SSC CHSL Tier-1 2024: Official Paper (Held On: 04 Jul, 2024 Shift 4) (Previous Year Paper)

The correct answer is: Option 3.

 

Key Points

• The primary issue in the sentence is the incorrect verb form "be study."
• The correct verb form should be "be studying" to indicate the continuous tense.
• The correct phrase should be "I will be studying around 7 o'clock," ensuring grammatical correctness and clarity.

Therefore, the correct answer is Option 3.

 

Correct Sentence: "I will be studying around 7 o'clock."

The correct answer is '3' i.e. this part of the sentence has an error.

Key Points

• In the third part of the given sentence, the plural form of the verb 'were' is incorrect.
• In the given sentence, the subject 'She' is singular and should be followed by the singular form of the verb 'was'.
• The correct sentence should use the singular form of the verb to match the singular subject.
• Therefore, the singular form of the verb 'was' should be used in place of the plural form 'were'.

Correct sentence: She was singing beautifully in the concert hall last night.

The correct answer is Option 1.

 

Key Points

• The primary issue in the sentence is the use of the verb "participate" without the correct subject-verb agreement.
• Since the subject is singular ("My daughter"), the verb should be in the singular form.
• The correct verb form should be "participates" (singular verb).
• Thus, the error is located in part A of the sentence.

Therefore, the correct answer is A.

 

Correct Sentence: "My daughter participates in the dance competition that is organised every year by the Lion's Club."

The correct answer is Option 4.

 

Key Points

• In the 4^th sentence, the correct phrasal verb should be "sort out" which means to organize or resolve something.
• The phrase "sort out the contradicting stories" makes sense in the context of the police inspector trying to resolve or make sense of the conflicting information.

Therefore, the correct answer is Option 4.

 

Correct Sentence: "The police inspector was trying to sort out the contradicting stories in the scene of the accident."

 

Additional Information

• Option 1: "lighten up" means to make something less serious, which is not suitable in this context.
• Option 2: "rush out" means to produce something quickly, which does not fit the context.
• Option 3: "sign up" means to register or enlist, which is irrelevant here.

The correct answer is 'conclusion'.

 

Key Points

• The context tells us that after studying the negative impacts of junk food, nutritionists have concluded that firms who produce it are misleading the public by portraying their products in false light as healthy.
• "Conclusion" ( निष्कर्ष) fits well as it denotes a final decision or judgment based on reasoning.
• Other options ("assumption", "derivation", "solution") do not fit the context as appropriately as "conclusion".

Therefore, the correct answer is 'Option 1'.

 

Complete Passage: Nutrition experts have researched the bad effects of junk food and have come to the conclusion that junk food manufacturing companies are fooling the people by showing deceptive advertisements that show junk food as healthy. We must substitute junk food with healthier food like fruits and vegetables. So the next time you think of grabbing that burger, hotdog, pizza, samosa, kachori or even ice cream in a restaurant, eating joint or a party, stop your instincts and look for some healthier food options instead.

 

Additional Information

• Assumption (मान्यता): An assumption is something that is accepted as true without proof.
• Derivation (व्युत्पत्ति): Derivation refers to deriving something from a source.
• Solution (समाधान): A solution refers to solving a problem.

The correct answer is 'showing'.

 

Key Points

• The context tells us that after studying the negative impacts of junk food, nutritionists have concluded that firms who produce it are misleading the public by portraying their products in false light as healthy.
• "Showing" (दिखा) fits well as it denotes to let somebody see somebody/something.
• Other options ("observing", "assuming", "blowing") do not fit the context of describing the impact of forest fires on forests and biodiversity.

Therefore, the correct answer is 'Option 2'.

 

Complete Passage:  Nutrition experts have researched the bad effects of junk food and have come to the conclusion that junk food manufacturing companies are fooling the people by showing deceptive advertisements that show junk food as healthy. We must substitute junk food with healthier food like fruits and vegetables. So the next time you think of grabbing that burger, hotdog, pizza, samosa, kachori or even ice cream in a restaurant, eating joint or a party, stop your instincts and look for some healthier food options instead.

 

Additional Information

• Observing (देखना): "Observing" means watching carefully.
• Assuming (मान लेना): "Assuming" means taking for granted.
• Blowing (उड़ाना): "Blowing" means moving air or causing something to move.

The correct answer is 'healthier'.

 

Key Points

• The context tells us that junk food needs to be replaced with better choices like fruits and vegetables.
• The appropriate adjective should indicate something that is beneficial to health.
• "Healthier" (स्वस्थ) fits well as it denotes a state of being more beneficial to health, which aligns with the context.
• Other options ("expensive", "cleaner", "powerful") do not fit the context of describing something beneficial to health.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage: Nutrition experts have researched the bad effects of junk food and have come to the conclusion that junk food manufacturing companies are fooling the people by showing deceptive advertisements that show junk food as healthy. We must substitute junk food with healthier food like fruits and vegetables. So the next time you think of grabbing that burger, hotdog, pizza, samosa, kachori or even ice cream in a restaurant, eating joint or a party, stop your instincts and look for some healthier food options instead.

 

Additional Information

• Expensive (महंगा): "Expensive" means costing a lot of money.
• Cleaner (स्वच्छ): "Cleaner" means more clean.
• Powerful (शक्तिशाली): "Powerful" means having a lot of strength or power.

The correct answer is: grabbing.

 

Key Points

• The context tells us that we must learn to resist our impulse to obtain that burger, hotdog, pizza, samosa, kachori, or even ice cream the next time we're at a party, restaurant, or eating establishment.
• Grabbing (पकड़ना) means to take hold of something (in this case, 'food') which fits the blank contextually.
• Other options ("skipping", "grabbing", "building") do not fit the context of describing the ongoing process in the passage.

Therefore, the correct answer is 'Option 4'.

 

Complete Passage:  Nutrition experts have researched the bad effects of junk food and have come to the conclusion that junk food manufacturing companies are fooling the people by showing deceptive advertisements that show junk food as healthy. We must substitute junk food with healthier food like fruits and vegetables. So the next time you think of grabbing that burger, hotdog, pizza, samosa, kachori or even ice cream in a restaurant, eating joint or a party, stop your instincts and look for some healthier food options instead.

 

Additional Information

• Skipping (छोड़ना): "Skipping" means to omit or leave out.
• Turning (मोड़): "Turning" means to move your body, or part of your body, so that you are facing in a different direction.
• Building (निर्माण करना): "Building" means to construct.

The correct answer is 'options'.

 

Key Points

• The context tells us that we must consider choosing something healthier to eat.
• "Options" (विकल्प) is the correct option as it means something that you can choose to do.
• Other options ("chances", "comparisons", "additions") do not fit the context of selecting the most appropriate choice.

Therefore, the correct answer is 'Option 1'.

 

Complete Passage: Nutrition experts have researched the bad effects of junk food and have come to the conclusion that junk food manufacturing companies are fooling the people by showing deceptive advertisements that show junk food as healthy. We must substitute junk food with healthier food like fruits and vegetables. So the next time you think of grabbing that burger, hotdog, pizza, samosa, kachori or even ice cream in a restaurant, eating joint or a party, stop your instincts and look for some healthier food options instead.

Additional Information

• Chances (संभावनाएँ): "Chances" implies possibilities or probabilities.
• Comparisons (तुलनाएँ): "Comparisons" means evaluating the similarities and differences.
• Additions (जोड़): "Additions" means something added.

The correct answer is: Option 3 i.e. Longing.

Key Points

• The word "Desire" means a strong feeling of wanting to have something or wishing for something to happen. (इच्छा)
• Example: She has a strong desire to travel the world.
• "Longing" refers to a yearning desire or craving for something that is often out of reach or unattainable. (लालसा)
• Example: He felt a deep longing for his childhood home.
• Hence, we can infer that the synonym of 'desire' is 'longing'

Therefore, the correct answer is: Longing.

Additional Information

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

• Loathing (घृणा): A feeling of intense dislike or disgust.
• Example: She felt a deep loathing for the corrupt politician.
• Aversion (अरुचि): A strong dislike or disinclination.
• Example: He has a strong aversion to spiders.
• Disgust (घिन): A feeling of revulsion or profound disapproval aroused by something unpleasant or offensive.
• Example: The sight of the rotting food filled him with disgust.

The correct answer is: Variegated.

Key Points

• The word "uniform" means something that is consistent and unchanging in form or character. (समान)
• Example: The soldiers were dressed in uniform attire for the parade.
• "Variegated" refers to something that has different colors or is varied in appearance. (विविध)
• Example: The garden was filled with variegated plants, each with a unique pattern of colors.
• Hence, we can infer that the opposite of 'uniform' is 'variegated'.

Therefore, the correct answer is: Variegated.

Additional Information

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

• Fixed (स्थिर): Something that is securely placed or fastened and is not subject to change.
• Example: The picture frame was fixed to the wall with nails.
• Paired (जोड़ा हुआ): Two things that are matched together.
• Example: He paired the wine with the cheese for a perfect combination.
• Balanced (संतुलित): Something that is in a state of equilibrium or equal proportions.
• Example: She maintained a balanced diet to stay healthy.

The correct answer is: Option 3 i.e. apology.

Key Points

• The word "mistake" means an action or judgment that is misguided or wrong. (गलती)
• Example: Leaving the door unlocked was a mistake.
• "Apology" refers to a regretful acknowledgment of an offense or failure. (माफी)
• Example: He offered a heartfelt apology for his behavior.
• Hence, the correct word to substitute "a letter of mistake" is "a letter of apology".

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

Additional Information

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

• Circumstance (परिस्थिति): A fact or condition connected with or relevant to an event or action.
• Example: We found ourselves in a difficult circumstance.
• Gratitude (आभार): The quality of being thankful; readiness to show appreciation for and to return kindness.
• Example: She expressed her gratitude to the host for the wonderful evening.

The correct answer is: outdated.

Key Points

• The word "obsolete" means something that is no longer in use or has become out of date due to being replaced by something newer and more efficient. (अप्रचलित)
• Example: Typewriters have become obsolete with the advent of computers.
• "Outdated" refers to something that is old-fashioned or no longer useful because it has been replaced by something newer and more modern. (पुराना)
• Example: The software was outdated and needed to be upgraded to the latest version.
• Hence, we can infer that the word "outdated" is an appropriate substitute for "obsolete".

Therefore, the correct answer is: outdated.

Additional Information

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

• Modern (आधुनिक): Relating to the present or recent times as opposed to the remote past.
• Example: The building features a modern design with sleek lines and large windows.
• Advanced (उन्नत): Far on or ahead in development or progress.
• Example: Advanced technology has enabled us to connect with people across the globe instantaneously.
• Current (वर्तमान): Belonging to the present time; happening or being used or done now.
• Example: The current trend in fashion is leaning towards sustainability.

The correct answer is: Option 4.

Key Points

• The word "Couragious" is incorrectly spelt. The correct spelling is "Courageous" which means having or showing courage; brave. (साहसी)
• "Courageous" means being able to face and deal with danger or fear without flinching. (साहसी)
• Example: The firefighters were courageous as they rescued people from the burning building.

Therefore, the correct answer is: Option 4 i.e. Couragious.

Additional Information

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

• Physiologist (शरीर विज्ञानी): A scientist who studies the functions and mechanisms occurring in living organisms.
• Example: The physiologist explained how the human body reacts to different types of exercise.
• Gracious (दयालु): Courteous, kind, and pleasant.
• Example: She was gracious enough to thank everyone for their help.
• Contagious (संक्रामक): Able to be transmitted from one person to another through direct or indirect contact.
• Example: The flu is highly contagious and can spread rapidly in crowded places.

The correct answer is: Option 2 i.e. Funcktions.

Key Points

• The word "Funcktions" is incorrectly spelled. The correct spelling is "Functions."
• ​"Functions" refers to an event or activity typically organized for a specific purpose. (कार्यक्रम)
• Example: She attends many social functions throughout the year.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Marriage (शादी): The legally or formally recognized union of two people as partners in a personal relationship.
• Example: They have been happily living together since their marriage last year.
• Prefers (पसंद करना): To like one thing or person better than another; to choose one thing rather than something else.
• Example: She prefers tea over coffee.
• Wearing (पहनना): To have clothing, jewelry, etc., on your body.
• Example: He is wearing a new jacket today.

The correct answer is: Option 3 i.e. Luminous.

Key Points

• The word "dismal" means something that is depressing, gloomy, or causing a mood of sadness. (निराशाजनक)
• Example: The weather was dismal, with dark clouds and continuous rain.
• "Luminous" refers to something that is bright, shining, and full of light; it is the opposite of gloomy or dark. (प्रकाशमान)
• Example: The room was luminous, filled with natural sunlight streaming through the windows.
• Hence, we can infer that the opposite of 'dismal' is 'luminous'.

Therefore, the correct answer is: Luminous.

Additional Information

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

• Sadden (दुखी करना): To cause someone to feel sorrow or unhappiness.
• Example: The news of his departure saddened everyone in the office.
• Cheap (सस्ता): Low in cost, or of low quality.
• Example: The store offers a variety of cheap goods, but they are not very durable.
• Dainty (नाज़ुक): Delicately small and pretty.
• Example: She wore a dainty lace dress to the party.

The correct answer is Option 2.

Key Points

• The word 'Noble' means honest; full of courage and care for others; belonging to the highest social class.(महान, सज्जन)
• Example - He was a noble man with a kind heart and a strong sense of justice.
• 'Common' means happening or often found or in many places; usual.(सामान्य, साधारण)
• Example - English is a common language in many countries.
• Hence, we can infer that the antonym of 'Noble' is 'Common'.

Therefore, the correct answer is 'Common'.

Additional Information Here are the options explained along with their Hindi meanings and example sentences.

• Grand (भव्य, शानदार) - Impressive and large or important.
• Example - She threw a grand party for her birthday.
• Indescribable (अवर्णनीय) - Too good or bad to be described
• Example - The painting captured an indescribable sense of peace.
• Magical (दिलकश, मनोहर) - That seems to use magic; wonderful and exciting.
• Example - There is one magical moment in the film when they meet for the first time.

The correct answer is Option 3.

Key Points

• The idiom 'A bolt from the blue' means something unexpected, surprising, or shocking.(आकस्मिक घटना)
• Example - The resignation of the chairman came like a bolt from the blue.
• Hence, we can infer that the meaning of the idiom 'A bolt from the blue' is 'A sudden and unexpected event'.

Therefore, the correct answer is A sudden and unexpected event. 

Additional Information Here are the options explained along with their example sentences.

• Raining heavily - 'Raining cats and dogs' is the idiom used for raining heavily.

• Example - It was raining cats and dogs, so I couldn't walk to the store.

• Thunder and rain in a storm - There isn't a specific idiom for 'thunder and rain in a storm'.

• Example - We had to cancel our outdoor picnic due to the thunder and rain in the storm.

• A spontaneous but expected event - There isn't a specific idiom for 'a spontaneous but expected event'.

• Example - The sudden burst of applause from the audience was a spontaneous but expected event after the singer's incredible performance.

The correct answer is: Option 4 i.e. about.

Key Points

• The word "at" is a preposition used to indicate a location or position. However, it is not the correct preposition to use in the context of thinking or reflecting. (पर)
• Example: She was at the park when it started raining.
• "About" is a preposition used to indicate the subject of a thought, feeling, or discussion. It is the correct preposition to use in the context of thinking or reflecting. (के बारे में)
• Example: She was thinking about the fun they had during the trip.
• Hence, we can infer that the correct substitution for 'at' in the given context is 'about'.

Therefore, the correct answer is: Option 4 i.e. about.

Additional Information

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

• Beside (के बगल में): Used to indicate location next to something or someone.
• Example: She was sitting beside her friend.
• By (द्वारा): Used to indicate the means or agent performing an action.
• Example: The book was written by a famous author.

The correct answer is Option 1.

Key Points

• The word 'Vehement' means showing very strong (often negative) feelings, especially anger.(उग्र, प्रबल)
• Example - The storm was so vehement that it caused widespread damage.
• 'Mild' means not strong; not very bad; gentle, soft, or not severe.(हल्का, सौम्य)
• Example - He was mild and courteous in his dealings with others.
• Hence, we can infer that the antonym of 'Vehement' is 'Mild'.

Therefore, the correct answer is 'Mild'.

Additional Information Here are the other options explained along with their Hindi meanings and example sentences.

• Reliable (भरोसेमंद) - That you can trust; trustworthy, dependable, or consistent.

• Example - We need to find a reliable company to supply the goods.

• Passionate (जुनूनी) - Showing or caused by very strong feelings.

• Example - Football ran through his veins and he was very passionate about it.

• Smashed (टूट गया) - To break something, or to be broken violently and noisily into many pieces.

• Example - The vase was smashed into a thousand pieces.

The correct answer is: come under.

 

Key Points

• The context tells us that environmentalists have launched an attack on the new development sites.
• The phrase "come under attack" is an idiomatic expression meaning to be criticized or targeted.
• None of the other options fit the context of the sentence as appropriately as "come under."

​Hence, the correct sentence is: The new construction sites have come under attack by the environmentalists.

Additional Information

• "Come off" usually means to succeed or to happen as planned, which doesn't fit here.
• "Come upon" means to find or discover by chance, which is also not suitable.
• "Come out" means to be revealed or released, which does not fit the context either.

The correct answer is: Option 4.

Key Points

• The word "Benevolent" means showing kindness or goodwill; it refers to someone who is well-meaning and charitable. (दयालु)
• Example: The benevolent old man donated a significant portion of his wealth to charity.
• "Cruel" refers to someone who causes pain or suffering to others, either physically or emotionally; it is the opposite of being kind or benevolent. (क्रूर)
• Example: The cruel dictator showed no mercy towards his opponents.
• Hence, we can infer that the opposite of 'benevolent' is 'cruel'.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Happy (खुश): Feeling or showing pleasure or contentment.
• Example: She was very happy to receive the news of her promotion.
• Patient (धैर्यवान ): Able to accept or tolerate delays, problems, or suffering without becoming annoyed or anxious.
• Example: The teacher was very patient with the slow learners in the class.
• Harmless (निर्दोष): Not likely to cause harm or injury.
• Example: The small, harmless snake slithered away into the bushes.

The correct answer is: To act carefully in a difficult situation.

Key Points

• The idiom "Walk a tightrope" means to act carefully in a difficult or risky situation, trying to balance conflicting demands or avoid making mistakes. (एक कठिन स्थिति में सावधानी से कार्य करना)
• Example: As a manager, she had to walk a tightrope between keeping the employees happy and ensuring the company's profitability.
• "To act carefully in a difficult situation" implies being cautious and considerate in actions to avoid failure or negative outcomes. (एक कठिन परिस्थिति में सावधानीपूर्वक कार्य करना)
• Example: Negotiating peace between the two warring nations required the diplomat to act carefully in a difficult situation.

Therefore, the correct answer is: To act carefully in a difficult situation.

The correct answer is Option 2.

 

Key Points

• The phrase "always takes his dog for a walk" is the grammatically correct order of words.
• The placement of "always" (adverb) before "takes" (verb) ensures the sentence flows correctly and logically.
• None of the other options provide a grammatically correct or natural-sounding sentence.

 

Correct Sentence: "He always takes his dog for a walk in the park."

The correct answer is: Option 2 i.e. Opacity.

Key Points

• The word "transparency" means the quality of being easily seen through or detected; openness, and clarity in communication or procedures. (पारदर्शिता)
• Example: The transparency of the glass allowed us to see the beautiful garden outside.
• "Opacity" refers to the quality of being obscure, not transparent, or hard to see through; lack of clarity or transparency. (अस्पष्टता)
• Example: The opacity of the frosted glass ensured privacy in the room.
• Hence, we can infer that the opposite of 'transparency' is 'opacity'.

Therefore, the correct answer is: Option 2 i.e. Opacity.

Additional Information

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

• Reliability (विश्वसनीयता): The quality of being trustworthy or performing consistently well.
• Example: The reliability of the new software ensured that the system rarely crashed.
• Coherence (सामंजस्य): The quality of being logical and consistent.
• Example: The coherence of his argument made it very convincing.
• Clarity (स्पष्टता): The quality of being clear and easy to understand.
• Example: The clarity of her explanation helped everyone understand the complex topic.

Given word: 'COUNTED'

After arranged in alphabetical order:

 

Now,

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

Hence, the correct answer is "Option 4".

The logic followed here is:

For, KEAY

For, SMIG

For, CWSR

If we two letters backwards from S we have Q but here it is R, so it dose not follows the pattern.

For, MGCA 

So all the options except CWSR follows the pattern.

Hence the correct answer is "Option 3".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

Given Equation: 26 B 3 C 5 D 120 A 4 = ?

BODMAS Rule:

Decoding the given information:

 

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

⇒ 26 × 3 + 5 - 120 ÷ 4 = ?

⇒ 26 × 3 + 5 - 30 = ?

⇒ 78 + 5 - 30 = ?

⇒ 83 - 30 = 53

Hence, the correct option is "Option 3".

Given Equation: 24 T 36 P 48 Q 32 R 40 T 53 = ?

BODMAS Rule:

Decoding the given information:

 

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

⇒ 24 + 36 ÷ 48 × 32 - 40 + 53 = ?

⇒ 24 + 24 - 40 + 53 = ?

⇒ 101 - 40 = 61.

Hence, the correct option is "Option 4".

BODMAS table

Given equation: If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’ and ‘D’ stands for ‘–’

Option 1) 109 B 6 D 16 A 2 C 6

Putting the sign in equation

⇒109 x 6 - 16 ÷ 2 + 6 

⇒109 x 6 - 8 + 6 

⇒654 - 8 + 6

⇒660 - 8

⇒652

Option2) 109 A 6 D 16 B 2 C 6

⇒109 ÷ 6 - 16 x 2 + 6

⇒18.16 - 16 x 2 + 6

⇒18.16 - 32 + 6

⇒24.16 - 32

⇒-7.84

Option3) 109 B 6 A 16 D 2 C 6

⇒109 x 6 ÷ 16 - 2 + 6

⇒109 x 0.375 - 2 + 6

⇒40.875 - 2  + 6

⇒46.875 - 2

⇒44.875

Option 4) 109 C 6 D 16 A 2 B 6

⇒109 + 6 - 16 ÷ 2 x 6

⇒109 + 6 - 8 x 6

⇒109 + 6 - 48

⇒115 - 48

⇒67

Hence the correct answer is "Option 1".

The logic followed here is :

So, 8000 is the missing number of the series.

Hence the correct answer is "Option 3".

The logic followed here is:

'How are you' is coded as 'Co De Ki' 

'you look happy' is coded as 'Th De Mo'

Here you is coded as - De

How / are - Co / Ki

look / happy - Th / Mo

Hence the correct answer is "Option 3".

The logic followed here is:

So, 'TIZ' is the missing letter cluster of the series.

Hence the correct answer is "Option 4".

The paper after unfolded will be

Hence, the correct answer will be "Option 3".

The logic followed here is:

Logic: Animals and the sounds they make.

Here,

Dogs : Bark → Dogs make the sound Bark.

Similarly,

Donkeys : Bray → Donkeys make the sound Bray.

Hence, the correct answer is "Option 2".

The logic followed here is:

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

Now,

For, (35, 5, 7)

⇒ 5 × 7 = 35

For, (108, 12, 9)

⇒ 12 × 9 = 108

Similarly, for (91, 13, 7)

⇒ 13 × 7 = 91 

Hence, the correct answer is "Option 3".

From the given open dice:

**} is the opposite side of ***

^ is the opposite side of #

& is the opposite side of @.

Hence the correct answer is "Option 2".

The logic followed here is:

Logic: Opposites/Antonyms.

Here,

Pleasure : Pain → Pleasure and Pain are antonyms (opposites).

Similarly,

Gentle : Brutal → Gentle and Brutal are antonyms (opposites).

Hence, the correct answer is "Option 4".

Given word: 'POWDERS'

After arranged in alphabetical order:

 

Now,

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

Hence, the correct answer is "Option 4".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 1".

The logic followed here is:

So, '164' is the missing term of the series.

Hence, the correct answer is "Option 2".

The logic followed here is: The new element is added in each next step

hence the correct answer is "Option 3".

The least possible venn diagram for the given statement is as follows:

(I)  All dolls are paper - FALSE (Only some bag is doll and some bag is paper, so all doll are paper dose not follows)

(II) Some bags are wood - FALSE (Some part of bag is paper and all paper is wood but some part of bag is also doll, so it may be a posiibility but not definitely true case.)

So, neither conclusion I nor II follows

Hence, the correct answer is "Option 3".

The logic followed here is:

So, 'SNUX' will be the correct alternative that will complete the series.

Hence, the correct answer is "Option 2".

From the given open dice

VIII is the opposite side of VI

IX is the opposite side of X

V is the opposite side of VII

Hence, the correct answer is "Option 2".

The logic followed here is:

'now or never' is coded as 'ak bj ut' 

'never be late' is coded as 'bj tl cv'

Here, the codes for

now / or - ak / ut

be / late - tl / cv

So, the code for 'never' is 'bj'

Hence, the correct answer is "Option 3".

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

1. Number of rectangles = $( \frac{2×(2+1)}{2})×(\frac{3×(3+1)}{2})$) = $( \frac{2×3}{2})×(\frac{3×4}{2})$ = $( \frac{6}{2})×(\frac{12}{2})$ = 3 × 6 ⇒18

 

 

2. Total number of rectangles = 13

As marked, there are a total of (18 + 13) = 31 rectangles.

Hence, "Option 4" is the correct answer.

Additional InformationFormula used:

Number of rectangles = $( \frac{n×(n+1)}{2})×(\frac{m×(m+1)}{2})$

Where,

number of rows = n

number of columns = m

Decoding the codes:

 

Given:  V / K × T + M × O

It means V is the son of K, T is the daughter of K, T is the wife of M, and O is the child of M

So, K is O's mothers father.

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: (1^st number × 8) = 2^nd number.

Now,

For, 17 : 136

⇒ 17 × 8 = 136

For, 23 : 184

⇒ 23 × 8 = 184.

Similarly, for 29 ∶ ?

⇒ 29 × 8 = 232

Hence, the correct answer is "Option 1".

Given:

The student worked for 16 hours a day over 5 subjects, and the total marks obtained are 400 out of 500.

The distribution of time spent and marks obtained are shown in the pie charts.

Time spent on Math = 40% of 16 hours

Marks obtained in Math = 21% of 400 marks

Formula used:

Time spent on Math = (Percentage of time spent on Math) × (Total time in hours)

Marks obtained in Math = (Percentage of marks in Math) × (Total marks obtained)

Calculation:

For time spent on Math:

⇒ Time spent = 40% × 16 hours

⇒ Time spent = (40/100) × 16

⇒ Time spent = 6.4 hours

For marks obtained in Math:

⇒ Marks obtained = 21% × 400 marks

⇒ Marks obtained = (21/100) × 400

⇒ Marks obtained = 84 marks

∴ The student spent 6.4 hours on Math and obtained 84 marks in Math.

Given:

Simplify the given expression.

Formula used:

Order of operations (PEMDAS/BODMAS): Parentheses, Exponents (or Orders), Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right)

Calculation:

[ 3 × 6 - 3 { 2 ( 2 ÷ (1)/(2) - 2 ) + 2 ÷ (1)/(2) } - 18 ]

⇒ [ 3 × 6 - 3 { 2 ( 2 ÷ 0.5 - 2 ) + 2 ÷ 0.5 } - 18 ]

⇒ [ 3 × 6 - 3 { 2 ( 4 - 2 ) + 4 } - 18 ]

⇒ [ 3 × 6 - 3 { 2 × 2 + 4 } - 18 ]

⇒ [ 3 × 6 - 3 { 4 + 4 } - 18 ]

⇒ [ 3 × 6 - 3 × 8 - 18 ]

⇒ [ 18 - 24 - 18 ]

⇒ -24

∴ The correct answer is option (4).

Given:

Height (h) = 27 cm

Diameter (d) = 30 cm

Radius (r) = d/2 = 15 cm

π = 22/7

Formula used:

Total Surface Area (TSA) of a right circular cylinder = 2πr(h + r)

Calculation:

TSA = 2 × 22/7 × 15 × (27 + 15)

⇒ TSA = 2 × 22/7 × 15 × 42

⇒ TSA = 2 × 22 × 15 × 6

⇒ TSA = 3960 cm²

∴ The correct answer is option 1.

Shortcut Trick

Total work = LCM(24, 12) = 24 units.

Akhil's efficiency = 24 ÷ 24 = 1 unit/day.

Shyam's efficiency = 24 ÷ 12 = 2 units/day.

Combined efficiency = 1 + 2 = 3 units/day.

Time taken together = Total work ÷ Combined efficiency = 24 ÷ 3 = 8 days.

∴ The correct answer is 8 days.

Alternate Method

Given:

Time taken by Akhil = 24 days

Time taken by Shyam = 12 days

Formula Used:

Total Work = LCM of given days

Efficiency = Total Work ÷ Time taken

Calculations:

⇒ Total Efficiency of Akhil and Shyam = 1 + 2 = 3 units/day

⇒ Time taken to complete the work together = Total Work ÷ Total Efficiency

⇒ Time taken = 24 ÷ 3 = 8 days

∴ The correct answer is 8 days.

Additional Information

Direct Formula for 2 Persons

If person A takes x days and person B takes y days to finish a task, time taken together = (x × y) ÷ (x + y) days.

Pipes and Cisterns

Operates on the same logic as Time & Work. An inlet pipe has positive efficiency (adds to total work) while an outlet pipe has negative efficiency (subtracts from total work).

Work and Wages

Total wages earned are always distributed in the exact ratio of the total work done by each individual. If they work for the same duration, wages are split purely based on their efficiency ratio.

Alternate Days Working

Find the combined work done in one complete cycle (e.g., A works day 1, B works day 2 → 1 cycle = 2 days). Divide total work by cycle work to find the number of cycles, then add remaining days as needed.

Given:

The bar graph shows the production of three types of buses (A, B, and C) over the years.

We are required to find the year in which the percentage production of B type buses to C type buses is the maximum.

Formula used:

Percentage = (Production of B type buses / Production of C type buses) × 100

Calculation:

For 2013:

⇒ Percentage = (30 / 25) × 100 = 120%

For 2014:

⇒ Percentage = (27.5 / 22.5) × 100 = 122.22%

For 2015:

⇒ Percentage = (35 / 22.5) × 100 = 155.56%

For 2016:

⇒ Percentage = (22.5 / 30) × 100 = 75%

The maximum percentage of B type buses to C type buses is in the year 2015, which is 155.56%.

∴ The correct answer is option (3): 2015.

Given:

The graph shows the marks obtained by Riya and Rida in six subjects in the CBSE 12^th exam.

The maximum marks in Maths, Physics, and Chemistry are 140, and in English, IP, and Biology are 180.

We need to find the percentage of marks obtained by Riya in Chemistry.

Formula used:

Percentage = (Marks obtained / Maximum marks) × 100

Calculation:

Marks obtained by Riya in Chemistry = 130

Maximum marks in Chemistry = 140

⇒ Percentage = (130 / 140) × 100

⇒ Percentage = 92.86%

∴ The percentage of marks obtained by Riya in Chemistry is 92.86%.

Shortcut Trick

The arc length of a sector is proportional to its central angle.

For 30°, arc length = 5.5 cm.

For 360° (full circle), Circumference = 5.5 × (360 / 30) = 5.5 × 12 = 66 cm.

2 × (22 / 7) × r = 66 ⇒ r = (66 × 7) / 44 = 1.5 × 7 = 10.5 cm.

∴ The correct answer is 10.5 cm.

Alternate Method

Given:

Central angle (θ) = 30°

Arc length (l) = 5.5 cm

π = 22/7

Formula Used:

Length of arc (l) = (θ / 360°) × 2πr

Calculations:

⇒ 5.5 = (30 / 360) × 2 × (22 / 7) × r

⇒ 5.5 = (1 / 12) × (44 / 7) × r

⇒ 5.5 = (44 / 84) × r

⇒ r = (5.5 × 84) / 44

⇒ r = (1 / 8) × 84

⇒ r = 10.5 cm

∴ The correct answer is 10.5 cm.

Additional Information

Area of a Sector

The area of a sector with central angle θ is given by (θ / 360°) × πr² or (1 / 2) × arc length × radius.

Circumference and Area of Circle

For a circle of radius r, the Circumference = 2πr and the Area = πr².

Radian Measure

If θ is in radians, the arc length is simply l = r × θ, where 180° = π radians.

Given:

Line AB is the straight line, and AT is a tangent.

∠AOQ = 94°

∠BOQ = 180° - ∠AOQ = 180° - 94° = 86°

∠BAT = 90° (Radius is perpendicular to the tangent line)

Formula used:

In ΔBOQ, OB = OQ (radii of the circle) ⇒ ∠OQB = ∠OBQ

∠OBQ + ∠OQB + ∠BOQ = 180° (sum of angles in a triangle)

Calculations:

⇒ ∠OBQ + ∠OQB + ∠BOQ = 180°

⇒ 86° + 2∠OBQ = 180°

⇒ 2∠OBQ = 180°- 86°

⇒ 2∠OBQ = 94°

⇒ ∠OBQ = 47°

In ΔABT, ∠ABT + ∠BAT + ∠ATQ = 180° (sum of angles in a triangle)

⇒ ∠ATQ = 180° - (47° + 90°)

⇒ ∠ATQ = 180° - 137°

⇒ ∠ATQ = 43°

∴ ∠ATQ = 43°.

Given:

Principal total (P_total) = ₹8,000

Time (t) = 2 years

Interest received = ₹720

Rate of interest in scheme 1 (r₁) = 5% per annum

Rate of interest in scheme 2 (r₂) = 4% per annum

Formula used:

Simple Interest (SI) = $\frac{P \times r \times t}{100}$

Calculation:

Let the amount invested in scheme 1 be ₹x.

Then, the amount invested in scheme 2 = ₹(8,000 - x).

Interest from scheme 1 = $\frac{x \times 5 \times 2}{100}$

Interest from scheme 2 = $\frac{(8,000 - x) \times 4 \times 2}{100}$

Total interest = ₹720

⇒ $\frac{x \times 5 \times 2}{100} + \frac{(8,000 - x) \times 4 \times 2}{100} = 720$

⇒ $\frac{10x}{100} + \frac{64,000 - 8x}{100} = 720$

⇒ $\frac{10x + 64,000 - 8x}{100} = 720$

⇒ $\frac{2x + 64,000}{100} = 720$

⇒ 2x + 64,000 = 72,000

⇒ 2x = 72,000 - 64,000

⇒ 2x = 8,000

⇒ x = 4,000

∴ The amount of money invested in scheme 1 is ₹4,000, which is option (4).

Shortcut Trick

To keep Expenditure constant when Price increases by r%:

Percentage Reduction in Consumption = [r ÷ (100 + r)] × 100

Given r = 40%: Reduction = [40 ÷ (100 + 40)] × 100 = (40 ÷ 140) × 100

⇒ (2 ÷ 7) × 100 = 200 ÷ 7 = 28 4/7 %

∴ The correct answer is 28 4/7 %.

Alternate Method

Given:

⇒ Increase in Price = 40%

⇒ Total Expenditure = Constant

Formula Used:

⇒ Expenditure = Price × Consumption

⇒ If Expenditure is constant, Price is inversely proportional to Consumption.

Calculations:

⇒ Let the initial Price = 100 units and initial Consumption = 100 units.

⇒ Initial Expenditure = 100 × 100 = 10000 units.

⇒ New Price = 100 + 40% of 100 = 140 units.

⇒ To keep Expenditure same, New Consumption = Total Expenditure ÷ New Price

⇒ New Consumption = 10000 ÷ 140 = 500 ÷ 7 units.

⇒ Decrease in Consumption = 100 − (500 ÷ 7) = (700 − 500) ÷ 7 = 200 ÷ 7 units.

⇒ Percentage Decrease = (Decrease ÷ Initial Consumption) × 100

⇒ Percentage Decrease = (200 ÷ 7 ÷ 100) × 100 = 200 ÷ 7 % = 28 4/7 %.

∴ The correct answer is 28 4/7 %.

Additional Information

Constant Product Rule

When the product of two variables is constant (P × C = E), an increase in one by x/y requires a decrease in the other by x/(x+y).

Price Decrease Scenario

If the price decreases by r%, the consumption must increase by [r ÷ (100 − r)] × 100% to maintain the same expenditure.

Fraction to Percentage Conversion

Common fractions for quick calculation: 1/7 ≈ 14.28% | 2/7 ≈ 28.57% (which is 28 4/7 %).

Given:

What is the smallest number that must be added to 19487161 so that it is divisible by 11?

Formula used:

Divisibility Rule of 11: A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11.

Calculation:

Number: 19487161

Sum of digits in odd positions: 1 + 4 + 7 + 6 = 18

Sum of digits in even positions: 9 + 8 + 1 + 1 = 19

Difference: 19 - 18 = 1

To make the number divisible by 11, we need to make the difference 0 or a multiple of 11.

⇒ The smallest number = 11 - 1 = 10

Hence, Smallest number is 10.

∴ The correct answer is option 4.

Given:

Two parallel chords of length 5 units and 8 units are on opposite sides of the center of a circle of radius 7 units.

We need to find the distance between the chords.

Formula used:

In a right triangle:

OM = √(r² - AM²), where OM is the perpendicular distance from the center to the chord.

Calculation:

For the chord of length 5 units:

⇒ AM = 1/2 × 5 = 2.5 units

⇒ OM² = r² - AM²

⇒ OM = √(7² - 2.5²)

⇒ OM = √(49 - 6.25)

⇒ OM = √42.75 = 6.54 units

For the chord of length 8 units:

⇒ CN = 1/2 × 8 = 4 units

⇒ ON² = r² - CN²

⇒ ON = √(7² - 4²)

⇒ ON = √(49 - 16)

⇒ ON = √33 = 5.74 units

Therefore, the distance between the chords:

⇒ Distance = OM + ON

⇒ Distance = 6.54 + 5.74 = 12.28 units

∴ The distance between the chords is 12.28 units.

Given:

If cot θ = $\dfrac{3}{4}$, θ is an acute angle

Formula used:

cot θ = $\dfrac{\text{adjacent}}{\text{opposite}}$

sin²θ + cos²θ = 1

tan θ = $\dfrac{\text{opposite}}{\text{adjacent}}$

Calculation:

Given: cot θ = $\dfrac{3}{4}$

⇒ Opposite side = 4, Adjacent side = 3

⇒ Hypotenuse = $\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$

⇒ sin θ = $\dfrac{4}{5}$, cos θ = $\dfrac{3}{5}$

⇒ tan θ = $\dfrac{4}{3}$

sin θ + cos θ - tan θ = $\dfrac{4}{5} + \dfrac{3}{5} - \dfrac{4}{3}$

⇒ $\dfrac{4 + 3}{5} - \dfrac{4}{3}$

⇒ $\dfrac{7}{5} - \dfrac{4}{3}$

⇒ $\dfrac{21 - 20}{15}$

⇒ $\dfrac{1}{15}$

∴ The correct answer is option (1).

Given:

A mixture contains alcohol and water in the ratio of 12 : 5. On adding 14 liters of water, the ratio of alcohol to water becomes 4 : 3. The quantity of alcohol in the mixture is:

Formula used:

Let the quantity of alcohol be 12x liters and the quantity of water be 5x liters.

After adding 14 liters of water, the new quantity of water = 5x + 14 liters.

The ratio of alcohol to water becomes 4 : 3.

Thus, $\frac{12x}{5x + 14} = \frac{4}{3}$

Calculation:

$\frac{12x}{5x + 14} = \frac{4}{3}$

⇒ 12x × 3 = 4 × (5x + 14)

⇒ 36x = 20x + 56

⇒ 36x - 20x = 56

⇒ 16x = 56

⇒ x = $\frac{56}{16}$

⇒ x = 3.5

Quantity of alcohol = 12x = 12 × 3.5 = 42 liters

∴ The correct answer is option 2.

Given:

Base diameter of cylinder (d) = 60 cm

Height of cylinder (h) = 10 cm

Formula used:

Lateral Surface Area (LSA) = 2πrh

Total Surface Area (TSA) = 2πrh + 2πr²

Calculation:

Radius (r) = d/2 = 60/2 = 30 cm

LSA = 2πrh = 2×π×30×10 = 600π cm²

TSA = 2πrh + 2πr² = 2×π×30×10 + 2×π×30² = 600π + 1800π = 2400π cm²

Ratio (LSA : TSA) = 600π : 2400π

⇒ 1 : 4

∴ The correct answer is option (4).

Given:

Initial expenditure percentage = 72%

Income increase percentage = 12%

Expenditure increase percentage = 5%

Formula used:

New Income = Initial Income × (1 + Income increase percentage/100)

New Expenditure = Initial Expenditure × (1 + Expenditure increase percentage/100)

Savings = Income - Expenditure

Percentage change in savings = ((New Savings - Initial Savings) / Initial Savings) × 100

Calculation:

Let initial income be 100

Initial expenditure = 72% of 100 = 72

Initial savings (y) = 100 - 72 = 28

New income = 100 × (1 + 12/100)

⇒ New income = 100 × 1.12 = 112

New expenditure = 72 × (1 + 5/100)

⇒ New expenditure = 72 × 1.05 = 75.6

New savings (x) = 112 - 75.6 = 36.4

Percentage change in savings = ((36.4 - 28) / 28) × 100

⇒ Percentage change in savings = (8.4 / 28) × 100

⇒ Percentage change in savings = 0.3 × 100 = 30%

∴ The correct answer is option (4).

Shortcut Trick

Shortcut Trick

For infinitely many solutions, the ratios of the coefficients of x, y, and the constant terms must be equal: a₁/a₂ = b₁/b₂ = c₁/c₂.

Substitute values: k/12 = 3/k = −(k − 3)/−k.

Equating the first two ratios: k/12 = 3/k ⇒ k² = 36 ⇒ k = 6 (since k must be positive).

Verifying with the second and third ratios: 3/6 = (6 − 3)/6 ⇒ 1/2 = 3/6 (True).

∴ The correct answer is 6.

Alternate Method

Given Equations:

Equation 1: kx + 3y − (k − 3) = 0

Equation 2: 12x + ky − k = 0

Comparing with standard form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0:

a₁ = k, b₁ = 3, c₁ = −(k − 3)

a₂ = 12, b₂ = k, c₂ = −k

Formula Used:

For coincident lines (infinitely many solutions): a₁/a₂ = b₁/b₂ = c₁/c₂

Calculations:

⇒ From the first two ratios: k/12 = 3/k

⇒ k × k = 12 × 3

⇒ k² = 36

⇒ k = √36 ⇒ k = 6 or k = −6

⇒ Now, check with the second and third ratios: 3/k = (k − 3)/k

⇒ 3k = k(k − 3)

⇒ 3k = k² − 3k

⇒ k² − 6k = 0

⇒ k(k − 6) = 0

⇒ k = 0 or k = 6

⇒ The common positive value for both conditions is k = 6.

∴ The correct answer is 6.

Additional Information

Consistent and Inconsistent Systems

A system of equations is consistent if it has at least one solution (unique or infinite) and inconsistent if it has no solution.

Unique Solution (Intersecting Lines)

Condition: a₁/a₂ ≠ b₁/b₂. The lines cross at exactly one point (x, y).

No Solution (Parallel Lines)

Condition: a₁/a₂ = b₁/b₂ ≠ c₁/c₂. The lines are parallel and never meet.

Infinite Solutions (Coincident Lines)

Condition: a₁/a₂ = b₁/b₂ = c₁/c₂. Both equations represent the same line.

Shortcut Trick

Ratio of distances covered in the same time:

A : B = 100 : 80 = 5 : 4

B : C = 100 : 95 = 20 : 19

A : B : C = (5 × 5) : (4 × 5) : (19 × 1) → No, equate B: A : B : C = 25 : 20 : 19

When A = 100 (i.e., 25 × 4), C = 19 × 4 = 76

Distance A beats C = 100 − 76 = 24 m

∴ The correct answer is 24 m.

Alternate Method

Given:

Total distance of the race = 100 m

When A covers 100 m, B covers (100 − 20) = 80 m.

When B covers 100 m, C covers (100 − 5) = 95 m.

Calculations:

⇒ Ratio of speeds (or distances in same time) A/B = 100/80

⇒ Ratio of speeds (or distances in same time) B/C = 100/95

⇒ To find A/C, multiply the ratios: (A/B) × (B/C) = (100/80) × (100/95)

⇒ A/C = (5/4) × (20/19)

⇒ A/C = 100/76

⇒ This means when A covers 100 m, C covers 76 m.

⇒ Distance by which A beats C = 100 − 76 = 24 m.

∴ The correct answer is 24 m.

Additional Information

Relative Speed in Races

In a race of length L, if A beats B by distance d, the ratio of their speeds is V_A/V_B = L/(L − d).

Successive Beats Rule

If A beats B by x meters and B beats C by y meters in a race of L meters, A beats C by (x + y − xy/L) meters.

Time Headstart

If A gives B a start of t seconds, it means B starts t seconds before A or A finishes t seconds before B for the same distance.

Shortcut Trick

For melting n spheres into one, the large radius R follows: R³ = r₁³ + r₂³ + ... + r_n³.

Given diameters are 6, 8, 10 cm, so radii are 3, 4, 5 cm.

R³ = 3³ + 4³ + 5³ = 27 + 64 + 125 = 216

R = √³216 = 6 cm.

∴ The correct answer is 6 cm.

Alternate Method

Given:

Diameters of three spheres: D₁ = 6 cm, D₂ = 8 cm, D₃ = 10 cm

Formula Used:

Volume of a solid sphere = (4/3) × π × r³

Calculations:

⇒ Radius of 1^st sphere (r₁) = 6 ÷ 2 = 3 cm

⇒ Radius of 2^nd sphere (r₂) = 8 ÷ 2 = 4 cm

⇒ Radius of 3^rd sphere (r₃) = 10 ÷ 2 = 5 cm

⇒ Total volume of new sphere = Volume₁ + Volume₂ + Volume₃

⇒ (4/3) × π × R³ = (4/3) × π × (r₁³ + r₂³ + r₃³)

⇒ R³ = 3³ + 4³ + 5³

⇒ R³ = 27 + 64 + 125 = 216

⇒ R = √³216 = 6 cm

∴ The correct answer is 6 cm.

Additional Information

Total Surface Area of Sphere

The total surface area of a sphere is given by 4 × π × r².

Volume of Hemisphere

A hemisphere is half a sphere, so its volume is (2/3) × π × r³.

Recasting Principle

Whenever a solid object is melted and recast into another shape, the total volume remains constant, provided there is no wastage.

Curved Surface Area of Hemisphere

The CSA of a hemisphere is 2 × π × r² and the Total Surface Area (TSA) is 3 × π × r².

Given:

In triangle ABC, AB = AC.

BC is extended to D such that CD = AB and ∠ADC = 30°.

Formula used:

In an isosceles triangle, the base angles are equal.

The sum of angles in any triangle = 180°.

Calculation:

Since AB = AC and CD = AB

So, AB = AC = CD

In Δ ACD,

AC = CD

So, ∠ ADC = ∠ DAC = 30° 

And, ∠ ACD = 180 - (∠ ADC + ∠ DAC)

⇒ ∠ ACD = 180 - (30 + 30) = 180 - 60 = 120° 

Now, 

∠ ACB = 180 - ∠ ACD = 180 - 120 = 60°

Since AB = BC,

∠ ABC = ∠ ACB = 60°

Since two angles of a triangle are 60°, so third angle also will be 60° (as sum of angles of a triangle is 180°)

Hence, the angles of triangle ABC are 60°, 60°, and 60°.

Shortcut Trick Directly calculate the Weighted Average of the books. Total items = 4 + 5 + 6 = 15 books. Weighted Sum = (4 × 50) + (5 × 60) + (6 × 70) = 200 + 300 + 420 = ₹920. Average Cost = 920 ÷ 15 = ₹61.333... ∴ The correct answer is ₹61.33. Alternate Method Given: Number of books (n1) = 4, Price (p1) = ₹50 Number of books (n2) = 5, Price (p2) = ₹60 Number of books (n3) = 6, Price (p3) = ₹70 Formula Used: Average = (Total Value) ÷ (Total Number of Units)

⇒ Total Cost = (4 × 50) + (5 × 60) + (6 × 70) ⇒ Total Cost = 200 + 300 + 420 = ₹920 ⇒ Total Books = 4 + 5 + 6 = 15 ⇒ Average Cost = 920 ÷ 15 ⇒ Average Cost = 61.3333... ∴ The correct answer is ₹61.33. Additional Information Weighted Average Formula It is calculated as Σ(ni × xi) ÷ Σni, where n is the frequency and x is the value. Rounding Decimals When rounding to two decimal places, check the third decimal; if it is 5 or more, round up the second digit. Properties of Average The average always lies between the minimum and maximum values of the data set (50 < 61.33 < 70).

Given:

A shopkeeper buys 1800 kg wheat for ₹32,400. If 20% of this wheat is spoiled due to rain, at what rate (₹/kg) should he sell the rest to earn 20%?

Formula used:

Selling Price (SP) = Cost Price (CP) × (1 + Profit Percentage)

Calculation:

Total wheat = 1800 kg

Cost Price (CP) = ₹32,400

Wheat spoiled = 20% of 1800 kg

⇒ Wheat spoiled = 0.20 × 1800 = 360 kg

Remaining wheat = 1800 - 360 = 1440 kg

Desired Profit = 20%

Selling Price (SP) = CP × (1 + 0.20)

⇒ SP = ₹32,400 × 1.20

⇒ SP = ₹38,880

Rate per kg = SP / Remaining wheat

⇒ Rate per kg = ₹38,880 / 1440 kg

⇒ Rate per kg = ₹27

∴ The correct answer is option (3).

Given:

A 35% profit is made when a discount of 35% is given on the marked price of an item.

Formula used:

MP/CP = (100 + profit%) / (100 - discount%)

Profit% = [(SP - CP) / CP] × 100

Calculations:

MP/CP = (100 + 35) / (100 - 35) = 135 / 65

⇒ MP/CP = 27/13

MP = 27, CP = 13

If discount is 45%, then

SP = 27 - 27 × 45/100 = 27(1 - 45/100) = 27 × 55/100 = 297/20 = 14.85

So, profit = SP - CP = 14.85 - 13 = 1.85

Thus, Profit% = 1.85/13 × 100 = 185/13 = 14$\frac{3}{13}$%

∴ The correct answer is option (3).

Given:

If the income of Neha is 5% more than that of Monica, then the income of Monica is what percentage less than that of Neha?

Formula used:

Let Monica's income be M .

Neha's income = M + $\dfrac{5}{100} \times M$

Neha's income = 1.05M

Calculation:

Let Neha's income be N .

N = 1.05M

Monica's income = M

Percentage by which Monica's income is less than Neha's income:

⇒ $\dfrac{N - M}{N} \times 100$

⇒ $\dfrac{1.05M - M}{1.05M} \times 100$

⇒ $\dfrac{0.05M}{1.05M} \times 100$

⇒ $\dfrac{0.05}{1.05} \times 100$

⇒ $\dfrac{5}{105} \times 100$

⇒ $\dfrac{100}{21}$

⇒ $4\dfrac{16}{21}$%

∴ The correct answer is option (4).

Given:

The production data for wheat and maize over five years is given:

Years: 2016-17 to 2020-21

Wheat production (in lakh tonnes): 650, 800, 680, 700, 640

Maize production (in lakh tonnes): 200, 240, 220, 260, 300

Formula used:

Average production = $\dfrac{\text{Sum of production over years}}{\text{Number of years}}$

Calculation:

For wheat:

⇒ Sum of production = 650 + 800 + 680 + 700 + 640 = 3470 lakh tonnes

⇒ Average wheat production = $\dfrac{3470}{5}$ = 694 lakh tonnes

For maize:

⇒ Sum of production = 200 + 240 + 220 + 260 + 300 = 1220 lakh tonnes

⇒ Average maize production = $\dfrac{1220}{5}$ = 244 lakh tonnes

⇒ Difference in average production = 694 - 244 = 450 lakh tonnes

∴ The correct answer is option (1) 450.

The correct answer is C, B, A

Key Points

• Option 4 is the correct answer which arranges the states in descending order of their population growth rate according to Census 2011.
• The states in descending order of population growth rate are: Meghalaya, Arunachal Pradesh, Bihar.
• Meghalaya had the highest population growth rate among the three states listed.
• Arunachal Pradesh followed Meghalaya in terms of population growth rate.
• Bihar had the lowest population growth rate among the three states listed.

Additional Information

• The Census of India, 2011, is the 15^th National Census survey conducted by the Census Organization of India.
• Population growth rate is a crucial metric that indicates the rate at which the number of individuals in a population increases in a given time period.
• The growth rate of population in a region is influenced by factors such as birth rate, death rate, and migration rate.
• Understanding population growth rates helps in planning and resource allocation for the development and welfare of the population.

The correct answer is Maasai

Key Points

• Maasai is a tribe that predominantly lives in Kenya and Tanzania.
• They are known for their distinct culture, customs, and dress.
• Unlike the other tribes listed in the question (Gond, Santhal, Tharu), the Maasai do not have a presence in India.
• The Maasai people are semi-nomadic and are known for their traditional lifestyle and resistance to modern cultural influences.

Additional Information

• Gond is one of the largest tribal groups in India, found mainly in Madhya Pradesh, Chhattisgarh, Maharashtra, Odisha, and Andhra Pradesh.
• Santhal is a prominent tribe in India, primarily residing in Jharkhand, West Bengal, Bihar, and Odisha.
• Tharu is a tribal community living in the Terai region of Uttarakhand, Uttar Pradesh, and Bihar in India.
• These tribes (Gond, Santhal, Tharu) contribute to India's rich cultural and ethnic diversity.

The correct answer is James Watt

Key Points

• James Watt was the first to use the term 'horsepower' to quantify the power produced by an engine.
• He coined the term in the late 18^th century as a way to help market his improved steam engine.
• Watt's definition of horsepower was based on the amount of work a horse could do over a certain period.
• This unit of measurement became widely adopted and is still used today to describe the power output of engines.

Additional Information

• James Watt was a Scottish inventor, mechanical engineer, and chemist who made significant improvements to the Newcomen steam engine.
• His enhancements to the steam engine played a key role in the Industrial Revolution by making it more efficient and powerful.
• The watt, a unit of power in the International System of Units, is named in his honor.
• Watt's contributions to engineering and energy measurement have had a lasting impact on technology and industry.

The correct answer is Justified

Key Points

• Justified is not an alignment option for text in a cell in most spreadsheet applications.
• Common text alignment options in spreadsheet applications include Left, Center, and Right alignments.
• Text alignment determines how the text is positioned within the cell.
• Proper text alignment enhances the readability and organization of data in a spreadsheet.

Additional Information

• Left alignment aligns the text to the left side of the cell.
• Center alignment centers the text horizontally within the cell.
• Right alignment aligns the text to the right side of the cell.
• Some spreadsheet applications may offer additional alignment options, such as Top, Middle, and Bottom vertical alignments.