SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 1) (Previous Year Paper)

The logic followed here is:

• 
  
• 
  

Similarly,

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Hence, 'HYERQPA' is the correct answer.

The Venn diagram that best illustrates the relationship between Sports, Badminton, and Hockey is shown below:

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Both badminton and hockey are name of two different sports.

Hence, 'option 1' is the correct answer.

Given:

F I R _ D F _ _ E D F _ T _ D F I _ E _

Checking all the options:

1. E I S I E U D

F I R E D / F I S E D / F I T E D / F I U E D

Here, the series is completed.

2. E I S I E U E

F I R E D / F I S E D / F I T E D / F I U E E

3. E G S J E U E

F I R E D / F G S E D / F  T E D / F I U E E

4. E H S I E U D

F I R E D / F H S E D / F I T E D / F I U E D

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

The answer figures which is the exact mirror image of the given problem figure when the mirror is held at the right side is shown below:

Hence, 'option 2' is the correct answer.

Here, we use the BODMAS table given below:

Given:

⇒ 14 − 19 + 240 × 16 ÷ 61

As per the given data:

Given:

⇒ 14 − 19 + 240 × 16 ÷ 61

After changing the signs as per the table:

⇒ 14 ×​ 19 - 240 ÷ 16 + 61

Apply BODMAS rule:

⇒ 14 × 19 - 15 + 61

⇒ 266 - 15 + 61

⇒ 327 - 15 = 312

Here, the value of the equation is '312'.

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

Given:

(2, 2, 4)

(1, 6, 6)

(7, 2, ?)

Logic: 'Row wise'

First row → Third no. = [First no. × Second no.]

First row (2, 2, 4) →

⇒ (2 × 2) = 4

Second row (1, 6, 6) →

⇒ (1 × 6) = 6

Similarly, for the third row (7, 2, ?) →

⇒ (7 × 2) = 14

Here, the missing number is '14'.

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

The logic followed here is:

Logic: Richness Intensity.

Here,

Poor : Destitute → Destitute is an extreme form of being Poor.

Similarly,

Rich : Affluent → Affluent is an extreme form of being Rich.

Hence, the correct answer is "Option 2".

The paper when unfolded will appear as shown below:

 

Hence, 'option 2' is the correct answer.

The least possible Venn diagram is:

Conclusions:

I. Some soaps are bottles. → Does not follow (There is no definite relation between soaps and bottles. Hence, false)

II. Some buckets are bottles. → Does not follow (There is no definite relation between buckets and bottles. Hence, false)

III. Some soaps are containers. → Follows (As, All bottles are containers, Some containers are buckets and All buckets are soaps)

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

By using the symbols in the table given below, we can draw the following family tree:

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Clearly, K is father of A.

Hence, 'Father' is the correct answer.

Given:

29 ∶ 111 ∶∶ 72 ∶ ? ∶∶ 36 ∶ 139

Logic: Second no. = [(First no. × 4) - 5]

29 : 111 →

⇒ [(29 × 4) - 5]

⇒ (116 - 5) = 111

36 : 139 →

⇒ [(36 × 4) - 5]

⇒ (144 - 5) = 139

Similarly, for '72 : ?' →

⇒ [(72 × 4) - 5]

⇒ (288 - 5) = 283

Here, '72 : 283' is the correct pair.

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

Here, we use the BODMAS table given below:

Given:

⇒ 3 − 17 + 3 + 16 × 8 = 60

(1) 17 and 8, − and ×

⇒ 3 − 17 + 3 + 16 × 8 = 60

After interchanging the sign and number:

⇒ 3 × 8 + 3 + 16 - 17 = 60

Apply BODMAS rule:

⇒ 24 + 3 + 16 - 17

⇒ 43 - 17

⇒ 26

Here, the equation is not satisfied.

(2) 3 and 17, − and ×

⇒ 3 − 17 + 3 + 16 × 8 = 60

After interchanging the sign and number:

⇒ 17 × 3 + 17 + 16 - 8 = 60

Apply BODMAS rule:

⇒ 51 + 17 + 16 - 8

⇒ 84 - 8

⇒ 76

Here, the equation is not satisfied.

(3) 3 and 16, − and ×

⇒ 3 − 17 + 3 + 16 × 8 = 60

After interchanging the sign and number:

⇒ 16 × 17 + 16 + 3 - 8 = 60

Apply BODMAS rule:

⇒ 272 + 16 + 3 - 8

⇒ 291 - 8

⇒ 283

Here, the equation is not satisfied.

(4) 17 and 16, − and ×

⇒ 3 − 17 + 3 + 16 × 8 = 60

After interchanging the sign and number:

⇒ 3 × 16 + 3 + 17 - 8 = 60

Apply BODMAS rule:

⇒ 48 + 3 + 17 - 8

⇒ 68 - 8 = 60

⇒ 60 = 60

⇒ '3 × 16 + 3 + 17 - 8 = 60'

Here, the equation is satisfied.

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

The logic followed here is:

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Hence, 'TWGK' is the correct answer.

The logic followed here is:

• 
  
• 
  

Similarly,

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Hence, 'BIEG' is the correct answer.

Given:

(121, 81, 2)

(88, 54, 2)

Logic: Third no. = [(First no. ÷ 11) - (Second no. ÷ 9)]

(121, 81, 2) →

⇒ [(121 ÷ 11) - (81 ÷ 9)]

⇒ (11 - 9) = 2

(88, 54, 2) →

⇒ [(88 ÷ 11) - (54 ÷ 9)]

⇒ (8 - 6) = 2

Checking all the given options:

1. (13, 5, 9)

⇒ [(13 ÷ 11) - (5 ÷ 9)]

⇒ (1.18 - 0.55) = 0.625

2. (78, 6, 45)

⇒ [(78 ÷ 11) - (6 ÷ 9)]

⇒ (7.09 - 0.66) = 6.394

3. (31, 56, 98)

⇒ [(31 ÷ 11) - (56 ÷ 9)]

⇒ (2.81 - 6.22) = (-3.41)

4. (77, 18, 5)

⇒ [(77 ÷ 11) - (18 ÷ 9)]

⇒ (7 - 2) = 5

Here, (77, 18, 5) shows a similar relation to the given set of numbers.

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

The logic followed here is:

• 
  
• 
  

Similarly,

• 
  

Hence, 'CPUUMF' is the correct answer.

The logic followed here is:

• 
  
• 
  

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Similarly,

• 
  

Hence, '9116' is the correct answer.

The logic followed in the given figure series is:

From Figure (1) to (2):

The symbol move as shown below and the symbol (=) changes into a new symbol star.

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From Figure (2) to (3):

The symbol move as shown below and the symbol star changes into a new symbol F.

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From Figure (3) to (4):

The symbol move as shown below and the symbol F changes into a new symbol 9.

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

The symbol move as shown below and the symbol 9 changes into a new symbol triangle.

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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:

3. Thankful
4. Thereafter
5. Thistle
6. Thorough
7. Threaten
8. Throat

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

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

The logic followed here is:

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Hence, '510' is the correct answer.

Given:

45 ∶ 15 ∶∶ 20 ∶ 10 ∶∶ 125 ∶ ?

Logic: First no. = [(Second no.)² ÷ 5]

45 : 15 →

⇒ [(15)² ÷ 5]

⇒ (225 ÷ 5) = 45

20 : 10 →

⇒ [(10)2 ÷ 5]

⇒ (100 ÷ 5) = 20

Similarly, for '125 : ?' →

⇒ [(Y)2 ÷ 5] = 125

⇒ (Y)² = (125 × 5)

⇒ (Y)2 = 625

⇒ Y = 25

Here, '125 : 25' is the correct pair.

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

The correct mirror image of the given figure when the mirror is placed at AB is shown below:

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Hence, 'option 2' is the correct answer.

Logic: [(First no.) : {(First no × 2) + 1} : (First no.)³]

Checking all the given options:

1. 2 ∶ 5 ∶ 8 → [(2) : {(2 × 2) + 1} : (2)3] → [(2) : (5) : (2)3] 2. 5 ∶ 10 ∶ 125 →  [(5) : (5 × 2) : (5)3] → [(5) : (10) : (5)3] 3. 12 ∶ 25 ∶ 1728 → [(12) : {(12 × 2) + 1} : (12)3] → [(12) : (25) : (12)3] 4. 3 ∶ 7 ∶ 27 → [(3) : {(3 × 2) + 1} : (3)3] → [(3) : (7) : (3)3]

Here, in (5 : 10 : 125) different logic is followed.

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

The image embedded in given figure is as shown below:

Hence, 'option 2' is the correct answer.

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.

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From Figure (3) to (4):

The symbols are moved as shown below.

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

The symbols are moved as shown below.

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

The correct answer is increase bank rate.

Key Points

• The bank rate is the interest rate at which the central bank lends money to commercial banks.
• When the central bank increases the bank rate, it becomes more expensive for commercial banks to borrow money from the central bank.
• This, in turn, reduces the amount of credit that commercial banks can offer to their customers, thereby discouraging credit in the economy.

Additional Information

• Increasing the Cash Reserve Ratio (CRR) is another tool that the central bank can use to discourage credit.
• CRR is the amount of funds that commercial banks have to keep with the central bank as a percentage of their deposits.
• When the CRR is decreased, banks have more funds available to lend, which can lead to an increase in credit in the economy.
• Buying securities in the open market is a tool that the central bank can use to increase liquidity in the economy.
• When the central bank buys securities, it injects money into the economy, which can lead to an increase in credit.
• Therefore, this option is not suitable for discouraging credit in the economy.
• Reducing the Statutory Liquidity Ratio (SLR) is another tool that the central bank can use to increase the availability of funds for banks to lend.
• SLR is the percentage of deposits that banks have to keep in the form of liquid assets such as cash, gold, or government securities.
• When the SLR is reduced, banks have more funds available to lend, which can lead to an increase in credit in the economy.

The correct answer is the Exercise adult franchise.

Key Points

• The Fundamental Duties are enshrined in Part IV-A of the Constitution and were added by the 42nd Amendment in 1976.
• There are 11 Fundamental Duties listed in Article 51-A, which are non-justiciable in nature, meaning that they cannot be enforced by law.
• The exercise of the adult franchise is not a Fundamental Duty, but rather a Right given to citizens under Article 326 of the Constitution.
• 51(A)(a): Abide by the Constitution, respect its ideals, the National Flag, and the National Anthem.
• 51(A)(b): Cherish and follow ideals from the national struggle for freedom.
• 51(A)(c): Uphold the sovereignty, unity, and integrity of India.
• 51(A)(d): Defend the country and render national service when required.

Additional Information

• Exercise adult franchise refers to the right to vote in elections, which is a key feature of a democratic system.
• Safeguarding public property and abjuring violence is important for maintaining law and order in the country.
• Cherishing and following the noble ideals that inspired the national struggle for freedom is a way of paying homage to the leaders and movements that fought for India's independence.
• Upholding and protecting the sovereignty, unity, and integrity of India is crucial for maintaining national security and preventing any threats to the country's territorial integrity.

The correct answer is Pongal.

Key Points

• The festival with the meaning 'to boil' or 'boiling' in its name is Pongal.
• Pongal is a harvest festival celebrated in the southern Indian state of Tamil Nadu.
• The festival is named after the dish 'Pongal', which is made by boiling rice and lentils together with milk and jaggery.
• Pongal is celebrated for four days and is a time for thanksgiving to the sun god for a bountiful harvest.

Additional Information

• Onam is a harvest festival celebrated in the southern Indian state of Kerala.
• Vamana and the magnanimous daitya ruler Mahabali are remembered on Onam.
• Raja is a festival celebrated in the eastern Indian state of Odisha.
• The festival's second day marks the start of the solar month of Mithuna, which is when the rainy season begins.
• Bihu is a festival celebrated in the northeastern Indian state of Assam.
• Every Bihu falls on a unique day in the agricultural calendar.
• The Bohag Bihu heralds the beginning of the seeding season, the Kati Bihu the end of the paddies' sowing and transplanting, and the Magh Bihu the conclusion of the harvesting season.

The correct answer is to Carry out metabolic reactions in our body**.**

 Key Points

• Vitamins and minerals are essential nutrients that help our body to carry out metabolic reactions.
• These nutrients are required for the proper functioning of enzymes and hormones that regulate various physiological processes in our body.
• They also play a crucial role in maintaining the health of our bones, muscles, and immune system.
• Vitamins and minerals are found in a variety of foods, such as fruits, vegetables, whole grains, dairy products, and lean meats.

Additional Information

• Proper breathing is mainly regulated by the respiratory system, which involves the lungs, bronchi, and trachea..
• Sweating is a natural process of the body that helps to regulate body temperature and remove toxins.
• Fat storage is regulated by various hormones, such as insulin and leptin, that are produced by the endocrine system.

The correct answer is i - c, ii - d, iii - b, iv - a.

Key Points

• The correct match is i - c, ii - d, iii - b, iv - a.
• Electric current is the flow of electric charge while Ampere is the unit to measure the electric current.
• Voltage is the electric potential difference between two points while Volt is the unit to measure the voltage.
• Capacitance is the ability of a body to store an electric charge while Farad is the unit to measure the capacitance.
• Magnetic field is a field that surrounds a magnetic material or a moving electric charge while Tesla is the unit to measure the magnetic field.

Additional Information

• A unit of measurement is a specific amount of a quantity that is used as a benchmark for measuring other quantities of the same kind.
• It can be established and adopted by legislation or agreement.
• It is possible to express any other quantity of that type as a multiple of the measurement unit.
• A length, for instance, is a physical quantity.
• The metric system that is widely used as a benchmark for measurements is the International System of Units (SI).

The correct answer is 8 years.

Key Points

• Emperor Ashoka conquered Kalinga after 8 years of his coronation.
• Ashoka was coronated in 268 BCE and he conquered Kalinga in 261 BCE.
• Kalinga was a powerful kingdom in eastern India and Ashoka's conquest of it was a turning point in his life.
• The brutal war and its aftermath made Ashoka realize the futility of violence and he embraced Buddhism, becoming a champion of peace and non-violence.

Additional Information

• ​India's Kalinga is a historical region.
• Its borders have changed with the territory of its rulers, but generally speaking, it is classified as the eastern coastal region between the Mahanadi and Godavari rivers.
• Presently, the entirety of Odisha and a small portion of northern Andhra Pradesh make up the main territory of Kalinga.
• The Suryavamsa Gajapatis, the Bhoi dynasty, the Paralakhemundi Gangas, and the zamindaris of Ganjam and Vizagapatam were the medieval-age kings who ruled over the Kalinga region.

The correct answer is Article 141.

Key Points

• Article 141 of the Constitution of India states that the law declared by the Supreme Court is binding on all courts within the territory of India.
• This means that all lower courts, including high courts, must follow the rulings and judgments of the Supreme Court.
• The purpose of this provision is to ensure consistency and uniformity in the interpretation and application of laws across the country.

Additional Information

• Article 142 of the Constitution empowers the Supreme Court to pass any order or judgment necessary for doing complete justice in any matter before it.
• Article 143 of the Constitution allows the President to seek the opinion of the Supreme Court on any question of law or fact of public importance.
• Article 144 of the Constitution states that all authorities in India, including the judiciary, must act in aid of the Supreme Court.

The correct answer is Lance Naik Manju.

Key Points

• The first woman soldier skydiver of the Indian Army to have jumped from a height of 10,000 feet is Lance Naik Manju.
• She accomplished this feat in 2019 during the Army Day celebrations in Delhi.
• Lance Naik Manju is a member of the Indian Army's Army Service Corps and is based in Bengaluru.
• This achievement is significant as it breaks gender stereotypes and encourages more women to join the armed forces.

Additional Information

• Lieutenant General Madhuri Kanitkar is the third woman officer in the Indian Army to hold the rank of Lieutenant General.
• She was promoted to this rank in 2019 and is currently serving as the Deputy Chief of Integrated Defence Staff (Medical).
• Lieutenant General Rajshree Ramasethu is also a high-ranking woman officer in the Indian Army.
• She was the first woman officer to be appointed as a Judge Advocate General (JAG) in the Indian Army.
• Air Marshal Arti Sarin is the first woman officer to hold the rank of Air Marshal in the Indian Air Force.
• She retired in 2019 after serving for 37 years.

The correct answer is Uday Shankar.

Key Points

• Uday Shankar is known as the Father of Modern Dance in India for his contributions to the development of modern dance in the country.
• He was a pioneer in incorporating Indian classical dance forms with Western dance styles, creating a unique and innovative style of dance.
• Uday Shankar also established the first Indian dance school, the Uday Shankar India Culture Centre, in Almora, Uttarakhand.
• He is also known for his collaborations with famous artists such as Pablo Picasso and Igor Stravinsky.

Additional Information

• Birju Maharaj is a famous Kathak dancer and choreographer, known for his contributions to the classical dance form.
• He performed Kathak dance as an exponent of the Lucknow "Kalka-Bindadin" Gharana in India.
• Gopi Krishna was a Kathak dancer and choreographer, as well as a spiritual teacher and author.
• He learned Bharatnatyam as well.
• Guru Bipin Singh was a Manipuri dancer and choreographer, known for his contributions to the classical dance form.
• He founded the Manipuri Nartanalaya dance school in Calcutta in 1972 as well as the Govindji Nartanalaya dance school for women in Imphal.

The correct answer is Pt Jasraj.

Key Points

• The minor planet was named "Panditjasraj" after the Indian classical vocalist Pandit Jasraj by the IAU.
• Pandit Jasraj was a renowned Indian classical vocalist belonging to the Mewati Gharana.
• He was born in Haryana in 1930 and passed away in August 2020.

Additional Information

• Indian music director Hariprasad Chaurasia is a classical flautist and bansuri player in the Hindustani classical style.
• In 1984, he was awarded Sangeet Natak Academy.
• Pt Ravi Shankar was an Indian composer and sitarist.
• He was well known for his attempts to bring Indian music to the West and for having influenced popular music in the United States and Great Britain.
• Indian tabla player, composer, percussionist, music producer, and actor in motion pictures is Ustad Zakir Hussain. 
• Padma Shri (1988), Padma Bhushan (2002), and Padma Vibhushan (2023) were given to him.

The correct answer is Dadabhai Naoroji.

Key Points

• Dadabhai Naoroji was the first nationalist leader who gave the theory of the drain of wealth from India to England.
• He was a Parsi intellectual and a social reformer who was also known as the "Grand Old Man of India".
• Naoroji wrote a book in 1867 titled "Poverty and Un-British Rule in India" in which he explained how British colonialism was exploiting India's resources and draining its wealth.
• He estimated that India was losing around 200-300 million pounds annually to Britain due to various economic policies and practices.

Additional Information

• Mahatma Gandhi was a prominent leader in India's freedom struggle who advocated for non-violent civil disobedience and mass movements to achieve independence.
• After taking over as the Indian National Congress's leader in 1921, Gandhi oversaw national campaigns to abolish untouchability, promote women's rights, reduce poverty, foster interethnic and religious harmony, and, most importantly, achieve swaraj, or self-rule.
• RC Dutt was an Indian civil servant, economist, and writer who wrote extensively on India's economic and social conditions during the colonial period.
• He translated the Mahabharata and the Ramayana.
• SN Banerjee was a lawyer and politician who was one of the founders of the Indian National Congress and played a key role in the Swadeshi movement against British goods.
• To unite Muslims and Hindus for political action, Banerjee established the Indian National Association, a nationalist group.
• The theory of drain of wealth became a key concept in India's nationalist discourse and was used to highlight the economic exploitation of India by British colonialism.

The correct answer is Jammu and Kashmir.

Key Points

• The folk dance 'Kud' is from the state of Jammu and Kashmir.
• Khemraj received the Sangeet Natak Akademi award for his contribution to this particular folk dance.
• Kud is a community dance form that is performed during various festivals and occasions.
• The dance is usually performed by men and involves rhythmic movements and footwork.

Additional Information

• Famous folk dance of Haryana includes the Phag Dance, Saang Dance, Chhathi Dance, Khoria Dance, Dhamal Dance, and Daph Dance.
• Famous folk dance of Himachal Pradesh includes Nati, Dangi Folk Dance, Chhanak Chham Dance, Demon Dance, and Kayang.
• Famous folk dance of Punjab includes Bhangra, Giddha, Jhoomer, Malawi and Julli.

The correct answer is Sarai-i-Adl.

Key Points

• During Alauddin Khilji's reign, the cloth market was known as Sarai-i-Adl.
• Sarai-i-Adl was a market established by Alauddin Khilji to regulate the trade of cloth and prevent fraudulent practices.
• The market was located in Delhi and was known for its strict regulations and fair prices.

Additional Information

• Mandi is a term used for a market or a place where goods are sold.
• Every vendor had an account with the Market division.
• The Sultan received reports from the munhiyans, a clandestine group of spies, on how these markets were operating.
• During Alauddin Khilji's reign, the entire grain market was referred to as Shahna I Mandi.
• Alauddin had appointed Malik Qabul, who used to ride his horse and a few slaves to the marketplaces, to oversee all of the grain markets.

The correct answer is Madras and Bombay.

Key Points

• The Ryotwari Settlement was introduced in Madras and Bombay provinces during the British rule in India.
• Under this system, cultivators or farmers had to pay annual taxes directly to the government, unlike the Zamindari system where they paid taxes to intermediaries or landlords.
• The Ryotwari system was considered more beneficial for small and marginal farmers as they had direct access to the government and could negotiate the amount of taxes based on their produce and income.
• The system also helped in increasing agricultural productivity and revenue for the government.
• However, the system was criticized for being exploitative towards farmers in some cases, especially during famines and crop failures.

Additional Information

• The Central province was mainly governed under the Zamindari system, where intermediaries collected taxes from farmers and paid a fixed amount to the government.
• Assam and Bengal provinces had a mix of Zamindari and Mahalwari systems, where taxes were collected either by intermediaries or directly from farmers through village-level committees.
• Punjab province had a predominantly Mahalwari system, where large landlords or Zamindars collected taxes from farmers and paid a fixed amount to the government.

The correct answer is The Darjeeling and Sikkim Himalayas.

Key Points

• Kanchenjunga, the highest mountain peak in the Himalayas, lies in the Darjeeling and Sikkim Himalayas.
• The Darjeeling and Sikkim Himalayas are located in the eastern part of the Himalayan range.
• Kanchenjunga is the third highest mountain peak in the world with an elevation of 8,586 meters (28,169 feet).
• The Kanchenjunga mountain range is located on the border between India and Nepal.

Additional Information

• The Arunachal Himalayas are located in the easternmost part of the Himalayan range and are home to many peaks over 7,000 meters in height.
• The Arunachal Himalayas stretch from the Diphu Pass in the east to the eastern Himalayas of Bhutan.
• The Kashmir Himalayas are located in the northernmost part of the Himalayan range and are known for their scenic beauty and ski resorts.
• The ranges that comprise this area are the Pir Panjal, Zanskar, Ladakh, and Karakoram.
• The Uttarakhand Himalayas are located in the central part of the Himalayan range and are home to many famous peaks, including Nanda Devi and Kamet.

The correct answer is 24 beds.

Key Points

• District hospitals have on average 24 beds per lakh population.
• The report released by NITI Aayog in September 2021 highlights the best practices in the performance of district hospitals across India.
• The report aims to provide insights into the functioning of district hospitals and suggests ways to improve their performance.
• The report also emphasizes the need to strengthen the infrastructure and resources of district hospitals to provide quality healthcare to the people.

Additional Information

• The highest-ranking think tank for public policy within the Indian government is called NITI Aayog.
• It was replaced by the NDA government in 2015 as a top-down model replaced by the Planning Commission.
• The Lieutenant Governors of each UT, the Chief Ministers of Delhi and Puducherry, all state chief ministers, and a vice-chairman chosen by the prime minister make up the NITI Aayog council.
• Its chairperson is Narendra Modi.

It was founded on 1 January 2015.

The correct answer is 2015.

Key Points

• The 'Pradhan Mantri Kaushal Vikas Yojana' was launched in the year 2015.
• This scheme was launched by the Government of India to provide skill training to the youth of the country and make them employable.
• The main objective of this scheme is to create a workforce that is skilled and can contribute to the development of the nation.
• The scheme aims to train over 40 crore people in India by 2022.

Additional Information

• The PMKVY scheme's objectives are to improve the employability and working efficiency of potential and current daily wage earners by offering them high-quality training together with monetary incentives and benefits.
• The ₹8,000 average prize amount per participant has remained constant.
• The plan would provide recognition to wage earners who already possess a standard level of skill; the typical reward amount for these individuals is between ₹2000 and ₹2500.
• The government has approved an expenditure of ₹120 billion for this project.
• The program aims to train one crore young Indians between 2016 and 2023.
• Out of the 18 lakh candidates that enlisted for the scheme, 17.93 lakh had received training as of July 18, 2016.

The correct answer is Qatar.

Key Points

• Qatar is the host country for the FIFA World Cup 2022.
• The 22^nd FIFA World Cup, an international football competition for national teams, was held in 2022 and was overseen by FIFA.
• After a 3-3 draw after extra time, Argentina defeated the defending champion France 4-2 on penalties to win the championship.
• The Golden Ball went to Argentine captain Lionel Messi, who was chosen as the greatest player of the competition.

Additional Information

• Japan has hosted the FIFA World Cup twice, in 2002 with South Korea and in 2012 with Brazil for the FIFA Club World Cup.
• France has hosted the FIFA World Cup once in 1998, where they won the tournament on home soil.
• USA hosted the FIFA World Cup once in 1994, where they set a record for the highest average attendance in the history of the tournament.
• The FIFA Women's World Cup, which took place in 2023, was its ninth iteration.
• Australia and New Zealand co-hosted the competition, which ran from July 20 to August 20, 2023.
• After defeating England, the defending European champions, 1-0 in the championship match, Spain was declared the victor.

The correct answer is John Dalton.

Key Points

• John Dalton discovered that each chemical element is made up of a unique type of atom and that atoms differ by their mass in the early 1800s.
• Dalton proposed the atomic theory which explained the behavior of atoms and their interactions with other atoms.
• Dalton's atomic theory also stated that atoms cannot be created or destroyed in a chemical reaction and that compounds are formed by the combination of atoms in fixed ratios.
• Dalton's work laid the foundation for modern atomic theory and the periodic table of elements.

Additional Information

• Antoine Lavoisier is known as the father of modern chemistry.
• He made significant contributions to the understanding of combustion and the law of conservation of mass.
• Amedeo Avogadro proposed Avogadro's law.
• The law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
• Robert Boyle is known for Boyle's law.
• The law states that the volume of a gas is inversely proportional to its pressure at a constant temperature.

The correct answer is i - a, ii - b, iii - c, iv - d.

Key Points

• Addison's disease is caused due to adrenal gland disorder.
• Hashimoto's disease is caused due to thyroid gland disorder.
• Acromegaly is caused due to growth hormone disorder.
• SIADH is caused due to vasopressin disorder.

Additional Information

• Addison's disease is a rare disorder that occurs when adrenal glands do not produce enough hormones, causing fatigue, weight loss, and low blood pressure.
• Hashimoto's disease is an autoimmune disorder that affects the thyroid gland, causing an underactive thyroid gland, leading to weight gain, fatigue, and depression.
• Acromegaly is a hormonal disorder that occurs when the pituitary gland produces too much growth hormone, causing enlargement of hands, feet, and facial features.
• SIADH is a disorder that occurs when the body produces too much vasopressin hormone, leading to fluid retention and low sodium levels in the blood.
• Hormones and glands play a crucial role in regulating various bodily functions, and any disorder related to them can cause significant health issues.

The correct answer is Adarsh Kumar Goel.

Key Points

• Adarsh Kumar Goel was appointed as the Chairman of the National Green Tribunal (NGT) in July 2018.
• He is a former Supreme Court Judge and has also served as the Chief Justice of the Odisha High Court and the Gauhati High Court.
• Since taking office, Goel has ensured that all benches are operational by using video conferencing to hear cases from the benches in Bhopal, Chennai, Kolkata, and Pune.

Additional Information

• Former Chief Justice of India Uday Umesh Lalit is an Indian lawyer and former Supreme Court judge. 
• He worked as a senior lawyer at the Supreme Court before being elevated to the position of judge.
• Judge Anoop Kumar Mendiratta hails from India.
• He is a judge of the Delhi High Court at the moment. He was the Law Secretary of India in the past.
• Judge Vikram Nath sits on the Indian Supreme Court.
• He was a judge on the Allahabad High Court as well as the chief justice of the Gujarat High Court.

The correct answer is Yash Dhull.

Key Points

• Yash Dhull was the captain of the U-19 Indian cricket team in World Cup 2022.
• He led the team to the quarterfinals of the tournament.
• Yash Dhull is a promising young cricketer from Haryana who has been making waves in the domestic cricket.
• He is a right-handed middle-order batsman and a handy off-spinner.

Additional Information

• Vasu Vats, and Manav Parakh are not known names in Indian cricket and have not represented the country at any level.
• Yash Dhull was selected as the captain of the U-19 Indian cricket team in the World Cup 2022 based on his leadership skills and cricketing abilities.
• The U-19 Indian cricket team in World Cup 2022 had some talented players like Ravi Bishnoi, Divyansh Saxena, and Arjun Azad who impressed with their performances.
• The group leads all Under-19 national teams in ODI wins % and has won five Under-19 World Cups.
• The group has placed third three times and won the Under-19 World Cup five times.

The correct answer is Halite.

 Key Points

• Halite is a sedimentary mineral that forms in arid climates where seawater evaporates, leaving behind salt deposits.
• Halite is also known as rock salt and is commonly used as a seasoning or preservative in food.
• Halite forms isometric crystals.

Additional Information

• Zeolite is a group of minerals that are commonly used as catalysts, adsorbents, and ion exchangers in various industries.
• They are mostly made of silicon, aluminum, and oxygen.
• Calcite is a mineral that is used in the production of cement, lime, and as a building stone.
• Based on a comparison of scratch hardness, calcite is classified as having a hardness of 3 on the Mohs mineral hardness scale.
• Pyrite is a mineral that is commonly known as fool's gold and is often mistaken for gold due to its metallic luster, but it has no economic value.
• The most common sulfide mineral is pyrite.

The correct answer is All of a, b, and c.

Key Points

• Cotton, jute, and iron and steel were all modern industries that were in operation in India during British rule.
• Cotton was one of the most important industries during this time, with India being one of the largest cotton producers in the world.
• The British established cotton mills in India to process the raw cotton and export the finished products back to Britain.
• Jute was another important industry, with India being the largest producer of jute in the world.
• Jute mills were established in Bengal to process the raw jute and export the finished products.
• Iron and steel production also began to develop in India during the British rule.
• The Tata Iron and Steel Company was established in 1907 and became one of the largest steel producers in the world.

Additional Information

• Other modern industries that developed during British time included tea production, mining, and railway construction.
• By building the third-largest railroad network in the world, the British brought India together and made it possible for it to develop a modern economy.
• India was able to modernize thanks to the construction of telephone and telegraph lines, road networks, irrigation systems, dams, bridges, and canals.
• The founding of the cotton textile industry in Bombay in 1854 marked the beginning of India's modern industrial sector in an organized manner.

The correct answer is Haldia.

Key Points

• Haldia port is situated on the east coast of India, in the state of West Bengal, and not on the west coast.
• Mangaluru port is situated on the west coast of India, in the state of Karnataka.
• Kandla Port is situated on the west coast of India, in the state of Gujarat.
• Marmagao port is situated on the west coast of India, in the state of Goa.

Additional Information

• The west coast of India is a major hub for maritime trade and transportation, with several important ports located along its coastline.
• These ports serve as gateways for the movement of goods and commodities between India and other countries.
• Mangaluru port is a major port in Karnataka, handling a variety of cargo such as crude oil, petroleum products, coal, fertilizers, and timber.
• Kandla Port is one of the largest ports in India and is known for its container terminals, dry docks, and liquid cargo handling facilities.
• Marmagao port is a natural harbor located in Goa and is primarily used for the export of iron ore, manganese ore, and bauxite.
• Haldia port, on the other hand, is situated on the east coast of India and is primarily used for the handling of bulk cargo such as coal, iron ore, and petroleum products.

Formula used:

a² - b² = (a + b)(a - b)

Calculation

⇒ $\rm\frac{p^2-(q-r)^2}{(p+r)^2-q^2}+\frac{q^2-(p-r)^2}{(p+q)^2-r^2}+\frac{r^2-(p-q)^2}{(q+r)^2-p^2}$

⇒ [(p + q - r)(p - q + r)]/[(p + q + r)(p - q + r)] + [(p + q - r)(q - p + r)]/[(p + q + r)(p + q - r)] + [(p - q + r)(q  -p + r)]/[(p + q + r)(q - p + r)]

⇒ [(p + q - r)]/[(p + q + r)] + [q - p + r)]/[(p + q + r)] + [(p - q + r)]/[(p + q + r)]

⇒ [(p + q - r)]/[(p + q + r)] + [q - p + r)]/[(p + q + r)] + [(p - q + r)]/[(p + q + r)]

⇒ (p + q + r)/(p + q + r)

⇒ 1.

The value is 1.

Shortcut Trick

Let put p = q = r = 1

So,

$\rm\frac{p^2-(q-r)^2}{(p+r)^2-q^2}+\frac{q^2-(p-r)^2}{(p+q)^2-r^2}+\frac{r^2-(p-q)^2}{(q+r)^2-p^2}$

⇒ $\rm\frac{1^2-(1-1)^2}{(1+1)^2-1^2}+\frac{1^2-(1-1)^2}{(1+1)^2-1^2}+\frac{1^2-(1-1)^2}{(1+1)^2-1^2}$

⇒ $\rm\frac{1-0}{(4-1)}+\frac{1-0}{(4-1)}+\frac{1-0}{(4-1)}$

⇒ 1/3 + 1/3 + 1/3 = 1

Hence, The value is 1.

Given:

Marked price = 20% above the cost price

discount = 15%

Formula used:

Profit % = (Profit / Cost Price) x 100

Profit = SP - CP

Selling price = [1 - Discount% / 100] x MP

Solution:

Let the CP be 100.

Marked price = 100 + 20% of 100

= 120

Selling price = 120 * (100 - 15)%

= 102

Profit = 102 - 100

= 2

Profit % = (2 / 100) x 100

Hence, the Profit % is 2%.

Given:

Internal Diameter = Outer radius

Let internal radius = r, outer radius = R, and h = height of pipe

so

2r = R

formula used:-

Volume of cylinder = π(R2 - r2)h

and

Water in pipe = Internal base area × h

Calculation:

According to the question,

Water in pipe = 88/7

πr² × h = 88/7

⇒ 22/7 × r² × 1 = 88/7

⇒ r = 2 m

so

R = 2 × 2 m = 4m

and

Material Used = Volume of Pipe

Material Used = π(R² - r²)h

⇒ 22/7 × (4² - 2²) × 1

⇒ 37.7 m³

Hence option 1 is the correct answer.

GIVEN:

A boat can cover 120 km upstream and back in a total of 30 hours.

A boat can cover 25 km upstream and 40 km downstream in a total of 7 hours.

FORMULA USED:

Distance = Speed × Time 

Speed in upstream = Speed of boat in still water -  Speed in current water

Speed in downstream = Speed of  boat in still water + Speed in current water 

CALCULATION:

Let the speed of the boat in still water be x km/h and the speed of the boat in current water be y km/h 

Speed in downstream = x + y , Speed in upstream = x - y 

Now, Distance/Speed = Time 

⇒ 120/(x +y) + 120/(x -y) = 30 .........(1)

Also,

⇒ 40/(x +y) + 25/(x -y) = 7 ...........(2)

Now, on multiplying eq(2) by 3 and subtracting eq(1) it from  we get

⇒ 120/(x +y) + 120/(x -y) - 120/(x +y) - 75/(x -y) = 30 - 21

⇒ 45/( x -y) = 9

⇒( x -y) = 5  ..........eq(3)

Putting eq(3) in eq(1):

⇒ 120/(x +y) + 120/5 = 30 

⇒ 120/(x +y) = 30 - 24

⇒ (x +y) = 20  .......eq(4)

Solving both eq(3) and eq(4), we get:

⇒ x = 12.5

Distance the boat cover in 16 hours in still water = 12.5 × 16

⇒ 200 km.

The distance the boat cover in 16 hours in still water is 200km.

Given:

The ratio of length and breadth of a rectangle = 3 : 2

Formula used:

if A is the length and B is the breadth of the rectangle, then

Area of rectangle = A × B

Perimeter of rectangle = 2(A + B)

Calculation:

let length and breadth be 3x and 2x respectively

Now, According to the question

⇒ 3x × 2x = 150

⇒ 6x² = 150

⇒ x² = 25

⇒ x = 5

length = 3 × 5 = 15 cm

breadth =2 × 5 = 10 cm

perimeter of rectangle = 2(15 + 10)

perimeter of rectangle = 50 cm

∴The perimeter of the rectangle is 50 cm.

Given: 

2cotθ = 3 

Formula used: 

Sinθ = P/H 

Cosθ = B/H 

Tanθ = P/B 

Cotθ = B/P 

H2 = P2 + B2

where P = Perpendicular 

B = Base 

H = Height 

Calculation: 

2cotθ = 3 

⇒ cotθ = 3/2 

on comparing with (Cotθ = B/P), we get 

⇒ B = 3

⇒ P = 2 

According to Pythagorean theorem

⇒ H² = P² + B²

⇒ H2 = 22 + 32

⇒ H = √13 

⇒ Sinθ = 2/√13  

⇒ Cosθ = 3/√13  

⇒ Tanθ = 2/3 

Putting all the values in the given equation:

$\frac{\sqrt{13} \sin \theta-3 \tan \theta}{3 \tan \theta+\sqrt{13} \cos \theta}$= (√13 * 2/√13  - 3 *  2/3 )/ (3 *  2/3 + √13 * 3/√13)

⇒ (2 - 2)/(2 + 3)

⇒ 0

The value of the expression is 0.

Concept used:

The sum of variables/No. of variables = Average of variables

Calculation

The number of girls in the colleges C = 20% of 2500

⇒ 500

The number of girls in the colleges E = 26% of 2500

⇒ 650

The average number of girls in colleges C and E = (500 + 650)/2

⇒ 575

The average number of girls in colleges C and E is 575.

Given

2 + cos 49° cos 41° − sin 49° sin 41°

Concept used:

If A +B = 90º, then Sin(90 - A) = Cos B and vice versa.

Calculation

2 + cos 49° cos 41° − sin 49° sin 41°

⇒ 2 + cos(90 – 41) cos41 – sin(90 – 41).sin41

⇒ 2 + sin41.cos41 – cos41.sin41

⇒ 2 + 0

⇒ 2

The value of the expression is 2.

Calculation

Let the number of students in senior school be a.

The total amount charged from students of junior school = 325 × 80

⇒ 26000

The total amount charged from students of senior  school = 400 × a

⇒ 400a

The total amount charged from both the schools = (a + 80) × 352

⇒ (a + 80) × 352 = 2600 + 400a

⇒ 400a - 352a = 28160 - 26000

⇒ 48a = 2160 

⇒ a = 45.

The number of students from the senior school who went on the excursion is 45.

Shortcut Trick

Shortcut Trick

Relative speed in same direction = 20 − 17 = 3 km/h.

Convert relative speed to m/min = 3 × (1000/60) = 50 m/min.

Distance reduced in 8 minutes = 50 × 8 = 400 m.

Remaining distance = 500 − 400 = 100 m.

∴ The correct answer is 100 m.

Alternate Method

Policeman (P) 20 km/h

Thief (T) 17 km/h

Initial Gap = 500 m

Relative Motion Diagram

Given:

Initial distance = 500 m

Speed of Policeman (S_p) = 20 km/h

Speed of Thief (S_t) = 17 km/h

Time (t) = 8 minutes

Formula used: Distance = Relative Speed × Time

Relative speed (same direction) = S_p − S_t

⇒ Relative speed = 20 − 17 = 3 km/h

⇒ Speed in m/min = (3 × 1000) ÷ 60 = 50 m/min

⇒ Distance covered in 8 minutes = 50 × 8 = 400 m

⇒ Distance between them after 8 minutes = Initial distance − Relative distance covered

⇒ Distance = 500 − 400 = 100 m

∴ The correct answer is 100 m.

Additional Information

Relative Speed Concept

When two objects move in the same direction, relative speed is the difference (S₁ − S₂). In opposite directions, it is the sum (S₁ + S₂).

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert km/h to m/min, multiply by 1000/60 or 50/3.

Catching Time

Time to catch = Initial Distance ÷ Relative Speed. The distance covered by policeman until catching = S_p × Catching Time.

Given:

Chord = 40cm 

Distance from centre to chord = 21 cm

Concept:

The perpendicular drawn from the centre of the chord bisects the chord in two equal parts. 

Pythagoras Theorem:

OA² = OD² + AD²

Calculation:

Let AB be the chord of length 40 cm. 

⇒ OD be the perpendicular distance 

⇒ AO be the radius of the circle 

OA2 = OD2 + AD2

⇒ OA2 = 212 + (40/2)²

⇒ OA2 = 441 + 400 

⇒ OA2= 841

OA = √841

OA = 29

The radius (in cm) of the circle is 29.

Given:

A can do the work in 10 days

B can do the work in 15 days

C can do the work in 20 days

Formula used:

Work done = Time taken × Efficiency

Time taken ∝ 1/Efficiency

Calculation:

1st day work by A = 1/10

2nd day work by B = 1/15

3rd day work by  C = 1/20

Total work completed in 3 days

⇒ 1/10 + 1/15 + 1/20

⇒ (6 + 4 + 3)/60 = 13/60

Time taken to complete the work

⇒ 60/13

⇒ 4(8/13)

They finish the same work in 4(8/13) days.

 

Work done together in 1 day is:

⇒ 6 + 4 + 3 = 13

Total time required to complete the work ⇒ 60/13

⇒ $4\frac{8}{13}$ days

Shortcut Trick

Difference in percentage = 5% profit − (−5% loss) = 10%

Difference in selling price = Rs. 300

So, 10% of Cost Price = Rs. 300 ⇒ 1% = Rs. 30

Original Selling Price = 95% of Cost Price

Original Selling Price = 95 × 30 = Rs. 2,850

∴ The correct answer is Rs. 2,850.

Alternate Method

Given:

Loss percentage in the first case = 5%

Profit percentage in the second case = 5%

Difference in selling price = Rs. 300

Formula Used:

Selling Price at loss = CP × (100 − Loss%)/100

Selling Price at profit = CP × (100 + Profit%)/100

Total Difference = Rs. 300 (10%)

Original SP Cost Price New SP

95% 100% 105%

5% Loss

5% Profit

Calculations:

⇒ Let the Cost Price (CP) of the watch be 100x.

⇒ Original Selling Price (SP₁) = 100x − 5% of 100x = 95x

⇒ New Selling Price (SP₂) = 100x + 5% of 100x = 105x

⇒ Difference in Selling Price = SP₂ − SP₁

⇒ 105x − 95x = 300

⇒ 10x = 300

⇒ x = 30

⇒ Original Selling Price = 95x = 95 × 30 = Rs. 2,850

∴ The correct answer is Rs. 2,850.

Additional Information

Cost Price (CP) and Selling Price (SP)

Cost Price is the amount paid to purchase an article. Selling Price is the price at which the article is sold. Profit or loss is always calculated on the Cost Price unless stated otherwise.

Marked Price (MP)

It is the price on the label of an article. Discount is always offered on the Marked Price. Formula: SP = MP × (100 − Discount%)/100.

Successive Discounts

If two successive discounts of a% and b% are given, the effective net discount is given by the formula (a + b − ab/100)%.

Concept used:

a^m * aⁿ = a^m+n

Calculation

$\dfrac{4^{a + 4}-5 × 4^{a + 2}}{15×4^a-2^2×4^a}$

⇒ (4^a × 4⁴ - 5 × 4^a × 4²)/(15 × 4^a - 2² × 4a)

⇒ 4a (44 - 5 × 42)/4a  (15  - 22)

⇒ 4a(256 - 80)/4a(11)

⇒ 176/11 = 16

The value of the expression is 16.

Given :

720 ÷ 8 + 915 ÷ 15 − m + 32 × 5 = 1104 ÷ 16 × 111 ÷ 37

BODMAS Rule:

Calculation :

720 ÷ 8 + 915 ÷ 15 − m + 32 × 5 = 1104 ÷ 16 × 111 ÷ 37

⇒ 90 + 61 - m + 160 =  69 × 3

⇒ 151 - m + 160 =  207

⇒ m = 311 - 207

⇒ 104

∴ The answer is 104.

Shortcut Trick

Efficiency ratio of P : Q : R = 1 : 2 : 3 (since time taken by P is 2× and 3× respectively).

Total units of work = Combined efficiency × Total time = (1 + 2 + 3) × 2 = 12 units.

Time taken by Q alone = Total work ÷ Efficiency of Q = 12 ÷ 2 = 6 days.

∴ The correct answer is 6 days.

Alternate Method

Given:

Time for P = 2 × Time for Q = 3 × Time for R

Combined time for P, Q, and R = 2 days

Formula Used:

Efficiency = 1 ÷ Time | Total Work = Efficiency × Time

Calculations:

⇒ Let Efficiency of P = 1 unit/day

⇒ Efficiency of Q = 2 units/day (as P takes twice as long as Q)

⇒ Efficiency of R = 3 units/day (as P takes three times as long as R)

⇒ Combined Efficiency = 1 + 2 + 3 = 6 units/day

⇒ Total work = Combined Efficiency × Combined Time = 6 × 2 = 12 units

⇒ Time taken by Q = Total work ÷ Efficiency of Q = 12 ÷ 2 = 6 days

∴ The correct answer is 6 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the Time taken. If a person takes more time, their efficiency is lower.

Total Work Calculation

Total work can be calculated by finding the LCM of individual times or by multiplying the combined efficiency with the total days taken.

Work and Wages

When people work together, wages are distributed in the ratio of the work done by each person, which is the ratio of their efficiencies if they work for the same duration.

Shortcut Trick

For an equilateral triangle of side a, the circumradius (R) is given by the direct formula:

R = a ÷ √3

Given, side a = 12 cm.

R = 12 ÷ √3 = (4 × 3) ÷ √3 = 4√3 cm.

∴ The correct answer is 4√3 cm.

Alternate Method

Given:

Side of the equilateral triangle (a) = 12 cm

Formula Used:

Circumradius of an equilateral triangle (R) = a ÷ √3

Area of triangle (A) = (√3 ÷ 4) × a²

Circumradius (R) = (a × b × c) ÷ (4 × Area)

Calculations:

Using the standard circumradius formula for any triangle:

⇒ Area of the equilateral triangle = (√3 ÷ 4) × 12²

⇒ Area = (√3 ÷ 4) × 144 = 36√3 cm²

⇒ Circumradius (R) = (12 × 12 × 12) ÷ (4 × 36√3)

⇒ R = 1728 ÷ 144√3

⇒ R = 12 ÷ √3

⇒ R = (12 × √3) ÷ (√3 × √3)

⇒ R = 12√3 ÷ 3 = 4√3 cm

Option Analysis:

Option (1) 8√3 cm: This is incorrect as it is double the actual circumradius (equal to the diameter of the circumcircle).

Option (2) 2√3 cm: This is incorrect as it represents the inradius (r = a ÷ 2√3 = 12 ÷ 2√3 = 2√3 cm) of the triangle, not the circumradius.

Option (3) 6√3 cm: This is incorrect as it represents the height of the equilateral triangle (h = (√3 ÷ 2) × a = 6√3 cm), not the circumradius.

Option (4) 4√3 cm: This is the correct circumradius calculated using the formula R = a ÷ √3.

∴ The correct answer is 4√3 cm.

Additional Information

Inradius of an Equilateral Triangle

The inradius (r) is the radius of the incircle and is given by the formula: r = a ÷ 2√3. For a side of 12 cm, r = 2√3 cm.

Relation between Circumradius and Inradius

For any equilateral triangle, the circumradius (R) is always twice the inradius (r), i.e., R = 2 × r.

Height of an Equilateral Triangle

The height (h) of an equilateral triangle is given by h = (√3 ÷ 2) × a. It is also the sum of the circumradius and the inradius (h = R + r).

Given :

22 − [9 − {6 − (10 − 4 + 3)}] ÷ 2 × 3

BODMAS Rule:

Calculation :

22 − [9 − (6 − (10 − 4 + 3)}] ÷ 2 × 3

⇒ 22 - [9 - {6 - (13 - 4)}] ÷ 2 × 3

⇒ 22 - [9 - {6 - 9}] ÷ 2 × 3

⇒ 22 - [9 - {-3}] ÷ 2 × 3

⇒ 22 - [9 + 3] ÷ 2 × 3

⇒ 22 - [12] ÷ 2 × 3

⇒22 - 6 × 3

⇒ 22 - 18

⇒ 4

∴ The answer is 4.

Shortcut Trick

Relative Speed = 8 − 6 = 2 km/h.

Thief distance in 10 mins = 6 × (10/60) = 1 km.

Time to catch = Distance / Relative Speed = 1 / 2 = 0.5 hours.

Catching Distance = Speed of Policeman × Time = 8 × 0.5 = 4 km.

∴ The correct answer is 4 km.

Alternate Method

Given: Speed of Policeman (V_p) = 8 km/h, Speed of Thief (V_t) = 6 km/h, Time lag = 10 minutes.

Formula: Distance = Speed × Time

⇒ Initial distance lead by thief = 6 × (10 / 60) km = 1 km.

⇒ Relative Speed (same direction) = 8 − 6 = 2 km/h.

⇒ Time taken by policeman to catch thief = Distance / Relative Speed = 1 / 2 = 0.5 hours.

⇒ Distance covered by policeman = Speed × Time = 8 × 0.5 = 4 km.

∴ The correct answer is 4 km.

Additional Information

Relative Speed

When two objects move in the same direction, relative speed is (u − v). When moving in opposite directions, it is (u + v).

Time to Catch

Time = (Initial distance between them) ÷ (Relative Speed).

Proportionality Rule

If time is constant, Distance is directly proportional to Speed. Ratio of distances = Ratio of speeds.

Given

a = 101, b = 102 and c = 103

Formula used

1/2[(a - b)² + (b - c)² + (c - a)²] = a2 + b2 + c2 − ab − bc − ca

Calculation

⇒ a2 + b2 + c2 − ab − bc − ca =  1/2[(a - b)2 + (b - c)2 + (c - a)2]

 ⇒ a2 + b2 + c2 − ab − bc − ca =  1/2[(101 - 102)2 + (102 - 103)2 + (103 - 101)2]

 ⇒ a2 + b2 + c2 − ab − bc − ca =  1/2[12 + 12 + 22]

 ⇒ a2 + b2 + c2 − ab − bc − ca =  1/2[6]

 ⇒ a2 + b2 + c2 − ab − bc − ca = 3

The value is 3.

Calculation

The maximum difference is in the number of students of classes 10 and 7 = 68 - 44

= 24

The number of students in class 7 = 68

⇒ 24/68 × 100

⇒ 35.29%

The maximum difference is 35.29% of the number of students in Class 7.

Given:

Time = 12 years

The sum becomes four times of itself

Formula used:

Simple interest = (P × R × T)/100

Where P → Principal

T → Time

R → Rate

Calculation:

Let the principal be 'x'.

So, Amount = 4x

Simple interest = 3x

Simple interest = (P × R × T)/100

⇒ 3x = (x × R × 12)/100

⇒ R = (3 × 100)/12

⇒ R = 25%

The annual rate of interest is 25%.

Given

Kriti paid an EMI, which was 22% of her monthly salary

She spent the remaining salary on shopping of groceries and clothes in the ratio 7 ∶ 5.

She spent Rs. 18,200 on shopping of clothes.

Formula used:

Income = expenditure + savings

Calculation

Let the income be x.

The amount given to Emi = 22x/100

= 11x/50

Remaining amount = 39x/50

Expense on clothing = 5/12 × 39x/50

= 13x/40

⇒ 13x/40 = 18,200

⇒ x = 1400 × 40

⇒ x = 56000

If, in February 2022, her salary increased by 16%:

⇒ 56000 × 116/100

⇒ 64960

Her salary (in Rs.) in February is  64960.

Alternate Method

Let the income be x.

⇒ x × 78/100 × 5/12 = 18200

⇒ x = 56000

Salary in February = 56000 × 116/100 = 64960.

Given

 tan2α = $\rm\frac{2 tan \alpha}{1-tan^{2}\alpha}$

Formula used:

Tan 15° = Tan(45 – 30)°

By the trigonometry formula, we know,

Tan (A – B) = (Tan A – Tan B) /(1 + Tan A Tan B)

Calculation

Therefore, we can write,

tan(45 – 30)° = tan 45° – tan 30°/1+ tan 45° tan 30°

Now putting the values of tan 45° and tan 30° from the table we get;

tan(45 – 30)° = (1 – 1/√3)/ (1 + 1.1/√3)

tan (15°) = √3 – 1/ √3 + 1

= (√3 – 1)²/ [(√3)² - 1²]

= (3 + 1 - 2√3)/2 = 2 - √3

= 0.268

Hence, the value of tan (15°) is 0.268.

Alternate Method 

|

tan 30° = tan 2(15°)

By the trigonometry formula, we know,

 tan2α = $\rm\frac{2 tan \alpha}{1-tan^{2}\alpha}$,

Calculation

Therefore, we can write,

tan 30° = 2 × tan 15° /(1 - tan2 15°)

Now putting the values of tan 30° we get;

⇒ 1/ √3 = 2 tan 15° / (1 - tan2 15°)

let tan (15°) = x

⇒ 1/ √3 = 2x / (1 - x2)

⇒ x2 - 1 + 2√3 x = 0

⇒ x2 + 2√3 x - 1 = 0

From quadratic formula,

x = $\frac{-2√3 \pm \sqrt{(2√3)^2 -4(1)(-1) }}{2\times 1}$

⇒ x = $\frac{-2√3 \pm \sqrt{12 +4 }}{2\times 1}$

⇒ x = $\frac{-2√3 \pm \sqrt{16 }}{2\times 1}$

⇒ (4 - 2√3)/2 = 2 - √3

= 0.268

Hence, the value of tan (15°) is 0.268.

Given:

DE is the chord of a circle.

KD = 9 cm ; DE = 7 cm

Concept used:

If a tangent and a secant are drawn from a common point outside the circle then,

Tengent² = line of secant × (line of sacant - chord) 

Calculation:

From tangent and secant relation:

⇒ KH² = KD × KE

⇒ KH² = 9 × 16

⇒ KH = √144 = 12 cm

∴ The correct answer is 12 cm.

The correct answer is "CADB."

Key Points

• The sequence is organized logically to present the historical and philosophical development of the Aestheticism movement:
• Sentence C: "Aestheticism was a European arts movement which centred on the doctrine that art exists for the sake of its beauty alone." This sentence defines Aestheticism and its core principle.
• Sentence A: "The movement began in reaction to the ugliness of the industrial age." This sentence follows, explaining the context and reason for the emergence of the Aestheticism movement.
• Sentence D: "Its philosophical foundations were laid in the 18th century by Immanuel Kant." This sentence introduces the philosophical basis of the Aestheticism movement, providing a historical starting point.
• Sentence B: "This idea was amplified by JW von Goethe, JL Tieck and others in Germany." Finally, this sentence adds a specific example of how the Aestheticism idea was developed and popularized by influential figures in Germany.
• Hence, the answer is option 2.
• Correct sequence:

C. Aestheticism was a European arts movement which centred on the doctrine that art exists for the sake of its beauty alone.

A. The movement began in reaction to the ugliness of the industrial age.

D. Its philosophical foundations were laid in the 18th century by Immanuel Kant.

B. This idea was amplified by JW von Goethe, JL Tieck and others in Germany.

The correct answer is "Cowardise."

Key Points

• The word "Cowardise" is misspelt.
• The correctly spelt word is "Cowardice."
• It means a lack of courage; behaviour that shows that you are afraid. (साहस का कमी; भीरुता, कायरता)
• Example: Cowardice prevented me from doing what I knew I should do.
• Hence, the answer is option 3.

Additional Information

• Adequate: enough for what you need. (आवश्‍यकता के अनुसार पर्याप्त)
• Precaution: something that you do now in order to avoid danger or problems in the future. (भविष्‍य के ख़तरे या समस्‍या से बचने के लिए किया गया उपाय; एहतियात, सावधानी)
• Ridiculous: very silly or unreasonable. (मूखर्तापूर्ण या बेतुका)

The correct answer is "Opaque."

Key Points

• The word "Clear" means pure or easy to see through, with no marks or areas that are less transparent. (शुद्ध या देखने में आसान, बिना किसी निशान या कम पारदर्शी क्षेत्र के)
• Example: The water in the lake is so clear that you can see the bottom.
• ​The antonym of "Clear" is "Opaque."
• The word "Opaque" means not letting light through : not transparent. (प्रकाश को अंदर न आने देना : पारदर्शी नहीं)
• Example: I find her poetry a little too opaque.
• ​So, the correct answer is Option 2.
  

Additional Information

• Clean: not dirty. (साफ़, निर्मल, स्‍वच्‍छ)
• Mess: the state of being dirty or untidy; a person or thing that is dirty or untidy. (गंदगी या अव्‍यवस्‍था; गंदा या अव्‍यवस्थित व्‍यक्ति या वस्‍तु)
• Untidy: not tidy or well arranged. ((वस्‍तु, स्‍थान आदि) मैला-कुचैला या अव्‍यवस्थित, अस्‍त-व्‍यस्‍त)

The correct answer is "The new software was installed by Myra on her computer."

 

Key Points 

• The given sentence is in Active Voice. As per the given question we have to change it into Passive Voice.
• The structure of the given sentence is as follows:
• Subject + V2 + Object. (Active Voice)
• Subject (objective case)+ was/were + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is 'Myra.'​​
• The object of the given sentence is 'new software.'
• The subject will be put in place of the object and the object will be put in place of the subject.
• 'Installed' will be changed into 'was installed.'
• "New software" is a singular subject and we must use "was" with it.
• The preposition "by" is used to indicate the doer of the action in the passive voice.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.
  

​

Correct sentence: The new software was installed by Myra on her computer.

The correct answer is "Grew."

Key Points

• The word "Waned" means to become gradually weaker or less important. (क्षीण होना, कम हो जाना)
• Example: My enthusiasm was waning rapidly.
• ​The antonym of "Waned" is "Grew."
• The word "Grew" means to increase in size or number; to develop into an adult form. (आकार या संख्‍या की दृष्टि से बढ़ना; बड़ा होना)
• Example: The male deer grew large, branching horns called antlers.
• ​So, the correct answer is Option 4.
  

Additional Information 

• Declined: to become weaker, smaller or less good. ((किसी का) ह्रास होना, क्षीण होना)
• Dimmed: to become or make something less bright or clear. (धुँधला या अस्‍पष्‍ट हो जाना या कर देना)
• Abated: to become less strong; to make something less strong. (प्रकोप या प्रभाव का कम हो जाना या कम करना; धीमा होना)