SSC CHSL Tier-1 2021: Official Paper (Held On : 25 May 2022 Shift 1) (Previous Year Paper)

The correct answer is 'polyglot'.

Key Points

• We need to substitute the given group of words 'speaks many languages' with  one word from the following options:
• The marked option 'Polyglot means speaking or writing several languages,multilingual(एक से अधिक भाषा का ज्ञान या उसमें लेखन; बहुभाषी)
• Example: He was a polyglot and pundit in eight languages.
• From the meaning and the example sentence, it is clear that 'polyglot' is the one word for the given group of words.

Thus, the correct answer is option 1.

Additional Information

• Polynomial: an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)
• Polycentric: having many centers, especially of power or importance
• Polysyllabic: having more than one and usually more than three syllables

The correct answer is 'abhor'.

Key Points

• The given word 'loathe' means dislike someone or something very much (किसी व्‍यक्ति या वस्‍तु से नफ़रत करना)
• Example: These two neighbours loathe each other.
• The marked option 'abhor' means to hate something very much(अत्‍यधिक घृणा करना)
• From the given meaning and the example sentence, it is clear that 'abhor' and 'loathe' are synonyms of each other.

Therefore, the correct answer is option 2.​

Additional Information

• Entrench: establish (an attitude, habit, or belief) so firmly that change is very difficult or unlikely (स्थापित (एक दृष्टिकोण, आदत, या विश्वास) इतनी दृढ़ता से कि परिवर्तन बहुत कठिन या असंभावित है)

• Abjure: to promise publicly or formally that you will give up or not accept a belief or a way of behaving (औपचारिक अथवा सार्वजनिक रूप से (मत अथवा आचरण) का सशपथ त्याग करना; शपथ लेकर त्याग करना, छोड़ने की शपथ लेना)

• Meddle: to take too much interest in somebody’s private affairs or to touch something that does not belong to you (दूसरों के निजी मामलों में ज़रूरत से ज्‍यादा रुचि लेना या पराई चीज़ से छेड़-छाड़ करना; हस्‍तक्षेप करना)

The erroneously spelled word is 'ridikule'.

Key Points

• In this question, we need to choose the incorrectly spelled word from the given four options.
• This question is a type of erroneous spelling in context.
• The marked option 'Ridikule' is erroneous here, as its correct spelling is Ridicule.
• Ridicule means to laugh at someone or something in an unkind way.(खिल्‍ली उड़ाना, मज़ाक़ बनाना)
• Example: He was ridiculed by everyone for his conventional ideas.
• Therefore, the correct answer is option 2.

Additional Information

• exemplified: illustrate or clarify by giving an example
• burlesque: an absurd or comically exaggerated imitation of something, especially in a literary or dramatic work; a parody
• doggerel: comic verse composed in irregular rhythm

The correct answer is 'a deceitful person'.

Key Points

• A snake in the grass means a person who feigns friendship with the intent to deceive.
• Example: Don't trust him as he is a snake in the grass.
• From the meaning and the example sentence given above, it is clear that a snake in the grass means a deceitful person.
• Hence, the correct answer is option 2.

The erroneously spelled word is 'geity'.

Key Points

• In this question, we need to choose the incorrectly spelled word from the given four options.
• The marked option 'Geity' is erroneous here, as its correct spelling is Gaiety.
• Gaiety means a feeling of happiness and fun.
• Example: Let's enjoy the warmth and gaiety of this year's Diwali eve.
• ​Hence, the correct answer is option 2.

The correct answer is 'man of straw'.

Key Points

• We need to substitute the underlined segment with the correct segment from the following options:
• For this, we need to explore the meaning of the sentences in the options:
• Man of words is a person who can be trusted to keep a promise; he is a reliable person.
• Man of mars is not an idiom
• Man of straw means a man whose character is weak and who lacks definite beliefs.
• Men of grass is not an idiom.
• So, from the given options and from the given sentence context, it is clear that 'man of straw' substitutes the 'man of music' as a comedian is not at all reliable and has a lack of definite beliefs to be a warrior in times of war.

Therefore, the correct answer is option 3.

The correct answer is: Agitated

Key Points

• Perturbed means feeling or showing great concern or mental or emotional upset. (बड़ी चिंता या मानसिक या भावनात्मक परेशानी महसूस करना या दिखाना)

• Example - He apparently was not perturbed by the prospect of a police officer coming to call.

• Agitated means troubled in mind, disturbed, and upset. (मन में व्याकुलता : व्याकुल और व्याकुल।)

• Example - Susan seemed agitated about something.

• So, It is clear that the denotation of Perturbed is Agitated.

Therefore, the correct answer is option 2.

Additional Information

• Initiated means to cause something to begin. (कुछ शुरू करने के लिए कारण)
• Animated means using a process or method which makes pictures or models appear to move. (एक ऐसी प्रक्रिया या विधि का उपयोग करना जिससे चित्र या मॉडल हिलते हुए दिखाई दें)
• Triumphed means to have a very great success or victory. (बहुत बड़ी सफलता या जीत होना)

The correct answer is 'wizened'.

Key Points

  We need to substitute the given underlined segment with one word from the following options:

• Let's explore the meaning of the given options :
• Wizened means shrivelled or wrinkled with age.(उम्र के साथ सिकुड़ा हुआ या झुर्रीदार)
• Shrunken means reduced in size.(कम आकार का)
• Dried means  with all the liquid removed from it.(सारा तरल पदार्थ निकाल दिया गया)
• Bony means so thin that you can see the shape of the bones.(इतना पतला कि आप हड्डियों का आकार देख सकते हैं।)

Therefore, from the given meanings, the one word is 'Wizened'.

Hence, the correct answer is option 1.

The correct answer is 'deliberately'.

Key Points 

• We have to choose the appropriate word from the given options to fill the given blank as our marked option.
• The marked option 'deliberately' means on purpose,intentionally.
• Example: He didn't break traffic rules deliberately.
• The given sentence implies that 'Asha was purposefully made a fool by her friend.'
• Hence, the correct answer is option 4.

The correct answer is: A happy billionaire is never heard of.

Key Points 

• Active Voice describes a sentence where the subject performs the action stated by the verb. While in the Passive Voice, subject is acted upon by the verb.
• The given sentence is written in the Present simple tense.
• The structure of active voice = Subject + V1 + object
• The structure of passive Voice = Object + is/am/are + V3 + by + subject
• Rules of Conversion from Active to Passive Voice:
• Identify the subject, the verb, and the object.
• Change the object into the subject.
• Change the verb into the past participle form of the verb.
• Change the subject into an object.

Therefore, the correct answer is option 1.

Thus the passive voice will be: A happy billionaire is never heard of.

The correct answer is: The face of health sciences is likely to be altered by the most recent studies on the human body.

Key Points 

• The Active Voice describes a sentence where the subject performs the action stated by the verb. While in the Passive Voice, subject is acted upon by the verb.
• The given sentence is written in the Present simple tense.
• The structure of active voice = Subject + V1 + s/es + object
• The structure of passive Voice = Object + is/am/are + V3 + by + subject
• Rules of Conversion from Active to Passive Voice:
• Identify the subject, the verb, and the object.
• Change the object into the subject.
• Change the verb into the past participle form of the verb.
• Change the subject into an object.

Therefore, the correct answer is option 3.

Thus the passive voice will be: The face of health sciences is likely to be altered by the most recent studies on the human body.

The erroneous part is 'flowed besides'.

Key Points

• The given sentence is not grammatically correct.
• The error lies in part 2 of the sentence.
• The given sentence requires an appropriate preposition but here the word 'besides' is an adverb that means in addition to.
• The correct preposition is 'beside' which means next to, at the side of.
• Thus, 'flowed beside' is used instead of 'flowed besides' in the given sentence.
• Hence, the correct answer is option 3.

Correct Sentence: The river flowed beside the hillock in our village.

The correct answer is 'counter attack'.

Key Points

• The given Idiom 'Tit for tat' a situation in which you do something unpleasant to somebody because they have done something unpleasant to you.
• Example:  It is the maturity to be even more forgiving than tit for tat.
• From the given options, The marked option 'counter attack' is an attack made in response to one by an opponent.
• Therefore, The correct meaning is 'counter attack', and hence the correct answer is option 3.

The correct answer is 'overcame'.

Key Points

• The underlined segment is 'succumbed'. It's meaning is to stop fighting against something.(किसी चीज के खिलाफ लड़ना बंद करो।)
• The marked option 'overcame' means to manage to control or defeat somebody/something.(किसी को/कुछ को नियंत्रित करने या हराने के लिए प्रबंधन करें।)
• From the meanings of given words, we are clear that 'succumb' and 'overcame' both are antonyms of each other.('succumb' और  'overcame' दोनों एक दूसरे के विलोम हैं।)

Thus, the correct answer is option 2.

The correct answer is 'the best'.

Key Points

• The given sentence needs improvement.
• The underlined segment is erroneous here.
• We need to substitute it with the correct replacement given in one of the options.
• The given sentence implies that an extreme degree of quality in dress is required here.
• This shows superlative form will be used in the sentence and moreover, there is the usage of the definite article 'the' in the given sentence which concludes superlative adjectives will be used here as normally nouns with superlative adjectives normally have the article 'the' with it.

 

Therefore, the correct answer is 'the best' which is option 3.

The correct answer is "BDCA"

Key Points 

• Let's look at the correct sequence of the passage.
• Sentence B should be the starting point as it introduces the main character Jane, her orphan status, and her situation living with the Reeds.
• Following B, sentence D  provides specific information about Jane's age and further emphasizes her status as an outsider in the Reed family.
• After the context regarding Jane's situational living with the Reed family has been established,  sentence C naturally follows and delves more deeply into the relationships inside the family, focusing on Jane's female cousins.
• Sentence A continues the examination of Jane's relationships within the family and ends the paragraph with a highlight of Jane's  hardship living with the Reeds.

 

Hence, the correct sequence is B, D, C, A

The correct answer is option 3.

The correct passage is: B. Orphaned as an infant, Jane Eyre lives at Gateshead with her aunt, Sarah Reed, as the novel opens. D. Jane is ten years old, an outsider in the Reed family.  C. Her female cousins, Georgiana and Eliza tolerate but don't love her. A. Their brother, John, is more blatantly hostile to Jane, reminding her that she is a poor dependent of his mother.

The erroneously spelled word is 'Beautycian'.

Key Points

• In this question, we need to choose the incorrectly spelled word from the given four options.
• The marked option 'Beautycian' is erroneous here, as its correct spelling is beautician.
• Beautician is a person whose job is to improve the way people look with beauty treatments.(सौंदर्य उपचार के माध्यम से सौंदर्य निखारनेवाला व्यक्ति; सौंदर्यकार, सौंदर्य-विशेषज्ञ)
• Therefore, the correct answer is option 1.

The correct answer is 'no substitution required'.

Key Points

• The given sentence is having an underlined segment.
• We need to substitute the underlined segment if it is having any error with the given context of the sentence.
• Here in the last part of the sentence, we can see the use of 'were' which shows that the given sentence is in the past tense.
• As per the rules of parallelism, the tense of the first part of the sentence should be simple past tense.
• Therefore, 'were informed' will remain like that in the underlined segment.
• The correct answer is option 3.

The correct answer is 'Dangerous'.

Key Points

• The given word 'Perilous' means full of danger or risk. (जोखिम)
• Example: The journey through the jungle was perilous.
• ​The marked option 'Dangerous' is full of danger or risk(ख़तरनाक, भयंकर)
• From the given meaning and the example sentence, it is clear that 'Dangerous' and  Perilous' are synonyms of each other.
• Therefore, the correct answer is option 1.

Additional Information 

• Stimulus: something that causes activity, development or interest ((किसी को) सक्रिय करने, विकास की ओर ले जाने या (किसी में) रुचि बढ़ाने वाली कोई बात; उद्दीपक, प्रेरक, प्रोत्‍साहनकारी तत्‍व)
• Secure: free from worry or doubt; confident (संदेह या चिंता से मुक्त; आश्‍वस्‍त, सुरक्षित)
• Impetus: something that encourages something else to happen (ऐसी वस्‍तु जो दूसरी वस्‍तु की क्रियाशीलता को बढ़ावा दे; प्रेरणा, प्रोत्‍साहन)

The correct answer is 'Godsend'.

Key Points

• The given word 'Serendipity' means the fact of finding interesting or valuable things by chance.(नसीब)
• Example: The lottery is something one wins by serendipity not by hard work.
• ​The marked option 'Godsend' is something good that happens unexpectedly, especially at a time when it is needed.(आकस्मिक सौभाग्य)
• From the given meaning and the example sentence, it is clear that 'Serendipity and 'Godsend' are synonyms of each other.
• Therefore, the correct answer is option 2.

Additional Information

• Sibilance means a hissing sound created from the letter "s" or other letter combinations used to evoke an immersive response in the reader.(सिसकारी)
• Catastrophe means an event resulting in great loss and misfortune.(तबाही)
• Surreptitious means have been done secretly.(गुप्‍त रीति से किया गया)

The correct answer is 'to'.

Key Points

• The given sentence 'Psychologists discovered that there are two routes (1) ___________ achievement: conformity and originality'  requires an appropriate preposition to be filled in the blank number 1 from the given options.
• Here, the route is a way of achieving something and the given sentence implies the same meaning.
• Route is used with the preposition 'to' like in this.
• Example: Diligent hard work is the only route to success.
• ​Therefore, the correct preposition for the given blank is 'to'.
• Hence, the correct answer is option 4.

The correct answer is: down

Key Points

• Let's look at the meaning of the given words.
• Down means to or at a lower level or place; from the top towards the bottom of something. (करने के लिए या एक निचले स्तर या जगह पर; किसी चीज के ऊपर से नीचे की ओर)
• Beside means at the side of, or next to somebody/something. (के पक्ष में, या किसी के बगल में)
• Since means at a time after a particular time in the past. (अतीत के विशिष्‍ट समय बिंदु से बाद के किसी समय में, उस के बाद)
• At is used to show where somebody/something is or where something happens. (at का उपयोग यह दिखाने के लिए किया जाता है कि कोई व्यक्ति/कुछ कहाँ है या कुछ कहाँ होता है।)
• The implied meaning of the sentence is: Conformity entails taking the popular, well-worn routes.
• So, as per the meaning of the given words, "down" should be used in the given sentence.

Therefore, the correct answer is option 1.

Complete passage: Psychologists discovered that there are two routes (1) ___________ achievement: conformity and originality. Conformity means following the crowd (2) down conventional paths and (3) ___________ the status quo. Originality is taking the road (4) __________ traveled, championing a set of novel ideas that go against the grain but (5) __________ making things better.

The correct answer is 'maintaining'.

Key Points

• The given sentence 'Conformity means following the crowd down conventional paths and (3) ___________ the status quo. 'requires an appropriate word to be filled in the blank number 3 from the given options.
• Here and is used as a connector to join these two sentences, it shows that an action or condition is happening right now, frequently, or may happen in the future.
• This shows the usage of the present continuous tense (ing form of the verb).
• The marked option 'maintaining' means to keep something in good condition by checking and repairing it regularly.
• Example: Physical activity is an important factor in maintaining fitness.
• ​The given sentence also implies the same sense as the example sentence given above, and hence the most appropriate word for the given blank number 3 is maintaining.
• Therefore, the correct answer is option 4.

The correct answer is: less

Key Points

• Let's look at the meaning of the given words.
• Quietly means without making much noise. (ज्यादा शोर किए बिना)
• Far means a long way away; distant. (बहुत दूर; दूरस्‍थ)
• Frequently means things that occur over and over, especially in a relatively short time frame. (चीजें जो बार-बार घटित होती हैं, विशेष रूप से अपेक्षाकृत कम समय सीमा में)
• Less means a smaller amount of something, to a smaller degree, or not as much. (किसी चीज की छोटी मात्रा, कम मात्रा में, या उतनी नहीं)
• The implied meaning of the sentence is: Originality involves pursuing the less-traveled path.
• So, as per the meaning of the given words, "less" should be used in the given sentence.

Therefore, the correct answer is option 4.

Complete passage: Psychologists discovered that there are two routes (1) ___________ achievement: conformity and originality. Conformity means following the crowd (2) down conventional paths and (3) ___________ the status quo. Originality is taking the road (4) less traveled, championing a set of novel ideas that go against the grain but (5) __________ making things better.

The correct answer is: ultimately

Key Points

• Let's look at the meaning of the given words.
• Superficially means ​in a way that appears to be true, real or important until you look at it more carefully. (एक तरह से जो सत्य, वास्तविक या महत्वपूर्ण प्रतीत होता है जब तक कि आप इसे अधिक ध्यान से न देखें)
• Disinterestedly means unbiased by personal interest or advantage; not influenced by selfish motives. (व्यक्तिगत हित या लाभ से निष्पक्ष; स्वार्थी उद्देश्यों से प्रभावित नहीं)
• Advertently means in a careful deliberate manner. (सावधानीपूर्वक जानबूझकर तरीके से)
• Ultimately means finally, after a long and often complicated series of events.. (अंत में, घटनाओं की एक लंबी और अक्सर जटिल श्रृंखला के बाद)
• The implied meaning of the sentence is: Promoting a group of cutting-edge concepts that go against the mainstream but eventually improve things.
• So, as per the meaning of the given words, "ultimately" should be used in the given sentence.

Therefore, the correct answer is option 4.

Complete passage: Psychologists discovered that there are two routes (1) ___________ achievement: conformity and originality. Conformity means following the crowd (2) down conventional paths and (3) ___________ the status quo. Originality is taking the road (4) less traveled, championing a set of novel ideas that go against the grain but (5) ultimately making things better. 

Important Points

• Adding the suffix-ly to the end of an adjective turns the word into an adverb. The meaning of the word does not change and still conveys the same idea.
• If the word modifies the subject, you should use an adjective.
• If the word modifies the verb, you should use an adverb.

The logic followed here is:

Logic : In each pair second word is an instrument used for fixing or installing the tool (first word)

• Nut and Bolt : Wrenches

A wrench is a tool used for fixing nut and bolt.

• Screw : Screwdriver

A screwdriver is a tool for driving screws. They have a tip that fits into the head of the screw.

• Nail : ? 

Similarly, hammer is a tool used for fixing nail.

Hence, 'Hammer' is the correct answer.

The pattern followed here is :

Hence, '92' is the correct answer.

The positional values of the English alphabet are as follows:

The pattern followed here is:

'GREAT' is coded as '2015187'

'WORK' is coded as '11181523' 

'GOING' is coded as '7149157'

Similarly, 'WELL' will be coded as:

Hence, 'option 4' is the correct answer.

The logic followed here is:

Logic : First number × 4 = Second number

Let's check each option: 

1. 25 : 100 

⇒ 25 × 4 = 100

2. 22 : 66

⇒ 22 × 4 = 88 ≠ 66 

3. 24 : 96 

⇒ 24 × 4 = 96

4) 18 : 72

⇒ 18 × 4 = 72

Hence, 'option 2' is the correct answer.

The pattern followed here is as follows:

⇒ 11 × 1 + 2 = 11 + 2 = 13

⇒ 13 × 2 + 3 = 26 + 3 = 29

⇒ 29 × 3 + 4 = 87 + 4 = 91

⇒ 91 × 4 + 5 = 364 + 5 = 369

⇒ 369 × 5 + 6 = 1845 + 6 = 1851

Hence, '1851' is the correct answer.

The logic followed here is:

Car : Bonnet 

The front part of a car is called bonnet.

Similarly, Boat : ?

The front part of a boat is called bow.

Hence, 'Bow' is the correct answer.

The figure is given below:

The shaded portion is the embedded figure.

Hence, 'option 2' is the correct answer.

The positional values of English alphabets is as follows:

The pattern followed here is:

“CLIENT” is written as “LCEITN”

“CLOSED” is written as “LCSODE”

Similarly, “FAMILY” will be written as:

Hence, 'AFIMYL' is the correct answer.

The positional values of the English alphabet is as follows:

The pattern followed here is:

Hence, 'KPJ' is the correct answer.

The correct mirror image of the given figure when the mirror placed at MN is:

Hence, 

 is the correct answer.

The logic followed here is

Logic : (First number × 2) - 7 = Second number

• 14 : 21

⇒ (14 × 2) - 7 

⇒ 28 - 7 = 21

• 47 : 87 

⇒ (47 × 2) - 7 

⇒ 94 - 7 = 87

• 34 : ? 

⇒ (34 × 2) - 7 

⇒ 68 - 7 = 61

Hence, '61' is the correct answer.

The logic followed here is:

Logic : First number + Second number = Third number

• First row: 86, 72, 158

⇒ 86 + 72 = 158

• Second row: 98, 111, 209

⇒ 98 + 111 = 209

Similarly, third row: 76, 65, ?

⇒ 76 + 65 = 141

Hence, '141' is the correct answer.

The figure is given below:

The shaded portion is the embedded figure.

Hence, 'option 2' is the correct answer.

BODMAS Rule:

Given : 62 * 17 * 6 * 81 * 23 * 2 * 37 

Lets check each option:

1) +, =, ÷, −, +, × 

62 + 17 = 6 ÷ 81 - 23 + 2 × 37

62 + 17 = 0.07 - 23 + 2 × 37 

62 + 17 = 0.07 - 23 + 74

79 = 74.07 - 23

79 ≠ 51.07

2) −, ×, =, −, +, ×

62 - 17 × 6 = 81 - 23 + 2 × 37

62 - 102 = 81 - 23 + 74

62 - 102 = 155 - 23

- 40 ≠ 132

3) =, −, ×, +, −, +

62 = 17 - 6 × 81 + 23 - 2 + 37

62 = 17 - 486 + 23 - 2 + 37

62 = 77 - 488

62 ≠ - 411

4) +, ×, −, =, ×, +

62 + 17 × 6 - 81 = 23 × 2 + 37

62 + 102 - 81 = 46 + 37

164 - 81 = 83

83 = 83 

Hence, '+, ×, −, =, ×, +' is the correct answer.

The logic followed here is:

 

Red and yellow are common in both the dices.

Clearly, Green will be on the face opposite to the White.

Hence, 'Green' is the correct answer.

The logic followed here is:

When the folder paper is opened, the cuts will appear as follow

   

Hence, option 1) is the correct answer.

The option that represents the correct order of the given words as they would appear in an English dictionary is shown below:

5. Salesman 
6. Salmon
7. Salvation
8. Sanctuary
9. Sanitization

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

The option that represents the correct order of the given words as they would appear in an English dictionary is shown below:

5. Cucumber 
6. Culinary
7. Culminate
8. Curator
9. Curriculum

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

BODMAS RULE:

Let's check each option:

1. ÷, ×, +, –, =

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

After replacing the signs with mathematical operators, we get:

⇒25 ÷ 5 × 10 + 2 - 4 = 10 

⇒5 × 10 + 2 - 4 = 10 

⇒50 + 2 - 4 = 10

⇒52 - 4 = 10

⇒ 48 ≠ 10

2.×, ÷, –, +, =

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

After replacing the signs with mathematical operators, we get:

⇒25 × 5 ÷ 10 - 2 + 4 = 10  

⇒25 × 0.5 - 2 + 4 = 10 

⇒12.5 - 2 + 4 = 10

⇒ 14.5 ≠ 10

3. +, –, ÷, ×, =

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

After replacing the signs with mathematical operators, we get:

⇒25 + 5 - 10 ÷ 2 × 4 = 10  

⇒25 + 5 - 5 × 4 = 10

⇒25 + 5 - 20 = 10

⇒ 10 = 10

4. ÷, ×, –, +, =

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

After replacing the signs with mathematical operators, we get:

⇒25 ÷ 5 × 10 - 2 + 4 = 10 

⇒5 × 10 - 2 + 4 = 10 

⇒50 - 2 + 4 = 10

⇒ 52 ≠ 10

Hence, "+, –, ÷, ×, =" is the correct answer.

The logic followed here is:

Second number = (First number)³ + (Third number)²

First row- 2, 57, 7 → 2³ + 7² = 8 + 49 = 57

Second row- 6, 225, 3 → 63 + 32 = 216 + 9 = 225

Similarly,

Third row- 5, ?, 2 → 53 + 22 = 125 + 4 = 129

Hence, 129 is the correct answer.

The least possible Venn diagram is as follows:

Conclusions:

I. All compasses are erasers. → True (because all sharpeners are erasers and all compasses are sharpeners.)

II. Some compasses are pencils. → False (because no compass is pencil, all compasses are sharpeners.)

III. Some erasers are compasses.  → True (because sharpeners, pencils, compasses, all are erasers.)

Hence, “Only conclusions I and III follow”.

Given: A B Z _ P A B _ K P A B X K _ A B _ K P 

Let's check each option:

1) A C B Z → A B Z A P - A B C K P - A B X K B - A B Z K P 

2) A Y Z W → A B Z A P - A B Y K P - A B X K Z - A B W K P

3) K Y P W → A B Z K P - A B Y K P - A B X K P - A B W K P

• Here we can see a pattern.
• 3^rd letter is decreasing by -1, rest letters are the same.
• Z - 1 = Y; Y - 1 = X; X - 1 = W

4) K C Z W → A B Z K P - A B C K P - A B X K Z - A B W K P

Hence, ‘K Y P W’ is the correct answer.

The logic followed here is:

1724 - 8 = 1716

1716 - 27 = 1689

1689 - 64 = 1625

1625 - 125 = 1500

1500 - 216 = 1284

Hence, 1284 is the correct answer.

The logic followed here is:

First number ÷ 6 = Second number

1) 42 : 7 ⇒ 42 ÷ 6 = 7

2) 36 : 6 ⇒ 36 ÷ 6 = 6

3) 48 : 8 ⇒ 48 ÷ 6 = 8

4) 24 : 8 ⇒ 24 ÷ 6 = 4 ≠ 8

Hence, "24 : 8" is the odd one.

The number of triangles in given figure is as shown below

∴ There are 26 triangles in the given figure.

Hence, the correct answer is "26".

FORMULA USED:

Range = Highest number - lowest Number

Average =\() sum of number/total number

CALCULATIONS:

For finding the range,

we have to first arrange the number in ascending order

The range of the number of participants in the different Olympiads from College C is

⇒ 125,80,250,150,120 

arrange in ascending order, we get

⇒ 80, 125, 120, 150, 250

For the range of college C

⇒ Range = Highest Number - Lowest Number

⇒ 250 - 80

⇒ 170

For an average student in college E

⇒ average = sum of number/total number $=\frac{112+105+180+80+183}{5}=\frac{660}{5}=132$

 The difference between the Range of college C and the average of College E = Range- Average

⇒ 170 - 132

⇒ 38

∴ The difference is 38.

GIVEN:

The Group Leader of a group of 6 students reported that their average weight is 46 kg

For their individual weights, 5 of them answered: 50 kg, 52 kg, 40 kg, 44 kg, 48 kg

FORMULA USED:

 average= $\frac{sumof weightofallstudent}{total no of student}$ 

CALCULATIONS:-

⇒ Let the weight of the 6^th student= x kg

⇒ The average weight of all student

⇒  average=$\frac{sum\space of\space weight \space of\space all\space student}{total \space no \space of\space student}$

⇒ 46 = $\frac{50+52+40+44+48+x}{6}$ 

⇒ 276 = 234 + x

⇒ x =  276 - 234 = 42kg

⇒ Hence, The weight of the 6^th student is 42kg

GIVEN:

The number is 23_45678

Divisible by 22

Concept Used:

The divisibility rule of 11 is the difference between the sum of the odd place of a number and the sum of even place is equal to 0 or 11

The divisibility rule of 2 is the last digit of the number must be divisible by 2

CALCULATIONS:-

Let the blank place digit is x

If a number is divisible by 22 then the number also divisible by 2 and 11

Then the divisibility rule of 2 is the last digit of the number must be divisible by 2

The last digit of the number is divisible by 2

It satisfies the divisibility rule of 2

 For the divisibility rule of 11

⇒ Sum of digits of odd place = 2 + x + 5 + 7 = 14 + x

⇒ Sum of digits of even place = 3 + 4 + 6 + 8 = 21

The difference is,

⇒ 21 - (14 + x) = either 0 or 11

For 0

⇒ 21 - (14 + x) = 0

⇒ 21 - 14 - x = 0

⇒ x=7

For 11

⇒ 21 - (14 + x) = 11

⇒ 21 - 14 - x = 11

⇒ x = 7 - 11

⇒ x = -4

The digit cannot be negative

⇒ x = 7

Hence, The smallest natural number to be filled in the blank is 7

GIVEN:

The cost price of 70 articles is equal to the selling price of 40 articles

FORMULA USED:

 profit%=$\frac{profit}{costprice}\times 100$

CALCULATIONS:

The cost price of 70 articles is equal to the selling price of 40 articles

⇒ CP x 70= SP x 40

⇒ $\frac{CP}{SP}=\frac{4}{7}$

Let  CP=Rs.4 and SP=Rs.7

⇒ Profit = SP - CP = 7 - 4 = Rs. 3

Profit Percentage is

⇒ Profit% $=\frac{profit}{costprice}\times 100=\frac{3}{4}\times 100=3\times 25=75$

⇒ The Profit percentage is 75%

Shortcut Trick

Let the Selling Price (SP) of 1 article be 1 unit.

Total SP of 80 articles = 80 units.

Loss = SP of 6 articles = 6 units.

Cost Price (CP) = SP + Loss = 80 + 6 = 86 units.

Given 86 units = ₹11,180 ⇒ 1 unit = 11,180 ÷ 86 = ₹130.

∴ The correct answer is ₹130.

Alternate Method

Given: Total CP = ₹11,180, Number of articles = 80, Loss = 6 × SP.

Formulas: Loss = CP − SP | SP of 1 article = Total SP ÷ Quantity.

⇒ Loss = CP − SP

⇒ 6 × SP₁ = 11,180 − 80 × SP₁

⇒ 86 × SP₁ = 11,180

⇒ SP₁ = 11,180 ÷ 86

⇒ SP₁ = ₹130

∴ The correct answer is ₹130.

Additional Information

Loss in terms of SP

When loss is given as SP of 'n' articles, CP = (Quantity + n) × SP of 1 article.

Profit in terms of SP

When profit is given as SP of 'n' articles, CP = (Quantity − n) × SP of 1 article.

GIVEN:

a + b + c =10

ab + bc + ca = 30

FORMULA USED:

(a + b + c)2 = (a2 + b2 + c2 + 2(ab + bc + ca))

CALCULATIONS:

⇒ a + b + c =10 & ab + bc + ca = 30

⇒ (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

⇒ 10² =  a2 + b2 + c2 + 2(30)

⇒ 100 - 60 =  a2 + b2 + c2 

⇒ a2 + b2 + c2 = 40 

∴ The value of  a2 + b2 + c2  is 40.

Given:

Percentage of sugar in 700 grams cane sugar solution = 60%

Required percentage = 75%

Calculation:

⇒ Amount of sugar in 700 gms solution = 60% of 700

⇒ Amount of sugar in 700 gms solution = $\frac{60}{100}\times 700=60\times 7=420$ grams

⇒ Let x grams of sugar is added in the solution.

⇒ According to the question,

⇒ $\frac{420+x}{700+x}=\frac{75}{100}$

⇒ 4(420 + x) = 3(700 + x)

⇒ 1680 + 4x = 2100 + 3x

⇒ 4x – 3x = 2100 – 1680

⇒ x = 420 grams

Therefore, 420 grams of sugar should be added in to solution to make the sugar percentage equals to 75%.

Given:

The sum of the two numbers is 25

Their product is 144

Formula used:

(a - b)² = (a + b)² - 4ab

Calculation:

We have

x + y = 25           -----(1)  

⇒ xy = 144          -----(2)

By using the above identity

(x - y)² = (x + y)² - 4xy

(x - y)2 = (25)2 - 4 × 144

(x - y)2 = 625 - 576

(x - y)² = 49

(x - y) = 7

∴ The answer is 7.

Given: 

A = 24 days 

B = 80 days

B works alone for 2 days and A works alone on the 3^rd day  

Formula Used:

Work = Time × Efficiency

Calculation:

A = 24 days

B = 80 days

B works alone for 2 days and A works alone on the 3^rd day.

Work completed in 3 days = $2× \frac{1}{80}+\frac{1}{24}$

Work completed in 3 days = $\frac{1}{40}+\frac{1}{24}=\frac{3+5}{120}=\frac{8}{120}=\frac{1}{15}$

Work completed in 3 days = 15 units  

Total work is completed in = $3× 15=45$ days

 

∴ the whole work is completed in 45 days.

Shortcut Trick        Time        Work      Efficiency 

⇒ A      24         240             10   

⇒ B     80          240              3 

B works alone for 2 days and A works alone on the 3^rd day

work done in 3 days = 3 + 3 + 10 = 16

⇒ T = 240/16

⇒ T = 15 times

⇒ T = 15 × 3

⇒ T = 45 days 

∴ The time taken to complete the task is 45 days.

Given:

P=1000, R=20%, T= 1year

Formula used:

SI =  $\frac{P× R× T}{100}$

A = $P(1+\frac{R}{100})^T$

P= Principal

R= Rate of interest

T= Time

A = Amount

Calculation:

for compounded half-yearly, the rate gets halved and time gets doubled

⇒ R = 20/2

⇒ R = 10%

⇒ T = 1 × 2

⇒ T = 2 years

For SI

⇒ SI =  $\frac{P× R× T}{100}$

⇒ SI = $\frac{1000×10×2}{100}$

⇒ SI = Rs. 200

For CI

⇒ A = $P(1+\frac{R}{100})^T=1000(1+\frac{10}{100})^2$

⇒ A = $1000(1+\frac{1}{10})^2$

⇒ A = $1000(\frac{11}{10} × \frac{11}{10})$

⇒ A = Rs. 1210

⇒ I = A - P

⇒ I = 1210-1000

 

⇒ I = Rs. 210

Difference = CI - SI

⇒ 210-200

⇒ Rs.10

∴ The answer is Rs. 10.

Given:

The radius of the hemisphere is 21 cm

Formula used:

volume of hemisphere= ​​​​$\frac{2}{3}× \pi× r^3$​​​​​​

Calculation:

The radius of the hemisphere=21cm

The volume of hemisphere,

⇒ $\frac{2}{3}× \pi× r^3$

⇒ $\frac{2}{3}× \frac{22}{7}× 21× 21× 21$

⇒ 2 ×  22 × 3 × 7 × 21

⇒ 19404 cm³

The volume of the hemisphere is 19404 cm3.

Given:

Rakesh runs 4/3 times as fast as Mukesh 

Mukesh has a lead of 60 m 

Formula used:

Distance = Speed × Time 

Calculation:

Here, let us assume the speed of mukesh be 3y 

Then, rakesh speed is 4/3 times = 4/3× 3y = 4y

Now, let us take total distance be x 

As, rakesh gives a lead of 60m  to mukesh 

So, distance of rakesh covered = x 

Distance covered by mukesh =  x - 60

According to the given question, both will meet at the same time 

So, 

Distance  is directly proportional to Speed 

⇒ x/ ( x - 60) = 4y/3y 

⇒ x/( x - 60) = 4/3 

⇒ 3x = 4x- 240 

⇒ x = 240 m

Hence, at the distance of 240m from the starting point both of them will meet .

GIVEN:-

 

Formula Used:

Percentage=$\frac{intital value-final value}{initial value}\times 100$

CALCULATIONS:- 

From the above table,

Quality of food grains in 2018 is 70 (1000 ton)

Quality of food grains in 2019 is 65 (1000 ton)

Percentage decreased $=\frac{intital value-final value}{initial value}\times 100=\frac{70-65}{70}=\frac{5}{70}\times100=7.14$

The percentage drop in the production of food grains from 2018 to 2019 is 7.14

Given:

x2 = b - ax and x3(x3 + c) = d

Concept used:

If ax + b = c 

And 2x + 1 = 3 then, by comparison method, we have:

a = 2

b = 1

and c = 3

Calculations:

x2 = b - ax

⇒x2 - b = (- ax)

On dividing by x,

⇒x - $\frac{b}{x}$ = (- a) ---------------(1)

On cubing both sides, we get:

⇒(x - $\frac{b}{x}$)³ = (- a)³

⇒x³ - $\frac{b³}{x³}$ - 3b(x - $\frac{b}{x}$) = - a³

From equation (1), we have:(x - $\frac{b}{x}$) = - a

⇒x3 - $\frac{b³}{x³}$ - 3b(- a) = - a3

⇒x3 - $\frac{b^3}{x³}$ = - (a3 + 3ab) -----------(2)

And x3(x3 + c) = d

⇒(x3 + c) = $\frac{d}{x³}$

⇒(x3 - $\frac{d}{x³}$) = (- c) ---------------(3)

Now, by using the concept of comparison method from equations(1) and (2) and (3), we get:

Coefficient of (- $\frac{1}{x³}$) = d = b³

And Constant terms = - c = - (a3 + 3ab) 

⇒c = (a3 + 3ab) 

∴ The Required value of c = (a3 + 3ab) and d = b³. 

Shortcut Trick 

(a - b)³ = a³ - 3ab(a-b) - b³

⇒(x - $\frac{b}{x}$)3 = (- a)3  

⇒x3 - $\frac{b^3}{x³}$ = - (a3 + 3ab) 

⇒ x³ + (a3 + 3ab) = $\frac{b^3}{x³}$ 

⇒x³ (x3 + (a3 + 3ab) =b³ 

compairing the equation with x3(x3 + c) = d

we get c = (a3 + 3ab) and d = b3

GIVEN:

A bike is purchased for ₹50,000

Its rate depreciates at 10% annually

FORMULA USED:   

 Interest= $P\times (1+\frac{R}{100})^T$

Where P= The amount lent

R= Interest at the amount lent

T= Year amount lent for

CALCULATIONS:

⇒ The rate of interest depreciates annually is 

⇒  The value of the bike after T years= $its \space value \space T\space years\space ago ×(1− \frac{R}{100})^ T$

⇒  $36450=50000\times(1+\frac{(-10)}{100})^T$

⇒  $729=1000\times(1-\frac{1}{10})^T$

⇒  $\frac{729}{1000}=(\frac{9}{10})^T$

⇒ $(\frac{9}{10})^3 = (\frac{9}{10})^T$

⇒ On comparing both sides, we get

⇒ T = 3yrs                                                  

⇒ The value of the bike will be ₹36,450 after 3 years

Given:

2945 ÷ 19 – 11 × 5 = 29 + a

Formula used:

Calculation:

Simplifying the given equation and solving for a,

2945 ÷ 19 – 11 × 5 = 29 + a

155 - 55 = 29 + a

a = 100 - 29 = 71

∴ The value of a is 71.

Given:

15 kg of sugar cost ₹600

Formula used:

Rate of an item = $\frac{\text{amount of some quantity}}{\text {quantity}}$

Calculation:

Cost of 1kg sugar (in Rs.)= $\frac{600}{15}= 40$

∴ The cost of 25 kg of sugar is 40 × 25 = Rs. 1000.

Shortcut Trick

Cost Price (CP) = ₹380 and Loss = ₹140.

Selling Price (SP) = CP − Loss = 380 − 140 = ₹240.

Since a 20% discount is given on the Marked Price (MP), SP = 80% of MP.

80% of MP = ₹240 ⇒ 100% of MP = (240 ÷ 80) × 100 = 3 × 100 = ₹300.

∴ The correct answer is ₹300.

Alternate Method

Given: CP = ₹380, Loss = ₹140, Discount% = 20%.

Formulas: SP = CP − Loss | MP = SP × 100 ÷ (100 − Discount%)

⇒ Step 1: Calculate Selling Price (SP) = CP − Loss = 380 − 140 = 240.

⇒ Step 2: Relate SP to Marked Price (MP). SP = MP × (1 − 20/100) = MP × 0.8.

⇒ Step 3: MP = 240 ÷ 0.8 = 300.

∴ The correct answer is ₹300.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP). Formula: SP = MP − Discount.

Loss and Selling Price

When Cost Price (CP) is greater than Selling Price (SP), a loss occurs. Formula: Loss = CP − SP.

Shortcut Trick

For a sphere circumscribing a cube, its diameter is equal to the body diagonal of the cube.

Diameter = a√3 = 14√3 cm ⇒ Radius (r) = 7√3 cm.

Volume of the sphere = (4/3) × π × r³

Volume = (4/3) × (22/7) × (7√3)³ = 4312√3 cm³.

∴ The correct answer is 4312√3 cm³.

Alternate Method

Given:

Side of the cube (a) = 14 cm

Formula Used:

Diameter of a circumscribed sphere (D) = Body diagonal of the cube = a√3

Volume of a sphere = (4/3)πr³

Calculations:

⇒ Diameter of the sphere (D) = 14√3 cm

⇒ Radius of the sphere (r) = D ÷ 2 = 7√3 cm

⇒ Volume of the sphere = (4/3) × (22/7) × (7√3)³

⇒ Volume = (4/3) × (22/7) × (343 × 3√3)

⇒ Volume = 4 × 22 × 49 × √3

⇒ Volume = 88 × 49 × √3

⇒ Volume = 4312√3 cm³

∴ The correct answer is 4312√3 cm³.

Additional Information

Sphere Circumscribing a Cube

The sphere passes through all eight vertices of the cube. Its diameter is equal to the body diagonal: D = a√3.

Sphere Inscribed in a Cube

The sphere touches all six faces of the cube. Its diameter is equal to the side length of the cube: D = a.

Key Mensuration Formulas

Total Surface Area of a Cube = 6a² | Total Surface Area of a Sphere = 4πr².

Given:

The height and slant height of a right circular cone are 8 cm and 10 cm, respectively

Formula used:

Volume of the cone = $\frac{1}{3}\pi \left( l^2- h ^2\right)h$, where 'l' and 'h' are the slant height and height of the cone.

Calculation:

Volume of the cone = $\frac{1}{3}\times \frac{22}{7}\times \left ( 10^2 -8^2 \right)\times 8 = 301.71cm^3$

∴ The volume of the given cone is 301.71 cm3

Given:

A family spends ₹240 per month to buy sugar. A rise of 25% in the price of sugar compels the family to reduce the monthly consumption of sugar by 1.5 kg as it decides to spend the same amount of money on purchase of the commodity.

Formula used:

Rate × quantity = total cost

Calculation:

Let the old price of the sugar per kg be x and the number of kg of sugar purchased by the family be y.

Then, xy = 240 

After the new price, $1.25x(y-1.5)=240$

Substituting $y=\frac{240}{x}$ and solving for x,

$1.25x\left (\frac{240}{x}-1.5\right)=240$

$1.25×240-1.25× 1.5x=240$

$x=\frac{60}{1.25 × 1.5}=32$

125% of 32 = 1.25 × 32 = 40

∴ The increased price of the sugar is Rs. 40 per kg.

Given:

A table showing the numbers of laptops of three different brands sold from four different multi-brands store in the city during a certain month is given.

Formula used:

percentage difference of x from y = $\frac{y-x}{x}\times 100$

Calculation:

$\frac{50-45}{45}\times 100=\frac{1}{9}\times 100=11.1\%$

∴ The number of Lenovo Laptop sold by stores A during the given month is 11.1% more than the number of Dell laptops sold by Store D during the same month.

Given:

∆ABC is inscribed in a circle and DE is tangent to it.

Formula used:

The alternate segment theorem,

• The angle between a tangent and a chord at the point of contact is equal to the angle made by the chord in the alternate segment of the circle.

Calculation:

According to the alternate segment theorem, the angle between a tangent and a chord at the point of contact is equal to the angle made by the chord in the alternate segment of the circle

⇒∠ABC = ∠ACD

∴  The Required angle is ∠ABC.

Given:

$\frac{x - xcosec^230^{\circ}}{1 + cosec^230^{\circ}}$ = cos260° + 4cot245° – sec260°

Concept Used:

Trigonometric Values Substitution

Calculation:

⇒ $\frac{x - xcosec^230^{\circ}}{1 + cosec^230^{\circ}}$ = cos260° + 4cot245° – sec260°

⇒ Putting the trigonometric values, we get

⇒ cosec 30º = 2, cos 60º = $\frac{1}{2}$, cot 45º = 1, sec 60º = 2

⇒ $\frac{x-x\times 2^2}{1+2^2}=\left(\frac{1}{2}\right)^2 + 4 \times 1 -2^2$

⇒ $\frac{-3x}{5}=\frac{1}{4}+ 4-4$

⇒ $-3x=\frac{1}{4}\times 5=\frac{5}{4}$

⇒ $x=-\frac{5}{4\times 3}=-\frac{5}{12}$

Hence, the required value of x is $-\frac{5}{12}$.

Given:

An article price was reduced by 25%.

Formula used:

percentage increase = $\frac{\text{new price}}{\text{old price}}\times 100 - 100$

Calculation:

Let the old price of the article be Rs.100, which reduced to Rs. 75.

percentage increase = $\frac{100}{75}\times 100-100 =133.3 -100=33.3$

∴ The present price of the article must be increased by$33\frac{1}{3}\%$ to restore its former value.

The correct answer is Sonu Sood.

Key Points

• Sonu Sood's autobiography 'I am no Messiah' is out now; Rajkumar and Aparshakti congratulate the actor.
• Sonu Sood, who has worked towards helping the needy during the ongoing Covid-19 pandemic has inspired and won the hearts of many.
• The book will be co-authored by Meena Iyer.

Additional Information

• Sachin Ramesh Tendulkar is an Indian former international cricketer who captained the Indian national team.
• He is regarded as one of the greatest batsmen in the history of cricket.
• Paramahansa Yogananda was an Indian Hindu monk, yogi and guru who introduced millions to the teachings of meditation and Kriya Yoga through his organization.
• Avul Pakir Jainulabdeen Abdul Kalam was an Indian aerospace scientist and statesman who served as the 11^th President of India from 2002 to 2007.
• He was born and raised in Rameswaram, Tamil Nadu and studied physics and aerospace engineering.