SSC CHSL 2020 Official Paper 28 (Held on: 10 Aug 2021 Shift 1) (Previous Year Paper)

The correct answer is 'fare.'

Key Points

• Let us see the meanings of the given options:
• Fare: the amount of money you pay to travel by bus, train, taxi, etc. (किसी वाहन में यात्रा करने का भाड़ा; किराया)
• Rent: money that you pay regularly for the use of land, a house or a building. ((ज़मीन, मकान या इमारत) का किराया)
• Cost: the money that you have to pay for something. (क़ीमत, मूल्‍य)
• Charge: the price that you must pay for goods or services. (ख़रीदी गई वस्‍तु या सेवा पर शुल्‍क, ख़र्च, व्‍यय​)
• In the given sentence, we are talking about the amount of money you pay to travel by air.
• Correct sentence: The air fare has gone up significantly.

Additional Information

• Let us discuss the synonyms of the given words:

The correct answer is- 'misrable '

Key Points  

• In the given question, 'miserable' is correctly spelt.
• Its meaning is "very unhappy" (बहुत दुखी)
• Example: She's miserable living on her own.

Therefore, as per the points mentioned above, we find that the correct answer is option 4.

Additional Information 

• Moisture:- a liquid such as water in the form of very small drops, either in the air, in a substance, or on a surface (एक तरल जैसे पानी बहुत छोटी बूंदों के रूप में, या तो हवा में, किसी पदार्थ में, या सतह पर)
• Mature:- Mature people behave like adults in a way that shows they are well developed emotionally (परिपक्व लोग वयस्कों की तरह व्यवहार करते हैं जिससे पता चलता है कि वे भावनात्मक रूप से अच्छी तरह से विकसित हैं)
• Mischief:- behaviour, especially a child's, that is slightly bad but is not intended to cause serious harm or damage (व्यवहार, विशेष रूप से एक बच्चे का, जो थोड़ा खराब है लेकिन गंभीर नुकसान या क्षति का कारण नहीं है)

The correct answer is 'fluctuated​.'

Key Points

• Let us see the meanings of the given options:
• Fluctuated: to change frequently from one thing to another. (बार-बार उतार-चढ़ाव होना)
• Fumbled: to try to find or take hold of something with your hands in a nervous or careless way. (परेशानी की हालत में या लापरवाही से कुछ ढूँढ़ने या पकड़ने की कोशिश करना; टटोलना)
• Failed: to not be successful in something. (असफल होना)
• Faltered: to become weak or move in a way that is not steady. (अशक्त होना या अस्थिर होना; लड़खड़ाना​)
• In the given sentence, we are talking about the frequent changes in the prices of oil.
• Correct sentence: In the past month, the price of oil has fluctuated several times.

Additional Information 

• Let us discuss the synonyms of the given words:

The correct answer is 'been sitting​.'

Key Points

• The part 'being seating​' is incorrect as it is grammatically incorrect.
• Being refers to the present or continuous action, while been refers to the past or to something that started in the past but is continuing into the present.
• The meaning of the verb 'seat' is to sit down.
• Example: Please be seated.
• ​The meaning of the verb 'sit' is to put somebody into a sitting position; make somebody sit down.
• Example: He picked up his daughter and sat her down on a chair.
• ​Therefore, the use of 'being seating' in the sentence should be replaced with 'been sitting' to make it grammatically correct.
• ​​The correct sentence: How long have you been sitting on this bench?

​ 

Additional Information  

• The past indefinite tense, also known as simple past tense, is used to indicate a finished or completed action/task that occurred/happened at a specific point in time in the past. 
• Structure: Subject + verb in the past form + . . . . . + adverb of time + . . . . .
• Example: I ate a mango a few minutes ago.

Hinglish   

• भाग 'being seating​' गलत है क्योंकि यह व्याकरणिक रूप से गलत है।
• Being वर्तमान या निरंतर क्रिया को संदर्भित करता है, जबकि Been अतीत या किसी ऐसी चीज़ को संदर्भित करता है जो अतीत में शुरू हुई थी लेकिन वर्तमान में जारी है।
• 'Seat' क्रिया का अर्थ बैठना है।
• Example: Please be seated.
• क्रिया 'Sit' का अर्थ किसी को बैठने की स्थिति में रखना है; किसी को बैठाओ।
• Example: He picked up his daughter and sat her down on a chair.

The correct answer is 'yet living​.'

Key Points

• The part 'yet living' is incorrect as it is grammatically incorrect.
• The meaning of the word 'yet' is used with negative verbs or in questions for talking about something that has not happened but that you expect to happen.
• • Example: Has it stopped raining yet?
• ​An infinitive verb is essentially the base form of a verb with the word "to" in front of it.
• When you use an infinitive verb, the "to" is a part of the verb.
• The structure 'to + V1' to show that the next word is an infinitive verb.
• Example: I want to go there.
• ​Therefore, the use of 'yet living' in the sentence should be replaced with 'yet to live' to make it grammatically correct.​
• The correct sentence: We are yet to live in the same house.​

​ 

Additional Information  

• The past indefinite tense, also known as simple past tense, is used to indicate a finished or completed action/task that occurred/happened at a specific point in time in the past. 
• Structure: Subject + verb in the past form + . . . . . + adverb of time + . . . . .
• Example: I ate a mango a few minutes ago.

Hinglish

• भाग 'yet living' गलत है क्योंकि यह व्याकरणिक रूप से गलत है।
• शब्द 'yet' का प्रयोग नकारात्मक क्रियाओं के साथ या प्रश्नों में किसी ऐसी बात के बारे में बात करने के लिए किया जाता है जो हुआ नहीं है लेकिन आप होने की उम्मीद करते हैं।
• • Example: Has it stopped raining yet?
• एक इनफिनिटिव क्रिया अनिवार्य रूप से एक क्रिया का मूल रूप है जिसके सामने "to" शब्द होता है।
• जब आप एक अपरिमेय क्रिया का उपयोग करते हैं, तो "to" क्रिया का एक भाग होता है।
• संरचना 'to + V1' यह दिखाने के लिए कि अगला शब्द एक अपरिमेय क्रिया है।
• Example: I want to go there.
• इसलिए, व्याकरण की दृष्टि से इसे सही बनाने के लिए वाक्य में 'yet living' के उपयोग को 'yet to live' से बदल दिया जाना चाहिए।

The correct answer is- 'Oppose'

Key Points

• The most appropriate antonym of the given word 'Uphold' is 'Oppose'.
• Uphold: to defend or keep a principle or law, or to say that a decision that has already been made, especially a legal one, is correct (किसी सिद्धांत या कानून का बचाव या पालन करना, या यह कहना कि जो निर्णय पहले ही किया जा चुका है, विशेष रूप से कानूनी निर्णय सही है) 
• Example: Judge Davis upheld the county court's decision.
• Oppose: to disagree with something or someone, often by speaking or fighting against it, him, or her (किसी चीज या किसी से असहमत होना, अक्सर बोलकर या उसके खिलाफ लड़कर, उसके या उसके)
• Example: Most of the local residents opposed the closing of the school.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.

Additional Information  Let's look at the meaning of other words:

• Endorse: to make a public statement of your approval or support for something or someone (किसी चीज़ या किसी व्यक्ति के लिए आपकी स्वीकृति या समर्थन का सार्वजनिक बयान देना)
• Maintain: to continue to have; to keep in existence, or not allow to become less (जारी रखने के लिए; अस्तित्व में रहना, या कम नहीं होने देना)
• Support: to agree with and give encouragement to someone or something because you want him, her, or it to succeed (किसी व्यक्ति या किसी चीज़ से सहमत होना और उसे प्रोत्साहन देना क्योंकि आप चाहते हैं कि वह, उसे, या वह सफल हो)

The correct answer is 'No substitution required​.'

Key Points

• We use unless to say except if.
• Unless is a conditional word (like if), so we don’t use will or would in the subordinate clause:
• Example: You can't get a job unless you have experience.​
• Hence, the correct answer is 'No substitution required​.'

Additional Information   

• In references to the future with when, we use the present simple or the present perfect in the when-clause, not the future with shall and will
• Example: When the new park opens, I’ll go there every day.

Hinglish

• हम जब तक कहने के लिए unless उपयोग करते हैं।
• Unless एक सशर्त शब्द नहीं है (जैसे अगर), तो हम अधीनस्थ खंड में वसीयत या इच्छा का उपयोग नहीं करेंगे:
• Example: You can't get a job unless you have experience.​

The correct answer is- 'bridle' 

Key Points

• Let's look at the meaning of the marked option:
• Bridle: a set of leather straps that are put around a horse's head to allow its rider to control it (चमड़े की पट्टियों का एक सेट जो घोड़े के सिर के चारों ओर लगाया जाता है ताकि उसका सवार उसे नियंत्रित कर सके)
• Example: Polly saddled and bridled her favourite horse.
• Let's look at the meaning of the other given options:
• Stirrup: one of a pair of pieces of metal shaped like the letter D that hang from the side of a horse's saddle, used for resting your foot when you are riding (अक्षर डी के आकार के धातु के टुकड़ों में से एक जो घोड़े की काठी के किनारे से लटकता है, जब आप सवारी कर रहे होते हैं तो आपके पैर को आराम देने के लिए उपयोग किया जाता है)
• Bridal: of a woman about to be married, or of a marriage ceremony (एक महिला की शादी होने वाली है, या एक शादी समारोह के बारे में)
• Saddle: a seat on a bicycle, motorcycle, etc. (साइकिल, मोटरसाइकिल आदि पर बैठने की जगह।)

Hence, from the given meanings, we find that bridle is the correct one-word substitute.

The correct answer is 'Mother said that all the guests would arrive that night.'

Key Points

• The rules for changing Direct Speech to Indirect Speech:
• The given sentence is in Future Simple Tense.
• 'Will' changes to 'Would.'
• The reporting verb said/said to is changed in told, asked, demanded, ordered, enquired as per the nature of the sentence.
• Remove the commas and inverted commas.
• The first person in reported speech changes according to the subject of reporting speech.
• Use that in the sentence of indirect speech.
• Example: Shakespeare said, “I will write another drama tomorrow.” (Direct speech)

                 Shakespeare said that he would write another drama the next day. (Indirect speech)

Additional Information  

 

• If the sentence of Direct speech has a question that cannot be answered by saying yes or no then it does not use “if” or “whether” in its Indirect speech.
• Example:  She said to me, “Where did you buy this dress from?” (Direct speech)

                  She asked me where I had bought that dress from. (Indirect speech)

Hinglish  

• Direct Speech को Indirect Speech में बदलने का नियम:
• दिया गया वाक्य Future Simple Tense में है।
• Will, Would में बदल जाता है।
• Said/said to रिपोर्टिंग verb वाक्य की प्रकृति के अनुसार asked, demanded, ordered, enquired में बदल जाती है।
• Commas और inverted commas हटा दे।
• Reported speech में first person, reporting speech के subject के अनुसार बदलता है।
• Indirect speech के वाक्य में  that का प्रयोग करें।
• Example: Shakespeare said, “I will write another drama tomorrow.” (Direct speech)

                 Shakespeare said that he would write another drama the next day. (Indirect speech)

The correct answer is 'DACB.'

Key Points

• While arranging the parts of the passage given in options, we have to find some grammatical or contextual connections between them, so let’s find out.  
• The opener will be D as it introduces the context of the paragraph.
• After this, A will come as it adds information about the school of Ranji.
• After this, C will come as it is saying that Ranji is not having friends.
• B follows C as B talks about the discovery of a pool.
• The last sentence will be B as it is providing a conclusion to the context.
• ​​The correct sequence:

​

D. Ranji had been less than a month in Rajpur.

A. His school was closed as it was the height of summer.

C. As he had no friends yet, he wandered alone in the hills and forests.

B. It was on one such day that Ranji discovered a pool in the forest.

Additional Information  

 

• Steps for solving Para Jumbles:
• Clues include pronouns, like he, she, it, this, that, these, those; adverbs like formally, really; article a, an and the; definers like actually, finally, another; connectors like but, yet, both, also and neither nor, or, however, nevertheless.
• Now, with the help of clues, try to find out qualifier and qualified sentences, so that we can make pairs of qualified and qualifier sentences to eliminate the wrong choices given in the question.
• After making pairs, start eliminating the wrong choices or options given in the question.
• In case there is more than one choice, try to follow the sequence of sentences according to the occurrence of the events.

Hinglish

 

• विकल्पों में दिए गए गद्यांश के भागों को व्यवस्थित करते समय, हमें उनके बीच कुछ व्याकरणिक या प्रासंगिक संबंध खोजने होंगे, तो आइए जानें।
• Opener, D होगा क्योंकि यह पैराग्राफ के संदर्भ का परिचय देता है।
• इसके बाद, A आएगा क्योंकि यह रणजी के स्कूल के बारे में जानकारी जोड़ता है।
• इसके बाद, C आएगा क्योंकि यह कह रहा है कि रणजी के दोस्त नहीं हैं।
• B, C का अनुसरण करता है क्योंकि B एक पूल की खोज के बारे में बात करता है।
• अंतिम वाक्य B होगा क्योंकि यह संदर्भ को निष्कर्ष प्रदान कर रहा है।
• इसलिए, अनुक्रम 'DACB' है।

The correct answer is- 'Ordinary workers in a company'

Key Points

• The most appropriate meaning of the given idiom 'Rank and file​' is 'Ordinary workers in a company'.
• Let’s look at the meaning and example of the given phrasal verb:
• Rank and file- "Ordinary members who are not in a position of leadership, authority, or power." (साधारण सदस्य जो नेतृत्व, अधिकार या शक्ति की स्थिति में नहीं हैं।)
• E.g. The party's rank and file are beginning to question the prime minister's choice of advisers.
• ​​Thus from the explanation given above, we find that the  3^rd option is the correct choice.

The correct answer is- 'Abundant'

Key Points

• The most appropriate synonym of the given word 'Profuse' is 'Abundant'.
• Profuse: produced or given in large amounts (बड़ी मात्रा में उत्पादित या दिया गया) 
• Example: She was admitted to St Mary's Hospital with profuse bleeding.
• Abundant: more than enough (पर्याप्त से अधिक)
• Example: an abundant supply of food
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.

Additional Information     Let's look at the meaning of other words:

• Consistent: always behaving or happening in a similar, especially positive, way (हमेशा एक जैसा व्यवहार करना या घटित होना, विशेष रूप से सकारात्मक, तरीके से)
• Meagre: (of amounts or numbers) very small or not enough ((राशि या संख्या का) बहुत छोटा या पर्याप्त नहीं)
• Limited: small in amount or number (राशि या संख्या में छोटा)

The correct answer is - 'The sun was hidden by the clouds.'

Key Points

• The given sentence is in the Active voice, hence we need to convert it into the Passive voice.
• In the given sentence, the subject is 'The clouds' and the object is 'the sun' so for making the passive form of this sentence, we need to exchange the places of the object and subject.
• We need to follow these instructions while changing the active voice into the passive voice.
• The preposition 'by' will be used in the sentence.
• The objective case 'the sun' will be used as a subject form and it will take a singular verb.
• The subjective case 'The clouds' will be used as an object.
• In the given question which is in a form of the simple past, we follow this structure.
• Active form: Sub + V2 + object
• Passive form: Object+ was/were + V3+ by + subject
• So following these steps we finally get.

The correct passive form is - The sun was hidden by the clouds.

The correct answer is- 'Insert'

Key Points

• The most appropriate antonym of the given word 'Expunge' is 'Insert'.
• Expunge: to rub off or remove information from a piece of writing (लेखन के एक टुकड़े से जानकारी को मिटाने या हटाने के लिए) 
• Example: His name has been expunged from the list of members.
• Insert: to put something inside something else (किसी और चीज के अंदर कुछ डालना)
• Example: Insert the key in/into the lock.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.

Additional Information  Let's look at the meaning of other words:

• Remove: to take something or someone away from somewhere, or off something (किसी चीज को या किसी को कहीं से दूर ले जाना, या किसी चीज को उतारना)
• Deplete: to reduce something in size or amount, especially supplies of energy, money, etc. (आकार या मात्रा में कुछ कम करने के लिए, विशेष रूप से ऊर्जा, धन आदि की आपूर्ति।)
• Exhaust​: to make someone extremely tired (किसी को अत्यधिक थका देना)

The correct answer is 'BACD.'

Key Points

• While arranging the parts of the passage given in options, we have to find some grammatical or contextual connections between them, so let’s find out.  
• The opener will be B as it introduces the context of the paragraph.
• After this, A will come as it adds information about the subject, Jamawar.
• After this, C will come as it is talking about the usage of Jamawar.
• D follows C as D talks about the adulteration form of Pashmina which is Jamawar.
• The last sentence will be D as it is providing a conclusion to the context.
• Thus, the correct answer is 'BACD.'
• ​​The correct sequence:​

B. Jamawar (also spelled as Jamavar) is a fabric that has its roots in Kashmir.

A. The word Jama means ‘a robe or shawl’ and War means ‘Yard (the measuring unit)’.

C. People in the earlier times used to buy a yard of the shawl to protect themselves from the chilly winter.

D. The Jamawar is an adulterated form of Pashmina silk since it contains a blend of cotton and wool. 

Additional Information  

 

• Steps for solving Para Jumbles:
• Clues include pronouns, like he, she, it, this, that, these, those; adverbs like formally, really; article a, an and the; definers like actually, finally, another; connectors like but, yet, both, also and neither nor, or, however, nevertheless.
• Now, with the help of clues, try to find out qualifier and qualified sentences, so that we can make pairs of qualified and qualifier sentences to eliminate the wrong choices given in the question.
• After making pairs, start eliminating the wrong choices or options given in the question.
• In case there is more than one choice, try to follow the sequence of sentences according to the occurrence of the events.

Hinglish  

• विकल्पों में दिए गए गद्यांश के भागों को व्यवस्थित करते समय, हमें उनके बीच कुछ व्याकरणिक या प्रासंगिक संबंध खोजने होंगे, तो आइए जानें।
• Opener, D होगा क्योंकि यह पैराग्राफ के संदर्भ का परिचय देता है।
• इसके बाद, Aआएगा क्योंकि यह विषय, जमावार के बारे में जानकारी जोड़ता है।
• इसके बाद, C आएगा क्योंकि यह जमावार के उपयोग के बारे में बात कर रहा है।
• D, C का अनुसरण करता है क्योंकि D पश्मीना के मिलावट रूप के बारे में बात करता है जो कि जमावार है।
• अंतिम वाक्य D होगा क्योंकि यह संदर्भ को निष्कर्ष प्रदान कर रहा है।
• इसलिए, अनुक्रम 'BACD' है।

The correct answer is- 'Rinckle'

Key Points

• In the given question, 'Rankle' is correctly spelled.
• Its meaning is "to make someone annoyed or angry for a long time" (किसी को लंबे समय तक नाराज़ या नाराज़ करना)
• Example: The unkind way in which his girlfriend left him still rankled with him long after.

Therefore, as per the points mentioned above, we find that the correct answer is option 3.

Additional Information 

• Plump:- having a pleasantly soft, rounded body or shape (सुखद रूप से नरम, गोल शरीर या आकार होना)
• Gnaw:- to bite or chew something repeatedly, usually making a hole in it or gradually destroying it (किसी चीज को बार-बार काटने या चबाना, आमतौर पर उसमें छेद करना या धीरे-धीरे नष्ट करना)
• Muscle:- one of many tissues in the body that can tighten and relax to produce movement (शरीर में कई ऊतकों में से एक जो आंदोलन पैदा करने के लिए कस और आराम कर सकता है)

The correct answer is 'The Prime Minister chair a high-level meeting.'

Key Points

• The part 'The Prime Minister chair a high-level meeting' of the sentence is grammatically incorrect.
• The subject 'Prime Minister' is a singular noun.
• Therefore, we need a singular verb.
• ​Example: Justin is the fastest runner on the track team.
• ​The meaning of the verb 'chair' is to be the chairman or chairwoman of a meeting.
• Example: Who’s chairing the meeting this evening?
• ​Correct sentence: The Prime Minister chairs a high-level meeting with senior officials to review the Covid situation.

Additional Information 

• The meaning of the word 'chair' is the person who is controlling a meeting.
• Example: Please address your questions to the chair.

Hinglish   

 

• वाक्य का भाग 'The Prime Minister chair a high-level meeting' व्याकरण की दृष्टि से गलत है।
• Subject 'Prime Minister' एक singular संज्ञा है।
• इसलिए, हमें एकवचन क्रिया की आवश्यकता है।
• Example: Justin is the fastest runner on the track team.
• ​Verb 'chair' का अर्थ किसी बैठक का अध्यक्ष या अध्यक्ष होना है।
• Example: Who’s chairing the meeting this evening?

The correct answer is 'forever.'

Key Points

• The meaning of the idiom 'for good ' is permanently, forever.
• Idiom 'forever' का अर्थ हैं स्थायी रूप से, हमेशा के लिए।
• Example: She says she’s leaving him for good.

Additional Information 

• The meaning of the idiom 'Cry Wolf' is to keep asking for help when you do not need it, with the result that people think you do not need help when you really need it. ​
• Example: If you cry wolf too often, people will stop believing you.

The correct answer is- 'Aviary' 

Key Points 

• Let's look at the meaning of the given options:
• Aviary: a large cage (area surrounded by wire or bars) or closed space in which birds are kept as pets (एक बड़ा पिंजरा, तार या सलाखों से घिरा क्षेत्र या बंद जगह जिसमें पक्षियों को पालतू जानवरों के रूप में रखा जाता है)
• Example: The size of my loft for the hens would be 10ft x 8ft, fitted with aviary with inch half battens.
• Zoo: an area in which animals, especially wild animals, are kept so that people can go and look at them or study them (एक ऐसा क्षेत्र जिसमें जानवरों, विशेषकर जंगली जानवरों को रखा जाता है ताकि लोग जाकर उन्हें देख सकें या उनका अध्ययन कर सकें)
• Aquarium: a glass container in which fish and other water creatures can be kept (एक कांच का कंटेनर जिसमें मछली और अन्य जल जीव रखे जा सकते हैं)
• Apiary​​: a place where people keep bees, especially a collection of hives kept to provide honey (वह स्थान जहाँ लोग मधुमक्खियाँ रखते हैं, विशेष रूप से छत्तों का संग्रह जो शहद प्रदान करने के लिए रखा जाता है)

Hence, from the given meanings, we find that Aviary is the correct one-word substitute.

The correct answer is- 'desert'

Key Points

• The most appropriate synonym of the given word 'Forsake' is 'desert'.
• Forsake: to leave someone for ever, especially when they need you (किसी को हमेशा के लिए छोड़ने के लिए, खासकर जब उन्हें आपकी जरूरत हो) 
• Example: Do not forsake me!
• Desert: abandon (a person, cause, or organization) in a way considered disloyal or treacherous. परित्यक्त (एक व्यक्ति, कारण, या संगठन) एक तरह से विश्वासघाती या विश्वासघाती माना जाता है।
• Example: They were lost in the desert for nine days.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.

Additional Information    Let's look at the meaning of other words:

• Claim: to say that something is true or is a fact, although you cannot prove it and other people might not believe it (यह कहना कि कुछ सच है या तथ्य है, हालांकि आप इसे साबित नहीं कर सकते हैं और अन्य लोग इस पर विश्वास नहीं कर सकते हैं)
• Help: to make it possible or easier for someone to do something, by doing part of the work yourself or by providing advice, money, support, etc. (किसी के लिए कुछ करना संभव या आसान बनाने के लिए, काम का हिस्सा खुद करके या सलाह, पैसा, सहायता आदि प्रदान करके)
• Hold: to take and keep something in your hand or arms (अपने हाथ या बाहों में कुछ लेना और रखना)

The correct answer is 'lies.'

Key Points

• In the given sentence, we need to use the present tense.
• The present tense is used to describe things that are happening right now or things that are continuous.
• Lying and lie are grammatically incorrect.
• 'Is lying' is present continuous tense.
• Correct sentence: Their uniqueness lies in their manufacturing.

Additional Information

• Some adjectives are absolute, such as dead, unique.
• We do not usually use very before these ungradable adjectives:
• Example: The king was dead.

Hinglish

• दिए गए वाक्य में, हमें वर्तमान काल का उपयोग करने की आवश्यकता है।
• वर्तमान काल का उपयोग उन चीजों का वर्णन करने के लिए किया जाता है जो अभी हो रही हैं या जो चीजें निरंतर हैं।
• Lying and lie व्याकरण की दृष्टि से गलत है।
• 'Is lying', present continuous tense है।

Confusion Points

• 'Their' is a possessive adjective and 'uniqueness' is a noun which is singular.
• ​The verb 'lies' is according to the singular noun 'uniqueness'.

The correct answer is 'purely.'

Key Points

• Let us discuss the meanings of the given options:
• Purely: only or completely. (केवल, पूर्ण रूप से।)
• Absolutely: completely; totally. (पूरी तरह से; सर्वथा; संपूर्ण रूप से।)
• Merely: only; just. (केवल; मात्र।)
• Simply: used to emphasize how easy or basic something is. (किसी बात के आसान और प्रारंभिक या मामूली होने पर बल देने के लिए प्रयुक्त।)
• Here, the sentence is saying that the carpets are completely handmade.
• Correct sentence: These carpets are purely handmade and are knotted, not tufted.

Additional Information   

 

• Let us see the synonyms of the given words:

The correct answer is 'choose.'

Key Points

• Let us discuss the meanings of the given options:
• Choose: to decide which thing or person you want out of the ones that are available. (उपलब्‍ध वस्‍तुओं या व्‍यक्तियों में से चयन या चुनाव करना; चुनना।)
• Decide: to think about two or more possibilities and choose one of them. (दो या अधिक विकल्‍पों पर विचार कर एक का चयन करना।)
• Elect: to choose somebody to have a particular job or position by voting for him/her. (मतदान के द्वारा (किसी को) निर्वाचित करना या चुनना।)
• Indicate: to show that something is probably true or exists. (किसी बात के संभवतः सत्‍य या अस्‍तित्‍व में होने का संकेत करना, बताना, दिखाना।)
• Here, the sentence is talking about deciding between different carpets.
• Correct sentence: You can choose different carpets from a variety of silk or woolen ones.

Additional Information    

 

• Let us see the synonyms of the given words:

The correct answer is 'designed.'

Key Points

• Let us discuss the meanings of the given options:
• Defined: to explain and describe the meaning and exact limits of something. (किसी चीज़ के अर्थ और सटीक सीमाओं की व्याख्या और वर्णन करना।)
• Described: give a detailed account in words of. (शब्दों में विस्तृत विवरण देना।)
• Designed: decide upon the look and functioning of (a building, garment, or other objects), by making a detailed drawing of it. (एक इमारत, परिधान, या अन्य वस्तु) के रूप और कार्यप्रणाली पर निर्णय लेना, इसका विस्तृत चित्र बनाकर।)
• Devised: plan or invent (a complex procedure, system, or mechanism) by careful thought. (सावधानीपूर्वक विचार करके योजना या आविष्कार (एक जटिल प्रक्रिया, प्रणाली या तंत्र)।)
• Here, the sentence is talking about designing colourful themes.
• Correct sentence: These are designed in colourful themes.

Additional Information     

 

• Let us see the synonyms of the given words:

The correct answer is 'associated.'

Key Points

• Let us discuss the meanings of the given options:
• Assisted: help (someone), typically by doing a share of the work. (मदद (कोई), आमतौर पर काम का हिस्सा करके।)
• Attended: be present at (an event, meeting, or function). ((एक घटना, बैठक, या समारोह) में उपस्थित होना।)
• Abetted: encourage or assist (someone) to do something wrong, in particular to commit a crime. (कुछ गलत करने के लिए (किसी को) प्रोत्साहित करना या सहायता करना, विशेष रूप से अपराध करना।)
• Associated: connect (something) with something else because they occur together or one produces the other. ((कुछ) किसी और चीज से जुड़ना क्योंकि वे एक साथ होते हैं या एक दूसरे को उत्पन्न करता है।)
• Here, the sentence is talking about the association of carpet manufacturing with knotting.
• Correct sentence: The main art of carpet manufacturing is associated with the knotting.

Additional Information      

 

• Let us see the synonyms of the given words:

Given:

The logic followed here is:

(1) The arrow in the center rotates 90° in the anticlockwise direction in each step.

(2) Corner symbols rotate 90° in clockwise direction in each step.

• Outer symbols are changing according to the pattern shown below:

Hence, option (2) is the correct answer.

From the given information,

If Raman is the brother of the son of Kshitij’s son, implies Raman is the grandson of Kshitij, as shown below,

Hence, Raman is the grandson of Kshitij.

Given: FORTUNE is written as 716192122156.

The logic followed here is: adding 1 to the positional values of the letters, as shown below,

Similarly,

Hence, 16421163619 is the correct answer.

The least possible diagram is as follows:

Conclusions:

I. All computers are boxes → True (as all computers are calculators, and all calculators are boxes, so all computers are boxes too)

II. Some boxes are computers → True (as all computers are calculators, and all calculators are boxes, so part of calculators that are boxes are computers too)

Hence, both conclusions I and II follow.

The logical order is: 

1. Universe → It contains everything.
2. World → World is in Universe.
3. Asia → Asia is in the World.
4. Tamil Nadu → Tamil Nadu is a state in Asia.
5. Chennai → Chennai is the capital of Tamil Nadu.

Hence, 1, 3, 4, 5, 2 is the correct order.

Given: 

The logic followed here is: 

Detailed Explanation:

• The line AB is the mirror
• The given word "GRS?@915" ends with '5'. So the mirror image will start with "

" ⇒ Option 2 and 4 are eliminated.

• The given word "GRS?@915" has the second last digit "1", So the mirror image should be "

" ⇒ Option 1 is eliminated.

Hence, option (3) is the correct answer.

Given: a _ bcd _ _ aabc _ dea _ _ cd _ e 

By checking options and substituting accordingly,

(1) dabdade → a d b c d a b / a a b c d d e / a a d c d e e

(2) adabded → a a b c d d a / a a b c b d e / a d e c d d e

(3) adedabd → a a b c d d e / a a b c d d e / a a b c d d e

    ♦  Here  a a b c d d e is repeated.

(4) adebdda → a a b c d d e / a a b c b d e / a d d c d a e

    ♦  Option (3) gives a pattern of  a a b c d d e - a a b c d d e - a a b c d d e.

Hence, adedabd is the correct answer.

Given: (7, 4, 33)

The logic followed here is:

(7, 4, 33) → 7 + 4 = 11, 7 - 4 = 3 → 11 × 3 = 33

By checking options:

(9, 5, 56) → 9 + 5 = 14, 9 - 5 = 4 → 14 × 4 = 56

Hence, (9, 5, 56) is the correct answer.

The logic followed here is:

2^nd number = 1^st number + (Subtraction of digits of 1^st number)

3^rd number = 2^nd number + (Subtraction of digits of 2^nd number)

29 : 36 : 39

Second number = 29 + (9 - 2) = 29 + 7 = 36

Third number = 36 + (6 - 3) = 36 + 3 = 39

Similarly, 

48 : 52 : 55

Second number = 48 + (8 - 4) = 48 + 4 = 52

Third number = 52 + (5 - 2) = 52 + 3 = 55

Hence, the correct answer is "Option 3".

Given: DEBONAIR : EDRIOBAN :: HALLMARK : ?

The logic followed here is:

Similarly,

Hence, AHKRLLAM is the correct answer.

Given: 75 ÷ 18 + 51 × 8 − 82 = 87

By checking options and substituting accordingly,

(1) 5 and 2 → 72 ÷ 18 + 21 × 8 − 85

= 4 + 21 × 8 − 85

= 4 + 168 - 85

= 172 - 85

= 87

LHS = RHS

(2) 8 and 2 → 75 ÷ 12 + 51 × 2 − 28

= 6.25 + 51 × 2 − 28

= 6.25 + 102 - 28

= 108.25 - 28

= 80.25

≠ 87

LHR ≠ RHS

(3) 7 and 8 → 85 ÷ 17 + 51 × 7 − 72

= 5 + 51 × 7 − 72

= 5 + 357 - 72

= 362 - 72

= 290

≠ 87

LHR ≠ RHS

(4) 1 and 5 → 71 ÷ 58 + 15 × 8 − 82

= 1.22 + 15 × 8 − 82

= 1.22 + 120 - 82

= 121.22 - 82

= 39.22

≠ 87

LHR ≠ RHS

Hence, 5 and 2 is the correct answer.

Given: ENDORSE is written as VMWLIHV

The logic followed here is: reverse letters according to the English dictionary, as shown below, 

Similarly,

Hence, "RMHGIFXG" is the correct answer.

Given: Vishal has a total of Rs. 4,100 in the denominations of 5, 10, 20 and 50 rupee notes. He has an equal number of 5 and 10 rupee notes. The number of 20 rupee notes is double the number of 5 rupee notes. The number of 50 rupee notes is thrice the number of 10 rupee notes. 

Let the number of 5 and 10 rupee notes be 'x',

implies,

The number of 20 rupee notes is '2x',

and,

The number of 50 rupee notes is '3x'.

Then, according to the question,

 5(x) + 10(x) + 20(2x) + 50(3x) = 4100

5x + 10x + 40x + 150x = 4100

205x = 4100

x = 4100 ÷ 205

x = 20 

Hence, there are 20 notes of 5 rupee.

Given: 

The logic followed here is: only option (1) is embedded as shown below,

Hence, option (1) is the correct answer.

Important Points

• Do not get tensed by the complexity of the figures.
• Carefully understand the structure of the given question figure.
• The embedded figure may not be of exact size. It may be small or big.
• Sometimes the rotation or reflection of the figures may be confusing.
• So think wisely before selecting the answer.

By counting triangles:

Hence, 7 is the correct answer.

Given: Bed : Mattress : : Chair : ?

Mattress is for Bed.

Similarly,

Cushion is for Chair.

Hence, cushion is the correct answer.

Additional Information

• A cushion is a soft bag of some ornamental material, usually stuffed with wool, hair, feathers, polyester staple fiber, non-woven material, or even paper torn into fragments

By checking options:

The logic followed here is:

All of Delhi, Puducherry, Chandigarh, Jammu & Kashmir are Union Territories.

Whereas, 

Chandigarh does not have a legislative assembly.

Hence, Chandigarh is the odd one.

The logic followed here is:

The paper when unfolded will look like this:

Hence, option (1) is the correct answer.

Given: 8, 24, 48, 80, ?, 168

The logic followed here is:

Hence, "120" is the correct answer.

By checking options:

(1) ACFJ 

(2) LNQU

(3) KMQT

(4) QSVZ

Hence, KMQT is the odd one.

Given: Engineers, Educated Persons, Males

The logic followed here is:

All engineers are educated people, some engineers are males, and some educated people are males, as shown below:

 

Hence, option (3) is the correct answer.

The logic followed here is:

(First number - 1)² + 2 = Second number

6 : 27 → (6 - 1)² + 2  = 5² + 2 = 27

Similarly,

9 : ? → (9 - 1)² + 2 = 8² + 2 = 66

Hence, 66 is the correct answer.

By checking options:

(1) 11 : 123 → 11² + 2 = 121 + 2 = 123

(2) 17 : 291 → 17² + 2 = 289 + 2 = 291

(3) 15 : 227 → 15² + 2 = 225 + 2 = 227 

(4) 13 : 169 → 13² + 2 = 169 + 2 = 171 ≠ 169

Hence, 13 : 169 is the odd one.

Given: 

The logic followed here is:

Growth is the synonym of Expansion.

Similarly,

Urge is the synonym of Request.

Hence, urge : request is the correct answer.

Given: 

Logic: If two dice have the same face value in the given image on two of their faces then the third face of each dice is opposite to one another.

Thus, from the common face (6) and (5) from both the dice: 

 

 

Now, 1 is opposite to 2, thus '1' will be on the face opposite to the face showing the letter '2'.

Hence, 1 is the correct answer.

Given:

$\left(x-\frac{2}{x}\right)^3-\left(x+\frac{2}{x}\right)^3$

Concept used:

a³ - b³ = (a - b)(a² + ab + b²)

Calculation:

Let $\left(x-\frac{2}{x}\right)^3-\left(x+\frac{2}{x}\right)^3$ be a3 - b3

Now,

$\left(x-\frac{2}{x}\right)-\left(x+\frac{2}{x}\right)[\left(x-\frac{2}{x}\right)^2 + \left(x+\frac{2}{x}\right)^2 + \left(x+\frac{2}{x}\right) \left(x-\frac{2}{x}\right)]$

⇒ - 4/x[x² + 4/x² - 4 + x2 + 4/x2 + 4 + x2 - 4/x2]

⇒ - 4/x[3x2 + 4/x2]

⇒ - 4[3x + 4/x³]

∴ Required answer is - 4[3x + 4/x3]

Given:

Nalini's younger brother is 12 years old 

Let Nalini Age be X

Ratio of their age = 7 : 6

Calculation:

X : 12 = 7: 6

X = 14

So Nalini's age is 14 years.

Now after 6 years, their ages will be

Nalini :14+ 6 = 20

Younger Brother: 12 + 6 = 18

So, ratio = 20 : 18

10: 9

∴ The required ratio is 10: 9

Given:

10 men or 15 women can complete a work in 30 days

Calculation:

Let the new time be x days

Now,

10M × 30 = 15W × 30

⇒ 300M = 450W

⇒ 2M = 3W

Total work = 10 × 30 = 300 units

Now 15M and 27W = 15M and 18M [Converted women into men]

So, time = 300/33 = 100/11 days or $9\frac{1}{11}$days

∴ The required time is $9\frac{1}{11}$days

Shortcut Trick

Let initial Income = 100, which means Savings = 25 and Expenditure = 75.

New Income = 120 (increased by 20%) and Savings = 25 (remains constant).

New Expenditure = 120 − 25 = 95.

Increase in Expenditure = 95 − 75 = 20.

Percentage Increase = (20 ÷ 75) × 100 = 26 ²/₃%.

∴ The correct answer is 26 ²/₃%.

Alternate Method

Given:

A person saves 25% of his income.

Income increases by 20% while savings remain the same.

Formula Used:

Income = Expenditure + Savings

Percentage Increase = (Increase in Value ÷ Original Value) × 100

Initial Income = 100 Exp = 75 Sav = 25 New Income = 120 (+20%) Exp = 95 Sav = 25 + 20 % Increase = (20 ÷ 75) × 100 ≈ 26.66%

Calculations:

⇒ Let the initial income be 100 units.

⇒ Initial saving = 25% of 100 = 25 units

⇒ Initial expenditure = 100 − 25 = 75 units

⇒ After a 20% increase, the new income = 100 + 20% of 100 = 120 units

⇒ New saving = 25 units (as it remains the same)

⇒ New expenditure = 120 − 25 = 95 units

⇒ Increase in expenditure = 95 − 75 = 20 units

⇒ Percentage increase in expenditure = (20 ÷ 75) × 100

⇒ Percentage increase = (4 ÷ 15) × 100 = 80 ÷ 3 = 26 ²/₃%

∴ The correct answer is 26 ²/₃%.

Additional Information

Income-Expenditure Concept

The foundational equation is Income = Expenditure + Savings. Any change in income will exactly equal the sum of changes in expenditure and savings.

Constant Variable Effect

If savings remain constant, the entire absolute increase in income directly translates to the absolute increase in expenditure.

Percentage Change Formula

Percentage change is always calculated based on the initial value: % Change = [(Final − Initial) ÷ Initial] × 100.

Given:

A seven-digit number 23k567k is divisible by 3

Concept used:

Divisibility rule of 3 → If the sum of all digits of a number is divisible by 3

Calculation:

2 + 3 + k + 5 + 6 + 7 + k = 23 + 2k

Now, 23 + 2k is divisible by 3

So, the Nearest numbers which is divisible by 3 = 24, 27, 30, 33, 36, 39

Now, 2k ≠ 1, 7, 13

k ≤ 9

So, possible values of 2k = 4, 10, 16

So, the sum of all the values of 2k = 30

So, k = 15

∴ The required answer is 15

Given:

AD is the internal bisector of ∠A meeting BC at D

BD = 3.6 cm and BC = 8 cm

Concept used:

In ΔABC, if AD is the internal bisector of ∠A meeting BC at D, then AB/AC = BD/DC

Calculation:

DC = BC – BD

⇒ DC = 8 – 3.6 = 4.4

In the above figure, AD is the angle bisector of ∠A

So, AB/AC = BD/DC

⇒ AB/AC = 3.6/4.4

⇒ AB : AC = 3.6 : 4.4 = 9 : 11

∴ The ratio of AB to AC will be 9 : 11

Given:

Selling price = Rs. 425

Discount = 15%

And Profit % = 25%

Formula used:

Selling price(SP) = {(100 + Profit %)/100} × Cost price(CP)

Selling price = Marked price - Discount

Calculation:

Discount = 15% = 3/20

Let the market price be 20x And discount be 3x

SP = 20x - 3x = 17x

According to the question,

we get 17x = Rs. 425

⇒ x = 425/17 = Rs. 25

Now, Market price = 20x = 20 × 25 = Rs. 500

If MP = SP

⇒ CP × (125/100) = 500

CP = Rs. 400

∴ The cost price of the article is Rs. 400.

Calculation:

Expenditure in 2014 = 225

Expenditure in 2016 = 330

Expenditure in 2018 = 180

Total expenditure = 735

Average = 245

Revenue in 2017 = 400

Difference = 400 - 245 = 155

% = (155/400) × 100 = 38.75%

∴ Required answer is 38.75%

Given:

Principal= Rs. 12000

Time = 5 years

S.I = 6000

Concept used:

SI = Prt/100

Amount = P × {1 + (R/100)}^N

C.I = Amount - Principal

Calculation:

Let the rate of interest be x%

So, 6000 = (12000 × x × 5)/100

6000 = 60000x/100

6000 = 600x

x = 10

Now,

Amount = 12000 × 11/10 × 11/10 × 11/10

15972

So, C.I = 15972 - 12000

3972

∴ The required compound interest is Rs. 3972

Calculation:

Total students in science stream from school A, B, and D = 60 + 78 + 40

⇒ 178

Total students in vocational stream from school B, D, and E = 40 + 40 + 50

⇒ 130

Ratio = 178 : 130

⇒ 89 : 65

∴ Required ratio is 89 : 65

Given:

16\frac{1}{4}\div\left[2\frac{1}{6}+\left{4\frac{1}{3}-\left(2\frac{1}{2}+\frac{3}{4}\right)\right}\right]

Concept used:

Calculation:

16\frac{1}{4}÷\left[2\frac{1}{6}+\left{4\frac{1}{3}-\left(2\frac{1}{2}+\frac{3}{4}\right)\right}\right]

⇒ 65/4 ÷ [13/6 + {13/3 - (5/2 + 3/4)}]

⇒ 65/4 ÷ [13/6 + {13/3 - (10/4 + 3/4)}]

⇒ 65/4 ÷ [13/6 + {13/3 - 13/4}]

⇒ 65/4 ÷ [13/6 + {52/12 - 39/12}]

⇒ 65/4 ÷ [13/6 + 13/12]

⇒ 65/4 ÷ [26/12 + 13/12]

⇒ 65/4 ÷ 39/12

⇒ 65/4 × 12/39

⇒ 5

∴ Required answer is 5

Shortcut Trick

Let Original Selling Price (SP) = 300 units.

New SP = 33⅓% of 300 = 100 units.

Loss of 33⅓% means SP is 2/3 of CP ⇒ 2/3 × CP = 100 ⇒ CP = 150 units.

Selling at 40% of Original SP = 40% of 300 = 120 units.

Loss % = (150 − 120) ÷ 150 × 100 = 20%.

∴ The correct answer is Loss 20%.

Alternate Method

Given:

Selling price at 1^st condition = 33⅓% of original selling price

Loss at 1^st condition = 33⅓%

Selling price at 2^nd condition = 40% of original selling price

Formula Used:

Loss = Cost Price (CP) − Selling Price (SP)

Loss % = (Loss ÷ CP) × 100

Calculations:

⇒ Let Original Selling Price = SP and Cost Price = CP

⇒ Selling price in 1^st condition = 33⅓% of SP = SP ÷ 3

⇒ Loss % in 1^st condition = 33⅓% = 1/3

⇒ SP ÷ 3 = CP − (1/3 × CP)

⇒ SP ÷ 3 = 2/3 × CP

⇒ SP = 2 × CP

⇒ Selling Price in 2^nd condition = 40% of SP = 0.4 × (2 × CP) = 0.8 × CP

⇒ Since New SP is less than CP, there is a loss.

⇒ Loss = CP − 0.8 × CP = 0.2 × CP

⇒ Percentage Loss = (0.2 × CP ÷ CP) × 100 = 20%

∴ The correct answer is Loss 20%.

Additional Information

Cost Price & Selling Price

Profit occurs when Selling Price > Cost Price (Profit = SP − CP). Loss occurs when Cost Price > Selling Price (Loss = CP − SP).

Profit and Loss Percentage

Both profit and loss percentages are always calculated on the Cost Price unless stated otherwise. Formula: Profit/Loss % = (Profit or Loss ÷ CP) × 100.

Fractional Equivalents

Converting percentages to fractions speeds up calculations. For example, 33⅓% = 1/3, 20% = 1/5, and 40% = 2/5.

Given:

x + $1\over 15x$ = 3

Concept used:

a³ + b³ = (a + b)³ - 3ab(a + b)

Calculation:

x + $1\over 15x$ = 3

 

⇒ 3x + $1\over 5x$ = 9

Now,

27x³ + 1/125x³ = 9³ - (3.3x.1/5x)(9)

⇒ 27x3 + 1/125x3 = 729 - 81/5

⇒ 27x3 + 1/125x3 = 729 - 16.2

⇒ 27x3 + 1/125x3 = 712.8

⇒ 9x3 + 1/375x3 = (712.8)/3

⇒ 9x3 + 1/375x3 = 237.6

∴ The required answer is 237.6

Given:

x⁶ - 6√6y⁶ = (x² + Ay²)(x⁴ + Bx²y² + Cy⁴)

Concept used:

x³ - y³ = (x - y)(x² + xy + y²)

Calculation:

x⁶ - 6√6y⁶ = (x² + Ay²)(x⁴ + Bx²y² + Cy⁴)

⇒ (x²)³ - (√6y²)³ = (x² + Ay²)(x⁴ + Bx²y² + Cy⁴)

⇒ (x² - √6y²)(x⁴ + x² × √6y² + 6y⁴) = (x² + Ay²)(x⁴ + Bx²y² + Cy⁴)

Comparing both sides of the equation we get-

A = -√6, B = √6, C = 6

So, (A² - B² + C²) = 6 - 6 + 6² = 36

∴ The value of (A² - B² + C²) is 36.

Given:

AC is diameter and BD is a chord.

∠BOC = 40° and ∠AOD = 120°

Concept Used:

The angle made by an arc on the centre is always two times the angle made by the same arc on the circumference of a circle.

Calculation:

Join B to C

Given ∠BOC = 40° so, ∠BOA = (180 - 40) = 140°

Again, from the arc AB angle at centre O = 140° so, from the same arc AB angle on the circumference = 140/2 = 70°

Now, ∠DOC = 360 - (40 + 140 + 120) = 360 – 300 = 60°

So, from arc DC angle at centre O = 60° then angle at circumference i.e ∠DBC = 60/2 = 30° 

Now, ∠BEC = (180 – (70 + 30)) = 80°

∴ ∠BEC is equal to 80°

Given:

No of males = 20

The number of females and children is 4 more than that of males.

The average weight of males is 54 kg

The average weight of females is 49 kg

The average weight of children is 30 kg

The average weight of the whole group is 48.25 kg

Concept used:

Average = Sum of Observations/ Number of Observations

Calculation:

Number of Females + Children = 20 + 4 = 24

Let the number of females is x and the number of children be 24 – x

So total persons = 20 + 24 = 44

A/Q-

44 × 48.25 = 20 × 54 + 49 × x + (24 - x) × 30

⇒ 2123 = 1080 + 49x + 720 – 30x

⇒ 19x = 2123 – 1800

⇒ x = 17

So, Number of females = 17 and number of children = 24 - 17 = 7

The required difference is 17 - 7 = 10

∴ The required difference is 10.

Calculation:

Total exports of cars of type A in 2016 and 2018 = 275 + 300 = 575

Total exports of cars of type B in 2015 and 2017 = 250 + 275 = 525

Their Ratio = 575 : 525 = 23 : 21

∴ The required ratio is 23 : 21

Calculation:

Let total relief fund for all the students be 100x

Fund for Middle Class = 30% of 100x = 30x

Fund for Secondary Class = 27% of 100x = 27x

Difference between Middle Class and Secondary Class = 3x

A/Q-

30x = 6750

⇒ 3x = 675

∴ Rs 675 was collected more by the Middle classes as compared to the Secondary classes

Given:

ABC is a triangle inscribed in a circle

ΔACB is equal to 35°

Concept used:

The sum of opposite angles of a cyclic Quadrilateral is always 180°

Calculation:

We will join the points BP and AP

In the above figure, APBC is a cyclic quadrilateral.

So, ∠APB + ∠ACB = 180

⇒ ∠APB = 180 - 35

⇒ ∠APB = 145°

∴ The value of ∠APB is 145°

Given:

tanθ = 4/3

Concept used:

tanθ = p/b, sinθ = p/h, cosθ = b/h

h² = p² + b²

(where p = Perpendicular, b = Base, h = Hypotenuse)

Calculation:

tanθ = 4/3, So, p = 4 and b = 3

Now, h² = 4² + 3² = 16 + 9 = 25

⇒ h² = 25

⇒ h = 5

Now, sinθ = 4/5, cosθ = 3/5

So, (9sinθ + 12cosθ)/(27cosθ – 20sinθ) = (9 × 4/5 + 12 × 3/5)/(27 × 3/5 - 20 × 4/5)

= (36/5 + 36/5)/(81/5 - 80/5)

= (72/5)/(1/5)

= 72

∴ The required value is 72

Shortcut Trick

$\frac{9\sin θ+12\cos θ}{27\cos θ-20\sin θ}$

Taking cosθ as common from both numerator and denominator, we can write:

\(\frac{cosθ~ (9\tan θ+12)}{cosθ~ (27-20tanθ)}=\frac{ 9\tan θ+12}{ 27-20tanθ}\)

Putting tanθ = 4/3, we get the required answer of 72.

Given:

DE is parallel to BC

AD = 3 cm, BD = 6 cm and AE = 2 cm

Concept:

If ΔABC and ΔDEF are similar, then AB/DE = BC/EF = CA/FD

Calculation:

In the above figure, ΔABC and ΔADE are similar as -

1. ∠A is common
2. ∠ADE = ∠ABC(∵ DE ∥ BC)

So, AD/AB = AE/AC

⇒ 3/(3 + 6) = 2/(2 + CE)

⇒ 1/3 = 2/(2 + CE)

⇒ CE + 2 = 6

⇒ CE = 4 cm

∴ The length of CE is 4 cm.

Given:

$\frac{3(\cot^2 46^{\circ}-\sec^2 44^{\circ})}{2(\sin^2 28^{\circ}+\sin^2 62^{\circ})}+\frac{2\cos^2 60^{\circ}\tan^2 33^{\circ}\tan^2 57^{\circ}}{\sec^2(90-\theta)-\cot^2 \theta}$

Concept used:

 

Calculation:

$\frac{3(\cot^2 46^{\circ}-\sec^2 44^{\circ})}{2(\sin^2 28^{\circ}+\sin^2 62^{\circ})}+\frac{2\cos^2 60^{\circ}\tan^2 33^{\circ}\tan^2 57^{\circ}}{\sec^2(90-\theta)-\cot^2 \theta}$

⇒ $\frac{3(\cot^2 46^{\circ}-;cosec^2 46^{\circ})}{2(\sin^2 28^{\circ}+\cos^2 28^{\circ})}+\frac{2\cos^2 60^{\circ}\tan^2 33^{\circ}\cot^2 33^{\circ}}{cosec^2\theta-\cot^2 \theta}$

⇒ $\frac{-3}{2}+\frac{2\cos^2 60^{\circ}\tan^2 33^{\circ}\frac{1}{\tan^2 33^{\circ}}}{1}$

⇒ -3/2 + 2 × (1/2)²

⇒ -3/2 + 1/2

⇒ -1

∴ The required value is -1

Given:

3secθ + 4cosθ  = 4√3

Concept used:

secθ = 1/cosθ

Calculation:

3/cosθ + 4 cosθ = 4√3

⇒ 3 + 4 cos²θ = 4√3cosθ

⇒ 4 cos²θ - 2√3cosθ - 2√3cosθ + 3 = 0

⇒ 2cosθ(2cosθ - √3) - √3(2cosθ - √3) = 0

⇒ (2cosθ - √3)(2cosθ - √3) = 0

So, cosθ = √3/2

⇒ θ = 30^°

Now, 

(1 – sinθ + cosθ) = 1 - sin30 + cos30

⇒ 1 - 1/2 + √3/2

⇒ $\frac{1+\sqrt3}{2}$

∴ The required value is $\frac{1+\sqrt3}{2}$

Shortcut Trick

We can try with different standard values of θ(30, 45, 60) in the given equation and get θ = 30

Given:

The radius of a solid metallic sphere = 10 cm

The radius of a smaller sphere = 2 cm

Concept used:

Volume of Sphere = 4/3πr³

Calculation:

Let the number of smaller spheres formed be n

⇒ 4/3 × π × 10³ = n × 4/3 × π × 2³

⇒ n = (10/2)³

⇒ n = 125

∴ 125 such spheres can be formed.

Shortcut Trick

Upstream speed = 20 ÷ 1.25 = 16 km/h (Since 1 h 15 m = 1.25 h)

Boat speed in still water = Upstream speed + Current speed = 16 + 2 = 18 km/h

Downstream speed = Boat speed + Current speed = 18 + 2 = 20 km/h

Time downstream = Distance ÷ Downstream speed = 30 ÷ 20 = 1.5 hours

1.5 hours = 1 hour 30 minutes

∴ The correct answer is 1 h 30 m.

Alternate Method

Given:

Upstream Distance = 20 km

Upstream Time = 1 hour 15 minutes = 1 + 15/60 = 5/4 hours

Speed of Current (v) = 2 km/h

Formula Used:

Speed = Distance ÷ Time

Upstream Speed (U) = u − v

Downstream Speed (D) = u + v

(where u is the speed of boat in still water and v is the speed of current)

Calculations:

⇒ Upstream speed (U) = 20 ÷ (5/4) = 20 × 4/5 = 16 km/h

⇒ u − v = 16

⇒ u − 2 = 16

⇒ u = 18 km/h (Speed of Sunil in still water)

⇒ Downstream speed (D) = u + v = 18 + 2 = 20 km/h

⇒ Time to row 30 km downstream = 30 ÷ 20 = 1.5 hours

⇒ 1.5 hours = 1 hour + (0.5 × 60) minutes = 1 hour 30 minutes

∴ The correct answer is 1 h 30 m.

Additional Information

Speed of boat in still water (u)

It is the average of downstream and upstream speeds: u = (D + U) ÷ 2.

Speed of current/stream (v)

It is half the difference between downstream and upstream speeds: v = (D − U) ÷ 2.

Time, Speed, and Distance relation

Time = Distance ÷ Speed. For constant distance, speed is inversely proportional to time.

The correct answer is September.

Key Points

• Nutrition Month:
• It was celebrated to promote nutrition among Women and Children.
• It is also called Rashtriya Poshan Maah.
• Rashtriya Poshan Maah was celebrated in September 2020.
• Poshan Maah is celebrated every year to encourage Jan Bhagidaari in order to ensure health and nutrition for everyone. Every year Poshan Maah is celebrated all over the country under POSHAN Abhiyaan, launched in 2018.
• The importance of Nutrition in our lives was emphasized by Prime Minister Shri Narendra Modi in his popular programme "Mann ki Baat on 30^th August 2020.
• PM Narendra Modi announced to celebrate September as a month of nutrition.
• In his Mann Ki Baat programme, he laid emphasis on creating awareness to fight malnutrition among children, particularly the girl child.
• Gujarat Government launched a pilot project, Poshan Abhiyan, last year, which is a statewide mission to eradicate malnutrition among children.

The correct answer is Rahul Dravid.

Key Points

• Rahul Dravid holds the record for the most number of catches (210) taken by a non-wicketkeeper. In the 509 matches he played for India, he took a total of 406 catches.
• Rahul Dravid:
• He holds the record of most catches in Test cricket by a non-wicket keeper and also the record of highest scoring partnership in Test cricket with Sachin Tendulkar(6520 runs).
• He is a former Indian cricketer who is often called 'Mr. Dependable and The Great Wall'.
• He made his international ODI debut on 3 April 1996 against Sri Lanka and his test debut on 20 June 1996 against England.
• He has been felicitated with national awards like Arjuna Award, Padma Shri, and Padma Vibhushan awards and was inducted into the ICC Hall of Fame in 2018.

Additional Information

• Javagal Srinath
• He is a former Indian Cricketer and currently an ICC match referee.
• He is the first Indian fast bowler to take more than 300 wickets in One Day Internationals.
• He is one of eleven bowlers who took 300 wickets in one-day international cricket, and the only Indian fast bowler to take 300 wickets.
• Manoj Prabhakar
• He is a former Indian Cricketer.
• He was a right-arm medium-pace bowler and a lower-order batsman.
• VVS Laxman
• He is a former Indian international cricketer and a Former cricket commentator.
• He is known for his elegant stroke play.
• He is currently the Head of Cricket at the National Cricket Academy (NCA), and the head coach of the India Under-19 and India A teams.

The correct answer is Hirapur.

Key Points

• Indian Iron and Steel Company (IISCO)
• IISCO is an integrated steel plant located at Burnpur (now).
• It is a steel plant that is a part of the Steel Authority of India Limited (SAIL).
• It was established in 1918 as an Indian Iron and Steel Company under the flagship of the Martin Burn group.
• It was amalgamated with SAIL in 2006 and renamed IISCO Steel Plant.
• It has a crude steel production capacity of 2.5 million tonnes per year.
• SAIL is India's 3^rd and the world's 20^th largest steel-producing company with an annual production of **16.30 million metric tons respectively.**​

Important Points

• IISCO produced iron from an open-top blast furnace at Hirapur (later to be called Burnpur) in West Bengal for the first time in 1922.
• This full-fledged integrated steel plant is one of India’s oldest.
• The plant manufactures a range of products, over some of which it holds exclusive market dominance.
• Iron and steel produced by it have been acknowledged as being of the finest quality.

The correct answer is Durgapur.

Key Points

• CSIR's Central Mechanical Engineering Research Institute have developed world's largest 'solar tree'.
• It is installed at its residential complex in Durgapur in West Bengal.
• It is to promote the usage of Solar energy.
• The solar tree has been designed in a manner to ensure maximum exposure of each solar photovoltaic (PV) panel to sunlight and also the creation of the least amount of shadow area beneath.
• The installed capacity of the Solar Tre is above 11.5 kWp.
• It has the annual capacity to generate 12,000-14,000 units of Clean and Green Power.
• There are a total of 35 Solar PV Panels in each tree with a capacity of 330 wp (watts peak) each.

The correct answer is Arya Rajendran.

Key Points

• Arya Rajendran, a member of the Communist Party of India( Marxist) became the youngest mayor in India at the age of 21.
• She became mayor of  Thiruvananthpuram, Kerala's capital city.
• Mayor
• In India for all practical purposes, the municipal commissioner, a bureaucrat appointed by the state government, is the de facto head of the municipal body.
• Although the mayor is considered to be the political and executive head of the city, they hardly have any executive power.