SSC CHSL Tier-1 2024: Official Paper (Held On: 09 Jul, 2024 Shift 3) (Previous Year Paper)

The correct answer is: Option 2.

Key Points

• The phrase "as smart as" is used to make a comparison between two entities, indicating that they possess the same level of intelligence. (उतना ही स्मार्ट जितना)
• Example: She is as smart as her older brother.

Therefore, the correct answer is: Option 2 i.e**. 'as smart as'.**

Additional Information

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

• Most smart as (सबसे स्मार्ट जैसा): This phrase is incorrect in English grammar.
• Example: Incorrect: She is the most smart as her friend.
• More smart as (ज्यादा स्मार्ट जैसा): This phrase is also incorrect in English grammar.
• Example: Incorrect: He is more smart as his colleague.
• Smartest than (सबसे स्मार्ट): This phrase is incorrect because the correct comparative form is "smarter than."
• Example: Incorrect: She is the smartest than everyone in the class.

The correct answer is Option 2.

 

Key Points

• The primary issue in the sentence is the incorrect form of the verb "watched" in the phrase "did not watched."
• When using the auxiliary verb "did," the main verb should be in its base form.
• The correct phrase should be "did not watch," ensuring grammatical correctness.
• Thus, the error is located in part 2 of the sentence.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "She did not watch Frankenstein last night."

 

Additional Information

• 1: "last night." – This part of the sentence is grammatically correct and does not require any changes.
• 3: "She" – This part of the sentence is grammatically correct and does not require any changes.
• 4: "Frankenstein" – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is Option 2.

 

Key Points

• The primary issue in the sentence is the incorrect use of the phrase "called out." The correct phrase should be "called off."
• The phrase "called off" means to cancel or end something, which is appropriate in this context.
• The correct phrase should be "called off the strike," ensuring grammatical correctness and clarity.
• Thus, the error is located in Option 2 of the sentence.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "The workers called off the strike because the management acceded to all their demands."

 

Additional Information

• Option 1: "all their demands," – This part of the sentence is grammatically correct and does not require any changes.
• Option 3: "the management acceded to," – This part of the sentence is grammatically correct and does not require any changes.
• Option 4: "The workers called out," – This part of the sentence contains the error and should be corrected to "called off."

The correct answer is Option 2.

 

Key Points

• The primary issue in the sentence is the incorrect form of the verb "obtain."
• To maintain parallelism with the verb "make," the correct form should be "obtaining."
• The correct phrase should be "make money by obtaining resources," ensuring grammatical correctness and clarity.
• Thus, the error is located in part 2 of the sentence.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "A company can make money by obtaining resources more affordably."

 

Additional Information

• 1: "make money by," – This part of the sentence is grammatically correct and does not require any changes.
• 3: "A company can," – This part of the sentence is grammatically correct and does not require any changes.
• 4: "more affordably." – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is 'most easily'.

 

Key Points

• The word "most easily" indicates the highest degree of being easy, which suits the context of conversation being an art that is achievable with minimal effort.
• The other options: "most occasionally", "more easily", and "more likely" do not fit the context as appropriately.

​Therefore, the correct answer is 'Option 1'.

Complete Sentence: Conversation is indeed the most easily teachable of all arts.

Additional Information

• Most occasionally: This suggests infrequency, which doesn't fit the context of the teachability of conversation as an art.
• More easily: This implies a comparison but doesn't convey the superlative sense needed in this context.
• More likely: This implies probability, which doesn't suit the context of how teachable an art is.

The correct answer is 'subject'.

 

Key Points

• The word "subject" refers to a topic or theme of discussion, which is most appropriate for conversations.
• Selecting a subject that interests both you and your listeners is crucial for engaging conversation.
• The other options, "luxury", "credit", and "result" do not fit the context of initiating and maintaining an engaging conversation.

​Therefore, the correct answer is 'Option 3'.

Complete Sentence: All you need to do in order to become a good conversationalist is to find a subject that interests you and your listeners.

Additional Information

• Luxury: Refers to something expensive and desirable but not essential, which doesn't suit the context here.
• Credit: Refers to recognition or an acknowledgment of achievement, which is not relevant to selecting a conversation topic.
• Result: Refers to an outcome, which does not fit the context of discussing an engaging topic for conversation.

The correct answer is 'fellow’s'.

 

Key Points

• The word "fellow’s" means belonging to a person in the same position, involved in the same activity, or otherwise associated with another. (साथी का)
• When engaging in conversation, discussing the other person's hobby or interest is more engaging and polite.
• The other options: "self’s," "victim’s," and "worker’s" do not fit the context as appropriately.

​Therefore, the correct answer is 'Option 2'.

Complete Sentence: But the important thing is that you must talk about the other fellow’s hobby rather than your own.

Additional Information

• Self’s (स्वयं का): is incorrect as it does not align with the possessive context required.
• Victim’s (पीड़ित का): is incorrect as it implies harm or disadvantage, which is not relevant here.
• Worker’s (कर्मचारी का): is incorrect as it refers to someone engaged in a specific task or occupation, which is off-topic in this context.

The correct answer is 'popularity'.

 

Key Points

• The word "popularity" means the state or condition of being liked, admired, or supported by many people. (लोकप्रियता)
• In the context of the passage, talking about topics that interest your listeners helps you gain a reputation for being well-liked and engaging, hence increasing your popularity.
• The other options: "irrationality", "capacity", and "audacity" do not fit the context as appropriately.

​Therefore, the correct answer is 'Option 1'.

Complete Sentence: Therein lies the secret of your popularity.

Additional Information

• Irrationality (अकर्तव्यता): means the quality of being illogical or unreasonable.
• Capacity (क्षमता): means the ability or power to do something.
• Audacity (धृष्टता): means the willingness to take bold risks or show impudent behavior.

The correct answer is 'pleases'.

 

Key Points

• The word "pleases" means to cause to feel happy and satisfied. (प्रसन्न करना)
• In context, showing interest in other people's interests makes them happy and satisfied, enhancing your reputation as a good conversationalist.
• The other options: "admits," "accompanies," and "advances" do not fit the context as appropriately.

​Therefore, the correct answer is 'Option 2'.

Complete Sentence: There is nothing that pleases people so much as your interest in their interest.

Additional Information

• Admits (मानना): means to confess or acknowledge something.
• Accompanies (साथ देना): means to go somewhere with someone.
• Advances (प्रगति करना): means to move forward in a purposeful way.

The correct answer is: Option 2.

Key Points

• The word "bequeath" means to leave (a personal estate or one's body) to a person or other beneficiary by a will. (वसीयत में देना)
• Example: He bequeathed his entire estate to his daughter.
• "To" is used to indicate the recipient of something. (को)
• Example: She gave the book to her friend.
• Hence, the correct preposition to use in this context is "to".

Therefore, the correct answer is: Option 2.

Additional Information

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

• Into the old age home (पुराने उम्र के घर में): This phrase suggests movement or direction towards the inside of something.
• Example: She walked into the old age home to visit her grandmother.
• With the old age home (पुराने उम्र के घर के साथ): This phrase suggests association or accompaniment.
• Example: He worked with the old age home to improve their facilities.
• By the old age home (पुराने उम्र के घर द्वारा): This phrase indicates the agent performing the action.
• Example: The event was organized by the old age home.

The correct answer is Option 4.

 

Key Points

• The verb "speaks" is the most appropriate word to use in this context when referring to telling the truth.
• "Talks" can be replaced with "speaks" to convey the intended meaning accurately.
• Other options like "utters," "narrates," and "declares" do not fit well in the context of this sentence.
• Thus, "speaks" is the best choice to complete the sentence meaningfully.

Therefore, the correct answer is Option 4.

 

Correct Sentence: "He never speaks the truth."

 

Additional Information

• Option 1: "utters" – While "utters" means to speak or say something, it is more often used in a different context, such as uttering a sound or words.
• Option 2: "narrates" – This implies telling a story or giving an account of events, which doesn't fit well in this context.
• Option 3: "declares" – This implies making a formal or emphatic statement, which is not suitable here.
• Option 4: "speaks" – This is the most appropriate choice as it directly relates to telling the truth.

The correct answer is: Option 4.

Key Points

• The phrase "suggest you try calling" means recommending someone to make an attempt to call. (आपको कॉल करने की सलाह देना)
• Example: I suggest you try calling her in the evening when she's usually free.
• "Try" refers to making an attempt or effort to do something. (प्रयास करना)
• Example: He will try to finish his homework before dinner.
• Hence, we can infer that the correct phrase is "suggest you try calling".

Therefore, the correct answer is: Option 4.

Additional Information

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

• Option 1: asked you to call (आपसे कॉल करने को कहा):
• Example: She asked you to call her when you get home.
• Option 2: am suggesting you calling (मैं आपको कॉल करने का सुझाव दे रहा हूँ):
• Example: I am suggesting you calling him to resolve the issue.
• Option 3: ask you to try called (आपसे प्रयास करने के लिए कहा):
• Example: They ask you to try called the support team for assistance.

The correct answer is: Option 4.

Key Points

• The word "Ministir" is incorrectly spelt in the given sentence. The correct spelling should be "Minister". (मंत्री)
• Example: The minister will address the nation tomorrow.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Ravines (दर्रे): A deep, narrow gorge with steep sides.
• Example: The village is located near several deep ravines.
• Engineers (इंजीनियर): Professionals who design, construct, and maintain structures, machines, or systems.
• Example: The engineers are working on a new bridge design.
• Bridges (पुल): Structures built to span physical obstacles like water bodies, valleys, or roads.
• Example: The city has several beautiful bridges over the river.

The correct answer is: Option 1.

Key Points

• The word "optimistic" means having a hopeful and positive outlook about the future. (आशावादी)
• Example: The coach was optimistic that his team would win the championship.
• "Doubtful" refers to feeling uncertain or lacking conviction. (संदेहपूर्ण)
• Example: She was doubtful about the success of the new project.
• Hence, we can infer that the opposite of 'optimistic' is 'doubtful'.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Tasteful (स्वादिष्ट): Showing good aesthetic judgment or appropriate behavior.
• Example: The artist's work was both tasteful and innovative.
• Helpful (सहायक): Providing assistance or being useful.
• Example: The staff was very helpful in guiding us through the museum.
• Cheerful (प्रसन्न): Noticeably happy and optimistic.
• Example: Despite the bad news, she remained cheerful.

The correct answer is: Option 3.

Key Points

• The word "generous" means showing a readiness to give more of something, especially money, than is strictly necessary or expected. (उदार)
• Example: The generous donation from the philanthropist helped build a new library.
• "Kind" refers to being friendly, generous, and considerate. (दयालु)
• Example: She is always kind to her neighbors and helps them whenever she can.

Therefore, the correct answer is: kind.

Additional Information

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

• Great (महान): Of an extent, amount, or intensity considerably above the normal or average.
• Example: He achieved great success in his career.
• Shrewd (चतुर): Having or showing sharp powers of judgment; astute.
• Example: The shrewd businessman made a profitable deal.
• Popular (लोकप्रिय): Liked or admired by many people or by a particular person or group.
• Example: The new café has become very popular among the locals.

The correct answer is: Option 4.

Key Points

• The word "peak" means the highest point of a mountain or the highest level of something. (चोटी)
• Example: The climbers finally reached the peak of the mountain after a grueling ascent.
• "Peak" refers to the topmost point, especially of a mountain, and is the correct term to use when talking about reaching the highest point of Mount Everest. (चोटी)
• Example: He dreamed of standing on the peak of Everest, feeling on top of the world.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Pike (भाला): A type of spear or a predatory fish.
• Example: The soldier carried a long pike as a weapon.
• Pick (चुनना): To choose or select someone or something.
• Example: She had to pick a dress for the party.
• Peek (झांकना): To look quickly or secretly.
• Example: He took a quick peek at the surprise gift.

The correct answer is: reduce.

Key Points

• The word "alleviate" means to make something less severe or intense; to relieve or reduce. (कम करना)
• Example: She took painkillers to alleviate her headache.
• "Reduce" refers to making something smaller or less in amount, degree, or size. (घटाना)
• Example: We need to reduce our expenses to save more money.
• Hence, we can infer that a synonym for 'alleviate' is 'reduce'.

Therefore, the correct answer is: reduce.

Additional Information

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

• Worsen (बिगाड़ना): To make something worse or more severe.
• Example: His comments only served to worsen the situation.
• Soar (ऊंची उड़ान भरना): To fly or rise high in the air; to increase rapidly.
• Example: The eagle soared high above the mountains.
• Increase (बढ़ाना): To become or make greater in size, amount, or degree.
• Example: We need to increase our efforts to achieve our goals.

The correct answer is Option 3.

 

Key Points

• The sentence "The small size of his store makes it impossible for him to stock all the items." is grammatically correct as it stands.
• The subject "The small size of his store" correctly leads to the effect "makes it impossible for him to stock all the items."
• The verb "makes" correctly indicates the cause-effect relationship in the sentence.

Therefore, the correct answer is Option 3.

 

Correct Sentence: "The small size of his store makes it impossible for him to stock all the items."

 

Additional Information

• Option 1: "made them impossible" – This option is incorrect because "them" does not have a clear antecedent in the sentence.
• Option 2: "making it impossible" – This option is incorrect because it changes the structure and meaning of the sentence.
• Option 4: "is made it impossible" – This option is grammatically incorrect as it uses both "is" and "made" incorrectly together.

The correct answer is: Option 2.

Key Points

• The word "reverie" means a state of being pleasantly lost in one's thoughts; a daydream. (स्वप्निल अवस्था)
• Example: She was jolted out of her reverie by the sound of the phone ringing.
• "Reality" refers to the state of things as they actually exist, as opposed to an idealistic or notional idea of them. (वास्तविकता)
• Example: After the vacation, it was hard to return to reality and the daily grind.

Hence, the opposite of 'reverie' is 'reality'.

Additional Information

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

• Daydream (दिन का सपना): A series of pleasant thoughts that distract one's attention from the present.
• Example: He often daydreams about his future success.
• Trance (उत्कट ध्यान): A half-conscious state characterized by an absence of response to external stimuli.
• Example: She went into a trance during the meditation session.
• Fantasy (कल्पना): The faculty or activity of imagining impossible or improbable things.
• Example: He lives in a world of fantasy, always imagining himself as a superhero.

The correct answer is: Option 3.

Key Points

• The word "squirm" means to wriggle or twist the body from side to side, especially as a result of nervousness or discomfort. (कसमसाना)
• Example: He began to squirm in his seat when the teacher asked him a question.
• "Relax" means to make or become less tense or anxious; to rest or unwind. (आराम करना)
• Example: After a long day at work, I like to relax with a good book.

Hence, we can infer that the opposite of 'squirm' is 'relax'.

Additional Information

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

• Chat (बातचीत): To engage in informal conversation.
• Example: We had a pleasant chat over coffee.
• Pray (प्रार्थना करना): To address a solemn request or expression of thanks to a deity or other object of worship.
• Example: Every morning, she prays for her family's well-being.
• Speak (बोलना): To articulate or communicate in speech.
• Example: He was invited to speak at the conference.

The correct answer is: Option 1.

Key Points

• The word "meticulous" means showing great attention to detail; very careful and precise. (सावधान)
• Example: She was meticulous in her preparation for the exam, ensuring every detail was covered.
• "Careful" refers to making sure of avoiding potential danger, mishap, or harm; cautious. (सावधान)
• Example: He was careful when crossing the busy street to avoid any accidents.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Lazy (आलसी): Unwilling to work or use energy.
• Example: He is too lazy to clean his room.
• Intelligent (बुद्धिमान): Having or showing intelligence, especially of a high level.
• Example: She is very intelligent and excels in her studies.
• Selective (चयनात्मक): Relating to or involving the selection of the most suitable or best qualified.
• Example: He is very selective about the books he reads.

The correct answer is Option 2.

 

Key Points

• The primary issue in the sentence is the spelling error in the word "simpathy."
• The correct spelling of the word should be "sympathy."
• Thus, the error is located in part 2 of the sentence.

Therefore, the correct answer is Option 2.

 

Correct Sentence: "When the famous businessman faced a huge loss in his business, no one expressed sympathy."

 

Additional Information

• 1: "When the famous businessman," – This part of the sentence is grammatically correct and does not contain any spelling errors.
• 3: "in his business," – This part of the sentence is grammatically correct and does not contain any spelling errors.
• 4: "faced a huge loss," – This part of the sentence is grammatically correct and does not contain any spelling errors.

The correct answer is: Option 1.

Key Points

• The idiom "An old head on young shoulders" means a young person who acts or speaks with the wisdom or maturity of an older person. (एक युवा व्यक्ति जो वृद्ध व्यक्ति की तरह व्यवहार करता है या बोलता है)
• Example: Despite being only 16, John often provides advice with the wisdom of an old head on young shoulders.
• Explanation: The idiom signifies a young individual who displays maturity and understanding beyond their years. (यह मुहावरा एक युवा व्यक्ति को दर्शाता है जो अपनी उम्र से अधिक परिपक्वता और समझ दिखाता है)
• Example: Sarah's insightful comments during the meeting showed she had an old head on young shoulders.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Option 2: A young person who is lazy. (एक युवा व्यक्ति जो आलसी है)
• Example: Tom is a young person who is lazy and prefers playing video games all day.
• Option 3: A person who is slow at understanding things. (एक व्यक्ति जो चीजों को समझने में धीमा है)
• Example: Mary is often slow at understanding things, so she needs extra time to complete her tasks.
• Option 4: A young person who looks old. (एक युवा व्यक्ति जो बूढ़ा दिखता है)
• Example: Due to his health condition, Jake is a young person who looks old.

The correct answer is: Option 2.

Key Points

• The idiom "A wild goose chase" means a futile or hopeless pursuit of something that is unattainable or non-existent. (व्यर्थ खोज)
• Example: He went on a wild goose chase trying to find a rare book that doesn't exist.
• "Fruitless search" refers to an effort or search that yields no results or success. (व्यर्थ खोज)
• Example: After hours of looking, their attempt to find the missing keys proved to be a fruitless search.

Therefore, the correct answer is: Option 2.

Additional Information

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

• On a hunt (शिकार पर): The act of searching for or pursuing something, typically for food or sport.
• Example: They went on a hunt for deer in the forest.
• Fruitful search (सफल खोज): An effort or search that yields positive results or success.
• Example: Their search for a new manager was fruitful, and they hired a highly qualified candidate.
• Ideal seeking (आदर्श खोज): The pursuit of an ideal or perfect scenario.
• Example: She is always ideal seeking, trying to find the perfect balance in life.

The correct answer is: Option 4.

Key Points

• The word "rapid" means happening in a short time or at a fast pace. (तेज़)
• Example: The rapid growth of technology has changed the world significantly.
• "Hasty" refers to something done with excessive speed or urgency; hurried. (जल्दबाज़ी)
• Example: They made a hasty decision without considering all the facts.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Pervious (छिद्रयुक्त): Allowing water or other substances to pass through.
• Example: The soil was pervious, allowing rainwater to seep through quickly.
• Stubborn (ज़िद्दी): Having or showing dogged determination not to change one's attitude or position on something.
• Example: He was too stubborn to admit he was wrong.
• Grim (कठोर): Forbidding or uninviting.
• Example: The future looked grim after the company announced layoffs.

The logic followed here is:

A new arrow added in bottom of the existing arrow in each next figure and direction of the arrow is reversed from the previous one.

Hence, the correct answer is "Option 2".

The paper after unfolded will be:

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: Identifying Synonyms.

Here,

Smart : Intelligent → Smart and Intelligent are synonyms.

Similarly,

Liable : Accountable → Liable and Accountable are synonyms.

Modest : Humble → Modest and Humble are synonyms.

Outbreak : Eruption → Outbreak and Eruption are synonyms.

However,

Nimble : Sluggish → Nimble and Sluggish are antonyms, not synonyms.

Hence, the correct answer is "Option 1".

Given: 22 March 2000 was Wednesday.

Now,

2000 to 2009 = 9 Years (7 Ordinary Years and 2 Leap Years).

And, In 9 Years = 2 Leap years and 7 Ordinary Years.

So, 2 Leap Years have 4 odd days,

And, 7 Ordinary Years have 7 odd days.

Total odd days = 4 + 7 = 11.

11 odd days → 11/7 = 1 week and 4 odd days.

then, 22 March 2009 will be Wednesday + 4 = Sunday.

Now, the number of days between 22 March 2009 to 16 January 2010

= 284(March to December 2009) + 16(January 2010) = 300 days.

= 300 days → 300/7 = 42 weeks and 6 odd days.

So, 16 January 2010 will be Sunday + 6 = Saturday.

Hence, the correct answer is "Option 4".

The logic followed here is: 1^st letter +2; 2^nd letter - 3 and 3^rd letter + 4.

Hence, the correct answer is "Option 2".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 1".

The image embedded in given figure is as shown below:

Hence, "Option 3" is the correct answer.

Given Equation: 222 A 2 C 7 B 3 D 11 = ?

BODMAS Rule:

Decoding the given information:

 

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

⇒ 222 ÷ 2 + 7 × 3 - 11 = ?

⇒ 111 + 7 × 3 - 11 = ?

⇒ 111 + 21 - 11 = ?

⇒ 132 - 11 = ?

⇒ 121

Hence, the correct option is "Option 1".

The triangles are:

So, 20 triangles are there in the following figure.

Hence, the correct answer is "Option 3".

The image embedded in given figure is as shown below:

 

Hence, "Option 4" is the correct answer.

Given: 19 February 2014 was Wednesday.

Now,

2014 to 2022 = 8 Years (6 Ordinary Year and 2 Leap Year).

And, In 8 Years = 2 Leap years and 6 Ordinary Year.

So, 2 Leap Year has 4 odd days,

And, 6 Ordinary Year has 6 odd days.

Total odd days = 4 + 6 = 10.

10 odd days → 10/7 = 1 week and 3 odd days.

then, 19 February 2022 will be Wednesday + 3 = Saturday.

Hence, the correct answer is "Option 2".

The logic followed here is:

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

Now,

For, (120, 8, 15)

⇒ (8 × 15) = 120.

For, (144, 24, 6)

⇒ (24 × 6) = 144.

Similarly, For (115, 23, 5)

⇒ (23 × 5) = 115.

Hence, the correct answer is "Option 2".

The logic followed here is:

Hence, the correct answer is "Option 1".

Given statements:

No cloud is a mountain.

All mountains are rivers.

All rivers are oceans.

The least possible Venn diagram:

Conclusions:

(I) All rivers can never be clouds. - True (Because there is no direct relation between rivers and clouds so it can be possible)

(II) All mountains are oceans. - True (Because All mountains are rivers and All rivers are oceans, so all mountains are oceans it is definite)

So, Both conclusions I and II follow

Hence, the correct answer is "Option 3".

The logic followed here is:

Option 1) JKQP

Option 2) OPMK

Option 3) DEWV

Option 4) QRJI

Hence, the correct answer is "Option 2".

Given equation: 36 – 42 ÷ 26 + 13 × 14 = ?

If ‘+’ and ‘÷’ and ‘×’ and ‘–’ are interchanged then we get:

⇒ 36 × 42 + 26 ÷ 13 - 14 = ?

⇒ 36 × 42 + 2 - 14 = ?

⇒ 1512 + 2 - 14 = ?

⇒ 1514 - 14 = ? = 1500

Hence, the correct answer is "Option 2".

According to the given information:

Thus, the code for 'bright' = pl

Hence, the correct answer is "Option 1".

The logic followed here is:

EHJL is related to FJMP

BEGI is related to CGJM

Similarly, DGIK related ?

Hence, the correct answer is "Option 3".

Family Chart: 

Decoding the Symbols:

 

Given: M & N @ O # P $ Q

It means: M is the daughter of N, N is the husband of O, O is the mother of P and P is the brother of Q.

 

So, P is the 'Brother' of M.

Hence, the correct answer is "Option 3".

Option 1) 26 and 29

After interchange the numbers:

⇒ 26 + 46 − (48 ÷ 4) + (7 × 3) − 29 = 61

⇒ 26 + 46 − 12 + 21 − 29 = 61

⇒ 93 − 12− 29 = 61

⇒ 52 = 61

Option 2) 46 and 48

After interchange the numbers:

⇒ 29 + 48 − (46 ÷ 4) + (7 × 3) − 26 = 61

⇒ 29 + 48 − 11.5 + 21 − 26 = 61

⇒ 98 − 11.5 − 26 = 61

⇒ 60.5 = 61

Option 3) 46 and 26

After interchange the numbers:

⇒ 29 + 26 − (48 ÷ 4) + (7 × 3) − 46 = 61

⇒ 29 + 26 − 12 + 21 − 46 = 61

⇒ 76 − 12 − 46 = 61

⇒ 18 = 61

Option 4) 4 and 3

After interchange the numbers:

⇒ 29 + 46 − (48 ÷ 3) + (7 × 4) − 26 = 61

⇒ 29 + 46 − 16 + 28 − 26 = 61

⇒ 103 − 16 − 26 = 61

⇒ 61 = 61

Hence, the correct answer is "Option 4".

According to the given information:

Thus, the code for 'where' = ga

Hence, the correct answer is "Option 4".

According to the given dice:

• Alternate surface are opposite to each other.

Thus, the opposite side of 'Green' = Red.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: 1^st number ÷ 11 = 2^nd number.

Now,

For, 242 : 22

⇒ 242 ÷ 11 = 22.

For, 385 : 35

⇒ 385 ÷ 11 = 35.

Similarly, for 572 ∶ ?

⇒ 572 ÷ 11 = 52.

Hence, the correct answer is "Option 2".

The logic followed here is:

Hence, the correct answer is "Option 2".

The logic followed here is: 1^st letter -3; 2^nd letter - 4; and 3^rd letter - 2.

Hence, the correct answer is "Option 1".

Given:

Speed1 (S1) = 6 km/h

Speed2 (S2) = 8 km/h

Time difference at S1 = 2 minutes = 2/60 hours

Time difference at S2 = 3 minutes = 3/60 hours

Formula used:

Distance (D) = Speed × Time

Calculations:

Let D be the distance.

At 6 km/h:

Time1 = D/S1 + 2/60

At 8 km/h:

Time2 = D/S2 - 3/60

⇒ Time1 = Time2

⇒ $\frac{D}{6} + \frac{2}{60} = \frac{D}{8} - \frac{3}{60}$

⇒ $\frac{D}{6} - \frac{D}{8} = -\frac{3}{60} - \frac{2}{60}$

⇒ $\frac{D}{6} - \frac{D}{8} = -\frac{5}{60}$

⇒ $\frac{4D - 3D}{24} = -\frac{1}{12}$

⇒ $\frac{D}{24} = -\frac{1}{12}$

⇒ D = 2 km

∴ The distance covered by Tanya to reach the station is 2 km.

Given:

Centre (h, k, l) = (-1, 2, -3)

Radius (r) = 3 units

Formula used:

Equation of a sphere: $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$

Calculation:

Substitute the given values:

$(x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 3^2$

⇒ $(x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 9$

Expand and simplify:

$(x + 1)^2 = x^2 + 2x + 1$

$(y - 2)^2 = y^2 - 4y + 4$

$(z + 3)^2 = z^2 + 6z + 9$

Combine all terms:

$x^2 + 2x + 1 + y^2 - 4y + 4 + z^2 + 6z + 9 = 9$

Combine like terms:

⇒ $x^2 + y^2 + z^2 + 2x - 4y + 6z + 14 = 9$

Subtract 9 from both sides:

⇒ $x^2 + y^2 + z^2 + 2x - 4y + 6z + 5 = 0$

∴ The correct answer is option (4).

Given:

Selling Price (SP) = ₹5,00,000

Discount = 20%

Formula used:

Original Price (OP) = $\dfrac{SP}{1-\frac{Discount}{100}}$

Calculation:

OP = $\dfrac{5,00,000}{1-\frac{20}{100}}$

⇒ OP = $\dfrac{5,00,000}{0.8}$

⇒ OP = ₹6,25,000

∴ The correct answer is option (4).

Given:

6 engineers can complete the work in 5 days

5 skilled workers can complete the work in 7 days

7 engineers and 4 skilled workers are working together

Formula used:

Work done per day = 1 ÷ Time taken to complete the work

Total work done by engineers and skilled workers per day = (Work done by engineers per day + Work done by skilled workers per day)

Calculations:

Work done by 6 engineers in 1 day = 1 ÷ 5

⇒ Work done by 1 engineer in 1 day = (1 ÷ 5) ÷ 6 = 1 ÷ 30

Work done by 7 engineers in 1 day = 7 × (1 ÷ 30) = 7 ÷ 30

Work done by 5 skilled workers in 1 day = 1 ÷ 7

⇒ Work done by 1 skilled worker in 1 day = (1 ÷ 7) ÷ 5 = 1 ÷ 35

Work done by 4 skilled workers in 1 day = 4 × (1 ÷ 35) = 4 ÷ 35

Total work done by 7 engineers and 4 skilled workers in 1 day = 7 ÷ 30 + 4 ÷ 35

⇒ Total work per day = (245 + 120) ÷ 1050 = 365 ÷ 1050

⇒ Total work per day = 73 ÷ 210

⇒ Time taken to complete the work = 210 ÷ 73

⇒ Time taken = 2 ⁶⁴ / ₇₃ .

∴ The correct answer is days.

Given:

Proposals in 2016 = 40%

Buildings completed in 2016 = 10%

Formula used:

Ratio = Proposals / Buildings completed

Calculation:

⇒ Ratio = 40/10

⇒ Ratio = 4 : 1

∴ The ratio of proposals to buildings completed for the year 2016 is 4:1.

Given:

The marks obtained by the seven students in Chemistry are:

• Ayush = 65
• Aman = 104
• Sajal = 78
• Rohit = 84.5
• Muskan = 84.5
• Tanvi = 97.5
• Tarun = 45.5

Formula used:

The median is the middle value when the numbers are arranged in ascending order.

Calculation:

Arrange the Chemistry marks in ascending order: 45.5, 65, 78, 84.5, 84.5, 97.5, 104

The median is the 4^th value in the ordered list.

⇒ Median = 84.5

∴ The median raw score of the marks obtained by the seven students in Chemistry is 84.5.

Given:

$\sin θ = \frac{7}{25}$

Formula used:

$\cos^2 θ + \sin^2 θ = 1$

$\tan θ = \frac{\sin θ}{\cos θ}$

Calculation:

$\sin θ = \frac{7}{25}$

⇒ $\cos^2 θ = 1 - \sin^2 θ$

⇒ $\cos^2 θ = 1 - (\frac{7}{25})^2$

⇒ $\cos^2 θ = 1 - \frac{49}{625}$

⇒ $\cos^2 θ = \frac{625 - 49}{625}$

⇒ $\cos^2 θ = \frac{576}{625}$

⇒ $\cos θ = \frac{24}{25}$ (since θ is in the first quadrant, cos θ is positive)

⇒ $\tan θ = \frac{\sin θ}{\cos θ}$

⇒ $\tan θ = \frac{\frac{7}{25}}{\frac{24}{25}}$

⇒ $\tan θ = \frac{7}{24}$

∴ The correct answer is option (2).

Given:

The lines x + y = 10 and -3x + y = 2 have a unique solution.

What is the distance (in units) between the unique solution and the point of intersection of the line x + y = 10 and the x-axis?

Formula used:

Distance formula: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Calculation:

Solving the system of equations:

x + y = 10   ...(1)

-3x + y = 2   ...(2)

Subtracting (2) from (1):

⇒ x + y - (-3x + y) = 10 - 2

⇒ x + y + 3x - y = 8

⇒ 4x = 8

⇒ x = 2

Substituting x = 2 in (1):

⇒ 2 + y = 10

⇒ y = 8

So, the unique solution is (2, 8).

Point of intersection of x + y = 10 and x-axis:

On the x-axis, y = 0.

⇒ x + 0 = 10

⇒ x = 10

So, the point of intersection is (10, 0).

Using the distance formula:

⇒ Distance = $\sqrt{(10 - 2)^2 + (0 - 8)^2}$

⇒ Distance = $\sqrt{8^2 + (-8)^2}$

⇒ Distance = $\sqrt{64 + 64}$

⇒ Distance = $\sqrt{128}$

⇒ Distance = 8√2

∴ The correct answer is option (1).

Given:

$\frac{5+7\times 5\div 8\ of \ 5+3\div 3\times 5}{6\div 6\ of \ 4+9\times 9\div 3\times 2\times 2}$

Formula used:

Follow the BODMAS rule (Bracket, Order, Division, Multiplication, Addition, Subtraction) to solve the expression.

Calculations:

Numerator: $5 + 7 \times 5 \div 8\ of\ 5 + 3 \div 3 \times 5$

⇒ $5 + 7 \times 5 \div 40 + 1 \times 5$

⇒ $5 + \frac{7}{8} + 5$

⇒ $\frac{40 + 7 + 40}{8}$

⇒ $\frac{87}{8}$

Denominator: $6 \div 6\ of\ 4 + 9 \times 9 \div 3 \times 2 \times 2$

⇒ $6 \div 24 + 9 \times 3 \times 2 \times 2$

⇒ $\frac{1}{4} + 108$

⇒ $\frac{1 + 432}{4}$

⇒ $\frac{433}{4}$

Final Expression: 

⇒$\frac{87/8}{433/4}$ 

⇒ 87 / 866

∴ The value of the expression is 87 / 866.

Given:

The average marks scored by the students of a class is 75.

The average marks scored by the girls in the same class is 90.

The average marks scored by the boys in the same class is 70.

Formula used:

Let the number of boys be B and the number of girls be G.

Average marks of the class = (Total marks scored by boys + Total marks scored by girls) / Total number of students

Total number of students = B + G

Total marks scored by boys = 70B

Total marks scored by girls = 90G

Average marks = 75

Calculation:

75 = (70B + 90G) / (B + G)

⇒ 75(B + G) = 70B + 90G

⇒ 75B + 75G = 70B + 90G

⇒ 75B - 70B = 90G - 75G

⇒ 5B = 15G

⇒ B / G = 15 / 5

⇒ B / G = 3

⇒ B = 3G

Percentage of boys in the class = (B / (B + G)) × 100

⇒ Percentage of boys = (3G / (3G + G)) × 100

⇒ Percentage of boys = (3G / 4G) × 100

⇒ Percentage of boys = 3/4 × 100

⇒ Percentage of boys = 75%

∴ The correct answer is option (2).

Shortcut Trick

Since U and V are midpoints of TR and NJ, TR = NJ ⇒ TU = NV.

By SSS congruence, ΔSTU ≅ ΔMNV (ST = MN, SU = MV, TU = NV).

This gives ∠NMV = ∠TSU = 46° and ∠MNJ = 180° − (46° + 88°) = 46°.

In ΔMNJ, ∠MJN = 180° − (∠MNJ + ∠NMJ) = 180° − (46° + 79°) = 55°.

By SAS congruence, ΔSTR ≅ ΔMNJ ⇒ ∠SRT = ∠MJN = 55°.

Required measure = 7/11 × 55° = 35°.

∴ The correct answer is 35°.

Alternate Method

Given:

⇒ Sides ST = MN

⇒ Side TR = NJ

⇒ Median SU = Median MV

⇒ ∠TSU = 46°, ∠NMJ = 79°, and ∠MVN = 88°

Formula Used:

⇒ SSS Congruence Rule: If three sides are equal, the triangles are congruent.

⇒ SAS Congruence Rule: If two sides and the included angle are equal, the triangles are congruent.

  S T R U 46°      M N J V 79° 88°                  ∴ ∠SRT = 55°

Calculations:

⇒ Since SU and MV are medians, U and V divide the bases TR and NJ into equal halves.

⇒ TR = NJ ⇒ TR/2 = NJ/2 ⇒ TU = NV

⇒ Consider ΔSTU and ΔMNV: ST = MN, SU = MV, and TU = NV.

⇒ By SSS congruence, ΔSTU ≅ ΔMNV.

⇒ This implies corresponding angles are equal: ∠NMV = ∠TSU = 46°, and ∠SUT = ∠MVN = 88°.

⇒ In ΔMNV, using angle sum property: ∠MNV = 180° − (46° + 88°) = 46°.

⇒ Angle ∠MNJ is the same as ∠MNV, hence ∠MNJ = 46°.

⇒ In the full ΔMNJ, angle sum property gives: ∠MJN = 180° − (∠MNJ + ∠NMJ) = 180° − (46° + 79°) = 55°.

⇒ Now compare ΔSTR and ΔMNJ: ST = MN, TR = NJ, and the included angles ∠STR = ∠MNJ (since ΔSTU ≅ ΔMNV).

⇒ By SAS congruence, ΔSTR ≅ ΔMNJ.

⇒ Therefore, corresponding angles are equal: ∠SRT = ∠MJN = 55°.

⇒ Required value = 7/11 × ∠SRT = 7/11 × 55° = 35°.

∴ The correct answer is 35°.

Additional Information

Congruence of Triangles (SSS and SAS)

Two triangles are identically congruent if all three corresponding sides are equal (SSS), or if two sides and the included angle are equal (SAS). Congruent triangles have exactly the same size and shape.

Median of a Triangle

A line segment joining a vertex to the exact midpoint of the opposite side. It cleanly divides the opposite side into two identical half-segments.

Angle Sum Property

The sum of all interior angles in any planar triangle always equals 180°. This is a fundamental rule used repeatedly to find unknown missing angles.

Given:

Simple Interest (SI) = ₹4,050

Rate (R) = 9% per annum

Time (T) = 5 years

Formula used:

SI = $\frac{P \times R \times T}{100}$

Where, P = Principal

Calculations:

4050 = $\frac{P \times 9 \times 5}{100}$

⇒ 4050 = $\frac{45P}{100}$

⇒ 4050 = 0.45P

⇒ P = $\frac{4050}{0.45}$

⇒ P = 9000

∴ The correct answer is option (1).

Given:

Ramesh sells an article for ₹34,440 after allowing an 18% discount on the marked price and still manages to gain a 40% profit.

Formula used:

Selling Price (SP) = ₹34,440

Discount = 18%

Profit = 40%

Cost Price (CP) = SP / (1 + Profit)

Marked Price (MP) = SP / (1 - Discount)

Calculations:

CP = 34,440 / (1 + 0.40)

⇒ CP = 34,440 / 1.40

⇒ CP = ₹24,600

MP = 34,440 / (1 - 0.18)

⇒ MP = 34,440 / 0.82

⇒ MP = ₹42,000

If Ramesh sold the article at a 12% discount on the marked price:

New SP = MP × (1 - 0.12)

⇒ New SP = 42,000 × 0.88

⇒ New SP = ₹36,960

New Profit = (New SP - CP) / CP

⇒ New Profit = (36,960 - 24,600) / 24,600

⇒ New Profit = 12,360 / 24,600

⇒ New Profit = 0.5024 = 0.5024 × 100 = 50.24%

∴ The correct answer is option (1).

Given:

Number of pens sold = 60

Gain = Selling price of 12 pens

Formula used:

Gain % = (Gain/Cost price) × 100

Calculation:

Let the selling price of one pen be S.

Total selling price of 60 pens = 60 × S

Gain = 12 × S

⇒ Cost price = Selling price - Gain

⇒ Cost price = 60 × S - 12 × S = 48 × S

Now,

Gain % = (12 × S / 48 × S) × 100

⇒ Gain % = (12 / 48) × 100 = 25%

∴ The gain percentage is 25%.

Given:

In a right angle triangle with sides 12 cm and 16 cm and hypotenuse 20 cm, the length of altitude drawn on the hypotenuse from the opposite vertex is K. Find the value of K.

Formula used:

Area of triangle = 1/2 × base × height

Calculation:

Area using sides 12 cm and 16 cm:

⇒ Area = 1/2 × 12 × 16

⇒ Area = 96 cm²

Area using hypotenuse 20 cm and altitude K:

⇒ Area = 1/2 × 20 × K

Equating both areas:

⇒ 96 = 1/2 × 20 × K

⇒ 96 = 10K

⇒ K = 96/10

⇒ K = 9.6 cm

∴ The correct answer is option (1).

Given:

Old Salary = ₹200 per day

New Salary = ₹234 per day

Formula used:

Percentage Increase = $\dfrac{\text{New Salary} - \text{Old Salary}}{\text{Old Salary}} \times 100$

Calculation:

Percentage Increase = $\dfrac{234 - 200}{200} \times 100$

⇒ Percentage Increase = $\dfrac{34}{200} \times 100$

⇒ Percentage Increase = $\dfrac{34 \times 100}{200}$

⇒ Percentage Increase = 17%

∴ The correct answer is option (2).

Given:

Total production of C1 in 2022 = 4125

Percentage of production for C1 in 2022 = 27.5%

Total production ratio between 2019 and 2022 = 3:5

We need to find the total production of C3 in 2019.

Formula used:

Total production in 2022 (for all companies) = (Total production of C1 in 2022 / C1's percentage) × 100

Total production in 2019 (for all companies) = (Total production in 2022 × 3) / 5

Total production of C3 in 2019 = (C3's percentage in 2019 × Total production in 2019) / 100

Calculation:

Total production in 2022 = (4125 / 27.5) × 100

⇒ Total production in 2022 = 15000

Total production in 2019 = (15000 × 3) / 5

⇒ Total production in 2019 = 9000

Total production of C3 in 2019 = (17.5 / 100) × 9000

⇒ Total production of C3 in 2019 = 1575

∴ The total production of C3 in the year 2019 is 1575.

Given:

The income of the company for different years is:

2000: 60 lakhs

2001: 60 lakhs

2002: 40 lakhs

2003: 50 lakhs

2004: 30 lakhs

Formula used:

Average income = (Sum of incomes) / (Number of years)

Calculation:

Total income = 60 + 60 + 40 + 50 + 30 = 240 lakhs

Number of years = 5

Average income = 240 / 5 = 48 lakhs

Now, check the years where the income is less than 48 lakhs:

2000: 60 (greater than 48)

2001: 60 (greater than 48)

2002: 40 (less than 48)

2003: 50 (greater than 48)

2004: 30 (less than 48)

∴ The income of the company is less than the average income in 2 years (2002 and 2004).

Given:

A tangent is drawn from a point at a distance of 25 cm from the Centre of a circle C(0, r) of radius 7 cm.

Formula used:

Length of tangent from a point to a circle = $\sqrt{d^2 - r^2}$

Where, d = distance from the center of the circle to the point, r = radius of the circle

Calculation:

Length of tangent = $\sqrt{25^2 - 7^2}$

⇒ Length of tangent = $\sqrt{625 - 49}$

⇒ Length of tangent = $\sqrt{576}$

⇒ Length of tangent = 24 cm

∴ The correct answer is option (4).

Given:

A tangent is drawn from a point that is at a distance of 37 cm from the center of the circle O, and the diameter is 24 cm. The length (in cm) of the tangent is:

Formula used:

In a right-angled triangle formed by the radius, the tangent, and the line from the external point to the center:

$OP^2 = OT^2 + PT^2$

Where,

OP = Distance from the center to the external point = 37 cm

OT = Radius of the circle = 12 cm (since diameter is 24 cm)

PT = Length of the tangent

Calculation:

$37^2 = 12^2 + PT^2$

⇒ $1369 = 144 + PT^2$

⇒ $PT^2 = 1369 - 144$

⇒ $PT^2 = 1225$

⇒ $PT = \sqrt{1225}$

⇒ PT = 35 cm

∴ The correct answer is option (4).

Given:

One candidate secured 35% of votes and is defeated by 381 votes.

Formula used:

Let total votes be V.

Votes secured by the winning candidate = 65% of V

Votes secured by the losing candidate = 35% of V

Difference in votes = 381

Calculation:

65% of V - 35% of V = 381

⇒ 0.65V - 0.35V = 381

⇒ 0.30V = 381

⇒ 1270

∴ The correct answer is option (3).

Given:

Radius (r) = 6 cm

Slant height (l) = 10 cm

We need the height (h) of the cone to find the volume. Use the Pythagorean theorem:

Formula used:

h = √(l² - r²)

Volume of the cone = (1/3) × π × r² × h

Calculation:

h = √(10² - 6²)

⇒ h = √(100 - 36)

⇒ h = √64

⇒ h = 8 cm

Now, volume = (1/3) × π × 6² × 8

⇒ Volume = (1/3) × π × 36 × 8

⇒ Volume = (1/3) × π × 288

⇒ Volume = 96π cm³

∴ The volume of the cone is 96π cm³.<

Given:

Areas of three adjacent faces of a cuboidal box:

• Area 1 = 120 cm²
• Area 2 = 72 cm²
• Area 3 = 60 cm²

Formula used:

Volume of cuboid = √(Area 1 × Area 2 × Area 3)

Let the dimensions of the cuboid be l, b, and h. We have:

• l × b = 120
• b × h = 72
• h × l = 60

Volume of the cuboid (V) = l × b × h = √(l × b × b × h × h × l)

Calculation:

V = √(120 × 72 × 60)

⇒ V = √518400

⇒ V = 720 cm³

∴ The volume of the cuboid is 720 cm³.