MP Forest Guard/Jail Prahari: (12 June 2026, All Shift) Memory-Based Paper (Previous Year Paper)

The correct answer is Management contract.

Key Points Horizontal FDI, vertical FDI, and Conglomerate FDI are different types of FDI. A management contract is not part of FDI.

 Important PointsForeign Direct Investment (FDI):

Foreign direct investment refers to the investment made by one nation in another nation through investment in manufacturing, business or purchasing a corporation. It is usually done through securities and shares. According to WTO, "FDI occurs when an investor based in one country acquires an asset in another country with the intent to manage the asset."

FDI increases foreign capital inflow helps in boosting the economic production of the country and is generally preferred over other kinds of investments. These investments are nondebt and nonvolatile and their gains rely on the performance of projects.

Types of FDI

Based on the entry:

• Greenfield investment: It consists of developing a completely new company in a foreign country. It leads to more capital outlay and transfer of all technical know-how and managerial skills.
• Brownfield investment: It consists of acquiring an already established business in a foreign country. These investments help In gaining a competitive edge in the international business.

Based on the type of activity:

• Horizontal FDI: It refers to the investment in the foreign business which is similar to the business that has been carried out in the home country. E.g. Coca cola and Standard chartered bank.
• Vertical FDI: This is a type of investment where foreign companies undertake activities that are not similar to the activities performed in the home country. These are further classified into backward FDI, forward FDI, and conglomerate FDI.
• Backward FDI: Here the firm in the home country acquires assets from the foreign country to use them as input for production.
• Forward FDI: It occurs when the company invests or acquires another company to provide a market network or mix up the operations that are produced in the home country.
• Conglomerate FDI: In this type of foreign investment, the company invests or acquires firms that do not perform similar kinds of operations. For example, a manufacturing firm buys a service firm.

Hence, the correct answer is management contracts.

The correct answer is Jahangir.

Key Points

1. Shalimar Bagh is a Mughal garden in Srinagar, Jammu, and Kashmir, India, linked through a channel to the northeast of Dal Lake.
2. It is also known as Shalimar Gardens, Farah Baksh, and Faiz Baksh.
3. The other famous shoreline garden in the vicinity is Nishat Bagh, 'The Garden of Delight'.
4. The Bagh was built by Mughal Emperor Jahangir, for his wife Nur Jahan, in 1619.
5. The Bagh is considered the high point of Mughal horticulture.
6. It is now a public park and also referred to as the "Crown of Srinagar".

Important Points

1. Nur-ud-din Muhammad Salim son of Akbar known by his imperial name, Jahangir  (31 August 1569 – 28 October 1627), was the fourth Mughal Emperor, who ruled from 1605 until his death in 1627.
2. His imperial name in Persian means 'conqueror of the world

Additional Information

1. Jammu and Kashmir is a region administered by India as a union territory and consisting of the southern portion of the larger Kashmir region, which has been the subject of a dispute between India and Pakistan since 1947, and between India and China since 1962.
2. Area: 42,241 km²
3. Population: 1.23 crores
4. Srinagar is the main city and the summer capital of Jammu and Kashmir’s Indian Union territory.
5. The city is renowned for its natural scenery, parks, waterfronts, and houseboats.
6. Shalimar Bagh is a Mughal garden in Srinagar city in Jammu and Kashmir, India.

The correct answer is ​Humayun's Tomb

In News

• India's First Sunken Museum will open at the Humayun Tomb complex in Delhi on July 29, 2024.

Key Points

• Union Culture and Tourism Minister Gajendra Singh Shekhawat and Prince Rahim Aga Khan will attend the opening.
• The museum design is inspired by traditional Indian 'baolis' (stepwells), integrating historical and modern elements.
• Exhibits include:
• Restored artifacts from Humayun’s Tomb.
• Rare items such as 'farmans', an astrolabe, a celestial sphere, and a 16th/17th-century warrior’s helmet.
• Technological features:
• 3-D videos depicting historical scenes.
• Detailed scale models of the Nizamuddin Dargah complex.
• Humayun’s Tomb:
• Constructed in 1569-70, commissioned by Empress Bega Begum.
• First garden tomb in India, influencing Mughal architecture including the Taj Mahal.
• The tomb is a UNESCO World Heritage Site known for its Persian architectural influences and intricate designs.

The correct answer is Sulfuric acid / sulphuric acid.

• Sulfuric acid is the chemical name of ‘oil of vitriol’.

Key Points

• Sulfuric acid is a dense, colourless, oily, corrosive liquid.
• It is one of the most commercially important of all chemicals.
• It is prepared industrially by the reaction of water with sulfur trioxide.
• Vitriol is any of certain hydrated sulfates or sulfuric acid.
• Uses of Sulphuric acid (H₂SO₄):
• In lead storage battery.
• In the manufacturing of HCl.
• In the manufacturing of Alum.
• In the manufacturing of fertilisers,
  

drugs, detergents and explosives.

Additional Information

• Blue or roman vitriol is cupric sulfate (CuSO4).
• Green vitriol is also called copperas, a name formerly applied to all the vitriols is ferrous sulfate
• White vitriol is zinc sulfate (ZnSO4).
• Red, or rose, vitriol is cobalt sulfate (CoSO4).
• Uran vitriol is a native uranium sulfate [U(SO4)2].

The correct answer is Non-Resident Indians.

Key Points

• Non-Resident Indians (NRIs) are Indian citizens who do not reside in India.
• NRIs hold an Indian passport but live outside India for employment, business, or education.
• The status of an NRI is crucial for taxation purposes in India, as it determines their tax liability on income earned in India and abroad.
• NRIs are allowed to vote in Indian elections, but they must be physically present in their constituency to vote.
• They can also maintain bank accounts in India and invest in Indian securities and properties under certain conditions.

Additional Information

• The concept of Non-Resident Indian (NRI) is defined under the Foreign Exchange Management Act, 1999 (FEMA) and the Income Tax Act, 1961.
• NRIs are eligible for certain tax exemptions on their income earned abroad, but they must pay taxes on any income that is earned in India.
• The Reserve Bank of India (RBI) allows NRIs to open specific types of bank accounts such as NRE (Non-Resident External) and NRO (Non-Resident Ordinary) accounts for managing their income earned in India and abroad.
• There are specific schemes and benefits available for NRIs wanting to invest in India to encourage remittances and investment from the Indian diaspora.

The correct answer is Maldives.

Key Points

• The Maldivian Rufiyaa is the official currency of the island nation Maldives.
• Its issuance is regulated by the Maldives Monetary Authority.
• The currencies of Fiji, Kiribati and Marshall Islands, respectively, are Fijian Dollar, Kiribati Dollar and US Dollar respectively.

the correct answer is Option 3.

Key Points

• Since its formation in 1994, the United Communist Party of Nepal (Maoists) has gone through a number of radical transformations, shifting from a guerrilla warfare unit to a key democratising force within Nepali politics.
• The party’s early history is defined by its role in launching the ‘people’s war’ of 1996, a decade-long civil war that resulted in the loss of some 16 000 lives and halted the country’s economic development. The Maoists’ original aim was to benefit the poor and marginalised sectors of Nepali society by uprooting the monarchy and feudalism.
• The Maoists have also achieved two other key victories. Following their entrance into peaceful politics in 2006, the Maoists gained the largest number of votes in the April 2008 Constituent Assembly election, winning 220 out of 575 elected seats. But their biggest achievement so far has been the overthrow of the monarchy in 2008. Many analysts maintain that the Maoist-initiated war sped up this outcome by at least a few decades.
• Yet the Maoists have failed to make progress on other key matters. Despite the impressive political developments, the Constituent Assembly failed to produce the new constitution it was originally tasked with writing, and its dissolution has left the country in a political and constitutional deadlock.

The Correct Answer is Ratadiya Ri Dheri.

In News

• 4500-year-old Harappan civilisation remains discovered near Pak border in Rajasthan.

Key Points

• A Harappan site has been discovered at Ratadiya Ri Dheri in Jaisalmer, Rajasthan.
• This is the first known Indus Valley settlement in the Jaisalmer district.
• The site is located 17 km northwest of Sadewala in Pakistan, where Harappan traces were earlier found.
• This discovery bridges the archaeological gap between northern Rajasthan and Gujarat.
• Previously, Pilibanga was the most prominent Harappan site in Rajasthan.
• Pilibanga was studied by Luigi Pio Tessitori, an Italian Indologist, and excavated in the 1960s.
• The Harappan civilization is among the oldest civilizations, along with Egypt and Mesopotamia.
• It developed along the Indus River, hence also known as the Indus Valley Civilization.
• It is classified as a Bronze Age civilization, known for using copper-based alloys.

The correct answer is Kisan Kanya.

Key Points

• Kisan Kanya was a 1937 Hindi Cinecolor feature film which was directed by Moti Gidwani and produced by Ardeshir Irani of Imperial Pictures.
• It is largely remembered by the Indian public on account of it being India's first indigenously made colour film

 Important Points

• Dadasaheb Phalke's silent Raja Harishchandra (1913) is the first feature film made in India.
• The first Indian sound film, Ardeshir Irani's Alam Ara (1931), was commercially successful.
• By the 1930s, the industry was producing over 200 films per year.

The correct answer is Article 109. 

Key Points

• Article 109 -  A Money Bill shall not be introduced in the Council of States.
• A money Bill is defined in Article 110 of the Indian Constitution.
• Money bills are concerned with financial matters like taxation, public expenditure, etc.
• The bill is significant for Indian Polity and governance as many important issues like Aadhar Bill, Insolvency, and Bankruptcy Bill are also related to it.

Additional Information

• Article 354: Application of provisions relating to the distribution of revenues while a proclamation of emergency is in operation.
• Article 193 speaks about the Penalty for sitting and voting before making an oath or affirmation under Article 188 or when not qualified or when disqualified.
• Article 298 of the Constitution deals with the power to carry on trade.

सही विकल्प अव्ययीभाव समास।

Key Points

• यथोचित'  अव्ययीभाव समास का उदाहरण है।
• “यथोचित” में अव्ययीभाव समास है
• अव्ययीभाव समास का संधि-विग्रह “यथा+उचित” होगा तथा समास-विग्रह “उचित के अनुसार” होगा।
• अव्ययीभाव समास - जब समास में सम्मिलित पूर्वपद अव्यय हो तथा उसके योग से पूर्ण समस्तपद अव्यय बन जाए तो अव्ययीभाव समास समास होता है |
• जैसे- यथास्था - स्थान के अनुसार
• यथामति - मति के अनुसार

Additional Information

सही उत्तर है - "जब भी मैं ससुराल गया, मेरा आदर-सत्कार हुआ" l

Key Points

• जब भी मैं ससुराल गया, मेरा आदर-सत्कार हुआ - प्रस्तुत वाक्य 'मिश्र वाक्य' का उदाहरण है l
• ऐसे वाक्य जिनमें सरल वाक्य के साथ-साथ कोई दूसरा उपवाक्य भी हो, वे वाक्य मिश्र वाक्य कहलाते हैं। मिश्र वाक्योँ की रचना एक से अधिक ऐसे साधारण वाक्योँ से होती है, जिनमेँ एक प्रधान वाक्य होता है एवं दूसरा वाक्य आश्रित होता है।
• इस वाक्य में मुख्य उद्देश्य और मुख्य विधेय के अलावा एक या अधिक समापिका क्रियाएँ होती हैं।
• मिश्र वाक्य में प्रधान वाक्य को आश्रित उपवाक्य से जोड़ने के लिए जो आपस में ‘कि’; ‘जो’; ‘क्योंकि’; ‘जितना’; ‘उतना’; ‘जैसा’; ‘वैसा’; ‘जब’; ‘तब’; ‘जहाँ’; ‘वहाँ’; ‘जिधर’; ‘उधर’; ‘अगर/यदि’; ‘तो’; ‘यद्यपि’; ‘तथापि’; आदि का प्रयोग किया जाता है।

अन्य विकल्प :-

• जल्दी से घर आ आओ, कमरे में सामान पड़ा है, श्याम के घर मेरा आदर हुआ - यह तीनों वाक्य सरल वाक्य के उदाहरण l

Additional Information

• शब्दों के सार्थक मेल को वाक्य बोलते है।
• रचना के आधार पर वाक्य के तीन भेद होते हैं :-
• सरल वाक्य:- ऐसा वाक्य जिसमें एक ही क्रिया एवं एक ही कर्ता हो और उन वाक्यों का एक ही उद्देश्य हो, ऐसे वाक्य को सरल वाक्य कहा जाता है।
• उदाहरण:- बच्चे क्रिकेट खेलते हैं।
• संयुक्त वाक्य:- दो या दो से अधिक सरल वाक्य योजक शब्दों के द्वारा जुड़कर बनते हैं संयुक्त वाक्य को विभाजित करने पर पुनः सरल वाक्य प्राप्त होते हैं।
• उदाहरण:- राम ने बहुत मेहनत की लेकिन परीक्षा में सफल नहीं हुआ।
• मिश्र वाक्य के उदाहरण:- 
• वह कौन-सा मनुष्य है जिसने महाप्रतापी राजा भोज का नाम न सुना हो।
• यह वही भारत देश है जिसे पहले सोने की चिड़िया कहा जाता था।

वाक्य के रेखांकित अंश गहरी नींद से जाग गया, के लिए उचित मुहावरा ​तंद्रा भंग हो जाना होगा।

अत: विकल्प 2 सही उत्तर है, अन्य विकल्प असंगत है। 

Key Points

• तंद्रा भंग हो जाना: यह मुहावरा किसी की हल्की नींद या ध्यान भटकने की स्थिति समाप्त होने की बात करता है,
• चाहे वह ध्यान से किसी दूसरी चीज में लगा हो या फिर हल्की नींद में हो।
• इसका प्रयोग किसी के अचानक से जाग जाने की स्थिति को भी दर्शाता सकता है, इसलिए यहाँ यह विकल्प सबसे उपयुक्त मुहावरा है।

अन्य विकल्प-

• गिरह बाँधना: यह मुहावरा किसी बात को ध्यानपूर्वक सुनने या याद रखने से संबंधित होता है।
• यह विकल्प वाक्य की स्थिति से मेल नहीं खाता।
• अपना रंग दिखाना: यह मुहावरा किसी के असली चरित्र या स्वभाव के प्रकट होने से संबंधित होता है,
• जो इस वाक्य की स्थिति से मेल नहीं खाता।
• साये से भागना: यह मुहावरा बेकार की चिंता या अनावश्यक डर से भागने के संदर्भ में प्रयोग होता है।
• यह विकल्प भी वाक्य की स्थिति के लिए उपयुक्त नहीं है।

Additional Informationमुहावरे के अन्य उदाहरण- 

'उपमेय में उपमान का निषेधरहित आरोप हो' तो कौन सा अंलकार होता है- रूपक

Key Points

​जहां उपमेय में उपमान का निषेध रहित आरोप होता है तो वहाँ रूपक अलंकार होता है। 

• दूसरे शब्दों में जहाँ गुण की अत्यंत समानता के कारण उपमेय में ही उपमान का अभेद आरोप कर दिया हो, वहाँ रूपक अलंकार होता है।
• जैसे - चरण कमल बंदों हरि राई।
• यहां पर चरणों को कमल के समान बताया गया है अर्थात उपमेय उपमान के रूप में प्रदर्शित किया गया है इसलिए यहां पर रूपक अलंकार है।

अन्य विकल्प: 

Additional Information

सही उत्तर 'ठंडा-स्तब' हैं।

• दिए गए विकल्पों में,'ठंडा-स्तब' तद्भव-तत्सम युग्म असुमेलित है।
• ठंडा का तत्सम शब्द 'शीत' है।

Key Points

अन्य विकल्पों का विश्लेषण:

Additional Information

"अल्पसंख्यक" का सही व‍िलोम शब्‍द बहुसंख्‍यक है। अन्‍य व‍िकल्‍प असंगत हैं। 

Key Points

• अल्पसंख्यक का अर्थ- कम जनसंख्या वाला (पक्ष)
• बहुसंख्‍यक का अर्थ- गिनती में बहुत, अनेक, बहुत
• अल्‍पसंख्‍यक का व‍िलोम बहुसंख्‍यक है।

अन्‍य व‍िकल्‍प- 

Important Pointsकुछ अन्‍य व‍िलोम शब्‍द- 

Additional Information 

'सुवरण को खोजत फिरत, कवि व्यभिचारी, चोर' पंक्ति में अलंकार है- श्लेष

Key Points

• चरन धरत चिंता करत चितवत चारों ओर।, सुबरन को खोजत, फिरत कवि, व्यभिचारी, चोर।, पंक्ति में श्लेष अलंकार है।
• उक्त दोहे में सुबरन शब्द के एक से अधिक अर्थ हैं।
• कवि के संदर्भ में इसका अर्थ सुंदर वर्ण (शब्द), व्यभिचारी के संदर्भ में सुंदर रूप रंग और चोर के संदर्भ में इसका अर्थ सोना है।

Additional Information

मुहावरों का सही अर्थ से मिलान, विकल्प 3 में दिया गया है।

अन्य विकल्प असंगत है।

Key Pointsदिए गए मुहावरों के अर्थ से समझा जा सकता है, कि सही उत्तर क्या होगा- 

• आँखें पथरा जाना: यह मुहावरा इंतजार की लम्बी अवधि को व्यक्त करता है,
• जिसमें व्यक्ति की आँखें थक जाती हैं और किसी की बहुत देर तक राह देखने को कहते हैं।
• काँटे बिछाना: इसका अर्थ होता है किसी के रास्ते में बाधा उत्पन्न करना या कठिनाइयाँ खड़ी करना।
• उल्टी गंगा बहाना: यह मुहावरा तब प्रयोग किया जाता है जब कोई व्यक्ति या परिस्थिति सामान्य धारणा के विपरीत,
• असामान्य या अप्रत्याशित कार्य करता है। इसका मतलब है नियम विरुद्ध कार्य करना।
• कलई खुलना: यह मुहावरा उस समय प्रयोग होता है, जब किसी की असलियत सबके सामने आ जाती है या किसी रहस्य का पता चल जाता है।

तो, सही मिलान इस प्रकार है:

• आँखें पथरा जाना - b. राह देखते थक जाना
• काँटे बिछाना - a. बाधा डालना
• उल्टी गंगा बहाना - d. नियम विरुद्ध कार्य करना
• कलई खुलना - c. रहस्य का पता चल जाना​

Additional Informationमुहावरा- मुहावरा एक ऐसा वाक्य होता है जो वाक्य की रचना करने पर अपना एक अलग अर्थ या विशेष अर्थ प्रकट करता है,

इनका प्रयोग करने से भाषा, आकर्षक,प्रभावपूर्ण तथा रोचक बन जाती है।

मुहावरे के अन्य उदाहरण-​

'उसने खाया है।' वाक्य में 'पूर्ण वर्तमान काल' है क्योंकि क्रिया के जिस रूप से कार्य के अभी पूरे होने का पता चलता है। उसे पूर्ण वर्तमान काल कहते है। अन्य विकल्प असंगत हैं। 

Key Points

अन्य विकल्प

• वह गया था। यह पूर्ण भूतकाल का उदाहरण है।
• तुम जाते हो। यह संभाव्य वर्तमान काल का उदाहरण है।
• शायद तुमने देखा होगा। यह संदिग्ध वर्तमान काल का उदाहरण है।
• नोट:- Present Perfect Tense के हिंदी वाक्यों की क्रियाओं के अंत में चुका है, चुकी है, चुके हैं, चुका हूं, लिया है, दिया है, या है, यी है, ये हैं, दा है, दी है, दे हैं आदि शब्द आते हैं। Present Perfect Tense के वाक्य कहलाते हैं। वह मंत्री जी को पत्र लिख चुका है।

Additional Information 

सही उत्तर है - ‘परकीया’।

• स्वकीया का विलोम परकीया होगा।
• परकीया का अर्थ : अपने पति के सिवाय दूसरे पुरुष से भी प्रेम करने वाली स्त्री।
• स्वकीया का अर्थ : वह विवाहिता स्त्री जो केवल अपने पति से प्रेम करती हो।

Key Points अन्य विकल्प:

• शोक का का अर्थ : किसी आत्मीय की मृत्यु के कारण होने वाला दुख, मातम, पीड़ा, रंज।
• विषाद का अर्थ है : दुःख, अवसाद, उदासी।
• सुराज का अर्थ है : . स्वराज्य, अच्छा या सुखद राज्य।

Additional Information

• किसी शब्द का विलोम शब्द उस शब्द के अर्थ से उल्टा या विपरीत अर्थ वाला होता है।
• विलोम शब्द के उदाहरण:-
• आय – व्यय
• ऐसा – वैसा
• कनीय – वरीय
• गमन – आगमन

दिए गए विकल्पों में सही उत्तर ‘उत् + नयन’ है। 

Key Points

• उन्नयन का संधि विच्छेद “उत् + नयन” होता है।
• उन्नयन के संधि विच्छेद में “व्यंजन संधि” लागू होती है।
• व्यंजन संधि- एक व्यंजन से स्वर अथवा व्यंजन के मेल से उत्पत्र विकार को व्यंजन संधि कहते हैं।
• उदाहरण :
• अहम् + कार = अहंकार।
• उत् + लास = उल्लास।

Additional Information

• संधि - दो शब्दों के मेल से जो विकार (परिवर्तन) होता है उसे संधि कहते हैं।
• संधियाँ मुख्य रूप  तीन प्रकार की होती हैं -

1. स्वर संधि
2. व्यंजन संधि
3. विसर्ग संधि

• स्वर संधि - दो स्वरों के मेल से होने वाले विकार (परिवर्तन) को स्वर-संधि कहते हैं।
• उदाहरण :
• मुनि + ईश = मुनीश।
• ज्ञान + उपदेश = ज्ञानोपदेश।
• सदा + एव = सदैव।
• विसर्ग संधि -  विसर्ग (:) के बाद स्वर या व्यंजन आने पर विसर्ग में जो विकार (परिवर्तन) होता है उसे विसर्ग-संधि कहते हैं।
• उदाहरण :
• मनः + बल = मनोबल।
• दुः + शासन = दुश्शासन।
• निः + फल = निष्फल।

“तुलसी के वास्ते ही जैसे राम ने अवतार लिया' इस वाक्य में किसी के लिए होने का भाव दिखने से 'सम्प्रदान कारक' सही विकल्प होगा। 

Key Points

Additional Information

सही उत्तर है - ‘अन्धकार’।

• तिमिर शब्द का पर्यायवाची शब्द अन्धकार होगा।
• तिमिर के अन्य पर्यायवाची शब्द : अंधेरा, तमिस्त्रा, तम आदि।

Key Pointsअन्य विकल्प:

• प्रकाश के पर्यायवाची शब्द : ज्योति, दीप्ति, प्रभा आदि।
• रात्रि के पर्यायवाची शब्द : रैन, रजनी, यामिनी, तमी, निशि, त्रियामा, विभावरी, क्षणदा, शर्वरी, रात आदि।
• सूर्य के पर्यायवाची शब्द : सूरज, रवि, दिनकर, दिवाकर, प्रभाकर, भास्कर आदि।

Additional Informationसमानार्थी शब्द:

• वे शब्द जिनका अर्थ एक समान होता हैं समानार्थी शब्द कहलाते हैं।
• समानर्थी शब्द को हम पर्यायवाची शब्द भी कहते है। ‘पर्याय’ का अर्थ है ‘समान’ तथा ‘वाची’ का अर्थ है ‘बोले जाने वाले’ अर्थात
  

समान बोले जाने वाले शब्दों को हम पर्यावाची शब्द या समानार्थी शब्द कहते है।

पर्यायवाची शब्द के उदाहरण :

• गौरव - मान, सम्मान, महत्त्व, बड़प्पन।
• झंडा - ध्वजा, केतु, पताका, निसान।
• हंस - चक्रांग, मानसौक, कलहंस, मराल, कारंडव, सरस्वती वाहन।
• इन्द्राणि - इन्द्रवधू, मधवानी, शची, शतावरी, पोलोमी।

अशुद्ध वाक्य है- बाघ और बकरी एक घाट पर पानी पीती हैं।

• अन्य सभी वाक्यों में लिंग, वचन, पुरुष, काल, कारक आदि का क्रिया के साथ ठीक-ठीक प्रयोग हुआ है।

Key Points 

• अशुद्ध वाक्य- बाघ और बकरी एक घाट पर पानी पीती हैं।
• दिए गये वाक्य में 'वचन प्रयोग' की त्रुटि है।
• यहाँ 'पीती' सार्थक शब्द नही है और इससे सही अर्थ प्रकट नही हो रहा।
• अत: सार्थक शब्द 'पीते' होना चाहिए। क्योंकि वाक्य में 'बाघ और बकरी' दोनों की बात की जा रही है।
• सही वाक्य - बाघ और बकरी एक घाट पर पानी पीते हैं।

Important Points वचन संबंधी अशुद्धियों के कुछ अन्य उदाहरण -

Additional Information 

सही उत्तर 'कुतरना' है।

• दिए गए विकल्पों में, 'कुतरना' शब्द में उपसर्ग का प्रयोग नहीं है।
• कुतरना में 'कुतर' मूल शब्द और 'ना' प्रत्यय है।​

Key Pointsअन्य** विकल्पों का **विश्लेषण: 

Additional Information

• प्रत्यय: शब्द के उपरांत जिस शब्द का प्रयोग किया जाता है वह प्रत्यय है।
• जैसे - ता, औना, अन, अत-  श्रो + ता = श्रोता
• उपसर्ग​:शब्दों तथा धातुओं के पूर्व में संयुक्त हो नये सार्थक शब्दों का निर्माण करने वाले शब्दों को उपसर्ग कहते हैं।
• उपसर्गों से निर्मित शब्द -

'लब्धप्रतिष्ठ, व्यवहृत' विकल्प के सभी शब्द शुद्ध हैं।

Key Points

• शुद्ध वर्तनी - जिस शब्द में जितने वर्ण या अक्षर जिस अनुक्रम में प्रयुक्त होते है उन्हें उसी क्रम में लिखना ही वर्तनी है।
• उदाहरण - अहार-आहार, अत्याधिक-अत्यधिक, अलोचना-आलोचना आदि।

Additional Information

सही उत्तर है - 'अग्नि'।

• हुताशन शब्द का पर्यायवाची शब्द अग्नि होगा।
• हुताशन के अन्य पर्यायवाची शब्द : वैश्वानर, शुचि, ज्वाला, आग, अनल, पावक, दहन, ज्वलन, धूमकेतु, कृशानु आदि।

Key Pointsअन्य विकल्प:

• निर्धन के पर्यायवाची शब्द : गरीब, रंक, कंगाल, दीन, दरिद्र आदि।
• अगणित के पर्यायवाची शब्द : अनगिनत, असंख्य, कोटिशः, करोड़ों, असंख्य, बहुत आदि।
• अखंड के पर्यायवाची शब्द :  पूर्ण, समस्त, सम्पूर्ण, अविभक्त, समूचा, पूरा आदि।

Additional Informationपर्यायवाची शब्द ​:

• वे शब्द जिनका अर्थ एक समान होता हैं पर्यायवाची शब्द कहलाते हैं।
• समानर्थी शब्द को हम पर्यायवाची शब्द भी कहते है। ‘पर्याय’ का अर्थ है ‘समान’ तथा ‘वाची’ का अर्थ है ‘बोले जाने वाले’ अर्थात
  

समान बोले जाने वाले शब्दों को हम पर्यावाची शब्द या समानार्थी शब्द कहते है।

पर्यायवाची शब्द के उदाहरण :

• आदर्श - प्रतिमान, मानक, प्रतिरूप, नमूना।​
• फूट - मतभेद, मनमुटाव, अनबन, परस्पर, कलह।
• हंस - चक्रांग, मानसौक, कलहंस, मराल, कारंडव, सरस्वती वाहन।

सही उत्तर अधिकरण कारक है।  

Key Points

• "नाव जल में तैरती हैl"  वाक्य में अधिकरण कारक है l
• वाक्य में 'में' परसर्ग आने पर 'अधिकरण कारक' हैl
• अधिकरण कारक को 'में, 'पर' परसर्ग द्वारा पहचाना जाता है,  जैसे – मोहन मैदान में खेल रहा है, मनोज छत पर पढ़ रहा है।

अन्य विकल्प :

Important Points

कारक का अर्थ होता है किसी कार्य को करने वाला। यानी जो भी क्रिया को करने में भूमिका निभाता है, वह कारक कहलाता है।

कारक के मुख्यतः आठ भेद होते हैं :

1. कर्ता कारक – ने
2. कर्म कारक – को
3. करण कारक – से
4. सम्प्रदान कारक – के लिए
5. अपादान कारक – से
6. संबंध कारक – का, के, की
7. अधिकरण कारक – में, पर
8. संबोधन कारक – हे,हो,अरे,वाह

वाक्य में चिन्ह का प्रयोग नहीं किया गया है- 'लाघव चिन्ह'

• किसी शब्द को संक्षेप रूप में लिखने के लिए लाघव चिन्ह का प्रयोग किया जाता है।
• शब्द को संक्षेप में लिख देने के कारण इस चिन्ह को संक्षेपसूचक चिन्ह कहते हैं।
• लाघव चिन्ह का चिन्ह (०) होता है।

जैसे-

• पंडित का संक्षेप रूप पं० तथा प्रोफ़ेसर का संक्षेप रूप प्रो० होता है।

Key Points

• "स्वराज हमारा जन्मसिद्ध अधिकार है।" : बाल गंगाधर तिलक
• उद्धरण चिन्ह - ( “…” )
• पूर्णविराम चिन्ह - ( । )
• अपूर्ण विराम चिन्ह - ( : )

Additional Information

सही उत्तर 'कारक, भगोड़ा' है।

• 'कारक और भगोड़ा'  शब्द में 'कृत्' प्रत्यय का प्रयोग हुआ है।
• कृ + अक = कारक
• भाग +ओड़ा=भगोड़ा
• अतः ‘कारक’ में ‘अक’ प्रत्यय और ‘कृ’ मूल शब्द है।
• तथा भगोड़ा में ‘ओड़ा’ प्रत्यय और ‘भाग’ मूल शब्द है।

Key Points 

अन्य विकल्पों का विश्लेषण​:

Additional Information 

• प्रत्यय: शब्द के उपरांत जिस शब्द का प्रयोग किया जाता है वह प्रत्यय है।
• संस्कृत व्याकरण मेँ शब्दोँ और मूल धातुओँ से जो प्रत्यय जुड़ते हैँ, वे प्रत्यय दो प्रकार के होते हैँ –
• कृदन्त प्रत्यय – कृत प्रत्यय क्रिया या धातु के अंत में लगते हैं तथा इनसे बने शब्दों को कृदंत कहते हैं।
• जैसे-पाचक,नंदक,नंदन,भुक्त,भोक्तव्य,भोक्ता आदि।
• तद्धित प्रत्यय-संज्ञा,सर्वनाम तथा विशेषण के अंत में लगते हैं तथा इनसे बने शब्दों को तद्धित प्रत्यय कहते हैं।
• जैसे-सुनार,जुआरी,पालनहार,बचपन,मिठास आदि।

The erroneous part is 'the alcohol will slowly evaporates'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'the alcohol will slowly evaporate' should be used instead of 'the alcohol will slowly evaporates'.
• The given sentence is in the future indefinite tense.
• The structure of these kinds of sentences is: Subject + shall/ will + base form of the verb + object.
• Example: I will travel around the world.
• Therefore, the base form of the verb i.e. 'evaporate' should be used.
• Thus, the correct answer is Option 3.
  

Correct Sentence: Alcohol is volatile, which means that over time the alcohol will slowly evaporate.

The correct answer is option 3) i.e. 'a policy of making delays in decision making.'

Key Points

• Let's look at the meaning of the given idiom/ phrase:
• The phrase 'fabian policy' means a policy of delays and cautions while making a decision.
• Example:
• The Government's fabian policies in job creation are frustrating for the youth.
• Hence, the only possible answer is option 3, 'a policy of making delays in decision making', 

which exactly resembles the meaning of the given idiom/ phrase.​

Correct meaning: a policy of making delays in decision making.

The correct answer is: Option 1)

Key Points

• The word "fabulous" means something that is extraordinarily good or wonderful. (अद्भुत)
• Example: The view from the top of the mountain was simply fabulous.
• "Remarkable" refers to something that is worthy of attention; extraordinary. (उल्लेखनीय)
• Example: Her performance in the play was truly remarkable.

Hence, we can infer that a synonym of 'fabulous' is 'remarkable'.

Additional Information

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

• Resourceful (साधन संपन्न): Having the ability to find quick and clever ways to overcome difficulties.
• Example: She was very resourceful and managed to solve the problem quickly.
• Regrettable (खेदजनक): Causing or deserving regret.
• Example: It was a regrettable mistake that cost the company a lot of money.
• Restful (आरामदायक): Providing or conducive to rest.
• Example: The vacation was very restful and relaxing.

The correct answer is 'Omniscient.'

Key Points

• Let us explore the given options:-
• 'Egoist' is a person who is overly concerned with his or her own desires, needs, or interests.
• Example: An egoist is a person who is his own best friend.
• 'Vandal' is a person who deliberately destroys or damages property belonging to others.
• Example: A vandal with a chainsaw cut down a tree.
• 'Omniscient' is a person who knows everything.
• Example: The novel has an omniscient narrator.
• 'Gullible' is a person who is easily duped or cheated.
• Example: He must have been pretty gullible to fall for that old trick.
  

Hence, the correct answer is option 3*.*

The correct answer is: To focus or concentrate intensely on something

Key Points

• The idiom "zone in on" means to focus intensely on a specific target, subject, or task, often excluding distractions. (किसी विशिष्ट लक्ष्य, विषय या कार्य पर तीव्रता से ध्यान केंद्रित करना, अक्सर विकर्षणों को छोड़कर)
• Example: As the detective investigated the crime scene, he began to zone in on the crucial details that would help solve the case.

Therefore, the correct answer is option 2.

The correct option is: Lethal.

Key Points

• "Mortal" in this context refers to something that is subject to death or fatal. (नश्वर)
• ​For example: Every mortal has their own unique journey through the tapestry of life.
• "Lethal" means sufficient to cause death, which is synonymous with "mortal" when discussing fate. (घातक)
• For Example: A single dose of the substance was lethal enough to endanger life.
• The term "mortal" is frequently used in existential discussions, as well as in the context of human vulnerability and the inevitability of death.
• "Delightful," "Sincere," and "Overjoyed" are not synonyms for "mortal." These words carry completely

Therefore, the correct answer is 'option 4'.

Additional Information

• In literature and philosophy, the concept of mortality often addresses the nature of human existence and the contrast between life and death, the ephemeral and the eternal.
• "Delightful" refers to something very pleasant. (आनंददायक)
• For Example: The children had a delightful time playing in the park.
• "Sincere" means free from deceit or hypocrisy. (ईमानदार)
• For Example: His sincere efforts in the community were well recognized.
• "Overjoyed" means extremely happy. (अत्यधिक प्रसन्न)
• For Example: She was overjoyed to find her lost wedding ring.

The correct answer is: all that happened

Key Points

• Replace "all which happen" with "all that happened" to make the sentence correct.
• "which" is used to add information to objects, items, people, situations, etc. Because "which" indicates a non-restrictive (optional) clause.
• Example - She seemed more talkative than usual, which was because she was nervous.
• "That" is used to indicate a specific object, item, person, condition, etc.
• Example - I didn't know that she was married.
• "Yesterday" is mentioned in the sentence therefore we have to use "happened" as it is referring to some past incidents.

Therefore, the correct answer is option 3.

Corrected sentence: I am sorry for all that happened yesterday.

The correct answer is "was punished"

Key Points

• The most appropriate option to fill in the blank is "was punished" (option 2).
• "was punished" - This option is grammatically correct and suitable for the sentence as it uses the correct verb form for the subject "he". The past tense form of "punish" is "punished".
• Example: She was punished for breaking the school rules.

Hence, the correct answer is "was punished"

Additional InformationLet's see the other given options:

• "were punish" - This option is grammatically incorrect as "were" is the past tense form of "be" which cannot be used with "punish". It should be "were punished" or "was punished" depending on the subject of the sentence.
• Example: They were punished for their misbehavior.
• "have punish" - This option is grammatically incorrect as it uses the wrong verb form. "Have" is a helping verb used to form the present perfect tense, but "punish" is a transitive verb that requires an object. The correct form would be "have punished".
• Example: They have punished the students who were caught cheating.
• "have punished" - This option is grammatically correct, but it does not fit well in the given sentence as it refers to a completed action in the past with a present perfect tense which suggests a connection to the present. The past simple tense would be more appropriate in this case.
• Example: The teacher has punished the student for his mistake.

The correct answer is '2' i.e. The student said, "The teacher has explained the lesson clearly." .

Key Points

• The given sentence is in indirect speech, and the task is to convert it into direct speech.
• In indirect speech, the past perfect tense (had explained) turns into present perfect tense (has explained) when converted to direct speech.
• The correct option is Option 2: The student said, "The teacher has explained the lesson clearly."

Correct sentence: The student said, "The teacher has explained the lesson clearly.".

Additional Information

• Rules for converting indirect to direct speech:
• In the past perfect tense, the verb remains unchanged in direct speech.
• Quotation marks (" ") are used to enclose the statement.
• Ensure the reporting verb (said) is followed by a comma before the quoted speech.
• Other options explained:
• Option 1: Incorrect because it uses the simple past tense (explained), which changes the tense.
• Option 3: Incorrect because it uses the past perfect tense (had explained), which is inconsistent with the original tense.
• Option 4: Incorrect because it uses the simple present tense (explains), which is inconsistent with the original tense.

The correct answer is 'No error.'

Key Points

• The given sentence has no error, so it is grammatically correct.
• दिए गए वाक्य में कोई त्रुटि नहीं है, इसलिए यह व्याकरणिक रूप से सही है।
• Therefore, the correct answer is 'No error.'
• ​​Correct sentence: Posture refers to how you position your body when you're sitting, standing or lying down.

Additional Information 

• The meaning of the word 'Posture' is the position in which someone holds their body when standing or sitting. ('Posture' शब्द का अर्थ वह स्थिति है जिसमें कोई खड़े या बैठे हुए अपने शरीर को धारण करता है।)
• Example: I got out of the car in an alert posture.

The correct answer is 'Economics has always been my favourite subject since class 9 in school'.

Key Points

• In the given sentence usage of 'have' is incorrect.
• 'Economics' is used with a singular verb when it is referring to a subject that deals with the production, distribution, and consumption of goods and services and with the theory and management of economies or economic systems.
• Example: Economics provides the foundation for all other cultural endeavors.
• It functions as a plural noun when it is related to financial aspects.
• Example: The economics of the project are very doubtful.
• 'Has' is used with the third person singular.
• Example: He has a great idea.
• 'Have' is used with the first and second person singular present and plural tenses and the third person plural present tense.
• Example: They also have a wonderful gift shop.
• Therefore in the given sentence 'have' should be replaced by 'has' because economics is singular.
• Hence, option 1 is the correct answer.

The correct sentence is: 'Economics has always been my favourite subject since class 9 in school'.

Additional Information

• Many 'indefinite pronouns' look like they should be plural but refer to only a singular subject and therefore require a singular verb form.
• Example: Each, everyone, nobody, nothing.

Hinglish

• दिए गए वाक्य में 'have' शब्द का प्रयोग गलत है।
• 'Economics' का प्रयोग singular verb के साथ किया जाता है जब यह किसी ऐसे विषय का जिक्र करता है जो वस्तुओं और सेवाओं के उत्पादन, वितरण और खपत से संबंधित है और अर्थव्यवस्थाओं या आर्थिक प्रणालियों के सिद्धांत और प्रबंधन से संबंधित है।
• उदाहरण: Economics provides the foundation for all other cultural endeavors.
• यह वित्तीय पहलुओं से संबंधित होने पर plural noun के रूप में कार्य करता है।
• उदाहरण: The economics of the project are very doubtful.
• Third person singular के साथ 'Has' का प्रयोग किया जाता है।
• उदाहरण: He has a great idea.
• 'Have' का प्रयोग first और second person singular वर्तमान और plural tense और third person plural वर्तमान काल के साथ किया जाता है।
• उदाहरण: They also have a wonderful gift shop.
• इसलिए दिए गए वाक्य में 'have' को 'has' से बदल देना चाहिए क्योंकि economics singular है।
• अत: विकल्प 1 सही उत्तर है।
• कई 'indefinite pronouns' ऐसे दिखते हैं जैसे वे plural होने चाहिए लेकिन केवल singular subject को संदर्भित करते हैं और इसलिए एकवचन क्रिया रूप की आवश्यकता होती है।
• उदाहरण:  Each, everyone, nobody, nothing.

सही वाक्य है: 'Economics has always been my favourite subject since class 9 in school'.

The correct answer is 'a, a.'

Key Points  

• The only articles in English are ‘the’ and ‘a/an’.
• Use the article "a or an" to indicate any non-specified member of a group or category.
• If a word begins with a vowel sound, then the correct article is 'an'; otherwise, if it begins with a consonantal sound, the correct article is 'a'.
• The definite article 'the' is used before a noun to indicate that the identity of the noun is known to the reader. 
• Example: 
• We are looking for an apartment.
• I own a cat and two dogs.
• I love to visit the building.
• Here we are talking about any non-specific "meter and kilometer" and both of them starts with a consonant sound.
• So we must use "a" in both the blanks.
• Hence, the correct answer is Option 1.
  

​

​Correct sentence: Hundred centimeters make a meter and thousand meters make a kilometer.

The correct answer is '3' i.e. King Midas asked his daughter to take her breakfast and bring a few roses from the garden .

Key Points

• In indirect speech, the tense and pronouns are changed appropriately.
• The pronoun "her" is used in indirect speech as King Midas was addressing his daughter.
• The verb "bring" remains unchanged as it is part of the instruction.
• The correct option reflects both the instruction of taking breakfast and bringing roses accurately.

Correct sentence: King Midas asked his daughter to take her breakfast and bring a few roses from the garden.

Additional Information

• Direct Speech: The original statement is quoted exactly as spoken by the speaker.
• Indirect Speech: The statement is paraphrased while maintaining the original meaning, with changes in tense, pronouns, and word order where necessary.

The correct answer is Option 1.

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: "Someone must have interfered with the encryption codes."
• To convert to passive voice: Place the object "the encryption codes" at the beginning.
• Change the active verb form "must have interfered" to "must have been interfered with" (past modal passive).
• Ensure the phrase "by someone" is implied but can be omitted for simplicity unless necessary.

Therefore, the correct answer is Option 1.

Correct Sentence: "The encryption codes must have been interfered with."

Additional Information

• Option 1: "The encryption codes must have been interfered with." – Correct passive voice conversion.
• Option 2: "The encryption codes must have interfered by someone." – Incorrect structure, missing "been" and incorrect verb form.
• Option 3: "The encryption codes must be interfered with by someone." – Incorrect tense (present modal passive).
• Option 4: "The encryption codes must had been interfered with." – Incorrect modal auxiliary verb usage ("must had").

The correct answer is Was the homework completed by Sarah?

Key Points

Let us have a look at the type and tense of the given statement.

• The given statement is an Interrogative statement in the simple past tense beginning with Did.
• Sarah is the subject and homework is the object.
• In passive voice, the subject and the object interchange.
• Also, do, does, did change to is/are/am/was/were.
• The tense and the meaning of the statement do not change in the passive voice.

Hence, the correct answer is Was the homework completed by Sarah?

Additional Information

Sentences can generally be divided into the following four types:

• Declarative sentence: It tells us something.
• Examples: Rita likes reading, Shivani loves music, Geeta goes to school, etc.
• Interrogative sentence: It asks something.
• Examples: Does Rita like reading? , Does Shivani Love music?, Does Geeta go to school? etc.
• Imperative sentence: It commands something.
• Examples: Place the book on the table, Fetch me a pail of water, Please be seated, etc.
• Exclamatory sentence: It expresses a state of mind like surprise, sorrow, joy, wonder, etc
• Examples: Hurray! We have won the match (joy), Alas! I failed the exam (sorrow), etc.

The correct answer is 'Pilgrim'. 

Key Points

• Pilgrim: a person who makes a journey, often a long and difficult one, to a special place for religious reasons
• Example: All were silent, only the pilgrim woman went on in measured tones, drawing in her breath.

Thus the correct answer is Option 2

Additional Information

• The meaning of the other words given in the options as follows:
• Hermit: a person who lives alone and apart from the rest of society, especially for religious reasons
• Example: The town derives its name from a hermit who lived here in the 7th and 8th centuries.
• Saint: a person acknowledged as holy or virtuous and regarded in Christian faith as being in heaven after death
• Example: This place is dedicated to a seventh-century saint.
• Mendicant: someone, especially a member of a religious group, who lives by asking people they do not know for money
• Example: She abandoned her job and her career, and lived as a homeless mendicant on the streets of Philadelphia.

The correct answer is- 'Sanguine'

Key Points 

• let's look at the meaning of the given word and the correct answer.
• Optimistic (adjective): hoping or believing that good things will happen in the future. (आशा करना या विश्वास करना कि भविष्य में अच्छी चीजें होंगी।)
• ​Example: She is optimistic about her chances of winning a gold medal.
• Sanguine(adjective): Optimistic or positive, especially in an apparently bad or difficult situation. (आशावादी या सकारात्मक, विशेष रूप से स्पष्ट रूप से बुरी या कठिन स्थिति में।)
• Example: They are less sanguine about the prospects for peace.
  

Hence, the word Sanguine is the most appropriate synonym for Optimistic.

Additional Information   

• Let's explore the meaning of other options:
• Pessimistic(adjective):  thinking that bad things are more likely to happen or emphasizing the bad part of a situation. (यह सोचना कि बुरी चीजें होने की संभावना अधिक होती है या किसी स्थिति के बुरे हिस���से पर जोर देना।)
• Example: The tone of the meeting was very pessimistic.
• Uncaring(adjective): not worrying about other people's troubles or doing anything to help them. (दूसरे लोगों की परेशानियों के बारे में चिंता न करना या उनकी मदद के लिए कुछ भी नहीं करना।)
• Example: The charity criticized the city for its "callous, uncaring attitude" to the homeless.
• Carefree(adjective): having no problems or not being worried about anything. (कोई समस्या न होना या किसी बात की चिंता न होना।)
• Example: I remember my carefree student days.

The correct answer is 'Option 3'.

Key Points

• A) Identification of the Main Verb
• In the sentence "Objects moving within this curved space-time follow geodesics," the primary action or the main verb is 'follow'. It tells us what the objects do.
• B) Function of 'moving'
• The word 'moving' modifies the noun 'Objects'. It provides more information about which objects are being discussed (specifically, those that are in motion within the space-time).
• C) Grammatical Classification
• A verb ending in '-ing' that functions as an adjective to describe a noun is called a present participle. In this context, "moving within this curved space-time" is a participial phrase acting as an adjective.

Therefore, the correct answer is Present participle acting as adjective.

Additional Information

• Main verb: Incorrect because the main verb of the clause is "follow."
• Gerund: Incorrect because a gerund is an '-ing' form of a verb that functions as a noun (e.g., "Moving is difficult"). Here, it functions as a descriptor.
• Infinitive verb: Incorrect because an infinitive is the base form of a verb, usually preceded by "to" (e.g., "to move").

The correct answer is 'Option 2'.

Key Points

• Definition of a Complex Sentence:
• A complex sentence consists of one independent clause (a clause that can stand alone as a sentence) and at least one dependent (subordinate) clause (a clause that cannot stand alone).
• Analysis of the Sentence:
• The sentence is: "This deep connection between space and time implies that the passage of time is not universal but relative."
• Independent Clause: "This deep connection between space and time implies" (Contains a subject and a verb and expresses a complete thought, though it requires an object).
• Dependent Clause: "...that the passage of time is not universal but relative." This is a noun clause acting as the direct object of the verb "implies." It starts with the subordinating conjunction "that" and cannot stand alone as a complete sentence in this context.

Therefore, the correct answer is Complex sentence.

Additional Information

• Simple sentence: Contains only one independent clause with a single subject and predicate (e.g., "Space and time are connected.").
• Compound sentence: Contains at least two independent clauses joined by a coordinating conjunction like 'and', 'but', or 'or' (e.g., "Space is curved, and time is relative.").
• Compound-complex sentence: Contains at least two independent clauses and at least one dependent clause.

The correct answer is 'Option 2'.

Key Points

• Gravitational Time Dilation
• The passage explains that according to the General Theory of Relativity, time runs differently depending on the gravitational potential of a region. Specifically, time slows down near massive bodies where gravity is stronger.
• Observation in Satellites
• The passage explicitly states: "clocks aboard satellites tick slightly faster than those on Earth's surface due to weaker gravity."
• This confirms that the primary reason mentioned in the text for the difference in clock speed between satellites and Earth is the strength of the gravitational field.

Therefore, the correct answer is They experience weaker gravitational fields than clocks on Earth.

Additional Information

• Option 1: While the passage mentions that relative motion affects time perception (Special Relativity), it specifically attributes the satellite clock phenomenon to gravitational potential (General Relativity).
• Option 3: Magnetic fields are not discussed in the passage as a factor affecting the passage of time.
• Option 4: Solar radiation is not mentioned in the passage as a reason for time dilation.

Shortcut Trick

Rate for 8 months = (30% ÷ 12) × 8 = 20%.

Total periods in 2 years (24 months) = 24 ÷ 8 = 3 periods.

Using Ratio Method (20% = 1/5): Principal : Amount = 5³ : 6³ = 125 : 216.

125 units = Rs. 24,000 ⇒ 1 unit = 192.

Amount (216 units) = 216 × 192 = Rs. 41472.

∴ The correct answer is Rs. 41472.

Alternate Method

Given: Principal (P) = Rs. 24,000, Annual Rate (R) = 30%, Time (T) = 2 years.

Formula Used: Amount (A) = P(1 + r/100)ⁿ

⇒ Effective Rate for 8 months = (30 × 8) ÷ 12 = 20%

⇒ Number of periods (n) = (2 × 12) ÷ 8 = 3

⇒ A = 24000 × (1 + 20/100)³

⇒ A = 24000 × (1.2)³

⇒ A = 24000 × 1.728

⇒ A = 24 × 1728 = 41472

∴ The correct answer is Rs. 41472.

Additional Information

Effective Rate for Compounding

When interest is compounded quarterly (4 times a year), the rate becomes R/4 and time becomes 4T. For 8-month compounding, the factor is 8/12 of the annual rate.

Difference between SI and CI

The difference between CI and SI for 2 years is P(R/100)² and for 3 years is P(R/100)² × (3 + R/100).

Successive Percentage Formula

For two successive cycles of r%, the effective rate is [r + r + (r×r)/100]%. For three cycles of 20%, it is 72.8%.

Shortcut Trick

Simplify ratios first: A ∶ B = 3 ∶ 6 = 1 ∶ 2 and B ∶ C = 7 ∶ 28 = 1 ∶ 4.

Make B common: Multiply (1 ∶ 2) by 1 and (1 ∶ 4) by 2.

A ∶ B = 1 ∶ 2 and B ∶ C = 2 ∶ 8.

Combined ratio A ∶ B ∶ C = 1 ∶ 2 ∶ 8.

∴ The correct answer is 1 ∶ 2 ∶ 8.

Alternate Method

Given:

Ratio A ∶ B = 3 ∶ 6

Ratio B ∶ C = 7 ∶ 28

Calculations:

⇒ A/B = 3/6 = 1/2

⇒ B/C = 7/28 = 1/4

⇒ To combine, we need the value of B to be the same in both ratios.

⇒ LCM of B values (2 and 1) is 2.

⇒ A ∶ B = 1 ∶ 2

⇒ B ∶ C = (1 × 2) ∶ (4 × 2) = 2 ∶ 8

⇒ Therefore, A ∶ B ∶ C = 1 ∶ 2 ∶ 8

∴ The correct answer is 1 ∶ 2 ∶ 8.

Additional Information

Compounding of Ratios

To combine two ratios (a ∶ b) and (b ∶ c), multiply the terms to make the common variable 'b' equal in both sets.

Simplification Rule

A ratio remains unchanged if both its terms are multiplied or divided by the same non-zero number.

Compound Ratio

The compound ratio of (a ∶ b) and (c ∶ d) is (ac ∶ bd).

Shortcut Trick

Net percentage = (Quantity₁ × Percentage₁ + Quantity₂ × Percentage₂) ÷ Total Quantity

Net water % = (2 × 12 + 3 × 5) ÷ (2 + 3)

Net water % = (24 + 15) ÷ 5 = 39 ÷ 5 = 7.8%

7.8% can be written as 7(4/5)%.

∴ The correct answer is 7(4/5) %.

Alternate Method

Given:

Quantity 1 = 2 litres, Water % = 12%

Quantity 2 = 3 litres, Water % = 5%

⇒ Water in first mixture = 12% of 2 = 0.12 × 2 = 0.24 litres

⇒ Water in second mixture = 5% of 3 = 0.05 × 3 = 0.15 litres

⇒ Total water in resulting mixture = 0.24 + 0.15 = 0.39 litres

⇒ Total quantity of resulting mixture = 2 + 3 = 5 litres

⇒ Resulting percentage = (0.39 ÷ 5) × 100

⇒ Resulting percentage = 39 ÷ 5 = 7.8%

⇒ 7.8 = 7 + 0.8 = 7 + 8/10 = 7(4/5)

∴ The correct answer is 7(4/5) %.

Additional Information

Alligation Rule

It relates concentrations and quantities: (Cheaper quantity) ÷ (Dearer quantity) = (Dearer rate − Mean rate) ÷ (Mean rate − Cheaper rate).

Weighted Average

Used when different groups have different weights: Average = (n₁w₁ + n₂w₂) ÷ (n₁ + n₂).

Replacement Method

Final Concentration = Initial Concentration × [1 − (Removed/Total)]ⁿ, where n is the number of operations.

Shortcut Trick

When a father says he was as old as the son is now at the time of the son's birth, the father's current age is always double the son's current age.

Son's current age = Father's age ÷ 2

Son's current age = 40 ÷ 2 = 20 years

Age 5 years ago = 20 − 5 = 15 years

∴ The correct answer is 15 years.

Alternate Method

Given:

Mallesh's current age = 40 years

Let the son's current age be x years.

According to the question, Mallesh's age at the time of his son's birth was equal to the son's current age (x).

⇒ Father's current age − Son's current age = Father's age at son's birth

⇒ 40 − x = x

⇒ 2x = 40

⇒ x = 20 years

⇒ Son's age 5 years ago = x − 5

⇒ 20 − 5 = 15 years

∴ The correct answer is 15 years.

Additional Information

Age Difference Property

The difference between the ages of two people remains constant regardless of the number of years that pass.

Ratio of Ages

If the ratio of ages is given at two different times, use the constant difference to balance the ratio units.

General Age Equation

If current age is A, then age 'n' years ago is (A − n) and age 'n' years hence is (A + n).

(\begin{array}{l} \frac{{\left( {0.0112 - 0.0012} \right);of;0.14; + ;0.25; \times ;0.2}}{{0.02; \times ;0.01}}\ = ;\frac{{\left( {0.01} \right)of;0.14; + ;0.05}}{{0.0002}}\ = ;\frac{{0.01; \times ;0.14; + ;0.05}}{{0.0002}}\ ; = ;\frac{{0.0014; + ;0.05}}{{0.0002}}\ = ;\frac{{0.0514}}{{0.0002}}\ = ;257 \end{array})

Shortcut Trick

⇒ CP = 100

⇒ MP = 100 + 180% = 280

⇒ Required SP for 12% profit = 112

⇒ Discount% = (280 − 112) ÷ 280 × 100

⇒ = 168 ÷ 280 × 100 = 60%

∴ Answer = 60%

Alternate Method

Given:

⇒ Marked price is 180% above CP

⇒ Profit = 12%

Assume:

⇒ CP = 100

Calculation:

⇒ MP = 100 + 180 = 280

⇒ SP for 12% profit = 100 + 12 = 112

⇒ Discount = MP − SP = 280 − 112 = 168

⇒ Discount% = (168 ÷ 280) × 100

⇒ = 60%

∴ Final Answer: 60%

Additional Information

1. Marked Price: MP = CP + Markup%

2. Profit Formula: SP = CP × (1 + Profit%)

3. Discount Formula: Discount% = (MP − SP) ÷ MP × 100

4. Shortcut: Always assume CP = 100 for quick calculation

Shortcut Trick

Break the expression into two parts: A = 34% of 50 and B = (4/6) × ³√512 × √36.

Step 1: A = 34% of 50 = 0.34 × 50 = 17.

Step 2: B = (4/6) × 8 × 6 = 4 × 8 = 32.

Step 3: y = A − B = 17 − 32 = −15.

∴ Answer = −15

Alternate Method 

Given:

Expression: y = 34% of 50 − (4/6) × ³√512 × √36

Formula used:

VBODMAS Rule: Vinculum, Bracket, Of, Division, Multiplication, Addition, Subtraction.

34% of 50 17 (4/6) × 8 × 6 32 − −15 Result (y)

Calculations:

Step 1: Simplify 34% of 50

⇒ (34 ÷ 100) × 50 = 17

Step 2: Simplify the radical terms ³√512 and √36

⇒ ³√512 = 8 (since 8³ = 512)

⇒ √36 = 6 (since 6² = 36)

Step 3: Solve the multiplication part

⇒ (4 ÷ 6) × 8 × 6 = 4 × 8 = 32

Step 4: Perform the subtraction

⇒ y = 17 − 32

⇒ y = −15

∴ The correct answer is (3) -15.

Additional Information

VBODMAS Rule

It defines the order of operations: Vinculum, Brackets, Of, Division, Multiplication, Addition, Subtraction. Here, 'Of' is treated as multiplication but solved before regular division/multiplication.

Percentage Interchange

x% of y is equal to y% of x. For example, 34% of 50 is the same as 50% of 34, which is 17.

Cube Roots and Square Roots

Memorizing basic roots helps speed up calculations: √36 = 6, √64 = 8, ³√216 = 6, ³√512 = 8, and ³√729 = 9.

Shortcut Trick

2/5 of Actual Selling Price (ASP) = 100% − 24% = 76% of CP.

⇒ Actual SP = 76% × 5 ÷ 2 = 190% of CP.

New Selling Price = 84% of Actual SP = 84% × 190% of CP.

⇒ New SP = 0.84 × 190% = 159.6% of CP.

Profit % = 159.6% − 100% = 59.6%.

∴ Answer = 59.6%

Alternate Method 

Given:

Loss = 24% when SP = 2/5 of Actual SP. Target SP = 84% of Actual SP.

Formula used:

Selling Price (SP) = CP × (100 − Loss%)/100 | Profit % = [(SP − CP) ÷ CP] × 100

CP = 100 New SP = 159.6 Actual SP = 190 Profit: 59.6% 2/5 ASP = 76

Calculations:

Let Cost Price (CP) = 100 units.

⇒ If Loss = 24%, then Selling Price (SP₁) = 100 − 24 = 76 units.

⇒ Given SP₁ = 2/5 × Actual SP.

⇒ 76 = 2/5 × Actual SP ⇒ Actual SP = (76 × 5) ÷ 2 = 190 units.

⇒ New Selling Price (SP₂) = 84% of Actual SP = 0.84 × 190.

⇒ New SP₂ = 159.6 units.

⇒ Profit = SP₂ − CP = 159.6 − 100 = 59.6 units.

⇒ Profit % = (59.6 ÷ 100) × 100 = 59.6%.

∴ The correct answer is option (1).

Additional Information

Successive Percentage

When a value is changed by a% and then by b%, net change = [a + b + (a × b)/100]%.

Marked Price and Discount

Selling Price = Marked Price × (100 − Discount%)/100. Also, CP × (100 + P%) = MP × (100 − D%).

Profit and Loss Basics

Profit % = (Profit/CP) × 100 and Loss % = (Loss/CP) × 100. Profit/Loss is always calculated on Cost Price unless stated otherwise.

Shortcut Trick

⇒ Net rate = 1/4 + 1/24 − 1/6

⇒ LCM = 24 ⇒ (6 + 1 − 4)/24 = 3/24 = 1/8

⇒ So tank fills in 8 hours

⇒ Half tank ⇒ 8/2 = 4 hours

∴ Answer = 4 hours

Alternate Method

Given:

Pipe A fills in 4 hr

Pipe B fills in 24 hr

Pipe C empties in 6 hr

Formula Used:

Net work rate = Sum of filling rates − emptying rate

Calculation:

⇒ Net rate = 1/4 + 1/24 − 1/6

⇒ = (6 + 1 − 4)/24 = 3/24 = 1/8

⇒ Time for full tank = 8 hr

⇒ Time for half tank = 4 hr

∴ The correct answer is 4 hours.

Additional Information

Net Rate: Add filling, subtract emptying

LCM Method: Use common denominator for speed

Half Work: Time halves if rate same

Exam Tip: Always find net rate first

Shortcut Trick

⇒ Final = 5P ⇒ Interest = 4P

⇒ SI = P × r × t / 100 ⇒ 4P = P × r × 12 / 100

⇒ r = (4 × 100) / 12 = 33.33%

∴ Answer = 33.33%

Alternate Method

Given:

Amount becomes 5 times in 12 years

Formula Used:

SI = (P × r × t) / 100

Amount = P + SI

Calculation:

⇒ Let principal = P

⇒ Amount = 5P

⇒ SI = 5P − P = 4P

⇒ Using SI formula:

⇒ 4P = (P × r × 12) / 100

⇒ Cancel P:

⇒ 4 = (r × 12) / 100

⇒ r = (4 × 100) / 12

⇒ r = 33.33%

∴ The correct answer is 33.33%.

Additional Information

Simple Interest: SI = (P × r × t)/100

Amount Relation: A = P + SI

Shortcut: Multiply factor − 1 gives interest multiple

Exam Tip: Cancel P early

Shortcut Trick

Consecutive numbers ⇒ average = (first + last) ÷ 2

⇒ = (1 + 60) ÷ 2 = 61 ÷ 2

⇒ = 30.5

∴ Answer = 30.5

Alternate Method

Given:

Natural numbers from 1 to 60

Formula:

Average = (Sum of numbers) ÷ Total numbers

Sum of first n natural numbers = n(n + 1) ÷ 2

Calculation:

⇒ Sum = 60 × 61 ÷ 2 = 1830

⇒ Total numbers = 60

⇒ Average = 1830 ÷ 60 = 30.5

∴ Final Answer = 30.5

Additional Information

Consecutive Numbers: Average = (First + Last) ÷ 2

Sum Formula: n(n+1) ÷ 2

Key Insight: Middle value represents average

Tip: Use shortcut instead of full summation

Shortcut Trick

⇒ Amount doubles in 8 years ⇒ Growth factor = 2

⇒ 8 times = 2³

⇒ Time for 8 times = 3 × 8 = 24 years

∴ Answer = 24 years

Alternate Method

Given:

⇒ Amount doubles in 8 years

Concept:

⇒ A = P(1 + r)^t

Step 1:

⇒ 2P = P(1 + r)⁸

⇒ (1 + r)⁸ = 2

Step 2:

⇒ For 8 times:

⇒ 8P = P(1 + r)^t

⇒ (1 + r)^t = 8 = 2³

Step 3:

⇒ (1 + r)^t = [(1 + r)⁸]³

⇒ ⇒ t = 8 × 3 = 24 years

∴ Final Answer: 24 years

Additional Information

1. Compound Interest: A = P(1 + r)^t

2. Doubling Concept: If amount doubles → growth factor = 2

3. Exponential Growth: Multiples follow powers (2, 4, 8 = 2³)

4. Shortcut: Time multiplies with power

Shortcut Trick

Volume of Sphere = (4/3) × π × r³ = 38808 cm³.

Using 11 divisibility rule for Surface Area (4πr²): Only 5544 is divisible by 11.

Calculation: (5+4) − (5+4) = 0. Divisible by 11.

∴ The correct answer is 5544 cm².

Alternate Method

Given: Volume (V) = 38808 cm³

Formula Used: Volume = (4/3)πr³ and Surface Area = 4πr²

⇒ 38808 = (4/3) × (22/7) × r³

⇒ r³ = (38808 × 3 × 7) ÷ (4 × 22)

⇒ r³ = 441 × 21 = 9261

⇒ r = √³(9261) = 21 cm

⇒ Surface Area = 4 × (22/7) × 21 × 21

⇒ Surface Area = 88 × 3 × 21 = 5544 cm²

∴ The correct answer is 5544 cm².

Additional Information

Properties of Sphere

A Sphere is a perfectly round geometrical object in three-dimensional space. Unlike other solids, it has no edges or vertices.

Hemisphere Formulas

For a Hemisphere of radius r, the curved surface area is 2πr² and the total surface area is 3πr².

Volume Ratios

If the radius is doubled, the Surface Area increases by 4 times (2²) and the Volume increases by 8 times (2³).

Shortcut Trick

Ratio of Perimeter (P) to Breadth (B) is 5 : 1 ⇒ P = 5B

We know P = 2(L + B) ⇒ 2(L + B) = 5B ⇒ 2L = 3B ⇒ L : B = 3 : 2

Let Length = 3x and Breadth = 2x.

Area = 3x × 2x = 6x² = 216 ⇒ x² = 36 ⇒ x = 6

Length = 3x = 3 × 6 = 18 cm.

∴ The correct answer is 18 cm.

Alternate Method

Given:

Ratio of perimeter to breadth = 5 : 1

Area of the rectangle = 216 sq. cm

Formulas Used:

Perimeter of rectangle = 2(L + B)

Area of rectangle = L × B

Length (L) Breadth (B) Area = 216 sq. cm

Calculations:

⇒ Perimeter / Breadth = 5 / 1

⇒ 2(L + B) / B = 5

⇒ 2L + 2B = 5B

⇒ 2L = 3B

⇒ L / B = 3 / 2

⇒ Let Length (L) = 3x and Breadth (B) = 2x

⇒ Area = L × B = 216

⇒ 3x × 2x = 216

⇒ 6x² = 216

⇒ x² = 216 ÷ 6 = 36

⇒ x = √36 = 6

⇒ Length = 3x = 3 × 6 = 18 cm

∴ The correct answer is 18 cm.

Additional Information

Perimeter of a Rectangle

The total distance around the outside of a rectangle. It is given by P = 2(L + B), where L is the length and B is the breadth.

Area of a Rectangle

The total space enclosed within the boundary of a rectangle. It is calculated as Area = L × B.

Diagonal of a Rectangle

A straight line connecting the opposite corners of a rectangle. It is calculated using the Pythagoras theorem: Diagonal = √(L² + B²).

Shortcut Trick

Let Total Work be LCM(3, 4, 12) = 12 units.

Efficiency of 1 Man = 4, 1 Woman = 3, 1 Boy = 1.

Target time = 1 day, so total efficiency needed = 12 units/day.

Efficiency of (1 Man + 1 Woman) = 4 + 3 = 7 units.

Efficiency required from boys = 12 − 7 = 5 units.

Number of boys required = 5 ÷ 1 = 5 boys.

∴ The correct answer is 5 boys.

Alternate Method

Given: Time taken by 1 Man = 3 days, 1 Woman = 4 days, 1 Boy = 12 days.

Formula Used: Total Work = Efficiency × Time

⇒ Efficiency of 1 Man + 1 Woman + x Boys = 12 (to complete in 1 day)

⇒ (4 × 1) + (3 × 1) + (1 × x) = 12

⇒ 7 + x = 12

⇒ x = 12 − 7

⇒ x = 5

∴ The correct answer is 5 boys.

Additional Information

Work Equivalence Formula

M₁D₁H₁ = M₂D₂H₂ where M is number of workers, D is days, and H is hours.

Efficiency Concept

Efficiency is inversely proportional to time. If a person completes work in 'n' days, their 1-day work (efficiency) is 1/n.

Combined Work

When multiple people work together, their individual efficiencies are added to find the total work rate.

Shortcut Trick

Find the common difference (k): (36 − 16) = (72 − 52) = (80 − 60) = (88 − 68) = 20.

The least number is LCM(36, 72, 80, 88) − k.

LCM(36, 72, 80, 88) = 7920.

Required Number = 7920 − 20 = 7900.

Sum of digits = 7 + 9 + 0 + 0 = 16.

∴ The correct answer is 16.

Alternate Method

Given divisors and their respective remainders:

To find the Least Common Multiple (LCM) of 36, 72, 80, and 88:

⇒ Prime factorisation:

⇒ 36 = 2² × 3²

⇒ 72 = 2³ × 3²

⇒ 80 = 2⁴ × 5

⇒ 88 = 2³ × 11

⇒ LCM = 2⁴ × 3² × 5 × 11

⇒ LCM = 16 × 9 × 5 × 11 = 7920

⇒ The least number (N) = LCM − Common Difference

⇒ N = 7920 − 20 = 7900

⇒ Sum of digits of N = 7 + 9 + 0 + 0 = 16

∴ The correct answer is 16.

Additional Information

LCM with Constant Difference

When a number leaves remainders r₁, r₂, r₃ when divided by a, b, c such that (a−r₁) = (b−r₂) = (c−r₃) = k, the number is LCM(a, b, c) − k.

LCM with Same Remainder

If the number leaves the same remainder 'r' in each case when divided by a, b, c, then the least such number is LCM(a, b, c) + r.

Divisibility of Sum of Digits

If the sum of digits of a number is divisible by 3 or 9, then the number itself is divisible by 3 or 9 respectively.

Shortcut Trick

Let Savings = 1 unit.

Expenditure = 1 + 300% of 1 = 4 units.

Income = Expenditure + Savings = 4 + 1 = 5 units.

Using Net Deviation: Increase in (Exp × %E) + (Sav × %S) = Inc × %I

(4 × %E) + (1 × 20) = 5 × 30 ⇒ 4 × %E = 150 − 20 = 130 ⇒ %E = 32.5%.

∴ The correct answer is 32.5%.

Alternate Method

Given: Expenditure is 300% more than savings.

⇒ Let Initial Savings = ₹100

⇒ Initial Expenditure = 100 + (300% of 100) = ₹400

⇒ Initial Income = 400 + 100 = ₹500

⇒ New Income (30% increase) = 500 × 1.30 = ₹650

⇒ New Savings (20% increase) = 100 × 1.20 = ₹120

⇒ New Expenditure = New Income − New Savings = 650 − 120 = ₹530

⇒ Increase in Expenditure = 530 − 400 = ₹130

⇒ Percentage Increase = (130 ÷ 400) × 100 = 32.5%

∴ The correct answer is 32.5%.

Additional Information

Income-Expenditure Relation

Income is the sum of Expenditure and Savings. Income = Expenditure + Savings.

Percentage Increase Shortcut

Percentage Change = (Final Value − Initial Value) ÷ Initial Value × 100.

Weighted Average in Income

Income % change = (Exp Ratio × Exp % change + Sav Ratio × Sav % change) ÷ Total Ratio.

Shortcut Trick

In a partnership, Profit Ratio = Capital Ratio × Time Ratio

Let Naveen's investment time be T months.

Ratio of their profits = (Sunil's capital × Sunil's time) ÷ (Naveen's capital × Naveen's time)

2 / 3 = (11 × 8) / (12 × T)

24T = 264 ⇒ T = 11

∴ The correct answer is 11 months.

Alternate Method

Given:

Investment ratio of Sunil and Naveen = 11 : 12

Time period for Sunil = 8 months

Profit ratio of Sunil and Naveen = 2 : 3

Formula Used:

Profit = Investment × Time

Calculations:

⇒ Let the time period for Naveen be T months.

⇒ (Investment of Sunil × Time of Sunil) / (Investment of Naveen × Time of Naveen) = Profit of Sunil / Profit of Naveen

⇒ (11 × 8) / (12 × T) = 2 / 3

⇒ 88 / 12T = 2 / 3

⇒ 88 × 3 = 24 × T

⇒ 264 = 24T

⇒ T = 264 ÷ 24

⇒ T = 11 months

∴ The correct answer is 11 months.

Additional Information

Simple Partnership

When investments of all partners are for the exact same time period, the profit or loss is distributed among the partners purely in the ratio of their original investments. (Profit ∝ Capital)

Compound Partnership

When investments are for different time periods, equivalent capitals are calculated for a unit of time by multiplying capital with time. Profit ratio = (C₁ × T₁) : (C₂ × T₂) : (C₃ × T₃).

Working vs Sleeping Partner

A working partner actively manages the business and receives a fixed salary or a specific percentage of the total profit first. The remaining profit is then distributed among all partners (including the working partner) in their capital ratio.

Given: 

(81^{x-3}) ÷ (81^4) = (\sqrt[6]{9^{24}})

Formula used:

a^m ÷ aⁿ = a^m-n

(a^m)ⁿ = a^mn

()(\sqrt[n]{x} = x^{\frac{1}{n}})

If a^x = a^y, then x = y

Calculation:

(81^{x-3}) ÷ (81^4) = (\sqrt[6]{9^{24}})

⇒ (81^{x-3-4}) = (\sqrt[6]{9^{24}})

⇒ (81^{x-3-4}) = (\sqrt[6]{9^{2(12)}})

⇒ (81^{x-3-4}) = (\sqrt[6]{81^{12}})

⇒ (81^{x-3-4}) = ({81^{\frac{12}{6}}})

⇒ (81^{x-3-4}) = (81^{2})

Now, on comparing the power with same base, we get,

⇒ x - 3 - 4 = 2

⇒ x - 7 = 2

⇒ x = 9

∴ The required value of 'x' is 9.

Shortcut Trick

Profit Ratio P : Q : R = 1430 : 1870 : 2420 = 13 : 17 : 22.

Total Profit units = 13 + 17 + 22 = 52 units.

Since time is constant, Investment Ratio = Profit Ratio.

52 units = Rs. 52,000 ⇒ 1 unit = Rs. 1,000.

Q investment = 17 units × 1,000 = Rs. 17,000.

∴ The correct option is C.

Alternate Method

Given:

Total investment = Rs. 52,000

Profit of P = Rs. 1430, Profit of Q = Rs. 1870, Profit of R = Rs. 2420

Formula Used:

Investment Ratio = Profit Ratio (When time period of investment is same for all partners)

Profit Ratio Analysis

P: 13u

Q: 17u

R: 22u

Total Units = 52 = Rs. 52,000

Calculations:

Profit Ratio P : Q : R = 1430 : 1870 : 2420

⇒ P : Q : R = 143 : 187 : 242 (Dividing by 10)

⇒ P : Q : R = 13 : 17 : 22 (Dividing by 11)

Sum of ratio parts = 13 + 17 + 22 = 52

⇒ Q’s Investment = (17 / 52) × 52000

⇒ Q’s Investment = 17 × 1000

⇒ Q’s Investment = Rs. 17,000

∴ The correct option is C.

Additional Information

Simple Partnership

When investments are for the same duration, Profit₁ : Profit₂ = Capital₁ : Capital₂.

Compound Partnership

When investments are for different durations, Profit Ratio = (C₁ × T₁) : (C₂ × T₂), where C is capital and T is time.

Calculating Capital

Capital = Profit ÷ Time. If profit ratio and time ratio are known, the capital ratio can be derived directly.

The correct answer is Assam.

Key Points

• Manas National Park is located in Assam.
• It is also a UNESCO World Heritage Site.
• It is home to animals like wild buffaloes, Royal Bengal Tiger, golden langur, hispid hare, etc.
• It has been named after the river Manas, which is a tributary of the river Brahmaputra.

Additional Information

• Kanha National Park is located in Madhya Pradesh.
• Ranthambore National Park is situated in Rajasthan.

The correct answer is Iran.

Key Points

• Lotus Temple was designed by an architect Furiburz Sabha who belongs to Iran.
• It is the last of seven Major Bahai temples built around the world.
• Shape- Lotus Flower.
• Lotus Temple was Built in 1986.
• Its structure made up of pure white marble.
• The architect Furiburz Sabha chose the lotus as the symbol common to Hinduism, Buddhism, Bhai Temple Jainism, and Islam.

The correct answer is All of the above.

Key Points

• The Round Table Conferences were a series of three conferences conducted by the Labour Party-led British government to deliberate upon and bring about constitutional reforms in British India during 1930-32.
• The conferences were based on the recommendation of Muhammad Ali Jinnah to Lord Irwin, the then Viceroy of India and James Ramsay MacDonald, the then British Prime Minister, and the Simon Commission report.
• The First Round Table Conference was held between 12^th November 1930 and January 1931 in London.
• The following Issues discussed in the First Round Table Conference

1. Federal structure
2. Provincial constitution
3. Provinces of Sindh and NWFP
4. Minorities
5. Defence services
6. Franchise
7. Executive responsibility to the legislature
8. Dr B R Ambedkar demanded separate electorates for the ‘untouchables’.
9. Tej Bahadur Sapru moved the idea of an All-India Federation. This was supported by the Muslim League. The princely states also supported this on the condition that their internal sovereignty is maintained.

The correct answer is Madhya Pradesh.

Key Points.

• Madhya Pradesh was the largest producer of pulses at over 25.23 percent among other Indian states. Maharashtra was the second largest producer of pulses in the country that year at around 16.33 percent.
• Wheat, Jau, Jwar, Bajra, Maize, and Pulses are the food crops of Rajasthan.
• India is the largest producer (25% of global production), the consumer (27% of world consumption), and the importer (14%) of pulses in the world.​

Additional Information 

• Uttar Pradesh comes under the top farming state in India and the rank of Uttar Pradesh is counted under major state-wise crop production in India, bajra, rice, sugarcane, food grains, and many more.

The correct answer is 1 only.

Important Points

Hathigumpha inscription:

• From Udaigiri, near Bhubaneswar in Odisha. So, statement 1 is correct.
• It was inscribed by Kharavela, the then Emperor of Kalinga in India.
• It consists of seventeen lines in a Central-Western form of Prakrit incised in a deep-cut Brahmi script on the overhanging brow of a natural cavern called Hathigumpha in the southern side of the Udaigiri hill. So, statement 2 is NOT correct.
• It faces straight towards the Rock Edicts of Ashoka at Dhauli, situated at a distance of about six miles.
• It is said to be one of the earliest biographical sketches of a king in India.
• The inscription is dated the 13th year of Kharavela's reign, which has been dated variously by scholars from the 2nd century BCE to the 1st century CE.
• Paleographically, the inscription dates from the mid-1st century BCE to the early 1st century CE.

​

The correct answer is Nilgiri Hills.

Key Points

• The Nilgiri Hills are located at the junction of the Eastern and Western Ghats, forming a unique ecological hotspot.
• These hills are part of the Western Ghats, a UNESCO World Heritage Site, and are one of the most significant biodiversity hotspots in the world.
• The Nilgiri Hills are situated in the southern part of India, spanning across Tamil Nadu, Kerala, and Karnataka.
• This region is renowned for its tea plantations, eucalyptus forests, and rolling grasslands, making it a major tourist destination.
• Ooty (Udhagamandalam), often referred to as the "Queen of Hill Stations," is located in the Nilgiri Hills.

Additional Information

• Eastern Ghats:
• The Eastern Ghats run along the eastern coast of India, stretching from Odisha to Tamil Nadu.
• They are not continuous like the Western Ghats and are characterized by hill ranges like the Nallamala and Mahendragiri Hills.
• This region experiences a semi-arid climate with patches of tropical forests.
• Western Ghats:
• The Western Ghats are a continuous mountain range parallel to the western coast of India.
• They are known for their dense forests, monsoon-fed rivers, and immense biodiversity.
• This region influences the monsoon climate in India and is home to numerous endemic species.
• Nilgiri Biosphere Reserve:
• The Nilgiri Hills form part of the Nilgiri Biosphere Reserve, which is India's first biosphere reserve established in 1986.
• It is home to species like the Nilgiri Tahr, Lion-tailed Macaque, and Indian Elephant.
• Significance of Biodiversity:
• The Nilgiri Hills contribute to India's ecological balance by serving as a transition zone between the Eastern and Western Ghats.
• The region supports diverse flora and fauna and is critical for maintaining India's natural heritage.
• Tourism in Nilgiris:
• Major attractions include Ooty, Coonoor, and the Nilgiri Mountain Railway, a UNESCO World Heritage Site.
• Tourism supports the local economy and promotes cultural and ecological awareness.

• Vibrations inside the ear are amplified by the three bones, namely the hammer, anvil and stirrup in the middle ear.
• Ear in the human body performs two functions, namely: Hearing and maintaining the balance of the body.
• An Ear consists of three major sections namely: Outer Ear, middle ear and Inner Ear.

The correct answer is Unemployment during the recessionary phase of the trade cycle

Key Points

• Unemployment occurs when a person who is actively searching for employment is unable to find work.
• It is often used as a measure of the health of the economy.
• Types of Unemployment
• Disguised Unemployment:
• The phenomenon when more people are employed than actually needed. Hence statement 1 is correct.
• Example: agricultural and the unorganized sectors of India.
• Seasonal Unemployment:
• Unemployment occurs during certain seasons of the year.
• Example: Agricultural laborers.
• Structural Unemployment:
• Unemployment arising from the mismatch between the jobs and the skills of the available workers in the market. Hence statement 2 is correct.
• Many people do not get jobs due to a lack of requisite skills and due to the poor educational level.
• Cyclical Unemployment:
• It is the result of the business cycle. Hence statement 3 is not correct.
• Unemployment rises during recessions and declines with economic growth.
• ​Technological Unemployment:
• It is the loss of jobs due to changes in technology.
• ​Frictional Unemployment:
• Frictional Unemployment is also known as Search Unemployment. Hence statement 4 is not correct.
• It refers to the time lag between the jobs when an individual is searching for a new job or is switching between the jobs.
• ​Vulnerable Employment:
• This means people are working informally without proper job contracts.
• These persons are deemed ‘unemployed’ since records of their work are never maintained.

The correct answer is Chanderi.

• The Koshak-Mahal is the most important palace at Chanderi, Ashoknagar (Madhya Pradesh). It is a square building with 35.36 m.
• Koshak Mahal is a complex of four palaces of equal dimensions standing at equal distance from one another.
• Entirely built of white local sandstone, all the four mansions of Koshak Mahal are identical.

Additional Information

• Each one is three-storeyed and is three aisles deep on either side, measuring, like a perfect cube, a little more than 15.24 m.
• The first storey has a comfortable division of its plan into chambers and corridors, strictly devoted to its residential purpose.
• The second storey has an ingenious, yet extremely simple technique of roofing.
• The third has the conventional flat ceiling with the use of pillars and brackets.

Various types of asexual reproduction:

The correct answer is Taj Mahal.

Key Points

• Taj Mahal is a UNESCO-acclaimed World Heritage site in Uttar Pradesh. 
• ​The Taj Mahal was designated as a UNESCO World Heritage Site in 1983 for being "the jewel of Muslim art in India".
• Taj Mahal
• It is located on the right bank of the Yamuna River in Agra district of Uttar Pradesh.
• It was built by Mughal Emperor Shah Jahan in memory of his wife Mumtaz Mahal with construction starting in 1632 AD and completed in 1648 AD.
• Ustad-Ahmad Lahori was the main architect of the Taj Mahal.
• The large double storied domed chamber, which houses the cenotaphs of Mumtaz Mahal and Shah Jahan, is a perfect octagon in plan.

Additional Information

• Sarnath Stupa
• ​Dhamek Stupa is one of the most famous and Buddhist stupas located in Sarnath near Varanasi in Uttar Pradesh, India
• It was built in 249 B.C.E. by the great Mauryan king Ashoka.
• It bears special significance among all the Buddhist stupas as it is believed to be the "seat of the holy Buddha", where Lord Buddha had preached his first sermon after attaining enlightenment at Bodhgaya.
• Allahabad Fort  ​
• It is a fort built by the Mughal emperor Akbar at Allahabad, Uttar Pradesh.
• It stands on the banks of the Yamuna near its confluence with the river Ganges.
• It is recognised by the Archaeological Survey of India as a monument of national importance.

The correct answer is 31st October.

Key Points 

• India celebrates the National Unity Day or Ekta Diwas on 31st October. 
• In 2014, the Government of India introduced Rashtriya Ekta Diwas, or National Unity Day with an aim to pay tribute to Sardar Vallabhbhai Patel on his birth anniversary.
• Rashtriya Ekta Diwas was inaugurated by Prime Minister Narendra Modi in 2014, by paying tribute to the Sardar Vallabhbhai Patel's statue and flagging a program which was known as Run For Unity in New Delhi.
• The Government of India has constructed a huge statue of Sardar Vallabhbhai Patel near the Narmada River in Gujarat in memory of the Iron Man of India.

Additional Information

Sardar Vallabhbhai Patel:

• Patel was born on 31 October 1875 at Nadiad, Gujarat, India, and died on 15 December 1950 in Bombay.
• Patel, during the first three years of Indian independence, served as Deputy Prime Minister, Minister of Home Affairs, Minister of Information, and Minister of State.
• He served as the first Indian municipal commissioner of Ahmadabad from 1917 to 1924 and was elected as municipal president from 1924 to 1928.
• Sardar Vallabhbhai Patel was the second candidate after Mahatma Gandhi to the presidency of the 1929 Lahore session of the Indian National Congress.

The correct answer is 14th November.

Key Points 

• World Diabetes Day is the primary global awareness campaign focusing on diabetes mellitus and is held on 14 November each year.
• Led by the International Diabetes Federation (IDF), each World Diabetes Day focuses on a theme related to diabetes.
• The theme of World Diabetes Day is "The Nurse and Diabetes".

Additional Information 

• There are 2 types of diabetes: 
• Type-2 diabetes is a largely preventable and treatable non-communicable disease that is rapidly increasing in numbers worldwide.
• Type 1 diabetes is not preventable but can be managed with insulin injections.

The correct answer is Boyle’s Law.

• According to Boyle’s Law at a constant temperature, the volume of a gas is inversely proportional to pressure.

Key Points

• Boyle’s Law
• At constant temperature, the volume of a definite mass of a gas is inversely proportional to the pressure.
• P. V = constant

Additional Information

• Charles’ Law:
• At constant pressure, the volume of a fixed mass of a gas is directly proportional to its absolute temperature.
• (V ∝T)
• Gay-Lussac’s Law
• At constant volume, the pressure of a given mass of a gas is directly proportional to the temperature in Kelvin.
• (P∝{T})
• Graham’s Law of Diffusion
• According to this law, the rate of diffusion of a gas is inversely proportional to the square root of its density.

The correct answer is Water.

Key Points

Xylem:

• Water Transport: Xylem is responsible for the transport of water and dissolved minerals from the roots to other parts of the plant.
• It forms a network of interconnected tubes that extend from the root system to the leaves.
• Structure and Components: Xylem tissue is composed of several types of specialized cells.
• The main conducting cells in xylem are called tracheary elements, which include tracheids and vessel elements. These cells have thick, lignified cell walls that provide structural support and prevent collapse under the tension created during water transport.
• Unidirectional Flow: The movement of water through xylem occurs in a unidirectional manner, primarily driven by transpiration, which is the loss of water vapor through the stomata on the leaves.
• This process creates a negative pressure or tension, pulling water upward from the roots to the upper parts of the plant.

Phloem:

• Nutrient Transport: Phloem is responsible for the transport of organic nutrients, such as sugars, amino acids, and hormones, from the site of production (usually leaves) to other parts of the plant.
• It allows the distribution of these nutrients to areas of growth, storage, or metabolic activity.
• Structure and Components: Phloem tissue consists of several cell types, including sieve tube elements, companion cells, phloem fibers, and phloem parenchyma cells.
• The main conducting cells are the sieve tube elements, which form sieve tubes. These cells lack nuclei and have perforated sieve plates that allow the movement of nutrients between adjacent cells.
• Bidirectional Flow: The movement of nutrients through phloem can occur in both upward (from source to sink) and downward (from sink to source) directions.
• This bidirectional flow is facilitated by pressure gradients and active transport mechanisms. Source tissues, such as mature leaves, produce sugars and load them into the phloem, while sink tissues, such as developing fruits or roots, consume the nutrients.

Pietra Dura is a fine inlay work with semi-precious stones.

Important Points

• Pietra Dura is an elaborate architectural technique introduced by Shah Jahan during his reign.
• His reign is known as the Golden Age of the Mughal Architecture who built some of the extraordinary buildings and forts like the Taj Mahal, the Red Fort, Jama Masjid, and Shalimar Bagh.
• His buildings include Persian styles, fine white marbles, domes, symmetrical designs, curved lines, etc.
• One of the distinctive features of his building is Petra Dura or Parchin Kari where semi-precious stones like lapis lazuli, topaz, and onyx were carved into the fine marble to create different floral images.
• Pietra Dura inlays were prominent in the Red Fort at Delhi where a series of Pietra Dura were inlaid behind the emperor's throne.

Hence, we can conclude that Pietra Dura is a floral design embedded into marbles.

Confusion Points

• Pietra Dura Coloured, hard stones placed in depressions carved into marble or sandstone create beautiful, ornate patterns with precious stones adorning the walls with flowers.

Explanation:

Bakelite is a polymer that is made up of the monomers phenol and Formaldehyde. This phenol-Formaldehyde is a Thermosetting polymer.

Some important properties of Bakelite are listed below.

• It can be easily Molded.
• Very smooth molding can be obtained from this polymer.
• Bakelite moldings are heat resistant and scratch-resistant.
• Owing to its low electrical conductivity, bakelite is resistant to electric current.

Bakelite structure:

Important Points

• Bakelite is used for making electrical switches.
• Melamine is used for floor tiles.

The correct answer is Gamma Rays.

Key Points

• Gamma rays have the shortest wavelength and highest frequency (energy) in the electromagnetic spectrum.
• They are electromagnetic waves with wavelengths in the range of 10^-12m and frequencies around 10²⁰- 10²⁴ Hz.
• They have a high penetrating power.
• They are a result of decaying radioactive material and can also be found in outer space.
• They are used in medical applications for sterilisation of equipment and cancer treatment.

Additional Information

• Other radiations in the Electromagnetic spectrum are:

The correct answer is High elongation.

Explanation:

Polymers

• They are giant molecules. They are important chemicals in our bodies (proteins, poly(nucleic acids)), in plants (starch, cellulose), and in our everyday lives (fibres, plastics, elastomers).
• Every polymer has its own characteristics, but most polymers have the following general properties.

Additional Information 

• Characteristics of Polymers
• Low specific gravity and high specific strength
• Thermal and electrical insulations
• Corrosion and weather resistances
• They can be processed in various ways to produce thin fibres or intricate parts (High elongation)
• Ease in design and manufacturing of complicated structures
• Outstanding aesthetic appeal due to ease in the adoption of permanent colours
• Mass production with low energy-intensive manufacturing techniques
• Ease in printability and adhesion
• Ease in handling and cleanliness
• Offering tremendous scope of physical and chemical modification to meet industrial and consumer requirement
• Tremendous adaptability to low-cost production.

The correct answer is Acquired Immuno-Deficiency Syndrome

Key Point

• AIDS:
• AIDS stands for Acquired immune deficiency syndrome.
• It is a syndrome caused by a virus termed HIV (human immunodeficiency virus).
• This virus affects the immune system in humans and makes them much more vulnerable to infections and diseases.
• It is a disease that progressed initially foar a long period without any symptoms.
• When the HIV virus attacks the T-cells in the immune system, it makes your body weak symptoms like a headache, fever, sore joints, and muscles, etc start appearing. When AIDS remains unattended, it leads to death.

The correct answer is Just before it touches the ground.

Key Points

• When an object reaches the ground it has its maximum value of kinetic energy just before touching the ground.
• Since kinetic energy + potential energy = Constant, so on reaching the ground, the potential energy of an object becomes zero.
• So eventually, the kinetic energy on reaching the ground becomes maximum.

Additional Information

• Kinetic energy is the work needed to accelerate a body of a given mass from rest to its stated velocity.
• K.E. = (1\over2) mv², where, m= mass of the body, v= velocity of the given group.
• Potential energy is stored energy that depends upon the relative position of various system parts.
• P.E. = mg h, where, m= mass of the body, g= gravitational acceleration, h= height.
• When the stone was at top of the roof it has P.E. = maximum, K.E.= zero. Because the stone was in idle condition so velocity, v=0, K.E.=0.
• Just after the stone is dropped, P.E. is started reducing, and the velocity is increasing, which in turn increases its K.E.
• When the stone is just halfway, K.E. and P.E. just become half of their actual values.
• When the stone touches the ground, its velocity v=0, so K.E. =0, and P.E. again get restored to its original value.
• The law of conservation of energy states that energy can neither be created nor destroyed, it transforms from one form to another.
• So in the course of the stone dropped from the roof of a house to its reaches at the ground, K.E. and P.E. transform between each other.
• But every time, K.E. + P.E. = Total energy = Constant must be maintained.

The correct answer is Pune.

Key Points

• National Institute of Virology
• It was established at Pune, Maharashtra in 1952 as Virus Research Centre (VRC).
• It was an outcome of the global programme of the Rockefeller Foundation (RF) of the USA for investigating the Arthropod-Borne viruses.
• The research activities of the Institute are coordinated by a Scientific Advisory Committee (SAC) consisting of eminent scientists.
• The Institute was designated as one of the collaborating laboratories of the World Health Organization (WHO) in 1967 and it started functioning as the regional centre of the WHO for South-East Asia for arbovirus studies from 1969.
• In 1995 it has been redesignated as the WHO Collaborating Centre for Arbovirus and Haemorrhagic Fever Reference and Research and Rapid Diagnosis of Viral Diseases.
• Director- Prof. Priya Abraham

The correct answer is Specific Gravity.

The correct answer is Speed is constant.

Key Points

• Circular motion is a movement of an object along the circumference of a circle or rotation along a circular path.
• The distance and displacement are different at every instance at any particular point of time.

Confusion Points

• While the speed is a scalar quantity, in uniform motion, it remains constant.
• As, Velocity is a vector quantity, and the direction of movement changes continuously, velocity changes continuously.
• Due to this, the object is in accelerated motion.

Important Points

About the Circular Motion:

• As the direction of the velocity changes at every instant, it is an accelerated motion.
• During the motion, the particle repeats it's paths along the same trajectory.
• Thus the motion is periodic.

Uniform Circular Motion:

• During circular motion, if the speed of the period remains constant, it is a Uniform Circular Motion. Hence option 4 is correct.

The correct answer is Gamma rays.

• Gamma rays consist of high-energy waves that can travel great distances at the speed of light and generally have a great ability to penetrate other materials.
• For that reason, gamma rays (such as from cobalt-60) are often used in medical applications to treat cancer and sterilize medical instruments.

Important Points

• Ultraviolet (UV) light has shorter wavelengths than visible light.
• The wavelength range is from 100-400 nm.
• Although UV waves are invisible to the human eye, some insects, such as bumblebees, can see them.
• This is similar to how a dog can hear the sound of a whistle just outside the hearing range of humans.
• These invisible rays that are part of the energy that comes from the sun, that can burn the skin and cause skin cancer.
• It is widely used in industrial processes and in medical and dental practices for a variety of purposes, such as killing bacteria, creating fluorescent effects, curing inks and resins, phototherapy, and suntanning.
• Light radiates from a source in waves.
• Each wave has two parts: an electric part, and a magnetic part. That's why light is called Electromagnetic Radiation.
• Visible light is usually having wavelengths in the range of 400–700 nm (4.00 × 10⁻⁷ to 7.00 × 10⁻⁷ m), between the infrared and the ultraviolet.
• X-rays have much higher energy and much shorter wavelengths than ultraviolet light.
• X-rays have very small wavelengths, between 0.01 to 10 nanometers.
• The use of x-rays is checking for fractures (broken bones), chest x-rays can spot pneumonia. Mammograms use x-rays to look for breast cancer.

Additional Information

• X-rays were first observed and documented in 1895 by German scientist Wilhelm Conrad Roentgen.
• Radio waves, television waves, and microwaves are all types of electromagnetic waves.

CONCEPT:

Storage of Sodium

• Sodium is a highly reactive alkali metal.
• It reacts vigorously with oxygen and moisture present in air, forming sodium oxide and sodium hydroxide.
• This reaction can lead to the ignition of sodium, as it generates heat and hydrogen gas, which is flammable.

EXPLANATION:

• To prevent sodium from reacting with air or moisture, it is stored under a non-reactive liquid like kerosene.
• Kerosene acts as a protective barrier, isolating sodium from air and water, thereby preventing unwanted reactions.

Additional Information

• Absolute alcohol can react with sodium, forming hydrogen gas and sodium alkoxide.
• Petrol is highly volatile and flammable, which increases the risk of fire when combined with sodium.
• CHCl₃ (chloroform) is not commonly used for sodium storage and may not effectively isolate sodium from air and moisture.

Therefore, sodium is usually kept in kerosene to ensure its safe storage and prevent reactions with air and moisture.

The correct answer is Changing the shape of the body.

Key Points

• The rate of change of displacement is called velocity.
• Velocity is a vector quantity, which has both magnitude and direction.
• SI Unit of velocity is m/sec.
• It may be positive or negative.
• If a body is moving on a circular then after completing one complete cycle, its average velocity is zero.
• The velocity of an object is the speed of an object moving in a definite direction.
• Velocity changes with the speed and direction of motion of the body.
• Changing the shape of the body will not affect the velocity of the body.

The correct answer is the Microwave.

Key Points

• A microwave oven uses microwaves to heat food.
• In the case of microwave ovens, the commonly used radio wave frequency is roughly 2,500 megahertz (2.5 gigahertz).
• Radio waves in this frequency range absorbed by water, fats, and sugars. When they are absorbed they are converted directly into atomic motion or vibration.
• Therefore heavy motion or vibration is converted into heat.

Important Points

• Microwaves are not absorbed by most plastics, glass, or ceramics.
• The frequency of the Microwave equals the resonance frequency of water. Therefore foods could be heated up by the oscillation of water molecules.

Additional Information

• An Electric heater, Electric blub (with filament), Electric iron is the electrical device that converts an electric current into heat.
• They working on the principle of the Joule heating effect.
• An electric current passing through a resistor will convert that electrical energy into heat energy.

The correct answer is calcium and phosphorus.

Key Points:

• The structure that holds the body up is made of bone.
• Additionally, it supports the body's major organs and anchors the muscles.
• It is a solid, unyielding tissue.
• A dense matrix made of calcium and phosphate molecules contains the bone cells.
• A different kind of connective tissue called a ligament can join two bones together.
• This tissue is extremely flexible.
• Another form of connective tissue is the tendon, which links bones and muscles.

Additional Information:

• Tendons are fibrous tissues with little flexibility and tremendous strength.
• The cells of cartilage are widely spaced.
• Sugars and proteins make up the solid matrix.
• In addition to the nose, ear, trachea, and larynx, cartilage smoothes the surfaces of bones at joints.
• Areolar connective tissue can be found in the bone marrow, around blood vessels and nerves, and between the skin and muscles.
• It supports internal organs, fills empty space inside the organs, and aids in tissue restoration.

The Correct answer is Edwin Hubble.

Key Points 

• 'Expanding Universe'
• Edwin Hubble, an American astronomer, and was the first to prove that the universe is expanding.
• According to Expanding Universe theory, the universe is presently expanding.
• Hubble proved that there is a direct relationship between the speeds of distant galaxies and their distances from Earth.
• This is now known as Hubble’s Law.

Additional Information

• Black Hole
• It refers to a point in space where the matter is so compressed as to create a gravity field from which even light cannot escape.
• The concept was theorized by Albert Einstein in 1915 and the term ‘black hole’ was coined in the mid-1960s by American physicist John Archibald Wheeler.
• Usually, the black holes belong to two categories:
• One category ranges between a few solar masses and tens of solar masses. These are thought to form when massive stars die.
• The other category is supermassive black holes.
• These range from hundreds of thousands to billions of times that of the sun from the Solar system to which Earth belongs.
• In April 2019, the scientists at the Event Horizon Telescope Project released the first-ever image of a Black Hole (more precisely, of its shadow).
• The Event Horizon Telescope is a group of 8 radio telescopes (used to detect radio waves from space) located in different parts of the world.
• Gravitational waves are created when two black holes orbit each other and merge.