SSC CHSL Tier-1 2024: Official Paper (Held On: 08 Jul, 2024 Shift 4) (Previous Year Paper)

The correct answer is Option 4)

Key Points

• In the given sentence, the present continuous form of the verb 'are working' is incorrect.
• The correct tense to use here is the present perfect continuous tense to indicate the duration of an action that started in the past and is still continuing.
• Therefore, the correct form should be 'have been working' instead of 'are working'.

Hence, the correct statement is: How long have you been working for your current employer and why don’t you look for better opportunities?

Additional Information

• The present perfect continuous tense is used to show that something started in the past and has continued up until now. The structure is subject + have/has + been + verb-ing.
• Example: I have been reading this book for two hours.
• The present continuous tense is used to describe actions that are happening at the moment of speaking. The structure is subject + am/is/are + verb-ing.
• Example: She is reading a book now.

The correct answer is Option 4)

Key Points

• In the fourth part of the given sentence, the phrase 'dropped of' is incorrect.
• The correct phrase should be 'dropped off'.
• The term 'dropped off' means to fall asleep or to leave something at a specific place.
• Therefore, the correct form should be used in place of the incorrect phrase 'dropped of'.

Hence, the correct statement: The judges eliminated the classical singer, as she dropped off in the middle of the competition.

Additional Information

• The term 'dropped off' can be used in different contexts:
• Example: I dropped off the package at the post office.
• Example: He dropped off to sleep during the movie.
• Ensure the correct usage of phrases to maintain grammatical accuracy in sentences.

The correct answer is Option 1)

Key Points

• The word "each" refers to every one of two or more people or things, considered separately. (प्रत्येक)
• Example: Each student was given a certificate for participation.
• "Each" implies that every individual member of a group is being referred to separately. (प्रत्येक)
• Example: Each of them received a gift.

Therefore, the correct answer is Option 1)

Additional Information

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

• None (कोई नहीं): Not any.
• Example: None of the answers were correct.
• They (वे): Used to refer to two or more people or things previously mentioned or easily identified.
• Example: They are going to the park.
• All (सभी): Used to refer to the whole quantity or extent of a particular group or thing.
• Example: All the students passed the exam.

The correct answer is Option 1)

Key Points

• In the second part of the given sentence, the use of the article 'an' is incorrect.
• The correct article to use with 'east' is 'the' because 'east' is a specific direction.
• Therefore, the correct form should be 'in the east' instead of 'in an east'.

Hence, the correct statement is: The sun rises in the east and sets in the west.

Additional Information

• In English grammar, directions (north, south, east, west) are usually preceded by the definite article 'the' when referring to a specific region or direction.
• Example: He traveled to the north of the country.

The correct answer is Option 2)

 

Key Points

• The word "custom" best fits in the context, referring to a traditional practice or a usual way of doing things in Europe at that time.

Therefore, the correct answer is Option 2)

Additional Information

• The word "motive" refers to a reason for doing something, which doesn't fit the context here.
• The word "conventions" refers to widely accepted ways or standards, which is close but not as precise as "custom".
• "Ritualistic" refers to the characteristic of rituals, which implies more ceremonial actions rather than just traditional practices.

The correct answer is Option 1)

Key Points

• Context of the Sentence: The text describes the falcons as "long-winged birds of prey".
• Meaning of 'Resembling': The word "resembling" means 'looking like' or 'similar to'.
• Relevance to the Sentence: By saying falcons are resembling hawks, it clarifies that falcons look similar to hawks.
• Simplification for Understanding: Many readers may not know what long-winged birds of prey are by specific names, so the comparison to hawks helps visualize their appearance better.
• Logical Fit: The sentence makes sense with "resembling" as it seamlessly integrates the similarity for better comprehension.

Therefore, the correct answer is 'Option 1'.

Additional Information

• 'Favouring': Would imply preference, which is not the intended meaning here.
• 'Echoing': This means to repeat or imitate sound, contextually irrelevant.
• 'Subjugating': Means bringing under control, which does not fit the description context.

The correct answer is Option 1)

Key Points

• Context of the Sentence: The text describes the behavior of falcons trained to stay on their masters' wrists.
• Meaning of 'Perch': The word "perch" means to rest or sit on something, typically used for birds sitting on branches or similar objects.
• Relevance to Falcons: Falcons are birds, so "perching" is a suitable term describing their trained behavior.
• Visual Accuracy: Using "perch" helps readers accurately visualize a bird sitting calmly on a person's wrist, a common practice in falconry.
• Behavior Description: "Perch" implies a stable and patient position, aligning with the falcon's trained behavior of waiting for commands.
• Clarity and Precision: "Perch on their master's wrist" conveys the intended meaning clearly and precisely.

Therefore, the correct answer is 'Option 1'.

Additional Information

• 'Sitting': Too generic and does not specifically describe the bird's behavior.
• 'Lurch': Means to make an abrupt, unsteady movement, which is not relevant here.
• 'Chirp': Refers to the sound birds make, not their sitting behavior.

The correct answer is Option 3)

 

Key Points

• Context of the Sentence: The text describes the falcons' action of quickly attacking their prey.
• Meaning of 'Dart': The word "dart" means to move swiftly or suddenly, which is commonly used to describe the fast movement of birds or other swift creatures towards their target.
• Relevance to Falcons: Falcons are known for their speed and precision when hunting, making "dart" an ideal term to describe their rapid attack.
• Visual Accuracy: "Dart" vividly portrays the quick, sharp movement of a falcon closing in on its prey.
• Hunting Behavior: The use of "dart" reflects the characteristic hunting style of falcons, emphasizing their agility and swiftness.
• Clarity and Precision: "Dart at their prey" provides a clear and precise description of the falcons' action, enhancing the reader's understanding of their hunting method.

Therefore, the correct answer is 'Option 3'.

Additional Information

• 'Flight': Refers to the act of flying, which is too general and does not capture the specific action of attacking prey.
• 'Dashed': Means to run or move quickly, but is less precise and commonly used for ground movement.
• 'Leapt': Implies a jumping action, which is not suitable for the aerial dive of a falcon.

The correct answer is Option 3)

Key Points

• Context of the Sentence: The text describes the action of a messenger being sent to let Henry know about his election as king.
• Meaning of 'Inform': The word "inform" means to tell someone about something in a straightforward manner, particularly relevant when imparting important news.
• Relevance to the Situation: "Inform" is appropriately used to describe the act of conveying crucial and official news, such as being elected king.
• Clarity: "Inform" clearly denotes the act of communicating significant information.
• Tone: Using "inform" maintains the formal tone of the historical context.
• Direct Communication: "Inform" signifies a direct and clear way of conveying essential information, which suits the narrative.

Therefore, the correct answer is 'Option 3'.

Additional Information

• 'Nullify': Means to make something invalid, which is unrelated to informing someone of an event.
• 'Communicate': Although it means to share information, it is broader and less direct than "inform".
• 'Convey': While it can mean to communicate, its usage here would be less direct than "inform" and can imply a wider range of activities.

The correct answer is Option 1)

Key Points

• In the second part of the given sentence, the word 'allowed' is incorrect.
• The sentence context implies a future event, hence a future tense form should be used.
• The correct form should indicate that men will be eligible to participate for the first time in the 2024 Paris Games.
• Therefore, the correct phrase should be 'are eligible' instead of 'allowed'.

Hence, the correct statement is: Men are eligible for Olympic artistic swimming for the first time at the 2024 Paris Games, the IOC confirmed on Thursday.

Additional Information

• When indicating future events, it is crucial to use the appropriate tense to avoid confusion.
• The term 'are eligible' is suitable for indicating a state that will be true in the future, aligning with the context of the 2024 Paris Games.

The correct answer is Option 1)

Key Points

• The word "Consciencious" is incorrectly spelt. The correct spelling is "Conscientious" which means wishing to do one's work or duty well and thoroughly. (ईमानदार)
• Example: She is a conscientious student who always completes her assignments on time.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Conscience (अंतरात्मा): A person's moral sense of right and wrong.
• Example: His conscience wouldn't allow him to lie to his parents.
• Conscious (सचेत): Being aware of and responding to one's surroundings; awake.
• Example: She was conscious of the fact that everyone was staring at her.
• Conspicuous (प्रकट): Standing out so as to be clearly visible.
• Example: The red dress made her conspicuous in the crowd.

The correct answer is Option 4)

Key Points

• The idiom "to read between the lines" means:
• To understand or find the hidden meaning in something. (छिपे हुए अर्थ को समझना)
• Example: When you read between the lines of her letter, you can tell that she is not happy with the situation.
• "To grasp the hidden meaning" refers to understanding the underlying or implicit meaning that is not immediately obvious. (गुप्त अर्थ को समझना)
• Example: The detective was able to grasp the hidden meaning behind the suspect's words.

Therefore, the correct meaning of the given idiom is: To grasp the hidden meaning.

Additional Information

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

• To read aloud (जोर से पढ़ना): To read something so that other people can hear you.
• Example: The teacher asked the student to read aloud the passage from the book.
• To whisper (फुसफुसाना): To speak very softly using one's breath without using one's vocal cords.
• Example: She had to whisper the secret into her friend's ear.
• To read without concentration (ध्यान के बिना पढ़ना): To read something without paying full attention.
• Example: He was so distracted that he read the entire page without concentration.

The correct answer is Option 3)

Key Points

• The word "industrious" means hardworking and diligent. (मेहनती)
• Example: Her industrious nature earned her the title of Employee of the Month.
• "Lazy" refers to someone who is unwilling to work or use energy. (आलसी)
• Example: He is too lazy to clean his room.

Hence, we can infer that the opposite of 'industrious' is 'lazy'.

Additional Information

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

• Hazy (धुंधला): Lacking clarity.
• Example: The details of the contract were hazy and unclear.
• Efficient (कुशल): Achieving maximum productivity with minimum wasted effort or expense.
• Example: The new machine is much more efficient than the old one.
• Pricey (महंगा): Expensive.
• Example: The restaurant was too pricey for our budget.

The correct answer is Option 1)

Key Points

• The word "Terminate" means to bring something to an end or halt. (समाप्त करना)
• Example: The company decided to terminate the contract due to non-compliance.
• "Begin" refers to the start of something; the opposite of ending or terminating. (आरंभ करना)
• Example: The ceremony will begin at 10 AM sharp.

Hence, we can infer that the opposite of 'terminate' is 'begin'.

Additional Information

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

• Mark (चिह्नित करना): To make a visible impression or trace on something.
• Example: Please mark your attendance on the sheet.
• Conclude (समाप्त करना ): To bring something to an end, similar to terminate.
• Example: The meeting will conclude at 5 PM.
• Die (मरना): To cease to live or exist.
• Example: The plant will die without water.

The correct answer is Option 2)

Key Points

• The phrase "right as rain" means in excellent health or perfectly fine. (बिल्कुल ठीक)
• Example: After a good night's sleep, he felt right as rain and ready to tackle the day.
• "Fit and in excellent health" refers to someone who is in a good physical condition and is healthy. (स्वस्थ और उत्तम स्वास्थ्य में)
• Example: The doctor confirmed that the athlete was fit and in excellent health to participate in the marathon.

Hence, we can infer that "right as rain" is an appropriate substitute for "fit and in excellent health".

Additional Information

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

• Left out in the cold (ठंड में छोड़ दिया): Ignored or excluded from a group or activity.
• Example: He felt left out in the cold when he wasn't invited to the meeting.
• Up in the arms (हाथों में ऊपर): Very angry or upset.
• Example: The community was up in the arms over the proposed construction project.
• On cloud nine (नौवें बादल पर): Extremely happy.
• Example: She was on cloud nine after hearing the news of her promotion.

The correct answer is Option 2)

Key Points

• The word "Their" is a possessive adjective used to indicate that something belongs to or is associated with a group of people or things. (उनका)
• Example: The students left their books on the table.
• "Their" is used to show possession, indicating that the skills belong to the artists. (उनका)
• Example: Their house is the one with the red door.

Therefore, the correct answer is: Option 2)

Additional Information

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

• There (वहां): Refers to a place or position.
• Example: The book is over there on the shelf.
• They’re (वे हैं): Contraction of "they are".
• Example: They’re going to the park this afternoon.
• They (वे): Used to refer to two or more people or things previously mentioned or easily identified.
• Example: They are very talented artists.

The correct answer is Option 1)

Key Points

• The word "adressed" is incorrectly spelt. The correct spelling is "addressed".
• Meaning: To speak to someone directly or to write the name and address on an envelope. (पता लिखना या संबोधित करना)
• Example: The principal addressed the students during the assembly.
• Correct Word: Addressed (संबोधित किया)
• Example: She addressed the letter to her friend in New York.

Therefore, the correct answer is Option 1)

Additional Information

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

• Special (विशेष): Better, greater, or otherwise different from what is usual.
• Example: She received a special award for her outstanding performance.
• Gathering (सभा): An assembly or meeting, especially a social or festive one or one held for a specific purpose.
• Example: There was a large gathering at the community hall.
• Perfectly (संपूर्ण रूप से): In a manner or way that could not be better.
• Example: She performed the dance perfectly.

The correct answer is Option 2)

Key Points

• "main" refers to the most important or central part of something. (मुख्य)
• Example: The main objective of the project is to improve community health.

Hence, we can infer that the appropriate word to fill in the blank is 'main'.

Additional Information

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

• Mane (अयाल): The long hair on the neck of a horse, lion, or other animal.
• Example: The horse's mane was neatly braided for the show.
• Mean (मतलब): To signify or intend something.
• Example: What do you mean by that statement?
• Mine (मेरा): Possessive form referring to something that belongs to the speaker.
• Example: This book is mine.

The correct answer is Option 4)

Key Points

• The phrase 'look thorough' is incorrect.
• The correct phrase that fits the context is 'look after', which means to take care of someone.
• Look after is a phrasal verb commonly used to denote taking care of someone or something.
• Example: She looks after her younger brother when her parents are at work.
• Therefore, the correct phrase is 'look after'.

Hence, the correct statement is: As there was no one to look after the orphan, he had to take refuge in the orphanage.

Additional InformationThe other options do not fit the context:

• look through: to examine or read something quickly.
• look upon: to regard or consider.
• look down upon: to regard with contempt.
• Using the correct phrasal verb is essential for conveying the intended meaning accurately.

The correct answer is Option 3)

Key Points

• In the given sentence, the phrase "I will preparing of" is incorrect.
• The correct phrase should be "I have to prepare for".
• Using the correct form of the verb "prepare" and the correct preposition "for" is essential for proper grammar.

Hence, the correct statement is: I cannot go out tonight because I have to prepare for my interview tomorrow.

Additional Information

• It is important to use the correct verb form and preposition in sentences to convey the intended meaning clearly and correctly.
• In this case, "prepare" is the correct verb form to use, and "for" is the appropriate preposition.

The correct answer is Option 3)

Key Points

• The word 'effects' is commonly misused in place of 'affects'.
• 'Affects' is a verb meaning to have an impact or influence on something.
• 'Effects' is a noun meaning the result or outcome of a particular influence.
• Therefore, 'affects' should be used in the given sentence.

Hence, the correct answer is 'option 3.'

The correct answer is Option 3)

Key Points

• The phrase 'made a complaint' is the correct and commonly used expression in English.
• Options 1 and 2 are incorrect because we do not "say" a complaint; we "make" a complaint.
• Option 4 is incorrect because "terribly complained" is not a standard or grammatically correct expression.

Hence, the correct statement is: He made a complaint to the manager about the terrible food in the hostel.

Additional Information

• The verb "make" is commonly used with nouns like "complaint", "decision", "effort", etc.
• Example: She made an effort to improve her grades.
• Using the correct verb-noun collocation is essential for proper grammar and clear communication in English.

The correct answer is Option 2)

Key Points

• The word "berth" means a fixed bed or bunk on a ship, train, or other means of transport. (बर्थ)
• Example: He reserved a lower berth for the overnight journey.
• "Birth" refers to the act or process of being born; the beginning of life as a physically separate being. (जन्म)
• Example: She is excited about the birth of her first child.
• Hence, the correct words are "berth" and "birth".

Therefore, the correct answer is Option 2)

Additional Information

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

• Option 1: birth; berth
• birth (जन्म): The act or process of being born.
• Example: The birth of a child is a joyful event.
• berth (बर्थ): A fixed bed or bunk on a ship, train, or other means of transport.
• Example: She was assigned an upper berth on the train.
• Option 3: birth; birth
• birth (जन्म): The act or process of being born.
• Example: The birth of twins is always a special occasion.
• Option 4: berth; berth
• berth (बर्थ): A fixed bed or bunk on a ship, train, or other means of transport.
• Example: He was happy to get a lower berth for the journey.

The correct answer is Option 1)

Key Points

• The word "Peace" means a state of tranquility or quiet; freedom from disturbance or conflict. (शांति)
• Example: After years of war, the country finally experienced peace.
• "Turmoil" refers to a state of great disturbance, confusion, or uncertainty. (अशांति)
• Example: The stock market was in turmoil after the unexpected news.
• Hence, we can infer that the opposite of 'Peace' is 'Turmoil'.

Additional Information

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

• Refusal (अस्वीकृति): The act of refusing or denying.
• Example: His refusal to cooperate made the situation worse.
• Strange (अजीब): Unusual or surprising; difficult to understand or explain.
• Example: He had a strange feeling that something was wrong.
• Harmony (सामंजस्य): The combination of simultaneously sounded musical notes to produce chords and chord progressions having a pleasing effect.
• Example: They lived together in perfect harmony.

The correct answer is Option 4)

Key Points

• The word "heir" means a person who is legally entitled to inherit property or a title upon the death of its owner. (उत्तराधिकारी)
• Example: The king's eldest son is the heir to the throne.
• "Heir" refers to someone who inherits or is in line to inherit, especially in the context of royalty or nobility. (उत्तराधिकारी)
• Example: Prince Charles is the heir to the British throne.

Therefore, the correct answer is: heir.

Additional Information

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

• Air (हवा): The invisible gaseous substance surrounding the earth, a mixture mainly of oxygen and nitrogen.
• Example: The fresh air was a welcome change after being indoors all day.
• Ere (पहले): An archaic or poetic term meaning "before."
• Example: We must leave ere dawn breaks.
• Err (भूल करना): To make a mistake.
• Example: To err is human; to forgive, divine.

Given : 79 – 43 + (23 + 75) × 3 – (30 ÷ 15) × 4 = 175

According to the question, after replacing the numbers :

Option - (1): 3 and 4

79 – 43 + (23 + 75) × 3 – (30 ÷ 15) × 4 = 175 ⇒ 79 – 43 + (23 + 75) × 4 – (30 ÷ 15) × 3 = 175

79 – 43 + (23 + 75) × 4 – (30 ÷ 15) × 3 = 175

79 – 43 + 98 × 4 – 2 × 3 = 175

79 + 392 - 43 - 6 = 175 

471 - 43 - 6 = 175

422 ≠ 175 (LHS ≠ RHS)

Option - (2): 23 and 43

79 – 43 + (23 + 75) × 3 – (30 ÷ 15) × 4 = 175 ⇒ 79 – 23 + (43 + 75) × 3 – (30 ÷ 15) × 4 = 175

79 – 23 + (43 + 75) × 3 – (30 ÷ 15) × 4 = 175

79 – 23 + 118 × 3 – 2 × 4 = 175

79 + 354 - 23 - 8 = 175

433 - 23 - 8 = 175

402 ≠ 175 (LHS ≠ RHS)

Option - (3): 75 and 30

79 – 43 + (23 + 75) × 3 – (30 ÷ 15) × 4 = 175 ⇒ 79 – 43 + (23 + 30) × 3 – (75 ÷ 15) × 4 = 175

79 – 43 + (23 + 30) × 3 – (75 ÷ 15) × 4 = 175

79 – 43 + 53 × 3 – 5 × 4 = 175

79 + 159 - 43 - 20 = 175

238 - 43 - 20 = 175

175 = 175 (LHS = RHS)

Option - (4): 75 and 79

79 – 43 + (23 + 75) × 3 – (30 ÷ 15) × 4 = 175 ⇒ 75 – 43 + (23 + 79) × 3 – (30 ÷ 15) × 4 = 175

75 – 43 + (23 + 79) × 3 – (30 ÷ 15) × 4 = 175

75 – 43 + 102 × 3 – 2 × 4 = 175

75 + 306 - 43 - 8 = 175

381 - 43 - 8 = 175

330 ≠ 175 (LHS ≠ RHS)

Hence, "Option 3" is the correct answer.

The logic followed here is: No specific pattern is followed here, random digits are assigned to each letter of the word.

'DEAL' is coded as '0368'

And,

'DEAF' is coded as '2630'

As 'D', 'E', and 'A' are common, therefore it can be concluded that :

F is coded as → 2

So, the code for 'F' is '2'.

Hence, "Option 1" is the correct answer.

Logic: (4) is added to the position values according to the English alphabetic series.

​​So,

'STAUNCH' is related to 'WXEYRGL'

​ 

​And,

'BLISS' is related to 'FPMWW'

​ 

​Similarly,

'COWARD' is related to

​ 

Hence, "Option 1" is the correct answer.

The logic followed here is: ​

Option (1): ZABX

Option (2): KPQJ

Option (3): NMNM

Option (4): TGHS

Thus, out of all the options "ZABX" is the odd one out.

Hence, "Option 1" is the correct answer.

The number of semi-circles in the given figure is shown below :

Here, as marked there are a total of 5 semi-circles.

Hence, "5" is the correct answer.

Given word: 'PRAISE'

After arranged in alphabetical order:

 

Now,

there are no alphabets that will remain unchanged if each of the letters in the word 'PRAISE' is arranged in English alphabetical order.

Hence, the correct answer is "Option 3".

The image embedded in the given figure is as shown below :

∴ Here, the given figure is embedded in option Figure - 2.

Hence, the correct answer is "Option 2".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

Given word: 'CHEMISTRY'

After arranged in alphabetical order:

 

Now,

there are Two alphabets "C" and "Y" that will remain unchanged if each of the letters in the word 'CHEMISTRY' is arranged in English alphabetical order.

Hence, the correct answer is "Option 3".

Decoding the Symbols:

Given: E & P @ D% K # L 

E & P → E is the wife of P.

P @ D  → P is the son of D.

D% K → D is the father of K.

​

K # L → K is the sister of L.

Here, E is the sister-in-law or brother's wife of K.

Hence, the correct answer is "Option 2".

The logic followed here is :

1. First box alternate series → Diagonal elements interchange positions.

2. Second box alternate series → Elements shift in the clockwise direction at the corners and the center element is replaced by a new element.

Thus, the final series is :

 

Hence, "Option 1" is the correct answer.

Logic: 

1^st letter:- Prime number series is subtracted from the positional value of the 1^st letter,

2^nd letter:- Prime number series is added from the positional value of the 2^nd letter,

3^rd letter:- (3) is added then (2) is subtracted from the positional value of the 3^rd letter.

​​So,

Hence, "Option 3" is the correct answer.

The faces opposite to each other are shown below:

\

⇒ As the alternate positions become opposite to each other, the remaining two faces become opposite to each other.

So, opposite pairs are:

P → U

S → T

Q → R

Therefore, 'T' is the opposite of 'S'.

Hence, "T" is the correct answer.

Logic: 

First and second letters → (2) and (3) are added to the position value respectively.

Third and fourth letters → (2) and (1) are added to the position value respectively.

​​So,

'LDWR' is coded as 'NGUQ'

​ 

​And,

'BFKZ' is coded as 'DIIY'

​ 

​Similarly,

'YTGX' is coded as

​ 

Hence, "Option 1" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some buttons are shoes → Does not follow (As all shoes are ties, some ties are pants and all pants are buttons. So it is possible but not definite.)

II. No ties are buttons → Does not follow (As some ties are pants and all pants are buttons. So, no direct relation is given between ties and buttons therefore it is false.)

∴ Here, Neither conclusion (I) nor (II) follow.​

Hence, the correct answer is "Neither conclusion (I) nor (II) follows"

Logic: (5) is added to the position values according to the English alphabetic series.

​​So,

Hence, "Option 1" is the correct answer.

The logic followed here is:

Logic: (1^st number × 2) + 17 = 2^nd number.

Now,

For, 21 : 59

⇒ (21 × 2) + 17 = 42 + 17 = 59.

For, 32 : 81

⇒ (32 × 2) + 17 = 64 + 17 = 81.

Similarly, for 29 ∶ ?

⇒ (29 × 2) + 17 = 58 + 17 = 75.

Hence, the correct answer is "Option 2".

Given Equation: 404 B 2 D 101 A 101 C 6 = ?

BODMAS Rule:

Decoding the given information:

 

Now replacing the sign from left to right using BODMAS Rule, we get:

⇒ 404 × 2 - 101 ÷ 101 + 6 = ?

⇒ 404 × 2 - 1 + 6 = ?

⇒ 808 - 1 + 6 = ?

⇒ 814 - 1 = 813.

Hence, the correct option is "Option 3".

Logic : Alternately (1) and (3) are subtracted and added respectively.

Hence, "141" is the correct answer.

Given : (86 ÷ 43) + (66 ÷ 33) × 2 + 72 – 6 × 4 = 177

According to the question, after replacing the numbers :

Option - (1): 43 and 2

(86 ÷ 43) + (66 ÷ 33) × 2 + 72 – 6 × 4 = 177 ⇒ (86 ÷ 2) + (66 ÷ 33) × 43 + 72 – 6 × 4 = 177

(86 ÷ 2) + (66 ÷ 33) × 43 + 72 – 6 × 4 = 177

43 + 2 × 43 + 72 – 6 × 4 = 177

43 + 86 + 72 - 24 = 177

201 - 24 = 177

177 = 177 (LHS = RHS)

Option - (2): 2 and 72

(86 ÷ 43) + (66 ÷ 33) × 2 + 72 – 6 × 4 = 177 ⇒ (86 ÷ 43) + (66 ÷ 33) × 72 + 2 – 6 × 4 = 177

(86 ÷ 43) + (66 ÷ 33) × 72 + 2 – 6 × 4 = 177

2 + 2 × 72 + 2 – 6 × 4 = 177

2 + 144 + 2 - 24 = 177

148 - 24 = 177

144 ≠ 177 (LHS ≠ RHS)

Option - (3): 2 and 4

(86 ÷ 43) + (66 ÷ 33) × 2 + 72 – 6 × 4 = 177 ⇒ (86 ÷ 43) + (66 ÷ 33) × 4 + 72 – 6 × 2 = 177

(86 ÷ 43) + (66 ÷ 33) × 4 + 72 – 6 × 2 = 177

2 + 2 × 4 + 72 – 6 × 2 = 177

2 + 8 + 72 - 24 = 177

82 - 24 = 177

58 ≠ 177 (LHS ≠ RHS)

Option - (4): 2 and 6

(86 ÷ 43) + (66 ÷ 33) × 2 + 72 – 6 × 4 = 177 ⇒ (86 ÷ 43) + (66 ÷ 33) × 6 + 72 – 2 × 4 = 177

(86 ÷ 43) + (66 ÷ 33) × 6 + 72 – 2 × 4 = 177

2 + 2 × 6 + 72 – 2 × 4 = 177

2 + 12 + 72 - 8 = 177

86 - 8 = 177

78 ≠ 177 (LHS ≠ RHS)

Hence, "Option 1" is the correct answer.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: Synonym relationship.

Here,

Adhere : Comply → Adhere is a synonym of Comply.

Similarly,

Accord : Harmony → Accord is a synonym of Harmony.

Busy : Engaged → Busy is a synonym of Engaged.

Eager : Keen → Eager is a synonym of Keen.

However,

Jubilant : Depressed → Jubilant is not a synonym of Depressed; in fact, they are antonyms.

Hence, the correct answer is "Option 3".

The faces opposite to each other are shown below:

⇒ As the alternate positions become opposite to each other, the remaining two faces become opposite to each other.

So, opposite pairs are:

X → VI

VII → V

IX → VIII

Therefore, 'VIII' is the opposite of 'IX'.

Hence, "VIII" is the correct answer.

The logic followed here is:

Logic: (2^nd number + 3^rd number) × 3 = 1^st number.

Now,

For, (60, 15, 5)

⇒ (15 + 5) × 3 = 20 × 3 = 60.

For, (96, 24, 8)

⇒ (24 + 8) × 3 = 32 × 3 = 96.

Similarly, for (156, 39, 13)

⇒ (39 + 13) × 3 = 52 × 3 = 156.

Hence, the correct answer is "Option 4".

Given : 34 + 56 × 8 ÷ 2 - 16 = ?

According to the question, after replacing the signs :

‘+’ and ‘-’ are interchanged 

‘×’ and ‘÷’ are interchanged

So,​​

34 - 56 ÷ 8 × 2 + 16 = ?

34 - 7 × 2 + 16 = ?

34 + 16 - 14 = ?

50 - 14 = ?

36 = ?

Hence, "36" is the correct answer.

Given:

Distance between the centers of two circles (d) = 81 cm

Radius of the first circle (r₁) = 42 cm

Radius of the second circle (r₂) = 51 cm

Formula used:

Length of the direct common tangent (L) is given by:

$L = \sqrt{d^2 - (r₁ - r₂)^2}$

Calculations:

Substitute the given values:

⇒ L = $\sqrt{81^2 - (51 - 42)^2}$

⇒ L = $\sqrt{6561 - (9)^2}$

⇒ L = $\sqrt{6561 - 81}$

⇒ L = $\sqrt{6480}$

⇒ L = $\sqrt{6480} , \text{cm}$

⇒ L = 36√5 cm

∴ The length of the direct common tangent is 36√5.

Shortcut Trick

The age difference between Ram and Rahul remains constant at 20 years.

n years ago: Ratio is 3 : 1 ⇒ Difference = 2 units = 20 years ⇒ 1 unit = 10 years. (Rahul = 10)

2n years hence: Ratio is 15 : 11 ⇒ Difference = 4 units = 20 years ⇒ 1 unit = 5 years. (Rahul = 55)

The total time gap between n years ago and 2n years hence is 3n.

Gap in Rahul's age = 55 − 10 = 45 ⇒ 3n = 45 ⇒ n = 15.

∴ The correct answer is 15.

Alternate Method

Given:

Current age difference = 20 years.

Ratio n years ago = 3 : 1.

Ratio 2n years later = 15 : 11.

Let current ages of Ram and Rahul be R and r.

⇒ R − r = 20 ⇒ R = r + 20

From the condition n years ago:

⇒ (R − n) = 3 × (r − n)

⇒ (r + 20 − n) = 3r − 3n

⇒ 2n + 20 = 2r ⇒ r = n + 10 --- (Eq. 1)

From the condition 2n years later:

⇒ (R + 2n) ÷ (r + 2n) = 15 ÷ 11

⇒ 11 × (r + 20 + 2n) = 15 × (r + 2n)

⇒ 11r + 220 + 22n = 15r + 30n

⇒ 220 − 8n = 4r ⇒ r = 55 − 2n --- (Eq. 2)

Equating Eq. 1 and Eq. 2:

⇒ n + 10 = 55 − 2n

⇒ 3n = 45

⇒ n = 15

∴ The correct answer is 15.

Additional Information

Constant Age Difference

The difference between the ages of two persons always remains constant, regardless of the number of years passed or gone by.

Ratio Scaling in Ages

If the age difference is D and the ratio is a : b, then 1 ratio unit = D ÷ (a − b). This helps find individual ages quickly.

Time Gap Calculation

The total time interval between x years ago and y years hence is calculated as (x + y) years.

Given:

∠BAD = 118º

∠ACB = 80º

CD = AC (so ΔACD is isosceles)

Solution:

Step 1: Use the exterior angle theorem in ΔACD

Since ΔACD is isosceles, we have:

⇒ ∠CAD = ∠CDA

From the exterior angle theorem:

∠ACB = ∠CAD + ∠CDA

Given ∠ACB = 80º, and since ∠CAD = ∠CDA:

⇒ 80º = 2∠CAD

⇒ ∠CAD = 40º

Step 2: Find ∠BAC using the exterior angle theorem

We are given ∠BAD = 118º. From the exterior angle theorem in ΔABC:

∠BAD = ∠BAC + ∠CAD

⇒ 118º = ∠BAC + 40º

⇒ ∠BAC = 118º - 40º = 78º

Step 3: Use the angle sum property in ΔABC

In ΔABC, the sum of interior angles is 180º:

∠BAC + ∠ABC + ∠ACB = 180º

Substitute the known values:

78º + ∠ABC + 80º = 180º

⇒ ∠ABC = 180º - 158º = 22º

∴ The value of ∠ABC is 22º.

Given:

Present value of the machine = Rs. 80,000

Depreciation rate per year = 5%

Formula Used:

Value after n years = Present Value × (1 - Depreciation Rate)ⁿ

Calculation:

Depreciation Rate = 5% = 0.05

n = 2 years

Value after 2 years = 80,000 × (1 - 0.05)²

⇒ Value after 2 years = 80,000 × (0.95)²

⇒ Value after 2 years = 80,000 × 0.9025

⇒ Value after 2 years = 72,200

The value of the machine after 2 years will be Rs. 72,200.

Calculation:

1. For the radius of an incircle of an equilateral triangle:

Radius = $\frac{s}{2 \sqrt{3}}$

This statement is correct as it matches the formula.

2. For the area of a sector:

Area = $\frac{1}{2} \times (\text{arc length} \times R)$

This statement is correct as it matches the formula.

3. For the length of an arc:

Length of an arc = $\frac{\text{central angle made by the arc}}{360^\circ} \times 2 \pi r$

Given statement: Length of an arc = $\frac{\text{central angle made by the arc}}{360^\circ} \times \pi r^2$

This statement is incorrect because the given formula is for the area of a sector, not the length of an arc.

4. For congruent and similar circles:

Circles are congruent if they have the same radii while similar circles may have different radii.

This statement is correct.

The correct answer is option 3.

Given:

cos⁴θ - sin⁴θ = 4/5

Formula used:

1. Difference of squares identity: cos⁴θ - sin⁴θ = (cos²θ - sin²θ)(cos²θ + sin²θ)
2. cos²θ + sin²θ = 1
3. cos 2θ = cos²θ - sin²θ
4. sin 4θ = 2sin 2θ cos 2θ

Calculation:

cos⁴θ - sin⁴θ = (cos²θ - sin²θ)(cos²θ + sin²θ)

⇒ cos⁴θ - sin⁴θ = cos²θ - sin²θ (since cos²θ + sin²θ = 1)

So, cos²θ - sin²θ = 4/5

cos 2θ = cos²θ - sin²θ

⇒ cos 2θ = 4/5

Find sin 2θ using the Pythagorean identity

sin² 2θ + cos² 2θ = 1

Substitute cos 2θ = 4/5:

sin² 2θ + (4/5)² = 1

sin² 2θ + 16/25 = 1

sin² 2θ = 1 - 16/25 = 9/25

⇒ sin 2θ = 3/5

sin 4θ = 2sin 2θ cos 2θ

Substitute sin 2θ = 3/5 and cos 2θ = 4/5:

⇒ sin 4θ = 2 × (3/5) × (4/5) = 24/25

∴ The value of sin 4θ is 24/25.

Shortcut Trick

Total Surface Area (TSA) of a hollow hemispherical bowl = 3πR² + πr²

Given: Outer radius (R) = 8 cm and Inner radius (r) = 6 cm.

TSA = π(3 × 8² + 6²) = π(192 + 36) = 228π cm².

Cost of polishing π cm² = Rs. 50 ⇒ Total Cost = 228 × 50 = Rs. 11,400.

∴ The correct answer is Rs. 11,400.

Alternate Method

Given:

Inner radius (r) = 6 cm

Outer radius (R) = 8 cm

Polishing rate = Rs. 50 per π cm²

Formula Used:

Total Surface Area = Outer CSA + Inner CSA + Area of the Ring

TSA = 2πR² + 2πr² + π(R² − r²)

Calculations:

⇒ Outer CSA = 2 × π × 8² = 128π cm²

⇒ Inner CSA = 2 × π × 6² = 72π cm²

⇒ Area of Top Ring = π(8² − 6²) = π(64 − 36) = 28π cm²

⇒ Total Surface Area = 128π + 72π + 28π = 228π cm²

⇒ Cost of polishing π cm² = Rs. 50

⇒ Total Polishing Cost = (228π / π) × 50

⇒ Total Polishing Cost = 228 × 50 = Rs. 11,400

∴ The correct answer is Rs. 11,400.

Additional Information

Volume of a Hollow Hemisphere

The volume of the material of a hollow hemispherical bowl is given by V = (2/3)π(R³ − r³), where R is the outer radius and r is the inner radius.

Surface Area of a Solid Hemisphere

For a solid hemisphere of radius R, the total surface area is TSA = 3πR², which includes the curved surface (2πR²) and the flat circular base (πR²).

Surface Area of a Sphere

The total surface area of a complete sphere is 4πR², and its volume is (4/3)πR³.

Given:

Radius of the sphere (r) = 14 cm

Painting cost per square centimetre = Rs. 5

Formula Used:

Surface area of a sphere = 4πr²

Total cost = Surface area × Painting cost per square centimetre

Calculation:

Surface area of the sphere = 4πr²

⇒ Surface area = 4 × (22/7) × 14²

⇒ Surface area = 4 × (22/7) × 196

⇒ Surface area = 4 × 22 × 28

⇒ Surface area = 2464 cm²

Total cost = Surface area × Painting cost per square centimetre

⇒ Total cost = 2464 × 5

⇒ Total cost = Rs. 12,320

The cost of painting the ball is Rs. 12,320.

Given:

Total number of students = 115

Frequency densities and intervals:

Marks 20.5 to 30.5: Frequency density ≈ 0.5

Marks 30.5 to 40.5: Frequency density ≈ 1.5

Marks 40.5 to 50.5: Frequency density ≈ 2.5

Marks 50.5 to 60.5: Frequency density ≈ 3.0

Marks 60.5 to 70.5: Frequency density ≈ 2.0

Marks 70.5 to 80.5: Frequency density ≈ 1.0

Marks 80.5 to 90.5: Frequency density ≈ 1.0

Formula used:

Frequency = Frequency density × Width of the bar

Qualified students: Marks > 40.5

Non-qualified students: Marks ≤ 40.5

Calculation:

Step 1: Calculate the number of qualified students (marks above 40.5)

Marks 40.5 to 50.5: Frequency = 2.5 × 10 = 25

Marks 50.5 to 60.5: Frequency = 3.0 × 10 = 30

Marks 60.5 to 70.5: Frequency = 2.0 × 10 = 20

Marks 70.5 to 80.5: Frequency = 1.0 × 10 = 10

Marks 80.5 to 90.5: Frequency = 1.0 × 10 = 10

Total number of qualified students = 25 + 30 + 20 + 10 + 10 = 95

Step 2: Calculate the number of non-qualified students (marks ≤ 40.5)

Marks 20.5 to 30.5: Frequency = 0.5 × 10 = 5

Marks 30.5 to 40.5: Frequency = 1.5 × 10 = 15

Total number of non-qualified students = 5 + 15 = 20

Step 3: Calculate the ratio of qualified to non-qualified students

⇒ Ratio = Number of qualified students / Number of non-qualified students

⇒ Ratio = 95 / 20

⇒ Ratio = 19 : 4

∴ The ratio of the number of qualified students to the number of non-qualified students is 19 : 4.

Given:

Ram invested a certain sum of money at simple interest.

It amounted to 5/4 of itself in 3 years.

Formula Used:

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T) / 100

Amount (A) = Principal (P) + Simple Interest (SI)

Calculation:

Let the Principal be P.

Amount after 3 years = $\frac{5}{4}$ × P

Simple Interest (SI) = Amount - Principal = $\frac{5}{4}P - P$

SI = $\frac{P}{4}$

We know:

SI = P × R × 3 / 100

⇒ $\frac{P}{4}$ = P × R × 3 / 100

⇒ $\frac{1}{4}$ = R × 3 / 100

⇒ $\frac{100}{4}$ = 3R

⇒ 25 = 3R

⇒ R = $\frac{25}{3}$

⇒ R = 8.333

The rate per cent per annum is 8.33%.

Given:

5% of 2% of 3

Formula Used:

Percentage Formula: (a)/(100) × b

Calculation:

5% of 2% of 3

First, calculate 2% of 3:

2% of 3 = (2)/(100) × 3

⇒ 0.02 × 3

⇒ 0.06

Next, calculate 5% of 0.06:

5% of 0.06 = (5)/(100) × 0.06

⇒ 0.05 × 0.06

⇒ 0.003

5% of 2% of 3 is equal to 0.003.

First Division students:

2019: 20 students

2020: 70 students

2021: 85 students

Total number of students in 2020 (from the graph):

First Division: 70 students

Second Division: 80 students

Third Division: 95 students

Failed: 5 students

Total number of students in 2020 = 70 + 80 + 95 + 5 = 250 students

Total First Division students in 2019, 2020, and 2021 = 20 + 70 + 85 = 175 students

⇒ Ratio = 175 / 250

⇒ Ratio = 7/10

∴ The ratio of the number of students who passed with first division in all three years to the total number of students in 2020 is 7 : 10.

Given:

Month: May

The chart provides the sales of various fruits in the month of May:

Pear: 50 units

Apple: 70 units

Orange: 65 units

Kiwi: 42 units

Melon: 58 units

Peach: 45 units

Formula used:

Difference = Most sold fruit - Lowest sold fruit

Calculation:

Most sold fruit = Apple (70 units)

Lowest sold fruit = Kiwi (42 units)

⇒ Difference = 70 - 42 = 28 units

∴ The most sold fruit in May is Apple, and it sold 28 units more than the lowest-sold fruit, which is Kiwi.

Given:

Meena buys 24 bangles and gets 6 bangles free.

Formula Used:

Discount Percentage = (Free Items / Total Items Purchased) × 100

Calculation:

Total Items Purchased = 24 + 6 = 30

Free Items = 6

Discount Percentage = (6 / 30) × 100

⇒ Discount Percentage = (1 / 5) × 100

⇒ Discount Percentage = 0.2 × 100

⇒ Discount Percentage = 20%

The correct answer is option 2.

Given:

A : B = 2 : 3

B : C = 7 : 8

Calculation:

$\frac{A}{C}$ = $\frac{A}{B}$ × $\frac{B}{C}$

⇒ $\frac{A}{C}$ = ​$\frac{2}{3}$ × $\frac{7}{8}$

⇒ $\frac{A}{C}$ = $\frac{7}{12}$

So, A : C = 7 : 12

The correct answer is option 4.

Given:

The table shows the number of students admitted to different courses over the years 2015 to 2020.

Calculation:

We need to check whether any course had a consistent growth or decline in admissions over the years.

Engineering does not have consistent growth or decline.

Science does not have consistent growth or decline due to the decrease from 2015 to 2016.

Arts does not have consistent growth or decline.

Management shows consistent growth in admissions from 2015 to 2020.

Engineering:

2015: 1200

2016: 1362 (increase)

2017: 1351 (slight decrease)

2018: 1409 (increase)

2019: 1421 (increase)

2020: 1400 (slight decrease)

Science:

2015: 850

2016: 821 (decrease)

2017: 870 (increase)

2018: 921 (increase)

2019: 931 (increase)

2020: 950 (increase)

Arts:

2015: 450

2016: 525 (increase)

2017: 624 (increase)

2018: 615 (slight decrease)

2019: 795 (increase)

2020: 750 (slight decrease)

Management:

2015: 240

2016: 275 (increase)

2017: 286 (increase)

2018: 293 (increase)

2019: 300 (increase)

2020: 320 (increase)

∴ The Management course had consistent growth in admissions from 2015 to 2020.

Shortcut Trick

When two cubes are joined face to face, the two faces at the junction are hidden from the total surface.

A single cube has 6 faces, so two separate cubes have 12 faces. Joining them removes 2 faces.

Total faces in the cuboid = 12 − 2 = 10 faces.

Area of one face = edge² = 5 × 5 = 25 cm².

Total Surface Area = 10 × 25 = 250 cm².

∴ The correct answer is 250 cm².

Alternate Method

Given:

Edge of each cube (a) = 5 cm.

Formula Used:

Total Surface Area (TSA) of a cuboid = 2 × (lb + bh + hl)

Calculations:

When two cubes are joined face to face, the length increases while breadth and height remain constant.

⇒ Length of the cuboid (l) = 5 cm + 5 cm = 10 cm

⇒ Breadth of the cuboid (b) = 5 cm

⇒ Height of the cuboid (h) = 5 cm

⇒ Total Surface Area = 2 × (10 × 5 + 5 × 5 + 5 × 10)

⇒ Total Surface Area = 2 × (50 + 25 + 50)

⇒ Total Surface Area = 2 × (125)

⇒ Total Surface Area = 250 cm²

Therefore, the correct answer is option (2).

∴ The correct answer is 250 cm².

Additional Information

Volume of Cuboid

The total space occupied by the cuboid is given by V = l × b × h. For this cuboid, V = 10 × 5 × 5 = 250 cm³.

Lateral Surface Area

The area of the four side walls of the cuboid is 2h(l + b). For this cuboid, LSA = 2 × 5(10 + 5) = 150 cm².

Diagonal of Cuboid

The length of the longest diagonal is given by √(l² + b² + h²). Here, diagonal = √(100 + 25 + 25) = √150 = 5√6 cm.

Given:

Tanvi can do a work in 25 days.

Tai can complete the same work in 30 days.

They started the work together for 5 days.

Formula Used:

Work done by Tanvi in one day = 1/25

Work done by Tai in one day = 1/30

Total work done in one day by both = (1/25) + (1/30)

Calculation:

Work done by Tanvi and Tai together in one day:

$\frac{1}{25} + \frac{1}{30} = \frac{6 + 5}{150} = \frac{11}{150}$

Work done by Tanvi and Tai together in 5 days:

⇒ 5 × $\frac{11}{150}$ = $\frac{55}{150}$ = $\frac{11}{30}$

Work left:

⇒ 1 - $\frac{11}{30}$ = $\frac{30}{30}$ - $\frac{11}{30}$ = $\frac{19}{30}$

Therefore, the amount of work left is $\frac{19}{30}$.

Given:

The average weight of 35 students in a class = 40 kgs.

Average weight of 5 students who left = 42 kgs.

Formula Used:

Average weight = Total weight / Number of students

Calculation:

Total weight of 35 students = 35 × 40

⇒ Total weight of 35 students = 1400 kgs

Total weight of 5 students who left = 5 × 42

⇒ Total weight of 5 students who left = 210 kgs

Total weight of remaining 30 students = Total weight of 35 students - Total weight of 5 students who left

⇒ Total weight of remaining 30 students = 1400 - 210

⇒ Total weight of remaining 30 students = 1190 kgs

Average weight of remaining 30 students = Total weight of remaining 30 students / 30

⇒ Average weight of remaining 30 students = 1190 / 30

⇒ $\frac{1190}{30} = 39 \frac{2}{3} \text{ kgs}$

The average weight of the remaining 30 students is 39 (2/3) kgs.

Given:

One candidate got 42% of the total votes and lost by 800 votes.

Formula Used:

Total votes = Number of votes for the losing candidate / Percentage of votes for the losing candidate

Calculation:

Let total votes be V.

Votes for the losing candidate = 42% of V = 0.42V

Votes for the winning candidate = 0.42V + 800

Total votes = Votes for the losing candidate + Votes for the winning candidate

V = 0.42V + (0.42V + 800)

V = 0.84V + 800

⇒ V - 0.84V = 800

⇒ 0.16V = 800

⇒ V = 800 / 0.16

⇒ V = 5000

The total number of votes that were cast is 5000.

Given:

Profit by A = 10%

Profit by B = 60%

Profit by C = 12 (1/2)% = 12.5%

D paid = Rs. 59.40

Formula Used:

Let the initial cost price be x .

Final Price = Initial Price × (1 + Profit/100)

Calculation:

Let the price at which A buys it be x .

Price after A's sale = x × 1.10

Price after B's sale = x × 1.10 × 1.60

Price after C's sale = x × 1.10 × 1.60 × 1.125

D paid Rs. 59.40, so:

⇒ x × 1.10 × 1.60 × 1.125 = 59.40

⇒ x × 1.98 = 59.40

⇒ x = 59.40/1.98

⇒ x = 30

The price at which A bought it is Rs. 30.

Given:

Two triangles ABC and DEF are similar.

The smallest side of ABC is equal to 15 units.

The sides of ABC are in the ratio 3 ∶ 4 ∶ 5.

The area of DEF is half of the area of ABC.

Formula Used:

Ratio of sides of similar triangles = Ratio of corresponding sides

Ratio of areas of similar triangles = (Ratio of corresponding sides)²

Calculation:

Let the sides of triangle ABC be 3x, 4x, and 5x.

Given the smallest side of ABC is 15 units:

3x = 15

⇒ x = 15 / 3

⇒ x = 5

So, the sides of triangle ABC are 3×5 = 15 units, 4×5 = 20 units, and 5×5 = 25 units.

Let the sides of triangle DEF be a, b, and c, where c is the largest side.

Since the area of DEF is half of the area of ABC:

Ratio of areas of ABC and DEF = 2:1

So, (Ratio of corresponding sides)² = 2

⇒ Ratio of corresponding sides = $\sqrt{2}$

Thus, the ratio of sides of ABC to DEF is 1:$\sqrt{2}$

The largest side of DEF:

25 / $\sqrt{2}$

⇒ 25/√2

The largest side of DEF is 25/√2 units.

Given:

Expression: 720 + 48 ÷ 8 × 5 - 6 × 3

Formula Used:

Follow the order of operations (PEMDAS/BODMAS): Parentheses, Exponents (i.e. powers and square roots, etc.), Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right).

Calculation:

First, perform the division and multiplication:

48 ÷ 8 = 6

6 × 5 = 30

6 × 3 = 18

Now, substitute these values back into the expression:

⇒ 720 + 30 - 18

Next, perform the addition and subtraction:

⇒ 720 + 30 = 750

⇒ 750 - 18 = 732

The simplified expression is 732.

Shortcut Trick

Ratio of time taken (Upstream : Downstream) = 3 : 1

Since distance is constant, Speed ratio (Upstream : Downstream) = 1 : 3

⇒ Ratio of (Boat speed : Stream speed) = (3 + 1) : (3 − 1) = 4 : 2 = 2 : 1

Given Boat speed = 8 km/h (2 parts) → Stream speed (1 part) = 4 km/h.

∴ The correct answer is 4 km/h.

Alternate Method

Given:

Speed of boat in still water (u) = 8 km/h

Let the speed of the stream be v km/h.

Formula Used:

Downstream Speed (S_down) = u + v

Upstream Speed (S_up) = u − v

Distance = Speed × Time

Calculations:

Let the distance be D km and the downstream time be t hours.

⇒ Downstream speed = 8 + v km/h

⇒ Upstream speed = 8 − v km/h

⇒ Time taken upstream = 3t hours

Since the distance D is the same in both cases:

⇒ (8 + v) × t = (8 − v) × 3t

⇒ 8 + v = 3 × (8 − v)

⇒ 8 + v = 24 − 3v

⇒ v + 3v = 24 − 8

⇒ 4v = 16

⇒ v = 4 km/h

∴ The correct answer is 4 km/h.

Additional Information

Downstream and Upstream Speed

Downstream Speed (D) = u + v, where u is boat speed in still water and v is stream speed. Upstream Speed (U) = u − v.

Calculating Component Speeds

Boat speed in still water: u = (D + U) ÷ 2. Stream speed: v = (D − U) ÷ 2.

Speed-Time Inverse Relationship

When the distance traveled is constant, speed is inversely proportional to time: S₁ ÷ S₂ = T₂ ÷ T₁.

Given:

The expression: $\frac{2 \times 2+2}{2 \div 2 \times 2}$ ÷ $\frac{\frac{1}{2} \div \frac{1}{2} \text { of } \frac{1}{2}}{\frac{1}{2}+\frac{1}{2} \text { of } \frac{1}{2}}$

Step 1: Solve the first part

$\frac{2 \times 2 + 2}{2 \div 2 \times 2}$

⇒ Numerator = 2 × 2 + 2 = 4 + 2 = 6

⇒ Denominator = 2 ÷ 2 × 2 = 1 × 2 = 2

⇒ First part = 6 / 2 = 3

Step 2: Solve the second part

$\frac{\frac{1}{2} \div \frac{1}{2} \text { of } \frac{1}{2}}{\frac{1}{2} + \frac{1}{2} \text { of } \frac{1}{2}}$

First, we simplify each part:

Numerator: $\frac{1}{2} \div \frac{1}{2} \text { of } \frac{1}{2}$ = 1/2 × 4 = 2

Denominator: $\frac{1}{2} + \frac{1}{2} \text { of } \frac{1}{2}$ = 1/2 + 1/4 = 2/4 + 1/4 = 3/4

⇒ Second part = 2 / (3/4) = 2 × 4/3 = 8/3

Step 3: Combine the results

⇒ First part ÷ Second part = 3 ÷ 8/3 = 3 × 3/8 = 9/8

⇒ Final answer = $1 \frac{1}{8}$

∴ The value of the expression is $1 \frac{1}{8}$.

The correct answer is White flag

Key Points

• A White flag is not a compulsory piece of equipment for a football referee.
• Essential equipment for a football referee includes items such as watch(es), whistle(s), and red and yellow cards.
• These tools help the referee manage the game, keep time, and enforce the rules effectively.
• Other non-compulsory items may be used at the referee's discretion but are not mandated by the official regulations.

Additional Information

• The Laws of the Game are established by the International Football Association Board (IFAB) and specify the required equipment for referees.
• Referees must carry a whistle to signal the start and stop of play, and red and yellow cards to discipline players.
• They must also have a watch to keep track of the match time and any additional time to be added.
• While other items like notebooks, pens, and coin for the toss are commonly used, they are also not strictly compulsory.

The correct answer is Magahi

Key Points

• Magahi is not one of the classical languages of India.
• The classical languages of India include Kannada, Malayalam, Odiya, Tamil, Sanskrit, and Telugu.
• A language is declared as a classical language based on its rich heritage and independent tradition.
• The criteria for classical language status include antiquity of early texts/recorded history over a period of 1500-2000 years and a body of ancient literature or texts, which is considered a valuable heritage by generations of speakers.
• Recognition as a classical language also involves a distinction between the classical language and its modern form.

Additional Information

• Kannada was declared a classical language in 2008.
• Malayalam received its classical language status in 2013.
• Odiya was granted classical language status in 2014.
• The first language to be declared as classical in India was Tamil in 2004.
• Sanskrit and Telugu are also recognized as classical languages, having been declared in 2005 and 2008 respectively.
• The Union Cabinet approved the inclusion of Marathi, Assamese, Bengali, Pali, and Prakrit, raising the count from six to eleven. These additions reflect the expanding understanding of India's rich linguistic heritage in October 2024.

The correct answer is Gir forest

Key Points

• The Gir forest is the only natural habitat of the Asiatic Lion (Panthera leo persica).
• Located in the state of Gujarat, India, the Gir National Park and Wildlife Sanctuary is the last refuge of the Asiatic Lion.
• The park was established in 1965 and covers a total area of 1,412 square kilometers.
• Conservation efforts in Gir have been successful in increasing the population of Asiatic Lions from a mere 20 in the early 20^th century to over 500 today.
• The ecosystem of Gir forest is unique, supporting a rich biodiversity that includes leopards, deer, antelopes, and numerous bird species.

Additional Information

• The Asiatic Lion once roamed across the Middle East and India but is now restricted to the Gir forest.
• The Government of India and the Gujarat state government have implemented several conservation programs to protect the Asiatic Lion.
• In addition to Gir, there are efforts to identify and establish alternative habitats to ensure a healthy and genetically diverse population.
• The Gir forest is also a significant cultural and historical site, attracting numerous tourists and wildlife enthusiasts from around the world.

The correct answer is Clove oil

Key Points

• Clove oil is an olfactory indicator.
• Olfactory indicators are substances whose smell varies depending on whether they are in acidic or basic solutions.
• Clove oil changes its smell in different pH conditions, making it useful for detecting acidity or basicity.

Additional Information

• Turmeric is a natural indicator but not an olfactory one; it changes color in acidic and basic solutions.
• Petunia and cabbage juice are also used as pH indicators but are not olfactory indicators.
• Olfactory indicators are particularly useful in scenarios where visual indicators might not be practical or available.

The correct answer is Purandara Das

Key Points

• Syama Shastri, Tyagaraja, and Muthuswami Dikshitar are considered the 'Trinity of Carnatic Music'.
• They are renowned composers and are highly revered in the Carnatic music tradition.
• Purandara Das is not part of this trinity. Although he is a significant figure in Carnatic music, he lived earlier and is often referred to as the "father of Carnatic music."
• The contributions of the 'Trinity of Carnatic Music' have had a profound influence on the development and propagation of Carnatic music.
• Their compositions are still widely performed and form a crucial part of the Carnatic music repertoire.

Additional Information

• Syama Shastri (1762–1827), Tyagaraja (1767–1847), and Muthuswami Dikshitar (1775–1835) were contemporaries and their works have been foundational in Carnatic music.
• They have composed thousands of kritis (songs) that are still sung and cherished by Carnatic musicians and enthusiasts alike.
• Their compositions are known for their intricate melodies, rich rhythmic patterns, and deep devotion.
• Purandara Das (1484–1564) is credited with systematizing the teaching of Carnatic music and composing thousands of devotional songs known as "Devaranamas".