = ∠SRQ = 90°).

Since the equal angle is perfectly included between the equal sides, the SAS (Side-Angle-Side) criterion applies.

RHS does not apply here because the hypotenuses (PR and SQ) are not given as equal initially.

∴ The correct answer is ∆PQR ≅ ∆SRQ by SAS.

Alternate Method

Given:

Points P and S are on the same side of the line segment QR.

∠PQR = 90°

∠SRQ = 90°

PQ = SR

P Q R S

Calculations:

⇒ Let us compare the two right-angled triangles, ∆PQR and ∆SRQ.

⇒ PQ = SR (Given in the problem)

⇒ ∠PQR = ∠SRQ = 90° (Given right angles)

⇒ QR = RQ (This is the common base side shared by both triangles)

⇒ Because two sides and the included angle of ∆PQR perfectly match two sides and the included angle of ∆SRQ, the SAS property is satisfied.

⇒ Checking vertex correspondence: Vertex P corresponds to S, Vertex Q corresponds to R, and Vertex R corresponds to Q.

⇒ Therefore, the triangles are congruent: ∆PQR ≅ ∆SRQ.

∴ The correct answer is ∆PQR ≅ ∆SRQ by SAS.

Additional Information

SAS (Side-Angle-Side) Congruence

If two sides and the included angle of one triangle are absolutely equal to the corresponding parts of another triangle, the two triangles are congruent.

RHS (Right angle-Hypotenuse-Side) Congruence

Two right-angled triangles are congruent if their hypotenuses and one corresponding side are strictly equal.

Vertex Correspondence Principle

When writing congruence statements, the order of vertices must align. If ∠Q = ∠R and PQ = SR, then vertex Q maps to R, and vertex P maps to S.

Shortcut Trick

We can use the successive percentage change formula: Net Change % = a + b + (a × b) ÷ 100

Here, Markup (a) = +26% and Discount (b) = −32%

Net Change = 26 − 32 + (26 × −32) ÷ 100

Net Change = −6 − 8.32 = −14.32%

The negative sign indicates a loss of 14.32%.

∴ The correct answer is 14.32%.

Alternate Method

Given:

Markup percentage = 26%

Discount percentage = 32%

Formula Used:

MP = CP × (1 + Markup% ÷ 100)

SP = MP × (1 − Discount% ÷ 100)

Loss% = [(CP − SP) ÷ CP] × 100

Calculations:

⇒ Let Cost Price (CP) = 100

⇒ Marked Price (MP) = 100 + 26 = 126

⇒ Selling Price (SP) = 126 × (1 − 32 ÷ 100)

⇒ SP = 126 × 0.68

⇒ SP = 85.68

⇒ Loss = CP − SP = 100 − 85.68 = 14.32

⇒ Loss % = (14.32 ÷ 100) × 100 = 14.32%

∴ The correct answer is 14.32%.

Additional Information

Successive Percentage Change

When a value is sequentially changed by a% and then by b%, the net percentage change is given by the formula: Net % = a + b + (a × b) ÷ 100.

Markup and Discount Relation

The final Profit or Loss percentage is simply the successive application of the Markup percentage and the Discount percentage. Using the successive formula: Profit/Loss % = Markup% − Discount% − (Markup% × Discount%) ÷ 100.

Selling Price Link

The Selling Price acts as a bridge between the Cost Price and Marked Price. SP = CP × (100 ± Profit/Loss)% and SP = MP × (100 − Discount)%.

Shortcut Trick

Using the algebraic difference of cubes identity: x³ − y³ = (x − y)(x² + y² + xy)

Substitute x = sinA and y = cosA into the given expression directly:

⇒ [(sinA − cosA)(sin²A + cos²A + sinA × cosA)] ÷ (sinA − cosA)

⇒ sin²A + cos²A + sinA × cosA

⇒ 1 + sinA cosA

∴ The correct answer is 1 + sinA cosA.

Alternate Method

Given:

Expression: (sin³A − cos³A) ÷ (sinA − cosA)

Formula Used:

a³ − b³ = (a − b)(a² + ab + b²)

sin²A + cos²A = 1

Calculation:

⇒ Expand the numerator using the difference of cubes formula.

⇒ Numerator = (sinA − cosA)(sin²A + cos²A + sinA × cosA)

⇒ Substitute this expansion back into the fraction:

⇒ [(sinA − cosA)(sin²A + cos²A + sinA × cosA)] ÷ (sinA − cosA)

⇒ The common term (sinA − cosA) cancels out from the numerator and the denominator.

⇒ We are left with: sin²A + cos²A + sinA × cosA

⇒ Applying the basic trigonometric identity sin²A + cos²A = 1.

⇒ 1 + sinA cosA

∴ The correct answer is 1 + sinA cosA.

Additional Information

Sum of Cubes Identity

a³ + b³ = (a + b)(a² − ab + b²). This is extremely useful for expressions like (sin³A + cos³A) ÷ (sinA + cosA) which easily simplifies to 1 − sinA cosA.

Basic Trigonometric Identities

1 + tan²A = sec²A and 1 + cot²A = cosec²A. These fundamental identities along with sin²A + cos²A = 1 are frequently used to simplify complex trigonometric fractions.

Value Substitution Strategy

For algebraic or trigonometric simplifications where options are in terms of functions, substituting standard angles like A = 30° or 60° (avoiding values where the denominator becomes zero) can help quickly verify the correct option during exams.

Given:

Total production in 2021 = 2,00,00,000

Percentage of type D cars = 20%

Formula used:

Central Angle = (Percentage of Type × 360) / 100

Calculations:

Central Angle for type D = (20 × 360) / 100

⇒ Central Angle = 7200 / 100

⇒ Central Angle = 72°

∴ The central angle representing the production of type D cars in 2021 is 72°.

Shortcut Trick

For a right-angled isosceles triangle, the area can be directly related to its hypotenuse (h) using the relation: Area = h² ÷ 4

⇒ 50 = h² ÷ 4

⇒ h² = 200

⇒ h = √200 = 10√2

∴ The correct answer is 10√2 units.

Alternate Method

Given:

Area of the right-angled isosceles triangle = 50 sq. units

Formula Used:

Area of a triangle = (1 ÷ 2) × base × height

Pythagoras Theorem: Hypotenuse = √(base² + height²)

Calculations:

⇒ Let the equal sides (base and height) be 'a' units.

⇒ Area = (1 ÷ 2) × a × a = 50

⇒ a² = 50 × 2

⇒ a² = 100

⇒ a = 10 units

⇒ Now, applying Pythagoras Theorem to find the hypotenuse:

⇒ Hypotenuse = √(a² + a²)

⇒ Hypotenuse = √(10² + 10²)

⇒ Hypotenuse = √(100 + 100)

⇒ Hypotenuse = √200

⇒ Hypotenuse = 10√2 units

∴ The correct answer is 10√2 units.

Additional Information

Right-angled Isosceles Triangle Properties

The angles in a right-angled isosceles triangle are always 90°, 45° and 45°. The ratio of its sides is consistently 1 : 1 : √2.

Perimeter

The perimeter of a right-angled isosceles triangle with equal sides 'a' is given by P = a(2 + √2).

Hypotenuse-Area Relationship

If the length of the hypotenuse is 'h', the area can be easily determined directly as Area = h² ÷ 4 without calculating the lengths of the legs.

Given:

Monthly income of Aditya = ₹54,000

Percentage spent on Food = 23%

Formula used:

Amount spent on Food = (Percentage on Food × Total Income) / 100

Calculations:

Amount spent on Food = (23 × 54000) / 100

⇒ Amount spent on Food = 1242000 / 100

⇒ Amount spent on Food = ₹12,420

∴ Aditya spends ₹12,420 on Food.

Shortcut Trick

Expenditure : Savings = 80% : 20% = 4 : 1 (Total = 5 parts).

By weighted average rule: Overall Change = (w₁x₁ + w₂x₂) ÷ (w₁ + w₂)

⇒ 20 = (4 × 10 + 1 × x) ÷ 5

⇒ 100 = 40 + x ⇒ x = 60%

∴ The correct answer is 60%.

Alternate Method

Given:

Initial Income = ₹16,000

Expenditure = 80% of Income

Income increase = 20%

Expenditure increase = 10%

Formula Used:

Income = Expenditure + Savings

Percentage Increase = [(New Value − Old Value) ÷ Old Value] × 100

Calculations:

⇒ Initial Expenditure = (80 ÷ 100) × 16000 = ₹12,800

⇒ Initial Savings = 16000 − 12800 = ₹3,200

⇒ New Income = 16000 + (20% of 16000) = 16000 + 3200 = ₹19,200

⇒ New Expenditure = 12800 + (10% of 12800) = 12800 + 1280 = ₹14,080

⇒ New Savings = 19200 − 14080 = ₹5,120

⇒ Increase in Savings = 5120 − 3200 = ₹1,920

⇒ Percentage Increase in Savings = (1920 ÷ 3200) × 100 = 60%

∴ The correct answer is 60%.

Additional Information

Percentage Change

It measures the difference between a new value and an old value as a percentage of the old value: Percentage Change = [(New Value − Old Value) ÷ Old Value] × 100.

Successive Percentage

When a value undergoes two consecutive percentage changes of a% and b%, the effective overall percentage change is given by: Net Change = a + b + (a × b) ÷ 100.

Weighted Average (Mixture Concept)

When a base quantity is divided into two parts, the overall percentage change is equivalent to the weighted average of the changes in the individual parts: Overall Change = (w₁x₁ + w₂x₂) ÷ (w₁ + w₂).

Shortcut Trick

To find the remainder when a number is divided by 9, apply the casting out nines technique.

Cancel out any digits or groups of digits in 28735429 that sum to 9.

Cancel 9, the pair (2 + 7), and the pair (5 + 4).

The remaining digits are 8, 3, and 2.

Sum of remaining digits = 8 + 3 + 2 = 13 ⇒ 1 + 3 = 4.

∴ The correct answer is 4.

Alternate Method

Given:

Number = 28735429

Divisor = 9

Method Used:

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

Calculations:

⇒ Sum of digits = 2 + 8 + 7 + 3 + 5 + 4 + 2 + 9

⇒ Sum of digits = 40

⇒ Divide 40 by 9: 40 = 9 × 4 + 4

⇒ The remainder obtained is 4.

⇒ Alternatively, the sum of digits of 40 = 4 + 0 = 4.

∴ The correct answer is 4.

Additional Information

Divisibility Rule of 3

A number is completely divisible by 3 if the sum of its digits is divisible by 3. The remainder obtained is the same as dividing the sum of digits by 3.

Divisibility Rule of 11

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

Divisibility Rule of 8

A number is divisible by 8 if the number formed by its last three digits is exactly divisible by 8.

Digital Root Concept

The single-digit value obtained by repeatedly summing the digits of a number is its digital root, which gives the exact remainder when the number is divided by 9.

Shortcut Trick

If the angles of a triangle are in an Arithmetic Progression (i.e., one angle is the average of the other two), the middle angle is always π/3 (or 60°).

Checking the given options, only the first set contains π/3 and sums to π radians.

Sum = π/6 + π/3 + π/2 = π.

Average of π/6 and π/2 = (π/6 + π/2) ÷ 2 = (4π/6) ÷ 2 = π/3.

∴ The correct answer is π/6, π/3, π/2.

Alternate Method

Given:

One angle of a triangle is the arithmetic average of the other two angles.

Formula Used:

Sum of interior angles in a triangle = π radians.

Average = (Sum of values) ÷ Number of values

A B C π/6 π/3 π/2 Right-Angled Triangle with Angles in A.P.

Calculations:

⇒ Let the three angles of the triangle be A, B, and C.

⇒ According to the given condition, let B be the average of A and C: B = (A + C) ÷ 2

⇒ Multiplying by 2, we get: 2B = A + C

⇒ We know the sum property of triangles: A + B + C = π

⇒ Substituting A + C = 2B in the sum equation:

⇒ B + (A + C) = π

⇒ B + 2B = π

⇒ 3B = π → B = π/3

⇒ Since B = π/3, the remaining sum is A + C = π − π/3 = 2π/3

⇒ Checking the first set of angles from the options: π/6, π/3, π/2

⇒ Here, the middle angle is π/3. Sum of the other two angles = π/6 + π/2 = π/6 + 3π/6 = 4π/6 = 2π/3.

⇒ The first set identically matches all our derived geometric conditions.

∴ The correct answer is π/6, π/3, π/2.

Additional Information

Arithmetic Progression of Angles

When the angles of a triangle are in an Arithmetic Progression (A.P.), the middle angle is always exactly 60° (or π/3 radians), unconditionally regardless of what the other two adjacent angles are.

Sum of Angles Property

The sum of interior angles in any Euclidean planar triangle is strictly equal to 180° (which is algebraically equivalent to π radians). Universal formula: A + B + C = π.

Radian and Degree Conversion

To convert a measurement from radians to degrees, we multiply the given radian value by 180°/π. For example, π/6 × (180°/π) = 30° and π/2 × (180°/π) = 90°.

Shortcut Trick

The line joining an external point to the centre of the circle bisects the angle between the tangents.

⇒ ∠APO = ∠APB ÷ 2 = 60º ÷ 2 = 30º

The radius is always perpendicular to the tangent at the point of tangency, so ∠OAP = 90º.

In right-angled △OAP, the sum of all interior angles is 180º.

⇒ ∠POA = 180º − (90º + 30º) = 60º

∴ The correct answer is 60º.

Alternate Method

Given:

PA and PB are tangents to the circle with centre O.

Angle between tangents ∠APB = 60º

Formula Used:

Sum of angles in a quadrilateral is 360º.

Radius is perpendicular to the tangent at the point of contact.

60º

?

O

P

A

B

Calculation:

Since PA and PB are tangents to the circle at A and B respectively:

⇒ ∠OAP = 90º and ∠OBP = 90º

In quadrilateral OAPB, the sum of all interior angles is 360º.

⇒ ∠OAP + ∠OBP + ∠APB + ∠AOB = 360º

⇒ 90º + 90º + 60º + ∠AOB = 360º

⇒ 240º + ∠AOB = 360º

⇒ ∠AOB = 360º − 240º = 120º

In △OAP and △OBP:

⇒ OA = OB (Radii of the same circle)

⇒ OP = OP (Common side)

⇒ PA = PB (Tangents from an external point are equal)

⇒ △OAP ≅ △OBP (SSS congruence criterion)

Therefore, the common side OP bisects ∠AOB.

⇒ ∠POA = ∠AOB ÷ 2

⇒ ∠POA = 120º ÷ 2 = 60º

∴ The correct answer is 60º.

Additional Information

Properties of Tangents to a Circle

Tangents drawn from an external point to a circle are equal in length (PA = PB). They subtend equal angles at the centre, and they are equally inclined to the line joining the external point to the centre.

Tangent-Radius Theorem

A tangent at any given point of a circle is strictly perpendicular to the radius passing through the point of contact. This implies ∠OAP = 90º.

Cyclic Quadrilateral Formation

When tangents are drawn from an external point, the quadrilateral formed by the two tangents and the two radii (OAPB) has opposite angles summing to 180º (∠APB + ∠AOB = 180º), making it a cyclic quadrilateral.

Shortcut Trick

Let B's present age be x.

Then A = 3x, and C = x + 5.

Total sum: 3x + x + x + 5 = 75 ⇒ 5x = 70 ⇒ x = 14.

Present ages: B = 14 years, A = 3 × 14 = 42 years.

Ratio of (B − 5) to (A + 3) = (14 − 5) : (42 + 3) = 9 : 45 = 1 : 5.

∴ The correct answer is 1 : 5.

Alternate Method

Given:

A is thrice as old as B ⇒ A = 3B

C is 5 years elder than B ⇒ C = B + 5

Sum of ages of A, B, and C = 75 years

Formula Used:

Past age = Present age − Number of years

Future age = Present age + Number of years

Calculations:

Let the present age of B be x.

⇒ Present age of A = 3x

⇒ Present age of C = x + 5

According to the given condition, sum of their ages is 75:

⇒ 3x + x + (x + 5) = 75

⇒ 5x + 5 = 75

⇒ 5x = 70

⇒ x = 14

Now, calculate the required ages:

⇒ Present age of B = 14 years

⇒ Present age of A = 3 × 14 = 42 years

⇒ Age of B five years ago = 14 − 5 = 9 years

⇒ Age of A three years from now = 42 + 3 = 45 years

Find the required ratio:

⇒ Required Ratio = 9 : 45

⇒ Required Ratio = 1 : 5

∴ The correct answer is 1 : 5.

Additional Information

Past and Future Ages

If the present age is x, then age n years ago is (x − n) and age n years from now is (x + n).

Constant Difference

The difference between the ages of two persons always remains constant irrespective of past, present, or future times.

Ratio of Ages

If the ratio of present ages of A and B is a : b, then their actual ages can be assumed as ax and bx respectively, where x is a common constant multiplier.

Given:

Wages of Rahul in November = ₹11500

Wages of Sunil in November = ₹10500

Formula used:

Percentage = $\dfrac{\text{Wages of Sunil}}{\text{Wages of Rahul}} \times 100$

Calculation:

⇒ Percentage = $\dfrac{10500}{11500} \times 100$

⇒ Percentage = $\dfrac{10500 \times 100}{11500}$

⇒ Percentage = 91.30%

∴ Sunil's wages in November are 91.30% of Rahul's wages in November.

Shortcut Trick

For inverse variation, the product of the two variables is always constant.

x₁ × y₁ = x₂ × y₂

2 × 6 = 3 × y

12 = 3 × y ⇒ y = 4

∴ The correct answer is 4.

Alternate Method

Given:

x varies inversely as y.

When x = 2, y = 6.

Formula Used:

If x ∝ 1/y, then x × y = k (where k is a constant)

Calculations:

⇒ First, find the constant k using the initial values.

⇒ k = 2 × 6 = 12

⇒ Now, substitute x = 3 and k = 12 into the relation.

⇒ 3 × y = 12

⇒ y = 12 ÷ 3

⇒ y = 4

∴ The correct answer is 4.

Additional Information

Direct Variation

If two quantities change in the same proportion, they are in direct variation. The ratio between them remains constant: x ÷ y = k.

Joint Variation

Occurs when a variable is directly proportional to the product of two or more other variables. Example formula: x = k × y × z.

Compound Ratio

The ratio obtained by multiplying the antecedent parts together and the consequent parts together. If a:b and c:d are two ratios, the compound ratio is (a × c) : (b × d).

Shortcut Trick

Effective interest percentage for the first sum = 15% × 3 = 45%

Interest on the first sum = 45% of 5000 = ₹2,250

Effective interest percentage for the second sum = 12% × 4 = 48%

Interest on the second sum = 48% of 8000 = ₹3,840

Positive difference = 3840 − 2250 = 1590

∴ The correct answer is ₹1,590.

Alternate Method

Given:

P₁ = ₹5,000, R₁ = 15%, T₁ = 3 years

P₂ = ₹8,000, R₂ = 12%, T₂ = 4 years

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Calculations:

⇒ SI₁ = (5000 × 15 × 3) ÷ 100

⇒ SI₁ = 50 × 45 = ₹2,250

⇒ SI₂ = (8000 × 12 × 4) ÷ 100

⇒ SI₂ = 80 × 48 = ₹3,840

⇒ Difference = SI₂ − SI₁

⇒ Difference = 3840 − 2250 = ₹1,590

P1 = ₹5,000

15% × 3 yrs

SI1 = ₹2,250

P2 = ₹8,000

12% × 4 yrs

SI2 = ₹3,840

Difference = ₹3,840 − ₹2,250 = ₹1,590

∴ The correct answer is ₹1,590.

Additional Information

Compound Interest Formula

The accumulated amount over T years is calculated using the formula A = P(1 + R/100)^T.

SI vs CI Difference

For exactly 2 years, the difference between CI and SI on the same principal is P(R/100)². For 3 years, the exact difference formula is P(R/100)² × (3 + R/100).

Rule of 72

A well-known approximation stating that the time needed to double an investment at a compound rate of R% is roughly 72 ÷ R years.

Shortcut Trick

Relative speed (same direction) = 108 − 90 = 18 km/h

Relative speed in m/s = 18 × (5/18) = 5 m/s

Time to meet = Distance ÷ Relative speed

Time to meet = 1635 ÷ 5 = 327 s

∴ The correct answer is 327 s.

Alternate Method

Given:

Length of the circular track = 1635 m

Speed of Varun = 90 km/h

Speed of Sandeep = 108 km/h

Formula Used:

Time to meet for the first time = Track Length ÷ Relative Speed

Relative speed (same direction) = S₁ − S₂

Calculations:

⇒ Speed of Varun = 90 × (5/18) = 25 m/s

⇒ Speed of Sandeep = 108 × (5/18) = 30 m/s

⇒ Relative speed = 30 − 25 = 5 m/s

⇒ Time to meet = 1635 ÷ 5 = 327 s

∴ The correct answer is 327 s.

Additional Information

Meeting for the first time anywhere on the track

When moving in the same direction: Time = Distance ÷ (S₁ − S₂). When moving in opposite directions: Time = Distance ÷ (S₁ + S₂).

Meeting at the starting point

The time taken to meet at the starting point for the first time is the LCM of the times taken by each individual to complete one full round.

Relative Speed

Relative speed is the speed of a moving object with respect to another. If they move in the same direction, speeds subtract; if opposite, speeds add.

Unit Conversion

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

Shortcut Trick

Total capacity = LCM(25, 50, 100) = 100 units ⇒ Efficiency: M = 4, N = 2, S = 1.

Let the total time taken to fill the tank be T minutes.

Pipe N works for exactly 10 mins, S works for (T − 15) mins, and M works for (T − 10) mins.

⇒ (10 × 2) + 1 × (T − 15) + 4 × (T − 10) = 100

⇒ 5T − 35 = 100 ⇒ 5T = 135 ⇒ T = 27 minutes.

∴ The correct answer is 27 minutes.

Alternate Method

Given:

Time taken by pipe M to fill the tank = 25 minutes

Time taken by pipe N to fill the tank = 50 minutes

Time taken by pipe S to fill the tank = 100 minutes

Calculations:

⇒ Let the total time taken to fill the tank completely be T minutes.

⇒ Initially, pipes N and S are opened. After 10 minutes, pipe N is shut, which means pipe N operates for exactly 10 minutes.

⇒ Pipe M is opened after 10 minutes and continues until the end, so it operates for (T − 10) minutes.

⇒ Pipe S starts from the beginning but is closed 15 minutes before the tank is full, meaning it operates for (T − 15) minutes.

⇒ Total Work = (Work by N) + (Work by S) + (Work by M)

⇒ (10 × 2) + 1 × (T − 15) + 4 × (T − 10) = 100

⇒ 20 + T − 15 + 4T − 40 = 100

⇒ 5T − 35 = 100

⇒ 5T = 135

⇒ T = 27 minutes

∴ The correct answer is 27 minutes.

Additional Information

Pipes & Cisterns Concept

If a pipe can fill a tank in x hours, its efficiency (the fraction of the tank filled in 1 hour) is 1/x. Always compute Total Capacity using the LCM of individual times.

Leaving/Joining Work Strategy

Whenever pipes open or close at different intervals, assign a variable for the total filling time (T) and define the operating duration of each pipe in terms of T. Sum up their individual work outputs and equate them to the Total Capacity.

Negative Work (Outlet Pipes)

If a pipe empties the tank, its efficiency is treated as negative. The total work equation becomes: Total work = Positive work − Negative work.

Calculation:

We have,

21- 4.9 ÷ 7 + 3.9 × 0.4 + 0.9

⇒ 21 - 4.9 × 1/7 + 3.9 × 0.4 + 0.9

⇒ 21 - 0.7 + 3.9 × 0.4 + 0.9

⇒ 21 - 0.7 + 1.56 + 0.9

⇒ 23.46 - 0.7 

⇒ 22.76

∴ The correct answer is option (4).

Given:

Students enrolled in Institute B in 2019 = 350

Students enrolled in Institute B in 2020 = 375

Students enrolled in Institute B in 2022 = 200

Total students enrolled in Institute A in 2018 = 150

Total students enrolled in Institute A in 2020 = 300

Total students enrolled in Institute A in 2021 = 250

Formula used:

Ratio = $\dfrac{\text{Total students in Institute B (2019, 2020, 2022)}}{\text{Total students in Institute A (2018, 2020, 2021)}}$

Calculations:

Total students in Institute B (2019, 2020, 2022) = 350 + 375 + 200 = 925

Total students in Institute A (2018, 2020, 2021) = 150 + 300 + 250 = 700

⇒ Ratio = $\dfrac{925}{700}$

⇒ Ratio = $\dfrac{37}{28}$

∴ The correct answer is 37 : 28.

Shortcut Trick

Average temperature of 31 days in January = 24ºC

Total deviation for first 16 days = 16 × (22 − 24) = −32

Total deviation for last 16 days = 16 × (26 − 24) = +32

Net deviation = −32 + 32 = 0

Temperature on the 16^th day = Average + Net Deviation = 24 + 0 = 24ºC

∴ The correct answer is 24ºC.

Alternate Method

Given:

Average temperature of first 16 days = 22ºC

Average temperature of last 16 days = 26ºC

Average temperature of the entire month (31 days) = 24ºC

Formula Used:

Temperature of overlapped day = (Sum of part 1) + (Sum of part 2) − (Total sum)

First 16 days: 22ºC

Last 16 days: 26ºC

16^th Day

Entire Month (31 days): 24ºC

Calculations:

⇒ Sum of temperatures of first 16 days = 16 × 22 = 352

⇒ Sum of temperatures of last 16 days = 16 × 26 = 416

⇒ Total sum of temperatures for the entire month = 31 × 24 = 744

⇒ Temperature on the 16^th day = (352 + 416) − 744

⇒ Temperature on the 16^th day = 768 − 744 = 24

∴ The correct answer is 24ºC.

Additional Information

Arithmetic Mean (Average)

The average is the sum of all values divided by the total number of values. Formula: Average = Sum ÷ Count.

Overlapping Groups Principle

When two subsets overlap on a single item (like the middle day in a month), the value of the overlapping item is determined by adding the sum of both subsets and subtracting the total sum of all items.

Deviation Method

The sum of total deviations from the exact average is always zero. This property can be used as a smart shortcut to quickly find missing or overlapping values by balancing the positive and negative net deviations against the base average.

The correct answer is: Ample.

Key Points

• The word "Abundant" means existing or available in large quantities; plentiful. (प्रचुर मात्रा में)
• Example: The garden was abundant with flowers in full bloom.
• "Ample" refers to enough or more than enough; plentiful. (पर्याप्त)
• Example: There is ample time to complete the assignment.
• Hence, we can infer that the synonym of 'Abundant' is 'Ample'.

Therefore, the correct answer is: Ample.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Scarce (दुर्लभ): Limited in quantity; not enough.
• Example: During the drought, water became scarce.
• Barren (बंजर ): Not productive; devoid of life.
• Example: The barren land could not support any crops.
• Difficult (कठिन): Needing much effort or skill to accomplish.
• Example: The exam was so difficult that many students failed.

The correct answer is: Option 1.

Key Points

• The word "stoic" means someone who can endure pain or hardship without showing their feelings or complaining. (असंवेदनशील)
• Example: Despite the chaos around her, she remained stoic and calm.
• "Stoic" refers to a person who does not show response to good or bad events. (असंवेदनशील)
• Example: He was stoic in the face of criticism and did not let it affect him.

Therefore, the correct answer is: Option 1.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Sceptic (संशयवादी): A person inclined to question or doubt accepted opinions.
• Example: As a sceptic, she questioned all the traditional beliefs.
• Cynic (निंदक): A person who believes that people are motivated purely by self-interest.
• Example: He is a cynic who always doubts the intentions of others.
• Phobic (फोबिक): A person who has an extreme or irrational fear of something.
• Example: She is phobic about spiders and can't stand being near them.

The correct answer is Option (3) i.e. POQRS

Key Points

• The sentence begins with "P the city bus was overcrowded", which introduces the main subject.
• Following it, "O as it was the last one of the evening" provides the reason for the overcrowding.
• Q and this gave an opportunity" continues, indicating the consequence of the overcrowding situation.
• R to the pickpockets" specifies who benefited from the opportunity created.
• S to try their skill" completes the sentence by explaining what the pickpockets did with the opportunity.

Therefore, the correct answer is POQRS.

Additional Information

• Option 1 (SRPOQ): This option starts with "to try their skill to the pickpockets," which is an incomplete and incorrect beginning for the sentence.
• Option 2 (PSORQ): This option follows a similar structure, but it disrupts the logical flow by placing "and this gave an opportunity" before explaining the overcrowding.
• Option 4 (SROPQ): This option starts with "to try their skill to the pickpockets" and then explains the overcrowding, which creates an illogical and fragmented sentence structure.

The correct answer is 4 i.e. this part of the sentence has an error.

Key Points

• In this part of the sentence, the word "students" should be in the singular form "student" to agree with the singular subject "Every".
• The corrected part should read 'Every student in the hostel' to make the sentence grammatically correct.

Hence, the correct answer is option 4.

Correct sentence: Every student in the hostel decided to travel to Delhi to witness the Republic Day parade.

Additional Information

• The subject and verb must agree in number, meaning both need to be singular or both need to be plural.
• When a singular subject is followed by a phrase or clause that starts with words such as along with, besides, or as well as, the number of the subject does not change. Use a singular verb. For example: The teacher, along with her students, is going on a trip.

The correct answer is: Disinterested.

Key Points

• The word "inquisitive" means having or showing an interest in learning things; curious. (जिज्ञासु)
• Example: Her inquisitive nature made her a great scientist, always eager to discover new things.
• "Disinterested" refers to having no personal interest or involvement; impartial. (निष्पक्ष)
• Example: As a judge, it is important to remain disinterested and impartial.
• Hence, we can infer that the opposite of 'inquisitive' is 'disinterested'.

Therefore, the correct answer is: Disinterested.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Comprehensive (व्यापक): Including or dealing with all or nearly all elements or aspects of something.
• Example: The report was comprehensive, covering all the major aspects of the project.
• Itemised (सूचीबद्ध): Presenting as a list of individual items.
• Example: The invoice was itemised, detailing every single expense.
• Intrusive (आक्रामक): Causing disruption or annoyance through being unwelcome or uninvited.
• Example: His intrusive questions made everyone uncomfortable.

The correct answer is Option 2.

 

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "The meal was not prepared by us."
• To convert to active voice: Place the original subject "we" at the beginning.
• Change the passive verb form "was not prepared" to "did not prepare" (simple past active).

Therefore, the correct answer is Option 2.

 

Correct Sentence: "We did not prepare the meal."

 

Additional Information

• Option 1: "We had not prepare the meal." – Incorrect verb form ("prepare" should be "prepared").
• Option 3: "We did not preparing the meal." – Incorrect verb form ("preparing" should be "prepare").
• Option 4: "We did prepare the meal." – Incorrect in negation context, does not match the negative structure of the original sentence.

The correct answer is: Option 3.

Key Points

• The word "organise" means to arrange systematically; to put in order. (व्यवस्थित करना)
• Example: She decided to organise her wardrobe by color and type of clothing.
• "Arrange" refers to putting things in a neat, attractive, or required order. (सज्जित करना)
• Example: He arranged the books on the shelf alphabetically.

Therefore, the correct answer is: Option 3.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Derange (विकृत करना): To disturb the arrangement or order of.
• Example: The sudden change in plans deranged all his previous arrangements.
• Disorder (अव्यवस्था): A state of confusion or a lack of order.
• Example: The house was in complete disorder after the party.
• Confuse (भ्रमित करना): To make someone unable to think clearly.
• Example: The instructions were so complicated that they confused everyone.

The correct answer is Option 4.

 

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "You must do the homework."
• To convert to passive voice: Place the object "the homework" at the beginning.
• Change the active verb form "must do" to "must be done" (modal verb passive).
• Add the preposition "by" followed by the original subject "you".

Therefore, the correct answer is Option 4.

 

Correct Sentence: "You must do the homework."

 

Additional Information

• Option 1: "You should have done the homework." – Incorrect modal verb (should have done) does not match "must be done".
• Option 2: "You do the homework." – Incorrect in conveying the necessity implied by "must".
• Option 3: "You will do the homework." – Incorrect future tense, does not match the modal verb "must".

The correct answer is: Option 1 i.e. 'I will definitely attend the conference.'

Key Points

• The word "definitely" means without doubt; certainly. (निश्चित रूप से)
• Example: She will definitely be at the party tonight.
• "Definitely" is the correct spelling used to express certainty. (निश्चित रूप से)
• Example: I will definitely finish my work by the end of the day.

Therefore, the correct answer is: Option 1 i.e. 'I will definitely attend the conference.'

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Definlty (गलत वर्तनी): This is an incorrect spelling of 'definitely'.
• Example: The word 'definlty' is a common misspelling of 'definitely'.
• Definetely (गलत वर्तनी): This is an incorrect spelling of 'definitely'.
• Example: 'Definetely' is often misspelled by those who are unsure of the correct spelling.
• Definately (गलत वर्तनी): This is an incorrect spelling of 'definitely'.
• Example: Many people mistakenly write 'definately' instead of 'definitely'.