The correct answer is- 'Cardiologist' 

Key Points 

• Let's look at the meaning of the marked option:
• Cardiologist: a doctor who specializes in treating diseases of the heart (एक डॉक्टर जो दिल की बीमारियों के इलाज में माहिर है)
• Example: A lower proportion of cardiologists and urban physicians consented to participate.
• Let's look at the meaning of the other given options:
• Orthopaedic​: the treatment or study of bones that have not grown correctly or that have been damaged (हड्डियों का उपचार या अध्ययन जो ठीक से विकसित नहीं हुआ है या क्षतिग्रस्त हो गया है)
• Urologist​: a doctor who specializes in the study or treatment of the function and disorders of the urinary system. (एक डॉक्टर जो यूरिनरी प्रणाली के कार्य और विकारों के अध्ययन या उपचार में माहिर है।)
• Paediatrician​​: a doctor who has special training in medical care for children (एक डॉक्टर जिसके पास बच्चों की चिकित्सा देखभाल में विशेष प्रशिक्षण है)
  

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

The correct answer is- 'Subsikuent'

Key Points

• In the given question, 'Substituent​' is correctly spelt.
• Its meaning is "a person or thing acting or serving in place of another.​" (एक व्यक्ति या वस्तु दूसरे के स्थान पर अभिनय या सेवा करना)
• Example: So the glycolate substituent makes the thiol non-volatile and hence non-odorous.

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

Additional Information 

• Permanent:- lasting for a long time or for ever (लंबे समय तक या हमेशा के लिए स्थायी)
• Dominant:- more important, strong, or noticeable than anything else of the same type (एक ही प्रकार की किसी भी चीज़ की तुलना में अधिक महत्वपूर्ण, मजबूत, या ध्यान देने योग्य)
• Temporary:- not lasting or needed for very long (बहुत लंबे समय तक चलने वाला या आवश्यक नहीं)

The correct answer is- 'Archaeology' 

Key Points 

• Let's look at the meaning of the marked option:
• Archaeology: the study of the buildings, graves, tools, and other objects that belonged to people who lived in the past, in order to learn about their culture and society (इमारतों, कब्रों, औजारों और अन्य वस्तुओं का अध्ययन जो अतीत में रहने वाले लोगों से संबंधित थे, ताकि वे अपनी संस्कृति और समाज के बारे में जान सकें।)
• Example: Excavating human remains is one of the most exciting parts of archaeology.
• Let's look at the meaning of the other given options:
• Entomology: the scientific study of insects (कीटों का वैज्ञानिक अध्ययन)
• Arachnology​: a person who specializes in the study of spiders and other arachnids (एक व्यक्ति जो मकड़ियों और अन्य अरचिन्ड के अध्ययन में माहिर है)
• Etymology: the study of the origin and history of words, or a study of this type relating to one particular word (शब्दों की उत्पत्ति और इतिहास का अध्ययन, या एक विशेष शब्द से संबंधित इस प्रकार का अध्ययन)

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

The correct answer is 'My mother told me that the baby had been crying all day.'

Key Points

• The rules for changing Direct Speech to Indirect Speech:
• The given sentence is in Present Perfect Continuous Tense.
• Present Perfect Continuous Tense changes to Past Perfect Continuous Tense.
• 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: Isha said, “Kavya has been crying for 2 hours .” (Direct speech)
  

                 Isha said that the Kavya had been crying for 2 hours. (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 Present Perfect Continuous Tense में है।
• Present Perfect Continuous Tense, Past Perfect Continuous Tense 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: Isha said, “Kavya has been crying for 2 hours .” (Direct speech)
  

                 Isha said that the Kavya had been crying for 2 hours. (Indirect speech)

The correct answer is 'to home.'

Key Points

• The error lies in Part (to home) of the sentence.
• Going to is not a tense.
• It is a special structure that we use to talk about the future.
• "Home" is not a proper noun and it is an adverb of location.
• "To" needs to be omitted.
• ​Therefore, the use of 'to home' in the sentence should be replaced with 'home' to make it grammatically correct.
• ​Correct sentence: I am going home soon after the programme gets over.

Additional Information  

 

 

 

• We can use not … ever instead of never, but never is much more common.
• Example: She has never been a friend of ours.

Hinglish   

 

• त्रुटि वाक्य के Part (to home) में निहित है।
• Going to, tense नहीं है।
• यह एक विशेष संरचना है जिसका उपयोग हम भविष्य के बारे में बात करने के लिए करते हैं।
• "Home" एक proper noun नहीं है और यह adverb of location है।
• "To" को छोड़ना होगा।
• इसलिए, वाक्य के 'to home' का उपयोग 'home' के साथ प्रतिस्थापित किया जाना चाहिए, इसे व्याकरणिक रूप से सही बनाने के लिए।

The correct answer is- 'work late into the night'

Key Points

• The most appropriate meaning of the given idiom 'Burn the midnight oil​' is 'work late into the night'.
• Let’s look at the meaning and example of the given phrasal verb:
• Burn the midnight oil- "To stay awake late at night to work or study" (काम करने या पढ़ने के लिए देर रात तक जागना)
• E.g. Jill has been burning the midnight oil lately; I guess she has a big exam coming up.
• ​​  Thus from the explanation given above, we find that the  2nd option is the correct choice.

The correct answer is 'CABD.'

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 C as it introduces the context of the paragraph.
• After this, A will come as it adds information about the subject.
• After this, B will come as it is talking about the list of qualities read by the headmaster.
• D follows B as D talks about how the subject got chosen for the award.
• The last sentence will be D as it is providing a conclusion to the context.
• ​​The correct sequence:​

C. At my high school graduation, the awards were being presented for achievement, contribution to the school, the community, scholarship, and more.

A. I sat patiently through them knowing they were not for me.

B. The headmaster read the list of qualities this year’s best student award had - most giving, contributed most to society, and so on.

D. But when I heard my name called, I began to cry as I could not believe that I was actually chosen for the award.

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 ग��� गद्यांश के भागों को व्यवस्थित करते समय, हमें उनके बीच कुछ व्याकरणिक या प्रासंगिक संबंध खोजने होंगे, तो आइए जानें।
• Opener, C होगा क्योंकि यह पैराग्राफ के संदर्भ का परिचय देता है।
• इसके बाद, Aआएगा क्योंकि यह विषय के बारे में जानकारी जोड़ता है।
• इसके बाद, B आएगा क्योंकि यह प्रधानाध्यापक द्वारा पढ़े गए गुणों की सूची के बारे में बात कर रहा है।
  

D, B का अनुसरण करता है क्योंकि D इस बारे में बात करता है कि पुरस्कार के लिए विषय कैसे चुना गया।

• अंतिम वाक्य D होगा क्योंकि यह संदर्भ को निष्कर्ष प्रदान कर रहा है।
• इसलिए, अनुक्रम 'CABD' है।

The correct answer is 'teaches students.'

Key Points

• The error lies in Part (teaches students) of the sentence.
• We need to apply the Subject-Verb agreement.
• As the subject 'schools' is a plural noun, we need a plural verb 'teach.'
• ​Therefore, the use of 'teaches students' in the sentence should be replaced with 'teach students' to make it grammatically correct.
• ​Correct sentence: Due to the lockdown most schools teach students through online classes.

Hinglish   

 

• त्रुटि वाक्य के Part (teaches students) में निहित है।
• हमें  Subject-Verb agreement को लागू करने की आवश्यकता है।
• चूंकि  subject 'schools' एक plural noun है, हमें plural verb 'teach' की आवश्यकता है।
• इसलिए, वाक्य के 'teaches students' का उपयोग 'teach students' के साथ प्रतिस्थापित किया जाना चाहिए, इसे व्याकरणिक रूप से सही बनाने के लिए।

The correct answer is 'did not plan.'

Key Points

• The error lies in Part (did not plan) of the sentence.
• The simple past tense shows that you are talking about something that has already happened.
• Unlike the past continuous tense, which is used to talk about past events that happened over a period of time, the simple past tense emphasizes that the action is finished.
• ​Therefore, the use of 'did not planning' in the sentence should be replaced with 'did not plan' to make it grammatically correct.
• ​Correct sentence: The migrant said that he did not plan to come back to the city for quite some time.

Additional Information    

 

 

 

• We can use not … ever instead of never, but never is much more common.
• Example: She has never been a friend of ours.

Hinglish    

 

• त्रुटि वाक्य के Part (did not plan) में निहित है।
• Simple past tense दर्शाता है कि आप किसी ऐसी चीज के बारे में बात कर रहे हैं जो पहले ही हो चुकी है।
• Past continuous tense के विपरीत, जिसका उपयोग समय की अवधि में हुई पिछली घटनाओं के बारे में बात करने के लिए किया जाता है, simple past tense इस बात पर जोर देता है कि क्रिया समाप्त हो गई है।
• इसलिए, वाक्य के 'did not planning' का उपयोग 'did not plan' के साथ प्रतिस्थापित किया जाना चाहिए, इसे व्याकरणिक रूप से सही बनाने के लिए।

The correct answer is- 'Appear'

Key Points

• The most appropriate synonym of the given word 'Emerge' is 'Appear'.
• Emerge: to appear by coming out of something or out from behind something (किसी चीज से या किसी चीज के पीछे से बाहर आकर प्रकट होना) 
• Example: She emerged from the sea, blue with cold.
• Appear: to start to be seen or to be present (दिखना या उपस्थित होना शुरू करना)
• Example: He suddenly appeared in the doorway.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.

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

• Enforce: to make people obey a law, or to make a particular situation happen or be accepted (लोगों को कानून का पालन करने के लिए, या किसी विशेष स्थिति को होने या स्वीकार करने के लिए)
• Erase: to remove something, especially a pencil mark by rubbing it (किसी चीज को हटाने के लिए, विशेष रूप से एक पेंसिल के निशान को रगड़कर निकालना)
• Close: to (cause something to) change from being open to not being open ((कुछ करने के लिए) खुले होने से खुले न होने में बदलना)

The correct answer is- 'To become conscious again'

Key Points

• The most appropriate meaning of the given idiom 'To come round​' is 'To become conscious again'.
• Let’s look at the meaning and example of the given phrasal verb:
• To come round- "to return to a former condition especially" (विशेष रूप से पूर्व स्थिति में लौटने के लि���)
• E.g. All things will come round to him who will but wait.
• ​​ Thus from the explanation given above, we find that the  3rd option is the correct choice.

The correct answer is 'compulsory.'

Key Points

• Let us discuss the meanings of the given options:
• Compulsory: required by law or a rule; obligatory. (कानून या नियम द्वारा आवश्यक; अनिवार्य।)
• Suggested: put forward for consideration. (विचारार्थ प्रस्तुत करना।)
• Registered: entered or recorded on an official list or directory. (आधिकारिक सूची या निर्देशिका में दर्ज या दर्ज किया गया।)
• Temporary: lasting for only a limited period of time; not permanent. (केवल एक सीमित अवधि के लिए स्थायी; स्थायी नहीं।)
• Here, the sentence is talking about airbags that are obligatory.
• Correct sentence: The government is making air bags compulsory for front seat passengers in all cars.

Additional Information     

 

• Let us see the synonyms of the given words:

The correct answer is**-** 'dissappear'

Key Points

• In the given question, 'disappear​' is incorrectly spelt as 'dissappear'. Disappear is the correct spelling.
• Its meaning is "If people or things disappear, they go somewhere where they cannot be seen or found" (अगर लोग या चीजें गायब हो जाती हैं, तो वे कहीं चले जाते हैं जहां उन्हें देखा या पाया नहीं जा सकता)
• Example: The search was called off for the sailors who disappeared in the storm.

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

Additional Information 

• Executive:- someone in a high position, especially in business, who makes decisions and puts them into action (उच्च पद पर कोई व्यक्ति, विशेष रूप से व्यवसाय में, जो निर्णय लेता है और उन्हें कार्य में लगाता है)
• Development:- the process in which someone or something grows or changes and becomes more advanced (वह प्रक्रिया जिसमें कोई या कुछ बढ़ता है या बदलता है और अधिक उन्नत हो जाता है)
• Movement:- a change of position (स्थिति का परिवर्तन)

The correct answer is- 'attraction'

Key Points

• The most appropriate antonym of the given word 'Repulsion' is 'attraction'.
• Repulsion: to push away or refuse something or someone unwanted, especially to successfully stop a physical attack against you (किसी चीज या अवांछित व्यक्ति को दूर धकेलना या मना करना, विशेष रूप से आपके खिलाफ शारीरिक हमले को सफलतापूर्वक रोकने के लिए) 
• Example: The enemy attack was quickly repulsed.
• Attraction**:** something that makes people want to go to a place or do a particular thing (कुछ ऐसा जिससे लोग किसी स्थान पर जाना चाहते हैं या कोई विशेष कार्य करना चाहते हैं)
• Example: The opportunity to travel is one of the main attractions of this job.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.

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

• Addiction: an inability to stop doing or using something, especially something harmful (कुछ करने या उपयोग करने से रोकने में असमर्थता, विशेष रूप से कुछ हानिकारक)
• Complacence: a feeling of calm satisfaction with your own abilities or situation that prevents you from trying harder (अपनी क्षमताओं या स्थिति से शांत संतुष्टि की भावना जो आपको कठिन प्रयास करने से रोकती है)
• Disgust: a strong feeling of disapproval and dislike at a situation, person's behaviour, etc. (किसी स्थिति, व्यक्ति के व्यवहार आदि पर अस्वीकृति और नापसंदगी की तीव्र भावना)

The correct answer is 'who won.'

Key Points

• The relative pronoun 'which' is used for animals in general or non-living things.
• Example: Raghav bought the top hybrid car, which will help him save on gas.
• “Who” is a subjective pronoun and “Whom” is an objective pronoun.
• “Who” is always subject to a verb, and “whom” is always working as an object in a sentence.
• If you can replace the word with “he” or "she,” use who.
• If you can replace it with “him” or “her,” use whom.
• Examples: 
• Who would like to go on vacation?
• I do not know with whom I will go to the prom.
• ​Whose is a possessive pronoun.
• Use it when you're asking (or telling) to whom something belongs.
• Example: Whose chair is this?
• ​Therefore, the use of 'which' in the sentence should be replaced with 'who' to make it grammatically correct.
• ​​Correct sentence: This is the student who won the first prize in the recitation.

Additional Information 

• A pronoun is “any member of a small class of words found in many languages that are used as replacements or substitutes for nouns and noun phrases, and that have a very general reference,” such as I, you, he, this, it, who, what.
• Types:
• Personal pronouns
• Possessive pronouns
• Relative pronouns
• Reflexive pronouns
• Intensive pronouns
• Indefinite pronouns
• Demonstrative pronouns
• Interrogative pronouns
• Reciprocal pronouns
• Distributive pronouns

Hinglish 

• Relative pronoun 'which' का प्रयोग सामान्यतया जानवरों या चीजों के लिए किया जाता है।
• Example: Raghav bought the top hybrid car, which will help him save on gas.
• “Who” एक subjective pronoun  है और “Whom” एक objective pronoun  है।
• “Who” हमेशा एक verb के अधीन होता है, और “Whom” हमेशा एक वाक्य में एक object के रूप में कार्य करता है।
• यदि आप शब्द को 'he' या 'she' से बदल सकते हैं, तो who का उपयोग करें।
• यदि आप इसे “him” या “her” से बदल सकते हैं, तो whom उपयोग करें।​
• Examples: 
• Who would like to go on vacation?
• I do not know with whom I will go to the prom.
• Whose, possessive pronoun है।
• इसका उपयोग तब करें जब आप पूछ रहे हों (या बता रहे हैं) कि कुछ किसका है।
• Example: Whose chair is this?
• इसलिए, वाक्य में 'which' का उपयोग 'who' के साथ प्रतिस्थापित किया जाना चाहिए, इसे व्याकरणिक रूप से सही बनाने के लिए।
• इसलिए, सही उत्तर 'who it belonged' है।​

The correct answer is 'ACDB.'

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 A as it introduces the context of the paragraph.
• After this, C will come as it is talking about the timing to reach the test centre.
• After this, D will come as it is talking about the effects of not reaching the test centre before 10 a.m.
• B follows D as B talks about the admit card.
• The last sentence will be B as it is providing a conclusion to the context.
• ​​The correct sequence:​

A. The test procedure starts at 10 a.m. in all the test centres.

C. You are, therefore, required to reach the test centre by 9.30 a.m.

D. Remember that, if you report after 10 a.m., you will not be admitted.

B. When you enter the test hall, you should have your Test Admit Card with you.

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 हो���गे, तो आइए जानें।
• Opener, A होगा क्योंकि यह पैराग्राफ के संदर्भ का परिचय देता है।
• इसके बाद, C आएगा क्योंकि यह परीक्षा केंद्र तक पहुंचने के समय के बारे में बात कर रहा है।
• इसके बाद D आएगा क्योंकि यह सुबह 10 बजे से पहले परीक्षा केंद्र नहीं पहुंचने के प्रभावों के बारे में बात कर रहा है।
• B, D का अनुसरण करता है क्योंकि B एडमिट कार्ड के बारे में बात करता है।
• अंतिम वाक्य B होगा क्योंकि यह संदर्भ को निष्कर्ष प्रदान कर रहा है।
• इसलिए, अनुक्रम 'ACDB' है।

The correct answer is 'The game was being enjoyed by Shashi.'

Key Points

• The given sentence is in Past Continuous Tense and Active Voice.
• The rule for changing a Past Continuous Tense from Active voice to Passive voice:
• Interchange the object and subject with each other, i.e. object of the active sentence become the subject of the passive sentence.​
• Structure: Subject + was/were + V1+ ing + object (Active Voice)
  

                  Object + was/were + being + past participle (V3) + (by + subject) (Passive Voice) 

• Example: Disha was arranging the things. (Active Voice)
  

                The things were being arranged by Disha. (Passive Voice)

Additional Information

• In Active Voice, a sentence emphasizes the subject performing an action.
• In Passive Voice, the sentence emphasizes the action or the object of the sentence.
• Example: He reads a novel. (Active Voice)
  

                A novel is read by him. (Passive Voice)​

Hinglish  

• दिया गया वाक्य Past Continuous Tense और Active Voice में है।
• Past Continuous Tense  को Active Voice से Passive voice में बदलने का नियम:
• Object और Subject को एक दूसरे के साथ बदलें, यानी Active Voice का Object, Passive Voice का Subject बन जाता है।
• संरचना: Subject + was/were + V1+ ing + object (Active Voice)
  

                  Object + was/were + being + past participle (V3) + (by + subject) (Passive Voice) 

• Example: Disha was arranging the things. (Active Voice)
  

                The things were being arranged by Disha. (Passive Voice)

The correct answer is 'safety.'

Key Points

• Let us discuss the meanings of the given options:
• Safety: the condition of being protected from or unlikely to cause danger, risk, or injury. (खतरे, जोखिम या चोट से सुरक्षित होने या होने की संभावना नहीं।)
• Ability: possession of the means or skill to do something. (कुछ करने का साधन या कौशल होना।)
• Cruelty: cruel behaviour or attitudes. (क्रूर व्यवहार।)
• Agility: ability to move quickly and easily. (जल्दी और आसानी से चलने की क्षमता।)
• Here, the sentence is talking how the mother monkey protected her baby.
• Correct sentence: The mother monkey picked up her baby and climbed up the tree to safety.

Additional Information      

 

• Let us see the synonyms of the given words:

The correct answer is- 'Confusing'

Key Points 

• The most appropriate antonym of the given word 'Lucid' is 'Confusing'.
• Lucid: clearly expressed and easy to understand, or (of a person) thinking or speaking clearly (स्पष्ट रूप से व्यक्त और समझने में आसान, या (किसी व्यक्ति का) स्पष्ट रूप से सोचना या बोलना) 
• Example: She gave a clear and lucid account of her plans for the company's future.
• Confusing: to mix up someone's mind or ideas, or to make something difficult to understand (किसी के दिमाग या विचारों को मिलाना, या किसी चीज़ को समझना मुश्किल बनाना)
• Example: You're confusing him! Tell him slowly and one thing at a time.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.

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

• Obvious: easy to see, recognize, or understand (देखने, पहचानने या समझने में आसान)
• Acidic: containing acid (एसिड युक्त)
• Clear: easy to understand, hear, read, or see (समझने, सुनने, पढ़ने या देखने में आसान)

The correct answer is- 'predicament'

Key Points

• The most appropriate synonym of the given word 'Dilemma' is 'predicament'.
• Dilemma: a situation in which a difficult choice has to be made between two different things you could do (ऐसी स्थिति जिसमें दो अलग-अलग चीजों के बीच एक कठिन चुनाव करना पड़ता है जो आप कर सकते हैं) 
• Example: The president is clearly in a dilemma about/over how to tackle the crisis.
• Predicament: an unpleasant situation that is difficult to get out of (एक अप्रिय स्थिति जिससे बाहर निकलना मुश्किल है)
• Example: She is hoping to get a loan from her bank to help her out of her financial predicament.
• 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:

• Fascination: to interest someone a lot (किसी को बहुत ज्यादा दिलचस्पी लेना)
• Importance: the quality of being important (महत्वपूर्ण होने की गुणवत्ता)
• Attraction: something that makes people want to go to a place or do a particular thing (कुछ ऐसा जिससे लोग किसी स्थान पर जाना चाहते हैं या कोई विशेष कार्य करना चाहते हैं)

The correct answer is 'other.'

Key Points

• Either is used when referring to a choice between two options.
• Example: Either one deserves to win.
• The word other is used with uncountable and plural nouns.
• Example: She's going to the cinema with other friends.
• We use every + singular noun to refer individually to all the members of a complete group of something.
• Example: There’s a photograph on the wall of every child in the school.
• Each is often followed by a prepositional phrase ending in a plural word (Each of the cars), thus confusing the verb choice.
• Each is always singular and requires a singular verb.
• Example: Each of them is going on a trip.
• Here, the sentence is talking how the mother monkey protected her baby.
• Correct sentence: An open-minded person can very easily accept as well as respect the other person's viewpoint or ideas.

Additional Information      

 

• We use each to refer to the individual things or persons in a group of two or more:
• Example: We spent five days on the coast and each day we swam in the ocean.

Hinglish

• दो विकल्पों के बीच किसी विकल्प का जिक्र करते समय किसी का उपयोग किया जाता है।
• ​Example: Either one deserves to win.
• Other शब्द का प्रयोग बेशुमार और बहुवचन संज्ञाओं के साथ किया जाता है।​
• Example: She's going to the cinema with other friends.
• हम every + singular noun का उपयोग व्यक्तिगत रूप से किसी चीज के पूर्ण समूह के सभी सदस्यों को संदर्भित करने के लिए करते हैं।
• Example: There’s a photograph on the wall of every child in the school.
• Each  के बाद plural शब्द (Each of the cars) में समाप्त होने वाला एक prepositional phrase होता है, इस प्रकार क्रिया पसंद को भ्रमित करता है।
• Each हमेशा singular होता है और उसे singular verb की आवश्यकता होती है।
• Example: Each of them is going on a trip.

The correct answer is '​listens.'

Key Points

• As the second half of the sentence is in the Present Tense, we must use the Present Tense in the first part also.
• Hence, we need to use 'listens' to make it grammatically correct.
• ​​Correct phrase: Such a person willingly and cordially listens to others' views, accepts their different ideas, ....

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  

• जैसा कि वाक्य का दूसरा भाग Present Tense में है, हमें पहला भाग में भी Present Tense का उपयोग करना चाहिए।
• इसलिए, हमें इसे व्याकरणिक रूप से सही बनाने के लिए 'listens' का उपयोग करने की आवश्यकता है।

The correct answer is 'successfully.'

Key Points

• Let us discuss the meanings of the given options:
• Eventfully: in the end, especially after a long delay, dispute, or series of problems. (अंत में, विशेष रूप से एक लंबी देरी, विवाद या समस्याओं की श्रृंखला के बाद।)
• Successfully: in a way that accomplishes a desired aim or result. (एक तरह से जो वांछित उद्देश्य या परिणाम को पूरा करता है।)
• Habitually: by way of habit; customarily. (आदत से; प्रथागत रूप से।)
• Clearly: in a clear manner; with clarity. (स्पष्ट तरीके से; स्पष्टता के साथ।)
• Here, the sentence is saying that successful implementation.
• Correct phrase: ......and even goes ahead to implement them successfully.

Additional Information    

 

• Let us see the synonyms of the given words:

The correct answer is '​is created.'

Key Points

• In this sentence, we are talking about "Creation of positive and vibrant energy", therefore we need to use Present Tense.
• Here we are writing the sentence in a Passive voice and the structure should be:
• Subject + is/am/are + V3 + object
• Example: Football is played by us.
• Hence, we need to use 'is created' to make it grammatically correct.
• ​​Correct phrase: With an open mindset, positive and vibrant energy is created that not only helps such people .....

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   

• इस वाक्य में, हम "Creation of positive and vibrant energy" के बारे में बात कर रहे हैं, इसलिए हमें Present Tense का उपयोग करने की आवश्यकता है।
• यहां हम एक Passive voice में वाक्य लिख रहे हैं और संरचना इस प्रकार होनी चाहिए:
• Subject + is/am/are + V3 + object
• Example: Football is played by us.

The correct answer is 'but.'

Key Points

• Not only … but also is used to connect and emphasize two phrases or two words at the same position.
• Different Structures: 
• Subject + Verb + not only + Adjective + but also + Adjective
• Subject + Verb + not only + Adverb + but also + Adverb
• Subject + Verb + not only + Noun + but also + Noun
• Subject + not only + Verb + but also + Verb
• Example: I like not only cheesecake but also cake.
• Correct phrase: ..... such people but also keeps other people around them happy.

Additional Information       

 

• We use each to refer to the individual things or persons in a group of two or more:
• Example: We spent five days on the coast and each day we swam in the ocean.

Hinglish 

• Not only … but also एक ही स्थिति में दो वाक्यांशों या दो शब्दों को जोड़ने और उन पर जोर देने के लिए भी उपयोग किया जाता है।
• विभिन्न संरचनाएं:
• Subject + Verb + not only + Adjective + but also + Adjective
• Subject + Verb + not only + Adverb + but also + Adverb
• Subject + Verb + not only + Noun + but also + Noun
• Subject + not only + Verb + but also + Verb
• Example: I like not only cheesecake but also cake.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. Three middle small figure interchange their positions in clockwise direction.

2. When the Lower middle small figure changes their position it is replace by a new small figure.

3. The Triangle figure rotates in a clockwise direction in each corner of square and it is also rotated a clockwise direction of its own position.

Final series is:

Hence, ‘option 1’ is the correct answer.

According to the sequence in the dictionary:

The correct order of the given words is:

1. Fragile
2. Frame
3. Fraudster
4. Freedom
5. Fresher

Hence, the correct answer is "1, 5, 4, 2, 3".

The pattern followed here is:

 

Hence, '101' is the correct answer.

The logic followed here is:

Warrior : Battlefield → Warriors perform their martial arts on the battlefield.

Similarly,

Actor : Stage → Actors perform their acting on stage.

Hence, ‘Actor : Stage’ is the correct answer.

The Logic here is as follows:

{(1^st Number)² × 2^nd number} = 3^rd Number

In (5, 14, 350)

{(1^st Number)² × 2^nd number}

= 5² × 14

= 25 × 14

= 350 = 3^rd Number

Now check the all options,

Option (1) (8, 16, 340)

{(1^st Number)² × 2^nd number}

= 8² × 16

= 64 × 16

= 1024 ≠ 3^rd Number

Option (2) (6, 12, 232)

{(1^st Number)² × 2^nd number}

= 6² × 12

= 36 × 12

= 432 ≠ 3^rd Number

Option (3) (3, 20, 380)

{(1^st Number)² × 2^nd number}

= 3² × 20

= 9 × 20

= 180 ≠ 3^rd Number

Option (4) (7, 9, 441)

{(1^st Number)² × 2^nd number}

= 7² × 9

= 49 × 9

= 441 = 3^rd Number

Hence, the correct answer is "(7, 9, 441)".

The Venn diagrams best represent the relationship between - Mammals, Animals, Giraffe figures are shown below:

All Giraffes are mammals and all mammals are animals.

Hence, ‘option 3’ is the correct answer.

The logic is here is:

1^st number × 12 = 2^nd number.

Option (1): 17 : 204

Now, follow the logic:

17 × 12 = 204 = 2^nd number

This option follows the pattern.

Option (2): 11 : 132

11 × 12 = 132 = 2^nd number

This option follows the pattern.

Option (3): 7 : 84

7 × 12 = 84 = 2^nd number

This option follows the pattern.

Option (4): 9 : 99

Now, follow the logic:

9 × 12 = 108 ≠ 2^nd number

This option do not follow the pattern.

Hence, pair “9 : 99” is an odd one.

The logic followed here is:

Option (1) (201, 402, 603) → All numbers are divisible by 3.

Option (2) (108, 300, 501) → All numbers are divisible by 3.

Option (3) (111, 222, 333) → All numbers are divisible by 3.

Option (4) (202, 404, 909) → 202 and 404 are not divisible by 3.

Hence, ‘Option (4)’ is the correct answer.

The table is alphabets place value:

The pattern followed here is:

Step 1: Consonants alphabets coded as the number next alphabets.

• Consonants alphabet + 1 = new alphabet

Step 2: Vowel alphabets coded as the next vowel alphabets.

Given:

 BIOLOGY: COUMUHZ

Similarly,

CHEMISTRY: ?

Hence, 'CHEMISTRY' is coded as "DIINOTUSZ".

The table is alphabets place value:

The pattern followed here is:

Step 1: Alphabets which place value in two-digit its place value multiply by 2 and coded as the number.

Step 2: Alphabets which place value in one-digit its place value coded as the number.

DORM is coded as 4303626 

And,

FIRST is coded as 69363840

Similarly,

Hence, 'CANCER' is coded as "31283536".

Statements:

Some managers are bosses.

Some doctors are managers.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some managers are executives → False (Because there are no statements given for executives)

II. Some doctors are bosses → False (It is possible but not definite)

Hence, “Neither conclusion I nor II follows.”

The number of triangles in the given figure is:

So, there are a total of 13 triangles in the figure.

Hence, ‘13’ is the correct answer.

The logic followed here is:

Given:

Eye’ is related to ‘Glasses’ → Glasses are an object that clears the vision of the eyes.

Similarly,

‘Kidney’ is related to ‘Dialyser’→ Dialyser is a machine that use for dialysis of kidney.

Hence, ‘Kidney’ is the correct answer.

The opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surfaces are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces:-

 

Option (1) & → % is opposite to &.

Option (2) % → & is opposite to %.

Option (3) # → + is opposite to #.

Option (4) $→$ is opposite to @.

So, when the table will be constructed, the letters ‘$ and @’ will be opposite to each other.

Hence, ‘$’ is the correct answer.

The embedded part of this image is:

Hence, option (1) is the correct answer.

Given :- T _ R _ _ S _ D T _ R D _ S _ D

By checking options and substituting accordingly.

Option (1) D S T R T T R → T D R S / T S R D / T T R D / T S R D.

Option (2) S D T D S T T → T S R D / T S D D / T S R D / T S T D

Option (3) S D T R S T R → T S R D / T S R D / T S R D / T S R D

Option (4) S T S R R T R → T S R T / S S R D / T R R D / T S R D

     ►  Option (3) gives a pattern of T S R D - T S R D - T S R D - T S R D.

Hence, ‘S D T R S T R’ is the correct answer.

The correct mirror image of the given figure when the mirror is held at the right side is:

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

Additional Information 

In Mirror image left side and right side changed vice-versa where top and bottom remain same.

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

The logic followed here is:

Option (1) Engineer → An engineer applies mathematics and science to develop technical solutions to constructs buildings, houses and etc.

Option (2) Architect → An architect is a person who plans, designs and oversees the construction of buildings, houses and etc.

Option (3) Designer → A designer is a person whose job is to make drawings or plans showing how buildings, houses will be made.

Option (4) Doctor → A doctor is a medical term. He is not contribute any help to making a house and building.

Hence, All contribute to making houses and buildings except doctors.

Hence, “Doctor” is an odd one.

Alternate MethodThe logic followed here is:

Option (1) Engineer → Engineer is the technical term.

Option (2) Architect → Architect is the technical term.

Option (3) Designer → Designer is the technical term.

Option (4) Doctor → Doctor is the medical term.

Hence, “Doctor” is an odd one.

The pattern followed here is,

Let (1^st number : 2^nd number)

(2^nd number)³ + 4 = 1^st number

Now follow the steps:

68 : 4

=> 4³ + 4 = 64 + 4 = 68 = 1^st number

And,

220 : 6

=> 6³ + 4 = 216 + 4 = 220 = 1^st number

Similarly,

? : 7

=> 7³ + 4 = 343 + 4 = 347 = 1^st number

Hence, "347" is correct answer.

Given:

1. The sum of the salaries of three persons, A, B and C, is ₹66,500.

=> A + B + C = 66,500 ---------- eq. (i)

2. B's salary is half the salary of C.

=> B = C / 2 ---------- eq. (ii)

3. B's salary is 125% of A's salary.

=> B = 125% A

=> B = 5 / 4 × A

From eq. (i)

=> C / 2 = 5A / 4

=> A = 4C / 10 ---------- eq. (iii)

From eq. (ii) and eq. (iii) put the value of B and A in eq. (i)

=> 4C / 10 + C / 2 + C = 66500

=> (4C + 5C + 10 C) / 10 = 66500

=> 19C / 10 = 66500

=> C = (66500 × 10) / 19

=> C = 665000 / 19

=> C = 35000

Hence, Salary of C is “35000”.

The pattern followed here is:

Step 1: Each consonants are coded as their positional value = Number code.

Step 3: Vowels coded as their vowel order.

A - 1, E - 2, I - 3, O - 4, U - 5

GOD is coded as 15.

And, 

DEVIL is coded as 43,

Similarly, 

HUMEN = ?

Hence, the correct answer is "42".

The image obtained when the paper is unfolded is,

Hence, "option 4" is the correct answer.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except 'BEGLN’.

Hence, “BEGLN” is the odd one.

Option (1) 11 × 6 + 3 = 69

After interchange signs + and ×, and the numbers 3 and 6.

11 + 3 × 6 = 69

11 + 18 = 69

29 = 69 (LHS ≠ RHS)

Option (2) 9 × 3 + 6 = 33

After interchange signs + and ×, and the numbers 3 and 6.

9 + 6 × 3 = 33

9 + 18 = 33

27 = 33 (LHS ≠ RHS)

Option (3) 12 × 3 + 6 = 30

After interchange signs + and ×, and the numbers 3 and 6.

12 + 6 × 3 = 30

12 + 18 = 30

30 = 30 (LHS = RHS)

Option (4) 7 + 3 × 6 = 48

After interchange signs + and ×, and the numbers 3 and 6.

7 × 6 + 3 = 48

42 + 3 = 48

45 = 48 (LHS ≠ RHS)

Hence, “Option (3)” is the correct answer.

Preparing the family tree using the following symbols,

Given:

1. Divya and Monika are sisters.

2. Monika is the mother of Anamika.

3. Kishore is the son of Anamika.

4. Lillu is the son of Divya.

Here, Anamika's gender is not confirmed. So, Anamika is either male or female.

Hence, Anamika is the "Cousin" of Lillu.

Given:

sin2 x – 3cos2 x = 0

Formula used:

tan²x = sin²x/cos²x

tan 60° = √3

Calculation:

sin2 x – 3cos2 x = 0

sin²x/cos²x = 3

⇒ tan²x = 3

⇒ tanx = √3

⇒ tanx = √3 = tan 60° 

⇒ x = 60° 

∴ The value of x is 60°

Calculation:

The total number of students who scored less than 20 marks = (2 + 8 + 7 + 8) = 25

Total number of students = 40

The percentage of the students who scored less than 20 marks = (25/40 × 100)

⇒ 125/2

⇒ 62.5%

∴ The required percentage is 62.5

Given:

$\frac{5 \cot θ + √ 3 :cosec: θ}{2√3: cosec: θ + 3 \cot θ}=1,0^{\circ} <θ<90^{\circ}$

Formula used:

cotθ = cosθ/sinθ 

cosecθ = 1/sinθ 

Calculation:

$\frac{5 \cot θ + √ 3 :cosec: θ}{2√3: cosec: θ + 3 \cot θ}=1,0^{\circ} <θ<90^{\circ}$

⇒ 5cotθ + √3cosecθ = 2√3cosecθ + 3cotθ 

⇒ (5cotθ – 3cotθ) = (2√3cosecθ – √3cosecθ)

⇒ 2cotθ = √3cosecθ 

⇒ 2 × cosθ/sinθ = √3 × 1/sinθ 

⇒ 2cosθ = √3

⇒ cosθ = √3/2 = cos 30° 

So, θ = 30° 

Now,

The value of $\frac{\frac{7}{2} \cot^2 θ- \frac{3}{4} :cosec^2 θ}{4 \sin^2 θ+\frac{3}{2} \tan^2 θ}$

⇒ (7/2 cot²30° – 3/4 cosec²30°)/(4 sin²30° + 3/2 tan²30°)

⇒ 7/2 × (√3)² – 3/4 × (2)²/4 × (1/2)² + 3/2 × (1/√3)²

⇒ (7/2 × 3) – (3/4 × 4)/(4 × 1/4) + (3/2 × 1/3)

⇒ (21/2 – 3)/(1 + 1/2)

⇒ (21 – 6)/2/(2 + 1)/2

⇒ (15/2)/(3/2)

⇒ (15/2 × 2/3)

⇒ 5

∴ The required value is 5

Given:

The sum of the square of the sides of a rhombus = 1600 cm²

Concept used:

The side of a rhombus is equal

Calculation:

Let the side of the rhombus be a

Sum of side of rhombus = 4a

Now,

According to the question

⇒ 4a² = 1600 cm²

⇒ a² = (1600/4)

⇒ a² = 400

⇒ a = 20 cm

∴ The side of the rhombus is 20 cm

Given:

∠AOB = 116° 

Calculation:

According to the question

⇒ ∠AOB + ∠APB = 180° 

⇒ 116° + ∠APB = 180° 

⇒ ∠APB = (180° – 116°)

⇒ ∠APB = 64° 

Now,

⇒ ∠OPB = ∠APB/2

⇒ ∠OPB = 64°/2

⇒ ∠OPB = 32° 

∴ The required value of ∠OPB is 32°

Given:

The value of $\sqrt{\cos 60^{\circ} \cos 30^{\circ}- \sin60^{\circ} \sin 30^{\circ}}$

Formula used:

cos 60° = 1/2

cos 30° = √3/2

sin 60° = √3/2

sin 30° = 1/2

Calculation:

$\sqrt{\cos 60^{\circ} \cos 30^{\circ}- \sin60^{\circ} \sin 30^{\circ}}$

⇒ √(1/2 × √3/2) – (√3/2 × 1/2)

⇒ √(√3/4 – √3/4)

⇒ 0

∴ The required value is 0

Given:

x, y and z are three positive numbers

y is 4/5 times of x

z is 5/8 times of y

The average of reciprocals of the numbers x, y and z = 17/240

Formula used:

Average = sum of observations/Number of observations

Calculation:

y is 4/5 times of x

⇒ y = x × 4/5

⇒ y = 4x/5

And, z is 5/8 times of y

⇒ z = y × 5/8

⇒ z = 4x/5 × 5/8

⇒ z = x/2

Now,

The average of reciprocals of the numbers x, y and z = 17/240

⇒ (1/x + 1/y + 1/z)/3 = 17/240

⇒ 1/x + 1/y + 1/z = 17/80

Now,

⇒ 1/x + 5/4x + 2/x = 17/80

⇒ (4 + 5 + 8)/4x = 17/80

⇒ 17/4x = 17/80

⇒ x = 80/4

⇒ x = 20

Now,

Put the value of x in y = 4x/5 

⇒ y = (4 × 20/5)

⇒ y = 16

Now,

The average of 3 times of x and 5 times of y = (3 × 20 + 5 × 16)/2

⇒ (60 + 80)/2

⇒ 140/2

⇒ 70

∴ The required average is 70

Given:

Principal = Rs. 7500

The rate of interest for the first two years = 20%

The rate of interest for the next two years = 10%

Formula used:

CI = P[(1 + R/100)^T – 1]

CI = CI₁ + CI₂

Calculation:

According to the question

CI for the first two year

⇒ CI₁ = P[(1 + R/100)T – 1]

⇒ Rs. 7500[(1 + 20/100)² – 1]

⇒ Rs. 7500[(120/100)² – 1]

⇒ Rs. 7500[(6/5 × 6/5) – 1]

⇒ Rs. 7500(36/25 – 1)

⇒ Rs. (7500 × 11/25)

⇒ Rs. 3300

Now,

CI for the next two year

P will be = Rs. (7500 + 3300) = Rs. 10800

⇒ CI₂ = P[(1 + R/100)T – 1]

⇒ Rs. 10800[(1 + 10/100)² – 1]

⇒ Rs. 10800[(110/100)² – 1]

⇒ Rs. 10800[(11/10 × 11/10) – 1]

⇒ Rs. 10800(121/100 – 1)

⇒ Rs. (10800 × 21/100)

⇒ Rs. 2268

Now,

CI = CI1 + CI2

⇒ Rs. (3300 + 2268)

⇒ Rs. 5568

∴ The required CI is Rs. 5,568

Given:

Total number of students = 80

Total number of resource persons = 10

The amount spent for distributing sweets to each student = 30% of the total number of students

The amount spent towards each resource person = 40% of the total number of students.

Calculation:

According to the question

⇒ (80 × 30/100 of 80) + (10 × 40/100 × 80)

⇒ (80 × 24) + (4 × 80)

⇒ Rs. (1920 + 320)

⇒ Rs. 2240

∴ The total amount spent for sweets distribution in the workshop was Rs. 2,240

Calculation:

The total number of vehicles of type A produced in 2013, 2015 and 2017 = (120 + 240 + 360) = 720

$31\frac{1}{4}\%$ of the total number of vehicles of type A produced in 2013, 2015 and 2017 = (720 × 125/400)

⇒ 225

So, 225 is equal to the number of vehicles of type B produced in the year 2016

∴ The required year is 2016

Shortcut Trick

By AA similarity, ▵PRQ ∼ ▵SRP because ∠R is common and ∠QPR = ∠PSR.

Ratio of corresponding sides: PR / SR = QR / PR

PR² = QR × SR

SR = QR − QS = 18 − 10 = 8 cm

PR = √(18 × 8) = √144 = 12 cm

∴ The correct answer is 12 cm.

Alternate Method

Given:

QS = 10 cm, QR = 18 cm, ∠PSR = ∠QPR

Formula Used:

AA Similarity Criterion: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar, and their corresponding sides are in the same ratio.

P Q R S 10 cm 8 cm QR = 18 cm

Calculations:

⇒ In ▵PQR, S is a point on QR.

⇒ SR = QR − QS = 18 − 10 = 8 cm

⇒ Compare ▵PRQ and ▵SRP:

⇒ ∠PRQ = ∠PRS (Common Angle)

⇒ ∠QPR = ∠PSR (Given)

⇒ ∴ ▵PRQ ∼ ▵SRP (By AA Similarity)

⇒ PR / SR = QR / PR

⇒ PR² = QR × SR

⇒ PR² = 18 × 8

⇒ PR² = 144

⇒ PR = √144 = 12 cm

∴ The correct answer is 12 cm.

Additional Information

AA Similarity Criterion

Two triangles are similar if two pairs of corresponding angles are equal. The order of vertices is crucial for defining side ratios correctly.

Geometric Mean Property

In similar triangles formed by a common angle and specific vertex equalities, a side often acts as the geometric mean: side² = part1 × part2.

Area of Similar Triangles

If ▵ABC ∼ ▵DEF, then Area(▵ABC) / Area(▵DEF) = (AB/DE)² = (BC/EF)² = (AC/DF)².

Given:

2x + 3y + 4z = 11, 8x3 + 27y3 + 64z3 = 105 and xyz = 1

Formula used:

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

Calculation:

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

2x³ + 3y³ + 4z³ – 3 × 2x × 3y × 4z = (2x + 3y + 4z) (2x² + 3y² + 4z² – 2x × 3y – 3y × 4z – 2x × 4z)

⇒ 8x3 + 27y3 + 64z3 – 72xyz = (2x + 3y + 4z) (4x2 + 9y2 + 16z2 – 6xy – 12yz – 8xz)

⇒ 105 – 72 = 11 × (4x2 + 9y2 + 16z2 – 6xy – 12yz – 8xz)

⇒ 33 = 11 × (4x2 + 9y2 + 16z2 – 6xy – 12yz – 8xz)

⇒ (4x2 + 9y2 + 16z2 – 6xy – 12yz – 8xz) = (33/11)

⇒  (4x2 + 9y2 + 16z2 – 6xy – 12yz – 8xz) = 3

∴ The required value is 3

Given:

The marked price of a juicer mixer = Rs. 5,500

The three successive discounts = 40%, 30% and 20% respectively

Formula used:

SP = MP × (100 – Discount%)/100

Calculation:

The marked price of a juicer mixer = Rs. 5,500

The Selling price = Rs. 5,500 × (100 – 40)/100 × (100 – 30)/100 × (100 – 20)/100

⇒ Rs. (5,500 × 60/100 × 70/100 × 80/100)

⇒ Rs. (5,500 × 3/5 × 7/10 × 4/5)

⇒ Rs. (22 × 3 × 7 × 4)

⇒ Rs. 1,848

∴ The selling price of the juicer mixer is Rs. 1,848

Given:

The number 4A306768B2 is divisible by both 8 and 11

Concept used:

Divisibility rule of 8 - If the last three digits of a number are divisible by 8, then the number is completely divisible by 8.

Divisibility rule of 11 - If the difference between the sum of the digits at the odd and even places equals 0 or divisible by 11, then the number is divisible by 11.

Calculation:

According to the divisibility rule of 8, we have 8B2 should be divisible by 8

By dividing the number 8B2, the smallest values of B, we put is 3

So, the number is 832, which is completely divisible by 8.

Now,

The updated number = 4A30676832

The difference between the sum of the digits at the odd and even places = (4 + 3 + 6 + 6 + 3) – (A + 0 + 7 + 8 + 2)

⇒ [22 – (A + 17)] = 0 or 11

⇒ A – 5 = 0 or 11

If we put the value of A be 0

Then, 

⇒ (A – 5) = 0

⇒ A = 5

∴ The smallest possible values of A and B will be A = 5, B = 3

Calculation:

Total number of students of graduate level in five different institutes = 12400

Total number of students of graduate level in P, R and T = (25 + 14 + 12)% = 51%

⇒ (12400 × 51/100)

⇒ 6324

The average number of students of graduate level in P, R and T = (6324/3)

⇒ 2108

Now,

Total number of students of post graduate level in five different institutes = 8000

Total number of students of post graduate level in P, R and T = (36 + 17 + 10)% = 63%

⇒ (8000 × 63/100)

⇒ 5040

The average number of students of post graduate level in P, R and T = (5040/3)

⇒ 1680

Now,

The difference between the average number of students of graduate level in institutes P, R and T to the average of students of postgraduate level in institutes P, R and T = (2108 – 1680)

⇒ 428

∴ The required difference is 428

Calculation:

The number of students that appeared at the scholarship examination from College X = 3000

The number of students that qualified at the scholarship examination from College X = 1800

The ratio of the number of students that appeared to the number of students that qualified at the scholarship examination from College

X = (3000: 1800)

⇒ 5 : 3

∴ The required ratio is 5 : 3

Shortcut Trick

Multiply the given equation by 3: 3x + 1/x = 15.

Use the direct shortcut: If a + b = k, then a³ + b³ = k³ − 3abk.

Here, a = 3x, b = 1/x, so ab = 3 and k = 15.

Value = 15³ − 3 × 3 × 15 = 3375 − 135 = 3240.

∴ The correct answer is 3240.

Alternate Method

Given: x + 1/(3x) = 5

Formula Used: (a + b)³ = a³ + b³ + 3ab(a + b)

⇒ Multiply the given equation by 3 on both sides:

⇒ 3 × (x + 1/(3x)) = 3 × 5

⇒ 3x + 1/x = 15

⇒ Cubing both sides of the equation:

⇒ (3x + 1/x)³ = 15³

⇒ (3x)³ + (1/x)³ + 3 × 3x × (1/x) × (3x + 1/x) = 3375

⇒ 27x³ + 1/x³ + 9 × (3x + 1/x) = 3375

⇒ Substitute (3x + 1/x) = 15:

⇒ 27x³ + 1/x³ + 9 × 15 = 3375

⇒ 27x³ + 1/x³ + 135 = 3375

⇒ 27x³ + 1/x³ = 3375 − 135 = 3240

∴ The correct answer is 3240.

Additional Information

Algebraic Cube Identity

The basic identity for the cube of a sum is (a + b)³ = a³ + b³ + 3ab(a + b). It is frequently used to find the sum of cubes when the sum and product of two terms are known.

Reciprocal Power Shortcut

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k. This can be extended to coefficients: if ax + b/x = k, then (ax)³ + (b/x)³ = k³ − 3(ab)k.

Successive Calculation

To find higher powers like x⁶, first find the square (x² + 1/x²) and then cube that result, or vice versa.

Given:

The ratio of angles = 1 : 2 : 3

Concept used:

Sine rule = a/sinA = b/sinB = c/sinC

Calculation:

  

Let A = x, B = 2x and C = 3x

⇒ ∠A + ∠B + ∠C = 180° [angle sum property]

⇒ x + 2x + 3x = 180° 

⇒ 6x = 180° 

⇒ x = 30° 

⇒ ∠A = 30°, ∠B = 60° and ∠C = 90° 

Now,

As we know that,

⇒ a/sin30° = b/sin60° = c/sin90° 

⇒ a/1/2 = b/√3/2 = c/1

⇒ a = 1, b = √3 and c = 2

So, a : b : c = 1 : √3 : 2

∴ The required ratio is 1 : √3 : 2

Given:

1 + 4x2 + 16x4 = 512 and 1 – 2x + 4x2 = 64

Calculation:

1 + 4x2 + 16x⁴

Factorizing the number, we get

⇒ (1 – 2x + 4x²) (1 + 2x + 4x²) 

Now,

Let the value of (1 + 2x + 4x2) be x

Then,

⇒ (1 + 2x + 4x2) = (1 + 4x2 + 16x⁴)/(1 – 2x + 4x2)

⇒ x = 512/64

⇒ x = 8

∴ The required value is 8

Shortcut Trick

Earnings are directly proportional to the total man-hours (People × Hours).

Initial man-hours = 15 × 6 = 90 units.

Given, 90 units = ₹900 ⇒ 1 unit = ₹10.

New man-hours = 20 × 10 = 200 units.

Total money earned = 200 units × ₹10 = ₹2,000.

∴ The correct answer is ₹2,000.

Alternate Method

Given:

Number of people (M₁) = 15, Working hours (H₁) = 6, Earnings (W₁) = ₹900

Number of people (M₂) = 20, Working hours (H₂) = 10, Earnings (W₂) = ?

Using the Chain Rule formula:

(M₁ × H₁) / W₁ = (M₂ × H₂) / W₂

⇒ (15 × 6) / 900 = (20 × 10) / W₂

⇒ 90 / 900 = 200 / W₂

⇒ 1 / 10 = 200 / W₂

⇒ W₂ = 200 × 10

⇒ W₂ = 2000

∴ The correct answer is ₹2,000.

Additional Information

Chain Rule Concept

The general formula for work and wages is (M₁ × D₁ × H₁ × E₁) / W₁ = (M₂ × D₂ × H₂ × E₂) / W₂, where M is men, D is days, H is hours, E is efficiency, and W is work or wages.

Direct and Inverse Proportion

Wages are directly proportional to the number of men and hours, while the time required to complete a fixed piece of work is inversely proportional to the number of men.

Wage Calculation

Total Wage = (Rate per man-hour) × (Total number of man-hours). In this case, the rate was ₹10 per man-hour.

Given:

The ratio of sides of a triangle = 1/3 : 1/5 : 1/4

Perimeter = 141 cm

Calculation:

Let the ratio of sides of triangle be 1x/3, 1x/5 and 1x/4 respectively

According to the question

⇒ x/3 + x/5 + x/4 = 141

⇒ (20x + 12x + 15x)/60 = 141

⇒ 47x/60 = 141

⇒ 47x = (141 × 60)

⇒ 47x = 8460

⇒ x = 180

Now,

The greatest side = x/3 = (180/3) = 60 cm

The smallest side = x/5 = (180/5) = 36 cm

The difference between greatest side and smallest side = (60 – 36) = 24 cm

∴ The required difference is 24 cm

Given:

Gaurav bought some articles at 5 for Rs. 6

Gaurav sold them at 10 for Rs. 11

Formula used:

Loss = CP – SP

Loss% = Loss/CP × 100

Calculation:

Cost price of articles = Rs. 6/5

Selling price of articles = Rs. 11/10

Loss = Rs. (6/5 – 11/10)

⇒ (12 – 11)/10

⇒ 1/10

Loss% = (1/10/6/5 × 100)

⇒ (1/10 × 5/6 × 100)

⇒ (1/12 × 100)

⇒ 25/3

⇒ $8\frac{1}{3}\%$

∴ The loss% is $8\frac{1}{3}\%$

Given:

The length of a chord of a circle = 8√3 cm

Concept used:

The tangents drawn at the ends of a chord of a circle make equal angles with the chord.

Calculation:

If a perpendicular is drawn from O to AB, then it will touch AB at M

So, length of AM = 8√3 ÷ 2 = 4√3

Now, in ΔAOM

∠AOM =  60° [The tangents drawn at the ends of a chord of a circle make equal angles with the chord]

So, Sin 60° = AM/OA

⇒ √3/2 = 4√3/OA

⇒ 1/2 = 4/OA

⇒ OA = 2 × 4

⇒ 8 cm

∴ Length of radius is 8 cm

Shortcut Trick

Since Distance is constant, Speed is inversely proportional to Time (S₁ × T₁ = S₂ × T₂).

Convert times to minutes: T₁ = 148 min and T₂ = 96 min.

Ratio of Time = 148 : 96 = 37 : 24.

Ratio of Speed = 24 : 37.

If 24 units = 48 km/h, then 1 unit = 2 km/h ∴ 37 units = 37 × 2 = 74 km/h.

∴ The correct answer is 74 km/h.

Alternate Method

Given:

Initial Speed (S₁) = 48 km/h

Initial Time (T₁) = 2 hr 28 min = (2 × 60) + 28 = 148 min

New Time (T₂) = 1 hr 36 min = (1 × 60) + 36 = 96 min

Formula Used:

Distance = Speed × Time

Calculations:

⇒ Distance (D) = S₁ × T₁

⇒ D = 48 × (148/60) km

⇒ New Speed (S₂) = D ÷ T₂

⇒ S₂ = [48 × (148/60)] ÷ (96/60)

⇒ S₂ = (48 × 148) ÷ 96

⇒ S₂ = 148 ÷ 2

⇒ S₂ = 74 km/h

∴ The correct answer is 74 km/h.

Additional Information

Speed-Time Inverse Relation

When Distance is fixed, the ratio of speeds is the inverse of the ratio of times taken (S₁:S₂ = T₂:T₁).

Unit Conversion

To convert Speed from km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Average Speed

For a journey with different speeds but equal distances, Average Speed = 2S₁S₂ ÷ (S₁ + S₂).

Concept Used:         

Follow the BODMAS rule according to the table given below:

Calculation:

$\frac{284}{5} ÷ \left[\left(\frac{4}{5} × (15+35)-11\frac{3}{5}\right)\right]$

⇒ 284/5 ÷ [(4/5 × (15 + 35) – 58/5)]

⇒ 284/5 ÷ [(4/5 × 50 – 58/5)]

⇒ 284/5 ÷ (40 – 58/5)

⇒ 284/5 ÷ (200 – 58)/5

⇒ (284/5 ÷ 142/5)

⇒ (284/5 × 5/142)

⇒ 2

∴ The required value is 2

The correct answer is Avni Doshi.

• Avni Doshi is the author of the novel ‘Burnt Sugar’.

Key Points

• Avni Doshi is an American novelist.
• Her debut novel, "Girl in White Cotton" was published in India in 2019.
• In 2020, it was published in the United Kingdom under the title Burnt Sugar.
• The novel was shortlisted for the 2020 Booker Prize.

Additional InformationKiran Desai

• Kiran Desai is an Indian author.
• Desai's first novel, "Hullabaloo in the Guava Orchard" was published in 1998 and it won the Betty Trask Award.
• Her novel "The Inheritance of Loss" won the 2006 Man Booker Prize and the National Book Critics Circle Fiction Award.
• In January 2015, The Economic Times listed her as one of 20 "most influential" global Indian women.

Vikas Bahl

• Vikas Bahl is an Indian film producer, screenwriter, and director in Hindi cinema.
• He used to produce films under Phantom Films and was the former head of UTV Spot Boy.
• He has won three National Film Awards (2011, 2014)and one Filmfare Award (2015).

Salman Rushdie

• Sir Ahmed Salman Rushdie FRSL is a British-American novelist and essayist of Indian descent.
• His second novel "Midnight's Children" won the Booker Prize in 1981.
• He received the Golden PEN Award, Hans Christian Andersen Literature Award (2014), PEN Pinter Prize (UK), St. Louis Literary Award from the Saint Louis University Library Associates, State Prize for Literature (Austria), and Swiss Freethinkers Award 2019.

The correct answer is Article 20.

• Article 20 of the Constitution of India makes provision for protection in respect of conviction for offenses.

Key Points

• Article 20 grants three kinds of protection against arbitrary and excessive punishment to an accused person, whether a citizen or foreigner or a legal person like a company or a corporation.

1. No ex-post-facto law.
2. No double Jeopardy.
3. No self-incrimination.

Additional InformationArticle 18

• Abolition of titles, except Military and academic distinctions.

Article 19 

• It guarantees the citizens of India the following six fundamentals freedoms:-

1. Freedom of Speech and Expression.
2. Freedom of Assembly.
3. Freedom of form Associations.
4. Freedom of Movement.
5. Freedom of Residence and Settlement.
6. Freedom of Profession, Occupation, Trade, and Bussiness

Article 21

• Provides protection of life and personal liberty.

Important Points

• The total number of parts in the Indian Constitution- 25.
• The total articles in the Indian Constitution - 470.
• The total number of schedules - 12.

The correct answer is Maharashtra.

• The Ajanta caves are situated in Maharashtra.

Key Points

• The Ajanta Caves are approximately 30 rock-cut Buddhist cave monuments dating from the 2nd century BCE to about 480 CE.
• The Ajanta caves are situated in the Aurangabad district of Maharashtra.
• The figures in these caves were done using fresco painting.
• The paintings are generally themed around Buddhism – the life of Buddha and Jataka stories.
• The outlines of the paintings were done in red colour.
• One of the striking features is the absence of blue colour in the paintings.
• The caves were designated a UNESCO Heritage site in 1983.

Additional Information

The correct answer is Lord Cornwallis.

• Lord Cornwallis was the Governor-General of Bengal when the Permanent Settlement was introduced there in 1793.

Key Points

• Permanent Settlement is also known as Permanent Settlement of Bengal was an agreement between the British East India Company and the Landlords of Bengal to fix the land revenue.
• Land revenue was the major source of income for the British in India.
• Permanent Settlement was one such land revenue system.
• It was first introduced in Bengal and Bihar and later it was introduced in Madras and Varanasi.
• This system was also known as the Zamindari system.

Additional Information

Lord Cornwallis

• He is known as the 'Father of Civil Services in India'.

• He created the post of District Judges'.

• Third Anglo-Mysore War and Treaty of Srirangapatnam.

• First-person to codify laws in 1793.

Warren Hastings

• First Governor-General of Bengal.
• He abolished the dual system of administration.
• He introduced Izaredari System in 1773.
• Regulating Act of 1773 and Pitt’s India Act of 1784.
• Rohilla war in 1774.
• He established Supreme Court in Calcutta.
• Foundation of the Asiatic Society of Bengal (1784)
• First Anglo-Maratha War (1775-1782) ended with the Treaty of Salbai.
• The second Anglo-Mysore war (1780-1784) ended with the Treaty of Mangalore.

Sir John Macpherson

• Sir John Macpherson was a British administrator in India.
• He was the acting Governor-General of Bengal from 1785 to 1786.

Sir John Shore

• He introduced the first Charter act of 1793.
• He was famous for his Policy of Non-intervention.
• Battle of Kharda (1795).

The correct answer is National Waterway 6 - Sutlej.

Key Points

• National Waterways 6 is a 71 km waterway between Lakhipur and Bhanga of the Barak River.
• The NW - 6 passes through Assam, Nagaland, Mizoram, Manipur, Tripura, and Arunachal Pradesh.

Additional InformationNational Waterway 2 - Brahmaputra

• National Waterway 2 (NW-2) is a section of the Brahmaputra River between the Bangladesh border near Dhubri and Sadiya in Assam.
• It is 891 km long and was established in 1988.

National Waterway 4 - Krishna

• National Waterway 4 is a part of the Krishna and Godavari river system.
• It is 1095 km long and was established in 2008.
• It connects the Indian states of Telangana, Andhra Pradesh, Tamil Nadu, and the union territory of Puducherry.

National Waterway 1 - Ganga

• The National Waterway 1 (NW-1) or Ganga-Bhagirathi-Hooghly river system runs from Prayagraj (Allahabad) in Uttar Pradesh to Haldia in West Bengal.
• It is 1620 km long and was established in 1986.
• The NW-1 passes through West Bengal, Jharkhand, Bihar, and Uttar Pradesh.

Important Points

• Longest waterway in India - National Waterway 1.
• Smallest waterway in India - National Waterway 69 (5 km, Manimutharu river Tamil Nadu).
• The longest river in India is the Ganges.
• The smallest river in India is the Arvari river (Rajasthan).
• The longest river island in the world is Majuli Island (Brahmaputra).