SSC CHSL Tier-1 2024: Official Paper (Held On: 03 Jul, 2024 Shift 2) (Previous Year Paper)

The erroneous part is: and cannot be put on.

Key Points

• In the fourth part of the given sentence, the phrase 'put on' is incorrect.
• The correct phrase should be 'put off', which means to delay or postpone something.
• Therefore, the correct phrase should be used in place of the incorrect one.

Hence, the correct answer is option 4.

Correct sentence: Urgent activities are those things that you must do immediately, as they require quick action and cannot be put off.

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

Key Points

• In the second part of the given sentence, the verb form 'taking' is incorrect.
• The correct form should be 'will take' to match the future tense.
• The verb 'will' should be followed by the base form of the verb, which is 'take' in this context.
• Example: The meeting will take place next Wednesday.

Hence, the correct answer is option 1.

Correct sentence: The meeting will take place next Wednesday.

Additional Information

• When constructing sentences in the future tense, always ensure that the modal 'will' is followed by the base form of the verb.
• Example: She will go to the market tomorrow.
• This rule applies to all subjects, whether singular or plural.
• Example: They will arrive at the station soon.

The correct answer is '2' i.e. this part of the sentence has an error.

Key Points

• In the second part of the given sentence, the phrasal verb 'grew out' is incorrect.
• The correct phrasal verb should be 'grew up', which means to mature or to become an adult.
• Therefore, the phrasal verb 'grew up' should be used in place of the incorrect phrasal verb 'grew out'.

Hence, the correct answer is option 3.

Correct sentence: When Christy grew up, he turned out to be a gentleman.

The correct answer is: quite amusing when.

Key Points

• In the second part of the given sentence, the verb 'amusing' is incorrect when describing Rashmi's reaction.
• Instead, it should be 'amused', which describes Rashmi's feeling.

Correct sentence: Rashmi was quite amused when she heard about what had happened.

Hence, the correct answer is option 2.

The correct answer is 'frustrating'.

 

Key Points

• The passage discusses the impact or emotion associated with certain experiences or events.
• The appropriate adjective should indicate a negative emotional response to a challenging situation.
• "Frustrating" (निराशा जनक) fits well as it denotes a feeling of being upset or annoyed, especially because of the inability to change or achieve something, which aligns with the context.
• Other options ("surprising", "interesting", "exciting") do not fit the context of describing a negative emotional response.

Therefore, the correct answer is 'Option 4'.

 

Additional Information

• Surprising (आश्चर्यजनक): "Surprising" means causing astonishment.
• Interesting (दिलचस्प): "Interesting" means arousing curiosity or interest.
• Exciting (रोमांचक): "Exciting" means causing great enthusiasm and eagerness.

The correct answer is 'wandering'.

 

Key Points

• The passage discusses the challenge of maintaining focus while trying to study.
• The appropriate word should indicate a difficulty or distraction that affects concentration.
• "Wandering" (आवारागर्द) fits well as it describes thoughts that are drifting away from the task at hand, which aligns with the context of struggling to focus.
• Other options ("tiring", "interesting", "worrying") do not fit the context of describing the distraction of thoughts while trying to study.

Therefore, the correct answer is 'Option 2'.

Additional Information

• Tiring (थकाऊ): "Tiring" means causing one to need rest or sleep.
• Interesting (दिलचस्प): "Interesting" means arousing curiosity or interest.
• Worrying (चिंताजनक): "Worrying" means causing anxiety or concern.

The correct answer is 'enhance'.

 

Key Points

• The context tells us about techniques that can be used to increase our concentration while studying.
• The appropriate verb should indicate an action that fits the context of the passage.
• "Enhance" (बढ़ाना) fits well as it denotes an action that aligns with the context of the passage.
• Other options ("discover", "commit", "convince") do not fit the context of describing the impact of forest fires on forests and biodiversity.

Therefore, the correct answer is 'Option 3'.

 

Additional Information

• Discover (खोजना): "Discover" means to find something.
• Commit (प्रतिबद्ध करना): "Commit" means to pledge or bind.
• Convince (मनाना): "Convince" means to persuade someone.

The correct answer is 'attempt'.

 

Key Points

• The passage likely discusses a scenario where an action is being taken.
• The appropriate verb should indicate an action that fits the context provided.
• "Attempt" (कोशिश करना) fits well as it denotes trying to do something, which aligns with the context.
• Other options ("announce", "imagine", "lead") do not fit the context of the action being described.

Therefore, the correct answer is 'Option 3'.

 

Additional Information

• Announce (की घोषणा): "Announce" means to make a public declaration.
• Imagine (कल्पना करना): "Imagine" means to form a mental image.
• Lead (नेतृत्व करना): "Lead" means to guide or direct.

The correct answer is 'focussed'.

 

Key Points

• The passage discusses the importance of maintaining attention and concentration in a given context.
• The appropriate adjective should indicate something that requires or demonstrates concentration or attention.
• "Focussed" (ध्यान केंद्रित) fits well as it denotes being concentrated on a particular task or goal, which aligns with the context.
• Other options ("joyful", "dazzling", "cautious") do not fit the context of describing the need for concentration and attention.

Therefore, the correct answer is 'Option 3'.

 

Additional Information

• Joyful (प्रसन्न): "Joyful" means feeling, expressing, or causing great pleasure and happiness.
• Dazzling (चमकदार): "Dazzling" means extremely bright, especially so as to blind the eyes temporarily.
• Cautious (सावधान): "Cautious" means careful to avoid potential problems or dangers.

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

Key Points

• The word "Immigrete" is incorrectly spelt and does not have a meaning in English. The correct spelling is "Immigrate". (प्रवासी होना)
• Immigrate refers to the act of coming to live permanently in a foreign country. (प्रवासी होना)
• Example: She decided to immigrate to Canada after getting a job offer there.

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

Additional Information

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

• Professional (पेशेवर): Relating to or connected with a profession.
• Example: She is a professional dancer who has performed all over the world.
• Combat (लड़ाई): Fighting between armed forces.
• Example: The soldiers were trained in hand-to-hand combat.
• Relevant (प्रासंगिक): Closely connected or appropriate to what is being done or considered.
• Example: His comments were not relevant to the topic we were discussing.

The correct answer is '4' i.e. on display is the correct phrase.

Key Points

• The phrase 'on display' is commonly used to indicate that something is being shown or exhibited in a place where people can see it.
• Other options such as 'upon display', 'into display', and 'in display' are incorrect and not commonly used in standard English.
• Therefore, the correct phrase to use in this context is 'on display'.

Hence, the correct answer is option 4.

Correct sentence: My sister’s paintings were on display at the national museum.

The correct answer is: Be preoccupied or obsessed with something.

Key Points

• The idiom "Have a bee in your bonnet" means to be preoccupied or obsessed with something. (किसी चीज़ के बारे में व्यस्त या जुनूनी होना)
• Example: She has a bee in her bonnet about recycling and is always talking about it.
• "Be preoccupied or obsessed with something" refers to having one's mind dominated by a single thought or idea. (किसी एक विचार या विचार से प्रभावित होना)
• Example: He is so preoccupied with his work that he forgets to eat.

Therefore, the correct answer is: Option 4 i.e. Be preoccupied or obsessed with something.

The correct answer is: Lazy.

Key Points

• The word "industrious" means someone who is diligent and hardworking; it refers to a person who puts in a lot of effort and is consistently productive. (परिश्रमी)
• Example: She is an industrious student who always completes her assignments on time.
• "Lazy" refers to someone who is unwilling to work or put in effort; it describes a person who prefers to avoid physical or mental exertion. (आलसी)
• Example: He is too lazy to clean his room, even when it gets very messy.
• Hence, we can infer that the opposite of 'industrious' is 'lazy'.

Therefore, the correct answer is: Lazy.

Additional Information

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

• Exhausting (थकाऊ): Causing one to feel very tired.
• Example: The long hike up the mountain was exhausting.
• Dizzy (चक्कर आना): Feeling as if everything is spinning around you and that you are not able to balance.
• Example: She felt dizzy after spinning around in circles.
• Skittish (चंचल): Easily frightened or excited.
• Example: The skittish horse bolted at the sound of the thunder.

The correct answer is: 'horrible'.

Key Points

• The word "ghastly" means something that is extremely unpleasant or horrifying. (भयानक)
• Example: The ghastly sight of the accident left everyone in shock.
• "Horrible" refers to something that is very unpleasant or bad, often causing fear or disgust. (भयानक)
• Example: The food at that restaurant was horrible; I couldn't even finish my meal.
• Hence, we can infer that the word 'ghastly' is best substituted with 'horrible' in this context.

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

Additional Information

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

• Comforting (सांत्वनादायक): Providing comfort or solace.
• Example: Her comforting words helped me get through a tough day.
• Pleasant (सुखद): Giving a sense of happy satisfaction or enjoyment.
• Example: We had a pleasant evening at the park.
• Agreeable (सहमत): Enjoyable and pleasurable; pleasant.
• Example: The weather was agreeable for a picnic.

The correct answer is: Non-combustible.

Key Points

• The word "flammable" means something that is easily set on fire or capable of burning quickly. (ज्वलनशील)
• Example: The chemical stored in the laboratory is highly flammable.
• "Non-combustible" refers to a material that does not catch fire or burn easily. (अज्वलनशील)
• Example: The building materials used are non-combustible to ensure safety.
• Hence, we can infer that the opposite of 'flammable' is 'non-combustible'.

Therefore, the correct answer is: Non-combustible.

Additional Information

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

• Incendiary (आग लगाने वाला): Designed to cause fires.
• Example: The incendiary device was found in the suspect's car.
• Nonexplosive (गैर-विस्फोटक): Not capable of causing an explosion.
• Example: This chemical is nonexplosive and safe to handle.
• Fire-resistant (अग्निरोधक): Not easily burned and able to withstand fire.
• Example: The fire-resistant coating on the walls helped prevent the spread of flames.

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

Key Points

• The word "contaminate" means to make something impure or unclean by exposure to or addition of a poisonous or polluting substance. (प्रदूषित करना)
• Example: Factory waste can contaminate rivers and harm the wildlife.
• "Clean" refers to removing dirt, marks, or stains from something; making something free from pollution or impurities. (साफ)
• Example: She spent hours cleaning the kitchen after the party.
• Hence, we can infer that the opposite of 'contaminate' is 'clean'.

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

Additional Information

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

• Rug (गलीचा): A floor covering of thick woven material or animal skin, typically not extending over the entire floor.
• Example: The new rug in the living room added a cozy touch.
• Spent (खर्च किया हुआ): Having been used and unable to be used again; exhausted.
• Example: He felt spent after the long day at work.
• Working (काम कर रहा): Engaging in physical or mental activity in order to achieve a purpose or result.
• Example: She is working hard to meet the deadline.

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

Key Points

• The word "Fastidious" means very attentive to and concerned about accuracy and detail. (अतिसंवेदनशील)
• Example: She was fastidious about her appearance, always making sure her clothes were perfectly pressed and her hair impeccably styled.
• "Lax" refers to not sufficiently strict, severe, or careful. (ढीला)
• Example: The lax security at the event made it easy for unauthorized persons to enter.
• Hence, we can infer that the opposite of 'Fastidious' is 'Lax'.

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

Additional Information

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

• Speedy (तेज़): Moving or capable of moving at high speed.
• Example: The speedy delivery service ensured that the package arrived the next day.
• Late (देर): Doing something or taking place after the expected, proper, or usual time.
• Example: He was late for the meeting because of heavy traffic.
• Scrupulous (ईमानदार): Very concerned to avoid doing wrong; extremely attentive to details.
• Example: The scrupulous accountant made sure every entry was accurate and justified.

The correct answer is: Option 2 i.e. vacant seat.

Key Points

• The word "barren" means something that is unproductive, empty, or lacking vegetation. (बंजर)
• Example: The farmer struggled with the barren land that yielded no crops.
• "Vacant" refers to something that is not occupied or filled; available for use. (खाली)
• Example: I found a vacant seat at the back of the bus.
• Hence, we can infer that "vacant seat" is the correct term to use instead of "barren seat".

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

Additional Information

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

• Deserted seat (निर्जन सीट): A seat that is abandoned or left empty by people.
• Example: The deserted seat in the park looked lonely.
• Hollow seat (खोखली सीट): A seat that is empty inside or has a space within.
• Example: The hollow seat was not very comfortable to sit on.
• Vacuous seat (अर्थहीन सीट): A seat that is empty or lacking in content.
• Example: His vacuous seat in the meeting room indicated his absence.

The correct answer is: Option 2 i.e. imperfect alignment.

Key Points

• The word "positioning" refers to the arrangement or placement of something in a particular position. (स्थिति निर्धारण)
• Example: The positioning of the furniture in the room made it look more spacious.
• "Alignment" refers to the arrangement in a straight line or in correct relative positions. In astronomy, it specifically refers to the celestial bodies being in line. (संरेखण)
• Example: The alignment of the planets is a rare astronomical event.
• Hence, the term "imperfect alignment" is more appropriate in the context of celestial bodies leading to a partial lunar eclipse.

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

Additional Information

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

• Imperfect revolution (अपूर्ण क्रांति): Refers to an incomplete or flawed orbit or cycle.
• Example: An imperfect revolution of the planet could lead to unstable climatic conditions.
• Imperfect alliance (अपूर्ण गठबंधन): Refers to a flawed or incomplete partnership or union.
• Example: The imperfect alliance between the two companies led to several operational challenges.
• Imperfect allegiance (अपूर्ण निष्ठा): Refers to a partial or flawed loyalty or commitment.
• Example: His imperfect allegiance to the cause was evident in his inconsistent efforts.

The correct answer is: To remain faithful to.

Key Points

• The idiom "Stick to one's guns" means to remain determined, resolute, or faithful to one's beliefs, decisions, or actions despite opposition or criticism. (अपने विचारों या निर्णयों पर दृढ़ रहना)
• Example: Despite the criticism from his colleagues, he decided to stick to his guns and continue with his original plan.
• "To remain faithful to" refers to staying loyal or true to someone or something. (वफादार रहना)
• Example: She remained faithful to her principles, even when it was difficult.

Therefore, the correct answer is: Option 1 i.e. 'To remain faithful to'.

Additional Information

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

• To shoot at (गोली चलाना): To fire a gun at someone or something.
• Example: The soldier was ordered to shoot at the target.
• To become a rebel (विद्रोही बनना): To oppose or defy authority or tradition.
• Example: He decided to become a rebel and fight against the unjust system.
• To become unfaithful to (अवफादार होना): To stop being loyal or faithful.
• Example: She feared he would become unfaithful to her.

The incorrectly spelt word is: Litrature.

Key Points

• The word "Litrature" is incorrectly spelled and should be "Literature". (साहित्य)
• "Literature" refers to written works, especially those considered of superior or lasting artistic merit. (साहित्य)
• Example: She is studying English literature at the university.

Therefore, the correct answer is: Option 1 i.e. Litrature.

Additional Information

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

• Reformation (सुधार): The action or process of reforming an institution or practice.
• Example: The reformation of the education system is a priority for the government.
• Schedule (अनुसूची): A plan for carrying out a process or procedure, giving lists of intended events and times.
• Example: The train schedule was posted on the bulletin board.
• Miserable (दुखी): Wretchedly unhappy or uncomfortable.
• Example: She felt miserable after losing her job.

The correct answer is: gifted with.

Key Points

• The phrase "gifted at" is not correct in this context. The correct preposition to use is "gifted with".
• The term "gifted with" is used to indicate that someone has a particular talent or ability.
• Using the correct preposition is essential for proper sentence structure and meaning.

Hence, the correct answer is option 2.

Correct sentence: The new chief is gifted with the power of eloquence.

The correct answer is: Option 3 i.e. took apart.

Key Points

• The word "dismantled" means to take something apart so that it is in separate pieces. (विखंडित करना)
• Example: The workers dismantled the old machinery to make space for the new equipment.
• "Took apart" refers to breaking something into its individual components, similar to dismantling. (विखंडित करना)
• Example: He took apart the clock to see how it worked.

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

Additional Information

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

• Took after (पर जाना): To resemble a parent or ancestor in appearance or behavior.
• Example: She really took after her mother in terms of talent and looks.
• Took back (वापस लेना): To retract or withdraw something said or done.
• Example: He took back his words after realizing he was wrong.
• Took up (उठा लिया): To begin a new hobby or activity.
• Example: She took up painting after retiring from her job.

The correct answer is: Option 1 i.e. Insignificance.

Key Points

• The word "frivolity" means lack of seriousness or sense; something that is not important or of little value. (मूर्खता, तुच्छता)
• Example: The meeting was filled with frivolity and lacked any real substance.
• "Insignificance" refers to the quality of being unimportant or trivial. (तुच्छता)
• Example: The insignificance of his comments was evident to everyone in the room.

Therefore, the correct answer is: Option 1 i.e. Insignificance.

Additional Information

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

• Consequence (परिणाम): The result or effect of an action or condition.
• Example: Every decision has a consequence, so choose wisely.
• Meaningful (सार्थक): Having a serious, important, or useful quality or purpose.
• Example: The conversation was deep and meaningful, touching on many important issues.
• Substantial (ठोस): Of considerable importance, size, or worth.
• Example: He made a substantial donation to the charity.

The correct answer is '3' i.e. in the heart of Telangana .

Key Points

• The phrase in the heart of is used to indicate that something is located in the central part of a place.
• Hyderabad is a major city in the state of Telangana, and it is centrally located within the state.
• The other options do not correctly convey the intended meaning or are grammatically incorrect.
• Therefore, the correct phrase to use is in the heart of Telangana.

Hence, the correct answer is option 3.

Correct sentence: The city of Hyderabad is located in the heart of Telangana.

Decoding the Symbols:

Now, checking options one by one:

Option - (1): L - F + K - P → L is the sister of F who is the father of K who is the sister of P.

Here, K is the brother's daughter or niece of L.

Option - (3): L ÷ Z × X - K → L is the brother of Z who is the mother of X who is the sister of K.

Here, K is either niece of nephew of L.

Option - (3): K - L × X ÷ U → K is the sister of L who is the mother of X who is the brother of U.

​

Here, K is the sister of L.

Option - (4): U + F + K ÷ P → U is the father of F who is the father of K who is the brother of P.

Here, K is the granddaughter of L.

So, out of all the options 'L - F + K - P' represents that K is the brother's daughter of L.

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

Given : AB_Z DEF_ G_IX JKL_ M_OV

By checking options :

Option 1) YGHVN → ABYZ / DEFG / GHIX / JKLV / MNOV → (It doesn't Follow the pattern)  

Option 2) CYHVN → ABCZ / DEFY / GHIX / JKLV / MNOV → (It doesn't Follow the pattern)

Option 3) CYGWN → ABCZ / DEFY / GGIX / JKLW / MNOV → (It doesn't Follow the pattern)

Option 4) CYHWN → ABCZ / DEFY / GHIX / JKLW / MNOV → (It follows the pattern)

So, out of all the options "Option - (4)" follows the pattern.

Hence, "Option 4" is the correct answer.

Given word: 'MENTOR'

After arranged in alphabetical order:

 

Now,

there is One alphabet "N" will remain unchanged if each of the letters in the word 'MENTOR' is arranged in English alphabetical order.

Hence, the correct answer is "Option 1".

According to the given figure:

The figure will appear when it is opened as follows:

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

Given Equation: 84 H 42 A 63 L 46 B 23 = ?

BODMAS Rule:

Decoding the given information:

 

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

⇒ 84 ÷ 42 + 63 × 46 - 23 = ?

⇒ 2 + 63 × 46 - 23 = ?

⇒ 2 + 2898 - 23 = ?

⇒ 2900 - 23 = 2877.

Hence, the correct option is "Option 4".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 1".

Decoding the Symbols:

Given: P @ Q # R & S @ T

P @ Q → P is the husband of Q.

Q # R → Q is the mother of R.

R & S → R is the sister of S.

​

S @ T → S is the husband of T.

​

So, T is the son's wife or daughter-in-law of P.

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

Given Equation: 52 M 36 Z 18 T 46 H 19 = ?

BODMAS Rule:

Decoding the given information:

 

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

⇒ 52 + 36 ÷ 18 - 46 × 19 = ?

⇒ 52 + 2 - 46 × 19 = ?

⇒ 52 + 2 - 874 = ?

⇒ 54 - 874 = -820.

Hence, the correct option is "Option 3".

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

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

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

The logic followed here is:

Logic: (1^st number ÷ 5) = 2^nd number.

Now,

For, 100 : 20

⇒ (100 ÷ 5) = 20.

For, 250 : 50

⇒ (250 ÷ 5) = 50.

Similarly, for 550 ∶ ?

⇒ (550 ÷ 5) = 110.

Hence, the correct answer is "Option 3".

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

Here, as marked there are a total of 18 triangles.

Hence, "18" is the correct answer.

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

Conclusions:

I. Some erasers are calculators → Does not follow (As no pen is a scale, all scales are erasers and all pens are calculators. So, it is possible but not definitely true)

II. No pen is an eraser → Does not follow (As no pen is a scale and all scales are erasers. So, no direct relation is given between erasers and scales, therefore it is false)

III. No scale is a calculator → Does not follow (As no pen is a scale and all pens are calculators. So, no direct relation is given between erasers and scales, therefore it is false)

∴ Here, Neither conclusions I, II nor III follows.​

Hence, the correct answer is "Neither conclusions I, II nor III follows"

The logic followed here is:

Logic: Synonyms.

Here,

Pleasure : Delight  → Pleasure and Delight are synonyms.

Similarly,

Demolish : Destroy  → Demolish and Destroy are synonyms.

Hence, the correct answer is "Option 3".

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

COMB is coded as 2681

And,

MOBE is coded as 8163

As, 'M', 'O', and 'B' are common, therefore it can be concluded that :

C is coded as → 2

E is coded as → 3

So, the code for 'E' is '3'.

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

Given : 198 × 9 + 29 - 7 ÷ 10 = ?

According to the question, after replacing the signs :

‘+’ and ‘-’ are interchanged and,

‘×’ and ‘÷’ are interchanged

So,​​

198 × 9 + 29 - 7 ÷ 10 = ? ⇒ 198 ÷ 9 - 29 + 7 × 10 = ?

198 ÷ 9 - 29 + 7 × 10 = ?

22 - 29 + 7 × 10 = ?

70 + 22 - 29 = ?

92 - 29 =?

63 = ?

Hence, "63" is the correct answer.

The logic followed here is:

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

Now,

For, 245, 49, 5

⇒ 49 × 5 = 245.

For, 144, 9, 16

⇒ 9 × 16 = 144

Similarly, For, 200, 8, 25

⇒ 8 × 25 = 200.

Hence, the correct answer is "Option 4".

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

​​So,

'COVER' is coded as '9 - 45 - 66 - 15 - 54'

​ 

​And,

'BOAST' is coded as '6 - 45 - 3 - 57 - 60'

​ 

​Similarly,

'APRON' is coded as 

​ 

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

The logic followed here is:

Logic: Synonyms Relationship.

Here,

Proud : Arrogant → Proud is a synonym of  Arrogant.

Similarly,

Authentic : Genuine → Authentic is a synonym of Genuine.

Hence, the correct answer is "Option 3".

The logic followed here is: (3), (10), and (1) are added to the first, second, and third letters position values according to the English alphabetic series respectively.

So,

​

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

The logic followed here is :-

From the given two different cubes the adjacent sides are as shown below :

As 5 is common on both the dice, it is clear that 9, 8, 7, and 2 are adjacent to it, and the remaining number i.e., 3the  will be opposite to it.

Opposite pairs:

8 → 2

9 → 7

5 → 3

So, the opposite side of "5" will be side "3".

Hence, the correct answer is "3".

The logic followed here is :

1. For '

' element → Number of triangles is increasing in the clockwise direction in the order of consecutive multiples of (3).

2) For '

' element → No change.

Thus, the final series is :

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

Logic : Alternately (4) and (3) are multiplied by each number subsequently.

Hence, "4032" is the correct answer.

Logic : (9) is added to each number in the given series.

Hence, "136" is the correct answer.

Given: 17 August 2003 was Sunday.

Now,

2003 to 2014 = 11 Years (8 Ordinary Years and 3 Leap Years).

And, In 11 Years = 3 Leap years and 8 Ordinary Years.

So, 3 Leap Years have 6 odd days,

And, 8 Ordinary Years have 8 odd days.

Total odd days = 6 + 8 = 14.

14 odd days → 14/7 = 2 weeks and 0 odd days.

then, 17 August 2014 will be Sunday + 0 = Sunday.

Now, the number of days between 17 August 2014 to 12 September 2014

= 14(August) + 12(September) = 26 days.

= 26 days → 26/7 = 3 weeks and 5 odd days.

So, 12 September 2014 will be Sunday + 5 = Friday.

Hence, the correct answer is "Option 3".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 2".

Given:

$\sin(30 + \theta) - \cos(60 - \theta)$

Formula used:

$\sin(30 + \theta) = \sin 30 \cos \theta + \cos 30 \sin \theta$

$\cos(60 - \theta) = \cos 60 \cos \theta + \sin 60 \sin \theta$

Calculation:

$\sin(30 + \theta) - \cos(60 - \theta)$

$\sin 30 \cos \theta + \cos 30 \sin \theta - (\cos 60 \cos \theta + \sin 60 \sin \theta)$

⇒ $\frac{1}{2} \cos \theta + \frac{\sqrt{3}}{2} \sin \theta - (\frac{1}{2} \cos \theta + \frac{\sqrt{3}}{2} \sin \theta)$

⇒ $\frac{1}{2} \cos \theta + \frac{\sqrt{3}}{2} \sin \theta - \frac{1}{2} \cos \theta - \frac{\sqrt{3}}{2} \sin \theta$

⇒ 0

∴ The correct answer is option (3).

Shortcut Trick

Using the ratio method: 45% = 9/20 and 30% = 3/10.

Cost Price to Selling Price ratios: (20 → 29) and (10 → 13).

Combined ratio for A to C: (20 × 10) : (29 × 13) = 200 : 377.

Given 377 units = ₹43,355 ⇒ 1 unit = 115.

Initial Cost Price for A = 200 × 115 = 23,000.

∴ The correct answer is ₹23,000.

Alternate Method

Given:

Profit of A = 45% | Profit of B = 30% | Final Price paid by C = ₹43,355

Let the cost price for A be x.

⇒ Price for B = x × (1 + 45/100) = 1.45x

⇒ Price for C = (1.45x) × (1 + 30/100) = 1.45x × 1.3

⇒ 1.885x = 43,355

⇒ x = 43,355 ÷ 1.885

⇒ x = 23,000

∴ The correct answer is ₹23,000.

Additional Information

Successive Percentage Formula

When two profits x% and y% occur successively, the net profit percentage is given by [x + y + (x × y)/100]%.

Ratio Method for Profit/Loss

Profit of P% means CP : SP = 100 : (100 + P). This can be simplified into fractions for faster calculations in chains.

Cost Price (CP) vs Selling Price (SP)

SP = CP × (100 + Profit%)/100. To find CP from SP, use CP = SP × 100 / (100 + Profit%).

Given:

The curved surface area of a right circular cylinder of height 14 cm, is 88 cm².

Formula used:

Curved Surface Area (CSA) of a cylinder = 2πrh

Total Surface Area (TSA) of a cylinder = 2πrh + 2πr²

Calculation:

Given CSA = 88 cm²

Height (h) = 14 cm

Using CSA formula:

2πrh = 88

⇒ 2 × (22/7) × r × 14 = 88

⇒ 2 × 22 × r × 2 = 88

⇒ 88r = 88

⇒ r = 1 cm

Now, using TSA formula:

TSA = 2πrh + 2πr²

⇒ TSA = 2 × (22/7) × 1 × 14 + 2 × (22/7) × 1²

⇒ TSA = 2 × 22 × 2 + 2 × (22/7)

⇒ TSA = 88 + (44/7)

⇒ TSA = 88 + 6.2857

⇒ TSA = 94.2857

⇒ TSA = (660/7) cm²

∴ The correct answer is option (3).

Given:

Area of ΔABC = 63 cm²

Area of ΔACD = 7 cm²

AC = 5 cm

Formula used:

If ΔABC ∼ ΔXYZ, then

ar(ΔABC) / ar(ΔXYZ) = (AB/XY)² = (BC/YZ)2 = (AC/XZ)2

Calculation:

In ΔABC and ΔACD

∠BAC = ∠ADC = 90° 

∠C = ∠C   (Common in both triangles)

So, ΔABC ∼ ΔDAC  (by AA Similarity)

Now,

ar(ΔABC) / ar(ΔACD) = (BC/AC)²

⇒ 63/7 = (BC/5)²

⇒ 9/1 = (BC/5)2

⇒ √(9/1) = BC/5

⇒ 3 = BC/5

⇒ BC = 5 × 3 = 15 cm

∴ The length of BC is 15 cm

Shortcut Trick

Equate Selling Price (SP) in terms of Cost Price (CP) and Marked Price (MP):

66% of MP = 110% of CP (since 10% profit is made)

⇒ 1% of MP = (110 / 66)% of CP = (5 / 3)% of CP

⇒ 80% of MP = (5 / 3) × 80% of CP = (400 / 3)% of CP = 133 1/3% of CP

⇒ New Profit % = 133 1/3% − 100% = 33 1/3%

∴ The correct answer is 33 (1)/(3) %.

Alternate Method

Given: SP₁ = 66% of MP, Profit = 10%, SP₂ = 80% of MP.

Formula: Cost Price (CP) = [Selling Price (SP) / (100 + Profit %)] × 100

⇒ Let Marked Price (MP) = ₹100

⇒ Case 1: SP₁ = 66% of 100 = ₹66

⇒ CP = (66 ÷ 110) × 100 = ₹60

⇒ Case 2: SP₂ = 80% of 100 = ₹80

⇒ Profit = SP₂ − CP = 80 − 60 = ₹20

⇒ Profit % = (20 ÷ 60) × 100 = (1/3) × 100

⇒ Profit % = 33 1/3%

∴ The correct answer is 33 (1)/(3) %.

Additional Information

CP and MP Relationship

The ratio of Marked Price to Cost Price is given by: MP/CP = (100 + Profit %)/(100 − Discount %).

Profit and Loss Basics

Profit % = (Profit ÷ CP) × 100, and Discount % = (Discount ÷ MP) × 100. Profit or Loss is always calculated on the Cost Price unless stated otherwise.

Successive Discounts

If two discounts d₁% and d₂% are given, the Equivalent Discount is [d₁ + d₂ − (d₁ × d₂)/100]%.

Given:

Enrollment data from 2015 to 2020 for different courses (Engineering, Science, Arts, Management)

Formula used:

Growth Rate (%) = [(Final Value - Initial Value) / Initial Value] × 100

Calculation:

For Engineering:

Initial Value (2015) = 1200, Final Value (2020) = 1400

Growth Rate = [(1400 - 1200) / 1200] × 100

⇒ Growth Rate = [200 / 1200] × 100

⇒ Growth Rate ≈ 16.67%

For Science:

Initial Value (2015) = 850, Final Value (2020) = 950

Growth Rate = [(950 - 850) / 850] × 100

⇒ Growth Rate = [100 / 850] × 100

⇒ Growth Rate ≈ 11.76%

For Arts:

Initial Value (2015) = 450, Final Value (2020) = 750

Growth Rate = [(750 - 450) / 450] × 100

⇒ Growth Rate = [300 / 450] × 100

⇒ Growth Rate ≈ 66.67%

For Management:

Initial Value (2015) = 240, Final Value (2020) = 320

Growth Rate = [(320 - 240) / 240] × 100

⇒ Growth Rate = [80 / 240] × 100

⇒ Growth Rate ≈ 33.33%

∴ The course with the highest growth rate is Arts, with a growth rate of approximately 66.67%.

Given:

The value of (17 + 15) ÷ 2 - 11 + 16 × 4 - 28 + 13 (-16 + 13) is:

Formula used:

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

Calculation:

(17 + 15) ÷ 2 - 11 + 16 × 4 - 28 + 13 (-16 + 13)

⇒ 32 ÷ 2 - 11 + 16 × 4 - 28 + 13 (-3)

⇒ 16 - 11 + 64 - 28 + 13 (-3)

⇒ 16 - 11 + 64 - 28 - 39

⇒ 5 + 64 - 28 - 39

⇒ 69 - 28 - 39

⇒ 41 - 39

⇒ 2

∴ The correct answer is option 3.

Shortcut Trick

Using the MDH formula: (M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

Given: (18 × 10) / (1/5) = (M₂ × 5) / (2/5)

⇒ 180 × 5 = M₂ × 5 × (5/2)

⇒ 180 = M₂ × (5/2)

⇒ M₂ = (180 × 2) / 5 = 72

∴ The correct option is 1.

Alternate Method

Given:

Initial men (M₁) = 18

Initial days (D₁) = 10

Initial work (W₁) = 1/5

New days (D₂) = 5

New work (W₂) = 2/5

Formula Used:

(M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

CASE 1 Men (M1) = 18 Days (D1) = 10 Work (W1) = 1/5 CASE 2 Men (M2) = ? Days (D2) = 5 Work (W2) = 2/5 M1 × D1 / W1 = M2 × D2 / W2

Calculations:

⇒ (18 × 10) / (1/5) = (M₂ × 5) / (2/5)

⇒ 180 × 5 = (M₂ × 5 × 5) / 2

⇒ 900 = (25 × M₂) / 2

⇒ 1800 = 25 × M₂

⇒ M₂ = 1800 / 25

⇒ M₂ = 72

∴ The correct option is 1.

Additional Information

MDH Rule / Chain Rule

The general formula is (M₁ × D₁ × H₁ × E₁) / W₁ = (M₂ × D₂ × H₂ × E₂) / W₂, where M is men, D is days, H is hours, E is efficiency, and W is work.

Inverse Proportion

For a constant amount of work, the number of men is inversely proportional to the number of days taken: M₁D₁ = M₂D₂.

Work and Efficiency

Total work is the product of the number of workers, the time they work, and their individual efficiency: W = M × D × H × E.

Given:

A, B, C are three points such that AB = 11 cm, BC = 13 cm, and AC = 24 cm.

Formula used:

For three points to lie on a circle, the sum of the lengths of any two sides must be greater than the third side (Triangle Inequality Theorem).

Calculation:

Check triangle inequality for AB, BC, and AC:

AB + BC > AC

11 + 13 > 24

24 = 24 (Not greater)

BC + AC > AB

13 + 24 > 11

37 > 11 (True)

AC + AB > BC

24 + 11 > 13

35 > 13 (True)

Since AB + BC is not greater than AC, the points A, B, C do not form a triangle and hence cannot lie on the same circle.

∴ The correct answer is option 1.

Shortcut Trick

For two circles touching externally at point M, the angle subtended by the direct common tangent PQ at the point of contact M is always 90°.

⇒ ∠PMQ = 90°

In triangle ΔPMQ, the sum of angles is 180°.

⇒ ∠MQP = 90° − ∠MPQ

⇒ ∠MQP = 90° − 38° = 52°

∴ The correct answer is 52°.

Alternate Method

Given:

∠MPQ = 38°

Circles touch at M; PQ is a direct common tangent.

Formula Used:

1. Lengths of tangents from an external point to a circle are equal.
2. Sum of angles in a triangle = 180°.

Calculations:

⇒ Let the common tangent at M intersect PQ at point R.

⇒ From point R, RP and RM are tangents to the first circle, so RP = RM.

⇒ From point R, RQ and RM are tangents to the second circle, so RQ = RM.

⇒ Thus, RP = RQ = RM. This implies R is the midpoint of PQ and RM = ½ PQ.

⇒ In ΔPMQ, if the median RM is half the side PQ, then ∠PMQ = 90°.

⇒ In ΔPMQ, ∠MPQ + ∠MQP + ∠PMQ = 180°

⇒ 38° + ∠MQP + 90° = 180°

⇒ ∠MQP = 180° − 128°

⇒ ∠MQP = 52°

∴ The correct answer is 52°.

Additional Information

Direct Common Tangent (DCT)

The length of the direct common tangent for two circles with radii r₁ and r₂ and distance d between centers is √(d² − (r₁ − r₂)²).

Tangents from an External Point

Tangents drawn from an external point to a circle are always equal in length and subtend equal angles at the center.

Circles Touching Externally

When two circles touch externally, the distance between their centers d = r₁ + r₂, and they have three common tangents (two direct and one transverse).

Shortcut Trick

Identify the vertices of the triangle formed by the lines and the x-axis (where y = 0).

Line 1 (2x + y = 6) intersects x-axis at (3, 0) and Line 2 (2x − y = −2) intersects x-axis at (−1, 0).

The base of the triangle along the x-axis is |3 − (−1)| = 4 units.

Solve the equations for the intersection point: Adding 2x + y = 6 and 2x − y = −2 gives 4x = 4 ⇒ x = 1. Substitute x = 1 in 2x + y = 6 ⇒ 2(1) + y = 6 ⇒ y = 4.

The height of the triangle is the y-coordinate of the intersection point, which is 4 units.

Area = 1/2 × base × height = 1/2 × 4 × 4 = 8 sq. units.

∴ The correct answer is 8 sq. units.

Alternate Method

Given Equations:

Equation 1: 2x + y = 6

Equation 2: 2x − y = −2

Formula Used:

Area of a triangle with base (b) and height (h) = 1/2 × b × h

Step-by-step Calculations:

⇒ Finding x-intercept of 2x + y = 6: Set y = 0 ⇒ 2x = 6 ⇒ x = 3. Point A is (3, 0).

⇒ Finding x-intercept of 2x − y = −2: Set y = 0 ⇒ 2x = −2 ⇒ x = −1. Point C is (−1, 0).

⇒ Solving for intersection point P: Adding (2x + y) and (2x − y) = 6 + (−2) ⇒ 4x = 4 ⇒ x = 1.

⇒ Substituting x = 1 into 2x + y = 6 ⇒ 2(1) + y = 6 ⇒ y = 4. Point P is (1, 4).

⇒ Base of triangle along x-axis = x_A − x_C = 3 − (−1) = 4 units.

⇒ Height of triangle = y-coordinate of P = 4 units.

⇒ Area = 1/2 × 4 × 4 = 8 sq. units.

Therefore, the calculation shows the area of the region is 8 sq. units, which matches Option (2).

∴ The correct answer is 8 sq. units.

Additional Information

Area of Triangle (Coordinate Geometry)

For vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), Area = 1/2 |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|.

Intercept Form of Linear Equation

A line can be represented as x/a + y/b = 1, where 'a' is the x-intercept and 'b' is the y-intercept.

Region Bounded by Axes

If a region is bounded by the y-axis, use the x-coordinate of the intersection as the height and the difference between y-intercepts as the base.

Given:

Expenditure on Education for Sushma = ₹7200

Expenditure on Education for Preeti = 24%

Formula used:

Central Angle = (Expenditure / Total Expenditure) × 360°

Calculation:

Sushma's Total Expenditure = ₹30,000

Sushma's Central Angle for Education = (7200 / 30,000) × 360°

⇒ Sushma's Central Angle for Education = 86.4°

Preeti's Central Angle for Education = (24 / 100) × 360°

⇒ Preeti's Central Angle for Education = 86.4°

Ratio of Central Angles = 86.4° : 86.4° = 1 : 1

∴ The correct answer is option (2) 1:1.

Given:

If a ∶ b = 3 ∶ 7 and b ∶ c = 4 ∶ 9

Formula used:

To find a ∶ b ∶ c, we need to make the values of b in both ratios equal.

Calculation:

a ∶ b = 3 ∶ 7

b ∶ c = 4 ∶ 9

Make the value of b equal in both ratios:

LCM of 7 and 4 = 28

Convert a ∶ b to have b = 28:

3 ∶ 7 = 3×4 ∶ 7×4 = 12 ∶ 28

Convert b ∶ c to have b = 28:

4 ∶ 9 = 4×7 ∶ 9×7 = 28 ∶ 63

Combine to get a ∶ b ∶ c:

12 ∶ 28 ∶ 63

∴ The correct answer is option 3.

Given:

Find the remainder when 179 × 172 × 173 is divided by 17.

Formula used:

Using the property of modular arithmetic:

(a × b) mod m = [(a mod m) × (b mod m)] mod m

Calculation:

179 mod 17 = 179 - (17 × 10) = 179 - 170 = 9

172 mod 17 = 172 - (17 × 10) = 172 - 170 = 2

173 mod 17 = 173 - (17 × 10) = 173 - 170 = 3

⇒ 179 × 172 × 173 mod 17 = (9 × 2 × 3) mod 17

⇒ 54 mod 17 = 54 - (17 × 3) = 54 - 51 = 3

∴ The correct answer is option 3.

Shortcut Trick

Width of the rectangular field = Area ÷ Length = 3600 ÷ 45 = 80 m.

Perimeter = 2 × (Length + Width) = 2 × (45 + 80) = 2 × 125 = 250 m.

∴ The correct answer is 250 m.

Alternate Method

Given:

Area of the rectangle = 3600 m²

Length (L) of the rectangle = 45 m

Formula Used:

1. Area = Length × Width (W)
2. Perimeter = 2 × (Length + Width)

Calculations:

⇒ Area = L × W

⇒ 3600 = 45 × W

⇒ W = 3600 ÷ 45

⇒ W = 80 m

⇒ Perimeter = 2 × (L + W)

⇒ Perimeter = 2 × (45 + 80)

⇒ Perimeter = 2 × 125

⇒ Perimeter = 250 m

Therefore, Option 4 is the correct choice.

∴ The correct answer is 250 m.

Additional Information

Properties of a Rectangle

A rectangle is a quadrilateral with four right angles. Opposite sides are equal and parallel. The diagonals bisect each other and are equal in length.

Important Formulas

1. Diagonal (d) = √(L² + W²)
2. If perimeter is P and length is L, then Width = (P ÷ 2) − L
3. A square is a special case of a rectangle where Length = Width.

Given:

A person wants to buy 10 chairs. The total cost of 10 chairs is ₹4,500. After bargaining, the shopkeeper agrees to decrease the cost of each chair by 20%. Then the person purchased 10% more chairs.

Formula used:

New Cost of Each Chair = Original Cost of Each Chair × (1 - Discount Percentage)

Total Cost = Number of Chairs × New Cost of Each Chair

Calculation:

Original Cost of Each Chair = ₹4500 / 10

⇒ Original Cost of Each Chair = ₹450

New Cost of Each Chair = ₹450 × (1 - 0.20)

⇒ New Cost of Each Chair = ₹450 × 0.80

⇒ New Cost of Each Chair = ₹360

Number of Chairs Purchased = 10 + (10 × 0.10)

⇒ Number of Chairs Purchased = 10 + 1

⇒ Number of Chairs Purchased = 11

Total Cost = 11 × ₹360

⇒ Total Cost = ₹3960

∴ The correct answer is option (3).

Given:

Income and Expenditure for the year 2001: 60 lakhs and 40 lakhs respectively

Income and Expenditure for the year 2002: 40 lakhs and 30 lakhs respectively

Formula used:

Profit = Income - Expenditure

Difference in Profit = Profit in 2001 - Profit in 2002

Calculation:

Profit in 2001 = 60 - 40

⇒ Profit in 2001 = 20 lakhs

Profit in 2002 = 40 - 30

⇒ Profit in 2002 = 10 lakhs

Difference in Profit = 20 - 10

⇒ Difference in Profit = 10 lakhs

∴ The difference of profit between the years 2001 and 2002 is 10 lakhs.

Given:

Production data for company B from 2012 to 2017 and for company C in specific years (2014, 2016, 2017).

Formula used:

Average Production = (Sum of Production for given years) / Number of Years

Difference in production = Average of Company B - Combined Average of specific years for Company A and Company C

Calculation:

Company B (2012-2017):

Total Production = 130 + 80 + 70 + 90 + 180 + 80 = 630 lakhs

Average Production of Company B = 630 / 6

⇒ Average Production of Company B = 105 lakhs

Company A (2012, 2014, 2015) Production:

Company A 2012 = 100 lakhs

Company A 2014 = 160 lakhs

Company A 2015 = 150 lakhs

Total Production of Company A = 100 + 160 + 150 = 410 lakhs

Company C (2014, 2016, 2017) Production:

Company C 2014 = 120 lakhs

Company C 2016 = 110 lakhs

Company C 2017 = 140 lakhs

Total Production of Company C = 120 + 110 + 140 = 370 lakhs

Combined Production = 410 (Company A) + 370 (Company C) = 780 lakhs

Number of Years Considered = 6 years

Combined Average Production = 780 / 6

⇒ Combined Average = 130 lakhs

Difference = 130 - 105

⇒ Difference = 25 lakhs

⇒ Difference in average production of Company B and the combined average of Company A and Company C together = 25 lakhs

∴ The correct difference is 25 lakhs.

Given:

A circle of diameter 26 cm has two equal parallel chords of length 10 cm each.

Formula used:

Let the radius of the circle be R, and the distance of each chord from the center be d₁ and d₂.

Using the perpendicular distance formula from the center to a chord:

$\sqrt{R^2 - (\frac{chord\ length}{2})^2} = distance\ from\ center\ to\ chord$

Calculations:

Radius (R) = $\frac{26}{2}$ = 13 cm

Half of chord length = $\frac{10}{2}$ = 5 cm

Distance from center to each chord (d₁ and d₂):

$\sqrt{13^2 - 5^2}$

⇒ $\sqrt{169 - 25}$

⇒ $\sqrt{144}$

⇒ 12 cm

The distance between the two chords = 2 × 12 = 24 cm

∴ The correct answer is option 2.

Shortcut Trick

Since each salary slab occurs for the same duration (3 months each), the overall average is the simple average of the distinct salary values.

Average = (12000 + 15000 + 21000 + 30000) ÷ 4

Average = 78000 ÷ 4 = 19500

∴ The correct answer is ₹19500.

Alternate Method

Given: Monthly salaries for 12 months in groups of 3 months each.

Formula Used: Average = Total Sum of Salaries ÷ Total Number of Months

⇒ Total salary for first 3 months = 3 × 12000 = ₹36,000

⇒ Total salary for next 3 months = 3 × 15000 = ₹45,000

⇒ Total salary for next 3 months = 3 × 21000 = ₹63,000

⇒ Total salary for last 3 months = 3 × 30000 = ₹90,000

⇒ Sum of all salaries = 36000 + 45000 + 63000 + 90000 = ₹2,34,000

⇒ Average salary = 234000 ÷ 12

⇒ Average salary = ₹19500

∴ The correct answer is ₹19500.

Additional Information

Arithmetic Mean

The simple average of n observations is calculated as (x₁ + x₂ + ... + x_n) ÷ n.

Weighted Average

When values have different weights/frequencies, Average = (Σw_ix_i) ÷ (Σw_i), where w is the weight (frequency).

Average of Groups

If every group has the exact same number of items, the overall average is simply the average of the individual group averages.

Given:

A policeman starts chasing a thief who is 500 m ahead of him. The speed of the thief is 18 km/h, and the speed of the policeman is 36 km/h.

Formula used:

Relative speed = Speed of policeman - Speed of thief

Time = Distance / Relative speed

Calculations:

Speed of thief = 18 km/h = 18 × (1000/3600) m/s = 5 m/s

Speed of policeman = 36 km/h = 36 × (1000/3600) m/s = 10 m/s

Relative speed = 10 m/s - 5 m/s = 5 m/s

Distance = 500 m

⇒ Time = 500 / 5

⇒ Time = 100 seconds

∴ The correct answer is option (1).

Given:

Initial Income (I₁) = ₹100

Initial Expenditure (E₁) = 75% of I₁ = ₹75

Initial Savings (S₁) = I₁ - E₁ = ₹100 - ₹75 = ₹25

New Income (I₂) = I₁ + 25% of I₁ = ₹100 + ₹25 = ₹125

New Expenditure (E₂) = E₁ + 10% of E₁ = ₹75 + ₹7.5 = ₹82.5

Formula used:

Percentage Increase in Savings = $\dfrac{New Savings - Initial Savings}{Initial Savings} \times 100$

Calculation:

New Savings (S₂) = I₂ - E₂ = ₹125 - ₹82.5 = ₹42.5

⇒ Percentage Increase in Savings = $\dfrac{₹42.5 - ₹25}{₹25} \times 100$

⇒ Percentage Increase in Savings = $\dfrac{₹17.5}{₹25} \times 100$

⇒ Percentage Increase in Savings = 70%

∴ The correct answer is option 3.

Given:

A fraction $\dfrac{3}{5}$ is decreased by $\dfrac{2}{5}$. The resulting fraction is then increased by 20%.

Formula used:

New Value = Original Value × (1 + Percentage Change)

Calculation:

Initial Fraction = $\dfrac{3}{5}$

Decreased Fraction: $\dfrac{3}{5} - \dfrac{2}{5} = \dfrac{1}{5}$

Increased by 20%: $\dfrac{1}{5} \times (1 + 0.20) = \dfrac{1}{5} \times 1.20$

⇒ $\dfrac{1}{5} \times 1.20 = \dfrac{1.20}{5} = \dfrac{6}{25}$

Percentage Change = $\dfrac{\dfrac{6}{25} - \dfrac{3}{5}}{\dfrac{3}{5}} \times 100\%$

⇒ $\dfrac{\dfrac{6}{25} - \dfrac{15}{25}}{\dfrac{3}{5}} \times 100\%$

⇒ $\dfrac{-9}{25} \times \dfrac{5}{3} \times 100$ %

⇒ $-60\%$

∴ The correct answer is option 3 i.e. decrease by 60%.

Given:

Principal (P) = ₹5,000

Time for first period (t₁) = 2 years

Rate for first period (r₁) = 10% per annum

Time for second period (t₂) = 3 years

Rate for second period (r₂) = 12% per annum

Formula used:

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

Calculation:

SI₁ = 5000 × $\frac{10 \times 2}{100}$

⇒ SI₁ = 5000 × 0.2

⇒ SI₁ = ₹1000

SI₂ = 5000 × $\frac{12 \times 3}{100}$

⇒ SI₂ = 5000 × 0.36

⇒ SI₂ = ₹1800

Total Interest = SI₁ + SI₂

⇒ Total Interest = 1000 + 1800

⇒ Total Interest = ₹2800

∴ The correct answer is option (1).

Given:

Surface area of cuboid (S) = 108 m²

Length (l) = 6 m

Breadth (b) = 3 m

Formula used:

S = 2(lb + bh + hl)

Where, h = height

Calculation:

108 = 2(6 × 3 + 3 × h + 6 × h)

⇒ 108 = 2(18 + 3h + 6h)

⇒ 108 = 2(18 + 9h)

⇒ 108 = 36 + 18h

⇒ 108 - 36 = 18h

⇒ 72 = 18h

⇒ h = 72 ÷ 18

⇒ h = 4 m

∴ The correct answer is option 2.

The correct answer is 15

Key Points

• 15 censuses had been completed in India as of the year 2011.
• The census in India is conducted every ten years by the Office of the Registrar General and Census Commissioner, under the Ministry of Home Affairs.
• The first census in India was conducted in 1872, but the first complete census was taken in 1881.
• The 2011 Census was the 15^th National Census of the country.
• The census provides critical data on population demographics, economic activity, literacy and education, housing and household amenities, urbanization, fertility and mortality, and many other socio-economic characteristics.

Additional Information

• The Census is one of the most reliable sources of data on various demographic and socio-economic parameters.
• It helps in planning and formulation of policies for the government at all levels.
• The Census of India 2011 was conducted in two phases: the House listing and Housing Census (April to September 2010) and the Population Enumeration (9^th to 28^th February 2011).
• India's census is the largest administrative exercise in the world, covering all individuals residing in the country.
• The next census was scheduled for 2021 but was postponed due to the COVID-19 pandemic.

The correct answer is 1037 females/1000 males

Key Points

• According to the Census of India 2011, the sex ratio in the Union Territory of Puducherry was 1037 females per 1000 males.
• This sex ratio indicates a higher number of females compared to males in Puducherry.
• The sex ratio is an important demographic indicator that reflects the status of women in society and helps in planning and policy-making for gender-related issues.

Additional Information

• The Census of India is conducted every 10 years by the Office of the Registrar General and Census Commissioner, under the Ministry of Home Affairs, Government of India.
• The census collects a wide range of demographic, social, and economic data that is essential for the planning and implementation of various government policies and programs.
• The 2011 Census was the 15^th National Census of the country since 1872 and the 7^th after independence.
• Besides sex ratio, other important metrics collected in the census include population density, literacy rate, and workforce participation rate.

The correct answer is 2 and 3

Key Points

• Statement 2: Article 5 of the Constitution does not pertain to the creation of new states. It deals with the citizenship at the commencement of the Constitution. The power to create new states is vested in Parliament under Article 3.
• Statement 3: The subjects in the Union List are exclusively under the purview of the Union Parliament. State Legislatures cannot enact laws on subjects in the Union List.
• Since both statements 2 and 3 are incorrect, the correct answer is option 3.

Additional Information

• Statement 1: It is correct that the Constitution of India does not use the word 'federation' but describes India as a 'Union of States'.
• Statement 4: Both the Parliament and State Legislatures can indeed pass laws on subjects listed in the Concurrent List, with the central law prevailing in case of conflict.
• The Constitution of India is a comprehensive document that lays down the framework for governance and the distribution of powers between the Union and the States.

The correct answer is Agra Gharana

Key Points

• The Agra Gharana is known for its blend of Khayal and Dhrupad-Dhamar styles.
• This Gharana emphasizes the importance of swara (notes) and laya (tempo) in its compositions.
• It has a rich history and has contributed significantly to Hindustani classical music.
• The compositions from this Gharana often feature intricate and robust patterns.
• Famous exponents of the Agra Gharana include Faiyaz Khan and Vilayat Hussain Khan.

Additional Information

• The Indore Gharana is known for its unique style of Khayal singing and was popularized by Ustad Amir Khan.
• The Gwalior Gharana is one of the oldest Khayal Gharanas and emphasizes the use of simple and straightforward compositions.
• The Patiala Gharana is famous for its elaborate and intricate taans (fast melodic passages).
• Gharanas are schools or styles of music that are passed down through generations, each with its own distinct features and techniques.

The correct answer is Govindacharya

Key Points

• Govindacharya is the author of the famous book 'Sangraha Choodamani', which deals with the current system of Carnatic music.
• 'Sangraha Choodamani' is an important text in the field of Carnatic music, offering a comprehensive overview of its system and theory.
• The book is highly regarded for its detailed classification and explanation of various ragas and musical compositions.

Additional Information

• Carnatic music is a system of music commonly associated with the southern part of India, known for its rich history and complex compositions.
• Theoretical texts like 'Sangraha Choodamani' play a crucial role in preserving and propagating the knowledge of Carnatic music to future generations.
• Govindacharya’s work continues to be a vital resource for students, practitioners, and scholars of Carnatic music.

The correct answer is Chief Justice of India

Key Points

• The digital platform FASTER was launched by the Chief Justice of India.
• FASTER stands for Fast and Secure Transmission of Electronic Records.
• This platform aims to ensure swift and secure transmission of court orders and other judicial documents.
• It enhances the efficiency of the judicial system by reducing delays in communication and implementation of court orders.

Additional Information

• The Supreme Court of India is the highest judicial forum and final court of appeal under the Constitution of India.
• The Chief Justice of India is the head of the judiciary of India and the Supreme Court.
• The Supreme Court consists of the Chief Justice and a maximum of 33 other judges, appointed by the President of India.
• The judiciary plays a crucial role in the interpretation and protection of the Constitution and the rights of individuals.
• Technological advancements like the FASTER platform are part of ongoing efforts to modernize the judicial system and improve access to justice.