SSC CGL 2024 Tier-I Official Paper (Held On: 19 Sept, 2024 Shift 1) (Previous Year Paper)

The logic followed here is:

Logic: (1st number - 10) × 3 = 2nd number.

Now,

For, 17 : 21

⇒ (17 - 10) × 3 = 7 × 3 = 21.

For, 22 : 36

⇒ (22 - 10) × 3 = 12 × 3 = 36.

Similarly, for 29 ∶ ?

⇒ (29 - 10) × 3 = 19 × 3 = 57.

Hence, the correct answer is "Option 4".

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

Conclusions:

I. Some parrots are eagles → Follow (As some eagles are sparrows and all sparrows are parrots. As some part of eagles is common with sparrows which whole comes in parrots, therefore it is true.)

II. No penguin is a sparrow → Follow (As all sparrows are parrots and no parrot is a penguin. As whole sparrows comes in parrots which cannot be penguin, therefore it is true.)

∴ Here, Both conclusions I and II follow.​

Hence, the correct answer is "Option 1".

The logic followed here is:​

Hence, "Option 1" is the correct answer.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 1".

The logic followed here is:

'TOUGH' is coded as '89251'

'GHOST' is coded as '93258'

Thus, code of 'S' is '3'.

Hence, "Option 2" is the correct answer.

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

1) Total triangles = [Number of parts × (1 + Number of parts)] ÷ 2

= [2 × (1 + 2)] ÷ 2

= [2 × 3] ÷ 2

= 6 ÷ 2

= 3

As there are 4 same types of triangles, therefore total number of triangles will be (3 × 4) = 12 

2. As marked there are total 3 triangles.

Thus, there are total (12 + 3) = 15 triangles.

Hence, "Option 4" is the correct answer.

BODMAS Table: 

Given equation: 20 + 10 × 2 − 4 ÷ 5 = ?

Now, if ‘+’ and ‘-‘ and ‘×' and '÷’ are interchanged, then:

⇒ 20 - 10 ÷ 2 + 4 × 5 = ?

⇒ 20 - 5 + 4 × 5 = ?

⇒ 20 - 5 + 20 = ?

⇒ 40 - 5 = 35

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: Synonyms

Here,

Wander : Ramble → Wander is a synonym of Ramble.

Similarly,

Stray : Random → Stray is a synonym of Random.

Hence, the correct answer is "Option 3".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 3".

The logic followed here is:

11 – 14 – 8 – 17

11 + 3 = 14

14 - 6 = 8

8 + 9 = 17

And, 

12 – 15 – 9 – 18

12 + 3 = 15

15 - 6 = 9

9 + 9 = 18

So, checking each option one by one:

Option 1) 3 – 6 – 2 – 8

3 + 3 = 6

6 - 6 = 0 ≠ 2 (LHS ≠ RHS)

2 + 9 = 11 ≠ 8 (LHS ≠ RHS)

Option 2) 5 – 8 – 3 – 10

5 + 3 = 8

8 - 6 = 2 ≠ 3 (LHS ≠ RHS)

3 + 9 = 12 ≠ 10 (LHS ≠ RHS)

Option 3) 4 – 7 – 12 – 18

4 + 3 = 7

7 - 6 = 1 ≠ 12 (LHS ≠ RHS)

12 + 9 = 21 ≠ 18 (LHS ≠ RHS)

Option 4) 6 – 9 – 3 – 12

6 + 3 = 9

9 - 6 = 3

3 + 9 = 12

Thus, out of all the options '6 – 9 – 3 – 12' follows the same logic as given.

Hence, "Option 4" is the correct answer.

Given word: KEYBOARD

After arranging in alphabetical order:

After arranged in alphabetical order,

Third alphabet from the right end is: O,

Second alphabet from the right end is: R,

Now,

there are 2 letters between O and R.

Hence, the correct answer is "Option 3".

The logic followed here is:

1. One shaded circle is eliminated from the bottom from each box subsequently.

2. One shaded circle is replaced alternately by element 'X' subsequently.

Thus, the final series is:

Hence, "Option 3" is the correct answer.

The logic followed here is:

'SHE' is written as 'EIT'

And,

'SAD' is written as 'DBT'

Similarly,

'SUN' is written as

Hence, "Option 4" is the correct answer.

Given series: B_ E N B_ C E N B B C_ N B B C E_ B_ C

Option 1) BCENB → BB E N BC C E N B B CE N B B C EN BB C → (It doesn't follow any pattern)

Option 2) BNECB → BB E N BN C E N B B CE N B B C EC BB C → (It doesn't follow any pattern)

Option 3) CNEBB → BC E N BN C E N B B CE N B B C EB BB C → (It doesn't follow any pattern)

Option 4) CBENB → BC E N BB C E N B B CE N B B C EN BB C → (It follows the pattern of: BCENB - BCENB - BCENB - BCENB - BC)

Hence, "Option 4" is the correct answer.

The logic followed here is :-

From the given two different dices the adjacent sides are as shown below :

As III and V are common on both the dices, it is clear that the remaining i.e. VI will be opposite to II.

So, the opposite side of "VI" will be side "II".

Hence, the correct answer is "Option 2".

BODMAS Table: 

After decoding signs:

Given equation: 1205 × 5 + 35 − 197 ÷ 18 = ?

After interchanging the signs then:

⇒ 1205 ÷ 5 - 35 + 197 × 18 = ?

⇒ ? = 241 - 35 + 197 × 18

⇒ ? = 241 - 35 + 3546

⇒ ? = 3787 - 35

⇒ ? = 3752

Hence, the correct answer is "3752".

The logic followed here is:

Hence, "Option 1" is the correct answer.

The logic followed here is :-

From the given two different dices the adjacent sides are as shown below :

As 8 and 9 are common on both the dices, it is clear that the remaining i.e. 7 will be opposite to 10.

So, the opposite side of "7" will be side "10".

Hence, the correct answer is "Option 4".

The logic followed here is:

Option 1) CHE

Option 2) AGD

Option 3) MSP

Option 4) FLI

Thus, out of all the options, 'CHE' is the odd one out.

Hence, "Option 1" is the correct answer.

The logic followed here is:

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

Now,

For, 14 : 30

⇒ (14 × 2) + 2 = 28 + 2 = 30.

For, 9 : 20

⇒ (9 × 2) + 2 = 18 + 2 = 20.

Similarly, for 4 ∶ ?

⇒ (4 × 2) + 2 = 8 + 2 = 10.

Hence, the correct answer is "Option 4".

The logic followed here is:

1. The element shift anticlockwise and is flipped horizontally.

Thus, the final series is:

Hence, "Option 1" is the correct answer.

The logic followed here is:

BIRTHDAY - IBTRDHYA

And,

BLAZER - LBZARE

Similarly,

REMOVE - ?

Hence, "Option 3" is the correct answer.

Decoding symbols:

Given: A × B ÷ C × D

A × B → A is the wife of B.

B ÷ C → B is the father of C.

C × D → C is the wife of D.

Thus, A is D's wife’s mother or mother-in-law.

Hence, the correct answer is "Option 3".

The logic followed here is:

'RUCK' is related to 'TWAI'

And,

'DPHM' is related to 'FRFK'

Similarly,

'KNOM' is related to

Hence, "Option 3" is the correct answer.

The logic followed here is: (Second Number × 6) + 1 = First Number

Option 1) 19 : 3

(3 × 6) + 1 = 19

18 + 1 = 19

19 = 19 (LHS = RHS)

Option 2) 55 : 9

(9 × 6) + 1 = 55

54 + 1 = 55

55 = 55 (LHS = RHS)

Option 3) 49 : 8

(8 × 6) + 1 = 49

48 + 1 = 49

49 = 49 (LHS = RHS)

Option 4) 24 : 4

(4 × 6) + 1 = 24

24 + 1 = 24

25 ≠ 24 (LHS ≠ RHS)

Thus, out of all the options '24 : 4' is the odd one out.

Hence, "Option 4" is the correct answer.

The correct answer is Pandit Vishnu Digambar Paluskar.

Key Points

• Pandit Vishnu Digambar Paluskar was one of the foremost figures in the revival of Hindustani classical music in the early 20th century.
• He founded the Gandharva Mahavidyalaya in 1901, which was instrumental in the democratization of classical music education.
• Pandit Omkar Nath Thakur was deeply influenced by Paluskar's teachings and philosophy of music.
• Paluskar's efforts were significant in promoting classical music among the masses and establishing structured music education in India.

Additional Information

• Pandit Vishnu Digambar Paluskar
• He was born on August 18, 1872, in Kurundwad, Maharashtra.
• He was a renowned Hindustani classical musician and is credited with creating a structured system of music education.
• Paluskar's efforts led to the founding of several music schools across India, ensuring the spread of classical music education.
• He composed many bhajans and patriotic songs, the most famous being "Raghupati Raghav Raja Ram".
• Gandharva Mahavidyalaya
• Established by Paluskar in 1901 in Lahore (now in Pakistan), it was the first institution to provide formal training in Hindustani classical music.
• The institution has branches all over India and continues to be a significant center for music education.
• Gandharva Mahavidyalaya’s curriculum blends traditional gurukul methods with modern educational techniques.
• Hindustani Classical Music
• It is one of the two main subgenres of Indian classical music, the other being Carnatic music.
• It originated in the northern part of India and encompasses a wide range of vocal and instrumental styles.
• Key features include ragas (melodic frameworks) and talas (rhythmic cycles).
• Music Education in India
• Formal music education in India has a rich history, with traditional gurukul systems being the earliest form of structured training.
• Modern institutions like Gandharva Mahavidyalaya and the Bhatkhande Music Institute have played crucial roles in popularizing classical music education.
• These institutions have produced many renowned musicians and have contributed significantly to the preservation and promotion of Indian classical music.

The correct answer is 0.035.

Key Points

• The rate of unemployment in Maharashtra for the year 2021-22 was reported to be 0.035 by the Ministry of Labour and Employment.
• This figure represents the proportion of the labor force that was unemployed during this period.
• Unemployment rate is a crucial economic indicator that reflects the overall health of an economy.
• A lower unemployment rate typically indicates better economic conditions and higher employment levels.

Additional Information

• Unemployment Rate:
• It is the percentage of the labor force that is jobless and actively seeking employment.
• The formula for calculating the unemployment rate is: (Number of Unemployed / Labor Force) x 100.
• It is a key indicator used to measure the economic health of a region.
• High unemployment rates may indicate economic distress, while low rates may suggest a healthy economy.
• Ministry of Labour and Employment:
• It is a branch of the Government of India responsible for protecting and safeguarding the interests of workers in general and the poor, deprived, and disadvantaged sections of the society.
• It aims to create a healthy work environment for higher production and productivity and to develop and coordinate vocational skill training and employment services.
• The Ministry oversees a number of labor laws, employment policies, welfare schemes, and initiatives aimed at improving the employment landscape in India.
• Economic Indicators:
• Economic indicators are statistics that provide information about the economic performance of a country and its economic health.
• Common indicators include GDP, unemployment rates, inflation rates, and consumer price indices.
• Policymakers, economists, and analysts use these indicators to understand the current state of the economy and to guide economic policy decisions.

The correct answer is Durga.

Key Points

• Navratri is a Hindu festival that spans nine nights and is dedicated to the worship of the Hindu deity Durga.
• During Navratri, nine forms of Durga, also known as Navdurga, are worshipped each day.
• The festival symbolizes the victory of good over evil, as it commemorates Durga's triumph over the buffalo demon Mahishasura.
• Navratri is celebrated with great fervor and involves fasting, feasting, dancing (Garba and Dandiya), and various cultural activities.

Additional Information

• Navratri:
• Navratri, meaning "nine nights," is a major Hindu festival observed in honor of the goddess Durga, who is regarded as the divine mother and the ultimate power in the universe.
• The festival occurs in the lunar month of Ashvin, which typically falls in September or October.
• The nine nights of Navratri are dedicated to the nine forms of Durga: Shailaputri, Brahmacharini, Chandraghanta, Kushmanda, Skandamata, Katyayani, Kalaratri, Mahagauri, and Siddhidatri.
• Each day of Navratri has its own significance, rituals, and practices, reflecting different aspects and attributes of the goddess Durga.
• Durga Puja:
• Durga Puja is a major festival celebrated particularly in the Indian states of West Bengal, Odisha, Assam, Tripura, and Bihar during the last five days of Navratri.
• It marks the victory of the goddess Durga over the evil buffalo demon Mahishasura, symbolizing the victory of good over evil.
• The festival is characterized by elaborate decorations, artistic displays, cultural performances, and grand processions.
• Devotees offer prayers, perform rituals, and partake in communal feasts during Durga Puja.
• Garba and Dandiya Raas:
• Garba and Dandiya Raas are traditional dance forms performed during Navratri, especially in the Indian state of Gujarat.
• Garba involves rhythmic clapping and circular movements around a central image or representation of the goddess Durga.
• Dandiya Raas, also known as "stick dance," involves pairs of dancers striking small sticks (dandiyas) together in sync with the music.
• These dance forms are not only a way to celebrate the festival but also a means to seek the blessings of the goddess and enjoy the festive spirit.
• Fasting and Feasting:
• Fasting during Navratri is a common practice among devotees, symbolizing purification and devotion.
• Different regions have their own fasting rules and dietary restrictions, often involving abstaining from grains, meats, and certain vegetables.
• Feasting on special Navratri delicacies, such as sabudana khichdi, kuttu ki puri, and various fruits, is an integral part of the celebration.
• The end of the fasting period is marked by communal feasts and sharing of food, signifying unity and joy.

The correct answer is Khan Abdul Ghaffar Khan.

Key Points

• Khan Abdul Ghaffar Khan, also known as Bacha Khan or Frontier Gandhi, was a prominent freedom fighter and a close associate of Mahatma Gandhi.
• He founded the Khudai Khidmatgar (Servants of God) movement in 1929, which was a non-violent movement against British rule.
• The Khudai Khidmatgar movement was based in the North-West Frontier Province (now Khyber Pakhtunkhwa, Pakistan).
• The movement played a significant role in the Indian independence struggle and promoted education, social reforms, and the unity of the Pashtun people.

Additional Information

• Khan Abdul Ghaffar Khan:
• Born on 6 February 1890, Khan Abdul Ghaffar Khan was a Pashtun independence activist who worked to end the British rule in India.
• He was a devout Muslim and a follower of non-violence, which earned him the nickname "Frontier Gandhi."
• He founded several educational institutions and worked towards the upliftment of the Pashtun community.
• He was awarded the Bharat Ratna, India's highest civilian award, in 1987.
• Khudai Khidmatgar Movement:
• The Khudai Khidmatgar movement was also known as the "Red Shirts" due to the red uniforms worn by its members.
• The movement emphasized non-violence, social reform, and the promotion of education and unity among the Pashtuns.
• It played a crucial role in mobilizing the Pashtun population against British colonial rule.
• Despite facing severe repression from the British authorities, the movement remained committed to its principles of non-violence and social justice.
• Other Related Leaders:
• Muhammad Ali Jinnah: He was the leader of the All-India Muslim League and the founder of Pakistan. He played a crucial role in the creation of Pakistan in 1947.
• Hakim Ajmal Khan: He was a prominent Indian freedom fighter and a renowned physician. He was one of the founders of the Jamia Millia Islamia University in Delhi.
• Maulana Muhammad Ali: He was a prominent Indian Muslim leader, scholar, and journalist who played a significant role in the Khilafat Movement and the Indian independence struggle.

The correct answer is 3.

Key Points

• Vijender Singh has represented India in the Olympics for a total of three times.
• He participated in the 2004 Athens Olympics, 2008 Beijing Olympics, and the 2012 London Olympics.
• Vijender Singh is a celebrated Indian boxer who has made significant contributions to the sport in India.
• He is notable for winning India's first-ever Olympic medal in boxing, which he achieved in the 2008 Beijing Olympics.

Additional Information

• Olympics Overview
• The Olympics are a leading international sporting event featuring summer and winter sports competitions in which thousands of athletes from around the world participate in a variety of competitions.
• The modern Olympic Games were first held in 1896 in Athens, Greece.
• The Olympics are held every four years, with the Summer and Winter Games alternating by occurring every four years but two years apart.
• The International Olympic Committee (IOC) is responsible for organizing the Games and overseeing the host city's preparations.
• Vijender Singh's Achievements
• Vijender Singh Beniwal, born on October 29, 1985, is an Indian professional boxer and former amateur boxer.
• He won a bronze medal in the middleweight category at the 2008 Beijing Olympics, making him the first Indian boxer to win an Olympic medal.
• Vijender has also won medals at the Commonwealth Games and the Asian Games, adding to his impressive list of achievements.
• He turned professional in 2015 and has since continued to make a mark in the professional boxing circuit.
• Boxing in the Olympics
• Boxing has been a part of the Olympic Games since its inclusion in the 1904 St. Louis Games.
• The competition is divided into different weight categories, and boxers compete in a knockout format to win medals.
• Olympic boxing matches are typically shorter than professional bouts, consisting of three three-minute rounds.
• The scoring system is based on the number of clean punches landed, and judges decide the winner if there is no knockout.

The correct answer is Wrestling.

Key Points

• India's first individual Olympic medal was won by Khashaba Dadasaheb Jadhav in the sport of wrestling.
• He won the bronze medal in the 1952 Helsinki Olympics.
• Khashaba Jadhav competed in the freestyle bantamweight category.
• This achievement marked a significant milestone for India in the Olympic Games.

Additional Information

• Olympic Games:
• The Olympic Games are a leading international sporting event featuring summer and winter sports competitions.
• Thousands of athletes from around the world participate in a variety of competitions.
• The Games are held every four years, with the Summer and Winter Games alternating by occurring every four years but two years apart.
• Freestyle Wrestling:
• Freestyle wrestling is a style of amateur wrestling that is practiced worldwide.
• It is one of the two wrestling disciplines featured in the Olympic Games, the other being Greco-Roman.
• In freestyle wrestling, competitors are allowed to use their legs for both offense and defense, which differentiates it from Greco-Roman wrestling.
• Khashaba Dadasaheb Jadhav:
• Khashaba Jadhav was an Indian wrestler who competed in the 1948 London Olympics and the 1952 Helsinki Olympics.
• He is remembered for his remarkable achievement in the 1952 Helsinki Olympics, where he won the bronze medal.
• Jadhav's victory was a historic moment for India, bringing the country its first individual Olympic medal.

The correct answer is Jagdish Bhagwati.

Key Points

• Jagdish Bhagwati is an eminent Indian-American economist known for his extensive research in international trade and economic development.
• He has served as a professor at Columbia University and has been a senior fellow at the Council on Foreign Relations.
• Bhagwati has received several prestigious awards and honors, including the Padma Vibhushan, India’s second-highest civilian award.
• He has authored numerous influential books and articles that have significantly shaped modern economic policies and theories.

Additional Information

• Prof. C.R. Rao Centenary Gold Medal
• This award was instituted in honor of Professor Calyampudi Radhakrishna Rao, a renowned statistician whose contributions have had a profound impact on statistical theory and its applications.
• The award recognizes outstanding contributions to the fields of statistics and probability.
• It aims to promote and encourage the pursuit of excellence in research and innovation in these fields.
• The inaugural award in 2021 highlighted the importance of statistical sciences in various domains including economics, medicine, and social sciences.
• International Trade and Economic Development
• International trade refers to the exchange of goods and services between countries, which allows nations to expand their markets and access goods and services that may not be available domestically.
• Economic development involves sustained and concerted actions by policymakers and communities to improve the standard of living and economic health of a specific area.
• Economists like Jagdish Bhagwati have emphasized the role of free trade in promoting economic growth and development, arguing that open markets lead to more efficient resource allocation and increased innovation.
• Debates in this field often revolve around the balance between globalization's benefits and its potential drawbacks, such as economic inequality and environmental impact.
• Columbia University
• Founded in 1754, Columbia University is an Ivy League research university located in New York City.
• It is one of the world's leading institutions for higher education and research, known for its distinguished faculty and alumni, including numerous Nobel laureates and influential public figures.
• The university's Department of Economics is highly regarded, offering rigorous programs and fostering innovative research in various economic fields.
• Columbia has played a significant role in shaping modern economic thought and policy, with many of its faculty members being prominent economists.

The correct answer is Geetanjali Lal.

Key Points

• Geetanjali Lal is a renowned Kathak dancer and not associated with Odissi dance.
• Kathak is one of the eight major forms of Indian classical dance. Its origin is traditionally attributed to the traveling bards of ancient northern India known as Kathakars or storytellers.
• Geetanjali Lal has made significant contributions to the Kathak dance form and is known for her performances and teaching.
• Other dancers mentioned in the options, such as Mayadhar Raut, Kiran Segal, and Kumkum Mohanty, are all associated with Odissi, a classical dance form from the state of Odisha.

Additional Information

• Odissi Dance:
• Odissi is one of the classical dance forms of India originating from the state of Odisha in eastern India.It is known for its grace, fluid movements, and expressive gestures.
• The dance form is characterized by its intricate footwork, elaborate costumes, and jewelry.
• Odissi draws heavily from the ancient Sanskrit texts on dance called the "Natya Shastra".
• Kathak Dance:
• Kathak is a North Indian classical dance form that originated from the storytelling tradition.
• It is known for its intricate footwork, spins, and expressive gestures.
• The dance form has both Hindu and Mughal influences, and it evolved during the Bhakti movement and later in the courts of the Mughal emperors.
• Mayadhar Raut:
• Mayadhar Raut is a celebrated guru and exponent of the Odissi dance form.
• He has contributed significantly to the revival and popularization of Odissi dance.
• Kiran Segal:
• Kiran Segal is a renowned Odissi dancer and has been trained under the guidance of prominent Odissi gurus.
• She has performed extensively in India and abroad, promoting the art form.
• Kumkum Mohanty:
• Kumkum Mohanty is a distinguished Odissi dancer and choreographer.
• She has been awarded several prestigious honors for her contributions to Indian classical dance.

The correct answer is Article 75.

Key Points

• Article 75 of the Indian Constitution deals with the appointment of the Prime Minister and other ministers by the President.
• It states that the Prime Minister shall be appointed by the President and the other Ministers shall be appointed by the President on the advice of the Prime Minister.
• The article also discusses the collective responsibility of the Council of Ministers to the House of the People (Lok Sabha).
• It mentions that the Ministers shall hold office during the pleasure of the President.

Additional Information

• Article 62
• Article 62 deals with the time of holding election to fill a vacancy in the office of President and the term of office of the elected person.
• It specifies that an election to fill the vacancy caused by the expiration of the term of office of President shall be completed before the expiration of the term.
• It also states that an election to fill a vacancy in the office of President occurring by reason of his death, resignation, or removal, or otherwise, shall be held as soon as possible after, and in no case later than six months from, the date of occurrence of the vacancy.
• Article 66
• Article 66 deals with the election of the Vice-President of India.
• The Vice-President is elected by the members of an electoral college consisting of the members of both Houses of Parliament.
• The election is held in accordance with the system of proportional representation by means of the single transferable vote and the voting is by secret ballot.
• Article 71
• Article 71 deals with matters relating to, or connected with, the election of a President or Vice-President.
• It states that all doubts and disputes arising out of or in connection with the election of a President or Vice-President shall be inquired into and decided by the Supreme Court whose decision shall be final.

The correct answer is President.

Key Points

• The oath of office to the Vice-President of India is administered by the President of India.
• This ceremony usually takes place in the Central Hall of Parliament.
• The Vice-President, before entering upon his office, makes and subscribes to an oath or affirmation.
• In the oath, the Vice-President swears to bear true faith and allegiance to the Constitution of India and to discharge the duties of his office faithfully.

Additional Information

• Chief Justice of India:
• The Chief Justice of India (CJI) is the head of the judiciary of India and the Supreme Court of India.
• The CJI is responsible for the allocation of cases and appointment of constitutional benches that deal with important matters of law.
• They hold the position until they reach the age of 65.
• Comptroller and Auditor General (CAG):
• The CAG is an authority, established by the Constitution of India, who audits all receipts and expenditure of the Government of India and the state governments.
• The CAG is also the external auditor of government-owned corporations and conducts supplementary audits of government companies.
• The CAG is appointed for a term of six years or until the age of 65, whichever is earlier.
• Prime Minister:
• The Prime Minister of India is the head of government and is appointed by the President of India.
• The Prime Minister leads the executive branch of the Government of India and is the chief advisor to the President of India.
• The Prime Minister is usually the leader of the party or coalition that has a majority in the Lok Sabha.

The correct answer is Anemometer.

Key Points

• The anemometer was invented by Italian architect and author Leon Battista Alberti in the year 1450.
• Anemometers are used to measure wind speed and direction.
• The term "anemometer" is derived from the Greek word "anemos," which means wind.
• Anemometers are essential tools in meteorology and are commonly used in weather stations, airports, and on ships.

Additional Information

• Transmissometer
• A transmissometer is an instrument used to measure the extinction coefficient (the loss of light intensity due to scattering and absorption) in the atmosphere.
• It is commonly used to determine visibility in meteorology and oceanography.
• Dropsonde
• A dropsonde is a weather reconnaissance device that is dropped from an aircraft to measure atmospheric conditions as it falls to the ground.
• It is equipped with sensors to measure temperature, humidity, pressure, and wind speed and direction.
• Ceiling Projector
• A ceiling projector is an optical device used in meteorology to measure the height of the cloud base above the ground.
• It projects a beam of light onto the clouds, and the height is determined by measuring the angle of the beam reflection.

The correct answer is Jallianwala Bagh massacre.

Key Points

• ​​​​​​The Amritsar Massacre, also known as the Jallianwala Bagh Massacre, happened on April 13, 1919. At the Jallianwala Bagh in Amritsar, Punjab, a sizable peaceful crowd had gathered to protest the Rowlatt Act and the detention of pro-independence activists Saifuddin Kitchlew and Satyapal.
• In opposition to the mass murder in Jalianwalla Bagh, Tagore surrendered his knighthood. Rabindranath Tagore's letter to Lord Chelmsford, the British viceroy, in which he revoked his knighthood in opposition to the mass murder at Jalianwalla Bagh.
• The Nobel laureate was given a moving account of the slaughter by Ruchi Ram Sahni, a former Trustee of The Tribune, which led Tagore to decline the knighthood. In 1915, two years after winning the Nobel Prize for Literature, Rabindranath Tagore was made a knight.
• The term "knight" might be applied to positions of higher aristocracy, such as landowners, despite the fact that it was mainly a title for a military function. In exchange for the vassals' fidelity, defence, and service, the higher nobles grant them their fiefs, or parcels of land.

Additional Information

• ​​​On 14 January 1931, on the day of Makar Sankranti, the British military force surrounded and open gunfires on the public present in the peaceful public meeting of freedom fighters at Singhpur Charanpaduka Maidan located on the banks of Urmila river in Chhatarpur district Madhya Pradesh. Charan Paduka Massacre has been called as the Jallianwala Bagh massacre of Madhya Pradesh.
• The Partition of Bengal was announced on 19 July 1905 by the then Viceroy Lord Curzon. It was implemented on 16 October 1905. However, in 1911 it was withdrawn by Lord Hardinge. The stated reason was to ease the administration. But the actual reason was to weaken the growing nationalism in Bengal and break the unity.
• The Chauri Chaura incident took place in British India on February 4, 1922, at Chauri Chaura in the Gorakhpur district of the United Province (modern Uttar Pradesh), when a sizable crowd of demonstrators taking part in the Non-cooperation movement battled with police, who then opened fire.

The correct answer is Santoor.

Key Points

• Tarun Bhattacharya is a renowned Indian Santoor player known for his significant contributions to Indian classical music.
• He was awarded the Sangeet Natak Akademi Award in 2018, which is one of the highest recognitions in the field of performing arts in India.
• Tarun Bhattacharya has been instrumental in popularizing the Santoor globally and has performed in various prestigious venues worldwide.
• He is a disciple of Pandit Ravi Shankar and has played a crucial role in innovating and evolving the playing technique of the Santoor.

Additional Information

• Santoor
• The Santoor is a hammered dulcimer, a stringed musical instrument originating from the valleys of Kashmir in India.
• It consists of a wooden trapezoid-shaped body with numerous strings stretched across it, played by striking the strings with a pair of curved mallets.
• The Santoor is commonly used in Indian classical music and is known for its distinct, melodious sound.
• The instrument has a significant presence in Sufi music and has been incorporated into various musical genres over time.
• Sangeet Natak Akademi Award
• The Sangeet Natak Akademi Award is a national honor bestowed by the Sangeet Natak Akademi, India's National Academy of Music, Dance & Drama.
• It was established in 1952 to recognize and reward outstanding achievements in the performing arts.
• Recipients of the award are given a citation, a cash prize, and a shawl as a mark of honor.
• This prestigious award is a testament to an artist's dedication and excellence in their respective field.
• Indian Classical Music
• Indian classical music is a rich tradition that dates back thousands of years and is categorized into two major traditions: Hindustani (North Indian) and Carnatic (South Indian).
• It is characterized by intricate ragas (melodic frameworks) and talas (rhythmic cycles) that form the basis of compositions and improvisations.
• Instruments like the sitar, tabla, veena, and santoor play pivotal roles in Indian classical music performances.
• The music is deeply spiritual, often associated with various deities and used in religious and ceremonial contexts.

The correct answer is Butterfly.

Key Points

• Butterflies belong to the Phylum Arthropoda, which is the largest phylum in the animal kingdom.
• Arthropods are characterized by their exoskeleton, segmented body, and jointed appendages.
• Butterflies fall under the class Insecta, which is the largest class within Arthropoda.
• Other examples of Arthropods include insects, arachnids (spiders), myriapods (millipedes and centipedes), and crustaceans (crabs, lobsters).

Additional Information

• Nereis
• Nereis belongs to the Phylum Annelida. They are segmented worms.
• They have a segmented body with setae or bristles on each segment, which helps in locomotion.
• Hirudinarla
• Hirudinarla, commonly known as leeches, also belong to the Phylum Annelida.
• Leeches have a flattened body with suckers at both ends, used for attachment and feeding.
• Pila
• Pila is a genus of freshwater snails, which belong to the Phylum Mollusca.
• Mollusks are characterized by a soft body, usually protected by a hard shell.

The correct answer is Afghanistan and Punjab.

Key Points

• Kamran Mirza was the second son of Babur, the founder of the Mughal Empire in India.
• According to the Timurid tradition, the empire was divided among the sons of the ruler.
• Kamran Mirza was given control of the territories of Afghanistan and Punjab.
• He was a significant figure in the early Mughal period, often in conflict with his brother, Humayun.

Additional Information

• Timurid Tradition:
• This tradition was followed by the descendants of Timur, the Central Asian conqueror, where the empire was divided among the sons of the ruler.
• This often led to internal conflicts and power struggles among the successors.
• Kamran Mirza:
• Born in 1509, he was the second son of Babur and brother to Humayun.
• He governed the strategic regions of Kabul and Lahore (Punjab) and frequently rebelled against Humayun.
• Humayun:
• He was the second emperor of the Mughal Empire, ruling from 1530–1540 and again from 1555–1556.
• His reign was marked by several challenges, including conflicts with his brothers and the Afghan ruler, Sher Shah Suri.
• Mughal Empire:
• Founded by Babur in 1526, it became one of the largest and richest empires in history.
• The empire is known for its significant cultural and architectural contributions, including the Taj Mahal.

The correct answer is Morris S Kharasch and Frank R Mayo.

Key Points

• Morris S Kharasch and Frank R Mayo are known for their pioneering work in organic chemistry, particularly in the study of the peroxide effect.
• They observed the peroxide effect in 1933, which is also known as the Kharasch effect.
• This effect involves the addition of reagents to unsaturated compounds in the presence of peroxides, which leads to anti-Markovnikov addition.
• The discovery of the peroxide effect has had significant implications for synthetic organic chemistry, enabling the development of new reactions and synthetic pathways.

Additional Information

• Peroxide Effect (Kharasch Effect)
• This effect refers to the anti-Markovnikov addition of hydrogen bromide (HBr) to alkenes in the presence of peroxides.
• In the absence of peroxides, HBr adds to alkenes according to Markovnikov's rule, where the hydrogen attaches to the carbon with the greater number of hydrogen atoms.
• However, in the presence of peroxides, the addition follows the anti-Markovnikov rule, where the hydrogen attaches to the carbon with fewer hydrogen atoms.
• This phenomenon is due to the formation of free radicals initiated by the decomposition of peroxides.
• Free Radical Mechanism
• The peroxide effect proceeds through a free radical mechanism, which involves three main steps: initiation, propagation, and termination.
• Initiation: Peroxides decompose to form free radicals.
• Propagation: The free radicals react with HBr to generate bromine radicals, which then add to the alkene, forming new free radicals.
• Termination: The free radicals combine to form stable products, terminating the chain reaction.
• Importance in Organic Synthesis
• The peroxide effect is utilized in various synthetic applications, allowing chemists to control the regiochemistry of addition reactions.
• It has paved the way for the development of new reactions and methodologies in organic synthesis.

The correct answer is To prohibit trade in rare and endangered species.

Key Points

• Fundamental Duties are a set of moral obligations enshrined in Part IVA of the Indian Constitution.
• These duties were added by the 42nd Amendment Act, 1976, upon the recommendations of the Swaran Singh Committee.
• They aim to promote a spirit of patriotism and uphold the unity of India.
• While the fundamental duties do not include "To prohibit trade in rare and endangered species," they do consist of duties like respecting the national flag, cherishing the heritage, and protecting the environment.

Additional Information

• Fundamental Duties
• Fundamental Duties are outlined in Article 51A of the Indian Constitution.
• There are currently 11 Fundamental Duties listed for the citizens of India.
• Some of the key duties include respecting the Constitution, promoting harmony, protecting the environment, and developing a scientific temper.
• These duties act as a reminder to citizens that while they enjoy their rights, they also have responsibilities towards the nation.
• 42nd Amendment Act, 1976
• Often referred to as the "Mini-Constitution" due to its wide-ranging impact on the Indian Constitution.
• It was enacted during the Emergency period under Prime Minister Indira Gandhi's government.
• In addition to introducing the Fundamental Duties, it also added the words "Socialist," "Secular," and "Integrity" to the Preamble.
• The amendment brought significant changes to the Constitution, including the extension of the duration of legislatures, administrative reforms, and judicial reforms.
• Swaran Singh Committee
• Formed in 1976 to make recommendations on constitutional amendments.
• The committee was headed by Swaran Singh, a senior Congress leader and former Union Minister.
• Its primary recommendations included the inclusion of Fundamental Duties and strengthening the Centre's power.
• The committee's recommendations laid the groundwork for the 42nd Amendment Act.
• Environment Protection
• While the Fundamental Duties do not explicitly mention prohibiting trade in rare and endangered species, they do emphasize the protection and improvement of the natural environment, including forests, lakes, rivers, and wildlife.
• Citizens are encouraged to develop a sense of environmental responsibility and contribute to the preservation of biodiversity.
• Various laws and policies, such as the Wildlife Protection Act, are in place to regulate and prohibit such trade.
• These efforts are crucial for maintaining ecological balance and safeguarding the country's natural heritage.

The correct answer is Capital investment in industries.

Key Points

• At the time of independence, India faced a severe shortage of capital for industrial development. The colonial rule had drained India's wealth, leaving the country with limited financial resources.
• The capital formation was very low, and there was a lack of institutions to provide long-term finance for industrial projects.
• Industrial infrastructure was underdeveloped, and there was an absence of modern technology, which required significant investment to upgrade.
• The government's focus was on agricultural development and poverty alleviation, which led to limited allocation of funds for industrialization.

Additional Information

• Market for industrial produce:
• India had a large and diverse market for industrial goods, but the purchasing power of the population was low due to widespread poverty.
• The demand for industrial products was limited to a small section of the urban population.
• Employment required for industries:
• India had a large pool of labor, but the majority were unskilled and engaged in agriculture.
• There was a need for training and skill development to make the workforce suitable for industrial employment.
• Land for industrial establishment:
• Availability of land was not a major issue, but the acquisition process was cumbersome and often faced resistance from local communities.
• There was also a lack of developed industrial zones and infrastructure to support large-scale industries.

This source code provides a detailed solution to the question, highlighting the key points related to the correct option and additional information about other associated terminologies.

The correct answer is Newton.

Key Points

• Newton is a unit of force, not energy.
• It is named after Sir Isaac Newton in recognition of his work in classical mechanics.
• One Newton is the force required to accelerate a one-kilogram mass by one meter per second squared.
• The symbol for Newton is "N".

Additional Information

• Joule (J)
• A Joule is a derived unit of energy in the International System of Units.
• It is equal to the energy transferred when applying a force of one Newton over a distance of one meter.
• The symbol for Joule is "J".
• Calorie (cal)
• A Calorie is a unit of energy commonly used in food energy content measurement.
• It is defined as the amount of heat needed to raise the temperature of one gram of water by one degree Celsius.
• The symbol for Calorie is "cal".
• Kilowatt hour (kWh)
• A Kilowatt hour is a unit of energy equivalent to one kilowatt (1 kW) of power expended for one hour.
• It is commonly used as a billing unit for energy delivered to consumers by electric utilities.
• The symbol for Kilowatt hour is "kWh".

The correct answer is Banks providing loans to individual members of SHGs.

Key Points

• The SHG-Bank Linkage Programme (SBLP) was launched by NABARD in 1992 as a pilot project to provide a cost-effective mechanism for providing financial services to the unreached and underserved rural poor.
• The program allows Self-Help Groups (SHGs) to open savings accounts in banks and avail loans.
• The SHG members collectively guarantee the repayment of loans, which reduces the risk for banks.
• This program has been instrumental in promoting financial inclusion and improving the socioeconomic conditions of rural women.

Additional Information

• Self-Help Groups (SHGs)
• SHGs are informal associations of people who come together to find ways to improve their living conditions.
• They are usually composed of 10-20 members who meet regularly to save and lend money to each other.
• The primary objective of SHGs is to promote savings and provide credit facilities to their members.
• SHGs play a crucial role in enhancing the socio-economic status of their members, especially women, by fostering a sense of community and collective responsibility.
• NABARD (National Bank for Agriculture and Rural Development)
• NABARD is an apex development bank in India, established on 12 July 1982.
• It is responsible for providing and regulating credit and other facilities for the promotion and development of agriculture, small-scale industries, cottage and village industries, handicrafts, and other rural crafts.
• NABARD also supports rural development projects by providing financial assistance and guidance.
• One of its significant initiatives is the SHG-Bank Linkage Programme, which aims to link SHGs with banks to facilitate access to financial services.
• Financial Inclusion
• Financial inclusion refers to the process of ensuring access to financial services and timely and adequate credit where needed by vulnerable groups such as weaker sections and low-income groups at an affordable cost.
• It aims to eliminate barriers to financial services and create opportunities for all individuals, especially the underprivileged, to participate in the formal financial system.
• Key components of financial inclusion include access to savings accounts, credit, insurance, remittances, and financial literacy.
• Promoting financial inclusion is crucial for achieving inclusive growth and reducing poverty.

The correct answer is 2016.

Key Points

• The Right of Persons with Disabilities Act was passed in the year 2016.
• This act replaced the earlier Persons with Disabilities (Equal Opportunities, Protection of Rights, and Full Participation) Act, 1995.
• The act aims to give effect to the United Nations Convention on the Rights of Persons with Disabilities, which India ratified in 2007.
• The act covers a range of rights and entitlements for persons with disabilities, including education, employment, and social security.

Additional Information

• Persons with Disabilities (Equal Opportunities, Protection of Rights, and Full Participation) Act, 1995
• This was the first comprehensive law in India concerning the rights of persons with disabilities.
• It provided for equal opportunities and full participation of persons with disabilities in society.
• The act focused on prevention and early detection of disabilities, education, employment, and non-discrimination.
• United Nations Convention on the Rights of Persons with Disabilities (UNCRPD)
• The UNCRPD is an international human rights treaty aimed at protecting the rights and dignity of persons with disabilities.
• Adopted on 13 December 2006 and entered into force on 3 May 2008.
• India signed the convention on 30 March 2007 and ratified it on 1 October 2007.
• The convention requires countries to promote, protect, and ensure the full and equal enjoyment of all human rights by persons with disabilities.
• Right of Persons with Disabilities Act, 2016
• This act was enacted to comply with the UNCRPD and to address the gaps in the 1995 Act.
• It recognizes 21 types of disabilities, compared to 7 in the 1995 Act.
• The act mandates that persons with disabilities have the right to equality, life with dignity, and respect for their integrity.
• It includes provisions for reservation in education and employment, social security, and accessibility.

The correct answer is Godavari river.

Key Points

• The Wardha River is one of the major tributaries of the Godavari River.
• The confluence of the Wardha River with the Wainganga River forms the Pranahita River, which eventually joins the Godavari River.
• The Godavari River is the second longest river in India after the Ganges and is often referred to as the 'Dakshina Ganga' or the South Ganges.
• The Godavari River basin is one of the largest river basins in India, covering several states including Maharashtra, Telangana, Andhra Pradesh, Chhattisgarh, and Odisha.

Additional Information

• Godavari River
• The Godavari River is the longest river in peninsular India and is revered as a sacred river in Hinduism.
• It originates from Trimbakeshwar in the Nashik district of Maharashtra.
• The river flows eastward for about 1,465 kilometers before emptying into the Bay of Bengal.
• The Godavari basin is rich in biodiversity and supports a wide range of flora and fauna.
• Wardha River
• The Wardha River originates from the Satpura Range in Madhya Pradesh.
• It flows southward through the states of Madhya Pradesh and Maharashtra.
• The river is known for its fertile plains which are used extensively for agriculture.
• The Wardha River is also important for its hydropower projects and irrigation facilities.
• Wainganga River
• The Wainganga River is another major tributary of the Godavari River.
• It originates from the Mundara village in Seoni district of Madhya Pradesh.
• The river flows through Madhya Pradesh and Maharashtra before merging with the Wardha River to form the Pranahita River.
• The Wainganga River basin is known for its rich mineral resources and dense forests.

The correct answer is Kushana.

Key Points

• The fourth Buddhist council was held during the rule of the Kushana emperor Kanishka.
• It was during this council that Buddhism got split into two schools - Hinayana and Mahayana.
• Hinayana, meaning the "Lesser Vehicle," focuses on individual enlightenment and adheres strictly to the original teachings of Buddha.
• Mahayana, meaning the "Greater Vehicle," emphasizes collective salvation and the role of Bodhisattvas (enlightened beings who delay their own Nirvana to help others achieve enlightenment).

Additional Information

• Buddhist Councils:
• The first Buddhist council was held at Rajagaha (Rajgir) under the patronage of King Ajatashatru.
• The second Buddhist council took place at Vaishali approximately 100 years after the Buddha’s death.
• The third Buddhist council was convened by Emperor Ashoka at Pataliputra (Patna).
• The fourth Buddhist council was held in Kashmir under the patronage of King Kanishka, a Kushan ruler.
• Hinayana (Theravada) Buddhism:
• Hinayana, also known as Theravada, is considered the "Doctrine of the Elders."
• It emphasizes individual enlightenment and adheres strictly to the original teachings of the Buddha as recorded in the Pali Canon.
• Mahayana Buddhism:
• Mahayana Buddhism developed as a more inclusive interpretation of the Buddha's teachings.
• It emphasizes the role of Bodhisattvas and the pursuit of enlightenment for the benefit of all beings.
• Mahayana texts include the Perfection of Wisdom Sutras and the Lotus Sutra.
• Kushan Empire:
• The Kushan Empire was a syncretic empire formed by the Yuezhi in the Bactrian territories in the early 1st century CE.
• Under King Kanishka, the empire reached its zenith and played a crucial role in the spread of Buddhism across Central Asia and into China.
• Kanishka is remembered for his support of Buddhism and the significant role he played in the establishment of the Mahayana school.

The correct answer is Kerala.

Key Points

• As of the Financial Year 2019, Kerala has the highest road density in India.
• Road density is measured as the length of the road per square kilometer of area.
• Kerala's extensive road network is a key factor in its high road density.
• Development in infrastructure and better connectivity are significant contributors to Kerala's high road density.

Additional Information

• Road Density:
• Road density refers to the total length of the road network per unit area of land. It is a key indicator of the development of a region's infrastructure.
• Higher road density indicates better connectivity and accessibility in the region, which can lead to improved economic activities and mobility.
• Kerala's Road Network:
• Kerala has a well-developed road network that includes national highways, state highways, district roads, and rural roads.
• The state's geographical features and high population density necessitate an extensive network of roads to ensure connectivity.
• Infrastructure Development:
• Infrastructure development plays a crucial role in enhancing the road density of a region. It involves the construction, maintenance, and improvement of roads.
• Investments in infrastructure lead to better road quality, reduced travel time, and increased safety for commuters.
• Economic Impact:
• High road density positively impacts the economy by facilitating smoother transportation of goods and services.Improved connectivity attracts investments, boosts tourism, and promotes overall economic growth.

The correct answer is Lockjaw.

Key Points

• Lockjaw is a common name for tetanus, a serious bacterial infection.
• Tetanus is caused by the bacterium Clostridium tetani, which produces a toxin affecting the nervous system.
• The condition is characterized by muscle stiffness and spasms, particularly in the jaw muscles, hence the name "lockjaw".
• Without treatment, tetanus can be fatal, but it is preventable through vaccination.

Additional Information

• Clostridium tetani:
• It is a spore-forming bacterium found in soil, dust, and animal feces.
• The spores can enter the body through wounds, especially deep puncture wounds, and produce a toxin called tetanospasmin.
• Tetanospasmin interferes with the nervous system, leading to severe muscle spasms.
• Tetanus Symptoms:
• Symptoms typically appear 3 to 21 days after infection.
• Common symptoms include muscle stiffness, difficulty swallowing, and jaw cramping (lockjaw).
• Severe cases can lead to muscle spasms in the back, neck, and other parts of the body.
• Tetanus Treatment:
• Treatment usually involves wound care, medications to control muscle spasms, and antibiotics to fight the infection.
• In severe cases, patients may require hospitalization and supportive care, including mechanical ventilation.
• Tetanus Prevention:
• The best way to prevent tetanus is through vaccination.
• The DTaP (diphtheria, tetanus, and acellular pertussis) vaccine is routinely given to children, and booster shots (Td or Tdap) are recommended for adults every 10 years.
• Proper wound care and hygiene can also help prevent tetanus infection.

Shortcut Trick

When perpendiculars drawn from opposite vertices of a quadrilateral to a diagonal are equal, that diagonal bisects the other diagonal.

Therefore, diagonal WY bisects diagonal ZX at intersection point O.

This directly means OX = OZ.

Given OX = 12 cm, the full length is ZX = 2 × OX.

⇒ ZX = 2 × 12 = 24 cm.

∴ The correct answer is 24 cm.

Alternate Method

            W Y X Z Q P O 12 cm

Given:

⇒ WXYZ is a quadrilateral with diagonal WY.

⇒ XQ ⊥ WY and ZP ⊥ WY.

⇒ XQ = ZP

⇒ OX = 12 cm

Method Used:

In ▵OXQ and ▵OZP:

⇒ ∠XQO = ∠ZPO = 90° (Given perpendiculars)

⇒ ∠XOQ = ∠ZOP (Vertically opposite angles are equal)

⇒ XQ = ZP (Given equal lengths)

⇒ ∴ ▵OXQ ≅ ▵OZP (By AAS congruence criterion)

Calculations:

⇒ Since ▵OXQ ≅ ▵OZP, their corresponding parts are equal.

⇒ OX = OZ (By CPCT - Corresponding Parts of Congruent Triangles)

⇒ Since OX = 12 cm, we have OZ = 12 cm.

⇒ The total length of diagonal ZX = OX + OZ

⇒ ZX = 12 + 12 = 24 cm.

∴ The correct answer is 24 cm.

Additional Information

AAS Congruence Rule

If any two angles and a non-included side of one triangle are equal to the corresponding angles and side of another triangle, the two triangles are congruent.

Area of Quadrilateral Property

If perpendiculars drawn from opposite vertices to a diagonal are equal in length, the diagonal divides the entire quadrilateral into two regions of exactly equal area.

Properties of Diagonals

Whenever a diagonal line of a quadrilateral divides the other diagonal into two equal halves, it must pass strictly through the midpoint of that second diagonal.

Shortcut Trick

The area of a parallelogram can be calculated directly by multiplying its base and the corresponding height.

Area = Base × Height

Area = 26 × 18 = 468 cm²

∴ The correct answer is 468 cm².

Alternate Method

Given:

Base of the parallelogram = 26 cm

Height of the parallelogram = 18 cm

Formula Used:

Area of a parallelogram = Base × Height

Calculations:

⇒ Area = 26 × 18

⇒ Area = 468 cm²

∴ The correct answer is 468 cm².

Additional Information

Area of a Parallelogram (Trigonometric)

It can also be calculated as the product of any two adjacent sides multiplied by the sine of the included angle: Area = a × b × sin(θ).

Perimeter of a Parallelogram

The perimeter is the total distance around the outside, given by the formula: 2 × (Sum of adjacent sides).

Area of a Rhombus

A rhombus is a special parallelogram with all equal sides. Its area is calculated as ½ × d₁ × d₂, where d₁ and d₂ are the lengths of the diagonals.

Area of a Trapezium

The area of a trapezium is given by ½ × (Sum of parallel sides) × Height.

Shortcut Trick

According to the Power of a Point theorem, for an external point at distance d from the center of a circle of radius r, the secant product is constant.

d² − r² = RA × RB

18² − r² = 7 × (7 + 5)

324 − r² = 84 ⇒ r² = 240

r = √240 = 4√15 cm.

∴ The correct answer is 4√15 cm.

Alternate Method

Given:

Distance from center O to external point R, OR = 18 cm.

Length of external secant segment RA = 7 cm.

Length of internal secant segment AB = 5 cm.

18 cm

O R A B P Q

7 cm 5 cm r

Formula Used:

Let a secant from point R pass through the center O, intersecting the circle at Q and P.

By the Secant-Secant Theorem: RA × RB = RQ × RP

Where RQ = OR − r and RP = OR + r.

Calculation:

⇒ Total length of secant RB = RA + AB = 7 + 5 = 12 cm

⇒ RQ × RP = (18 − r) × (18 + r)

⇒ RA × RB = 18² − r²

⇒ 7 × 12 = 324 − r²

⇒ 84 = 324 − r²

⇒ r² = 324 − 84 = 240

⇒ r = √240 = √(16 × 15) = 4√15 cm

∴ The correct answer is 4√15 cm.

Additional Information

Intersecting Secants Theorem

When two secant lines intersect outside a circle, the product of the external segment and the entire segment of one secant equals the product of the corresponding segments of the other secant.

Tangent-Secant Theorem

If a tangent and a secant are drawn from an exterior point, the square of the tangent segment length is equal to the product of the external secant segment and the entire secant segment length.

Power of a Point Theorem

For a point P at a distance d from the center of a circle with radius r, the product of the segments of any secant passing through P is constant and equal to |d² − r²|.

Shortcut Trick

If x + 1/x = 2, then x = 1.

Here, sin x and cosec x are reciprocals of each other.

So, sin x + 1/(sin x) = 2 ⇒ sin x = 1 and cosec x = 1.

Then, sin⁷ x + cosec⁷ x = 1⁷ + 1⁷ = 1 + 1 = 2.

∴ The correct answer is 2.

Alternate Method

Given:

sin x + cosec x = 2

Formula Used:

cosec x = 1 / sin x

Calculations:

⇒ sin x + 1 / sin x = 2

⇒ (sin² x + 1) / sin x = 2

⇒ sin² x + 1 = 2 sin x

⇒ sin² x − 2 sin x + 1 = 0

⇒ (sin x − 1)² = 0

⇒ sin x = 1

Since cosec x is the reciprocal of sin x:

⇒ cosec x = 1 / 1 = 1

Now, substituting the values in the required expression:

⇒ sin⁷ x + cosec⁷ x = (1)⁷ + (1)⁷

⇒ 1 + 1 = 2

∴ The correct answer is 2.

Additional Information

Algebraic Identity of Reciprocals

If x + 1/x = 2, then x must be equal to 1. This is a standard result derived from the perfect square (x − 1)² = 0.

Negative Reciprocal Sum

If x + 1/x = −2, then x must be equal to −1. Substituting this value helps evaluate higher powers without expanding.

Trigonometric Reciprocal Pairs

The pairs (sin x, cosec x), (cos x, sec x), and (tan x, cot x) are reciprocals. If the sum of any pair is 2, the individual value of each function is exactly 1.

Given:

Total marks obtained by C = 80 + 80 + 70 + 60 + 70 + 60 = 420

Total possible marks = 600

Formula used:

Percentage = $\frac{\text{Marks obtained}}{\text{Total marks}} \times 100$

Calculations:

Percentage = $\frac{420}{600} \times 100$

⇒ Percentage = $\frac{420 \times 100}{600}$

⇒ Percentage = 70%

Option 2 is the correct answer.

Given:

Sales in June = ₹24000

Sales in July = ₹18000

Total Sales = ₹25000 + ₹24000 + ₹18000 + ₹35000 + ₹26000 + ₹22000

Formula Used:

Percentage share = (Sales in June + Sales in July) / Total Sales × 100

Calculation:

Total Sales = ₹25000 + ₹24000 + ₹18000 + ₹35000 + ₹26000 + ₹22000

⇒ Total Sales = ₹150000

Sales in June and July = ₹24000 + ₹18000

⇒ Sales in June and July = ₹42000

Percentage share = (₹42000 / ₹150000) × 100

⇒ Percentage share = 0.28 × 100

⇒ Percentage share = 28%

The correct answer is option 1.

Shortcut Trick

Let the Son's present age be S. From the condition 10 years later, Father's present age H = 2S + 10.

From the age difference, Mother's present age W = H − S/3 = (2S + 10) − S/3 = 5S/3 + 10.

Sum of all ages is 90: (2S + 10) + (5S/3 + 10) + S = 90

⇒ 3S + 5S/3 + 20 = 90

⇒ 14S/3 = 70 ⇒ S = 15

Mother's present age = (5 × 15)/3 + 10 = 25 + 10 = 35 years.

∴ The correct answer is 35 years.

Alternate Method

Given:

Present sum of ages: H + W + S = 90

Difference between Husband and Wife: H − W = S / 3

After 10 years: S + 10 = (H + 10) / 2

Calculations:

⇒ From the future age relation, 2S + 20 = H + 10

⇒ H = 2S + 10

⇒ Substituting H into the difference equation:

⇒ W = H − S / 3

⇒ W = (2S + 10) − S / 3 = (5S / 3) + 10

⇒ Substituting H and W into the sum equation:

⇒ (2S + 10) + ((5S / 3) + 10) + S = 90

⇒ 3S + 5S / 3 + 20 = 90

⇒ 14S / 3 = 70

⇒ S = 70 × 3 ÷ 14 = 15 years

⇒ The mother's present age W = (5 × 15 / 3) + 10

⇒ W = 25 + 10 = 35 years

∴ The correct answer is 35 years.

Additional Information

Problems on Ages

If the current age is x, then the age after 'n' years will be (x + n), and the age 'n' years ago was (x − n).

Constant Age Difference

The absolute age difference between any two individuals remains constant throughout their lives, irrespective of the time period.

Ratio of Ages

When solving problems based on changing ratios over time, it is highly useful to equate the differences in their respective ratios, because the actual difference in their ages never changes.

Shortcut Trick

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

Here, a + 1/a = 7√3

⇒ a³ + 1/a³ = (7√3)³ − 3 × 7√3 = 1029√3 − 21√3 = 1008√3

Now apply the square formula (p² − 2) on the obtained result to get the 6th power:

⇒ a⁶ + a⁻⁶ = (1008√3)² − 2 = (1016064 × 3) − 2 = 3048192 − 2 = 3048190

∴ The correct answer is 3048190.

Alternate Method

Given:

a + 1/a = 7√3

Formula Used:

(x + y)² = x² + y² + 2xy

(x + y)³ = x³ + y³ + 3xy(x + y)

Calculations:

⇒ Squaring both sides of the given equation:

⇒ (a + 1/a)² = (7√3)²

⇒ a² + 1/a² + 2 × a × 1/a = 147

⇒ a² + 1/a² + 2 = 147

⇒ a² + 1/a² = 145

⇒ Cubing both sides of this new equation:

⇒ (a² + 1/a²)³ = 145³

⇒ (a²)³ + (1/a²)³ + 3 × a² × (1/a²) × (a² + 1/a²) = 3048625

⇒ a⁶ + 1/a⁶ + 3 × 1 × 145 = 3048625

⇒ a⁶ + a⁻⁶ + 435 = 3048625

⇒ a⁶ + a⁻⁶ = 3048625 − 435 = 3048190

∴ The correct answer is 3048190.

Additional Information

Square Identity Trick

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

Cube Identity Trick

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

Fifth Power Identity

If x + 1/x = k, then the value of x⁵ + 1/x⁵ = (x² + 1/x²)(x³ + 1/x³) − (x + 1/x).

Negative Power Identity

If x − 1/x = k, then x² + 1/x² = k² + 2 and x³ − 1/x³ = k³ + 3k.

Given:

Total marks obtained by Gunja = 112 + 119 + 99 + 97 = 427

Total possible marks = 700

Formula used:

Percentage = $\frac{\text{Marks obtained}}{\text{Total marks}} \times 100$

Calculations:

Percentage = $\frac{427}{700} \times 100$

⇒ Percentage = $\frac{427 \times 100}{700}$

⇒ Percentage = 61%

Option 2 is correct answer.

Shortcut Trick

By the Remainder Theorem, the required number to be subtracted is simply the remainder when the polynomial is divided by (x + 2).

Substitute x = −2 directly into the given expression:

Remainder = (−2)³ − 4(−2)² − 8(−2) + 11

Remainder = −8 − 16 + 16 + 11 = 3

∴ The correct answer is 3.

Alternate Method

Given:

Polynomial P(x) = x³ − 4x² − 8x + 11

Divisor = (x + 2)

Formula Used:

For a polynomial to be exactly divisible by (x + a), the remainder P(−a) must be zero. If we subtract the remainder from the polynomial, it becomes perfectly divisible.

Calculations:

⇒ Let the number to be subtracted be k.

⇒ Modified polynomial = x³ − 4x² − 8x + 11 − k

⇒ For perfect divisibility by (x + 2), substitute x = −2 and equate to zero.

⇒ (−2)³ − 4(−2)² − 8(−2) + 11 − k = 0

⇒ −8 − 4(4) + 16 + 11 − k = 0

⇒ −8 − 16 + 16 + 11 − k = 0

⇒ −8 + 11 − k = 0

⇒ 3 − k = 0

⇒ k = 3

∴ The correct answer is 3.

Additional Information

Remainder Theorem

If a polynomial P(x) is divided by a linear expression (x − a), the remainder is equal to P(a).

Factor Theorem

A polynomial P(x) has a factor (x − a) if and only if P(a) = 0. It is a specific condition of the Remainder Theorem where the remainder is zero.

Division Algorithm for Polynomials

Dividend = (Divisor × Quotient) + Remainder. If the remainder is subtracted from the dividend, the resulting polynomial is perfectly divisible by the divisor.

Shortcut Trick

Squaring the given equation sinA + cosA = √3 yields 1 + 2sinAcosA = 3, which gives sinAcosA = 1.

The expression tanA + cotA simplifies directly to 1 / (sinAcosA).

Thus, the given expression becomes 1 / (sinAcosA) + 2sinAcosA.

Substituting sinAcosA = 1 gives 1 / 1 + 2 × 1 = 3.

∴ The correct answer is 3.

Alternate Method

Given:

sinA + cosA = √3

Formula Used:

(a + b)² = a² + b² + 2ab

sin²A + cos²A = 1

tanA = sinA / cosA

cotA = cosA / sinA

Calculations:

⇒ Squaring both sides of the given equation:

⇒ (sinA + cosA)² = (√3)²

⇒ sin²A + cos²A + 2sinAcosA = 3

⇒ 1 + 2sinAcosA = 3

⇒ 2sinAcosA = 3 − 1

⇒ 2sinAcosA = 2

⇒ sinAcosA = 1

Now, evaluating the required expression:

⇒ tanA + cotA + 2sinAcosA

⇒ (sinA / cosA) + (cosA / sinA) + 2sinAcosA

⇒ [(sin²A + cos²A) / (sinAcosA)] + 2sinAcosA

⇒ 1 / (sinAcosA) + 2sinAcosA

Substitute the value of sinAcosA = 1 into the expression:

⇒ 1 / 1 + 2 × 1

⇒ 1 + 2 = 3

∴ The correct answer is 3.

Additional Information

Basic Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ − tan²θ = 1

cosec²θ − cot²θ = 1

Important Conversion

tanθ + cotθ can always be simplified directly as: (sinθ / cosθ) + (cosθ / sinθ) = (sin²θ + cos²θ) / (sinθcosθ) = 1 / (sinθcosθ).

Shortcut Trick

Successive multipliers for 10% and 20% discounts are 0.9 and 0.8 respectively.

Effective Selling Price = MP × 0.9 × 0.8

SP = 2250 × 0.72

SP = 1620

∴ The correct answer is 1620.

Alternate Method

Given: Marked Price (MP) = ₹2,250, First Discount (d₁) = 10%, Second Discount (d₂) = 20%

Formula Used: Selling Price (SP) = MP × (100 − d₁)/100 × (100 − d₂)/100

MP: 2250

−10%

2025

−20%

SP: 1620

⇒ First discount amount = 10% of 2250 = (10/100) × 2250 = 225

⇒ Price after first discount = 2250 − 225 = 2025

⇒ Second discount amount = 20% of 2025 = (20/100) × 2025 = 405

⇒ Final Selling Price = 2025 − 405 = 1620

∴ The correct answer is 1620.

Additional Information

Single Equivalent Discount

Two successive discounts of a% and b% are equal to a single discount of (a + b − ab/100)%.

Marked Price (MP)

MP is the price printed on the label of an article. Discount is always calculated on the MP.

Selling Price (SP)

SP is the final price after all discounts. SP = MP − Discount. If SP > CP, there is a profit.

Shortcut Trick Total weight = 4 + 3 + 2 + 1 = 10 parts, so Original price ∝ (10)2 = 100 parts. New total price ∝ 42 + 32 + 22 + 12 = 16 + 9 + 4 + 1 = 30 parts. Loss in value = 100 parts − 30 parts = 70 parts. 70 parts = ₹63,000 ⇒ 1 part = ₹900. Original price = 100 parts × ₹900 = ₹90,000. ∴ The correct answer is ₹90,000. Alternate Method Given: Weight ratio of the four broken pieces = 4 : 3 : 2 : 1 Loss after selling the pieces = ₹63,000 Formula Used: Cost (C) ∝ Weight (W)2 ⇒ C = kW2 Calculations:

⇒ Let the weights of the broken pieces be 4x, 3x, 2x, and 1x. ⇒ Total weight of the original diamond = 4x + 3x + 2x + 1x = 10x ⇒ Original cost of the diamond = k(10x)2 = 100kx2 ⇒ Cost of the broken pieces = k(4x)2 + k(3x)2 + k(2x)2 + k(x)2 ⇒ Total cost of the pieces = 16kx2 + 9kx2 + 4kx2 + 1kx2 = 30kx2 ⇒ Loss incurred = Original Cost − Total cost of pieces ⇒ Loss = 100kx2 − 30kx2 = 70kx2 ⇒ Given that the loss is ₹63,000: ⇒ 70kx2 = 63000 ⇒ kx2 = 63000 ÷ 70 = 900 ⇒ Original Cost = 100kx2 = 100 × 900 = 90,000 ∴ The correct answer is ₹90,000. Additional Information Direct Proportion When a quantity varies directly as the square of another, the relation is given by y = kx2. A proportional increase in x causes a quadratic increase in y. Loss on Breakage For any item whose value is proportional to the square of its weight, breaking it into smaller parts will strictly decrease its total value because (a + b)2 > a2 + b2 for any positive weights. Ratio Distribution If an amount is divided in the ratio a : b : c, the parts can be expressed as ax, bx, and cx where x is a common variable. The sum of the parts always equals the original amount.

Shortcut Trick

Initial actual price of vegetables = ₹10 per kg

New actual price for 1000 g = (₹7.2 ÷ 900) × 1000 = ₹8 per kg

Percentage change = [(Initial price − New price) ÷ Initial price] × 100

Percentage change = [(10 − 8) ÷ 10] × 100 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Initial price of vegetables = ₹10 per kg (1000 g)

New claimed selling price = ₹7.2 for a faulty weight of 900 g

Formula Used:

Actual price per kg = (Selling Price ÷ Faulty Weight) × 1000

Percentage Change = [(Initial Price − Actual New Price) ÷ Initial Price] × 100

Calculations:

⇒ Actual new price for 1000 g = (7.2 ÷ 900) × 1000

⇒ Actual new price = 0.008 × 1000 = ₹8 per kg

⇒ Decrease in price per kg = Initial Price − Actual New Price

⇒ Decrease = 10 − 8 = ₹2

⇒ Percentage change = (2 ÷ 10) × 100

⇒ Percentage change = 20%

∴ The correct answer is 20%.

Additional Information

Dishonest Dealer Concept

When a dealer claims to sell goods at cost price but uses a false weight, his profit percentage is given by [(True Weight − False Weight) ÷ False Weight] × 100.

Effective Price Standardization

Always standardize quantities (e.g., to 1 kg or 1000 g) before comparing prices or calculating profit/loss percentages to avoid calculation errors.

Percentage Change Formula

The general formula for percentage change is [(Final Value − Initial Value) ÷ Initial Value] × 100. A negative result indicates a decrease.

Shortcut Trick

The net percentage change in expenditure can be found using the successive percentage formula: x + y + (x × y) ÷ 100

Here, the price increases by 300% (x = +300) and consumption decreases by 70% (y = −70).

Net change = 300 − 70 + [300 × (−70)] ÷ 100

Net change = 230 − 210 = +20%

Since the result is positive, the expenditure increases by 20%.

∴ The correct answer is Increases, 20%.

Alternate Method

Given:

Percentage increase in price = 300%

Percentage decrease in consumption = 70%

Formula Used:

Expenditure = Price × Consumption

Calculations:

⇒ Let the initial price of tomatoes be ₹100 per kg and the initial consumption be 10 kg.

⇒ Initial Expenditure = 100 × 10 = ₹1000

⇒ New price after 300% increase = 100 + (300 ÷ 100) × 100 = ₹400 per kg

⇒ New consumption after 70% decrease = 10 − (70 ÷ 100) × 10 = 3 kg

⇒ New Expenditure = 400 × 3 = ₹1200

⇒ Change in Expenditure = 1200 − 1000 = ₹200 (Increase)

⇒ Percentage Increase = (200 ÷ 1000) × 100 = 20%

∴ The correct answer is Increases, 20%.

Additional Information

Successive Percentage Change

When a quantity is successively changed by x% and y%, the net percentage change is given by the formula: x + y + (x × y) ÷ 100. Use positive values for an increase and negative values for a decrease.

Price, Consumption, and Expenditure Relation

The foundational rule is Expenditure = Price × Consumption. If expenditure needs to remain constant while the price increases, consumption must be decreased proportionately.

Fraction Equivalent Method

For compound percentage calculations, converting percentages to fractional multipliers simplifies multiplication. For example, a 300% increase means multiplying the base value by 4, and a 70% decrease means multiplying the base value by 3/10.

Shortcut Trick

Length of the tangent = (Radius × Half of chord) ÷ Distance of chord from the center

Distance of chord from center = √(Radius² − Half-chord²) = √(20² − 16²) = 12 cm

Length of Tangent TA = (20 × 16) ÷ 12

TA = 320 ÷ 12 = 80 ÷ 3 = 26.67 cm

∴ The correct answer is 26.67 cm.

Alternate Method

Given:

Radius of the circle (OA) = 20 cm

Length of the chord (AB) = 32 cm

O M A B T 20 cm 16 cm 12 cm TA = ?

Calculations:

⇒ Let the line joining the center O and point T intersect the chord AB at point M.

⇒ The line from the center to the intersection of two tangents is the perpendicular bisector of the chord joining the points of tangency.

⇒ AM = AB ÷ 2 = 32 ÷ 2 = 16 cm.

⇒ In right-angled ΔOMA, using the Pythagoras theorem:

⇒ OM = √(OA² − AM²) = √(20² − 16²)

⇒ OM = √(400 − 256) = √144 = 12 cm.

⇒ In right-angled triangles ΔOMA and ΔOAT:

⇒ ∠AOM is common to both triangles.

⇒ ∠OMA = 90° (Since OT is perpendicular to AB)

⇒ ∠OAT = 90° (The radius to the point of tangency is perpendicular to the tangent)

⇒ ∴ ΔOMA ∼ ΔOAT (By AA similarity criterion).

⇒ The ratio of their corresponding sides will be proportional:

⇒ AM ÷ OM = TA ÷ OA

⇒ 16 ÷ 12 = TA ÷ 20

⇒ TA = (16 × 20) ÷ 12 = 320 ÷ 12

⇒ TA = 80 ÷ 3 = 26.666... ≈ 26.67 cm.

∴ The correct answer is 26.67 cm.

Additional Information

Properties of Tangents to a Circle

A tangent at any point of a circle is perpendicular to the radius through the point of contact. The lengths of two tangents drawn from an external point to a circle are always equal.

Perpendicular Bisector of a Chord

The perpendicular line drawn from the center of a circle to a chord bisects the chord into two equal halves. Conversely, a straight line drawn through the center to bisect a chord is always perpendicular to it.

Secant-Tangent Theorem

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the tangent length equals the product of the external secant length and the total secant length.

Given:

The expression to be evaluated is:

4 (1/6) ÷ 25 × 75 ÷ (1/5) of 125

Formula Used:

Use the BODMAS rule (Bracket, Order, Division and Multiplication, Addition and Subtraction) to simplify the expression.

Calculation:

Step-by-step simplification:

4 (1/6) ÷ 25 × 75 ÷ (1/5) of 125

First, simplify the "of" operation:

$\frac{1}{5} \text{ of } 125 = \frac{1}{5} × 125 = 25$

Now, substitute 25 back into the expression:

4 (1/6) ÷ 25 × 75 ÷ 25

Now, 4(1/6) = 25 / 6

Simplify the division and multiplication from left to right:

(25 /6) ÷ 25 × (75 ÷ 25)

(1/6)  × 3

1/2

The value of the expression is 1/2 .

Shortcut Trick

Total capacity = LCM of 9 and 21 = 63 units.

Efficiency of X = 7 units/hr, Y = 3 units/hr.

Work done in 1 cycle (2 hours) = 7 + 3 = 10 units.

In 6 cycles (12 hours), work done = 60 units, remaining = 3 units.

X fills the remaining 3 units in 3/7 hours.

∴ The correct answer is 12 ³/₇ hours.

Alternate Method

Given:

Time taken by Pipe X = 9 hours

Time taken by Pipe Y = 21 hours

Calculations:

⇒ Total work to be done = 63 units

⇒ Pipes are opened alternately starting with X.

⇒ Work done in 1st hour by X = 7 units

⇒ Work done in 2nd hour by Y = 3 units

⇒ Total work done in a 2-hour cycle = 7 + 3 = 10 units

⇒ In 6 cycles (12 hours), work done = 10 × 6 = 60 units

⇒ Remaining work = 63 − 60 = 3 units

⇒ In the 13th hour, it is Pipe X's turn.

⇒ Time taken by X to fill the remaining 3 units = 3 ÷ 7 hours

⇒ Total time taken = 12 + 3/7 = 12 ³/₇ hours

∴ The correct answer is 12 ³/₇ hours.

Additional Information

Alternate Working Rule

When entities work on alternate hours or days, calculate the work done in one complete cycle, multiply to get closest to the total work, and assign the remaining work to the entity whose turn is next.

Pipes & Cisterns

It operates similarly to Time and Work problems. The total capacity of the tank acts as Total Work (LCM of individual times) and the rate of filling is the Efficiency.

Emptying Pipes

If a pipe empties the tank instead of filling it, its efficiency is taken as negative, reducing the overall net work done per cycle.

Shortcut Trick Express all angles in terms of P to solve directly. Q = P − 20° and R = Q − 26° ⇒ R = P − 46° Sum of angles: P + (P − 20°) + (P − 46°) = 180° 3P − 66° = 180° ⇒ 3P = 246° ⇒ P = 82° ∴ The correct answer is 82°. Alternate Method Given: ⇒ P − Q = 20° ⇒ Q − R = 26° Formula Used: The sum of all interior angles in a triangle is 180°. ⇒ P + Q + R = 180°

P Q R P = ? P − 20° P − 46°

Calculations: ⇒ From the first equation, Q = P − 20° ⇒ From the second equation, R = Q − 26° ⇒ Substitute Q into the R equation: R = (P − 20°) − 26° = P − 46° ⇒ Sum of the angles: P + (P − 20°) + (P − 46°) = 180° ⇒ 3P − 66° = 180° ⇒ 3P = 246° ⇒ P = 246° ÷ 3 = 82° ∴ The correct answer is 82°. Additional Information Angle Sum Property of a Triangle The sum of all interior angles of a triangle is always equal to 180°. For any triangle ABC, ∠A + ∠B + ∠C = 180°. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. Classification by Angles Triangles are classified into Acute (all angles < 90°), Right (one angle = 90°), and Obtuse (one angle > 90°).

Shortcut Trick

Effective SI% for Scheme A = 8% × 5 = 40% of P.

Effective SI% for Scheme B = 5% × 7 = 35% of 4P = 140% of P.

Total Interest = 40% of P + 140% of P = 180% of P.

⇒ 180% of P = 1620 ⇒ P = 1620 ÷ 1.8 = 900.

Investment in Scheme B = 4P = 4 × 900 = 3600.

∴ The correct answer is ₹3,600.

Alternate Method

Given:

Rate of interest for Scheme A = 8% p.a., Time = 5 years

Rate of interest for Scheme B = 5% p.a., Time = 7 years

Total interest received = ₹1,620

Formula Used:

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

Calculations:

⇒ Let the principal amount invested in Scheme A be P.

⇒ Amount invested in Scheme B = 4P.

⇒ SI from Scheme A = (P × 8 × 5) ÷ 100 = 40P ÷ 100 = 0.4P

⇒ SI from Scheme B = (4P × 5 × 7) ÷ 100 = 140P ÷ 100 = 1.4P

⇒ Total Interest = SI from Scheme A + SI from Scheme B

⇒ Total Interest = 0.4P + 1.4P = 1.8P

⇒ 1.8P = 1620

⇒ P = 1620 ÷ 1.8 = 900

⇒ Amount invested in Scheme B = 4P = 4 × 900 = 3600

∴ The correct answer is ₹3,600.

Additional Information

Effective Interest Rate in SI

In Simple Interest, the effective interest rate for a given period is simply the product of the rate of interest and the time period (R × T)% of the principal.

Total Amount in Simple Interest

The total amount (A) obtained after T years is the sum of the principal (P) and the simple interest (SI). Formula: A = P + SI = P[1 + (R × T) ÷ 100].

Simple Interest vs Compound Interest

In SI, the interest is calculated only on the initial principal. In Compound Interest (CI), interest is calculated on the principal and also on the accumulated interest of previous periods.

Given:

Marks scored by the student in 6 subjects: 98, 97, 93, 94, 93, 92

Maximum marks per subject = 100

Formula used:

Average marks = $\frac{\text{Total marks obtained}}{\text{Total number of subjects}}$

Calculations:

Total marks obtained = 98 + 97 + 93 + 94 + 93 + 92 = 567

Average marks = $\frac{567}{6}$

⇒ Average marks = 94.5

The average marks scored by the student is 94.5

Shortcut Trick

Total distance = 150 + 250 = 400 m.

Relative speed in same direction = S₁ − S₂ = 400 ÷ 20 = 20 m/s.

Relative speed in opposite direction = S₁ + S₂ = 400 ÷ 5 = 80 m/s.

Solving, S₁ = (80 + 20) ÷ 2 = 50 m/s and S₂ = (80 − 20) ÷ 2 = 30 m/s.

Speeds in km/h = 50 × (18/5) = 180 km/h and 30 × (18/5) = 108 km/h.

∴ The correct answer is 180 km/h and 108 km/h.

Alternate Method

Given:

Length of first train (L₁) = 150 m

Length of second train (L₂) = 250 m

Time taken to cross in same direction (T₁) = 20 seconds

Time taken to cross in opposite direction (T₂) = 5 seconds

Formula Used:

Speed = Distance ÷ Time

Total distance covered to cross each other = L₁ + L₂

Calculations:

⇒ Total Distance = 150 + 250 = 400 m

⇒ Let the speed of the first train be u m/s and the second train be v m/s.

⇒ When running in the same direction, relative speed = u − v

⇒ u − v = 400 ÷ 20 = 20 m/s     ... (Equation 1)

⇒ When running in opposite directions, relative speed = u + v

⇒ u + v = 400 ÷ 5 = 80 m/s     ... (Equation 2)

⇒ Adding Equation 1 and Equation 2:

⇒ 2u = 100 ⇒ u = 50 m/s

⇒ Subtracting Equation 1 from Equation 2:

⇒ 2v = 60 ⇒ v = 30 m/s

⇒ Convert speeds to km/h by multiplying with (18/5):

⇒ Speed of first train = 50 × (18/5) = 180 km/h

⇒ Speed of second train = 30 × (18/5) = 108 km/h

∴ The correct answer is 180 km/h and 108 km/h.

Additional Information

Relative Speed

When two objects move in opposite directions, their relative speed is the sum of their individual speeds (S₁ + S₂). When moving in the same direction, it is the difference of their speeds (|S₁ − S₂|).

Distance While Crossing

When two trains cross each other, the total distance covered is always the sum of their lengths (L₁ + L₂), regardless of the direction they are moving.

Unit Conversion Trick

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

Shortcut Trick

Since both persons receive 1 more marble, the difference in their marble count remains 12.

The new ratio of Kavita's to Ravi's marbles is derived from 3 × Kavita = 4 × Ravi, giving a ratio of 4 : 3.

The difference in ratio parts is 4 − 3 = 1 unit.

Since 1 unit = 12 marbles, Kavita's new marble count = 4 units = 48 marbles.

Kavita's actual marbles before the addition = 48 − 1 = 47 marbles.

∴ The correct answer is 47 marbles.

Alternate Method

Given:

Kavita had 12 more marbles than Ravi had.

If each of them gets 1 more marble, 3 × (Kavita's new marbles) = 4 × (Ravi's new marbles).

Calculations:

⇒ Let Ravi's actual marbles = R

⇒ Kavita's actual marbles = R + 12

⇒ When both get 1 more marble, the difference between their totals remains 12.

⇒ 3 × (New Kavita) = 4 × (New Ravi)

⇒ (New Kavita) / (New Ravi) = 4 / 3

⇒ Difference in ratio = 4 units − 3 units = 1 unit

⇒ 1 unit corresponds to the difference of 12 marbles.

⇒ Kavita's new marbles = 4 units = 4 × 12 = 48 marbles

⇒ Kavita's actual marbles = 48 − 1 = 47 marbles

∴ The correct answer is 47 marbles.

Additional Information

Constant Difference Rule

When the same uniform quantity is added to or subtracted from two numbers, the numerical difference between the two numbers remains completely unchanged.

Ratio Translation

A mathematical statement equating two products in the form "a × A = b × B" translates directly into the inverse ratio form A : B = b : a.

Direct Unitary Method

When a given quantitative value corresponds to a specific difference in ratio parts, 1 ratio unit can be calculated directly by dividing the actual difference by the ratio part difference.

Shortcut Trick

By the rule of alligation, the ratio of quantities equals the cross-difference of their unit prices.

Ratio of quantities given = 15 kg : 5 kg = 3 : 1

Using the alligation cross ratio ⇒ (x − 30) : (30 − 10) = 3 : 1

⇒ (x − 30) ÷ 20 = 3

⇒ x − 30 = 60 ⇒ x = 90

∴ The correct answer is ₹90.

Alternate Method

Given:

Quantity of cheaper wheat (Q₁) = 15 kg

Price of cheaper wheat (P₁) = ₹10 per kg

Quantity of costlier wheat (Q₂) = 5 kg

Average price of the mixture (P_m) = ₹30 per kg

Let the price of the costlier wheat be P₂ = ₹x per kg.

Formula Used:

Total cost of mixture = Sum of individual costs

⇒ Q₁ × P₁ + Q₂ × P₂ = (Q₁ + Q₂) × P_m

Calculation:

⇒ 15 × 10 + 5 × x = (15 + 5) × 30

⇒ 150 + 5x = 20 × 30

⇒ 150 + 5x = 600

⇒ 5x = 600 − 150

⇒ 5x = 450

⇒ x = 90

∴ The correct answer is ₹90.

Additional Information

Rule of Alligation

It gives the exact ratio in which two ingredients at different prices must be mixed to obtain a desired average mixture price. Formula: Q_cheaper ÷ Q_costlier = (P_costlier − P_mean) ÷ (P_mean − P_cheaper).

Weighted Average Method

The rule of alligation is practically a simplified cross-multiplication of the weighted average formula P_m = (Q₁P₁ + Q₂P₂) ÷ (Q₁ + Q₂).

Versatility of Alligation

The Alligation shortcut is not only restricted to price and mixture amounts; it is universally applicable across chapters like Speed & Distance, Percentages, Profit & Loss, and Averages.

Shortcut Trick Divide the entire equation by cos2θ to get: 3tan2θ + 5 = 4sec2θ Substitute sec2θ = 1 + tan2θ into the equation: 3tan2θ + 5 = 4(1 + tan2θ) 5 − 4 = 4tan2θ − 3tan2θ ⇒ tan2θ = 1 Since θ is an acute angle, tanθ = 1. ∴ The correct answer is 1.

Alternate Method Given: 3sin2θ + 5cos2θ = 4 Formula Used: sin2θ + cos2θ = 1 tanθ = Perpendicular ÷ Base Calculations:

⇒ 3sin2θ + 3cos2θ + 2cos2θ = 4 ⇒ 3(sin2θ + cos2θ) + 2cos2θ = 4 ⇒ 3(1) + 2cos2θ = 4 ⇒ 2cos2θ = 1 ⇒ cos2θ = 1 / 2 ⇒ cosθ = 1 / √2 ⇒ Since θ is an acute angle, θ = 45° ⇒ tanθ = tan(45°) = 1 ∴ The correct answer is 1.

Additional Information Trigonometric Identities Fundamental identities: sin2θ + cos2θ = 1, sec2θ − tan2θ = 1, and cosec2θ − cot2θ = 1. Angles in the First Quadrant For any acute angle (0° < θ < 90°), all six trigonometric ratios (sin, cos, tan, cot, sec, cosec) are positive. Values at 45° When θ = 45°, the perpendicular and base of a right triangle are equal in length, giving tan(45°) = 1 and sin(45°) = cos(45°) = 1/√2.

The correct answer is: Option 1 i.e. To start or create something from the very beginning.

Key Points

• The idiom "Start from scratch" means to begin something from the very beginning without any prior preparation or advantage. (शुरुआत से शुरू करना)
• Example: After losing all their data, they had to start the project from scratch.
• "To start or create something from the very beginning" means initiating a task or project without any existing foundation, starting anew. (शुरुआत से कुछ बनाना या शुरू करना)
• Example: When they moved to a new country, they had to build their lives from scratch.

Therefore, the correct answer is: Option 1 i.e. To start or create something from the very beginning.

Additional Information

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

• To address an issue (किसी मुद्दे को संबोधित करना): To deal with or discuss a problem or matter.
• Example: The manager called a meeting to address the issue of low productivity.
• To develop something out of waste material (कचरे से कुछ विकसित करना): To create or produce something useful from discarded or recycled materials.
• Example: The artist was known for developing beautiful sculptures out of waste material.
• To point out something wrong (कुछ गलत इंगित करना): To identify or highlight an error or mistake.
• Example: She was quick to point out the errors in the report.

The correct answer is: Option 3 i.e. Bright.

Key Points

• The word "dark" means having very little or no light, not reflecting much light. (अंधेरा)
• Example: The room was so dark that I couldn't see anything.
• "Bright" refers to something that emits or reflects a lot of light, making it easy to see. (उज्ज्वल)
• Example: The sun is very bright today.
• Hence, we can infer that the opposite of 'dark' is 'bright'.

Therefore, the correct answer is: Option 3 i.e. Bright.

Additional Information

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

• Shadowy (छायादार): Full of shadows or difficult to see.
• Example: The old house looked very shadowy at night.
• Dim (मंद): Not bright or clear.
• Example: The light in the room was dim, making it hard to read.
• Gloomy (उदास): Dark or poorly lit, especially so as to appear depressing or frightening.
• Example: The weather was gloomy and it seemed like it would rain all day.

The correct answer is Option 4.

Key Points

• The paragraph discusses house sparrows and their current situation.
• Sentence D is the first sentence as it introduces the subject:
• "House sparrows can be found in most places with and without houses (or other structures)."
• Sentence B follows as it gives additional information about their commonality:
• "It is one of the most common birds along with the other two species, the European starling, and the rock pigeon."
• Sentence C is the third sentence because it talks about their presence and how they are often overlooked:
• "Their constant presence outside our homes makes it easy to overlook them."
• Sentence A is the fourth as it discusses the current issue affecting their population:
• "However, their population is declining nowadays due to noise pollution."
• The correct sequence is DBCA.

Coherent paragraph after rearrangement:

"House sparrows can be found in most places with and without houses (or other structures). It is one of the most common birds along with the other two species, the European starling, and the rock pigeon. Their constant presence outside our homes makes it easy to overlook them. However, their population is declining nowadays due to noise pollution."

The correct answer is 'Option 3'.

Key Points

• The person who performs magic to entertain people is called a "Magician".
• The term "Magician" is the most commonly used word for someone who performs magic shows or tricks for entertainment.

Hence, the correct answer is Option 3'.

Complete Sentence: A person who performs magic to entertain people is called a magician.

Additional Information

• Option 1: "Alchemist" refers to someone practicing an ancient and mystical form of science, not a performer of magic for entertainment.
• Option 2: "Angel" refers to a celestial being, which is unrelated to the act of performing magic for an audience.
• Option 4: "Palmist" refers to someone who reads palms, typically for fortune-telling, not performing magic tricks.

The correct answer is: Option 1 i.e. cohesion and erode.

Key Points

• "Cohesion" refers to the action or fact of forming a united whole. (संबद्धता)
• Example: The cohesion among the team members was evident in their smooth coordination during the project.
• The word "erode" means to gradually wear away or be worn away by natural agents. (क्षरण करना)
• Example: The coastline has been eroded by the sea.

Therefore, the correct answer is: cohesion and erode.

Additional Information

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

• Divergence (विचलन): The process or state of diverging.
• Example: There was a clear divergence between the two opinions.
• Relativity (सापेक्षता): The absence of standards of absolute and universal application.
• Example: The theory of relativity revolutionized physics.
• Severance (विच्छेद): The action of ending a connection or relationship.
• Example: The severance of diplomatic ties was a significant event.
• Revolution (क्रांति): A forcible overthrow of a government or social order, in favor of a new system.
• Example: The Industrial Revolution brought great changes to society.
• Controversy (विवाद): Disagreement, typically when prolonged, public, and heated.
• Example: The new policy caused a lot of controversy.
• Diminution (कमी): A reduction in the size, extent, or importance of something.
• Example: There has been a diminution in the number of students attending the school.

The correct answer is: Option 1 i.e. Festive.

Key Points

• The word "Desolate" means a place that is empty and without people, making it appear sad and lonely. (उजाड़)
• Example: The once bustling town is now desolate and abandoned.
• "Festive" refers to something that is related to a celebration or festival, bringing joy and cheer. (उत्सव)
• Example: The streets were decorated in a festive manner for the holiday season.
• Hence, we can infer that the opposite of "Desolate" is "Festive".

Therefore, the correct answer is: Option 1 i.e. Festive.

Additional Information

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

• Allusive (संकेतपूर्ण): Making indirect references.
• Example: His speech was allusive, hinting at past events without directly mentioning them.
• Frugal (मितव्ययी): Being economical with resources or money.
• Example: She lived a frugal life, saving money wherever she could.
• Melancholic (उदास): Feeling or expressing deep sadness.
• Example: The melancholic music made everyone in the room feel somber.

The correct answer is Option 3.

Key Points

• Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
• In the active voice, the sentence is: "The cashier had finished the assigned task on time."
• To convert to passive voice: Place the object "the assigned task" at the beginning.
• Change the active verb form "had finished" to "had been finished" (past perfect passive).
• Add the preposition "by" followed by the original subject "the cashier."
• Ensure the time phrase "on time" remains at the end of the sentence for clarity.

Therefore, the correct answer is Option 3.

Correct Sentence: "The assigned task had been finished by the cashier on time."

Additional Information

• Option 1: "The assigned task is finished by the cashier on time." – Incorrect tense (present simple passive).
• Option 2: "The assigned task has been finished by the cashier on time." – Incorrect tense (present perfect passive).
• Option 4: "The assigned task was finished by the cashier on time." – Incorrect tense (past simple passive).