SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 3) (Previous Year Paper)

Logic: [(First no.) : {(First no. × 2) - 1} : (First no.)²]

Checking all the given options:

(1) 11 : 21 : 121 → [(11) : {(11 × 2) - 1} : (11)²]

(2) 2 : 3 : 4 → [(2) : {(2 × 2) - 1} : (2)²]

(3) 7 : 15 : 49 → [(7) : {(7 × 2) + 1} : (7)²]

(4) 9 : 17 : 81 → [(9) : {(9 × 2) - 1} : (9)²]

Here, in (7 : 15 : 49) different logic is followed.

Hence, the correct answer is "7 : 15 : 49".

The logic followed in the given figure series is:

From Figure (1) to (2):

One more line is added.

From Figure (2) to (3):

One more line is added.

From Figure (3) to (4):

One more line is added.

From Figure (4) to Answer Figure (5):

One more line is added.

Hence, the correct answer is "Option (4)".

The fifteenth day of the month of June is a Saturday.

Saturday falls on these dates:

15 + 7 = 22

22 + 7 = 29

And the last day of June, i.e, 30 June is Sunday.

And 1^st of July will be Monday.

Monday falls on these dates:

1 + 7 = 8

8 + 7 = 15

15 + 7 = 22

22 + 7 = 29

30^th is Tuesday and 31^st is Wednesday.

Hence, the correct answer is "Wednesday".

The option that represents the correct order of the given words as they would appear in an English dictionary is:

3. Elaborate
4. Elapsed
5. Elite
6. Elongate
7. Elude

Hence, the correct answer is "3, 4, 1, 5, 2".

Logic: The first word is a country, and the second word is its capital city.

Portugal: Lisbon → Lisbon is the capital of Portugal.

Similarly,

Italy: Rome → Rome is the capital of Italy.

Here 'Italy: Rome' is the correct pair.

Hence, the correct answer is "Italy: Rome".

Additional Information

Here, we use the BODMAS table given below:

Given:

⇒ 72 @ 9 @3 @ 6 @ 6 @ 6 @ 6

(1) ÷, ×, +, =, -, +

⇒ 72 @ 9 @3 @ 6 @ 6 @ 6 @ 6

After putting the signs:

⇒ 72 ÷ 9 × 3 + 6 = 6 - 6 + 6

Apply BODMAS rule:

⇒ 8 × 3 + 6 = 12 - 6

⇒ 24 + 6 = 6

⇒ 30 = 6

Here, the equation is not satisfied.

(2) ÷, ×, +, =, ×, -

⇒ 72 @ 9 @3 @ 6 @ 6 @ 6 @ 6

After putting the signs:

⇒ 72 ÷ 9 × 3 + 6 = 6 × 6 - 6

Apply BODMAS rule:

⇒  8 × 3 + 6 = 36 - 6

⇒ 24 + 6 = 30

⇒ 30 = 30

Here, the equation is satisfied.

(3) ×, ÷, =, -, +, ×

⇒ 72 @ 9 @3 @ 6 @ 6 @ 6 @ 6

After putting the signs:

⇒ 72 × 9 ÷ 3 = 6 - 6 + 6 × 6

Apply BODMAS rule:

⇒ 72 × 3 = 6 - 6 + 36

⇒ 216 = 42 - 6

⇒ 216 = 36

Here, the equation is not satisfied.

(4) +. ×, =, -, ÷, +

⇒ 72 @ 9 @3 @ 6 @ 6 @ 6 @ 6

After putting the signs:

⇒ 72 + 9 × 3 = 6 - 6 ÷ 6 + 6

Apply BODMAS rule:

⇒ 72 + 27 = 6 - 1 + 6

⇒ 99 = 12 - 1

⇒ 99 = 11

Here, the equation is not satisfied.

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

Given:

14 : 54 :: 21 : 82 :: 5 : ?

Logic: Second no. = [(First no. × 4) - 2]

14 : 54 →

⇒ [(14 × 4) - 2]

⇒ (56 - 2) = 54

21 : 82 →

⇒ [(21 × 4) - 2]

⇒ (84 - 2) = 82

Similarly, for '5 : ?' →

⇒ [(5 × 4) - 2]

⇒ (20 - 2) = 18

Here, '5 : 18' is the correct pair.

Hence, the correct answer is "Option (4)".

The logic followed in the given figure series is:

From Figure (1) to (2):

The symbols are moved as shown below.

From Figure (2) to (3):

The symbols are moved as shown below and the symbol L changes into (=).

From Figure (3) to (4):

The symbols are moved as shown below.

From Figure (4) to Answer Figure (5):

The symbols are moved as shown below and the symbol O changes into 6.

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

As 2 and 1 are the common faces on both the dice, the remaining faces 6 and 5 are opposite to each other.

As 5 and 2 are the common faces on both the dice, the remaining faces 1 and 4 are opposite to each other.

Remaining faces 2 and 3 will be opposite to each other.

Hence, '2' is the correct answer.

The logic followed here is:

Hence, '46' is the correct answer.

Given:

F G H _ Y _ G _ U Y F_ H _ Y F G _ W _

Checking all the options:

1. U F H G V I Y

F G H U Y / F G H U Y / FG H V Y / F G I W Y

2. T G H G V H Y

F G H T Y / G G H U Y / FG H V Y / F G H W Y

3. T F H G V H Y

F G H T Y / F G H U Y / FG H V Y / F G H W Y

Here, the series is completed.

4. U G H G V H Y

F G H U Y / G G H U Y / FG H V Y / F G H W Y

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

Given:

(4, 16, 8)

(2, 14, 9)

Logic: Third no. = [(First no.) + (Second no. ÷ First no.)]

(4, 16, 8) →

⇒ [4 + (16 ÷ 4)]

⇒ (4 + 4) = 8

(2, 14, 9) →

⇒ [2 + (14 ÷ 2)]

⇒ (2 + 7) = 9

Checking all the given options:

1. (2, 8, 10)

⇒ [2 + (8 ÷ 2)]

⇒ (2 + 4) = 6

2. (2, 8, 6)

⇒ [2 + (8 ÷ 2)]

⇒ (2 + 4) = 6

3. (2, 8, 16)

⇒ [2 + (8 ÷ 2)]

⇒ (2 + 4) = 6

4. (2, 8, 1)

⇒ [2 + (8 ÷ 2)]

⇒ (2 + 4) = 6

Here, (2, 8, 6) shows a similar relation to the given set of numbers.

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

The correct mirror image from the following options, when the mirror is placed on the right side of the given figure is shown below:

Hence, 'option 4' is the correct answer.

The least possible Venn diagram is:

Conclusions:

I. Some barges are ships. → Follows (As, All ships are yachts. and All yachts are barges)

II. Some barges are boats. → Follows (As, Some boats are ships, All ships are yachts and All yachts are barges)

III. Some yachts are boats. → Follows (As, Some boats are ships and All ships are yachts)

Hence, 'All conclusions follow' is the correct answer.

The logic followed here is:

Similarly,

Hence, 'FUOJUTFS' is the correct answer.

The logic followed here is:

Similarly,

Hence, 'TFL' is the correct answer.

Given:

(4, 14, 828)

(3, 10, 620)

Logic: Third no. = [{(First no. × 100) + Second no.} × 2]

(4, 14, 828) →

⇒ [{(4 × 100) + 14} × 2]

⇒ [(400 + 14) × 2]

⇒ (414 × 2) = 828

(3, 10, 620) →

⇒ [{(3 × 100) + 10} × 2]

⇒ [(300 + 10) × 2]

⇒ (310 × 2) = 620

Checking all the given options:

1. (1, 10, 100)

⇒ [{(1 × 100) + 10} × 2]

⇒ [(100 + 10) × 2]

⇒ (110 × 2) = 220

2. (2, 50, 500)

⇒ [{(2 × 100) + 50} × 2]

⇒ [(200 + 50) × 2]

⇒ (250 × 2) = 500

3. (5, 10, 980)

⇒ [{(5 × 100) + 10} × 2]

⇒ [(500 + 10) × 2]

⇒ (510 × 2) = 1020

4. (4, 32, 98)

⇒ [{(4 × 100) + 32} × 2]

⇒ [(400 + 32) × 2]

⇒ (432 × 2) = 864

Here, (2, 50, 500) shows a similar relation to the given set of numbers.

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

Select the correct mirror image of the given combination when the mirror is placed at line MN as shown.

Hence, 'option 4' is the correct answer.

The image embedded in given figure is as shown below:

Hence, 'option 2' is the correct answer.

The least possible Venn diagram is:

Conclusions:

I. All yellow are roses. → Does not follow (As, Some roses are yellow and Some yellow are buses → Some yellow are roses)

II. Some buses are yellow. → Follows (As, Some yellow are buses)

III. All yellow are green. → Does not follow (As, Some yellow are buses and All buses are green → Some yellow are green)

Hence, 'Only conclusion II follows' is the correct answer.

The logic followed here is:

Hence, 'DJG' is the correct answer.

Given:

(10, 5, 65)

(9, 8, 89)

Logic: Third no. = [(First no. × Second no.) + (First no. + Second no.)]

(10, 5, 65) →

⇒ [(10 × 5) + (10 + 5)]

⇒ (50 + 15) = 65

(9, 8, 89) →

⇒ [(9 × 8) + (9 + 8)]

⇒ (72 + 17) = 89

Checking all the given options:

1. (12, 5, 89)

⇒ [(12 × 5) + (12 + 5)]

⇒ (60 + 17) = 77

2. (11, 10, 128)

⇒ [(11 × 10) + (11 + 10)]

⇒ (110 + 21) = 131

3. (4, 5, 29)

⇒ [(4 × 5) + (4 + 5)]

⇒ (20 + 9) = 29

4. (8, 7, 98)

⇒ [(8 × 7) + (8 + 7)]

⇒ (56 + 15) = 71

Here, (4, 5, 29) shows a similar relation to the given set of numbers.

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

The option that represents the correct order of the given words as they would appear in an English dictionary is:

1. Breakdown
2. Breakfast
3. Breathe
4. Breeding
5. Breeze
6. Brevity

Here, the correct order is '1, 6, 3, 4, 5, 2'.

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

The logic followed here is:

Logic: First and Second letter are exactly opposite to each other; First letter - 2 = Third letter

1. HSF → H ↔ S; H - 2 = F
2. FUD → F ↔ U; F - 2 = D
3. BYZ → B ↔ Y; B - 2 = Z
4. JOH → J ↔ Q ≠ O; J - 2 = H

Hence, 'JOH' is the correct answer.

Given:

(6, 4, 8)

(17, 6, 28)

Logic: First no. = [(Second no. + Third no.) ÷ 2]

(6, 4, 8) →

⇒ [(4 + 8) ÷ 2]

⇒ (12 ÷ 2) = 6

(17, 6, 28) →

⇒ [(6 + 28) ÷ 2]

⇒ (34 ÷ 2) = 17

Checking all the given options:

1. (8, 3, 12)

⇒ [(12 + 3) ÷ 2]

⇒ (15 ÷ 2) = 7.5

2. (12, 9, 11)

⇒ [(9 + 11) ÷ 2]

⇒ (20 ÷ 2) = 10

3. (11, 4, 19)

⇒ [(19 + 4) ÷ 2]

⇒ (23 ÷ 2) = 11.5

4. (13, 5, 21)

⇒ [(5 + 21) ÷ 2]

⇒ (26 ÷ 2) = 13

Here, (13, 5, 21) shows a similar relation to the given set of numbers.

Hence, the correct answer is "Option (4)".

The correct answer is Natya Shastra.

 Key Points

• Bharatanatyam is a classical dance form that originated in South India and is known for its intricate footwork, expressive gestures, and graceful movements.
• The theoretical foundations of Bharatanatyam can be traced back to the Natya Shastra, an ancient Indian treatise on the performing arts written by the sage Bharata.
• The Natya Shastra covers a wide range of topics related to dance, music, and theater, including the classification of dance forms, the elements of performance, and the roles of the performer and the audience.

Additional Information

• Arth Shastra is a treatise on economics and political science.
• It was written by Kautilya.
• Vaimanika Shastra is a text on aeronautics.
• It is attributed to the ancient Indian sage Maharishi Bharadwaja.
• Dharma Shastra is a collection of religious and ethical guidelines for Hindus.
• These texts are based on Puranas.

The correct answer is Atal Tunnel.

 Key Points

• Atal Tunnel is a 9.02 km long highway tunnel built under the Rohtang Pass in the Pir Panjal range of the Himalayas in Himachal Pradesh, India.
• It is the world's longest highway tunnel above an altitude of 3,000 meters.
• The tunnel is named after former Prime Minister of India, Atal Bihari Vajpayee, who initiated the project in 2002 and inaugurated it in 2020.
• The tunnel connects Manali to Lahaul-Spiti Valley throughout the year and reduces the distance between the two regions by about 46 km.

Additional Information

• Jawahar Tunnel is a 2.5 km long road tunnel on the National Highway 44 in Jammu and Kashmir, India.
• It is located at an altitude of 2,194 meters and connects Banihal with Qazigund.
• Syama Prasad Mookerjee Tunnel is also known as the Chenani-Nashri Tunnel.
• It is a 9.28 km long road tunnel on the National Highway 44 in Jammu and Kashmir, India.
• It is located at an altitude of 1,200 meters and connects Chenani with Nashri.
• Bhatan Tunnel is a 1.6 km long railway tunnel on the Konkan Railway route in Maharashtra, India.
• It is located at an altitude of 70 meters and connects the villages of Bhatan and Kamathe.

The correct answer is Seventh.

Key Points

• Jawahar Rozgar Yojana was started during the Seventh Five-Year Plan, which was implemented from 1985-90.
• The aim of this scheme was to create employment opportunities in rural areas and to improve infrastructure in these regions.
• The scheme was targeted towards the poor and unemployed people in rural areas.
• The funds for this scheme were provided by the central and state governments, and the implementation was done through the Panchayati Raj institutions.
• The scheme was later merged with the National Rural Employment Guarantee Act (NREGA) in 2006.

Additional Information

• The Fourth Five-Year Plan was implemented from 1969-74.
• It focused on increasing agricultural production and improving rural infrastructure.
• The Sixth Five-Year Plan was implemented from 1980-85.
• It aimed to achieve self-sufficiency in food production and improve the standard of living of people in rural areas.
• The Fifth Five-Year Plan was implemented from 1974-79.
• It focused on poverty alleviation, employment generation, and improving agricultural productivity.

The correct answer is Silicon.

 Key Points

• Period 6 of the Modern Periodic Table consists of elements from atomic number 55 (cesium) to atomic number 86 (radon).
• Silicon belongs to Period 3 of the Periodic Table and is not part of Period 6.
• Tungsten (atomic number 74), Rhenium (atomic number 75), and Platinum (atomic number 78) all belong to Period 6 of the Periodic Table.
• Tungsten is a transition metal that is commonly used in the manufacture of electrical contacts, filaments, and X-ray tubes.
• Rhenium is a rare and expensive metal that is used in high-temperature superalloys, as well as in the manufacture of electrical contacts and filaments.
• Platinum is a precious metal that is used in jewelry, as well as in the manufacture of catalytic converters, electrical contacts, and laboratory equipment.

Additional Information

• One type of chemical element is silicon.
• Its atomic number is 14 and its symbol is Si.
• It has a blue-grey metallic sheen and is a hard, brittle crystalline solid.
• It is a semiconductor and tetravalent metalloid.
• It belongs to the periodic table's group 14.

The correct answer is 2024.

Key Points

• Prime Minister announced the fortification of rice by 2024.
• The fortification of rice means adding essential micronutrients such as iron, zinc, and Vitamin B12 to the rice to improve its nutritional value.
• The fortification of rice is a part of the government's efforts to address malnutrition and improve the health of the population, especially children and women.
• The government of India's initiative to serve prepared lunches to students in all government elementary schools is known as the "Midday Meal Scheme."

Additional Information

• The fortification of rice is a cost-effective and sustainable approach to address micronutrient deficiencies, which are prevalent in India.
• The fortification of rice will not alter the taste, texture or cooking properties of rice and will be safe for consumption.
• The fortification of rice is already being implemented in some states of India, such as Odisha, Gujarat, and Andhra Pradesh, and has shown positive results in improving the nutritional status of the population.
• The fortification of rice is a part of the larger food fortification program of the government, which also includes fortification of wheat flour, oil, and salt.

The correct answer is Ireland.

Key Points

• The Directive Principles of State Policy of the Indian Constitution were borrowed from the Constitution of Ireland, which was adopted in 1937.
• The Directive Principles of State Policy are a set of guidelines for the government to frame policies and laws that promote the welfare of the people and establish a just and egalitarian society.
• They are not enforceable by any court, but they are considered fundamental in the governance of the country.

Additional Information

• The Constitution of Ireland also includes a set of Directive Principles, which are similar in nature to those of India.
• However, the Irish Constitution also includes Fundamental Rights that are justifiable, unlike the Indian Constitution.
• The US Constitution does not have Directive Principles, but it does have a Bill of Rights that guarantees certain fundamental rights to its citizens.
• The USSR (Union of Soviet Socialist Republics) was a federal socialist state that existed from 1922 to 1991.
• Its constitution also had a set of principles and rights, but they were geared towards promoting socialist ideals and collective ownership of property.
• China, on the other hand, has a socialist constitution that emphasizes the role of the Communist Party in governance and the protection of the rights of minorities and women.

The correct answer is Rs. 816.

 Key Points

• The national poverty line for 2011-12 was estimated at Rs. 816 per capita per month for rural areas of India.
• This poverty line was based on the Tendulkar Committee methodology, which calculated the minimum expenditure required for a person to meet their basic needs.
• The poverty line for urban areas was estimated at Rs. 1,000 per capita per month, which is higher than the rural poverty line due to higher living costs in cities.

Additional Information

• The Tendulkar Committee was formed in 2005 to revise the methodology for estimating poverty in India.
• It recommended using a consumption-based approach rather than an income-based approach.
• The poverty line is an important indicator of the level of poverty in a country and is used to measure progress in poverty reduction efforts.
• The poverty line in India has been criticized for being too low and not reflecting the true cost of living.
• Some experts have called for a higher poverty line that takes into account the cost of healthcare, education, and other essential services.
• The poverty line is used to identify people who are eligible for government welfare programs such as the National Rural Employment Guarantee Act (NREGA) and the Public Distribution System (PDS).

The correct answer is Chhattisgarh.

Key Points

• The 75-day festival of Bastar Dussehra is celebrated in the Indian state of Chhattisgarh.
• The festival is dedicated to the Hindu goddess Danteshwari, who is worshipped in the form of a wooden idol.
• The festival is unique because it is celebrated in the month of October, which is different from other Dussehra celebrations in India.
• During the festival, people from different communities come together to participate in cultural programs, dance, and music performances.
• The festival also features a grand procession of the goddess Danteshwari's idol, which is taken out in a chariot across the town.

Additional Information

• Odisha is known for its famous Dussehra festival called "Durga Puja," which is celebrated with great enthusiasm and devotion.
• Other festivals include Chatar Jatra, Naukhai, Puri Beach Festival, Chhau Festival, and Makar Mela.
• Jharkhand is known for its "Sarhul" festival, which is celebrated to worship the earth goddess and mark the beginning of the agricultural season.
• Other festivals include Karam, Makar, Rohini, and Sohrai.
• Bihar is known for its "Chhath Puja," which is celebrated to worship the sun god and is considered one of the most important festivals in the state.
• Other festivals include Sama Chakeva, Shravani Mela, Sonepur Cattle Fair and Makar Sankranti Mela.

The correct answer is Platyhelminthes.

Key Points

• Platyhelminthes are also known as flatworms.
• Flatworms have unsegmented, bilaterally symmetrical, soft bodies, with a triploblastic construction (comprising three layers of cells) and a lacking coelom, skeleton, and anus.
• Example includes Planaria, Liver fluke (Fasciola hepatica), and Tapeworm.

Additional Information

• Cnidaria includes jellyfish, corals, and sea anemones.
• They have radial symmetry, a single body opening, and stinging cells called cnidocytes.
• Ctenophora includes comb jellies.
• They have radial symmetry and cilia for movement but also have a complete digestive system.
• Porifera includes sponges.
• They have asymmetrical or radial symmetry, no true tissues, and filter food through pores in their bodies.

The correct answer is 7.

Key Points

• Megasthene's book Indica mentions 7 classes of Indian society.
• These classes were Brahmins, Kshatriyas, Vaishyas, Shudras, Agriculturists, Artisans, and Hunters.
• Brahmins were the highest class and were responsible for religious duties, while Kshatriyas were warriors and rulers.
• Vaishyas were merchants and traders, while Shudras were considered to be of lower status and performed menial tasks.
• Agriculturists, artisans, and hunters were also mentioned in the book as important members of society.

Additional Information

• 12 classes of Indian society were mentioned in the Manu Smriti, an ancient Hindu text.
• One of the earliest Sanskrit works that European philologists examined was the Manu Smriti.
• Sir William Jones was the one who translated it into English initially.
• 10 classes of Indian society were mentioned in the Vishnu Purana, another ancient Hindu text.
• Within the body of literature on Vaishnavism, is a significant Pancharatra text.
• 4 classes of Indian society were mentioned in the Rig Veda, one of the oldest Hindu scriptures. 
• Out of the numerous Shakhas that existed, only the Sakalya Shakha is extant.

The correct answer is rare earth elements.

 Key Points

• Lanthanides are a group of metallic elements that belong to the f-block of the periodic table.
• They are commonly known as rare earth elements because they are not found in large quantities in the Earth's crust and are difficult to extract.
• Lanthanides have unique magnetic, optical, and catalytic properties that make them useful in various applications, such as electronics, magnets, and batteries.
• Some of the lanthanides, such as neodymium and dysprosium, are critical materials for the production of high-tech products like smartphones, wind turbines, and electric vehicles.

Additional Information

• Alkali metals are a group of elements that belong to the s-block of the periodic table and have one valence electron.
• They are highly reactive and can explode when in contact with water or air.
• Inert gases, also known as noble gases, are a group of elements that belong to the p-block of the periodic table and have a full valence shell.
• They are chemically inert and rarely react with other elements.
• D-block elements are a group of metallic elements that belong to the d-block of the periodic table.
• They have variable oxidation states and are often used as catalysts or in the production of alloys.

The correct answer is Anaimalai Hills.

 Key Points

• Anaimalai Hills, also known as the Elephant Mountains, is a part of the Western Ghats, a mountain range that runs parallel to the western coast of India.
• There is a lot of wildlife in the Anaimalai Hills.
• Elephants can be found in several of these hills, including Eravikulam National Park, Chinnar Wildlife Sanctuary, Idamalayar Reserve Forest, Mankulam Forest Division, Parambikulam Wildlife Sanctuary, and Anamalai Tiger Reserve.
• The Western Ghats is a UNESCO World Heritage Site and is home to many endemic species of flora and fauna.

Additional Information

• Khasi Hills is a part of the Meghalaya Plateau in the northeast region of India.
• Because of its breathtaking scenery, the Khasi Hills region is sometimes referred to as the "Scotland of the East."
• Jaintia Hills is a part of the Garo-Khasi range in Meghalaya.
• The immaculate lakes, impressive waterfalls, enormous caverns, and unspoiled nature of the Jaintia Hills are what draw travelers there.
• Garo Hills is a part of the Garo-Khasi range and is located in the western part of Meghalaya.
• The vast Balpakram valley is formed by the passage of two mountain ranges through the Garo Hills: the Arabella and Tura mountains.

The correct answer is Sharath Kamal.

Key Points

• Major Dhyan Chand Khel Ratna Award is the highest sporting honor in India, named after the legendary hockey player Major Dhyan Chand.
• It was instituted in 1991-92.
• Sharath Kamal is a table tennis player from Tamil Nadu, India.
• He has represented India at the Olympics.
• He received the Padma Shri, India's fourth-highest civilian honor, in 2019 and the Khel Ratna Award, India's greatest sporting honor, in 2022.

Additional Information

• Venkatesh Prasad is a former Indian cricketer who played as a right-arm medium-fast bowler.
• He has also served as the bowling coach of the Indian cricket team.
• Deepika Kumari is an Indian archer who has won several national and international medals.
• She has represented India at the Olympics and is currently ranked world number 1 in women's recurve archery.
• Manpreet Singh is an Indian field hockey player.
• He has captained the Indian men's national team.

The correct answer is silk weavers.

 Key Points

• The Pattanulkars were silk weavers who migrated from Gujarat to the Vijayanagar state.
• The Pattanulkars were known for their expertise in silk weaving and were highly sought after by the rulers of the Vijayanagar state.
• The Vijayanagar state was a major center for silk trade and production, and the Pattanulkars played a significant role in the growth of the silk industry in the region.

Additional Information

• Gujarat has a rich tradition of textile production, and silk weaving is one of the major industries in the state.
• Goldsmiths were also an important community in Gujarat, and they were known for their skill in making intricate jewellry and other ornaments.
• Cotton is a major crop in Gujarat, and the state is one of the largest producers of cotton in India.
• Diamond cutting and polishing is a major industry in Surat, a city in Gujarat that is known as the diamond capital of India.

The correct answer is the Government of India Act, 1919.

Key Points

• The Montagu-Chelmsford Reforms introduced Dyarchy in the provinces through the Government of India Act, of 1919.
• Dyarchy was a system of government introduced by the British in India, which divided the powers of the government between the elected Indian ministers and the appointed British officials.
• The Government of India Act, of 1919 was also known as the Montagu-Chelmsford Reforms, named after the then Secretary of State for India, Edwin Montagu, and the Viceroy of India, Lord Chelmsford.
• The Act provided for the establishment of a bicameral legislature at the center and the provinces, with the lower house elected by the people and the upper house consisting of nominated members.

Additional Information

• The government of India Act, of 1935 abolished the system of Dyarchy and introduced Provincial Autonomy.
• August 1935 saw the royal assent of the Government of India Act 1935, an act passed by the British Parliament.
• The Greater London Authority Act of 1999 overtook it as the longest Act ever approved by the British Parliament.

The correct answer is Rabindranath Tagore.

Key Points

• Rabindranath Tagore was the first non-European to win a Nobel Prize in 1913 in literature for his work 'Gitanjali'.
• He was a Bengali poet, philosopher, and polymath who reshaped Bengali literature and music in the late 19^th and early 20^th centuries.
• He belonged to the Royal Asiatic Society as a fellow.
• The nickname "the Bard of Bengal" was applied to him.

Additional Information

• Dwarka Nath Tagore, a relative of Rabindranath Tagore, was a social reformer and philanthropist.
• He played an important role in the Bengal Renaissance.
• Bankim Chandra Chatterjee was a Bengali novelist, poet, and journalist.
• He wrote the Indian national song 'Vande Mataram'.
• Abanindranath Tagore was a Bengali artist and a nephew of Rabindranath Tagore.
• He is the creator of the "Indian Society of Oriental Art".

The correct answer is Assam.

Key Points

• Sattriya dance form belongs to the state of Assam, which is in the northeastern part of India.
• Ramkrishna Talukdar is a renowned Sattriya dancer and choreographer who has made significant contributions to the development and promotion of this dance form.
• Sattriya is a classical dance form that originated in the Vaishnav monasteries or satras of Assam in the 15^th century.
• It is characterized by graceful movements, intricate footwork, and expressive gestures that depict stories from Hindu mythology and the life of Lord Krishna.

Additional Information

• Kathak belongs to Uttar Pradesh.
• The tradition holds that the storytellers, or Kathakars, who traveled throughout ancient northern India, are the source of Kathak.
• Bharatanatyam belongs to Tamil Nadu.
• It conveys spiritual concepts and religious themes from South India, mostly related to Shaivism and Hinduism in general.
• Manipuri dance belongs to Manipur.
• It is among the greatest cultural accomplishments of the Meitei people of Manipur, who practice traditional Vaishnavism.

The correct answer is 58°C.

Key Points

• Al Aziziyah is a small town located in northwest Libya, and it is known for its scorching temperatures.
• The temperature of 58°C recorded in Al Aziziyah was on September 13, 1922, and it still holds the record for the highest recorded shade temperature.
• For a long time, this was thought to be the hottest temperature ever recorded on Earth, but a 2012 WMO review declared the record to be invalid.

Additional Information

• Al Aziziyah served as the capital of the Tripolitanian Republic, the first official republic in Arab history, from 1918 until 1922.
• Being on a trade route from the coast to the Nafusa Mountains and the Fezzan region to the south, ʽAziziya is an important trading center of the Sahel Jeffare plateau.
• Prior to 2001, it was the capital of the ʽAziziya District.
• The town's population was predicted to be above 23,399 in 2006.

The correct answer is Pandit Ayodhya Prasad.

 Key Points

• Pandit Ayodhya Prasad is associated with percussion instruments.
• Percussion instruments are musical instruments that are played by striking, shaking, or scraping.
• Percussion instruments are often used to provide rhythm and tempo in music.
• Indian classical music has a rich tradition of percussion instruments, with many different types of drums, cymbals, and other instruments used in various styles and genres.

Additional Information

• Pandit Ravi Shankar was a sitar player and composer who is widely regarded as one of the greatest Indian musicians of all time. 
• In 1999, Shankar received the Bharat Ratna, the highest civilian distinction in India.
• Vishwa Mohan Bhat is a Grammy-winning musician who plays the Mohan Veena, a modified slide guitar.
• He received the Sangeet Natak Akademi Award in 1998.
• Bismillah Khan was a Shehnai player who is considered one of the greatest Indian classical musicians of all time.
• Bismillah Khan received the Bharat Ratna in 2001.

The correct answer is Football.

 Key Points

• Rovers Cup is associated with Football.
• It is an annual football tournament that takes place in India.
• The tournament was started in 1891 by the British Army regiment known as the Rovers.
• The tournament has seen some of the top football clubs in India participate over the years.
• The current champions of the Rovers Cup are the Mohun Bagan Athletic Club.

Additional Information

• Tennis has tournaments like Wimbledon, the US Open, the French Open, the Australian Open, etc.
• Badminton has tournaments like the All England Open, World Championships, Sudirman Cup, Thomas Cup, Uber Cup, etc.
• Hockey has tournaments like the Hockey World Cup, Champions Trophy, Asian Games, Commonwealth Games, etc.

The correct answer is reports of Public Services Commissions.

 Key Points

• Article 323 of the Indian Constitution deals with the "Reports of Public Services Commissions."
• Public Services Commissions are constitutional bodies established to conduct the recruitment and selection of personnel for various government departments.
• The reports of Public Services Commissions are submitted to the President or the Governor, as the case may be, and are required to be laid before the State Legislature or the Parliament.
• The reports contain information on the work done by the Commission during the year, the number of applications received, the number of candidates selected, and other relevant details.

Additional Information

• The expenses of Public Services Commissions are charged on the Consolidated Fund of the State or the Union, as the case may be, and are audited by the Comptroller and Auditor General of India.
• "Functions of Public Services Commissions," is also important as the functions of these Commissions are specified in the Constitution and include conducting examinations and interviews, making appointments, and advising the government on matters related to recruitment and selection.
• The Constitution empowers the Parliament or the State Legislature to extend the functions of these Commissions to include recruitment and selection for any post under the government.

The correct answer is Only I.

Key Points

• The cell membrane is a thin, flexible barrier that separates the inside of a cell from its external environment.
• It is selectively permeable, meaning that it allows some substances to pass through while preventing others from entering or leaving the cell.
• This selectivity is achieved through various mechanisms such as ion channels, transporters, and pumps.
• Water can also move across the membrane through a process called osmosis, but it always moves from an area of higher concentration to an area of lower concentration.

Additional Information

• The lipid bilayer that makes up the cell membrane is composed of two phospholipid layers with cholesterol, a lipid component, strewn in between to maintain the proper fluidity of the membrane at different temperatures.
• Additionally, membrane proteins are present in the membrane.
• These proteins include integral proteins, which span the membrane and function as membrane transporters, and peripheral proteins, which cling slackly to the cell membrane's outer (peripheral) side and function as enzymes to promote interaction with the surrounding milieu.
• The function of glycolipids embedded in the outer lipid layer is comparable.
• Furthermore, cell membranes act as the attachment surface for a number of extracellular structures, including the cell wall, and are involved in a number of cellular activities including cell adhesion, ion conductivity, and cell signaling.

The correct answer is 0.

 Key Points

• Beach Volleyball teams do not have substitute players.
• Played on a sand court divided by a net, beach volleyball is a team sport between two teams of two or more players.
• The goal of the game is to send the ball over the net and land it on the court's opponent's side, much like indoor volleyball.
• In order to stop the other team from grounding the ball on their end of the court, each team collaborates as well.

Additional Information

• While the contemporary two-player game started in Santa Monica, California, beach volleyball most likely began in 1915 on Waikiki Beach in Hawaii.
• Since the Summer Olympics in 1996, it has been an Olympic sport.
• The FIVB Beach Volleyball World Championships and World Tour are organized by the Fédération Internationale de Volleyball (FIVB), which also serves as the sport's worldwide regulatory body.

The correct answer is A microfinance loan should be linked with a lien on the deposit account of the borrower.

 Key Points

• A microfinance loan is a collateral-free loan, meaning that it does not require any lien on the borrower's deposit account.
• Microfinance institutions provide small loans to low-income households and individuals who do not have access to traditional banking services.
• The annual household income limit for microfinance loans in India is up to Rs. 3,00,000.
• Microfinance loans are collateral-free, meaning that they do not require any security or guarantor for the loan.
• Microfinance loans are given to households, which typically include the husband, wife, and their unmarried children.

Additional Information

• Microfinance institutions in India play a crucial role in providing financial services to the unbanked population and promoting financial inclusion.
• Microfinance loans are usually given for income-generating activities such as small businesses, agriculture, and livestock rearing.
• Microfinance institutions also provide other financial services such as savings accounts, insurance, and remittances.
• In recent years, microfinance institutions in India have faced challenges such as over-indebtedness, high interest rates, and aggressive loan recovery practices, leading to concerns about the welfare of borrowers.

The correct answer is 1 April 2023.

Key Points

• The E-Waste Management Rules notified by the Union Ministry of Environment, Forest, and Climate Change will come into force from April 1, 2023.
• These rules are aimed at regulating the management of e-waste, which is a major environmental hazard due to the presence of toxic substances.
• The rules mandate the producers of electronic products to collect and dispose of e-waste in an environmentally sound manner.
• The rules also require the establishment of collection centers**,** dismantling and recycling facilities, and the adoption of best practices for handling e-waste.

Additional Information

• India ranks fifth globally in terms of generating e-waste.
• 2016's New E-Waste Management Regulations:
• Compact fluorescent bulbs, or CFLs, as well as other mercury-containing lamps and related equipment, are included.
• For the first time, producers are included in the Extended Producer Responsibility (EPR) framework together with the targets thanks to the Rules.
• Producers are now responsible for both the exchange and collection of e-waste.
• Manufacturers, dealers, refurbishers, and Producer Responsibility Organizations are among the other parties involved.
• The regulations now cover Compact Fluorescent bulbs (CFLs) and other bulbs that contain mercury.

Given:

A car covers a distance of 350 km in 5 hours and covers another 450 km at a speed of 90 km/h

Formula used:

Average speed = Total distance/ Total time

Calculation

Total distance covered = 350 km + 450 km = 800 km

Total time = 5 hour + 5 hour = 10 hours

Average speed = Total distance/ Total time

Average speed = 800/10 = 80 km/hr

His average speed for the whole journey is 80 km/hr.

Shortcut Trick

Identify the structure: Let a = 0.01 and b = 0.003.

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

Denominator = (5a)² − (5b)(5a) + (5b)² = 25(a² − ab + b²).

Expression = (a + b) / 25 = (0.01 + 0.003) / 25 = 0.013 / 25.

∴ The correct answer is 13/25 × 10⁻³.

Alternate Method

Given: Expression = (0.01³ + 0.003³) / (0.05² − 0.015 × 0.05 + 0.015²)

Formula Used: a³ + b³ = (a + b)(a² − ab + b²)

⇒ Let a = 0.01 and b = 0.003.

⇒ Numerator = (0.01 + 0.003) × (0.01² − 0.01 × 0.003 + 0.003²)

⇒ Numerator = 0.013 × (0.0001 − 0.00003 + 0.000009)

⇒ Denominator = 0.05² − 0.015 × 0.05 + 0.015²

⇒ Denominator = (5 × 0.01)² − (5 × 0.003) × (5 × 0.01) + (5 × 0.003)²

⇒ Denominator = 25 × (0.01² − 0.003 × 0.01 + 0.003²)

⇒ Result = [0.013 × (a² − ab + b²)] / [25 × (a² − ab + b²)]

⇒ Result = 0.013 / 25 = (13 × 10⁻³) / 25

∴ The correct answer is 13/25 × 10⁻³.

Additional Information

Algebraic Cubes Identity

The sum of cubes is factored as a³ + b³ = (a + b)(a² − ab + b²), which is frequently used to cancel out quadratic terms in fractions.

Scaling Properties

If each term in a quadratic expression is multiplied by a factor k, the total expression is multiplied by k². Here, k = 5, so the denominator became 25 times the numerator factor.

Decimal to Scientific Notation

A decimal like 0.013 can be expressed as 13 × 10⁻³ to simplify division and match standard option formats.

Formula used:

Effective discount = x + y - (x × y)/100

effective discount = (Article get free)/(Total articles) × 100

Calculation:

Scheme I. A discount of 30%

= 30%

Scheme II. Two successive discounts of 15%

= 15 + 15 - (15 × 15)/100

= 30 - 2.25

= 27.75%

Scheme III. Buy 2 get 1 free

So, effective discount for scheme B is = (Article get free)/(Total articles) × 100

= 1/(1 + 2 ) × 100 = 33.33%

Scheme IV. Buy 5 get 3 free

So, effective discount for scheme A is = (Article get free)/(Total articles) × 100

= 3/(5 + 3) × 100 = 37.5%

(4) has the maximum discount percentage.

Given:

Radius (R) = 22 cm

radius (r) = 16 cm

Formula Used:

Length of common tangent = 2√(R × r)

R & r are radii

Calculation:

Solution:

Length of common tangent = 2√(22 × 16)

= 2√(352cm²)

= 2 × 4 √(22cm²)

= 8√(22)

Therefore, the length of the common tangent between the two circles is approximately 8√(22) cm.

Given

If ΔABC and ΔDEF are congruent triangles

Concept

If ΔABC and ΔDEF are congruent triangles then:

The ratio of AC to DF is 1 ∶ 1

The perimeter of both triangles is equal

AB = DE, and BC = EF.

The ratio of the angles in both triangles is the same.

Calculation

Since ΔABC and ΔDEF are congruent triangles,

The ratio of AC to DF is 1 ∶ 1.

The incorrect answer is option 1.

Shortcut Trick

Divide the numerator and denominator by cos x to convert the expression into tan x.

Given tan x = 7/5.

Expression = [9(7/5) − 42/5] ÷ [15(7/5) + 21] = [63/5 − 42/5] ÷ [21 + 21]

Expression = [21/5] ÷ 42 = 21 ÷ (5 × 42) = 1 ÷ 10 = 0.1

∴ The correct answer is 0.1.

Alternate Method

Given: tan x = 7/5

Formula Used: Expression = (9 sin x − (42/5) cos x) ÷ (15 sin x + 21 cos x)

⇒ Divide every term by cos x:

⇒ Value = [9(sin x/cos x) − (42/5)(cos x/cos x)] ÷ [15(sin x/cos x) + 21(cos x/cos x)]

⇒ Value = [9 tan x − 42/5] ÷ [15 tan x + 21]

⇒ Substitute tan x = 7/5:

⇒ Value = [9 × (7/5) − 42/5] ÷ [15 × (7/5) + 21]

⇒ Value = [63/5 − 42/5] ÷ [21 + 21]

⇒ Value = [21/5] ÷ 42

⇒ Value = 21 ÷ (5 × 42) = 1/10 = 0.1

∴ The correct answer is 0.1.

Additional Information

Trigonometric Ratio Transformation

For expressions involving only sin x and cos x in a linear ratio, divide by cos x to utilize tan x directly without finding the hypotenuse.

Fundamental Identity

tan x = sin x ÷ cos x and cot x = cos x ÷ sin x.

Pythagorean Triplets

In a right triangle, p² + b² = h². For 7 and 5, h = √(49+25) = √74.

Given:

The difference between the cubes of two given natural numbers is 6272

Concept used:

x³ - y³ = (x - y)((x + y)²  - xy)

Calculation:

Let the two numbers be x and y.

x3 - y3 = (x - y)(x²+xy+y²)

x3 - y3 =(x-y)(x²+y²+xy-3xy+3xy)

x3 - y3 =(x-y)((x-y)²+3xy)

⇒ 6272 = 8(82  + 3xy)

⇒ 784 = (64  + 3xy)

⇒ 784 - 64  = 3xy

⇒ 720  = 3xy

⇒ xy = 720/3

⇒ xy = 240

The value is 240.

Given

a/b = 7/6

Concept used

Combining ratio

Calculation

a/b = 7/6 = k

a = 7k and b = 6k

⇒ $\frac{6a+13b}{6a-13b}$

⇒ (6 × 7k + 13 × 6k)/(6 ×​ 7k - 13 × 6k)

⇒ (120k)/(- 36k)

⇒ -10/3

The value is -10/3.

Shortcut Trick

Difference in start distance = 45 m − 25 m = 20 m.

Difference in time for B = 10 sec − 0 sec = 10 sec.

Speed of B = Distance ÷ Time = 20 ÷ 10 = 2 m/sec.

In the second case (dead heat), A runs 200 m in the same time B runs (200 − 45) = 155 m.

Time taken by A = 155 ÷ 2 = 77.5 sec.

∴ The correct answer is 77.5 sec.

Alternate Method

Given: Total distance = 200 m. Case 1: Start = 25 m, A wins by 10 sec. Case 2: Start = 45 m, Dead heat.

Formula Used: Time = Distance ÷ Speed

Let the speed of A be V_A and speed of B be V_B. Let T_A be the time taken by A to complete the race.

⇒ In Case 1: Distance for B = 200 − 25 = 175 m

⇒ Time taken by B = T_A + 10 = 175 / V_B ....(1)

⇒ In Case 2: Distance for B = 200 − 45 = 155 m

⇒ Time taken by B = T_A = 155 / V_B ....(2)

⇒ Subtracting equation (2) from (1):

⇒ (T_A + 10) − T_A = (175 / V_B) − (155 / V_B)

⇒ 10 = 20 / V_B

⇒ V_B = 20 ÷ 10 = 2 m/sec

⇒ Putting V_B in equation (2):

⇒ T_A = 155 ÷ 2

⇒ T_A = 77.5 sec

∴ The correct answer is 77.5 sec.

Additional Information

Dead Heat

A race situation where two or more contestants reach the finish line at the exact same time.

Head Start (Distance)

If A gives B a start of 'x' meters, it means B starts 'x' meters ahead of the starting point. B has to cover (Total Distance − x) meters.

Head Start (Time)

If A gives B a start of 't' seconds, it means B starts 't' seconds before A begins running.

Winning Margin

If A beats B by 'd' meters, it means when A reaches the finish line, B is 'd' meters behind it.

Given:

Ram can copy 60 pages in 15 hours.

Ram and Riya together can copy 180 pages in 30 hours

Formula Used:

Efficiency = Work done/Time Taken

Calculation:

By using the above formula

The efficiency of Ram is = 60/15= 4pages/hr

The efficiency of Ram and Riya = 180/30 = 6 pages/hr

The efficiency of Riya = 6 - 4 = 2 pages/hr

The time taken by Riya to copy 20 pages will be

⇒ 20/2= 10 hr

∴ The Time taken by Riya is 10 hours.

Given:

4 women and 7 men earn a total of  Rs. 11,480 in 7 days

10 women and 17 men earn a total of Rs. 36,360 in 9 days

Concept:

Total work = number of workers doing work × time taken to complete the work.

Calculation:

(4W + 7M) × 7 = 11,480

⇒ (4W + 7M) = 1640 ----(i)

(10W + 17M) × 9 = 36360

⇒ (10W + 17M) = 4040----(ii)

solving equations (i) and (ii)

⇒ 10W + 17.5M = 4100---- (iii)

⇒ 10W + 17M = 4040---- (iv)

by subtraction equations (iii) and (iv)

⇒ 0.5M = Rs. 60

Putting the value of G in equation (i)

⇒ 4W + 840= 1640

⇒ 4W = 800

⇒ W = Rs.200

According to the question:

Money earned by 11 women and 9 men in 13days

⇒ (11 × 200 + 9 × 120) × 13

⇒ (2200 + 1080) × 13

⇒ 3280 × 13 = 42640

∴ The required value is 42640.

Given:

Selling price of notebook = Rs 28

Profit Percentage = 12%

New selling price of notebook = 26.25

Concept Used:

Cost Price = (100/100 + profit%) × Selling price

Profit % = (Profit/C.P) × 100��������×100��������×100��������×100��������×100��������×100��������×100

Calculation:

Cost Price of pen = (100/100 + 12%) × 28

Cost Price of pen = ( 25/28)× 28 

= 25 Rs

When the pen is sold at Rs 26.25,

⇒ Profit = Selling Price – Cost Price

⇒ Profit = 26.25 – 25 = Rs 1.25

⇒ So, Profit % =(1.25/25) × 100

⇒ 5%

The profit percentage will be 5%.

Given:

Time taken by A to complete the work = 9 days

Time taken by B to complete the work = 12 days

Calculation:

Total work = L.C.M. of (12, 9) = 36 units

Efficiency of A = 36/9 = 4 units/day

Efficiency of B = 36/12 = 3 units/day

Combined efficiency of A and B = (3 + 4) = 7 units/day

If they work together on it for 5 days = 7 × 5 = 35 unit

The fraction of the work left is = 1/36

The fraction of the work left is 1/36

Given:

An aeroplane travels five times as fast as a bus.

Time is taken by bus to cover 60 km = 1 hour 20 minutes(4/3 hour)

Formula used:

Speed = Distance/time

Calculation:

Speed of bus = 60/(4/3)

⇒ 45 km/hr

Speed of aeroplane = 5 × 45

⇒ 225 km/hr

Distance covered in 25 minutes = 225 × 25/60

⇒ 93.75 km

Distance covered in 25 minutes by aeroplane is 93.75 km/hr.

Given:

Initial R = 4.5 %

Initial interest = Rs. 135

New R = 5%

Formula used:

Simple Interest = (Principle × Rate per annum ×Time)/100

Calculation:

Let deposit = Rs. a 

⇒ 135 = (a x 4.5 x 1)/100

⇒ a = 3000

Now,

Simple interest on 5% = (3000 x 5 x 1)/100

⇒ 150

Additional interest = 150 - 135 = Rs. 15

∴ Additional interest  in one year = Rs. 15

Shortcut Trick If 4.5 = 135

⇒ 1 = 30

⇒ 5 = 5 x 30 = 150

Additional interest = 150 - 135 = Rs.15

∴ Additional interest in one year is 15.

Given :

2 + (30 - 26)2 ÷ 83-2 × 0.5

BODMAS Rule:

Calculation :

2 + (30 - 26)2 ÷ 83-2 × 0.5

⇒ 2 + (4)2 ÷ 81 × 0.5

⇒ 2 + 2 × 0.5

⇒ 2 + 1

⇒ 3

∴ The answer is 3.

Given:

Equilateral triangle PQR with side PQ = 6 cm

Formula Used:

Circumradius of Equilateral triangle = side of equilateral triangle/√3

Concept Used:

Centroid Divide the median in the ratio 2 : 1

All the centres of the Equilateral triangle lie at the same point. Be it circumcenter, orthocenter, incentre, and centroid.

Calculation:

Since all the centres lie at the same point L, PL is also the circumradius of Equilateral Triangle PQR

Using the above formula,

PL = PQ/√3

⇒ PL = 6/√3

⇒ PL = 2√3 cm.

∴ The length of PL is 2√3 cm.

Given :

15 - (-5) × {4 - (7 - 3)} ÷ [3 × {5 + (-3) × (-6)}]

BODMAS Rule:

Calculation :

15 - (-5) × {4 - (7 - 3)} ÷ [3 × {5 + (-3) × (-6)}]

⇒ 15 - (-5) × {0} ÷ [3 × {5 + 18}]

⇒ 15 + 5 × 0 × 1/69

⇒15 + 0 = 15

∴ The answer is 15

Calculation

The number of marbles Madhuri has = 180

360° → 36 marbles

180° → 18

The number of marbles Madhuri has is 18

Given:

Spending on daily uses = 25%

Spending on house rent = 18%

Spending on travel = 16%

Saving = Rs. 861

Calculation:

Let total salary = a

25% = 1/4

18% = 9/50

16% = 4/25

⇒ a × 3/4 × 41/50 × 21/25 = 861

⇒ a = (861 × 50 × 25 × 4)/(3 × 41 × 21)

⇒ a = 5000/3

⇒ a = 1666(2/3).

The total salary is 1666(2/3).

Given:

sin θ + cosec θ = √5

Concept used:

x3 + 1/x3 = (x + 1/x)3 - 3(x + 1/x)

Calculation:

sin θ + cosec θ = √5

⇒ sin θ + 1/sin θ = √5

We know that 

x3 + 1/x3 = (x + 1/x)3 - 3(x + 1/x)

Here, x = sin θ 

sin3 θ + 1/sin3 θ = (√5)3 - 3(√5)

⇒ 5√5 - 3√5 = 2√5

∴ The required answer is 2√5.

Given : 

cosec θ + cot θ = 3/2 

Formula used :

cosec²θ - cot²θ = (cosec θ + cot θ)(cosec θ - cot θ) = 1 

Calculations :

cosec θ + cot θ = 3/2 ....(1)

cosec θ - cot θ = 2/3     ....(2)

Solving equations 1 and 2 , we get 

2cosec θ = 13/6 

⇒ cosec θ  = 13/12  

∴ cosec θ is equal to 13/12.

Given:

A, B and C together can finish the task in 12 days

A and B alone can finish the task in 36 days

Formula used:

Time taken = Total work/Efficiency

Calculation:

Total work be 36 units (lcm of 12 and 36)

A, B and C together can finish a task in 12 days

Efficiency of (A + B + C) = 36/12

= 3 units per day

Efficiency of (A) = 36/36 = 1 unit per day.

Efficiency of (B) = 36/36 = 1 unit per day.

Efficiency of C = 3 - 2 = 1 unit per day

C alone complete the same work = 36/1 = 36 days

Shortcut Trick

1-day work of (A + B + C) and (A) and (B) = (1/12) - (1/36) - (1/36) = 1/36

Total time taken by C alone = 36 days.

Given:

The diameter of a sphere is 7 cm.

Formula used:

The volume of a sphere = (4/3)πR3

Where R → The radius of the sphere

Calculations:

⇒ (4/3)πR3 

⇒ 4/3 × 22/7 × 3.5³

⇒  4/3 × 22/7 × 42.875

⇒ 179.67 cm3

The volume of the sphere is 179.67 cm3

Formula used:

Average of N numbers = sum of N numbers/N

Calculation:

Average demand of all 3 companies = (3800 + 4532 + 5318)/3 = 4550

Average production of all 3 companies = (3620 + 2829 + 2833)/3 = 3094

Required difference = 4550 - 3094 = 1456

∴ The correct answer is 1456.

The correct answer is "An undigestible criticism has been raised by one group of the club against the manager."

Key Points

• The given sentence is in Present Perfect Tense and Active Voice.
• The rule for changing a Present Perfect Tense from Active voice to Passive voice:
• Interchange the object and subject with each other, i.e. object of the active sentence become the subject of the passive sentence.​
• The subject is "one group of the club" and object is "an undigestible criticism" in active voice.
• So, the subject is "an undigestible criticism" and object is "One group of the club" in passive voice.
• Structure:
• Subject + has/have + V3 + Object (Active Voice)
• Object + has/have + been + V3 + by + Subject (Passive Voice)
• Example:
• Disha has arranged things. (Active Voice)
• Things have been arranged by Disha. (Passive Voice)
• Therefore, the​ correct answer is Option 4.

​​Correct sentence: An undigestible criticism has been raised by one group of the club against the manager.

The correct answer is "it was a blessing in disguise."

 

Key Points 

• The expression "it was a blessing in disguise" means that something initially perceived as a negative or unfortunate event turns out to have positive, beneficial, or advantageous consequences in the long run. (किसी चीज़ को शुरू में नकारात्मक या दुर्भाग्यपूर्ण घटना के रूप में देखा जाता है, लेकिन लंबे समय में उसके सकारात्मक, लाभदायक या लाभकारी परिणाम सामने आते हैं)
• Example: After losing my job, I thought it was a disaster, but looking back, it was a blessing in disguise.
• In other words, the true value or positive aspect of the situation becomes apparent only after some time has passed.
• Therefore, the​ correct answer is Option 4.​

The correct answer is "BCDA."

 

Key Points 

 

• The sequence is arranged to provide a logical and chronological flow of information about the Olympic Games. Here's the reasoning for the sequence:
• Sentence B: It introduces the Olympic Games, mentioning its origin in ancient Greece and its revival in the late 19^th century. This sets the historical context.
• Sentence C: It introduces a historical aspect by mentioning that before the 1970s, the Games were limited to amateur competitors. This provides additional context about the nature of the Games.
• Sentence D: It concludes the paragraph by stating that currently, the Games are open to all, including top professional athletes, showing a shift in the rules and inclusivity over time.
• Sentence A: It follows up by stating that the Olympic Games are now considered the world's foremost sports competition, establishing their significance.
• Therefore, the​ correct answer is Option 2.
• Correct sequence:

B. Olympic Games is an athletic festival that originated in ancient Greece and was revived in the late 19^th century.

C. Before the 1970s, the Games were officially limited to competitors with amateur status, but in the 1980s many events were opened to professional athletes.

D. Currently, the Games are open to all, even the top professional athletes in basketball and football (soccer).

A. The Olympic Games have come to be regarded as the world's foremost sports competition.

The correct answer is "Obssess."

 

Key Points 

• The incorrectly spelt word is "Obssess."
• The correct spelling is "Obsess."
• It means to completely fill your mind so that you cannot think of anything else. (किसी बात को दिमाग़ में ऐसे भर लेना कि कुछ और न सूझे, किसी बात से मन का पूर्णतया आविष्‍ट या ग्रस्‍त हो जाना)
• Example: He became obsessed with getting his revenge.
• Therefore, the​ correct answer is Option 3.

Additional Information

• Weave: to make cloth, etc. by passing threads under and over a set of threads that is fixed to a frame loom. ((कपड़ा आदि) बुनना, बुनाई करना)
• Heave: to lift, pull or throw somebody/something heavy with one big effort. (एक ही सफल प्रयास किसी भारी व्‍यक्ति या वस्‍तु को ऊपर उठाना, खींचना या फेंकना)
• Sieve: to put a liquid or powder through a sieve. (छानना (छलनी से))

The correct answer is "Sincerely."

Key Points

• The word "Earnestly" means with sincere and intense conviction; seriously. (दृढ़निश्‍चय के साथ)
• Example: He stood with his hands on his hips, his head tilted slightly as he listened earnestly to questions.
• The synonym of "Earnestly" is "Sincerely."
• The word "Sincerely" means in a sincere or genuine way. (निष्‍ठापूर्वक, सच्‍चाई से)
• Example: I am sincerely grateful to you for all your help.
• Therefore, the​ correct answer is Option 4.

Additional Information

• Wordily: in a way that contains a lot of words, or too many words. (एक तरह से जिसमें बहुत सारे शब्द हों, या बहुत सारे शब्द हों)
• Ambiguously: so as to be open to more than one interpretation. (अनेक अर्थ प्रकट करते हुए)
• Verbosely: in a way that uses too many words. (एक तरह से जो बहुत सारे शब्दों का उपयोग करता है)

The correct answer is "There was not enough food in the beggar's house."

 

 Key Points

• The words "enouf, enauf and enoufh" are incorrectly spelt.
• The correct spelling is "enough."
• It means as much or as many of something as necessary. (पर्याप्त, काफ़ी, जितना (मात्रा या संख्‍या) आवश्‍यक हो उतना)
• ​Example: We’ve saved enough money to buy a computer.
• Therefore, the​ correct answer is Option 2.

The correct answer is "Septuagenarian."

Key Points

• The word "Septuagenarian" means a person who is between 70 and 79 years old. (एक व्यक्ति जिसकी आयु 70 से 79 वर्ष के बीच है)
• Example: It is a great relief when you are a septuagenarian and have retired.
• The option that can be used as a one-word substitute for the given group of words is "Septuagenarian."
• Therefore, the​ correct answer is Option 1.

​

Additional Information

• Aged: of the age mentioned. (अमुक आयु का)
• Pensioner: a person who receives a pension, especially the retirement pension. (सेवानिवृत या पदनिवृत व्‍यक्ति)
• Oldie: an older person. (एक वृद्ध व्यक्ति)

Here, the erroneous part is "I play."

 

Key Points  

• The error lies in the part "I play."
• The sentence has a tense agreement error.
• Using "played" instead of "play" is appropriate because we are referring to a past activity ("childhood").
• Therefore, the​ correct answer is Option 3.

Correct sentence: I playe d cricket in my childhood with my sister.

The correct answer is "Declared."

 

Key Points

• The word "Announced" means to make something known publicly and officially. (घोषणा करना, ऐलान करना)
• Example: They announced that our train had been delayed.
• The synonym of "Announced" is "Declared."
• The word "Declared" means to state something publicly and officially or to make something known in a firm, clear way. ((कोई बात) सार्वजनिक और आधिकारिक रूप से घोषित करना, (किसी बात की) घोषणा करना)
• Example: They declared their support for the proposal.
• Therefore, the​ correct answer is Option 2.

 

Additional Information 

• Estrange: cause (someone) to be no longer on friendly terms with someone. ((किसी को) किसी के साथ मित्रतापूर्ण संबंध न रखने का कारण)
• Secret: something that is not or must not be known by other people. (गोपनीय बात (जो दूसरों को न पता हो न पता चले), दूसरों से छिपाने योग्‍य बात)
• Hid: to put or keep somebody/something in a place where he/she/it cannot be seen; to cover something so that it cannot be seen. (व्‍यक्ति या वस्‍तु को ऐसी जगह रखना जहाँ कोई देख न सके, छिपाना; किसी वस्‍तु को ऐसे ढकना कि वह दिखाई न दे, छिपा देना)

The correct answer is "Twisted."

 

Key Points

• The word "Crooked" means not straight or even, bent. (मुड़ा-तुड़ा, टेढ़ा-मेढ़ा)
• Example: That picture is crooked.
• The synonym of "Announced" is "Declared."
• The word "Twisted" means bent so that the original shape is changed or destroyed. (इस प्रकार मोड़ा जाता है कि मूल आकार बदल जाए या नष्ट हो जाए)
• Example: It was a twisted tree trunk.
• Therefore, the​ correct answer is Option 3.

 

Additional Information 

• Admirable: that you admire; excellent. (प्रशंसनीय; श्रेष्‍ठ)
• Taken: something that has been acquired or seized
• Toasted: cook or brown (food, especially bread or cheese) by exposure to a grill, fire, or other source of radiant heat. (ग्रिल, आग, या तेज गर्मी के अन्य स्रोत के संपर्क में आकर (भोजन, विशेष रूप से ब्रेड या पनीर) पकाना या भूरा करना)

The correct answer is "CDBA."

Key Points

• The correct sequence is arranged to provide a logical flow of information about science fiction (SF) and its characteristics.
• Sentence C: It introduces the definition of science fiction, stating that it is a genre that uses scientific premises, often in a fantastical manner in a narrative. This sets the foundation for understanding what science fiction is.
• Sentence D: It follows up by stating that science fiction is highly seeped into the reality of this world. This contrasts the fantastical elements mentioned in the previous sentence with the grounding in reality.
• Sentence B: It concludes the paragraph by introducing the concept of 'cognitive estrangement' and suggesting that it is a necessary means through which science fiction is usually understood. This ties back to the earlier mention of estrangement and provides a key idea for comprehending the genre.
• Sentence A: It expands on the idea of estrangement, explaining that in an SF narrative, some aspects are recognized as being related to the realities of our world, while other elements are estranged from reality, taking us to an unreal world.
• Therefore, the​ correct answer is Option 1.
• Correct sequence:

C. Science Fiction is a genre which manifests in itself the use of scientific premises often in a fantastical manner in a narrative.

D. It is highly seeped into the reality of this world.

B. Therefore, it is often suggested that 'cognitive estrangement' is a necessary means through which the SF is usually understood.

A. We recognise some aspects of an SF narrative with the realities of this world and some elements are estranged from the reality so as to take us to an unreal world.