SSC CHSL Tier-1 2024: Official Paper (Held On: 04 Jul, 2024 Shift 2) (Previous Year Paper)

The correct answer is Option 2)

Key Points

• The word 'melodiously' is the correct adverb to describe how Ragini plays the guitar.
• Adjectives describe nouns, while adverbs describe verbs, adjectives, or other adverbs.
• Example: "She sings beautifully." ('beautifully' is an adverb describing the verb 'sings')
• Using the correct form of words ensures clarity and precision in communication.
• Example: "He is a quick runner." ('quick' is an adjective describing the noun 'runner')
• "He runs quickly." ('quickly' is an adverb describing the verb 'runs')​

Hence, the correct statement is "Ragini plays the guitar melodiously."

Additional Information

• Other options either use incorrect forms or do not make grammatical sense:
• Option 1: "with a melody" is not how we typically describe playing an instrument.
• Option 3: "with melodiousness" is awkward and uncommon.
• Option 4: "melodious" is an adjective, not an adverb.

The correct answer is Option 4)

Key Points

• In the given sentence, the preposition 'for' used in 'for our Jobs and Careers Conference' is incorrect.
• The correct preposition should be 'at' or 'during'.
• The corrected sentence should be: 'I am writing to invite you to give a presentation at our Jobs and Careers Conference for engineering graduates.'

Hence, the correct statement is: I am writing to invite you to give a presentation at our Jobs and Careers Conference for engineering graduates.

Additional Information

• The prepositions 'at' and 'during' are commonly used to refer to events or periods of time.
• Example: He spoke at the annual meeting.
• Example: She will be presenting during the conference.

The correct answer is Option 3)

Key Points

• In the first part of the given sentence, the phrase 'I am hearing' is incorrect.
• In English, the verb 'hear' is stative and is not used in the continuous form.
• Instead of 'I am hearing', we should use 'I hear' to indicate perception through the sense of hearing.
• Example: I hear that the meeting is postponed.
• Therefore, the correct phrase should be 'I hear'.

Hence, the correct statement is: I hear that the heat wave is going to be worse this year.

Additional Information

• Stative verbs describe a state rather than an action and are generally not used in the continuous form.
• Example: I believe in fair play.
• Common stative verbs include: believe, know, understand, belong, contain, consist, love, hate, etc.
• Example: I understand your concerns.

The correct answer is Option 2)

Key Points

• Future Tense: The phrase "will get better" correctly uses the future tense to describe an improvement in health that is expected to happen by next week.
• Verb Agreement: The future tense is formed by using "will" before the base form of the verb, which in this case is "get."
• Clarity of Intention: Using "will" shows a clear intention or expectation of future improvement, which aligns with the meaning of the sentence.
• Context Appropriateness: The context of the sentence is about something expected to happen in the future, making "will get better" the most appropriate choice.
• Hope and Expectation: The phrase "I hope" sets the expectation, and "will get better" fits logically as it refers to a future event that is hoped for.
• Common Usage: This construction is commonly used in English to express hope for future improvements or changes.

Therefore, the correct answer is Option 2)

Additional Information

• Option 1: Uses present continuous tense "is getting," which is incorrect for a future expectation.
• Option 3: Incorrect usage of "have been getting," which is present perfect continuous tense, not appropriate for future hope.
• Option 4: Incorrect grammar as "is get" doesn't form a valid verb phrase.

The correct answer is Option 4)

 

Key Points

• The word "who" is a subject pronoun used to refer to people, fitting correctly in the context of the sentence.
• "Who" introduces a relative clause providing additional information about the man, i.e., what he used to do.
• Using "who" effectively connects the man with his action (telling fortunes), maintaining the sentence's grammatical structure.
• The sentence remains clear and understandable, preserving a smooth flow when "who" is used.
• "Who" is consistently employed in English to add information about a known person, ensuring proper syntax.
• According to standard English grammar rules, "who" is the appropriate relative pronoun to use after a noun referring to a person.

Therefore, the correct answer is Option 4.

 

Additional Information

• Option 1 (whom): "Whom" is used as an object pronoun, not as a subject pronoun, thus incorrect for the sentence.
• Option 2 (whose): "Whose" is a possessive pronoun, which would imply ownership, not suitable here.
• Option 3 (by whom): "By whom" changes the sentence to a passive construction, making it awkward and incorrect.

The correct answer is Option 2)

 

Key Points

• "Has" is the correct form of the verb to use here, aligning with the present perfect tense of the sentence structure.
• The present perfect tense ("has broken") indicates an action that occurred at an unspecified time before now.
• In this context, the present perfect tense is used to describe an action (breaking the door) that has a present relevance (the valuables are stolen).
• Using "has" ensures subject-verb agreement, as "somebody" is singular and requires a singular verb form.
• "Has broken" is a commonly used, grammatically correct phrase that fits well in conversational and narrative contexts.
• Maintaining the correct verb tense is crucial for the coherence and readability of the passage.

Therefore, the correct answer is Option 2.

 

Additional Information

• Option 1 (have): "Have" is a plural verb form, unsuitable for the singular subject "somebody."
• Option 3 (shall have): "Shall have" is future perfect tense, inappropriate for the context of the story.
• Option 4 (had): "Had" is past perfect tense, which is not suitable here since the action is relevant to the present.

The correct answer is Option 2)

 

Key Points

• "Quite" is used here to emphasize the extent of the fortune teller's shock.
• The adverb "quite" enhances the intensity of the adjective "shocked," making the expression stronger.
• The usage of "quite shocked" is a common, grammatically correct phrase in English.
• "Quite" fits the context well, describing the emotional reaction of the fortune teller adequately.
• Other options do not fit grammatically or contextually in the given sentence.

Therefore, the correct answer is 'Option 2.'

 

Additional Information

• Option 1 (many): "Many" is used to describe a large number of countable items and does not fit the context of describing the level of shock.
• Option 3 (so less): "So less" is grammatically incorrect; "less" is used with uncountable nouns and does not fit the instance of measuring shock.
• Option 4 (so more): "So more" is also grammatically incorrect and does not make sense in the given context.

The correct answer is Option 2)

 

Key Points

• The verb "commented" is in the past tense, which matches the narrative tense of the passage.
• Using the past tense "commented" ensures that the sentence remains consistent with the past narrative of the story.
• The word "commented" correctly introduces the direct speech that follows ("Every day he...").
• This choice provides a smooth transition from the description of events to the customer's remark.
• In narrative writing, reported speech or actions typically use the past tense to maintain a coherent timeline.

Therefore, the correct answer is 'Option 2.'

 

Additional Information

• Option 1 (comments): "Comments" is in the present tense and does not match the past tense narrative.
• Option 3 (comment): "Comment" is the base form of the verb and is not appropriate for this context.
• Option 4 (commenting): "Commenting" is the present participle and does not fit the structure of the sentence.

The correct answer is Option 4)

 

Key Points

• The verb "tells" is in the present tense, matching the habitual action described in the passage.
• A present tense verb is appropriate here to denote a routine or habitual action ("tells the fortunes of so many people").
• The use of "tells" emphasizes the regularity of the fortune teller's actions, contrasting with his inability to foresee his own crisis.
• In the customer's comment, "Every day he tells..." correctly parallels the habitual nature of the fortune teller's work.
• This choice maintains consistency with the narrative and logical flow of the passage.

Therefore, the correct answer is Option 4.

 

Additional Information

• Option 1 (tell): "Tell" is the base form of the verb and does not fit the structure of the sentence.
• Option 2 (telling): "Telling" is a present participle and does not make sense in the context of a habitual action.
• Option 3 (told): "Told" is in the past tense and does not match the present habitual action described.

The correct answer is Option 3)

Key Points

• In the given sentence, the preposition 'in' is incorrect.
• The correct preposition to use with time expressions such as 5:00 pm is 'at'.
• Therefore, the correct preposition that should be used in place of 'in' is 'at'.

Hence, the correct sentence is: His flight departs at 5:00 pm.

Additional Information

• Prepositions are important in indicating time, place, and direction. The preposition 'at' is used for specific times of the day.
• Example: The meeting starts at 3:00 pm.
• The preposition 'in' is used for longer periods, such as months, years, and parts of the day.
• Example: She was born in July.
• The preposition 'on' is used for specific days and dates.
• Example: The event is on Monday.

The correct answer is Option 1)

Key Points

• The word "Resourceful" means having the ability to find quick and clever ways to overcome difficulties. (साधन संपन्न)
• Example: She is a very resourceful manager who can handle any crisis with ease.
• "Incompetent" refers to lacking the necessary skills or ability to do something successfully. (अयोग्य)
• Example: His incompetence in managing the project led to its failure.

Hence, we can infer that the opposite of 'Resourceful' is 'Incompetent'.

Additional Information

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

• Immaculate (निर्मल): Perfectly clean or having no flaw.
• Example: Her house is always immaculate, no matter how busy she is.
• Ingenious (अविष्कारक): Clever, original, and inventive.
• Example: His ingenious solution to the problem was praised by everyone.
• Impeccable (निर्दोष): In accordance with the highest standards; faultless.
• Example: She has impeccable taste in fashion.

The correct answer is Option 1)

Key Points

• Common Collocation: The phrase "make a decision" is a common collocation in English. A collocation is a pair or group of words that are often used together.
• Standard Usage: "Make a decision" is widely recognized as the standard phrase used when describing the act of deciding something.
• Clarity and Understanding: Using "make" in this context ensures that the sentence is clear and easily understood by native English speakers.
• Context Suitability: The act of deciding upon a project requires a definitive action, which is best encapsulated by the verb "make."
• Decision-Making Process: The verb "make" pairs naturally with "decision" to describe the process of coming to a conclusion or judgment.
• Formality and Appropriateness: In both formal and informal contexts, "make a decision" is the most appropriate and conventional choice.

Therefore, the correct answer is Option 1)

Additional Information

• Option 2: "Frame" is not commonly used with "decision"; it's more appropriate for constructing sentences or policies.
• Option 3: "Build" is used for physical construction, not for decisions.
• Option 4: "Draw" is typically used with conclusions, not decisions.

The correct answer is Option 4)

Key Points

• The word "juvenile" refers to a young person or someone who is not yet an adult. It is often used to describe someone who is immature or childish. (किशोर)
• Example: Juvenile behavior is often characterized by impulsiveness and a lack of responsibility.
• "Adult" refers to a person who is fully grown or developed, typically someone who is mature and responsible. (वयस्क)
• Example: As an adult, you are expected to take responsibility for your actions and decisions.

Hence, we can infer that the opposite of 'juvenile' is 'adult'.

Additional Information

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

• Minor (अल्प): Refers to someone who is under the age of full legal responsibility.
• Example: As a minor, he is not allowed to vote or buy alcohol.
• Teenage (किशोरावस्था): Refers to someone who is in their teens, typically between the ages of 13 and 19.
• Example: Teenage years are often filled with a lot of emotional and physical changes.
• Puerile (बचकाना): Refers to behavior that is childishly silly or immature.
• Example: His puerile jokes were not appreciated by the serious audience.

The correct answer is Option 3)

Key Points

• The word "peice" is incorrectly spelled. The correct spelling is "piece".
• Meaning: A portion of an object or material. (टुकड़ा)
• Example: She gave me a piece of her mind.
• "Piece" refers to a portion or part of an object or material. (टुकड़ा)
• Example: He took a piece of bread from the basket.

Therefore, the correct answer is: Option 3 i.e. "piece".

Additional Information

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

• Praject (प्रोजेक्ट): Incorrect spelling of "project".
• Example: The project was due next week.
• Incrediblly (अविश्वसनीय): Incorrect spelling of "incredibly".
• Example: The show was incredibly entertaining.
• Foaund (पाया): Incorrect spelling of "found".
• Example: He found a coin on the street.

The correct answer is Option 3)

Key Points

• The word "condition" means a requirement that must be fulfilled before something else can happen. (शर्त)
• Example: She agreed to the job offer on the condition that she would receive regular promotions.
• "Would" is used to indicate a future action or state that is dependent on a condition. (करेंगे/होगा)
• Example: He said he would help me if I needed it.
• Hence, the correct substitution is 'on the condition that she would return'.

Additional Information

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

• Option 1: on the condition that she return (शर्त पर कि वह लौट आए): This option is grammatically incorrect because the verb form is not in the correct tense.
• Example: She agreed on the condition that she return the book.
• Option 2: on the conditions that she had return (शर्तों पर कि उसने वापसी की थी): This option is incorrect due to the misuse of "conditions" and wrong verb tense.
• Example: He accepted on the conditions that she had return the favor earlier.
• Option 4: on condition that she returned (शर्त पर कि वह लौट आई): Although this option is grammatically correct, it changes the tense of the original sentence.
• Example: She agreed on condition that she returned the money.

The correct answer is Option 4)

Key Points

• The phrase "in lieu of" means instead of or in place of something. (के बजाय)
• Example: She offered to cook dinner in lieu of paying rent.
• "Playing" refers to engaging in an activity for enjoyment or recreation. (खेलना)
• Example: The children spent the afternoon playing in the park.

Hence, the correct phrase "in lieu of playing" means instead of engaging in the activity of playing.

Additional Information

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

• Option 1: in lieu off playing (के बजाय): This is grammatically incorrect because "off" is a wrong preposition in this context.
• Example: Incorrect usage: He went to the library in lieu off playing football.
• Option 2: in lieu of play (के बजाय): This is grammatically incorrect because "play" should be in its gerund form "playing" to fit the context.
• Example: Incorrect usage: She chose to study in lieu of play.
• Option 3: on lieu of playing (के बजाय): This is grammatically incorrect because "on" is a wrong preposition in this context.
• Example: Incorrect usage: He read a book on lieu of playing video games.

The correct answer is Option 1)

Key Points

• The word "lousy" means something that is very poor or bad in quality. (बेकार)
• Example: The service at the restaurant was lousy, and the food was even worse.
• "Pitiful" refers to something that deserves or arouses pity, often due to its poor quality or condition. (दयनीय)
• Example: The pitiful state of the old house made it clear that it had been abandoned for years.

Hence, we can infer that the synonym of 'lousy' is 'pitiful'.

Additional Information

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

• Funny (मज़ेदार): Causing laughter or amusement.
• Example: The comedian's jokes were very funny and had everyone laughing.
• Moral (नैतिक): Concerned with the principles of right and wrong behavior.
• Example: The story had a strong moral lesson about the importance of honesty.
• Praiseworthy (प्रशंसनीय): Deserving approval and admiration.
• Example: Her efforts to help the homeless are truly praiseworthy.

The correct answer is Option 2)

Key Points

• The word "Peculiar" means something that is unusual or not typical; it can refer to something that is strange or odd. (अजीब)
• Example: She has a peculiar habit of humming while she works.
• "Strange" refers to something that is unusual or not normal, often implying a sense of mystery or unfamiliarity. (अजीब)
• Example: The house had a strange, eerie feeling to it.

Hence, we can infer that the synonym of 'Peculiar' is 'Strange'.

Additional Information

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

• Usual (सामान्य): Something that is commonly occurring or done; typical.
• Example: It is usual for him to take a walk in the evening.
• Frequent (अक्सर): Happening often or at short intervals.
• Example: He is a frequent visitor to the library.
• Revolutionary (क्रांतिकारी): Involving or causing a complete or dramatic change.
• Example: The invention of the internet was a revolutionary development.

The correct answer is Option 1)

Key Points

• The word "make up one's mind" means to decide what to do or choose a course of action. (निर्णय लेना)
• Example: She couldn't make up her mind whether to accept the job offer or not.
• "Decide" refers to making a choice or coming to a conclusion about something. (निर्णय करना)
• Example: He decided to go on a vacation after a long year of hard work.
• Hence, we can infer that "make up his mind" means to "decide".

Additional Information

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

• Think (सोचना): To consider or reflect on something.
• Example: She needs time to think about the proposal.
• Abandon (त्यागना): To leave something or someone completely.
• Example: They had to abandon the sinking ship.
• Abide (पालन करना): To accept or act in accordance with a rule, decision, or recommendation.
• Example: We must abide by the rules of the game.

The correct answer is Option 1)

Key Points

• The word "place" in this context means a particular position or point in space. (स्थान)
• Example: The place where the concert was held was packed with people.
• "Plight" refers to a dangerous, difficult, or otherwise unfortunate situation. (दुर्दशा)
• Example: The plight of the homeless is a serious issue that needs attention.

Hence, we can infer that the word 'plight' is more appropriate in the context of endangered species, as it highlights their dangerous and unfortunate situation.

Additional Information

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

• Perspective (दृष्टिकोण): A particular attitude toward or way of regarding something; a point of view.
• Example: Her perspective on the issue was quite different from mine.
• Position (स्थिति): A place where someone or something is located or has been put.
• Example: The position of the statue in the park is quite prominent.
• Prowess (कौशल): Skill or expertise in a particular activity or field.
• Example: His prowess in mathematics is well-known among his peers.

The correct answer is Option 3)

Key Points

• The word "alluring" means something that is very attractive or tempting. (आकर्षक)
• Example: The actress had an alluring charm that captivated everyone who met her.
• "Repulsive" refers to something that is extremely unpleasant or disgusting; it drives people away. (घृणित)
• Example: The smell from the garbage was so repulsive that people had to cover their noses.

Hence, we can infer that the opposite of 'alluring' is 'repulsive'.

Additional Information

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

• Enticing (लुभावना): Something that is attractive or tempting.
• Example: The job offer was enticing because of the high salary and benefits.
• Fascinating (मनमोहक): Extremely interesting or charming.
• Example: The documentary on marine life was absolutely fascinating.
• Glamorous (ग्लैमरस): Full of charm and elegance.
• Example: She looked glamorous in her evening gown at the awards ceremony.

The correct answer is: Sluggish.

Key Points

• The word "agile" means someone who is quick and light in movement or thought; someone who is nimble and active. (चुस्त)
• Example: The gymnast was incredibly agile, performing flips and twists with ease.
• "Sluggish" refers to someone or something that is slow-moving or lacking energy; the opposite of being agile. (सुस्त)
• Example: After the heavy meal, I felt sluggish and didn't want to move.

Hence, we can infer that the opposite of 'agile' is 'sluggish'.

Additional Information

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

• Active (सक्रिय): Engaging or ready to engage in physically energetic pursuits.
• Example: She is very active and participates in various sports.
• Energetic (ऊर्जावान): Showing or involving great activity or vitality.
• Example: The kids were energetic, running around the playground all day.
• Apathetic (उदासीन): Showing or feeling no interest, enthusiasm, or concern.
• Example: He was apathetic towards the charity event and didn't want to participate.

The correct answer is Option 3)

Key Points

• The phrase "left me in the lurch" means to abandon someone when they are in trouble or in a difficult situation. (मुसीबत में छोड़ देना)
• Example: He left me in the lurch when I needed him the most.
• "Refused to help me in my distress" means not providing assistance when someone is in a state of suffering or difficulty. (मेरी परेशानी में मदद करने से इनकार कर दिया)
• Example: My friends refused to help me in my distress, leaving me to cope on my own.

Therefore, the correct answer is: Option 3 i.e. refused to help me in my distress.

Additional Information

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

• Attempted to harass me (मुझे परेशान करने की कोशिश की): Tried to annoy or trouble me.
• Example: He attempted to harass me by constantly calling and messaging.
• Blamed only me for my failure (मेरी असफलता के लिए केवल मुझे दोषी ठहराया): Held me solely responsible for my failure.
• Example: They blamed only me for my failure in the project.
• Scorned me for committing mistakes (गलतियाँ करने के लिए मेरी अवहेलना की): Showed contempt or disdain towards me for making errors.
• Example: My teacher scorned me for committing mistakes in the exam.

The correct answer is Option 4)

Key Points

• The word "ascend" means to move upward, to rise, or to climb. (चढ़ना)
• Example: The balloon began to ascend into the sky.
• "Climb" refers to going or coming up a slope or staircase; to rise gradually to a higher point or level. (चढ़ना)
• Example: She had to climb several flights of stairs to reach her apartment.

Hence, we can infer that the synonym of 'ascend' is 'climb'.

Additional Information

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

• Arise (उठना): To emerge or become apparent.
• Example: New problems arise every day.
• Grab (पकड़ना): To take hold of something or someone suddenly.
• Example: He tried to grab the last cookie from the jar.
• Reach (पहुंचना): To arrive at a place, especially after some effort.
• Example: We finally reached the top of the hill.

The correct answer is Option 2)

Key Points

• The word "Produsing" is incorrectly spelt. The correct spelling is "Producing".
• Producing means creating or bringing forth something, especially through a process of manufacture or construction. (उत्पादन करना)
• Example: The factory is producing thousands of units every day.
• Produsing does not have a meaning in English as it is a misspelled word.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Bronze (कांस्य): A yellowish-brown alloy of copper with up to one-third tin.
• Example: The statue was made of bronze and looked magnificent.
• Heritage (विरासत): Property that is or may be inherited; an inheritance.
• Example: The cultural heritage of the country includes music, dance, and traditional crafts.
• Sculpture (मूर्तिकला): The art of making two- or three-dimensional representative or abstract forms, especially by carving stone or wood or by casting metal or plaster.
• Example: The museum has a beautiful sculpture of a famous historical figure.

Given: 23 January 2002 was Wednesday.

Now,

2002 to 2007 = 5 Years (4 Ordinary Years and 1 Leap Year).

And, In 5 Years = 1 Leap Year and 4 Ordinary Years.

So, 1 Leap Year has 2 odd days,

And, 4 Ordinary Years have 4 odd days.

Total odd days = 2 + 4 = 6.

then, 23 January 2007 will be Wednesday + 6 = Tuesday.

Now, the number of days between 23 January 2007 to 26 January 2007

= 3 days.

= 3 days → 3/7 = 0 weeks and 3 odd days.

So, 26 January 2007 will be Tuesday + 3 = Friday.

Hence, the correct answer is "Option 1".

Logic: 

First and third letters → (1) and (3) are added to the position values according to the English alphabetic series respectively.

Second and fourth letters → (2) and (4) are subtracted from the position values according to the English alphabetic series respectively.

​​So,

​

Hence, "Option - (4)" is the correct answer.

The logic followed here is:

Logic: (1^st number × 2^nd number) - 10 = 3^rd number.

Now,

For, (3, 12, 26)

⇒ (3 × 12) - 10

= 36 - 10 = 26.

For, (7, 9, 53)

⇒ (7 × 9) - 10

= 63 - 10 = 53.

Similarly, for (7, 5, 25)

⇒ (7 × 5) - 10

= 35 - 10 = 25.

Hence, the correct answer is "Option 3".

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

Conclusions:

I. All earth is space → Does not follow (As all space is wind and some wind is earth. So, it is possible but not definitely true)

II. Some wind is fire → Does not follow (As some wind is earth and some fire is earth. So, it is possible but not definitely true)

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

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

The logic followed here is:

Logic: Square of 1^st number = 2^nd number.

Now,

For, 11 : 121

⇒ 11² = 121.

For, 21 : 441

⇒ 21² = 441.

Similarly, for 31 ∶ ?

⇒ 31² = 961.

Hence, the correct answer is "Option 4".

Given: 26 November 2013 was Tuesday.

Now,

2013 to 2018 = 5 Years (4 Ordinary Years and 1 Leap Year).

And, In 5 Years = 1 Leap year and 4 Ordinary Years.

So, 1 Leap Year has 2 odd days,

And, 4 Ordinary Years have 4 odd days.

Total odd days = 2 + 4 = 6.

then, 26 November 2018 will be Tuesday + 6 = Monday.

Now, the number of days between 26 November 2018 to 29 November 2018

= 3 days.

= 3 days → 3/7 = 0 weeks and 3 odd days.

So, 29 November 2018 will be Monday + 3 = Thursday.

Hence, the correct answer is "Option 4".

Logic : Alternately (18) and (28) are added to each number subsequently.

Hence, "231" is the correct answer.

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

**Given :**​​

FJK : KOP

And,

MQR : RVW​

So, Checking the options one by one :

Option - (1): GMN : FLM

Option - (2): JMP : ORU

Option - (3): ADE : ZWV

Option - (4): PRS : SRP

​ 

Thus, out of all the options "JMP : ORU" follows the same pattern as given.

Hence, "Option - (2)" is the correct answer.

The logic followed here is :

1. For '

' element → Shifting back and forth to the opposite side.

2) For '

' element → Shifting in the clockwise direction from the center position towards the corner position.

3) For '

' element →  Shifting in the clockwise direction from the corner position towards the center position.

4) For '

' element → Shifting back and forth to the top center position.

5) For '

' element →  Shifting in the clockwise direction from the corner position towards the center position.

6) For '

' element → Shifting back and forth to the opposite side.

Thus, the final series is :

Hence, "Option - (4)" is the correct answer.

According to the given figure:

The figure will appear when it is opened as follows:

Hence, "Option - (1)" is the correct answer.

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

∴ Here, the given figure is embedded in option Figure - 1.

Hence, the correct answer is "Option- (1)".

Logic: (3) is added to the position values according to the English alphabetic series.

​​So,

Hence, "Option - (4)" is the correct answer.

Given Equation: 16 A 24 C 30 E 15 U 9 = ?

BODMAS Rule:

Decoding the given information:

 

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

⇒ 16 + 24 - 30 ÷ 15 × 9 = ?

⇒ 16 + 24 - 2 × 9 = ?

⇒ 16 + 24 - 18 = ?

⇒ 40 - 18 = 22.

Hence, the correct option is "Option 2".

Given Equation: 16 B 8 D 51 A 3 C 57 = ?

BODMAS Rule:

Decoding the given information:

 

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

⇒ 16 × 8 - 51 ÷ 3 + 57 = ?

⇒ 16 × 8 - 17 + 57 = ?

⇒ 128 - 17 + 57 = ?

⇒ 185 - 17 = 168.

Hence, the correct option is "Option 1".

The number of triangles in the given figure is shown below :

Here, as marked there are a total of 16 triangles.

Hence, "16" is the correct answer.

Logic : Odd number series is added to each number subsequently.

Hence, "133" is the correct answer.

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

∴ Here, the given figure is embedded in option Figure - 1.

Hence, the correct answer is "Option- (1)".

Logic:

First and second letter → (3) is added to the position values according to the English alphabetic series.

Second and third letter → (3) is added to the position values according to the English alphabetic series.

​​So, Checking the options one by one:

​Option - (1): BEH

Option - (2): RUX

Option - (3): KMP

Option - (4): NQT

Thus, out of all the options "KMP" is the odd one out

Hence, "Option - (3)" is the correct answer.

According to the given information,

Thus, according to the given codes 'vp' is the code for the word 'dirty'.

Hence, the correct answer is "vp".

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)".

Decoding the Symbols:

Given: Z × Y ÷ X − V + W 

Z × Y → Z is the wife of Y.

Y ÷ X → Y is the son of X.

X − V → X is the sister of V.

​

V + W → V is the mother of W.

Here, Z is the mother’s sister’s son’s wife of W.

Hence, the correct answer is "Option - (3)".

Logic : Even number series is added to each number subsequently.

Hence, "107" is the correct answer.

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)".

Given : 17 × 7 + (21 ÷ 3) × 5 – 28 + 34 = 72

According to the question, after replacing the numbers :

So,

Option - (1) : 21 and 28

17 × 7 + (21 ÷ 3) × 5 – 28 + 34 = 72 ⇒ 17 × 7 + (28 ÷ 3) × 5 – 21 + 34 = 72

17 × 7 + (28 ÷ 3) × 5 – 21 + 34 = 72

17 × 7 + 9.33 × 5 – 21 + 34 = 72

119 + 46.65 + 34 - 21 = 72

199.65 - 21 = 72

178.65 ≠  72 (LHS ≠ RHS)

Option - (2) : 7 and 3

17 × 7 + (21 ÷ 3) × 5 – 28 + 34 = 72 ⇒ 17 × 3 + (21 ÷ 7) × 5 – 28 + 34 = 72

17 × 3 + (21 ÷ 7) × 5 – 28 + 34 = 72

17 × 3 + 3 × 5 – 28 + 34 = 72

51 + 15 + 34 - 28 = 72

100 - 28 = 72

72 = 72 (LHS = RHS)

Option - (3) : 5 and 7

17 × 7 + (21 ÷ 3) × 5 – 28 + 34 = 72 ⇒ 17 × 5 + (21 ÷ 3) × 7 – 28 + 34 = 72

17 × 5 + (21 ÷ 3) × 7 – 28 + 34 = 72

17 × 5 + 7 × 7 – 28 + 34 = 72

85 + 49 + 34 - 28 = 72

168 - 28 = 72

140 ≠  72 (LHS ≠ RHS)

Option - (4) : 17 and 28

17 × 7 + (21 ÷ 3) × 5 – 28 + 34 = 72 ⇒ 28 × 7 + (21 ÷ 3) × 5 – 17 + 34 = 72

28 × 7 + (21 ÷ 3) × 5 – 17 + 34 = 72

28 × 7 + 7 × 5 – 17 + 34 = 72

196 + 35 + 34 - 17 = 72 

265 - 17 = 72

248 ≠  72 (LHS ≠ RHS)

Hence, "Option - (2)" is the correct answer.

Logic: (18) is added to the position values according to the English alphabetic series.

​​So,

AQLZ is related to SIDR

​ 

​And,

CPDV is related to UHVN

​ 

​Similarly,

EBRY is related to

​ 

Hence, "Option - (1)" is the correct answer.

Given:

Last year's monthly salary = ₹34,500

This year's monthly salary = ₹38,640

Formula Used:

Percentage Increase = (New Value - Old Value)/(Old Value) × 100

Calculation:

New Value = ₹38,640

Old Value = ₹34,500

Percentage Increase = (38,640 - 34,500)/(34,500) × 100

Percentage Increase = 4,140/34,500 × 100

⇒ Percentage Increase = 0.12 × 100

⇒ Percentage Increase = 12%

The percentage increase in Ranjan's monthly salary this year over his monthly salary last year is 12%.

Given:

Marked price = Rs. 1,000

Discount scheme (i): Two successive discounts of 25% and 5%

Discount scheme (ii): Two successive discounts of 20% and 10%

Formula Used:

Final price after successive discounts = Marked price × (1 - Discount 1) × (1 - Discount 2)

Calculation:

For scheme (i):

Discount 1 = 25% = 0.25

Discount 2 = 5% = 0.05

Final price after scheme (i) = 1000 × (1 - 0.25) × (1 - 0.05)

⇒ Final price after scheme (i) = 1000 × 0.75 × 0.95

⇒ Final price after scheme (i) = 1000 × 0.7125

⇒ Final price after scheme (i) = 712.5

For scheme (ii):

Discount 1 = 20% = 0.20

Discount 2 = 10% = 0.10

Final price after scheme (ii) = 1000 × (1 - 0.20) × (1 - 0.10)

⇒ Final price after scheme (ii) = 1000 × 0.80 × 0.90

⇒ Final price after scheme (ii) = 1000 × 0.72

⇒ Final price after scheme (ii) = 720

Difference in selling price = Final price after scheme (ii) - Final price after scheme (i)

⇒ Difference in selling price = 720 - 712.5

⇒ Difference in selling price = 7.5

The difference between the selling price under the two discount schemes is Rs. 7.5.

Formula Used:

Average sale per product = (Sum of sales for the product by all companies) ÷ 3

Total sales per company = Sum of sales for all products by the company

Calculations:

Step 1: Calculate the average sale per product.

Product A: (2750 + 2500 + 3500) ÷ 3 = 2916.67

Product B: (3250 + 3000 + 3150) ÷ 3 = 3133.33

Product C: (2250 + 1750 + 2400) ÷ 3 = 2133.33

⇒ The highest average sale per company is for the product B.

Step 2: Calculate the total sales per company.

Company X: 2750 + 3250 + 2250 = 8250

Company Y: 2500 + 3000 + 1750 = 7250

Company Z: 3500 + 3150 + 2400 = 9050

⇒ The lowest average sale per product is for the company Y.

∴ The highest average sale per company is for the product B and the lowest average sale per product is for the company Y.

Given:

First number (a) = 2

Second number (b) = 6

Third number (c) = 8

Formula Used:

Fourth proportional (d) = (b × c) / a

Calculation:

Fourth proportional = (6 × 8) / 2

Fourth proportional = 48 / 2

Fourth proportional = 24

The fourth proportional to 2, 6, 8 is 24.

Shortcut Trick

Let T_A and T_B be the times in minutes to run 3000 m.

Case 1: Arun runs 3000 m while Bhaskar runs 2600 m and loses by 0.5 min.

⇒ T_A = (2600 ÷ 3000) × T_B − 0.5 ⇒ T_A = (13/15)T_B − 0.5

Case 2: Bhaskar runs 3000 m while Arun runs 2500 m starting 2.5 min late.

⇒ T_B = (2500 ÷ 3000) × T_A + 2.5 ⇒ T_B = (5/6)T_A + 2.5

Substitute T_B: T_A = (13/15)((5/6)T_A + 2.5) − 0.5 ⇒ (5/18)T_A = 5/3 ⇒ T_A = 6 min, T_B = 7.5 min.

∴ The correct answer is 1.5 min.

Alternate Method

Given:

Total distance = 3 km = 3000 m.

Case 1: Bhaskar head start = 400 m, Arun beats him by 30 s = 0.5 min.

Case 2: Bhaskar time lead = 2.5 min, Arun beaten by 500 m.

Formula Used:

Time = Distance ÷ Speed

0 m 3000 m Case 1: Arun (3000m) wins by 0.5 min Bhaskar (2600m) starting at 400m Case 2: Bhaskar (3000m) wins Arun (2500m) starting 2.5 min late

Let V_A and V_B be the speeds of Arun and Bhaskar in m/min.

⇒ Case 1: 3000 ÷ V_A = (3000 − 400) ÷ V_B − 0.5

⇒ 3000 ÷ V_A = 2600 ÷ V_B − 0.5 --- (1)

⇒ Case 2: (3000 − 500) ÷ V_A = 3000 ÷ V_B − 2.5

⇒ 2500 ÷ V_A = 3000 ÷ V_B − 2.5 --- (2)

⇒ From (1), 1/V_A = (2600/V_B − 0.5) ÷ 3000

⇒ Substitute in (2): 2500 × [(2600/V_B − 0.5) ÷ 3000] = 3000/V_B − 2.5

⇒ (5/6) × (2600/V_B − 0.5) = 3000/V_B − 2.5

⇒ 13000/(6V_B) − 2.5/6 = 3000/V_B − 2.5

⇒ 2.5 − 5/12 = 3000/V_B − 6500/(3V_B)

⇒ 25/12 = (9000 − 6500) ÷ (3V_B) ⇒ 25/12 = 2500 ÷ (3V_B)

⇒ 3V_B = (2500 × 12) ÷ 25 ⇒ 3V_B = 1200 ⇒ V_B = 400 m/min

⇒ Time for Bhaskar (T_B) = 3000 ÷ 400 = 7.5 min

⇒ Substitute V_B in (1): 3000 ÷ V_A = 2600 ÷ 400 − 0.5 = 6.5 − 0.5 = 6 min

⇒ Time for Arun (T_A) = 6 min

⇒ Difference = 7.5 − 6 = 1.5 min

∴ The correct answer is 1.5 min.

Additional Information

Head Start vs Time Lead

A head start of 'x' meters means the opponent starts 'x' meters ahead. A time lead of 't' minutes means the opponent starts 't' minutes earlier than the other person.

Beating by Distance vs Time

If A beats B by 'd' meters, B is 'd' meters behind when A finishes. If A beats B by 't' minutes, B takes 't' minutes more than A to cover the same distance.

Relative Speed in Races

In a linear race, if both run in the same direction, relative speed is the difference of their speeds: V_rel = |V_A − V_B|.

Shortcut Trick

Ratio (Man : Son) 10 years ago = 5 : 1 (Difference = 4 units)

Ratio (Man : Son) 2 years hence = 4 : 2 = 2 : 1 (Difference = 1 unit)

Make difference equal: Multiply (2 : 1) by 4 ⇒ New Ratio = 8 : 4

Gap in Son's ratio units = 4 − 1 = 3 units. Total time gap = 10 + 2 = 12 years.

3 units = 12 years ⇒ 1 unit = 4 years.

Son's age 10 years ago = 1 unit = 4 years ⇒ Present age = 4 + 10 = 14 years.

∴ The correct answer is 14 years.

Alternate Method

Given:

Let the present age of the man be M and the son be S.

10 years ago: (M − 10) = 5 × (S − 10)

2 years hence: 2 × (M + 2) = 4 × (S + 2)

Calculations:

⇒ M − 10 = 5S − 50

⇒ M = 5S − 40 --- (Equation 1)

⇒ 2(M + 2) = 4(S + 2)

⇒ M + 2 = 2(S + 2)

⇒ M + 2 = 2S + 4

⇒ M = 2S + 2 --- (Equation 2)

⇒ 5S − 40 = 2S + 2

⇒ 3S = 42

⇒ S = 42 ÷ 3

⇒ S = 14 years

∴ The correct answer is 14 years.

Additional Information

Constant Age Difference

The difference between the ages of two people remains constant throughout their lives, regardless of how many years pass.

Sum of Ages Change

If the sum of ages of N people is X today, then after Y years, the new sum will be X + (N × Y).

Ratio Balancing Method

To solve age problems using ratios, always ensure the difference between the ratio parts of two individuals is made equal across different time periods.

Given:

Length of diagonal 1 (d₁) = 10 cm

Length of diagonal 2 (d₂) = 8.2 cm

Formula Used:

Area of rhombus = (1/2) × d₁ × d₂

Calculation:

Area = (1/2) × 10 × 8.2

⇒ Area = 5 × 8.2

⇒ Area = 41 cm²

The area of the rhombus is 41 cm².

Given:

In ΔABC, P and Q are the middle points of the sides AB and AC, respectively. R is a point on the segment PQ such that PR : RQ = 1 : 5. PR = 6 cm.

Formula Used:

In a triangle, the line segment joining the midpoints of two sides is parallel to the third side and half of it (Midpoint Theorem).

Calculation:

According to the Midpoint Theorem, PQ is parallel to BC and PQ = ½ BC.

Given PR : RQ = 1 : 5, so PR / RQ = 1 / 5.

Let RQ = x.

Then, PR = 6 cm and PR / RQ = 6 / x = 1 / 5.

⇒ 6 / x = 1 / 5

⇒ 6 = x / 5

⇒ x = 30 cm

Thus, PQ = PR + RQ = 6 + 30 = 36 cm.

Since PQ = ½ BC, we have:

⇒ BC = 2 × PQ

⇒ BC = 2 × 36

⇒ BC = 72 cm

The length of BC is 72 cm.

Given:

Number of boys = 40

Average weight of boys = 33 kg

Number of remaining students = 72 - 40 = 32

Average weight of remaining students = 15 kg

Formula Used:

Average weight of all students = (Total weight of all students) / (Total number of students)

Calculation:

Total weight of boys = 40 × 33

Total weight of boys = 1320 kg

Total weight of remaining students = 32 × 15

Total weight of remaining students = 480 kg

Total weight of all students = 1320 + 480

Total weight of all students = 1800 kg

Total number of students = 72

Average weight of all students = Total weight of all students / Total number of students

⇒ Average weight of all students = 1800 / 72

⇒ Average weight of all students = 25 kg

The average weight of all the students in the section is 25 kg.

Given:

Radius of the first circle (r₁) = 25 cm

Radius of the second circle (r₂) = 35 cm

Distance between the centers of the circles (d) = 80 cm

Formula used:

The length of the direct common tangent (D) between two circles is given by the formula:

D = √(d² - (r₁ - r₂)²)

The length of the transverse common tangent (T) between two circles is given by the formula:

T = √(d² - (r₁ + r₂)²)

Calculation:

Step 1: Calculate the length of the direct common tangent

⇒ D = √(80² - (35 - 25)²)

⇒ D = √(6400 - 10²)

⇒ D = √(6400 - 100)

⇒ D = √6300 cm

Step 2: Calculate the length of the transverse common tangent

⇒ T = √(80² - (35 + 25)²)

⇒ T = √(6400 - 60²)

⇒ T = √(6400 - 3600)

⇒ T = √2800 cm

Step 3: Calculate the ratio of the lengths

⇒ Ratio = T / D = √2800 : √6300 = √(2800/6300) = √(28/63) = √4/9 = 2/3 = 2 : 3

∴ The correct answer is option (4).

Shortcut Trick

Total work = LCM of 20, 10, and 5 = 20 units.

Combined efficiency of A, B, and C = 20 ÷ 5 = 4 units/day.

Combined efficiency of A and B = (20 ÷ 20) + (20 ÷ 10) = 1 + 2 = 3 units/day.

Efficiency of C = 4 − 3 = 1 unit/day.

Time taken by C alone = 20 ÷ 1 = 20 days.

∴ The correct answer is 20 days.

Alternate Method

Given:

Time taken by A = 20 days

Time taken by B = 10 days

Time taken by A, B, and C together = 5 days

Formula Used:

Total Work = LCM of time taken

Efficiency = Total Work ÷ Time

Calculations:

⇒ Efficiency of C = Total Efficiency − (Efficiency of A + Efficiency of B)

⇒ Efficiency of C = 4 − (1 + 2) = 1 unit/day

⇒ Time taken by C alone = Total Work ÷ Efficiency of C

⇒ Time taken = 20 ÷ 1 = 20 days

∴ The correct answer is 20 days.

Additional Information

Pipes & Cisterns

Similar to the Time & Work concept, but an outlet pipe that empties the tank is assigned a negative efficiency.

Work & Wages

Wages are divided in proportion to the total work done by each person, which matches the ratio of their efficiencies if they all work for the same number of days.

Alternate Day Work

Calculate the total work completed in one full cycle of alternating days, and then sequentially add the remaining work for the final fraction of days.

Shortcut Trick

Surface Area of a sphere is proportional to the square of its radius (r²).

Net percentage change = x + y + (x × y)/100

Here x = 25 and y = 25.

Increase % = 25 + 25 + (25 × 25)/100

Increase % = 50 + 6.25 = 56.25%

∴ The correct answer is 56.25%.

Alternate Method

Given: Increase in radius = 25%

Formula Used: Surface Area of a sphere = 4πr²

r = 4 units Initial Area ∝ 4²

r = 5 units New Area ∝ 5² Radius Ratio 4 : 5 (25% increase)

⇒ Let original radius r₁ = 4 units

⇒ New radius r₂ = 4 + (25% of 4) = 5 units

⇒ Original Surface Area A₁ = 4 × π × (4)² = 64π

⇒ New Surface Area A₂ = 4 × π × (5)² = 100π

⇒ Percentage Increase = [(A₂ − A₁) ÷ A₁] × 100

⇒ Percentage Increase = [(100π − 64π) ÷ 64π] × 100

⇒ Percentage Increase = (36 ÷ 64) × 100 = (9 ÷ 16) × 100 = 56.25%

∴ The correct answer is 56.25%.

Additional Information

Volume Percentage Change

Since Volume ∝ r³, if radius increases by 25% (ratio 4:5), the volume ratio becomes 4³:5³ = 64:125, resulting in a 95.31% increase.

General Successive Change Formula

For any two-dimensional measurement change (Area of circle, square, or sphere surface), total % change = x + y + (xy/100).

Sphere Properties

Surface Area = 4πr² and Volume = (4/3)πr³. For a hemisphere, Curved Surface Area = 2πr² and Total Surface Area = 3πr².

Given:

CD = 10 cm

BD = 6 cm

DM = CM (Since D is produced such that DM = CM)

Formula used:

We use the fact that in a right triangle, the line joining the mid-point of the hypotenuse to the opposite vertex is half of the hypotenuse.

Since DM = CM and C is the mid-point of CD:

CD = 2 × CM

Calculation:

Given CD = 10 cm

⇒ 10 = 2 × CM

⇒ CM = $\frac{10}{2} = 5$ cm

∴ The value of CM is 5 cm.

Given:

Markup on cost price = 25%

Discount on marked price = 10%

Final price paid by customer = Rs. 540

Formula Used:

Marked Price = Cost Price × (1 + Markup Percentage)

Sale Price = Marked Price × (1 - Discount Percentage)

Calculation:

Let the original cost price be Rs. C.

Marked Price = C × (1 + 0.25)

Marked Price = C × 1.25

Sale Price = Marked Price × (1 - 0.10)

Sale Price = C × 1.25 × 0.90

Sale Price = C × 1.125

Given Sale Price = Rs. 540

⇒ C × 1.125 = 540

⇒ C = 540 / 1.125

⇒ C = 480

The original cost price of the goods is Rs. 480.

Given:

Total period = 2015 to 2018

Stages of construction = 4

Stage 4 (Buildings completed) percentages for each year:

2015: 20%

2016: 10%

2017: 10%

2018: 10%

Formula used:

Total percentage of buildings completed = Sum of percentages for each year

Calculation:

⇒ Total percentage of buildings completed = 20% + 10% + 10% + 10%

⇒ Total percentage of buildings completed = 50%

∴ The total percentage of buildings completed during the period 2015 to 2018 is 50%.

Given:

Remainder when the first number is divided by the divisor = 6

Remainder when the second number is divided by the divisor = 7

Remainder when the sum of the two numbers is divided by the same divisor = 5

Formula Used:

If the remainders of two numbers when divided by the same divisor are r₁ and r₂, and the remainder when their sum is divided by the same divisor is r₃, then the divisor d can be found using:

r1 + r2 = r3 + kd

where k is an integer.

Calculation:

Given:

r₁ = 6

r₂ = 7

r₃ = 5

Using the formula:

6 + 7 = 5 + kd

⇒ 13 = 5 + kd

⇒ 13 - 5 = kd

⇒ 8 = kd

Since d must be a divisor of 8, the possible values for d are 1, 2, 4, and 8. However, the only option given that matches this is 8.

The divisor is 8.

Given:

The cost of rice is increased by 25%.

Its consumption is decreased by 30%.

Formula Used:

Percentage change in expenditure = (Change in cost) × (Change in consumption)

Calculation:

Let the original cost of rice be 100 units and the original consumption be 100 units.

New cost of rice = 100 + 25% of 100

New cost of rice = 100 + 25

New cost of rice = 125 units

New consumption of rice = 100 - 30% of 100

New consumption of rice = 100 - 30

New consumption of rice = 70 units

Original expenditure = 100 × 100

Original expenditure = 10000 units

New expenditure = 125 × 70

New expenditure = 8750 units

Percentage change in expenditure

⇒ (Original expenditure - New expenditure) / (Original expenditure) × 100

Percentage change in expenditure

⇒ (10000 - 8750) / (10000) × 100

Percentage change in expenditure

⇒ 1250 / 10000 × 100

Percentage change in expenditure

⇒ 12.5%

The expenditure of money decreased by 12(1/2)%.

Shortcut Trick

Put α = 15°, so 2α = 30°.

Expression: 1/sin⁴(90°−30°) + 1/(cos²(90°−30°) − 1) = 1/sin⁴60° + 1/(cos²60° − 1).

⇒ 1/(√3/2)⁴ + 1/((1/2)² − 1) = 16/9 + 1/(1/4 − 1) = 16/9 − 4/3 = 4/9.

Check options: Option (4) sec²30° × tan²30° = (2/√3)² × (1/√3)² = 4/3 × 1/3 = 4/9.

∴ The correct answer is sec² 2α tan² 2α.

Alternate Method

Given: Expression = 1/sin⁴(90° − 2α) + 1/(cos²(90° − 2α) − 1)

Formulas Used: sin(90°−θ) = cosθ; cos(90°−θ) = sinθ; 1−sin²θ = cos²θ

⇒ Expression = 1/cos⁴ 2α + 1/(sin² 2α − 1)

⇒ Expression = 1/cos⁴ 2α − 1/(1 − sin² 2α)

⇒ Expression = 1/cos⁴ 2α − 1/cos² 2α

⇒ Expression = (1 − cos² 2α) / cos⁴ 2α

⇒ Expression = sin² 2α / cos⁴ 2α = (sin² 2α / cos² 2α) × (1 / cos² 2α)

⇒ Expression = tan² 2α × sec² 2α

∴ The correct answer is sec² 2α tan² 2α.

Additional Information

Complementary Angle Rules

Trigonometric ratios change to their co-functions when the angle is (90° − θ): sin ↔ cos, tan ↔ cot, sec ↔ cosec.

Pythagorean Identities

Fundamental identities include sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Given:

The smallest angle measures 42º less than the greatest angle.

The remaining angle is 24º more than the smallest angle.

Formula Used:

Sum of angles in a triangle = 180º

Calculation:

Let the smallest angle be x º.

Largest angle = x + 42 º

Remaining angle = x + 24° 

Sum of angles: x + (x + 42) + (x + 24) = 180 º

⇒ 3x + 66 = 180

⇒ 3x = 180 - 66

⇒ 3x = 114

⇒ x = 38

Smallest angle = x = 38°. 

The measure of the smallest angle of the triangle is 38º.

Shortcut Trick

Assume Income = 100, Expenditure = 70, and Savings = 30.

Total Increase in Income = 15% of 100 = 15

Increase in Expenditure = 7.5% of 70 = 5.25

Increase in Savings = 15 − 5.25 = 9.75

Percentage Increase in Savings = (9.75 ÷ 30) × 100 = 32.5%

∴ The correct answer is 32.5%.

Alternate Method

Given:

Initial Expenditure = 70% of Income

Increase in Income = 15%

Increase in Expenditure = 7.5%

Formula Used:

Income = Expenditure + Savings

Percentage Increase = (Change ÷ Initial Value) × 100

Income = 100

Exp (70) Sav (30)

Inc +15% → 115 Exp +7.5% → 75.25 Sav → 39.75

Calculations:

Let initial Income = 100

⇒ Initial Expenditure = 70

⇒ Initial Savings = 100 − 70 = 30

⇒ New Income = 100 + 15% of 100 = 115

⇒ New Expenditure = 70 + 7.5% of 70

⇒ New Expenditure = 70 + 5.25 = 75.25

⇒ New Savings = 115 − 75.25 = 39.75

⇒ Increase in Savings = 39.75 − 30 = 9.75

⇒ Percentage Increase in Savings = (9.75 ÷ 30) × 100

⇒ Percentage Increase in Savings = 32.5%

∴ The correct answer is 32.5%.

Additional Information

Income-Expenditure Relationship

Income is always the sum of Expenditure and Savings. Any change in Income must be balanced by the sum of changes in Expenditure and Savings.

Weighted Average Rule

The percentage change in Income is the weighted average of percentage changes in Expenditure and Savings: %ΔIncome = (%ΔExp × Exp + %ΔSav × Sav) ÷ (Exp + Sav).

Alligation Method

Income problems can be solved using alligation where the ratio of Expenditure to Savings is the inverse of the differences between their percentage changes and the total income percentage change.

Given:

The expression: \rm 10 + 3{\frac{3}{5}} \div \left[ 2{\frac{2}{3}} \div \left{ 7{\frac{1}{6}} - \left( 2{\frac{1}{2}} + {\frac{2}{3}} \right) \right} \right]

Calculation:

Step 1: Solve the innermost bracket

⇒ 2(1/2) + 2/3 = 5/2 + 2/3

Convert to a common denominator:

⇒ 5/2 = 15/6 and 2/3 = 4/6

⇒ 15/6 + 4/6 = 19/6

Step 2: Subtract from 7(1/6)

⇒ 7(1/6) = 43/6

⇒ 43/6 - 19/6 = 24/6 = 4

Step 3: Divide 2(2/3) by 4

⇒ 2(2/3) = 8/3

⇒ 8/3 ÷ 4 = 8/3 × 1/4 = 8/12 = 2/3

Step 4: Divide 3(3/5) by 2/3

⇒ 3(3/5) = 18/5

⇒ 18/5 ÷ 2/3 = 18/5 × 3/2 = 54/10 = 27/5

Step 5: Add 10 to the result

⇒ 10 + 27/5 = 50/5 + 27/5 = 77/5

∴ The value of the expression is 77/5.

Given:

We need to calculate the ratio of the average production of refrigerators by companies A, B, and E for the years 2004-2005 to the average production of refrigerators by companies C and D for the years 2005-2006.

Formula used:

Average production = (Total production) / (Number of companies)

Calculation:

From the bar graph:

Production of refrigerators in 2004-2005:

Company A: 110

Company B: 160

Company E: 300

Total production for A, B, and E in 2004-2005 = 110 + 160 + 300 = 570

Average production for A, B, and E in 2004-2005 = 570 / 3 = 190

Production of refrigerators in 2005-2006:

Company C: 370

Company D: 490

Total production for C and D in 2005-2006 = 370 + 490 = 860

Average production for C and D in 2005-2006 = 860 / 2 = 430

Ratio:

Ratio = 190 / 430

⇒ Ratio = 190:430

⇒ Ratio = 19:43

∴ The required ratio is 19:43.

Given:

Year: 2001

State A:

Applied: 8000

Selected: 94

Formula used:

Percentage of candidates selected = (Number of candidates selected / Number of candidates applied) × 100

Calculation:

⇒ Percentage of candidates selected = (94 / 8000) × 100

⇒ Percentage of candidates selected = 1.175%

∴ The percentage of candidates selected over the candidates who applied in State A in 2001 is 1.175%.

Given:

Radius (r) = 3 cm

Height (h) = 14 cm

Formula Used:

Curved Surface Area (CSA) of a cylinder = 2π rh

Calculation:

Curved Surface Area (CSA) = 2 × 22/7 × 3 × 14

⇒ CSA = 2 × 22/7 × 3 × 14

⇒ CSA = 2 × 22 × 3 × 2

⇒ CSA = 2 × 22 × 6

⇒ CSA = 264 cm²

The curved surface area of the cylinder is 264 cm².

Given:

Principal (P) = ₹4,50,000

Simple Interest (SI) = ₹45,000

Rate of Interest (R) = 5% per annum

Formula Used:

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

Calculation:

We need to find T, so we rearrange the formula:

SI = (P × R × T) / 100

⇒ T = (SI × 100) / (P × R)

⇒ T = (45,000 × 100) / (4,50,000 × 5)

⇒ T = 45,00,000 / 22,50,000

⇒ T = 2 years

It will take 2 years for an amount of ₹4,50,000 to yield ₹45,000 as simple interest at a 5% per annum rate of interest.

The correct answer is West Indies and USA

Key Points

• West Indies and USA will host the 9^th Men's ICC T20 World Cup Cricket in 2024.
• This will be the first time the USA will co-host a major ICC event.
• The ICC T20 World Cup is one of the premier international championships in Twenty20 cricket.
• The tournament will feature teams from around the world competing for the title.
• Hosting the event in these countries aims to expand the cricketing footprint in the Americas.

Additional Information

• The ICC T20 World Cup was first held in 2007, and India won the inaugural tournament.
• The tournament is organized by the International Cricket Council (ICC), which is the global governing body for cricket.
• The decision to award the hosting rights to West Indies and USA is part of the ICC's efforts to globalize the game.
• Previous editions of the T20 World Cup have been held in various countries, including India, England, and Australia.
• The event will provide a significant boost to the development of cricket in the USA, where the sport is gaining popularity.

The correct answer is Maharshi Mahesh Yogi Ashram

Key Points

• The Beatles visited the Maharshi Mahesh Yogi Ashram in Rishikesh, India, in 1968.
• During their stay, they composed numerous songs influenced by classical Indian music and culture.
• This visit was part of their spiritual journey and interest in Transcendental Meditation taught by Maharshi Mahesh Yogi.
• Many of the songs written during this period were included in their "White Album".

Additional Information

• The Maharshi Mahesh Yogi Ashram, also known as the Beatles Ashram, is now a tourist attraction in Rishikesh.
• The Beatles' visit to India is considered a significant event in the history of rock music, showcasing the blending of Western and Eastern musical traditions.
• Their time in India also marked a period of prolific songwriting, contributing to the band's artistic evolution.

The correct answer is Sattriya

Key Points

• Sattriya is a classical dance form of Assam.
• It was introduced by the great Vaishnava saint and reformer of Assam, Sankardev.
• This dance form is an artistic way of presenting mythological teachings to the people.
• Sattriya dance is a combination of dance, drama, and music and is an important part of the Assamese culture.
• It is performed in the Sattras (monasteries) as a part of the daily rituals and as a part of special festivals.

Additional Information

• Sankardev was a 15^th-century saint-scholar, poet, and cultural icon of Assam.
• He played a key role in the cultural and religious history of Assam and laid the foundation of the Bhakti movement in Assam.
• Sattriya was recognized as one of the eight classical dance forms of India by the Sangeet Natak Akademi in 2000.
• The dance form has a rich tradition of over 500 years and continues to be a vital part of Assamese culture and heritage.

The correct answer is Ashwin

Key Points

• Dussehra festival is celebrated in the Hindu month of Ashwin.
• It marks the victory of Lord Rama over the demon king Ravana.
• The festival signifies the triumph of good over evil and is celebrated with great enthusiasm across India.
• In some regions, it is also known as Vijayadashami.
• The celebration includes the burning of effigies of Ravana, symbolizing the destruction of evil.

Additional Information

• The Hindu month of Ashwin typically falls in the Gregorian months of September and October.
• Dussehra is the culmination of the Navratri festival, which is a nine-day celebration dedicated to the worship of the Goddess Durga.
• It is one of the major festivals in India and is celebrated with various cultural performances, fairs, and processions.
• In some parts of India, people also celebrate the victory of Goddess Durga over the buffalo demon Mahishasura.
• Public celebrations include plays, dance dramas, and colorful processions depicting scenes from the Ramayana.

The correct answer is Myanmar

Key Points

• Chinlone (also known as Caneball) is the traditional sport of Myanmar.
• Chinlone is a combination of sport and dance, where players pass a ball made of rattan using their feet, knees, and heads.
• The game is typically played in a circle with teams or individually, focusing on skill and grace rather than competition.
• It is an integral part of Myanmar's culture and is often played during festivals and traditional events.

Additional Information

• Myanmar, formerly known as Burma, is a country in Southeast Asia bordered by Bangladesh, India, China, Laos, and Thailand.
• The official language is Burmese, and the country has a rich cultural heritage influenced by Buddhism.
• Myanmar gained independence from British colonial rule on January 4, 1948.
• The country is known for its diverse ethnic groups, traditional arts, and historical sites such as the ancient city of Bagan.

The correct answer is South Asian Association for Regional Cooperation

Key Points

• South Asian Association for Regional Cooperation (SAARC) is an organization of South Asian nations, established on December 8, 1985.
• SAARC aims to promote economic and regional integration among its member countries.
• The current member countries are Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, and Sri Lanka.
• The organization has its headquarters in Kathmandu, Nepal.
• SAARC's primary objectives include promoting the welfare of the peoples of South Asia and improving their quality of life, accelerating economic growth, social progress, and cultural development in the region.

Additional Information

• SAARC was established with the signing of the SAARC Charter in Dhaka, Bangladesh.
• Since its inception, SAARC has conducted several summits aimed at addressing regional issues and fostering cooperation.
• SAARC also includes nine observer states: Australia, China, the European Union, Iran, Japan, Mauritius, Myanmar, South Korea, and the United States.
• Various regional centers have been established under the auspices of SAARC to promote regional cooperation in specific areas, such as the SAARC Disaster Management Centre and the SAARC Agricultural Centre.

The correct answer is Uttarakhand

Key Points

• The Nanda Devi Biosphere Reserve is located in the state of Uttarakhand.
• It is recognized for its diverse flora and fauna, including several endangered species.
• The reserve is part of the UNESCO World Network of Biosphere Reserves since 2004.
• It encompasses the Nanda Devi and Valley of Flowers National Parks, which are known for their scenic beauty and rich biodiversity.
• The region is also culturally significant with many ancient temples and pilgrimage sites.

Additional Information

• The Nanda Devi Biosphere Reserve covers an area of about 5860.69 square kilometers.
• It is divided into three zones: core zone, buffer zone, and transition zone to ensure the protection of its delicate ecosystems.
• The core zone is strictly protected and human activities are restricted to minimize impact on wildlife.
• The reserve is a popular destination for trekking and mountaineering, attracting adventurers from around the world.
• Efforts are ongoing to balance conservation with sustainable development to benefit local communities.

The correct answer is A system that would promote the welfare of all rather than a few

Key Points

• The leaders of independent India decided to adopt a system that would promote the welfare of all rather than a few.
• This decision was rooted in the values of democracy, equality, and social justice.
• The aim was to ensure that the benefits of development and progress would reach all sections of society, not just a privileged few.
• This approach was also intended to reduce disparities in wealth and opportunities.

Additional Information

• The decision to promote the welfare of all was influenced by the principles enshrined in the Constitution of India, which was adopted on 26^th November 1949 and came into effect on 26^th January 1950.
• The Constitution lays down the framework for a democratic republic that assures its citizens justice, equality, and liberty.
• It includes Directive Principles of State Policy which guide the state in making policies aimed at social and economic welfare.
• The leaders believed that a just and equitable system would help in the nation-building process and promote social harmony.

The correct answer is Review

Key Points

• PARAKH stands for Performance Assessment, Review, and Analysis of Knowledge for Holistic Development.
• In February 2023, PARAKH was established as the first national assessment regulator in India.
• The initiative aims to standardize and improve the quality of assessments across various educational boards in India.
• PARAKH will set norms, standards, and guidelines for student assessment and evaluation for all recognized school boards across the country.
• The regulator will also ensure the equivalence of academic standards among different boards, thereby promoting uniformity in assessments.

Additional Information

• The establishment of PARAKH is part of the National Education Policy (NEP) 2020, which emphasizes the need for a holistic, multi-disciplinary approach to education.
• NEP 2020 aims to transform India's education system by 2040, making it more inclusive, flexible, and aligned with the needs of the 21^st century.
• PARAKH will also play a crucial role in the assessment reforms proposed by NEP 2020, including competency-based assessment and reducing the emphasis on rote learning.
• The regulator will work towards creating a more balanced and integrated assessment system that evaluates students' understanding, skills, and competencies.

The correct answer is Punjab

Key Points

• Parkash Singh Badal served as the Chief Minister of Punjab for five times.
• He was a prominent political figure in Punjab and a key leader of the Shiromani Akali Dal (SAD) party.
• His tenure as Chief Minister spanned across different terms, reflecting his significant influence and leadership in the state.
• Badal was known for his efforts towards agricultural development and addressing the issues of farmers in Punjab.
• He also played a crucial role in the political landscape of Punjab, contributing to various social and economic policies.

Additional Information

• Parkash Singh Badal was born on December 8, 1927, in Abul Khurana, Punjab.
• He was awarded the Padma Vibhushan, India's second-highest civilian award, in 2015 for his contributions to public affairs.
• He was a pivotal figure in Punjab politics, serving as the Chief Minister from 1970-1971, 1977-1980, 1997-2002, 2007-2012, and 2012-2017.
• Badal's leadership was characterized by a focus on rural development, infrastructure improvement, and welfare schemes for the underprivileged sections of society.
• He passed away on April 25, 2023, leaving behind a legacy of political service and dedication to Punjab.

The correct answer is 4 kg

Key Points

• 4 kg is the standard weight of the hammer for women in the hammer throw event.
• The hammer throw is a track and field event in which the athlete throws a heavy metal ball attached to a wire and handle.
• This event is part of the Olympic Games and World Championships in athletics.
• The hammer must be thrown from inside a circle with a diameter of 2.135 meters.
• The throw is measured from the inside edge of the circle to the nearest mark made by the fall of the hammer.

Additional Information

• The men's hammer weighs 7.26 kg (16 pounds).
• The hammer throw has been part of the men's track and field program since the 1900 Summer Olympics in Paris.
• The women's hammer throw was added to the Olympic program in the 2000 Sydney Games.
• Hammer throw technique involves the athlete spinning with the hammer several times before releasing it.
• Proper technique and strength are crucial for achieving maximum distance in the hammer throw.