SSC CHSL Tier-1 2021: Official Paper (Held On : 31 May 2022 Shift 2) (Previous Year Paper)

The erroneous part is 'write her'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'writing her' should be used instead of 'write her'.
• The future continuous tense, sometimes also referred to as the future progressive tense, is a verb tense that indicates that something will occur in the future and continue for an expected length of time.
• It is formed using the construction will + be + the present participle (the root verb + -ing).
• Example: Michael will be running a marathon this Saturday.
• Thus, the correct answer is Option 4.
  

Correct Sentence: She will be writing her examination by this time tomorrow.

The correct answer is 'Polemical'.

Key Points

• The most appropriate word for the given group of words is 'Polemical'.
• It means 'of or involving strongly critical or disputatious writing or speech (अत्यधिक आलोचनात्मक या विवादास्पद लेखन या भाषण को शामिल करना)
• Example: a polemical essay...
  

Correct Answer: Polemical

Additional Information

• Let's look at the meaning of other words:
• Poignancy: the quality of evoking a keen sense of sadness or regret; pathos. (मार्मिकता)
• Laudatory: expressing praise and commendation. (प्रशंसा और प्रशंसा व्यक्त करना)
• Putative: generally considered or reputed to be. (आम तौर पर माना जाता है या प्रतिष्ठित माना जाता है)

The correct answer is 'on'.

Key Points

• The most appropriate preposition for the given blank is 'on'.
• In the given context the preposition 'on' means 'supported by, fixed to or touching something, especially a surface'. (जब कोई वस्‍तु किसी अन्‍य वस्‍तु, विशेषतः उसकी सतह पर स्थित, संलग्‍न अथवा संबद्घ होती है, या सतह का संस्‍पर्श करती है, तब हम upon का प्रयोग करते हैं; पर, के ऊपर)
• Example: on the table/ceiling/wall...
• Thus, the correct answer is Option 3.
  

Correct Sentence: The children sat on the tables instead of the chairs.

The correct answer is 'Luminary'.

Key Points

• The most appropriate word for the given group of words is 'Luminary'.
• It means 'a person who inspires or influences others, especially one prominent in a particular sphere (एक व्यक्ति जो दूसरों को प्रेरित करता है या प्रभावित करता है, विशेष रूप से एक विशेष क्षेत्र में एक प्रमुख)'.
• Example: one of the luminaries of child psychiatry...|
  

Correct Answer: Luminary.

Additional Information

• Let's look at the meaning of other words:
• Lurch: a sudden movement forward or to one side. (एकाएक आगे की ओर या एक तरफ़ लुढ़कने की क्रिया)
• Luminaire: a complete electric light unit (used especially in technical contexts). [एक पूर्ण विद्युत प्रकाश इकाई (विशेष रूप से तकनीकी संदर्भों में प्रयुक्त)]
• Lunette: an arched aperture or window, especially one in a domed ceiling. (एक धनुषाकार छिद्र या खिड़की, विशेष रूप से एक गुंबददार छत में)

The correct answer is 'Polite'.

Key Points

• The most appropriate antonym of the given word 'Impudent' is 'Polite'.
• Impudent: very rude; lacking respect and not polite. (बहुत अशिष्‍ट; आदरभाव और नम्रता से रहित, निर्लज्ज)
• Example: The boy was punished for his impudent behavior/attitude.
• Polite: having good manners and showing respect for others. (सुशील और दूसरों का सम्‍मान करने वाला; नम्र, शिष्‍ट)
• Example: The assistants in that shop are always very helpful and polite.
  

Correct Answer: Polite.

Additional Information

• Let's look at the meaning of other words:
• Insolent: lacking respect; rude. (अवमानक; अभद्र, धृष्‍ट, गुस्‍ताख़)
• Confident: feeling or showing that you are sure about your own abilities, opinions, etc. (स्‍वयं की योग्‍यताओं, विचारों पर विश्‍वस्‍त; आत्‍मविश्‍वासी)
• Triumphant: feeling or showing great happiness because you have won or succeeded at something. (विजय या सफलता की प्राप्ति पर अत्‍यंत प्रसन्‍न; विजयोल्‍लसित)

The correct answer is 'calm'.

Key Points

• The most appropriate synonym of the given word 'tranquil' is 'calm'.
• Tranquil: quiet and peaceful. (शांत, प्रशांत)
• Example: tranquil scene/waters/ life...
• Calm: not excited, worried or angry; quiet. (शांत, चुपचाप)
• Example: Try to keep calm—there’s no need to panic.
  

Correct Sentence: Watching the setting sun and the calm surface of the water relaxes my mind.

Additional Information

• Let's look at the meaning of other words:
• Unsettled: (used about a situation) that may change; making people uncertain about what might happen. [(स्थिति) जिसमें परिवर्तन संभावित है, अस्थिर; भावी के विषय में अनिश्‍चित]
• Moving: causing strong feelings, especially of sadness. [भावावेश (विशेषतः विषाद) को जन्‍म देने वाली; हृदयस्‍पर्शी, प्रभावशाली]
• Roaring: making a very loud noise. [ज़ोर से शोर करते हुए, गरजते या दहाड़ते हुए]

The incorrectly spelt word is 'Whipe'.

Key Points

• Among the given options the incorrectly spelt word is 'Whipe'.
• Its correct spelling is 'Wipe'.
• It means 'to clean or dry something by rubbing it with a cloth, etc.' (कपड़े आदि से साफ़ करना या पोंछना)
• Example: She stopped crying and wiped her eyes with a tissue.
  

Correct Answer: Wipe.

Additional Information

• Let's look at the meaning of other words:
• Wit: the ability to use words in a clever and amusing way. (वाग्‍वैदग्‍ध्य, वाक्‌चातुर्य, हाज़िरजवाबी)
• Wish: to say to yourself that you want something that can only happen by good luck or chance. [किसी वस्‍तु की अभिलाषा या आशा करना (ऐसी इच्‍छा रखना जो भाग्‍य से या संयोगवश ही पूरी हो सकती हो)]
• Witch: (in past times and in stories) a woman who is thought to have magic powers. [(पूर्व समय और कहानियों में) जादूगरनी, टोनहाई या जादू-टोना करने वाली स्‍त्री]

The correct answer is 'Wisedom'.

Key Points

• Among the given Options the incorrectly spelt word is 'Wisedom'.
• Its correct spelling is 'Wisdom'.
• It means 'the ability to make sensible decisions and judgements because of your knowledge or experience'. [(ज्ञान या अनुभव के आधार पर) विवेकपूर्ण निर्णय लेने की क्षमता, समझदारी, बुद्धिमानी, अक़लमंदी]
• Example: I don’t see the wisdom of this plan [I do not think that it is a good idea].
  

Correct Answer: Wisedom.

Additional Information

• Let's look at the meaning of other words:
• Freedom: the state of not being held prisoner or controlled by somebody else. (स्‍वतंत्रता, आज़ादी; दूसरे की क़ैद या नियंत्रण से मुक्ति)
• Boredom: the state of being bored. (ऊब, बोरियत, अरुचि, नीरसता)
• Kingdom: a country that is ruled by a king or queen. (राजा या रानी द्वारा शासित देश; राज्‍य)

The correct answer is 'sea'.

Key Points

• The most appropriate word for the given blank is 'sea'.
• It means 'the salt water that covers large parts of the surface of the earth'. [(सामान्‍यतः) समुद्र, सागर]
• Example: Do you live by the sea?
• All the options except 1 are contextually incorrect here because after the article we use nouns.
• Here, 'sea' is the only noun.
• Thus, the correct answer is Option 1.
  

Correct Sentence: We love to go to the sea.

The correct answer is 'To express loyalty, respect, or support for something insincerely'.

Key Points

• The most appropriate meaning of the idiom 'To pay lip service' is 'To express loyalty, respect, or support for something insincerely'.
• To pay lip service: express approval of or support for (something) insincerely or without taking any significant action. [ईमानदारी से या कोई महत्वपूर्ण कार्रवाई किए बिना (कुछ) के लिए अनुमोदन या समर्थन व्यक्त करें]
• Example: They pay lip service to equality but they don't want to do anything about it.
  

Correct Answer: To express loyalty, respect, or support for something insincerely.

The correct answer is 'but Rhea is better'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'but Rhea is better' should be used instead of 'but Rhea is the best'.
• In the given sentence two dancers are being compared. In these kinds of cases, we should use a comparative degree.
• So the use of superlative degree is incorrect.
• Thus, the correct answer is Option 2.
  

Correct Sentence: Rhea and Heena are both great dancers, but Rhea is better.

The correct answer is 'In the theatre, the audience threw flowers on the screen.'

Key Points

• The given sentence is in Active Voice. As per the given question, we have to change it into Passive Voice.
• The structure of the given sentence is as follows:
• Subject + V2 + Object. (Active Voice)
• Subject (objective case) + was/were + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is 'the audience'.​​
• The object of the given sentence is 'Flowers.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'threw' will be changed into 'were thrown'.
• Lastly, the preposition 'by' will be added.
  

Correct Sentence: In the theatre, flowers were thrown by the audience.

The correct answer is 'necessary'.

Key Points

• Among the given options the correctly spelt word is 'necessary'.
• It means 'that is needed for a purpose or a reason'. [(प्रयोजन विशेष या कारण विशेष से) आवश्‍यक, ज़रूरी]
• Example: A good diet is necessary for a healthy life.
  

Correct Sentence: This rule is necessary to maintain discipline.

The erroneously spelt word is 'Solusion'.

Key Points

• Among the given Options the incorrectly spelt word is 'Solusion'.
• Its correct spelling is 'Solution'.
• It means 'a way of solving a problem, dealing with a difficult situation, etc.' [किसी समस्‍या, कठिनाई आदि से निपटने का ढंग; हल, समाधान]
• Example: a solution to the problem of unemployment...
  

Correct Answer: Solusion.

Additional Information

• Let's look at the meaning of other words:
• Trustworthy: that you can depend on to be good, sincere, honest, etc. [विश्‍वास-योग्‍य, विश्‍वसनीय, भरोसेमंद]
• Bonafide: real or genuine. [वास्‍तविक, प्रामाणिक, असली, सच्‍चा]
• Cultural: connected with the customs, ideas, beliefs, etc. of a society or country. [किसी समाज या देश की प्रथाओं, विचारधाराओं, विश्‍वासों आदि से संबंधित; सांस्‍कृतिक]

The correct answer is 'Contemporaries'.

Key Points

• The most appropriate word for the given group of words is 'Contemporaries'.
• It means 'a person who lives or does something at the same time as somebody else'. (समकालीन व्‍यक्ति)
• Example: The two men were exact contemporaries at university. 
  

Correct Answer: Contemporaries.

Additional Information

• Chauvinist: a person displaying aggressive or exaggerated patriotism. (आक्रामक या अतिरंजित देशभक्ति प्रदर्शित करने वाला व्यक्ति)
• Cosmopolitan: containing people from all over the world. (विश्‍व के विभिन्‍न भागों से आए व्‍यक्तियों वाला; सर्वदेशीय)
• Cynic: a person who believes that people only do things for themselves, rather than to help others. (व्‍यक्ति जो सबको स्‍वार्थी समझता हो; दोषदर्शी)

The correct answer is 'Foolish'.

Key Points

• The most appropriate antonym of the given word 'Judicious' is 'Foolish'.
• Judicious: (used about a decision or an action) sensible and carefully considered; showing good judgment. [(निर्णय या कार्रवाई) बुद्धिमत्तापूर्ण और सुविचारित; विवेकपूर्ण विवेक-सम्‍मत]
• Example: We should listen to the judicious opinion of that old man.
• Foolish: silly; not sensible. (बेवक़ूफ़; बेअक़ल, बुद्धिहीन, विवेकहीन)
• Example: I was foolish enough to trust him.
  

Correct Answer: Foolish.

Additional Information

• Let's look at the meaning of other words:
• Modest: not talking too much about your own abilities, good qualities, etc. [विनम्र, विनीत (अपनी क्षमताओं आदि का बखान न करने वाला)]
• Reserved: shy and keeping your feelings hidden. (संकोची तथा मनोभावों को छिपाकर रखने वाला)
• Authoritative: having authority; demanding or expecting that people obey you. (अधिकारिक; आदेशात्‍मक, आज्ञासूचक)

The correct answer is 'Everyone has good luck or success at a point of time'.

Key Points

• The most appropriate meaning of the given idiom 'Every dog has his day' is 'Everyone has good luck or success at a point of time'.
• It is a saying which is said to emphasize that everyone is successful or happy at some time in their life. 
• Example: I've been waiting a long time for success — four years — but every dog has its day.
  

Correct Answer: Everyone has good luck or success at a point of time.

The correct answer is 'stalked, tendrils, concealment'.

Key Points

• The most appropriate words for the given blanks are 'stalked, tendrils, concealment'.
• The most appropriate word for the first blank is 'stalked'. It means 'to follow something as closely as possible without being seen, heard or touched'. (बिना देखे, सुने या छुए किसी चीज का यथासंभव बारीकी से पालन करना)
• Example: He spent the weekend stalking deer to photograph them.
• In the second filler, the most appropriate word is 'tendrils'. It means 'a thin, stem-like part of a climbing plant that holds on to walls or other plants for support (चढ़ाई वाले पौधे का एक पतला, तना जैसा हिस्सा जो समर्थन के लिए दीवारों या अन्य पौधों पर टिका रहता है)
• Example: We measured the parameters of flat tendrils at nodes 11 and 17.
• In the third filler, the most appropriate word is 'concealment'. It means 'the action of hiding something or preventing it from being known (किसी चीज को छिपाने या जानने से रोकने की क्रिया).
• Example: the concealment of the weapons...
• Thus, the correct answer is Option 4.
  

Correct Sentence: Very carefully I stalked the tree I have referred to, and avoiding contact with the creepers, the upper tendrils and leaves of which might have been visible from where the tiger was lying, I climbed to the fork, where I had a comfortable seat and perfect concealment.

The correct answer is 'To happen'.

Key Points

• The most appropriate meaning of the given phrasal verb 'Come about' is 'To happen'.
• Come about: to happen. (घटित होना; होना)
• Example: She was late again, but I'm not sure how it came about this time.
  

Correct Answer: To happen.

The correct answer is 'ACBD'.

Key Points

• The given question is an example of a Para Jumble.
• We know that the first statement of a para-jumbled question is usually an independent general statement, a noun, a universal fact, starting of an incident, or it begins with 'most' or 'once'.
• Sentence A will be the first sentence because it is an introductory statement that tells us about the love story of the Taj Mahal.
• Sentence C will be used after it because it tells us how Prince Khurram fell in love with Arjumand Banu Begum in 1607.
• Banu Begum was the niece of Meherunissa (Nur Jahan). Meherunissa was the wife of Jahangir. Hence, Sentence B will be used next.
• Lastly, Sentence D will be used.
• Thus, the correct sequence: 
• A: The Taj Mahal's history is also one of the world's greatest love stories known to everyone.
• C: It all started in 1607, when Mughal Prince Khurram, first laid eyes on the lovely Arjumand Banu Begum.
• B: She was the neice of Meherunissa who was married to Prince Salim (later the Empress Nur Jahan.)
• D: Khurram, the son of Emperor Jahangir, Voiced his wish to marry Arjumand, and their marriage was celebrated with great pomp.
  

Correct Sequence: The Taj Mahal's history is also one of the world's greatest love stories known to everyone. It all started in 1607, when Mughal Prince Khurram, first laid eyes on the lovely Arjumand Banu Begum. She was the neice of Meherunissa who was married to Prince Salim (later the Empress Nur Jahan.) Khurram, the son of Emperor Jahangir, Voiced his wish to marry Arjumand, and their marriage was celebrated with great pomp.

The correct answer is 'value'.

Key Points

• The given passage is the story of 'The Grasshopper and the Ant'.
• The most appropriate word for the given blank is 'value'.
• In the given context the word 'value' means 'to consider something important or good (किसी महत्वपूर्ण या अच्छी बात पर विचार करना)'.
• Example: We value our partnership with the government.
• Here, the word 'value' is referring to a lesson.
• Thus, the correct answer is Option 1.
  

Correct Passage: The value that comes out of the story The Grasshopper and the Ant has to be subtly put to the children in such a way (2) ____________ they realise the worth of hard work, the pleasures of hard work and the comfort it offers. Laziness, which is a (3) __________ trait here, should be discouraged, (4) ____________ emphasizing on the (5) ____________ note which is hard work.

Mistake Points 

• Morals cannot be the correct answer as we need a singular subject as it is followed by a singular verb i.e. comes.
• Moral and Morals have different meanings.
• "Moral" refers to the ethical lesson or principle taught by a story or event.
• Example:- Our mayor is an outstanding example of high moral standards.
• In the plural form, "Morals" refers to a person's beliefs with respect to right and wrong, as well as his qualities in the areas of sexual morality and ethics as perceived by others.
• Example:- My grandmother always ended our conversations by telling me that she didn't care for the lax morals of today's young people.

Additional Information

• Let's look at the meaning of other words:
• enjoyment: pleasure or a thing that gives pleasure. (आनंद या आनंदित करने वाली वस्‍तु)
• morals: standards of good behavior. (अच्‍छे आचरण के मानदंड, सदाचार, नैतिकता)
• ending: the end (of a story, play, film, etc.). [कहानी, नाटक, सिनेमा आदि की समाप्ति]

Important Points

There is another word, "morale" we use it when referring to the mental or spiritual state of an individual or group.

Example:- When the teacher announced a pop quiz, the morale of the class quickly sank.

The correct answer is 'that'.

Key Points

• The given passage is the story of 'The Grasshopper and the Ant'.
• The most appropriate word for the given blank is 'that'.
• It is 'used for talking about a person or thing already known or mentioned'. (पूर्वज्ञात या पूर्व निर्दिष्ट व्‍यक्ति या वस्‍तु के विषय में चर्चा के लिए प्रयुक्त)
• Example: I’m reading the book that won the Sahitya Academy Award.
• In the given context 'that' relative pronoun is referring to the children.
• Thus, the correct answer is Option 1.
  

Correct Passage: The value that comes out of the story The Grasshopper and the Ant has to be subtly put to the children in such a way that they realise the worth of hard work, the pleasures of hard work and the comfort it offers. Laziness, which is a (3) __________ trait here, should be discouraged, (4) ____________ emphasizing on the (5) ____________ note which is hard work.

The correct answer is 'negative'.

Key Points

• The given passage is the story of 'The Grasshopper and the Ant'.
• The most appropriate word for the given blank is 'negative'.
• It means 'bad or harmful'. (बुरा या हानिप्रद)
• Example: The effects of the new rule have been rather negative.
• In the given context 'negative' is referring to the word 'laziness'.
• Thus, the correct answer is Option 4.
  

Correct Passage: The value that comes out of the story The Grasshopper and the Ant has to be subtly put to the children in such a way that they realise the worth of hard work, the pleasures of hard work and the comfort it offers. Laziness, which is a negative trait here, should be discouraged, (4) ____________ emphasizing on the (5) ____________ note which is hard work.

The correct answer is 'while'.

Key Points

• The given passage is the story of 'The Grasshopper and the Ant'.
• The most appropriate word for the given blank is 'while'.
• It means 'during the time that; when'. (उस समय जब; जब)
• Example: He always phones while we’re having lunch.
• Thus, as per the meaning given above, we can conclude that the correct answer is Option 4.
  

Correct Passage: The value that comes out of the story The Grasshopper and the Ant has to be subtly put to the children in such a way that they realise the worth of hard work, the pleasures of hard work and the comfort it offers. Laziness, which is a negative trait here, should be discouraged, while emphasizing on the (5) ____________ note which is hard work. 

Additional Information

• yet: up until the present or a specified or implied time; by now or then.
• thus: as a result or consequence of this; therefore.
• but: used to introduce a phrase or clause contrasting with what has already been mentioned.

The correct answer is 'positive'.

Key Points

• The given passage is the story of 'The Grasshopper and the Ant'.
• The most appropriate word for the given blank is 'positive'.
• Here, 'on the positive note' is a phrase. It means '(to finish) with an optimistic tone, with good news'. [(समाप्त करने के लिए) एक आशावादी स्वर के साथ, अच्छी खबर के साथ]
• Example: I should like to end on a positive note.
• Thus, the correct answer is Option 1.
  

Correct Passage: The value that comes out of the story The Grasshopper and the Ant has to be subtly put to the children in such a way that they realise the worth of hard work, the pleasures of hard work and the comfort it offers. Laziness, which is a negative trait here, should be discouraged, while emphasizing on the positive note which is hard work.

Additional Information

• Let's look at the meaning of other words:
• important: having great value or influence; very necessary. (महत्वपूर्ण; अत्‍यावश्‍यक)
• essential: completely necessary; that you must have or do. (परमावश्‍यक; सर्वथा अपेक्षित)
• critical: saying what is wrong with somebody/something. (दोषदर्शी, आलोचनात्‍मक)

The logic followed here is:

By using BODMAS (Brackets of division, multiplication, addition and subtraction) and going by the options,

Option (1) -, +, ÷, ×, =

Given equation: 25 * 5 * 10 * 2 * 4 * 3

Putting the signs: 25 - 5 + 10 ÷ 2 × 4 = 3

25 - 5 + 5 × 4 = 3

25 - 5 + 20 = 3

45 - 5 = 3

40 = 3

LHS ≠ RHS

Option (2) ×, ÷, -, +, =

Given equation: 25 * 5 * 10 * 2 * 4 * 3

Putting the signs: 25 × 5 ÷ 10 - 2 + 4 = 3

25 × 0.5 - 2 + 4 = 3

12.5 + 2 = 3

14.5 = 3

LHS ≠ RHS

Option (3) ÷, ×, +, -, =

Given equation: 25 * 5 * 10 * 2 * 4 * 3

Putting the signs: 25 ÷ 5 × 10 + 2 - 4 = 3

5 × 10 + 2 - 4 = 3

52 - 4 = 3

48 = 3

LHS ≠ RHS

Option (4) ÷, -, +, ×, =

Given equation: 25 * 5 * 10 * 2 * 4 * 3

Putting the signs: 25 ÷ 5 - 10 + 2 × 4 = 3

5 - 10 + 2 × 4 = 3

5 - 10 + 8 = 3

13 - 10 = 3

3 = 3

LHS = RHS

Hence, the correct answer is option (4).

In the above question, following pattern in followed.

n : n² × (n+1)

(7)² × 8 = 49 × 8 = 392

(9)² × 10 = 81 × 10 = 810

(15)² × 16 = 225 × 16 = 3600 (not 3150)

(12)² × 13 = 144 × 13 =1872

All the options, except option (3) follow this pattern

Hence, the correct answer is option (3)

The least possible Venn diagram for the given statements is as follows-

Conclusion:

I. All apples are nuts. → True (as all apples are bananas and all bananas are nuts)

II. All grapes are nuts. → True (as all grapes are bananas and all bananas are nuts)

III. No nuts are bananas. → False (as all bananas are nuts; some nuts will definitely be bananas)

Hence, only conclusions (I) and (II) follow.

The logic followed here is:

When the mirror is placed vertically to the object, the mirror image will be laterally inverted. In other words, the Left Hand Side and Right Hand Side will interchange their positions while the top and bottom will be same. 

Hence, the correct answer is option (2).

In the above series, following pattern is followed.

Hence, the correct answer is ZCFI.

The logic followed here is :

Just unfold the paper as it was folded. The diagonal lines are just the folding of the paper.

Only option (4) is showing the correct cut on the pa

per after unfolding. 

Hence, the correct answer is option (4)

Mistake Points

Option2:   

Option 4: 

Both the option appear to be same but are not same. Direction of the part indicated with in box is different in both the options.

The logic followed here is:

In the above code, every letter is replaced by +1 letter of them in the English alphabet series.

S (19) +1 = T (20)

C (3) + 1 = D (4)

H (8) +1 = I (9)

0 (15) +1 = P (16)

0 (15) +1 = P (16)

L (12) +1 = M (13)

'SCHOOL' is written as 'TDIPPM'

C (3) + 1 = D (4)

0 (15) +1 = P (16)

L (12) +1 = M (13)

L (12) +1 = M (13)

E (5) + 1 = F (6)

G (7) + 1 = H (8)

E (5) + 1 = F (6)

 'COLLEGE' is written as 'DPMMFHF'

U (21) + 1 = V(22)

N (14) + 1 = O (15)

I (9) + 1 =  J(10)

V (22) + 1 = W(23)

E (5) + 1 = F(6)

R (19) + 1 = S(20)

S (19) +1 = T (20)

I (9) + 1 =  J(10)

T(20) +1 = U(21)

Y(25) + 1 = Z(26)

 'UNIVERSITY' is written as 'VOJWFSTJUZ'

Hence, the correct answer is VOJWFSTJUZ.

Family chart:

According to the statement:

Nilesh is Kapil's father.

Hence, Nilesh is father of Kapil.

The logic followed here is:

i) In any two consecutive ordinary years, date of the next year will be one day ahead of the same day in the previous year.

ii) And if a leap year comes immediately after an ordinary year, then the day on a certain date of leap year will

(1) 1 day ahead of the same day of the ordinary year upto February,

(2) 2 days ahead of the same day of the ordinary year from March to December.

Therefore,

26 January 2019 = Saturday

26 January 2020 = Sunday 

26 January 2021 = Tuesday

26 January 2022 = Wednesday

From 26 January to 30 January 2022

30 - 26 = 4 days 

4 days after Wednesday is Sunday

Hence, the correct answer is Sunday.

The correct answer is option(3).

The coding is as follows

Ist letter is interchanged with 5th letter.

2nd, 3rd,and 4th letters are interchanged with 6th, 7th, and 8th letter.

ACCURATE : RATEACCU 

A is interchange with R

CCU is interchange with ATE

ANALYSIS : YSISANAL

A is interchange with Y

NAL is interchange with SIS.

CAPACITY : ?

C will be interchange with C

APA will be interchange with ITY

Therefore,

CAPACITY : CITYCAPA

Hence, the correct answer is CITYCAPA.

The logic followed here is:

The code follows like this

A(1)  + 1 = B(2)

B(2)  + 2 = D(4)

R(18) + 3 = U(21)

O(15) - 1 = N(14)

A(1) - 2 = Y(25)

D(4) - 3 = A(1)

"ABROAD" is written as "BDUNYA"

B(2) + 1 = C(3)

E(5) + 2 = G(7)

C(3) + 3 = F(6)

A(1) - 1 = Z(26)

M(13) - 2 = K(11)

E(5) - 3 = B(2)

"BECAME" is written as "CGFZKB"

Therefore,

C(3) + 1 = D(1)

A(1) + 2 = C(3)

N(14) + 3 = Q(17)

C(3) - 1 = B(2)

E(5) - 2 = C(3)

R(18) - 3 = O(15)

"CANCER" is written as "DCQBCO"

Hence, the correct answer is DCQBCO.

The logic followed here is:

There are 2 operations going on, first multiplying by even number and subtraction of prime number. And the series goes like this

13 × 2 = 26

26 - 3 = 23

23 × 4 = 92

92 - 5 = 87

87 × 6 = 522

So, the series is 13, 26, 23, 92, 87, 522

Hence, the correct answer is 92.

The correct answer is option (4)

Given Series: t _ r a s _ t _ s _ a _ _ _ t _ r _ s r t

Option 1: t s r a s r t /t s r a a r  t/ t s r a s r t

Option 2: t s r a s r t /a s r a s r  t/ t s r a s r t

Option 3: t s r a s r t /t s r a s r  t/ t s r t s r t

Option4: t s r a s r t /t s r a s r  t/ t s r a s r t

Series pattern: t s r a s r t /t s r a s r  t/ t s r a s r t.

Therefore, only s r t r s r t s a follows the pattern.

Hence, the correct answer is s r t r s r t s a.

The logic followed here is

By using BODMAS ( brackets, of, division, multiplication, addition and subtraction). And

 

Given equation: 130 S 61 R (23 P 4) S 83 R (62 Q 2) = ?

Putting  × in place of P,  ÷ in place of Q, + in place of R, - in place of S          

130 - 61 + (23 × 4) - 83 + (62 ÷ 2) = ?

130 - 61 + 92 - 83 + 31 = ?

253 - 61 - 83 = ?

253 - 144 = ?

109 = ?

Hence, the 109 will come in place of '?'

The logic followed here is:

In the above question, 23 is subtracted from the number to get the next number.

First row: 187- 23 =164

               164 - 23 = 141

Therefore, the series is 187, 164, 141

Second row  215 - 23 = 192

                     192 - 23 = 169

Therefore, the series is 215, 192, 169

Third row 178 - 23 = 155

                155 - 23 = 132

Therefore, the series is,178, 155,132

Hence, the correct answer is 132.

The logic followed here is

In a mirror image left changes to right and the right changes to left.

when placement of mirror not given, by default we will assume it in VERTICAL DIRECTION.

The letter adjacent to the mirror, will appear adjacent to it after the mirror just with the left changed to right and right changed to left.

Also, the starting letter of the word will be at last after the mirror.

Hence, the correct answer is option 1)

The pattern used in the given optionsis:

        (√First term - 2)² = Second term

Let's consider the option by applying the following logic:

Option 1) 100:81

(√100 - 2)² = 81

(10 - 2)2 = 81

(8)2 = 81

64 ≠ 81

thus this logic doesn't get applied over here, thus is this is the odd pair.

Option 2) 36:16

(√36 - 2)2 = 16

(6 - 2)2 = 16

(4)2 = 16

16 = 16

Option 3) 49:25

(√49 - 2)2 = 25

(7 - 2)2 = 25

(5)2 = 25

25 = 25

Option 4) 81:49

(√81 - 2)2 = 49

(9 - 2)2 = 49

(7)2 = 49

49 = 49

Hence the correct answer is option 1)

The logic followed here is:

lets interchange the numbers given in the option and solve this question by BODMAS RULE.

Option 1) 40 and 16

equation: (40 × 6) ÷ 8 + 14 - (7 × 16) + (13 × 12) = 26

(16 × 6) ÷ 8 + 14 - (7 × 40) + (13 × 12) = 26

LHS:

96 ÷ 8 + 14 - 280 + 156

12 + 14 - 280 + 56

182 - 280

-98

Thus, LHS is not equal to RHS.

Option 2) 8 and 12

equation: (40 × 6) ÷ 8 + 14 - (7 × 16) + (13 × 12) = 26

(40 × 6) ÷ 12 + 14 - (7 × 16) + (13 × 8) = 26

LHS:

240 ÷ 12 + 14 - 112 + 104

20 + 14 - 112 + 104

138 - 112

26

Thus LHS is equal to RHS.

Option 3) 6 and  12

equation: (40 × 6) ÷ 8 + 14 - (7 × 16) + (13 × 12) = 26

(40 × 12) ÷ 8 + 14 - (7 × 16) + (13 × 6) = 26

LHS:

480 ÷ 8 + 14 - 112 + 78

60 + 14 - 112 + 78

152 - 112

40 

Thus LHS is not equal to RHS.

Option 4)14 and 16

equation: (40 × 6) ÷ 8 + 14 - (7 × 16) + (13 × 12) = 26

(40 × 6) ÷ 8 + 16 - (7 × 14) + (13 × 12) = 26

LHS:

240 ÷ 8 + 16 - 98 + 156

30 + 16 - 98 + 156

202 - 98

104

Thus LHS is not equal to RHS.

Hence, 8 and 12 is the correct answer.

The logic followed here is:   

The series is as follows:,

6, 12, 20, 30, ?, 56

lets see the applied logic:

12 - 6 = 6

20 - 12 = 8

30 - 20 =10

if u see clearly the difference between two numbers increases by two in the next term.

Thus,

? - 30 = 12 (? = 42)

56 - 42 = 14

Hence, 42 is the correct answer.

The table in alphabets place value:

the pattern followed here is:

STEP 1: Consonants are coded as place value × 2

STEP2: Vowels are coded as place value.

'CHECK  is written as 6165622

And , SURGE is written as 382136145

Similarly,

PRIEST =?

 

HENCE, PRIEST is coded as,3236953840

The figure is given below:

The shaded portion is the embedded figure.

Hence, 'option 2' is the correct answer.

The logic followed here is:

Lets count the total number of triangles:

total number of small triangles enclosed in big triangles:8

total no of big triangles enclosing small triangles:2

Thus the total number of triangles = 8 + 2 = 10

Hence, the correct answer is 10.

The logic followed here is:

The applied logic in all pairs:  first number × 17 = second number

option 1) 19 : 323

19 × 17= 323

option 2) 43 : 731

43 × 17 = 731

option 3) 21 : 357

21 × 17 = 357

option 4) 15 : 356

15 × 17 = 255

Thus this is the odd pair which doesn't follow the logic as followed by other pairs.  

Hence, the correct answer is 15 : 356.

The logic followed here is:

Given : 19, 37, 74, 147, 294, ?

now lets find out the logic in the given series

19 × 2 - 1 = 37

37 × 2 = 74

74 × 2 - 1=147 

147 × 2 = 294

Here,  first the number is multiplied by two and then subtracted by 1 and in the next one it is only multiplied by 2.

thus continuing the series ,

294 × 2 - 1 = 587

Hence**, 587** will be the answer.

The logic followed here is

i) In a mirror image left changes to right and the right changes to left.

ii) When placement of mirror not given, by default we will assume it in VERTICAL DIRECTION

iii) The letter adjacent to the mirror will be adjacent to it  after the mirror image just with the left change to right and right changes to left vice-versa.

iv)The starting letter of the word will be at last after the mirror.

Hence, 

is the correct answer.

GIVEN:

Selling price = Rs18200

loss% = 15

FORMULA USED:

loss % = $Loss\over C.P.$ × 100 where,  C.P. is Cost Price

Loss = C.P. - S.P.  where C.P. is Cost Price and S.P. is Selling Price

CALCULATION:

Loss = C.P. - 18200 

Loss % = $( C.P. - 18200)\over C.P.$ × 100 

⇒ 15 = $(C.P.. -18200)\over C.P.$ × 100 

⇒ 15 C.P. = 100 C.P. - 1820000

⇒ 85C.P. = 1820000    ⇔ C.P. = Rs. 21,411.76 ≈ Rs. 21,412

Hence, Cost price  of the fridge is Rs. 21,412.

Shortcut Trick Loss% = 15% = 3/20

Ratio of C.P to S.P. = 20 : 17

⇒ 17 units = 18200

⇒ 20 units = (18200/17) × 20

⇒ Rs. 21411.76 = Rs. 21412 (approx)

GIVEN:

Marked price is Rs. 18000

successive discounts is 25% and 4%

additional discount is 5%

FORMULA USED:

S.P. = (1 – d1/100) × (1 – d2/100) × M.P. where, 

d1 and d2 are successive discount percentages respectively.

S.P. = Selling Price. and M.P. = marked price

CALCULATION:

Here, d1 = 25% and d2 = 4% and M.P. = 18,000

S.P. = (1-25/100) × (1-4/100) × 18000 = (1 -1/4) × (1 -1/25)  × 18,000

⇒ S.P. =  3/4 × 24/25 × 18,000 

⇒ S.P. = Rs. 12,960 

Now,

There is an additional discount of 5% on cash payment,

Hence,  additional discount of 5%  in amount = 12960 × 5/100 = Rs. 648

S.P. after additional discount = (12,960 – 648) = Rs. 12,312.

Hence, Selling price of the mobile on cash payment is Rs. 12,312.

Shortcut TrickNet effective discount = x + y - xy/100

So, 25% + 4% - (25 × 4)/100 = 29 - 1 = 28%

So, the cost after 2 successive discount given

⇒ 18,000 × 72% = Rs. 12,960

S.P. after an additional discount of 5%

⇒ Rs. 12,960 ×( 100 - 5)%

⇒ Rs. 12,960 × (95/100)

⇒ Rs. 12,312

GIVEN:

Speed of a motorboat is 15 km/h

distance of boat in downstream is 30 km

distance of boat in upstream is 30 km

Total time is 4hrs 30 minutes

FORMULA USED:

Distance = Speed  × Time 

Relative speed in downstream = (speed of motorboat + speed of stream)

Relative speed in upstream = (speed of motorboat – speed of stream )

CALCULATION :

As 1hour = 60 minutes

To convert minutes into hours divide it by 60, 

⇒ Time = (4 + 30/60) hours =  9/2 hours    

Now, let the stream's speed be x

⇒ Downstream speed = ( 15 + x) km/h

⇒ Upstream speed = ( 15 -x ) km/h

Now, Distance = speed × time

⇒ Hence, $Distance \over Speed$ = Time

⇒  $30\over( 15 + x )$ + $30\over ( 15 -x )$ = 9/2

⇒ $(15 +x +15 - x)\over225- x^2$ = 9/60 = $30 \over( 225 - x^2)$= $9 \over 60$ 

⇒ ( 200 = 225 - $x^2$ ) = $x^2$ = 25  

⇒ x = 5. 

Hence, the speed of the stream is 5 km/h.

Shortcut TrickBy hit and trial method

Let the speed of boat = u = 15km/h (given)

Let speed of the stream = v

Considering option(3), let v = 5km/h

So, Downstream speed (D) = 15 + 5 = 20km/h

Upstream speed (U) = 15 - 5 = 10km/h

Now, Total time taken = Distance/D + Distance/U

⇒ 30/20 + 30/10 = 3/2 + 3

⇒ 9/2 h = 4 h 30 mins

It satisfies the given condition. 

Hence, the speed of the stream is 5 km/h.

GIVEN:

Five colleges A, B, C, D, and E

Five different subjects i.e. Hindi, English, Maths, Science, and G.K.

number of students participated in olympiad from 5 different colleges in 5 different subjects

FORMULA USED:

Average = $sum of values\over number of values$ × 100

CALCULATION:

Number of students participated in English 

⇒ From college A = 98

⇒ From college B = 120

⇒ From college C = 80

⇒ From college D = 122

⇒ From college E = 105

Hence, sum of all the students in English olympiad from 5 colleges,

⇒ 98 + 120 + 80 + 122 + 105 = 525

Number of colleges = 5

⇒ Average = 525/5 = 105.

Hence, the average no. of students per college participated is 105.

Given:

Marked Price (M.P.) is Rs. 15,000

Selling Price (S.P.) is Rs. 13,500

Formula Used:

Discount % =  $discount\over M.P.$ × 100

Discount = M.P. - S.P.

Calculation: 

Discount = ( M.P. – S.P.)

⇒ Discount = (15,000 – 13,500)

⇒ Discount = Rs 1,500

Now,  Discount% = $1,500\over 15,000$ × 100 = 10%.

Hence, Discount percentage is 10%.

GIVEN :

2 years ago,

The population of a village was 1,000.

1^st year population increased by 10%

2^nd year population decreased by 10%

FORMULA USED:

Present population = Actual population × (1±$R \over 100$), where 

R is rate of increase and decrease and n is time.

CALCULATION:

Population after 1^st year increase,

⇒ 1,000 × (1+10/100) = 1,000 × 11/10 = 1,100

Population after 2^nd year decrease

⇒ 1,000 × 11/10 × (1-1/10) = 1,000 × 11/10 × 9/10 = 990.

Hence, Present population is 990.

GIVEN :

X = 5t

Y = 1/3 (t +1)

X = 3Y 

CALCULATION :

We have, X = 3Y      ... (1) 

So, put the value of X from equation (1) in X  = 5t 

⇒ 3Y = 5t      ... (2)

Now, put the value of Y i.e. Y = 1/3(t +1)  in equation (2) we have,

⇒ 3 × 1/3 × ( t+1) = 5t

⇒ t +1 = 5t 

⇒ 4t = 1 

⇒ t = 1/4.

Hence, the value of t is 1/4.

CONCEPT USED:

Divisibility rule :

10 = last digit should be zero.

7 =[Last 3 digit – remaining digits]  should be multiple of 7.

CALCULATION:

Number = 732XY

Divisor = 10 × 7

According to the divisibility rule of 10,

Y should be zero.

⇒ Then the value of Y = 0.

And number = 732X0

Now, check the divisibility of 7,

⇒ 32X - 7 

⇒ Here, possible values of X are = 1,2,3,4,5,6,7,8,9,0.

Now, put X =1,

321- 7 = 314.

⇒ 314/7 not divisible by 7.

Put X = 2,

322-7 = 315

⇒ 315/7 =45, which is divisible by 7.

Our required value of X = 2. Y = 0.

Now, the value of (X +Y) /2 = (2+0)/2 = 1.

Hence, the required value is 1.

GIVEN:

$x^4 + \frac{1}{x^4} =2207$

FORMULA USED:

(a + b)² = a² + b² + 2ab

where a and b = 1st and 2nd term respectively.

(a + b)³ = a³ + b³ + 3ab(a + b)

CALCULATION:

Now, $x^4 + \frac{1}{x^4}$  can be written as,

$(x^2 + \frac{1}{x^2})^2 = x^4 + \frac{1}{x^4} + 2.x^2.\frac{1}{x^2}$   

Here, a = x and b = 1/x respectively.

⇒ $x^4 + \frac{1}{x^4} = (x^2 + \frac{1}{x^2})^2 - 2$ ×$x^2.1/x^2$ 

⇒ 2207 =  $(x^2 + \frac{1}{x^2})^2$ - 2 

⇒ $(x^2 + \frac{1}{x^2})^2$ = 2209.

⇒ $(x^2 + \frac{1}{x^2})$ = 47      ... (1)

Now, again $(x^2 + \frac{1}{x^2})$ can be written as,

⇒ $( x+ \frac{1}{x})^2= x^2 + \frac{1}{x^2} + 2.x .\frac{1}{x}$ 

⇒ $(x^2+ \frac{1}{x^2})= ( x+\frac{1}{x})^2$ - 2 

⇒ 47 = $( x+ \frac{1}{x})^2$ -2

⇒ $( x+ \frac{1}{x})^2$ = 49 

⇒ (x +1/x) = 7      ... (2)

Now, take the cube of equation (2) on both sides, we  get

 $(x + \frac{1}{x})^3 = x^3 +\frac{1}{x^3} +3.x.\frac{1}{x}(x+\frac{1}{x})$     

Here a = x and b = 1/x.

⇒ 343 = $( x^3 + \frac{1}{x^3})$ + 3(7) 

⇒ $( x^3 + \frac{1}{x^3})$ = 322.

Now. $( x^5 + \frac{1}{x^5})$ can be written as,

⇒ $( x^5 + \frac{1}{x^5}) = ( x^2 + \frac{1}{x^2})( x^3 + \frac{1}{x^3}) -( x+ \frac{1}{x})$ 

⇒ ( 47 × 322 - 7) = 15127.

Hence, the value is 15,127.

GIVEN:

Discount is 15%

Profit is 6.25%

Marked Price is Rs. 5,000.

FORMULA USED:

Discount% = (Discount /M.P. )× 100

Discount = M.P. – S.P. where,

M.P. is Marked Price and S.P. is Selling Price.

Profit% = (Profit/C.P. ) × 100

Profit = S.P. – C.P.                 

C.P. = Cost Price.

CALCULATION:

Discount = 5000 – S.P.

⇒ Discount% = (Discount /M.P.) × 100

⇒ 15 = $( 5000 - S.P.)\over5000$ × 100

⇒ 750 = 5000 – S.P.

⇒ S.P. = Rs. 4,250

Profit = (4,250 – C.P.)

⇒ Profit% = (Profit/C.P.) × 100

⇒ 6.25 = $( 4250 -C.P.) \over C.P.$ × 100 

⇒ 6.25 C.P. = 4,25,000 - 100C.P.

⇒ 106.25 C.P. = 4,25,000

⇒ C.P. = Rs 4,000.

Hence, Cost Price of the chain is Rs 4,000.

Shortcut TrickHere, Discount = 15% = 3/20

Then, the Ratio of M.P. to S.P. = 20 : 17

Also, Profit% = 6.25% = 1/16

Then the Ratio of C.P. to S.P. = 16 : 17

Combining both the ratio, we get

C.P : S.P : M.P = 16 : 17 : 20

Now, 20 units = Rs. 5,000

⇒ 1 unit = 5000/20  Rs. 250

⇒ 16 units = 250 × 16 = Rs. 4000

GIVEN:

Average weight of 18 boys is 45 kg.

Average weight of 8 boys is 48.75 kg.

FORMULA USED:

Average = (Sum of Values)/(Number of Values)

CALCULATION:

Average of 18 boys = sum of 18 Boys/Number 

⇒ 45 = sum of 18 boys/18

⇒ Sum of 18 boys = ( 45 × 18) = 810

Average of remaining 8 Boys = Sum of 8 Boys/Number of boys.

⇒ 48.75 = Sum/8 

⇒ Sum of the remaining 8 boys = 390.

Sum of all the boys = (sum of 18 boys + Sum of remaining 8 boys)

⇒ Sum of all the boys = (810 + 390) = 1,200.

⇒ Number of all the boys = (18 + 8) = 26.

Average  = Sum of all the Boys/Number of Boys.

⇒ Average = 1200/26 = 46.15 kg.

Hence, Average Weight of all the boys is 46.15 kg.

FORMULA USED:

Average = sum of observation/ no. of observation.

CALCULATION:

Let the consecutive  natural numbers starting with 'm' as,

⇒ m, ( m+1), ( m+2 ), ( m+3), ( m+4)

Sum of numbers,

⇒ m + (m+1) + (m+2) + (m+3) + (m+4) = (5m + 10)

⇒ Total numbers = 5.

⇒ Average = Sum/Total Numbers 

⇒ Average = $5 ( m+2)\over 5$ = (m+2).

Hence, The average is (m+2).

Shortcut TrickIf the numbers are written in consecutive form,

i.e.  m, ( m+1), ( m+2 ), ( m+3), ( m+4)

Then the middle no. will be the average of the given numbers i.e.  ( m+2 )

GIVEN:

5 Persons prepare 5 Tables in 5 days.

FORMULA USED:

M1 × D1 × W2 = M2 × D2 × W1 Where,

M is no. of persons,

D is no. of days,

W is total work.

CALCULATION:

Here, M1 = 5 , D1 = 5 , W1= 5 

And, M2 = 25, W2 = 25 . D2 = ?

Now, using formula, we get,

⇒ M1 × D1 × W2 = M2 × D2 × W1

⇒ 5 × 5 × 25 = 25 × D2 × 5 

⇒ D2 = 5.

Hence, It will take 5 days to complete 25 tables.

FORMULA USED :

$( 4 sin^3x = 3 sin x- sin 3x)$

CALCULATION:

$( 4 sin^3x - 3 sinx + sin 3x)$      ... (1)

Now,

We know that, $4 sin^3x = 3 sinx -sin 3x$

⇒ $3 sinx - sin3x -3 sinx + sin3x$ = 0.

Hence, the value of the equation is 0.

Given:

The average weight of Family of 4 members is 45 kg.

After grandmother and grandfather's visit the average becomes 48 kg with total 6 members.

Concept Used: 

Average = Sum of all numbers/Total number

Calculation: 

There are four members in the family.

Total weight is

⇒ Average weight × total number of members 

⇒ 45 × 4

⇒ 180 kg

Total weight after 6 members in the family

⇒ Average weight × total members 

⇒ 48 × 6

⇒ 288 kg

Grandmother and Grandfather's age together is 

⇒ 288 - 180

⇒ 108

Now, average age of grandmother and Grandfather

⇒ Sum of their ages / 2

⇒ $\frac{108}{2}$ = 54 kg

∴ The Required average weight is 54 kg.

Given:

A chord of 10 cm passes through the centre of a circle.

Concept used:

The chord passing through the centre of the circle is its Diameter.

Calculations:

The chord which passes through the centre of circle is it's diameter,

hence, The chord of length 10 cm is also it's diameter.

$\therefore$ The Diameter of the circle is 10 cm.

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)

(2x)3 + (3y)3 + (4z)3 – 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)

∴ The required value is 8x3 + 27y3 + 64z3 – 72xyz .

Given:

Shares among four members of a company is 18%, 22%, 25% and 35% to Shourya, tanmay, bhanu and  dhanya respectively according to the table given.

The total shares initially is 10,000 and then tanmay sold 1000 shares to dhanya.

Calculations:

Dhanya share initially

⇒  35% of 10,000

⇒$\frac{35}{100}$ × 10,000

⇒ 3,500.

Now, total shares of dhanya after tanmay sold 1000 to her

⇒ 3,500 + 1,000

⇒ 4,500

∴ Total shares of Dhanya is 4500.

Calculations:

According to question,In class 8 we have ,

No. of students who likes guava = 10

No. of students who likes Orange = 20

No. of students who likes Mangoes = 30

Total students in class 8 = 10 + 20 + 30 = 60 

Now, percentage of no. of students who likes guava is = $\frac{10}{60}$ × 100 = $\frac{50}{3}$ = $16\frac{2}{3}$%

∴ Percentage of students who likes guavas is class 8 is $16\frac{2}{3}$%.

Formula used:

Area of Triangle = $\frac{1}{2}$ × Base × Height

Calculations:

According to the Question,

Area of quadrilateral ABCD,

⇒ Area of ∆ABC + Area of ∆ ADC

⇒ $\frac{1}{2}$× AC × BF + $\frac{1}{2}$× AC × DE

⇒ $\frac{1}{2}$× AC ( BF + DE )

⇒ $\frac{1}{2}$ × 10 ( 5 + 3 )

⇒ 40 cm²

∴The area of quadrilateral ABCD is 40 cm².

Given:

Diameter of solid hemisphere is 10 cm.

Formula used:

Total surface area of hemisphere = 3πr²

Calculations:

Total surface area of hemisphere = 3πr2

Total surface area of hemisphere,

⇒ 3 × (3.14) × $(\frac{10}{2})$² 

⇒ 3 × (3.14) × 25 

⇒ 235.5 cm2

∴ Total surface area of hemisphere is 235.5 cm².

Given:

Slant height is 11 m,

Radius of base is 10 m,

Rate of painting is Rs. 7 per m².

Formula used:

Total curved surface area = πrL

Calculations:

Total curved surface of Temple,

⇒  π.r.L

⇒ $\frac{22}{7}$ × 11 × 10

⇒ 110π m²

Cost of painting,

⇒ 110π × 7 = 770 × $\frac{22}{7}$ 

⇒ Rs. 2420

∴ Cost of painting the curved surface area of Temple is Rs. 2,420.

Concept used:

a% of b = $a \over 100$ × b

Calculation:

10% of A + 8% of B = ($\frac{3}{5}$) (12% of A + 16% of B)

⇒ [($\frac{10A}{100}$) + ($\frac{8B}{100}$)] = ($\frac{3}{5}$) [($\frac{12A}{100}$) + ($\frac{16B}{100}$)]

⇒ (10A + 8B) = ($\frac{3}{5}$) (12A + 16B)

⇒ (10A + 8B) × 5 = 3 × (12A +16B)

⇒ 50A + 40B = 36A + 48B

⇒ 50A – 36A = 48B – 40B

⇒ 14A = 8B

⇒ A/B = 8/14

⇒ A : B = 8 : 14 = 4 : 7

∴ The ration of A : B is 4 : 7.

Additional Information10% = 10/100

8% = 8/100

12% = 12/100

16% = 16/100

Formula used:

Mean proportion = √ab

Calculations:

 = √ab

Mean proportion of 144 and 225

⇒ √(144 × 225)

⇒ √(32400)

⇒ 180

∴ Mean proportion of 144 and 225 is 180.

Concept used:

Calculations:

$\left[2\frac{1}{4}\div\frac{3}{4}\right]+\left[5\frac{2}{3}\div\frac{17}{13}\right]-\left[3\frac{1}{3}\times\frac{6}{5}\right]+[17.98\div6.2]+[1.25\div0.5]$

⇒ $\left[\frac{9}{4}×\frac{4}{3}\right] + \left[\frac{17}{3}×\frac{13}{17}\right]-\left[\frac{10}{3}×\frac{6}{5}\right]+2.9 +2.5$

⇒ 3 + $\frac{13}{3}$ - 4 + 5.4

⇒ 8.4 + 4.3 - 4

⇒ 8.7

∴ The  Required simplified value is 8.7.