Here, we use the table given below:

​

Logic: Subtraction of 7 from the positional value of the first alphabet and addition of 4 and 2 to the positional value of the second and third alphabet respectively.

Given:

AMY : TQA →

YJZ : RNB →

Checking the given options:

1. EAT : XFV →

2. TRY : MVW →

3. PAL : JEN →

4. CUP : VYR →

Here, 'CUP : VYR' is similar to the given letter clusters.

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

Given:

333, 321, 328, 328, 323, 335,?

The logic followed in the given series is:

Here, '318' is the next number.

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

Here, we use the table given below:

​

Logic: '2' and '6' are added to the positional value of the first and second alphabet respectively.

Checking all the given options:

1. LNT →

2. GJP →

3. BDJ →

4. TVB →

Here, 'GJP' is different from the rest.

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

As per the given information:

Here, the code for 'rocket' is 'pi'.

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

Here, we use the table given below:

​

Logic: Rearrangement of the given letters.

Given:

HMQ : QMH →

PWY : YWP →

Checking all the given options:

1. QRT : RQT →

2. UWK : VXL →

3. LJH : HJL →

4. EJK : OPQ →

Here, 'LJH : HJL' is similar to the given letter clusters.

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

Preparing the family tree diagram by using the following symbols:

As per the given information:

 

 

 

 

 

Checking all the given options:

1. D % P # K + R % F

D is the mother of P, P is the husband of K, K is the sister of R and R is the mother of F.

Here, D is the aunt's mother-in-law of F.

2. F @ R + K + P % D

F is the brother of R, R is the sister of K, K is the sister of P and P is the mother of D.

Here, D is F's sister's son or daughter.

3. P $ D % R + K % F

P is the daughter of D, D is the mother of R, R is the sister of K and K is the mother of F.

Here, D is the maternal grandmother of F.

4. D % P + K @ R $ F

D is the mother of P, P is the sister of K, K is the brother of R and R is the daughter of F.

Here, D is the wife of F.

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

Given:

LT 48, ?, NV 42, OW 39, PX 36

Logic: '1' is added to the first two letter's position value and '3' is subtracted from the number.

Here, 'MU 45' is the missing term.

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

The logic followed in the given figure series is:

From Figure (1) to (2):

The symbols moving as shown below.

From Figure (2) to (3):

The symbols moving as shown below and E changes into 0.

From Figure (3) to (4):

The symbols moving as shown below.

From Figure (4) to Answer Figure:

The symbols moving as shown below and 0 changes into C.

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

Here, we use the table given below:

As per the given information:

Given:

31 C 48 B 7 D 69 A 23 =?

Putting sign as per the table:

⇒ 31 + 48 × 7 - 69 ÷ 23

Apply BODMAS rule:

⇒ 31 + 48 × 7 - 3

⇒ 31 + 336 - 3

⇒ 367 - 3 = 364.

Here, the value of the equation is '364'.

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

Here, we use the table given below:

Given:

⇒ 101 + 38 - 78 × 3 ÷ 9 = ?

After interchanging '×' and '÷' →

⇒ 101 + 38 - 78 ÷ 3 × 9

⇒ 101 + 38 - 26 × 9

⇒ 101 + 38 - 234

⇒ 139 - 234 = -95.

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

Statements: 

(I) Some editors are journalists.

(II) All journalists are writers.

(III) No writer is a reporter.

The Venn diagram as per the given statements:

Conclusion

(I) Some writers are editors → Follow (Because some editors are journalists and all journalists are writers, which means some writers are editors is definitely true)

(II) No reporter is a journalist → Follow (Because all journalists are writers and no writers are reporters, which means no reporter is a journalist is definitely true)

Hence, the correct answer is "Both conclusions I and II follow".

Hence, the correct answer is "Option 3".

Given:

Tomorrow = Tuesday

Today = Monday

100 days from today:

⇒ (100 ÷ 7) = 14 weeks (Monday) + 2 days (Tuesday, Wednesday)

⇒ The 100^th day will be Wednesday.

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

As per the given information:

Here, 'teaches' and 'science' are common so the code for 'mother' is '32' and the code for 'father' is '#'.

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

Logic: Second no. = [(First no.)² - 1]

Checking all the given options:

(1) 11 - 120 →

⇒ [(11)² - 1]

⇒ (121 - 1) = 120

(2) 13 - 168 →

⇒ [(13)2 - 1]

⇒ (169 - 1) = 168

(3) 15 - 224 →

⇒ [(15)2 - 1]

⇒ (225 - 1) = 224

(4) 18 - 325 →

⇒ [(18)2 + 1]

⇒ (324 + 1) = 325

Here, '18 - 325' is different from the others.

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

Given:

999, 995, 986, 970, 945,?

Logic: Subtraction of the square of the consecutive numbers from 2.

Here, the missing term is '909'.

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

Logic: Second no. = [(First no. × 9) - 7]

Checking all the given options:

(1) 21 : 182 →

⇒ [(21 × 9) - 7]

⇒ (189 - 7) = 182

(2) 11 : 92 →

⇒ [(11 × 9) - 7]

⇒ (99 - 7) = 92

(3) 17 : 146 →

⇒ [(17 × 9) - 7]

⇒ (153 - 7) = 146

(4) 31 : 284 →

⇒ [(31 × 9) + 5]

⇒ (279 + 5) = 284

Here, '31 : 284' is different from the rest.

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

The mirror image of the given figure is:

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

Here, we use the table given below:

​Given:

W_KY ENC YG_G ZIT _KWO

Logic: Addition of '1', '2', '3' and '4' to the positional values of the first, second, third and fourth alphabet.

By checking options and substituting accordingly:

(1) BXQGA → WBKY - XENC - YGQG - ZITG - AKWO

(2) CXQKA → WCKY - XENC - YGQG - ZITK - AKWO

Here, the series is logically correct.

(3) AYQGB → WAKY - YENC - YGQG - ZITG - BKWO

(4) DXRKA → WDKY - XENC - YGRG - ZITK - AKWO

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

Given: 'STRANGE'

Arranging in alphabetical order:

STRANGE → AEGNRST

Here, all the letters change their position.

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

The mirror image of the given figure is:

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

Logic: Second no. = [(First no.)³ - 5]

Given:

3 : 22 →

⇒ [(3)³ - 5]

⇒ (27 - 5) = 22

6 : 211 →

⇒ [(6)3 - 5]

​⇒ (216 - 5) = 211

Checking the given options:

(1) 8 : 509 →

⇒ [(8)³ - 3]

⇒ (512 - 3) = 509

(2) 5 : 113 →

⇒ [(5)3 - 12]

⇒ (125 - 12) = 113

(3) 7 : 330 →

⇒ [(7)3 - 13]

⇒ (343 - 13) = 330

(4) 4 : 59 →

⇒ [(4)3 - 5]

​⇒ (64 - 5) = 59

Here, '4 : 59' is similar to the given number pairs.

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

The counting of rectangles in the given figure:

Here, the number of rectangles is '11'.

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

Given:

A_DC _FHG IJ_K NPO QRT

Logic: Addition of '4' to the positional values of each alphabet.

By checking options and substituting accordingly:

(1) BEKMS → ABDC - EFHG - IJKK - MNPO - QRTS

(2) BELNU → ABDC - EFHG - IJLK - NNPO - QRTU

(3) BELMS → ABDC - EFHG - IJLK - MNPO - QRTS

Here, the series is logically correct.

(4) BEKNU → ABDC - EFHG - IJKK - NNPO - QRTU

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

Preparing the family tree diagram by using the following symbols:

As per the given information, the family tree diagram:

1. D is the son of E and M is the husband of E.

2. A is the mother of E and T is the husband of A.

Here, T is the father of D's mother.

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

Logic: Second no. = [(First no. × 8) - 8]

Given:

(63, 496) →

⇒ [(63 × 8) - 8]

⇒ (504 - 8) = 496

(42, 328) →

⇒ [(42 × 8) - 8]

⇒ (336 - 8) = 328

Checking the given options:

1. (48, 376) →

⇒ [(48 × 8) - 8]

⇒ (384 - 8) = 376

2. (25, 194) →

⇒ [(25 × 8) - 8]

⇒ (200 - 8) = 192

3. (37, 302) →

⇒ [(37 × 8) - 8]

⇒ (296 - 8) = 288

4. (63, 512) →

⇒ [(63 × 8) - 8]

⇒ (504 - 8) = 496

Here, (48, 376) is similar to the given number pairs.

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

The correct answer is Kathak.

Key Points

• Kathak is one of the eight major classical dance forms of India and originated in North India.
• The dance form has its roots in the Mughal era and is characterized by intricate footwork, graceful hand movements, and storytelling through facial expressions.
• Kathak is closely associated with Hindustani classical music and is often performed to the accompaniment of tabla, sarangi, and sitar.
• The nineteenth century saw the golden age of Kathak under the patronage of Wajid Ali Shah, the last Nawab of Oudh.
• He established the Lucknow Gharana with its strong accent on bhava, the expression of moods and emotions.
• The Jaipur Gharana is known for its layakari or rhythmic virtuosity and the Benaras Gharana is another prominent school of Kathak dance.
• The technique of movement in Kathak is unique.
• Today, Kathak has emerged as a distinct dance form.
• Being the only classical dance of India having links with Muslim culture, it represents a unique synthesis of Hindu and Muslim genius in art.
• Further, Kathak is the only form of classical dance wedded to Hindustani or North Indian music.

Additional Information

• ​Kathak dance is a combination of music, dance, and narrative.
• The name Kathak is derived from the Sanskrit word katha meaning story.
• This dance form traces its origins to the nomadic bards of ancient northern India, known as Kathaks, or storytellers.
• The present-day Kathak dance mainly depends on the medieval period Ras Lila, a local dance in the Braj region of Uttar Pradesh.

List of classical dances of India:​

The correct answer is NABARD in Mumbai.

Key Points

• NGO stands for Non-Governmental Organization, which is a non-profit organization that operates independently of any government. NGOs are usually involved in social, cultural, and environmental activities to promote social welfare.
• Microfinance is a financial service provided to low-income individuals or groups who do not have access to traditional banking services. Microfinance institutions provide small loans, savings, insurance, and other financial services to help people improve their livelihoods.
• MYRADA in Bangalore is an NGO that works in the areas of rural development, natural resource management, and microfinance. SEWA in Ahmedabad is another NGO that provides microfinance services to women entrepreneurs. ADITHI in Patna is an NGO that works for the empowerment of women and children through education, health, and livelihood programs.
• NABARD (National Bank for Agriculture and Rural Development) is a development bank that provides financial and technical assistance to rural areas in India. While NABARD supports microfinance institutions and self-help groups, it is not an NGO as it is a government-owned institution.

Additional Information

• A large amount of loan is not a basic principle of micro-financial institutions in India.
• The functions of Microfinance institutions are:
• Maintain macroeconomic stability.
• Avoid interest-rate caps.
• Refrain from distorting the market with unsustainable subsidized.
• High-delinquency loan programs.
• MFIs are financial companies that provide small loans to people who do not have any access to banking facilities.
• The definition of “small loans” varies between countries. In India, all loans that are below Rs. 1 lakh can be considered as microloans.
• Various types of institutions offer microfinance:
• ​Credit unions.
• Commercial banks.
• NGOs (Non-governmental Organizations).
• Cooperatives, and sectors of government banks.
• The emergence of “for-profit” MFIs is growing. In India, these 'for-profit' MFIs are referred to as Non-Banking Financial Companies (NBFC).

The correct answer is the Swaran Singh Committee.

Key Points

• The Fundamental Duties were incorporated in Part IV-A of the Indian Constitution through the 42^nd Constitutional Amendment Act, 1976.
• At present, there are eleven fundamental duties under Article 51 A of the Constitution.
• The idea of Fundamental Duties has been borrowed from the erstwhile USSR.
• Originally the duties were ten in number, later on through the 86^th Amendment Act, of 2002, the eleventh Fundamental duty was added.
• Fundamental duties are non-enforceable in nature.
• Swaran Singh Committee recommended the inclusion of Fundamental Duties in the Indian Constitution.

Additional Information 

• The Sarkaria Commission was set up on 9^th June 1983 by the Government of India.
• Aim: To review the relations between the Centre and the States.
• Justice Rajendra Singh Sarkaria, a retired Judge of SC of India, was the Chairman of the commission.
• The other two members of the commission were:
• Shri B. Sivaraman
• Dr S R Sen​
• PB Patil Committee was constituted for the evaluation of the Panchayat Raj system in 1984.
• The committee emphasized involving people and gave 184 recommendations for reforming the system and enabling greater participation.
• Balwant Rai Mehta Committee was appointed to examine the working of the community development program and the national extension service.
• Balwant Rai Mehta Committee was appointed in 1957.
• Balwant Rai Mehta was the chairman of this committee.
• The Balwant Rai Mehta Committee recommended establishing a three-tier Panchayati Raj structure.

The correct answer is Uttar Pradesh.

Key Points

• Pratham Bank was established in 1975 as the first Regional Rural Bank of India.
• Its Head Office was located in Moradabad, Uttar Pradesh.
• The bank was sponsored by Syndicate Bank and had its operations in 8 districts of Uttar Pradesh.
• The first Regional Rural Bank “Prathama Grameen Bank” was set up on October 2, 1975.
• At present, there are 82 RRBs in India.
• The equity of a regional rural bank is held by the Central Government, the concerned State Government and the Sponsor Bank in the proportion of 50:15:35
• The purpose was to include rural areas into the economic mainstream since around 70% of the Indian population was rural.
• Prathama Bank, with its head office in Moradabad, Uttar Pradesh was the first RRB.

Additional Information

• In October 1983, the Grameen Bank Project was transformed into an independent bank by government legislation.
• Today Grameen Bank is owned by the rural poor whom it serves. Borrowers of the Bank own 90% of its shares, while the remaining 10% is owned by the government.
• The journey of Vikas Bank which started as a small dream of like-minded friends to the proud moment of being a prestigious cooperative bank is a curious and inspirational one
• A group of social-minded youths of Sindhanur in Raichur district came together to form Vikas Yuvaka Mandali in 1979.

The correct answer is Gujarat.

 

Key Points

• Gujarat has been actively promoting its electronics and hardware manufacturing industry for the past few years, and this move is a part of that effort.
• The Semiconductor Policy aims to attract investments in semiconductor manufacturing, research and development, and related infrastructure in the state.
• The policy includes various incentives for semiconductor companies, such as subsidies on land, power, and water, and exemption from certain taxes and duties.
• The policy also aims to create a skilled workforce for the semiconductor industry by setting up training programs and collaborating with educational institutions.

 Additional Information

• Haryana: Haryana has been promoting its electronics industry through its Electronics System Design and Manufacturing (ESDM) Policy, but it has not launched a dedicated Semiconductor Policy.
• Madhya Pradesh: Madhya Pradesh has been promoting its electronics industry through its Electronics Manufacturing Policy, but it has not launched a dedicated Semiconductor Policy.
• Kerala: Kerala has been promoting its electronics industry through its Electronics and Hardware Manufacturing Policy, but it has not launched a dedicated Semiconductor Policy. However, Kerala has been in the news for its efforts to promote open source hardware and software, which could complement the semiconductor industry.

The correct answer is Australia.

Key Points

• India won the Border-Gavaskar trophy in 2023 by defeating Australia and qualified for the World Test championship Final.
• Border-Gavaskar trophy is a test cricket series played between India and Australia.
• The 2023 series was played in India and consisted of 4 test matches.
• India won the series 2-1 with one match ending in a draw.
• Australia has won the Border-Gavaskar trophy 5 times while India has won it 10 times.

Additional Information

• About Border Gavaskar Trophy
• It is a Test cricket series played between India and Australia.
• It is named after Alan Border of Australia and Sunil Gavaskar of India.
• Number of teams - 2
• Current trophy holder - India (10^th title)
• Most Runs - Sachin Tendulkar (3,235)
• Most wickets - Anil Kumble (105)
• Most successful - India (10 titles)
• First edition - 1996–97 (India)

The correct answer is Bhavabhuti.

Key Points

• Bhavabhuti was a renowned Sanskrit poet and playwright who lived during the 8^th century CE in India.
• Bhavabhuti (original name: Srikanth) was the court poet of King Yashovarman of Kannauj.
• He was the most illustrious dramatist and poet of the 8^th century.​
• Bhavabhuti wrote Malatimadhava, Mahaviracharita and Uttaramacharita.
• Uttararamacharita:
• It describes the Later Deeds of Lord Rama after the killing of Ravana and continues the story of Rama from his coronation to the expulsion of Sita and their final reunion.
• Malatimadhava:
• It is a complex love story of Malati and Madhava.
• Mahāvīracarita tells about the Rāma’s battle with Rāvaṇa.
• Hemchandra was a Jain scholar and poet who lived during the 12^th century CE and wrote extensively on Jainism and Indian philosophy.
• Kalhan was a Kashmiri historian who wrote the 'Rajatarangini', a chronicle of the kings of Kashmir, in the 12^th century CE.

 Additional Information

• Some important plays of Kalidas are:
• Vikramōrvaśīyam
• Mālavikāgnimitram
• Shakuntala
• Surdas
• The Bhakti poet from Agra is considered to be born between 1478 and 1483.
• Surdas was blind from birth and lived on the banks of the Yamuna river.
• He was the disciple of Vallabha Acharya.
• Surdas was a worshipper of Lord Krishna.
• He wrote poems in Brajbhasa in praise of Krishna.
• His composition Sur Sagar contains descriptions of Krishna.
• Gita ­Govinda by Kavi Jaydeva was written in Sanskrit.

The correct answer is It mentions that the state has its own religion.

Key Points

• The right to freedom of religion is a fundamental right guaranteed by the Indian Constitution under Articles 25 to 28.
• It grants individuals the freedom to profess, practice, and propagate any religion of their choice.
• It also prohibits discrimination on the grounds of religion and ensures that every person has the right to freely manage their religious affairs.
• The Indian Constitution recognizes the secular nature of the state and does not mention any state religion.
• The right to freedom of religion provides freedom to manage religious affairs, and this statement is true.
• This freedom includes the right to establish and maintain religious institutions, manage their own religious affairs, and regulate their own religious practices.
• The right to freedom of religion provides freedom of worship, and this statement is true.
• It guarantees the right to practice and propagate any religion of one's choice without any interference from the state or others.
• It is mentioned in Articles 25 to 28, and this statement is true.
• These articles outline the provisions for the right to freedom of religion in the Indian Constitution.
• It mentions that the state has its own religion, and this statement is false.
• The Indian Constitution recognizes the secular nature of the state and does not mention any state religion.

Additional Information 

• Originally, the Constitution provided for seven Fundamental Rights:

1. Right to equality (Articles 14–18)
2. Right to freedom (Articles 19–22)
3. Right against exploitation (Articles 23–24)
4. Right to freedom of religion (Articles 25–28)
5. Cultural and educational rights (Articles 29–30)
6. Right to property (Article 31)
7. Right to constitutional remedies (Article 32)

• However, the right to property was deleted from the list of Fundamental Rights by the 44^th Amendment Act, of 1978.
• Article 300-A in Part XII of the Constitution. So at present, there are only six Fundamental Rights

The correct answer is Only Statement iii is correct.

Key Points

• A liquidity trap is a situation where monetary policy becomes ineffective due to the zero lower bound on interest rates.
• ​Liquidity trap:
• A liquidity trap refers to a situation in which an increase in the money supply does not result in a fall in the interest rate but merely in addition to idle balances the interest elasticity of demand for money becomes infinite.
• Under normal conditions, an increase in money supply, resulting in excess cash balances, would cause an increase in bond prices, as individuals sought to acquire assets in exchange for money, and a corresponding fall in interest rates.
• The horizontal portion of the liquidity preference curve is referred to as the liquidity trap.
• In this portion of the curve, the demand for money is infinitely elastic with respect to the interest rate.
• Re­ductions in the interest rate, in this portion only, increase people’s desire to hold cash balances
• Statement 3 is correct as It is the point where speculative demand for money is infinitely elastic and the liquidity preference curve becomes perfectly elastic.
• In a liquidity trap, people prefer holding money regardless of the interest rate because they expect that the return on other assets will not be better. Therefore, the demand for money is infinitely elastic (it does not change with interest rates), and the liquidity preference curve becomes perfectly horizontal or elastic.

Additional Information"

• Speculative Demand for Money: In a liquidity trap, speculative demand for money is actually infinitely elastic, not inelastic. This means that people are willing to hold an unlimited amount of money at a particular low interest rate, because they expect interest rates to rise in the future, which would cause bond prices to fall.
• Liquidity Preference Curve: The curve becomes perfectly elastic (horizontal) at the liquidity trap, indicating that changes in the money supply will not affect interest rates because people prefer to hold money rather than invest in bonds.

Thus, this statement is incorrect because it incorrectly describes speculative demand for money as infinitely inelastic

The correct answer is Koneru Humpy.

Key Points

• The first Indian woman to win the World Rapid Chess Championship 2019 title is Koneru Humpy.
• She is India's youngest woman chess grandmaster player.
• In 2003, she was awarded Arjuna Award while in 2007, she was awarded Padma Shri.
• In 2015, she won a bronze medal in the Women's World Team Chess Championship.

Additional Information

• Vantika Agrawal is also an Indian chess player who has won several national and international championships.
• However, she did not win a medal in the Fide World Blitz Chess Championship in 2022.
• Bhakti Kulkarni is another Indian chess player who has represented India in several international tournaments.
• However, she did not win a medal in the Fide World Blitz Chess Championship in 2022.
• Rameshbabu Vaishali is an Indian chess player who has won several national and international championships.
• However, she did not win a medal in the Fide World Blitz Chess Championship in 2022.

The correct is Atal Road Tunnel.

Key Points

• Pir Panjal Railway Tunnel is located in Jammu and Kashmir and connects Banihal and Qazigund. It is the longest railway tunnel in India.
• Atal Tunnel:
• On October 3, 2020, Prime Minister Narendra Modi inaugurated the ‘Atal Tunnel’ the World’s Longest Highway Tunnel in Manali, Himachal Pradesh.
• The 9.02 Kilometre Long Tunnel has been constructed by the Border Roads Organisation (BRO) at a cost of INR 3, 300 crores.
• It connects Manali and Lahaul-Spiti Valley.
• Dr Syama Prasad Mookerjee Road Tunnel is located in Jammu and Kashmir and connects Srinagar and Leh.
• It is the longest road tunnel in India.
• Karbude Railway Tunnel is located in Maharashtra and is a part of the Konkan Railway.
• It is the longest railway tunnel on the Konkan Railway line.

Additional Information

• Atal Road Tunnel, also known as the Rohtang Tunnel, is located in Himachal Pradesh and connects Manali to Lahaul-Spiti Valley.
• It is the longest tunnel above 10,000 feet in the world.
• The tunnel is named after former Prime Minister of India, Atal Bihari Vajpayee, who laid the foundation stone for the project in 2002.
• The tunnel is a significant infrastructure development in the region as it provides all-weather connectivity to Lahaul-Spiti valley, which was earlier cut off from the rest of the country during winters due to heavy snowfall.
• The tunnel is expected to boost tourism in the region and also provide a strategic advantage to the Indian Army in the border areas.

The correct one is Himachal Pradesh.

Key Points

• Himachal Pradesh was declared as India's first carbon-neutral state in 2010.
• The state has taken various initiatives to reduce carbon emissions such as promoting renewable energy, afforestation, and energy-efficient practices.
• Himachal Pradesh has also introduced a carbon credit trading system to incentivize industries to reduce their carbon footprint.
• The state has set a target to become completely carbon-neutral by 2030.

Additional Information

• Arunachal Pradesh: Although the state has not been declared carbon-neutral, it has taken various initiatives to promote sustainable development and renewable energy sources.
• Madhya Pradesh: The state has been recognized for its efforts towards increasing forest cover and reducing carbon emissions. However, it has not been declared as a carbon-neutral state.
• Kerala: The state has also taken various steps towards reducing carbon emissions, but it has not been declared as a carbon-neutral state.

The correct answer is Ficus benghalensis.

Key Points

• The banyan tree is also known as the Indian banyan or Bengal fig.
• It is one of the largest trees in the world and can grow up to 30 meters tall.
• The banyan tree is considered sacred in Hinduism and is often planted near temples and other religious sites.
• Its aerial roots can grow into secondary trunks, making it appear as if there are multiple trees growing from a single root system.
• Ficus benghalensis' is the scientific name of Banyan.
• It is also known as the banyan fig and Indian Banyan.
• Banyan is a large, fast-growing, evergreen tree that is widely found across tropical and subtropical areas of the world.
• These trees begin growing on other trees as epiphytes and they eventually mature, completely killing the host tree.
• It produces large numbers of seeds that can be dispersed by both native and exotic birds.
• Family: Moraceae
• Order: Rosales

Additional Information

• Gossypium herbaceum is the scientific name for the cotton plant, which is used to produce cotton fiber.
• Santalum album, is the scientific name for sandalwood, a fragrant wood used in perfumes, cosmetics, and traditional medicine.
• Ananas comosus, is the scientific name for the pineapple, a tropical fruit with a sweet, juicy flesh.

The correct answer is extensive cultivation.

Key Points

• Extensive cultivation refers to the practice of cultivating large farms with moderately low inputs of labor and capital. It is also known as extensive subsistence agriculture.
• This type of cultivation is usually practiced in areas with low population density and abundant land resources.
• The main aim of extensive cultivation is to produce enough food to meet the needs of the family or community without the use of modern technology or intensive inputs.
• The crops grown in extensive cultivation are usually low-yielding and require less maintenance and care than in intensive cultivation.
• The other options are not correct because hybrid cultivation refers to the practice of growing genetically modified crops, intensive cultivation involves high inputs of labor and capital to produce high yields, and capitalist cultivation is a term used to describe large-scale commercial farming done by corporations.

Additional Information 

• Hybrid cultivation is a type of farming that involves the cross-breeding of two different plant varieties to create a new variety with desirable traits. This type of cultivation is often used to produce crops that are resistant to pests and diseases, have higher yields, and can tolerate harsh environmental conditions.
• Intensive cultivation is a type of farming that involves high inputs of labor, capital, and technology to produce high yields of crops. This type of cultivation is often used in areas with high population density and limited land resources.
• Capitalist cultivation is a term used to describe the large-scale commercial farming done by corporations. This type of cultivation is often characterized by the use of modern technology, high inputs of labor and capital, and the production of crops for the global market.

The correct answer is  62.8%.

Key Points

• The primary sector includes agriculture, forestry, fishing, and mining. As of 2011-2012, the percentage of women working in the primary sector in India was 62.8 percent.
• Women's participation in the workforce has been increasing in recent years, but there is still a significant gender gap.
• According to the World Bank, in 2019, the labor force participation rate for women in India was 22.3%, compared to 76.5% for men.
• The primary sector is an important part of the Indian economy, accounting for around 16% of the country's GDP in 2020.
• However, the sector is also facing challenges such as low productivity, climate change, and rural-urban migration.
• The government has implemented various policies and schemes to promote women's participation in the workforce, such as the Mahila Kisan Sashaktikaran Pariyojana (MKSP) for women farmers and the National Rural Livelihoods Mission (NRLM) for rural women.
• In addition to the primary sector, women are also employed in other sectors such as manufacturing, services, and the informal sector.
• However, women's participation in these sectors is also lower than men's, and they often face discrimination and unequal pay.

Additional Information

• Census:
• ​​Population Census is the total process of collecting, compiling, analyzing, and disseminating demographic, economic, and social data pertaining, at a specific time, to all persons in a country or a well-defined part of a country.
• The census is conducted under the provisions of the Census Act, of 1948.
• The bill for this Act was piloted by Sardar Vallabhbhai Patel, the then Home Minister of India.
• The population census is a Union subject under Article 246 of the Indian Constitution.
• In India, the population census is a Union subject (Article 246) and is listed at serial number 69 of the Seventh Schedule of the Constitution

The correct answer is Gussadi.

Key Points:

• Kanaka Raju
• He performs as an Indian gussadi dancer.
• He received the Padma Shri honor from the Indian government in 2021 for his contributions to the arts.
• Raju hails from the hamlet of Marlawai in the Komaram Bheem Asifabad district's Jainoor mandal.
• Gussadi dancing lessons have been taught by Raju for more than 40 years.
• In 1981, he again participated in the Republic Day procession.
• As of right now, he serves as the Kanaka Raju School of Gussadi dance's chief dance master.

Additional Information

• Wancho is a tribal folk dance form of the Wancho tribe in Arunachal Pradesh, India.
• It is characterized by slow, graceful movements and is performed during festivals and social events.
• Chalo dance is performed by the 'Nocte tribe' of Arunachal Pradesh to celebrate the auspicious festival of 'Chalo Loku'.
• Popir is a traditional dance form of the Sherdukpen tribe in Arunachal Pradesh, India.
• It is performed during the Losar festival to celebrate the Tibetan New Year and involves intricate footwork and the use of traditional musical instruments.

The correct answer is ppm.

Key Points

• The hardness of water is the measure of the concentration of dissolved minerals, primarily calcium and magnesium ions, in water.
• The most common unit of measuring water hardness is parts per million (ppm).
• Molarity is the measure of the concentration of a solution in terms of the number of moles of solute per liter of solution.
• It is not used to express water hardness.
• Normality is a measure of the concentration of a solution in terms of the number of equivalents of solute per liter of solution.
• It is also not used to express water hardness.
• A mole is the amount of a substance that contains the same number of particles as there are atoms in 12 grams of carbon-12. It is not used to express water hardness.

Additional Information

• Mole: It is a unit of measurement used in chemistry to express amounts of a chemical substance. It is defined as the amount of a substance that contains the same number of particles as there are atoms in 12 grams of carbon-12.
• Molarity: It is a measure of the concentration of a solution in terms of the number of moles of solute per liter of solution. It is commonly used in chemistry to express the concentration of a solution.
• Normality: It is a measure of the concentration of a solution in terms of the number of equivalents of solute per liter of solution. It is commonly used in acid-base chemistry to express the concentration of an acid or a base.
• Parts per million (ppm): It is a unit of measurement used to express the concentration of a substance in a solution. It is defined as the number of parts of a substance per one million parts of the solution. It is commonly used to express the concentration of minerals in water.

The correct answer is Credit cards.

Key Points

• Microfinance institutions in India primarily focus on providing financial services to the economically weaker sections of society who do not have access to formal banking services.
• The most common products offered by microfinance institutions in India are personal loans, insurance products, and savings accounts. These products are designed to meet the specific financial needs of the target customers and are offered at affordable interest rates.
• Credit cards are not typically offered by microfinance institutions in India. This is because credit cards are generally associated with higher credit risk and require a certain level of creditworthiness to qualify for them.
• Personal loans are one of the most popular products offered by microfinance institutions in India.
• These loans are typically used for meeting various personal expenses such as medical emergencies, education, and home renovation.
• Insurance products such as life insurance and health insurance are also commonly offered by microfinance institutions in India. These products provide financial protection to the customers and their families in case of unforeseen events.

Additional Information

• Personal loans: These are unsecured loans that do not require any collateral. The loan amount is typically small, and the repayment tenure can range from a few months to a few years.
• Insurance products: Microfinance institutions in India offer various insurance products such as life insurance, health insurance, and crop insurance. These products are designed to provide financial protection to the customers and their families in case of unforeseen events.
• Saving accounts: These are basic savings accounts that can be opened with a small deposit. The interest rates offered on these accounts are usually higher than those offered by traditional banks.

The correct answer is 2.13.

Key Points

• The minimum lane width is prescribed by the International Swimming Federation (FINA), which is the governing body for Swimming.
• The minimum lane width is important to ensure that swimmers have enough space to swim comfortably and safely without colliding with each other.
• FINA has prescribed different minimum lane widths for different types of competitions.
• For example, for Olympic Games, World Championships, and World Cup events, the minimum lane width is 2.5 meters. However, for other competitions, such as continental championships, the minimum lane width is 2.13 meters.
• Lane widths can also vary depending on the size of the pool. For example, in a 25-meter pool, the minimum lane width is 2.0 meters, whereas, in a 50-meter pool, the minimum lane width is 2.5 meters.

Additional Information

• About FINA:
• The Federation Internationale de Natation (FINA) is the world governing body for aquatic sports such as swimming, diving, water polo, and synchronized and open water swimming.
• FINA rules are used to manage state, national and international events such as the World Championships and the Olympics.
• The FINA Facilities Rules provide the best possible environment for competitive use and training.
• President: Julio C. Maglione (as of April 2021

The correct answer is Halocarbonyl.

Key Points

• The IUPAC group prefix of acyl halide compounds is "Halocarbonyl."
• Acyl halides are also known as acid halides, and they are compounds that contain a carbonyl group (C=O) and a halogen atom (F, Cl, Br, or I) attached to the same carbon atom.
• Alkoxycarbonyl is a group prefix used for compounds that contain an ester functional group (RCOOR') attached to an alkyl or aryl group.
• Carbamoyl is a group prefix used for compounds that contain a carbamate functional group (NH2COOR') attached to an alkyl or aryl group.
• Cyano is a group prefix used for compounds that contain a nitrile functional group (CundefinedN) attached to an alkyl or aryl group.

Additional Information

The correct answer is Lord Lytton.

Key Points

Vernacular Press Act 1878:

• ​British India passed the Vernacular Press Act (1878) to restrict press freedom and discourage criticism of British policy, notably the opposition that had risen since the commencement of the Second Anglo-Afghan War (1878–80).
• The Act was submitted by Lytton, the Viceroy of India at the time, and on March 14, 1878, the Viceroy's Council unanimously approved it. In order to "better control" the vernacular press and effectively penalize and prohibit "seditious literature" in "publications in oriental languages," the Vernacular Press Act (VPA) was passed.
• As a result, the British had nothing but hatred for the (non-English speaking) Indian press.
• It was also known as the Gagging Act.
• It was an act for the better control of publication in oriental languages.
• It was primarily targeted against Amrit Bazar Patrika.
• The act was repealed by Lord Ripon.

Additional Information

• Lord Dalhousie was the Governor-General of India from 1848 to 1856. He was known for his policies of annexation and modernization, including the Doctrine of Lapse and the construction of railways and telegraph lines.
• Lord Hastings was the Governor-General of India from 1813 to 1823. He was known for his military campaigns, including the Anglo-Nepalese War and the First Anglo-Burmese War.
• Lord Ripon was the Viceroy of India from 1880 to 1884. He was known for his liberal policies, including the repeal of the Vernacular Press Act and the introduction of local self-government.

The correct answer is Jharkhand.

Key Points

• The Tusu festival is primarily observed in Assam, the Tea-producing State, Northeastern Odisha, Southwest West Bengal, and Southeast Jharkhand.
• During this occasion, the goddess Tusu is worshipped. The focus is primarily on rivers. It is a unified expression of the agrarian society's shared trust and belief in the pleasure of crop gathering.
• It is thought that the term "Tusu" derives from the word "tush" for rice bran. Both a youthful child and a cosmic deity are representations of the Goddess Tusu.
• The ceremonies carried out during the Tusu Puja center on harvest-related ceremonies and songs of ethnic dedication chanted by women folk.
• Therefore, the Tusu festival is associated with Jharkhand.

Additional Information

State-Specific Festivals of India

The correct answer is Particle nature.

Key Points

Photoelectric effect:

• The phenomenon in which light energy forces a metal surface to release electrons is called the photoelectric effect.
• When the light hits, it shows the particle theory of light, and light is defined as a stream of photons or energy packets.
• The other phenomena such as interference, diffraction, and polarization can only be explained when the light is treated as a wave wherein the photoelectric effect, line spectra, and the production and scattering of x-rays demonstrate the particle nature of light.

Properties of Lightwaves:

• Not have any charge or we can say that they are neutral.
• Propagate as a transverse wave with both wave and particle nature.
• They move with a velocity the same as that of light i.e. 3 × 10⁸ m/s.
• It contains energy and it also contains momentum.
• They can travel in a vacuum and always travel in a straight line.

Additional Information

• Crystalline nature refers to the regular, repeating structure of a solid, which can affect how light interacts with it.
• However, it is not directly related to the photoelectric effect.
• Wave nature refers to the fact that light can exhibit interference and diffraction patterns, similar to water waves or sound waves.
• This is important in many areas of physics, but again, not directly relevant to the photoelectric effect.

The correct answer is Meerut.

Key Points

• The Revolt of 1857 was the first rebellion against the British East India Company.
• The first war of Indian Independence started on 10^th May 1857.
• The revolt was started at Meerut.
• It began as a revolt of the sepoys of the British East India Company’s army but eventually secured the participation of the masses.
• The issue of greased cartridges and military grievances has been over-emphasized as the factor for the Revolt of 1857.
• In March 1857, Mangal Pandey, a sepoy in Barrackpore, refused to use the cartridge and attacked his senior officers.
• He was hanged to death on 8^th April 1857.
• On 9^th May 1857, 85 soldiers in Meerut refused to use the new rifle and were sentenced to ten years’ imprisonment.
• The revolt is known by several names: the Sepoy Mutiny (by the British Historians), the Indian Mutiny, the Great Rebellion (by the Indian Historians), the Revolt of 1857, the Indian Insurrection, and the First War of Independence (by Vinayak Damodar Savarkar).
• Lord Canning was the British viceroy during the revolt of 1857.

Important Points

• The main causes of revolt were the contemporary Religious & Social, Political, and Economic scenarios of the country.
• The revolt is known by different names:
• The Sepoy Mutiny (by the British Historians)
• The Indian Mutiny
• The Great Rebellion (by the Indian Historians)
• The Revolt of 1857
• The First War of Independence (by Vinayak Damodar Savarkar)

Additional Information

• Agra: Agra was an important city during the Mughal era and was the capital of the Mughal Empire under Akbar, Jahangir, and Shah Jahan.
• Kanpur: Kanpur was one of the major centers of the revolt and was the site of the infamous Bibighar massacre, where British women and children were killed by rebels. However, it was not the starting point of the revolt.
• Delhi: Delhi was the center of the rebellion and the site of the formation of the rebel government, with Bahadur Shah Zafar as the nominal leader.

The correct answer is Pandit Hari Prasad Chaurasia.

Key Points

• He was born in Prayagraj.
• Famous classical flutist of the Hindustani classical tradition.
• Chaurasia belonged to the Maihar Senia Gharana (a community of performers who share a distinctive musical style), and he developed a rich personal style after years of experimentation and dedicated practice.
• Learned under the tutelage of famous flute player Bholanath Prasanna.
• Formed a group called Shiv-Hari with Santoor player Shiv Kumar Sharma.
• Was honored with many awards
• The Sangeet Natak Academy Award 1984
• Padma Bhushan 1992,
• Kalidas Samman 1999,
• Padma Vibhushan 2000,
• Sangeet Natak Academy Fellowship Award 2012, etc

Additional Information

• Ustad Zakir Hussain is a tabla player, percussionist, and composer who is known for his contributions to the world of Indian classical music.
• He has collaborated with several famous musicians, including Pandit Ravi Shankar and John McLaughlin.
• Ustad Bismillah Khan was a Shehnai player who is known for his mastery of the instrument.
• He was awarded the Bharat Ratna, India's highest civilian award, in recognition of his contributions to music.
• Ustad Vilayat Khan was a sitar player who is considered one of the greatest musicians of his generation.
• He was known for his innovative style and technical virtuosity.

Given :

A shopkeeper was selling a T-shirt at a discount of 10% so that he would earn a profit of 8%.

MP = 1080

Formula:

MP = SP × (100 - D)/100

SP = SP × (100 - P)/100

Calculation : 

Let the CP be x.

When the discount is 10%, profit is 8%,

Selling price = Cost price + Profit = x + 8% of x = 1.08x

∵ Marked price – Discount = Selling price

⇒ MP – 10% of MP = 1.08x

⇒ MP = 1.08x/0.9 = 1.2x

1.2x → 1080

x → 1080/1.2 = 900

The answer is 900.

Shortcut Trick 

(100 + P)/(100 - D) = MP/CP

⇒ 108/90 = 1080/CP

CP = 900

Given:

The difference between compound and simple interest on a certain amount of money at 4% per annum after 3 years is Rs. 76

Formula Used:

When calculated at simple interest

Interest = (p × r × t)/100

Where p, r and t respectively are the principal, rate of interest and time

When calculated at compound interest

Amount (A) = p (1 + r/100)ⁿ

Where p, r and n respectively are the principal, rate of interest and time

Compound interest = Amount – principal

Calculation:

Let the sum be Rs. 100%

Simple interest = (4% × 3) = 12%

Compounded interest 

⇒ 4% + 4% + 16/100% = 8.16%

⇒ 8.16% + 4% + (8.16 × 4)/100 = 12.4864%

According to the question

⇒ 12.4864% - 12% → 76

⇒ 0.4864% → 76

⇒ 1% → 76/0.4864 = 156.25

⇒ 100% → 15625

∴ The sum is 15625

Shortcut Trick

In Simple Interest, interest is always calculated on the Principal.

Total effective interest rate = 4% + 5% = 9%

Total Payable Amount = 100% (Principal) + 9% (Total SI) = 109% of 25,000

Amount = 25,000 × (109 ÷ 100) = 250 × 109 = 27,250

∴ The correct answer is Rs. 27,250.

Alternate Method

Given:

Principal (P) = Rs. 25,000

Rate in 1^st year (R₁) = 4%

Rate in 2^nd year (R₂) = 5%

Time (T) = 2 years

Formula Used:

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

Total Amount (A) = Principal + Total SI

Calculations:

⇒ Interest for Year 1 = (25000 × 4 × 1) ÷ 100 = Rs. 1,000

⇒ Interest for Year 2 = (25000 × 5 × 1) ÷ 100 = Rs. 1,250

⇒ Total Simple Interest = 1,000 + 1,250 = Rs. 2,250

⇒ Total Amount = Principal + Total Interest

⇒ Total Amount = 25,000 + 2,250 = Rs. 27,250

∴ The correct answer is Rs. 27,250.

Additional Information

Effective Simple Interest Rate

For consecutive years with different rates R₁, R₂, ..., R_n, the net rate is R_eff = R₁ + R₂ + ... + R_n.

Simple Interest vs Compound Interest

In SI, interest is only on the Principal, whereas in CI, interest is calculated on (Principal + accumulated Interest).

Amount Formula

Amount = P × [1 + (R₁ + R₂ + ... + R_n) ÷ 100], where P is the initial sum.

Given

Time taken by Aditya = 20 hours

Time taken by Vinay = 15 hours

Formula

Work = TIme × Efficiency

Calculation

Total work = LCM of 20 and 15 = 60

Efficiency of Aditya = 60/20 = 3

Efficiency of Vinay = 60/15 = 4

Time taken together = 60/(3 + 4) = 60/7 = 8(4/7) hours

The answer is 8(4/7) hours.

Given

Radius = 6 cm

Concept used

The tangent drawn is always perpendicular to the radius of the circle.

Calculation

OB = 6 cm

OA = 10 cm

AB² = OA² - OB²

AB2 = 102 - 62

AB2 = 100 - 36

AB = 8 cm

The answer is 8 cm.

Given

$\rm {(u - v)^3 + (v - w)^3 + (w - u)^3} \over {(u^2 - v^2)^3 + (v^2 - w^2)^3 + (w^2 - u^2)^3}$

Formula used

a² - b² = (a + b)(a - b)

a³ + b³ + c³ = 3abc  if a + b + c = 0

Calculation

$\rm {(u - v)^3 + (v - w)^3 + (w - u)^3} \over {(u^2 - v^2)^3 + (v^2 - w^2)^3 + (w^2 - u^2)^3}$

⇒ (u - v) + (v - w) + (w - u) = 0

⇒ $\rm {3(u - v) (v - w)(w - u)} \over {3(u^2 - v^2) (v^2 - w^2) (w^2 - u^2)}$ [using formula]

⇒ $\rm {(u - v) (v - w)(w - u)} \over {(u - v)(u + v) (v - w)(v + w) (w - u)(w + u)}$

⇒ $\rm 1 \over {(u + v)(v + w)(w + u)}$

∴ The answer is $\rm 1 \over {(u + v)(v + w)(w + u)}$

Given:

The successive discount are 20% and 15%.

Formula used:

Successive discount = X + Y - (XY)/100

Where,

X = First discount

Y = Second discount

Calculation:

Successive discount = X + Y - (XY)/100

X = 20%, Y = 15%

⇒ 20 + 15 - 300/100

⇒ 32%

∴ The single equivalent discount is 32%.

Formula used

sin2A + cos2A = 1

1/sin A = cosec A

1/cos A = sec A

Calculation

$\rm sinA \left(1 + {sinA\over cosA} \right) + cosA \left(1 + {cosA\over sinA} \right)$

⇒ sin A (cos A + sin A)/cos A + cos A(sin A + cos A)/sin A

⇒ (sin A + cos A) [(sin A/cos A) + (cos A/sin A)]

⇒ (sin A + cos A) [(sin²A + cos²A)/(cos A. sin A)]

⇒ (sin A + cos A) [1/(cos A. sin A)] 

⇒ $\frac {sin A }{ (cos A. sin A) } + \frac{ cos A }{ (cos A. sin A) }$

⇒ 1/cos A + 1/sin A

⇒ sec A + Cosec A

The answer is sec A + Cosec A.

Calculation

The total number of students admitted in schools B and D = 60 + 50 = 110

The total number of students admitted in schools A, C and E = 40 + 35 + 45 = 120

The ratio = 110: 120 = 11: 12

The answer is 11: 12

Given:

Third proportion = 1.8 and 9

Calculation:

Third proportion of 1.8 and 9 = 1.8 : 9 : : 9 : x

⇒ x = 9/0.2

⇒ x = 45

The third proportion is 45.

Given

w + 1/w = 6

Formula used

(w - 1/w)² = (w + 1/w)² - 4

Calculation

According to the above-given formula:

(w - 1/w)2 = (w + 1/w)2 - 4

⇒ (w - 1/w)2 = 62 - 4

⇒ (w - 1/w)2 = 32

⇒ (w - 1/w) = 4√2

The answer is 4√2.

Given

Cot1°. Cot2°. Cot3°. Cot4°. Cot5°  .... Cot178° Cot179°

Formula Used

cotθ = tan(90° - θ)

cotθ = 1/tanθ

Calculation

Cot1°. Cot2°. Cot3°. Cot4°. Cot5°  .... Cot178 Cot179°

Cot90° = 0.  (Since any value multiplied by 0 becomes 0, the value of the equation becomes 0)

⇒ 0

The answer is 0.

Given:

The largest 5-digit number that is exactly divisible by 88.

Concept used:

Reminder = dividend - quotient x divisor

Largest five-digit number = 99999

Calculation :

Divide the largest five-digit number by 88, and we got

remainder = 31

this means if the number was 31 less, it would be completely divisible by 88 After dividing 99999 with 88, we get 31 as the remainder.

so largest 5-digit number divisible by 88 = 99999-31 = 99968

Hence, '99968' is the correct answer.

Calculation

The difference in the enrolment of boys and girls enrolled in football in 2018 = 42 - 37 = 5

The difference in the enrolment of boys and girls enrolled in football in 2019 = 44 - 34 = 10

The difference in the enrolment of boys and girls enrolled in football in 2020 = 40 - 32 = 8

The difference in the enrolment of boys and girls enrolled in football in 2021 = 43 - 25 = 18

The difference in the enrolment of boys and girls enrolled in football in 2022 = 41 - 32 = 9

The answer is 2021.

Calculation

The number of workers doing U-type of work in 2006 = 22%

⇒ 22% of 54000 = 11880

The total number of workers doing W-type of work in 2005 = 10% of 47520

= 4752

The total number of workers doing X-type of work in 2005 = 15% of 47520

= 7128

Total workers in W and X type of work in 2005 = 4752 + 7128 = 11880

22% of 54000 = 10% of 47520(W) + 15% of 47520(X)

The answer is W and X

Given:

In ΔRST, points M and N are the points on sides RS and RT, respectively.

RM = $1 \over 3$ MS

ST = 5.6 cm

Concept Used:

For two similar triangles, the ratio of their areas will be in the ratio of the square of their corresponding sides.

Calculation:

 

ΔRST, ∠RMN = ∠RST (Corresponding angles)

∠R is a common angle.

∴ ΔRST ∼ ΔRMN

⇒ RM/RS = MN/ST

⇒ 1/4 = MN/5.6

⇒ MN = 1.4

So, Area of ΔRST / Area ΔRMN  = ST^{2 / MN²}

⇒ 5.6²/1.4²

⇒ 16

Suppose, the area of ΔRST is 16 sq. units, and the area of ΔRMN is 1 sq. units.

∴ Area of trapezium MNST = Area of ΔRST – Area of ΔRMN

⇒ 16 – 1

⇒ 15

Area of trapezium MNST : Area of ΔRMN = 15 : 1

The answer is 1/15.

Formula used:

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

Calculations:

${(3.321)^3 + (2.681)^3 + (1.245)^3 - 3 \times 3.321 \times 2.681 \times 1.245} \over {(3.321)^2 + (2.681)^2} + (1.245)^2 - (3.321 \times 2.681)-(2.681 \times 1.245)-(1.245 \times 3.321)$

Let a = 3.321, b = 2.681 and c = 1.245

⇒ [a3 + b3 + c3 - 3abc]/(a2 + b2 + c2 - ab - bc - ca) = (a + b + c)

⇒ 3.321 + 2.681 + 1.245

⇒ 7.247

The answer is 7.247.

Given:

Speed of one person, S₁ = 18 km/hour

Speed of second person, S₂ = 24 km/hour

T₁ – T₂ = 20 minutes

Formula used:

Speed = Distance/Time

Calculation:

Let the distance be x km.

Time taken by first person

⇒ Time = Distance/Speed

⇒ x/18 hour

Time taken by second person

⇒ x/24 hour

T₁ – T₂ = 20 minutes

⇒ x/18 – x/24 = 20/60

⇒ (4x – 3x)/72 = 1/3

⇒ x = 72/3

⇒ x = 24 km

∴ The distance travelled is 24 km.

 

Required distance = {(S₁ × S₂)/(S₂ – S₁)} × (T₁ – T₂)

⇒ {(18 × 24)/(24 – 18)} × (20/60)

⇒ (18 × 24)/6) × (1/3)

⇒ 24 km

∴ The distance travelled is 24 km

Shortcut Trick

Equate the total parts of the mixtures using their LCM to avoid complex fractions.

Total parts: A = 8 (5 + 3), B = 5 (2 + 3), C = 2 (1 + 1) → LCM(8, 5, 2) = 40 units.

Milk parts out of 40: A = 5 × (40 ÷ 8) = 25 units, B = 2 × (40 ÷ 5) = 16 units.

Target milk parts in C = 1 × (40 ÷ 2) = 20 units.

Apply alligation on milk: Ratio = (Target − B) : (A − Target) = (20 − 16) : (25 − 20).

∴ The correct answer is 4 : 5.

Alternate Method

Given:

Ratio of milk and water in Vessel A = 5 : 3

Ratio of milk and water in Vessel B = 2 : 3

Desired ratio in Vessel C = 1 : 1 (half milk and half water)

Formula Used:

By the Rule of Alligation, the ratio of mixed quantities is derived using cross-differences of concentrations.

Calculations:

Taking the fractional concentration of milk in each mixture:

⇒ Milk in Vessel A = 5 ÷ (5 + 3) = 5/8

⇒ Milk in Vessel B = 2 ÷ (2 + 3) = 2/5

⇒ Milk in Target Vessel C = 1 ÷ (1 + 1) = 1/2

Vessel A (5/8)

Vessel B (2/5)

Target (1/2)

1/2 − 2/5 = 1/10 5/8 − 1/2 = 1/8

Ratio = 1/10 : 1/8 = 4 : 5

Using the alligation cross-differences:

⇒ Quantity of A ÷ Quantity of B = (1/2 − 2/5) ÷ (5/8 − 1/2)

⇒ Quantity of A ÷ Quantity of B = (5/10 − 4/10) ÷ (5/8 − 4/8)

⇒ Quantity of A ÷ Quantity of B = (1/10) ÷ (1/8)

⇒ Ratio = (1/10) × (8/1) = 8 : 10 = 4 : 5

∴ The correct answer is 4 : 5.

Additional Information

Rule of Alligation

It helps find the ratio in which two components of given prices/concentrations are mixed to produce a mixture of a desired average value: (Q₁ ÷ Q₂) = (V₂ − V_avg) ÷ (V_avg − V₁).

LCM Method in Ratios

To avoid tricky fraction calculations, equate the total parts of all components by taking their LCM. Then convert the pure values into a common base scale before applying the alligation rule.

Replacement Method

If 'y' units of mixture are replaced by pure solvent 'n' times from an initial volume 'x' of pure liquid, the final quantity of pure liquid left is given by: Final = x × (1 − y/x)ⁿ.

Shortcut Trick

Candidate's votes as % of total votes = (3,82,500 ÷ 7,50,000) × 100 = 51%

Valid votes = 51% × (100 ÷ 60) = 85% of total votes.

Percentage of invalid votes = 100% − 85% = 15%

∴ The correct answer is 15%.

Alternate Method

Given:

Total voters = 7,50,000

Candidate's votes = 3,82,500 (which is 60% of valid votes)

Formula Used:

Total valid votes = Candidate's votes × (100 ÷ 60)

Invalid votes = Total votes − Valid votes

Invalid votes % = (Invalid votes ÷ Total votes) × 100

Total Votes = 7,50,000 (100%)

Valid Votes = 6,37,500 (85%)

15%

Candidate = 3,82,500 (60% of Valid)

Calculation:

⇒ Total valid votes = 3,82,500 × (100 ÷ 60)

⇒ Total valid votes = 3,82,500 × (5 ÷ 3) = 6,37,500

⇒ Invalid votes = 7,50,000 − 6,37,500 = 1,12,500

⇒ Percentage of invalid votes = (1,12,500 ÷ 7,50,000) × 100

⇒ Percentage of invalid votes = (1125 ÷ 7500) × 100 = 15%

∴ The correct answer is 15%.

Additional Information

Valid and Invalid Votes

In election problems, Total Votes Polled = Valid Votes + Invalid Votes. Percentages of candidates are usually calculated on the base of Valid Votes unless specified otherwise.

Percentage Formula

Percentage = (Part ÷ Whole) × 100. It expresses a number as a fraction of 100.

Base Change in Percentage

Always identify the correct base. Here, the candidate's 60% is based on valid votes, while the final answer requires a percentage based on total votes.

Given

CP = 3450

Repair Price = 450

SP = 5070

Formula used

Profit% = Profit/CP × 100

Calculation

The total cost of old phone = 3450 + 450 = 3900

Profit = 5070 - 3900 = 1170

Profit% = 1170/3900 × 100 = 30%

The answer is 30%.

Given

$\rm 3 - Sin^2A + Cos^2A \over{2 + 2Cos^2A}$

Formula used

Sin²A + Cos²A = 1

Calculation

⇒ (2 + 1 - Sin2A + Cos2A )/(2 + 2Cos2A)

⇒ (2 + Sin2A + Cos2A - Sin2A + Cos2A )/(2 + 2Cos2A)

⇒ (2 + 2Cos2A )/(2 + 2Cos2A) = 1

The answer is 1.

Given

If two tangents are inclined at an angle of 120°.

Radius = 6 cm.

Concept used

Tangents drawn from an external point are equal in length

Calculation

Let P be the external points and PA and PB be the two tangents drawn to the circle with centre O.

Given : ∠APB = 120°

Also radius = OA = OB = 6 cm

We know that tangents drawn from an external point are equally inclined to the line joining that point to the centre.

∠APO = ∠BPO = ∠APB/2 = 120/2 = 60°

Now In ∆OAP

∠OAP = 90°  (∵ Tangent is perpendicular to the radius at the point of contact)

Now in the right ∆OAP

∠OPA = 60°

tan 60° = OA/AP

⇒ √3 = 6/AP

⇒ AP = 6/√3 = 2√3

Also, tangents drawn from an external point are equal in length

⇒ AP = PB = 2√3

The answer is 2√3.

Given

The exterior angle at ∠A = 115°

Concept used

The sum of interior angle + exterior angle = 180°

Calculation

The interior angle at ∠A = 180 - 115 = 65°

∠A = ∠B = 65°

∠C = 180 - (65 + 65) = 50°

The answer is 50°.

Given:

The length of a cuboid is increased = 7%

The breadth of a cuboid is increased = 6%

Formula:

Volume of cuboid = l × b × h

Calculation: 

Let the length, breadth and height of the cuboid be 10 unit

Volume of cuboid = 10 × 10 × 10 = 1000 

New length of cuboid = 10 × (107/100) = 10.7

New breadth of cuboid = 10 × (106/100) = 10.6 

New height of cuboid = 10 

Volume of cuboid = 10.7 × 10.6 × 10 = 1134.2

Volume increase = 1134.2 - 1000 = 134.2

Volume percentage increase = (134.2/1000) × 100 = 13.42%

The answer is 13.42%

Shortcut Trick The successive increase = 7% + 6% + (7 × 6)%/100

⇒ 13.42%

The correct answer is "adventure."

 Key Points

• The sentence is about Abraham narrating a past experience to Reshma in a dramatic way.
• The word "escapade" implies that the experience was thrilling or exciting. (दुःसाहसिक घटना)
• Example: Her latest escapade was to camp outside a department store on the night before the sale.
• "Adventure" is the most appropriate option that conveys the same meaning as "escapade."
• "Adventure" means an experience or event that is very unusual, exciting or dangerous. (असाधारण, उत्तेजक और संकटपूर्ण अनुभव या घटना)
• Example: Our journey through the jungle was quite an adventure!
• The correct answer is option 3.

Additional Information

• Option 1, exertion, means physical or mental effort. (अत्‍यधिक शारीरिक प्रयास; थकाने वाला काम)
• Option 2, ordeal, means a difficult or painful experience. (अत्‍यंत अप्रिय या कठिन अनुभव, अग्नि-परीक्षा)
• Option 4, escape, means the act of escaping. (पलायन; भागने की क्रिया)