The correct answer is Option 2.

Key Points

• The primary issue in the sentence is the placement of the adverb "well" in the phrase "speaks Telugu well."
• Typically, adverbs of manner like "well" should follow the verb they modify.
• In this case, however, the given sentence "speaks Telugu well" is grammatically correct, as the adverb "well" correctly follows the verb "speaks" and the object "Telugu".
• Thus, there is no adverbial usage error in the sentence.

Therefore, the correct answer is Option 3.

Correct Sentence: "Mrs. Arunima speaks Telugu well."

Additional Information

• Option 1: "Mrs. Arunima" – This part of the sentence is grammatically correct and does not contain any errors.
• Option 2: "speaks" – This part of the sentence is grammatically correct and does not contain any errors.
• Option 4: "Telugu well" – This part of the sentence is grammatically correct and does not contain any errors.

The correct answer is Option 2.

Key Points

• The primary issue in the sentence is the use of the article "a" before the term "oasis."
• The correct article to use before a word starting with a vowel sound is "an".
• The correct phrase should be "an oasis," ensuring grammatical correctness.
• Thus, the error is located in Option 2 of the sentence.

Therefore, the correct answer is Option 2.

Correct Sentence: "According to the encyclopaedia, an oasis is an area which is made fertile by a source of freshwater."

Additional Information

• 1) "According to the encyclopaedia," – This part of the sentence is grammatically correct and does not require any changes.
• 3) "a source of freshwater." – This part of the sentence is grammatically correct and does not require any changes.
• 4) "which is made fertile by," – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is Option 3.

Key Points

• The primary issue in the sentence is the use of the verb "have" with the singular subject "He."
• Singular subjects typically require the verb "has."
• The correct phrase should be "He has," ensuring grammatical correctness and clarity.
• Thus, the error is located in part 3 of the sentence.

Therefore, the correct answer is Option 3.

Correct Sentence: "He has workers from Ireland and France in his factory."

Additional Information

• Part 1: "in his factory." – This part of the sentence is grammatically correct and does not require any changes.
• Part 2: "Ireland and France" – This part of the sentence is grammatically correct and does not require any changes.
• Part 4: "workers from" – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is Option 1.

Key Points

• The original sentence "Sarita speaks French best." is not grammatically correct.
• The correct usage should be "Sarita speaks French well."
• Using "well" is appropriate because it correctly modifies the verb "speaks."
• Thus, the error is located in the incorrect use of "best" in the sentence.

Therefore, the correct answer is Option 1.

Correct Sentence: "Sarita speaks French well."

Additional Information

• Option 2: "better" – This would imply a comparison and is not suitable without a comparative context.
• Option 3: "good" – "Good" is an adjective and should not be used to modify a verb.
• Option 4: "worst" – This is incorrect and would convey the opposite meaning.

The correct answer is 'within'.

Key Points

• The preposition "within" indicates being inside or inside the limits of something.
• In this context, "within the family unit" emphasizes the idea that lasting bonds, essential values, and comfort are developed inside the family.
• The other options: "between", "among", and "beyond" do not fit the context as appropriately.

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

Complete Sentence: Family plays a vital role in our lives, serving as a source of love, support, and stability. It is within the family unit that we develop lasting bonds, learn essential values, and find comfort during tough times.

Additional Information

• Between (के बीच): typically used to refer to something in a space separating two points.
• Among (के बीच में): used to indicate being a member or part of a group.
• Beyond (परे): means at or to the further side of something.

The correct answer is Option 4.

Key Points

• The adjective "challenging" describes something that is difficult and tests one's abilities.
• In this context, "challenging times" refers to periods of difficulty or hardship.
• The other options: "initial", "wasteful", and "joyful" do not fit the context as appropriately.

​Therefore, the correct answer is 'Option 4'.

Complete Sentence: Family plays a vital role in our lives, serving as a source of love, support, and stability. It is within the family unit that we develop lasting bonds, learn essential values, and find comfort during challenging times.

Additional Information

• Initial (प्रारंभिक): means occurring at the beginning.
• Wasteful (अपव्ययी): means using or expending something carelessly.
• Joyful (प्रसन्न): means feeling, expressing, or causing great pleasure and happiness.

The correct answer is Option 1.

Key Points

• The verb "offer" means to present or provide something.
• In this context, families "offer guidance, share experiences, and create cherished memories," which means they provide these benefits.
• The other options: "propose", "contribute", and "deliver" do not fit the context as appropriately as "offer".

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

Complete Sentence: Family plays a vital role in our lives, serving as a source of love, support, and stability. It is within the family unit that we develop lasting bonds, learn essential values, and find comfort during challenging times. Families provide a nurturing environment for personal growth and emotional well-being. They offer guidance, share experiences, and create cherished memories.

Additional Information

• Propose (प्रस्तावित करना): means to put forward an idea or plan for consideration.
• Contribute (योगदान देना): means to give something in order to help achieve or provide something.
• Deliver (प्रदान करना): means to bring and hand over something to the proper recipient or address.

The correct answer is Option 3.

Key Points

• The noun "cohesion" means the action or fact of forming a united whole.
• In this context, "the strength and cohesion of a family" emphasizes the unity and togetherness that contribute to individual happiness and societal harmony.
• The other options: "disruption", "intrusion", and "commotion" do not fit the context as appropriately.

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

Complete Sentence: Family plays a vital role in our lives, serving as a source of love, support, and stability. It is within the family unit that we develop lasting bonds, learn essential values, and find comfort during challenging times. Families provide a nurturing environment for personal growth and emotional well-being. They offer guidance, share experiences, and create cherished memories. The strength and cohesion of a family contribute to individual happiness, societal harmony, and the formation of a strong community.

Additional Information

• Disruption (विघटन): means disturbance or problems that interrupt an event, activity, or process.
• Intrusion (अतिक्रमण): means unwelcome or uninvited involvement.
• Commotion (हंगामा): means a state of confused and noisy disturbance.

The correct answer is Option 3.

Key Points

• The noun "foundation" refers to the basis or groundwork of anything.
• In this context, "the foundation of a strong community" emphasizes the fundamental role families play in building a strong and cohesive community.
• The other options: "undermining", "erosion", and "collision" do not fit the context as appropriately.

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

Complete Sentence: Family plays a vital role in our lives, serving as a source of love, support, and stability. It is within the family unit that we develop lasting bonds, learn essential values, and find comfort during challenging times. Families provide a nurturing environment for personal growth and emotional well-being. They offer guidance, share experiences, and create cherished memories. The strength and cohesion of a family contribute to individual happiness, societal harmony, and the foundation of a strong community.

Additional Information

• Undermining (कमजोर करना): means to damage or weaken someone or something gradually.
• Erosion (अपक्षय): means the gradual destruction or diminution of something.
• Collision (टक्कर): means an instance of one moving object or person striking violently against another.

The correct answer is: Option 3.

Key Points

• The word "Erudite" means having or showing great knowledge or learning. (विद्वान)
• Example: His erudite commentary on classical literature impressed everyone at the seminar.
• "Educated" refers to someone who has received a good amount of schooling or training, and is knowledgeable. (शिक्षित)
• Example: She is highly educated, having completed her PhD from a prestigious university.
• Hence, we can infer that the synonym of 'Erudite' is 'Educated'.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Strong (मजबूत): Having great physical power or being mentally resilient.
• Example: She has a strong will and always stands up for what she believes in.
• Humble (विनम्र): Having or showing a modest or low estimate of one's importance.
• Example: Despite his achievements, he remains a humble person.
• Honest (ईमानदार): Being truthful and sincere.
• Example: He is known for being an honest and trustworthy individual.

The correct answer is **Option 2**.

 

**Key Points**

- The primary issue in the sentence is the incorrect verb form "played" after "like".
- The verb "like" should be followed by the gerund form "playing" when indicating an activity one enjoys.
- The correct phrase should be "I like playing cricket after school," ensuring grammatical correctness and clarity.

Therefore, the correct answer is **Option 2**.

 

**Correct Sentence:** *"I like playing cricket after school."*

 

**Additional Information**

- **Option 1: "play"** – This option is incorrect because "like" should be followed by a gerund ("playing"), not the base form of the verb ("play").
- **Option 3: "having to play"** – This option is incorrect as it changes the meaning of the sentence and is not the correct form after "like".
- **Option 4: "played"** – This option is incorrect because it repeats the original error of using the past tense form.

The correct answer is Option 4.

Key Points

• The primary issue in the sentence is the incorrect verb form "helping."
• The verb "help" should be used in its base form to maintain parallel structure with "manage."
• The correct phrase should be "help in reducing," ensuring grammatical correctness and clarity.
• Thus, the error is located in the underlined segment of the sentence.

Therefore, the correct answer is Option 4.

Correct Sentence: "Yoga may manage pain and help in reducing stress."

Additional Information

• Option 1: "helped reduce" – This option uses the past tense "helped," which is not appropriate in this context.
• Option 2: "help reduction for" – This option is grammatically incorrect and does not fit the context of the sentence.
• Option 3: "help reduced" – This option is grammatically incorrect and does not fit the context of the sentence.

The correct answer is Option 2.

Key Points

• The sentence requires the article "a" before the noun phrase "successful raid".
• The phrase "an successful raid" is incorrect because "an" is used before words that start with a vowel sound, and "successful" starts with a consonant sound.
• The correct phrase should be "a successful raid".
• Thus, the error is located in the original segment of the sentence.

Therefore, the correct answer is Option 2.

Correct Sentence: "We have carried out a successful raid on a fraudulent minister."

Additional Information

• Option 1: "successful raid" – This option is incorrect because it omits the necessary article "a".
• Option 3: "these successful raid" – This option is incorrect because "these" is a plural demonstrative adjective used before plural nouns, while "raid" is singular.
• Option 4: "the successful raid" – This option is grammatically correct but changes the meaning slightly by specifying a particular raid, which may not be the intended meaning.

The correct answer is: Option 3.

Key Points

• The word "haughty" means arrogantly superior and disdainful. (अहंकारी)
• Example: She gave him a haughty look and walked away without saying a word.
• "Modest" refers to having or showing a moderate or humble estimate of one's importance. (विनम्र)
• Example: Despite his achievements, he remained modest and never boasted about his success.
• Hence, we can infer that the opposite of 'haughty' is 'modest'.

Therefore, the correct answer is: Option 3.

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 happy to see her friends after a long time.
• Indifferent (उदासीन): Having no particular interest or sympathy; unconcerned.
• Example: He was indifferent to the outcome of the match.
• Proud (गर्वित): Feeling deep pleasure or satisfaction as a result of one's own achievements.
• Example: She was proud of her son's accomplishments.

The correct answer is Option 4.

Key Points

• Homophones are words that sound the same but have different meanings and spellings.
• In the given sentence, "by" is the correct homophone to indicate proximity or location.
• The other options (bi, bye, buy) do not fit the context of the sentence.

Therefore, the correct answer is Option 4.

The correct answer is Option 2.

Key Points

• The sentence implies that after completing the pending assignments, the speaker plans to take a break or enjoy leisure time.
• Option 2, "take a holiday," fits perfectly in this context as it aligns with the idea of relaxing or enjoying time in Goa.
• Other options like "land a meal," "go bankrupt," or "forgive a debt" do not make logical sense in this context.

Therefore, the correct answer is Option 2.

The correct answer is: Option 2.

Key Points

• The word "forbidden" means something that is not allowed or prohibited. (निषिद्ध)
• Example: Entering the restricted area is forbidden without proper authorization.
• "Allowed" refers to something that is permitted or accepted. (अनुमत)
• Example: Pets are allowed in this park.
• Hence, we can infer that the opposite of 'forbidden' is 'allowed'.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Protected (सुरक्षित): Kept safe from harm or injury.
• Example: The wildlife reserve is protected by strict regulations.
• Prevented (रोक दिया गया): Stopped from happening or arising.
• Example: Measures were taken to prevent the spread of the disease.
• Banned (प्रतिबंधित): Officially or legally prohibited.
• Example: Smoking is banned in public places.

The correct answer is: Option 2.

Key Points

• The idiom "Fish out of water" means to feel uncomfortable or out of place in a particular situation. (असहज या अस्थानिक महसूस करना)
• Example: He felt like a fish out of water at the formal dinner party.
• "To be out of place" refers to feeling uncomfortable or not fitting in a particular situation or environment. (असहज महसूस करना)
• Example: She looked out of place in her casual clothes at the black-tie event.

Therefore, the correct answer is: Option 2.

Additional Information

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

• To die soon (जल्दी मरना): To pass away in a short period of time.
• Example: The doctor said he might die soon due to his critical condition.
• No knowledge of marine life (समुद्री जीवन के बारे में कोई ज्ञान नहीं): Lack of information or understanding about sea creatures and marine ecosystems.
• Example: He has no knowledge of marine life, which made the aquarium tour quite enlightening for him.
• Not good at swimming (तैरने में अच्छा नहीं): Lacking skill or proficiency in swimming.
• Example: Despite living near the beach, he is not good at swimming.

The correct answer is: Option 2.

Key Points

• The word "Comendation" is an incorrect spelling of the word "Commendation".
• "Commendation" means praise or approval. (प्रशंसा)
• Example: She received a commendation for her exceptional work on the project.
• The incorrect spelling "Comendation" is missing an "m".
• "Commendation" in Hindi is प्रशंसा.
• Example: उसे परियोजना पर उसके असाधारण कार्य के लिए प्रशंसा मिली।

Therefore, the correct answer is: Option 2.

Additional Information

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

• Reimbursement (प्रतिपूर्ति): The act of paying back money to someone.
• Example: She received reimbursement for her travel expenses.
• Intertwined (आपस में जुड़ा हुआ): Twisted or woven together.
• Example: Their lives became increasingly intertwined over the years.
• Competition (प्रतियोगिता): The activity or condition of striving to gain or win something by defeating others.
• Example: She won the first prize in the swimming competition.

The correct answer is: Option 2.

Key Points

• The word "Profiundly" is incorrectly spelt and should be "Profoundly". (गहरी तरह से)
• Example: He was profoundly affected by the news of the tragedy.
• "Profoundly" means to a great depth, very deeply, or intensely. (गहराई से)
• Example: Her speech was profoundly moving and left a lasting impact on everyone.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Unclean (अस्वच्छ): Not clean; dirty.
• Example: The kitchen was unclean and needed a thorough cleaning.
• Hearted (दिल): Having a specified feeling or attitude, often used in combination (e.g., warm-hearted).
• Example: She is a kind-hearted person who always helps others.
• Clothed (पहनाया हुआ): Wearing clothes.
• Example: The children were warmly clothed for the winter weather.

The correct answer is: Option 2)

Key Points

• The word "Generous" means showing a readiness to give more of something, especially money, than is strictly necessary or expected. (उदार)
• Example: She was generous with her time and helped everyone in the community.
• "Mean" refers to someone who is unwilling to give or share things, especially money; unkind or unfair. (कंजूस)
• Example: He was so mean that he wouldn't even lend his friend a small amount of money.
• Hence, we can infer that the opposite of 'Generous' is 'Mean'.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Needy (जरूरतमंद): Lacking the necessities of life; very poor.
• Example: The charity supports needy families in the local area.
• Clever (चतुर): Quick to understand, learn, and devise or apply ideas; intelligent.
• Example: She was very clever and always got top marks in her exams.
• Considerate (विचारशील): Showing concern for the rights and feelings of others.
• Example: He was considerate towards his neighbors and always helped them out.

The correct answer is Option 2.

Key Points

• The noun "weather" refers to the atmospheric conditions at a particular time and place.
• The sentence is describing the atmospheric conditions for today, so the appropriate word to use is "weather".
• Options 1, 3, and 4 are incorrect in this context.

Therefore, the correct answer is Option 2.

Complete Sentence: "The weather today will be cloudy and humid."

Additional Information

• Option 1: "waiter" is incorrect because a waiter is a person who serves food and drinks in a restaurant.
• Option 3: "wither" is incorrect because wither means to become dry and shriveled.
• Option 4: "whether" is incorrect because whether is a conjunction used to express a doubt or choice between alternatives.

The correct answer is: Option 1.

Key Points

• The word "Injustice" means the lack of fairness or justice; it refers to situations where rights are violated or unfair treatment is meted out. (अन्याय)
• Example: The case was a glaring example of injustice, where the innocent were punished and the guilty went free.
• "Discrimination" refers to the unjust or prejudicial treatment of different categories of people, especially on the grounds of race, age, or gender. (भेदभाव)
• Example: Many organizations are working to eliminate discrimination in the workplace.
• Hence, we can infer that a synonym of 'Injustice' is 'Discrimination'.

Therefore, the correct answer is: Discrimination.

Additional Information

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

• Equality (समानता): The state of being equal, especially in status, rights, and opportunities.
• Example: The organization fights for gender equality in all aspects of society.
• Demand (मांग): An insistent and peremptory request, made as if by right.
• Example: There is a high demand for skilled labor in the tech industry.
• Complacency (आत्मसंतोष): A feeling of smug or uncritical satisfaction with oneself or one's achievements.
• Example: His complacency after winning the first match cost him the championship.

The correct answer is: Option 1.

Key Points

• The idiom "Bells and whistles" means attractive but unnecessary features added to products. (आकर्षक लेकिन अनावश्यक सुविधाएँ जो उत्पादों में जोड़ी जाती हैं)
• Example: The new smartphone comes with all the bells and whistles, but I only need it to make calls and send texts.
• "Attractive but unnecessary features" refers to additional features that are meant to make a product more appealing but are not essential for its basic function. (आकर्षक लेकिन अनावश्यक सुविधाएँ)
• Example: The car has many attractive but unnecessary features like heated seats and a sunroof, which increase its price but not its functionality.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Option 2: An innovative development (एक नवोन्मेषी विकास)
• Example: The company is known for its innovative developments in renewable energy technology.
• Option 3: At a serious disadvantage (एक गंभीर नुकसान में)
• Example: Without proper training, new employees are at a serious disadvantage.
• Option 4: To take on a difficult task (एक कठिन कार्य को लेना)
• Example: She decided to take on the difficult task of reorganizing the entire department.

The correct answer is Option 3.

Key Points

• The phrase "come over" is appropriate in this context as it means to visit someone, which fits the given scenario.
• The other options ("come into", "come through", "come across") do not convey the intended meaning of visiting someone.
• Therefore, no improvement is needed for the underlined part of the sentence.

Therefore, the correct answer is Option 3.

Correct Sentence: "Since my friend was not feeling well, she asked me to come over and take care of her."

Additional Information

• Option 1: "come into" – This means to enter a place, which is not appropriate in this context.
• Option 2: "come through" – This means to succeed in a difficult situation, which is not appropriate in this context.
• Option 4: "come across" – This means to find something by chance, which is not appropriate in this context.

The logic followed here is:

Thus, the code for 'watch' is 'pa'.

Hence, the correct answer is "Option 3".

From the given open Dice:

$ and % is the opposite sides.

^ and # is the opposite sides.

@ and * is the opposite sides.

Hence, the correct answer is "Option 2".$

BODMAS Table: 

Given e×pression: 18 ÷ 9 + 24 × 3 – 16 = ?

After interchanging : ‘+’ ⇔  ‘–’ and ‘×’ ⇔ ‘÷’

Then we get, 18 × 9 − 24 ÷ 3 + 16

? = 18 × 9 − 8 + 16

? = 162 - 8 + 16

? = 178 - 8 = 170

Hence, the correct answer is "Option 2".

The paper after unfolded will be:

Hence, the correct answer is "Option 3".

The logic followed here is:

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: (1^st number)³ = 2^nd number.

Now,

For, 4 : 64

⇒ 4³ = 64

For, 9 : 729

⇒ 9³ = 729

Similarly, for 12 ∶ ?

⇒ 12³ = 1728

Hence, the correct answer is "Option 4".

The logic followed here is:

Hence, the correct answer is "Option 4".

Given Equation: 88 B 3 D 12 A 4 C 6 = ?

BODMAS Rule:

Decoding the given information:

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

⇒ 88 × 3 - 12 ÷ 4 + 6 = ?

⇒ 88 × 3 - 3 + 6 = ?

⇒ 264 - 3 + 6 = ?

⇒ 270 - 3 = 267.

Hence, the correct option is "Option 1".

The logic followed here is:

For, WVSO is related to XXUP 

For, ONKG is related to PPMH

Similarly, for 'VURN'

Hence, the correct answer is "Option 2".

Given: 19 November 2003 was Wednesday.

Now,

2003 to 2010 = 7 Years (5 Ordinary Years and 2 Leap Years).

So, 2 Leap Years have 4 odd days,

And, 5 Ordinary Years have 5 odd days.

Total odd days = 4 + 5 = 9.

9 odd days → 9/7 = 1 week and 2 odd days.

then, 19 November 2010 will be Wednesday + 2 = Friday.

Now, the number of days between 19 November 2010 to 25 March 2011

= 11 (remaining days in November) + 31 (December) + 31 (January) + 28 (February) + 25 (March) = 126 days.

= 126 days → 126/7 = 18 weeks and 0 odd days.

So, 25 March 2011 will be Friday + 0 = Friday.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (1^st number × 2^nd number) + 4 = 3^rd number.

Now,

For, (9, 21, 193)

⇒ (9 × 21) + 4 = 189 + 4 = 193.

For, (12, 15, 184) 

⇒ (12 × 15) + 4 = 180 + 4 = 184.

Similarly, for (8, 17, 140)

⇒ (8 × 17) + 4 = 136 + 4 = 140.

Hence, the correct answer is "Option 2".

Family Chart:

Decoding the Symbols:

Given: M ÷ N – O × P + Q

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

So, M is the sister of Q.

Hence, the correct answer is "Option 4".

The logic followed here is:

Hence, the correct answer is "Option 3".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

The logic followed here is:

Option 1) LNQ 

Option 2) CEH 

Option 3) TVY 

Option 4) PQT

Here, 'PQT' is odd among the given options.

Hence, the correct answer is "Option 4".

The logic followed here is:

Hence, the correct answer is "Option 3".

BODMAS Table: 

Given e×pression: 44 ÷ 78 + 6 - 3 × 19 = ?

After interchanging:  '+' ⇔ '÷' and '-' ⇔ '×'

Then 44 + 78 ÷ 6 × 3 - 19 = ?

? = 44 + 13 × 3 - 19

? = 44 + 39 - 19

? = 83 - 19 = 64

Hence, the correct answer is "Option 2".

Given word: 'MUSICAL'

After arranged in alphabetical order:

After arranged in alphabetical order,

Fourth alphabet from the left end is: L,

Second alphabet from the right end is: S,

Now,

there are 6 letters between L and S.

Hence, the correct answer is "Option 4".

The triangles are:

So, there are '5' triangles in the given figure.

Hence, the correct answer is "Option 3".

Given Statements:

No copper is silver.

All gold is copper.

All aluminium is gold.

The least possible Venn diagram for the given statement is:

Conclusions:

I. No aluminium is silver - True (Because, All aluminium is gold, all gold is copper and no copper is silver, so No aluminium is silver).

II. Some gold is silvers - False (Because, All gold is copper and no copper is silver, so it can not be possible only).

III. All aluminium is copper - True (Because, All aluminium is gold, and all gold is copper, implies that All aluminium is copper).

So, Both conclusions I and III follow.

Hence, the correct answer is "Option 4".

The paper after unfolded will be:

Hence, the correct answer is "Option 4".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

The logic followed here is:

From figure 1 to figure 2 and figure 3 to figure 4:

• Corner letters are shifting their position in clockwise direction.
• And middle letters interchange their position.

From figure 2 to figure 3 and figure 4 to figure 5:

• Top three and middle letter shift their position in anticlockwise direction.
• Added a new letter/ number in Bottom middle position in each figure.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: Synonym Relationship.

Here,

Withdraw : Extract → Withdraw and Extract are synonyms, meaning to take out or remove.

Similarly,

Exploit : Utilise → Exploit and Utilise are synonyms, meaning to make use of something effectively.

Hence, the correct answer is "Option 3".

The logic follows here,

Hence, the correct answer is "Option 2".

Given:

Antony and Julie together can complete the work in 15 days

Julie alone can complete the work in 20 days

Formula used:

Work rate of Antony and Julie together = Work rate of Antony + Work rate of Julie

Work rate = 1 / Time taken to complete the work

Calculation:

Work rate of Antony and Julie together = 1/15

Work rate of Julie alone = 1/20

⇒ 1/15 = Work rate of Antony + 1/20

⇒ Work rate of Antony = 1/15 - 1/20

⇒ Work rate of Antony = (4 - 3) / 60

⇒ Work rate of Antony = 1/60

⇒ Time taken by Antony alone = 1 / (Work rate of Antony)

⇒ Time taken by Antony alone = 60 days

∴ The correct answer is option 1.

Given:

Marked Price (MP) = ₹30

MP is 20% more than Cost Price (CP)

Percentage of expenditure on paper = 20%

Formula used:

MP = CP + 20% of CP

Cost of paper = 20% of CP

Calculation:

30 = CP + 0.2 × CP

⇒ 30 = 1.2 × CP

⇒ CP = 30 / 1.2

⇒ CP = 25

Cost of paper = 20% × 25

⇒ Cost of paper = 0.2 × 25

⇒ Cost of paper = 5

∴ The cost of paper used in a single copy of the book is ₹5.

Given:

If cotA = (5)/(12)

Formula used:

cotA = (adjacent)/(opposite)

secA = (hypotenuse)/(adjacent)

cosecA = (hypotenuse)/(opposite)

Calculation:

For cotA = (5)/(12)

Let opposite = 12k and adjacent = 5k

⇒ hypotenuse = √((12k)² + (5k)²)

⇒ hypotenuse = √(144k² + 25k²)

⇒ hypotenuse = √(169k²)

⇒ hypotenuse = 13k

secA = (hypotenuse)/(adjacent) = (13k)/(5k) = 13/5

cosecA = (hypotenuse)/(opposite) = (13k)/(12k) = 13/12

Given expression: √((secA - cosecA)) / √((secA + cosecA)) - √((17)/(7))

⇒ √((13/5 - 13/12)) / √((13/5 + 13/12)) - √((17)/(7))

⇒ √((156 - 65)/60) / √((156 + 65)/60) - √((17)/(7))

⇒ √((91)/(60)) / √((221)/(60)) - √((17)/(7))

⇒ √((91)/(60) × (60)/(221)) - √((17)/(7))

⇒ √((91)/(221)) - √((17)/(7))

⇒ (√(7×13))/(√(17×13)) - √((17)/(7))

⇒ √(7)/(√(17)) - √((17)/(7))

⇒ √((7)/(17)) - √((17)/(7))

⇒ (√((7)/(17)) - (√((17)/(7))))

Rationalize to get a common base:

⇒ (√((7)/(17)) × √((7)/(7))) - (√((17)/(7)) × √((17)/(17)))

⇒ (√((49)/(119))) - (√((289)/(119)))

⇒ (7)/(√(119)) - (17)/(√(119))

⇒ (7 - 17)/(√(119))

⇒ -10/(√(119))

∴ The correct answer is option (2).

Given:

List price (P) = ₹2,000

First discount = 15%

Second discount = 10%

Formula used:

Net Selling Price (SP) = P × (1 - d₁) × (1 - d₂)

Where, d₁ and d₂ are the successive discounts

Calculation:

SP = 2000 × (1 - 0.15) × (1 - 0.10)

⇒ SP = 2000 × 0.85 × 0.90

⇒ SP = 2000 × 0.765

⇒ SP = 1530

∴ The correct answer is option (3).

Given:

A father is presently 3 times his daughter's age. After 10 years he will be twice as old as her.

Formula used:

Let the daughter's present age be D years.

Father's present age = 3D years

After 10 years:

Daughter's age = D + 10

Father's age = 3D + 10

According to the problem, after 10 years, father will be twice as old as daughter:

3D + 10 = 2(D + 10)

Calculation:

3D + 10 = 2(D + 10)

⇒ 3D + 10 = 2D + 20

⇒ 3D - 2D = 20 - 10

⇒ D = 10

∴ The correct answer is option 3.

Shortcut Trick

For direct proportion, the ratio of Marks to Time remains constant.

Time required for 90 marks = (Time for 70 marks ÷ 70) × 90

⇒ Required Time = (6 ÷ 70) × 90

⇒ Required Time = 540 ÷ 70

⇒ Required Time = 54 ÷ 7 ≈ 7.714 hours

∴ The correct answer is 7.7 hours.

Alternate Method

Direct Proportion

70 Marks Time = 6 Hours

90 Marks Time = ?

Given:

Marks scored in 6 hours = 70

Target marks = 90

Formula Used:

When two quantities are directly proportional, their ratio is constant: M₁ ÷ T₁ = M₂ ÷ T₂

Calculations:

⇒ Let the required practice time be T hours.

⇒ 70 ÷ 6 = 90 ÷ T

⇒ 70 × T = 90 × 6

⇒ 70T = 540

⇒ T = 540 ÷ 70

⇒ T = 54 ÷ 7

⇒ T ≈ 7.714 hours

∴ The correct answer is 7.7 hours.

Additional Information

Direct Proportion

When two quantities increase or decrease together at a constant ratio. The general formula is x₁ ÷ y₁ = x₂ ÷ y₂.

Inverse Proportion

When an increase in one quantity results in a proportional decrease in another quantity. The general formula is x₁ × y₁ = x₂ × y₂.

Compound Ratio

The ratio obtained by multiplying the antecedents and the consequents of two or more ratios. For ratios a:b and c:d, the compound ratio is ac:bd.

Given:

An interval of 2 hours 25 minutes is wrongly estimated by 2 hours 30.5 minutes.

Formula used:

Error Percentage = $\left|\dfrac{\text{True Value} - \text{Estimated Value}}{\text{True Value}}\right| \times 100$

Calculations:

True Value = 2 hours 25 minutes = 2 × 60 + 25 = 145 minutes

Estimated Value = 2 hours 30.5 minutes = 2 × 60 + 30.5 = 150.5 minutes

Error = |145 - 150.5| = 5.5 minutes

Error Percentage = $\left|\dfrac{5.5}{145}\right| \times 100$

⇒ Error Percentage = $\dfrac{5.5}{145} \times 100$

⇒ Error Percentage = $\dfrac{550}{145}$

⇒ Error Percentage ≈ 3.79%

∴ The correct answer is $3 \frac{23}{29}$%.

Given:

A solid sphere of radius 8 cm is melted and then recast into small spherical balls each of diameter 4 cm.

Formula used:

Volume of sphere = (4/3)πr³

Calculation:

Volume of the original sphere = (4/3)π(8)³

⇒ Volume of the original sphere = (4/3)π(512)

⇒ Volume of the original sphere = (2048/3)π

Volume of one small ball = (4/3)π(2)³

⇒ Volume of one small ball = (4/3)π(8)

⇒ Volume of one small ball = (32/3)π

Number of small balls = Volume of the original sphere / Volume of one small ball

⇒ Number of small balls = (2048/3)π / (32/3)π

⇒ Number of small balls = 2048 / 32

⇒ Number of small balls = 64

∴ The correct answer is option (4).

Given:

We are analyzing the graph to find the ratio between companies where production is greater than demand and where demand is greater than production.

Formula used:

Compare the production and demand for each company and count how many have:

• Production greater than demand
• Demand greater than production

Calculation:

Companies with production greater than demand:

• Company 2: Production = 3660, Demand = 3150
• Company 3: Production = 3100, Demand = 2600
• Company 5: Production = 3700, Demand = 2800
• Company 6: Production = 4500, Demand = 3300

Total companies where production > demand = 4

Companies with demand greater than production:

• Company 1: Production = 1450, Demand = 2100
• Company 4: Production = 4200, Demand = 5000

Total companies where demand > production = 2

Ratio:

Ratio of companies with more production than demand to those with more demand than production = 4:2 = 2:1

∴ The required ratio is 2:1.

Given:

If the price of rice is reduced by 24%, it enables Alok to buy 10 kg more rice for ₹2,500.

Formula used:

Let the original price per kg be ₹x.

Reduced price per kg = x - 0.24x = 0.76x

Quantity bought at original price = 2500/x

Quantity bought at reduced price = 2500/0.76x

According to the question:

2500/0.76x - 2500/x = 10

Calculations:

2500/0.76x - 2500/x = 10

⇒ 2500 (1/0.76x - 1/x) = 10

⇒ 2500 (x - 0.76x)/(0.76x²) = 10

⇒ 2500 (0.24x)/(0.76x²) = 10

⇒ 2500 × 0.24/(0.76x) = 10

⇒ 600/0.76x = 10

⇒ 600 = 7.6x

⇒ x = 600/7.6

⇒ x = 78.95

Reduced price per kg = 0.76 × 78.95

⇒ Reduced price per kg = ₹60

∴ The correct answer is option (2).

Given:

The average of the areas of 2 similar triangles is 706.5 m² whose perimeters are in the ratio of 6 ∶ 11.

Formula used:

If the perimeters of two similar triangles are in the ratio a : b, then the ratio of their areas will be a² : b².

Calculation:

Let the areas of the two triangles be A1 and A2.

Given the average area, we have:

(A1 + A2) / 2 = 706.5

⇒ A1 + A2 = 706.5 × 2

⇒ A1 + A2 = 1413

The ratio of their areas will be (6²) : (11²) = 36 : 121.

Let the areas be 36k and 121k where k is a constant.

So,

36k + 121k = 1413

⇒ 157k = 1413

⇒ k = 1413 / 157

⇒ k = 9

Therefore,

A1 = 36 × 9 = 324

A2 = 121 × 9 = 1089

The difference in areas is:

1089 - 324 = 765

20% of the difference in areas:

20% of 765 = 0.20 × 765

⇒ 153

∴ The correct answer is option 1.

Given:

The radius of a sphere is increased by 5%. 

Formula used:

Surface Area of Sphere = 4πr²

Calculation:

Let the original radius be r.

New radius = r + 5% of r = r + 0.05r = 1.05r

Original surface area = 4πr²

New surface area = 4π(1.05r)²

⇒ New surface area = 4π(1.1025r²)

⇒ New surface area = 4πr² × 1.1025

Percentage increase in surface area = (New surface area - Original surface area) / Original surface area × 100

⇒ Percentage increase = (4πr² × 1.1025 - 4πr²) / 4πr² × 100

⇒ Percentage increase = (1.1025 - 1) × 100

⇒ Percentage increase = 0.1025 × 100

⇒ Percentage increase = 10.25%

∴ The correct answer is option 2.

Shortcut Trick

Assume a base average of 80 kg.

Calculate deviations: (67−80), (85−80), (70−80), (90−80), (103−80) → −13, +5, −10, +10, +23.

Sum of deviations = −13 + 5 − 10 + 10 + 23 = +15.

Average deviation = 15 ÷ 5 = +3.

Actual Average weight = Base + Average deviation = 80 + 3 = 83 kg.

∴ The correct answer is 83 kg.

Alternate Method

Given:

Weights of five friends = 67 kg, 85 kg, 70 kg, 90 kg, and 103 kg.

Formula Used:

Average = (Sum of all observations) ÷ (Total number of observations)

Calculations:

⇒ Total Weight = 67 + 85 + 70 + 90 + 103

⇒ Total Weight = 415 kg

⇒ Total Number of friends = 5

⇒ Average weight = 415 ÷ 5

⇒ Average weight = 83 kg

∴ The correct answer is 83 kg.

Additional Information

Sum of Observations

The sum of observations is always equal to the Average × Number of observations.

Property of Deviation

The algebraic sum of the deviations of a set of observations from their arithmetic mean is always zero.

Effect of Constant on Average

If every observation in a data set is increased, decreased, multiplied, or divided by a constant 'k', the average is also changed by the same constant 'k'.

Shortcut Trick

Apply the BODMAS rule directly to the expression.

⇒ 4 × 7 − 3 {28 ÷ 12}

⇒ 28 − 3 × (7/3)

⇒ 28 − 7 = 21

∴ The correct answer is 21.

Alternate Method

Given:

4 × 7 − 3 {7 × 4 ÷ (6 × 2)}

Formula Used:

BODMAS Rule (Brackets, Of, Division, Multiplication, Addition, Subtraction)

Calculations:

⇒ Step 1: Solve the innermost round bracket (6 × 2)

⇒ 4 × 7 − 3 {7 × 4 ÷ 12}

⇒ Step 2: Solve the multiplication inside the curly braces

⇒ 4 × 7 − 3 {28 ÷ 12}

⇒ Step 3: Simplify the division inside the curly braces

⇒ 4 × 7 − 3 {7 / 3}

⇒ Step 4: Perform the multiplication operations outside

⇒ (4 × 7) − (3 × 7 / 3)

⇒ 28 − 7

⇒ Step 5: Perform the final subtraction

⇒ 21

∴ The correct answer is 21.

Additional Information

BODMAS Rule

It determines the correct sequence of mathematical operations to simplify expressions systematically: Brackets ((), {}, []), Of, Division, Multiplication, Addition, and Subtraction.

Order of Brackets

When working with nested brackets, always resolve them from the inside out. Begin with round parenthesis (), proceed to curly braces {}, and conclude with square brackets [].

Left-to-Right Evaluation

Multiplication and Division share the same priority level in the order of operations. They should generally be evaluated from left to right as they appear in the expression.

Given:

City P Shows: A = 11.3, B = 6, C = 18, D = 1, E = 1.5

Formula used:

Average = Total Shows / Number of Categories

Calculations:

Total Shows in City P = 11.3 + 6 + 18 + 1 + 1.5

⇒ Total = 37.8

Number of Categories = 5

⇒ Average = 37.8 / 5

⇒ Average = 7.56

∴ The average number of entertainment shows held in city P is 7.56 hundreds or 756 shows.

Given:

Radius of Circle 1 (r₁) = 16 cm

Radius of Circle 2 (r₂) = 4 cm

Formula used:

PQ = √(d² - (r₁ - r₂)²)

Where, d = r₁ + r₂

Calculations:

d = r₁ + r₂ = 16 + 4 = 20 cm

r₁ - r₂ = 16 - 4 = 12 cm

PQ = √(20² - 12²)

⇒ PQ = √(400 - 144)

⇒ PQ = √256

⇒ PQ = 16 cm

∴ The correct answer is 16cm.

Shortcut Trick

For two successive percentage decreases of a% and b%, the effective percentage decrease is given by the formula: (a + b − (a × b)/100)%.

Given: a = 15% and b = 20%.

Net Decrease = 15 + 20 − (15 × 20) / 100

Net Decrease = 35 − 300 / 100 = 35 − 3 = 32%.

∴ The correct answer is 32%.

Alternate Method

Given:

First year decrease = 15%

Second year decrease = 20%

Calculations:

⇒ Let the initial price of the car be ₹100.

⇒ Price after 1^st year decrease (15%) = 100 − (15% of 100) = 100 − 15 = ₹85.

⇒ Price after 2^nd year decrease (20%) = 85 − (20% of 85).

⇒ 20% of 85 = (20 × 85) / 100 = 1700 / 100 = ₹17.

⇒ Price after 2 years = 85 − 17 = ₹68.

⇒ Total decrease in price = Initial Price − Final Price = 100 − 68 = 32.

⇒ Total percentage decrease = (32 / 100) × 100 = 32%.

∴ The correct answer is 32%.

Additional Information

Successive Percentage Change Formula

For two successive changes of x% and y%, the net change is (x + y + (xy/100))%. Use positive values for increase and negative values for decrease.

Successive Discount Rule

A series of discounts d₁, d₂, d₃... can be calculated using the multiplying factor method: Final Value = Initial Value × (1 − d₁/100) × (1 − d₂/100)...

Percentage Decrease vs. Final Value

If a value is decreased by x%, the remaining value is (100 − x)% of the original value.

Given:

A person borrowed some money at the rate of 8% per annum for the first two years, at the rate of 11% per annum for the next three years, and at the rate of 16% per annum for the period beyond five years. If he pays a total interest of ₹21,400 at the end of nine years, how much money did he borrow (round to the nearest unit)?

Formula used:

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

Where,

P = Principal amount

R = Rate of interest

T = Time period

Calculation:

Let the borrowed amount be P.

Interest for the first 2 years at 8%:

SI₁ = P × 8 × 2 / 100

⇒ SI₁ = 0.16P

Interest for the next 3 years at 11%:

SI₂ = P × 11 × 3 / 100

⇒ SI₂ = 0.33P

Interest for the remaining 4 years at 16%:

SI₃ = P × 16 × 4 / 100

⇒ SI₃ = 0.64P

Total interest paid after 9 years:

SI_total = SI₁ + SI₂ + SI₃

⇒ 21400 = 0.16P + 0.33P + 0.64P

⇒ 21400 = 1.13P

⇒ P = 21400 / 1.13

⇒ P = 18938.0531

⇒ P ≈ ₹18,938

∴ The correct answer is option 2.

Shortcut Trick

Let the Cost Price (CP) be 100%.

As the shopkeeper charges 14% more, Selling Price (SP) = 100% + 14% = 114%.

According to the question, 114% = ₹18,240.

1% = 18,240 ÷ 114 = ₹160.

100% (CP) = 160 × 100 = ₹16,000.

∴ The correct answer is ₹16,000.

Alternate Method

Given:

Selling Price (SP) of the mobile phone = ₹18,240

Profit percentage (markup) = 14%

Formula Used:

Cost Price (CP) = [SP ÷ (100 + Profit %)] × 100

Calculations:

⇒ Cost Price (CP) = [18,240 ÷ (100 + 14)] × 100

⇒ CP = [18,240 ÷ 114] × 100

⇒ CP = 160 × 100

⇒ CP = ₹16,000

∴ The correct answer is ₹16,000.

Additional Information

Profit and Loss Basic Formulas

Profit = Selling Price (SP) − Cost Price (CP). Profit % = (Profit ÷ CP) × 100.

Selling Price for Loss

If there is a loss, SP = CP × [(100 − Loss %) ÷ 100].

Marked Price and Discount

Selling Price = Marked Price (MP) − Discount. Discount is always calculated on the MP.

Cost Price for Loss

CP = [SP × 100] ÷ (100 − Loss %).

Given:

How many numbers between 10 and 65 are divisible by 2, 3, and 4?

Formula used:

To find numbers divisible by 2, 3, and 4, we need to find numbers divisible by LCM(2, 3, 4).

LCM(2, 3, 4) = 12

Calculation:

Numbers between 10 and 65 divisible by 12:

First number: 12 × 1 = 12

Second number: 12 × 2 = 24

Third number: 12 × 3 = 36

Fourth number: 12 × 4 = 48

Fifth number: 12 × 5 = 60

⇒ There are 5 numbers between 10 and 65 that are divisible by 12.

∴ The correct answer is option 1.

Given:

Total tourists = 2,50,000

Russian tourists = 15%

Tourists above 50 years = 10%

Formula used:

Russian tourists = Total tourists × Percentage of Russian tourists

Russian tourists above 50 years = Russian tourists × Percentage of tourists above 50 years

Calculation:

Russian tourists = 2,50,000 × 15%

⇒ Russian tourists = 37,500

Russian tourists above 50 years = 37,500 × 10%

⇒ Russian tourists above 50 years = 3,750

∴ The number of Russian tourists above 50 years is 3,750.

Shortcut Trick

Lead distance of thief = Speed × Time = 8 × (30/60) = 4 km.

Relative speed = Policeman speed − Thief speed = 12 − 8 = 4 km/h.

Time to catch = Lead distance ÷ Relative speed = 4 ÷ 4 = 1 hour.

Time in minutes = 1 × 60 = 60 minutes.

∴ The correct answer is 60 minutes.

Alternate Method

Given: Speed of Policeman = 12 km/h, Speed of Thief = 8 km/h, Start delay = 30 minutes.

Formula Used: Time = Distance ÷ Relative Speed; Distance = Speed × Time.

Policeman (P) Thief (T) Catch (M)

Lead = 4 km

Chase = 8 km Vp = 12 km/h Vt = 8 km/h

⇒ Time lead = 30 minutes = 30/60 hours = 0.5 hours.

⇒ Initial distance (Lead) = Speed of Thief × Time lead = 8 × 0.5 = 4 km.

⇒ Relative speed = (12 − 8) km/h = 4 km/h.

⇒ Time taken by policeman to catch = Initial distance ÷ Relative speed = 4 ÷ 4 = 1 hour.

⇒ 1 hour = 60 minutes.

∴ The correct answer is 60 minutes.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, the relative speed is the difference between their individual speeds: V_rel = V₁ − V₂.

Relative Speed in Opposite Direction

When two objects move towards each other or away from each other in opposite directions, the relative speed is the sum: V_rel = V₁ + V₂.

Unit Conversion

To convert km/h to m/s, multiply the speed by 5/18. To convert m/s to km/h, multiply by 18/5.

Given:

Let C be a circle with center O and AB be a chord of C such that the length of AB is equal to the radius of C. Let D be any point on the major arc of AB. Find ∠AOB and ∠ADB, respectively.

Formula used:

1. The angle subtended by a chord equal to the radius in a circle is 60º.
2. The angle subtended by the same chord at the circumference on the major arc is half of the angle subtended at the center.

Calculation:

Given AB = radius of C

⇒ ∠AOB = 60º

For ∠ADB,

⇒ ∠ADB = 1/2 × ∠AOB

⇒ ∠ADB = 1/2 × 60º

⇒ ∠ADB = 30º

∴ The correct answer is option (4).

Given:

The perimeter of a rectangle is 70 cm and its diagonal is 25 cm.

Formula used:

Perimeter (P) = 2(l + b)

Diagonal (d) = √(l² + b²)

Area (A) = l × b

Calculation:

2(l + b) = 70

⇒ l + b = 35

√(l² + b²) = 25

⇒ l² + b² = 625

Let l + b = 35 and l² + b² = 625

We know (l + b)² = l² + b² + 2lb

⇒ 35² = 625 + 2lb

⇒ 1225 = 625 + 2lb

⇒ 600 = 2lb

⇒ lb = 300

∴ The correct answer is option 3.

Given:

In a triangle ABC, D and E are two points on sides AB and AC, respectively, such that DE is parallel to BC and AD ∶ DB = 3 ∶ 5.

AC = 5.6 cm

Formula used:

Since DE is parallel to BC, triangles ADE and ABC are similar.

Therefore, AD/DB = AE/EC

Given AD ∶ DB = 3 ∶ 5, we can write AD/DB = 3/5

Calculation:

Let AE = x, then EC = AC - AE = 5.6 - x

According to the similarity ratio, AD/DB = AE/EC

⇒ 3/5 = x / (5.6 - x)

⇒ 3(5.6 - x) = 5x

⇒ 16.8 - 3x = 5x

⇒ 16.8 = 8x

⇒ x = 16.8 / 8

⇒ x = 2.1

∴ The correct answer is option 2.

The correct answer is Nicolaus Copernicus.

Key Points

• Nicolaus Copernicus (1473 - 1543) was born in Kingdom of Poland.
• Nicolaus work "De revolutionibus orbium coelestium" (On the Revolutions of the Celestial Spheres), gives the information about heliocentric model.
• it provided information that the Sun in centre of Universe and rotation of Planets around the sun.
• It was published in 1543, the year of his death.

Additional Information

• Immanuel Kant (1724-1804) is widely known for modern philosophy.
• His important work "Critique of Practical Reason," Kant discusses his theory of ethics, including the famous concept of the Categorical Imperative, which is a universal moral law.
• He also made contributions to "Nebular Hypothesis," proposing that solar systems develop from rotating clouds of gas, anticipating later theories of stellar and planetary formation.
• Galileo Galilei (1564 - 1642) was Italain Mathematician, Physicist, and Astronomer
• Galileo is famous for his improvements to the telescope.
• He made contributions to the study of motion and mechanics, the laws of falling bodies.
• Pierre Simon - Laplace (1749 - 1827): was French Mathematician and Astronomer
• He laid the foundations of statistics and probability theory.
• His work in mathematics led to the development of Laplace's equation.
• He also developed the Laplace Nebular Hypothesis independently of Kant.

The correct answer is Jaipur Pink Panthers.

Key Points

• Jaipur Pink Panthers team was formed in 2014.
• It is owned by Bollywood actor Abhishek Bachhann.
• Their home ground is Sawai Maan Singh Stadium Jaipur.
• The team has won Pro Kabaddi league title in 2014.

Additional Information

• Kabaddi is sport originated in India. The hindi meaning "Holding Hands"
• It is played between two teams consisting of 7 players in each team.
• Some important tournaments are: Pro Kabaddi League, Kabaddi world Cup, Asian Games, Southa Asian Games, Kabaddi masters, Federation Cup, Super Kabaddi League.
• The terms related to Kabaddi are: Raid, Defense, Scoring, Duration.

The correct answer is Tarang Sanchar.

Key Points

• Tarang Sanchar, a web portal for information sharing on mobile towers and EMF Emission Compliances, has been launched by the Department of Telecom (DoT), Ministry of Communications, to generate confidence and conviction about the safety and harmlessness of mobile towers, as well as dispelling myths and misconceptions.
• The EMF Portal provides a public interface with a simple map-based search tool for seeing mobile towers in the neighborhood of any location.
• Anyone may request an EMF emission measurement at a site by paying a small cost of Rs. 4000/- online.
• The test will be conducted by the DoT's Local Telecom Enforcement Resource and Monitoring (TERM) filed unit (the requestor may be present if he so wishes), and test reports will be supplied.

Additional Information

• National Optical Fibre Network (NOFN): An initiative aimed at connecting 250,000-gram panchayats with optical fiber to improve broadband access in rural India.
• BharatNet: The upgraded version of NOFN, focusing on providing high-speed internet connectivity to rural and remote areas through a robust optical fiber infrastructure.
• Bharat Sanchar Nigam Limited (BSNL): A state-owned telecommunications company in India that plays a crucial role in providing telecom services, including broadband, across urban and rural areas.

The correct answer is 3 min.

Key Points

• In freestyle wrestling, a single round lasts for 3 minutes, with a 30-second break between the first and second periods.
• Wrestlers typically compete in two periods of 3 minutes each in international competitions.
• Rules and Scoring: Wrestlers can score points through various techniques, including takedowns, reversals, and near falls. Matches are won by accumulating points or pinning the opponent.
• Weight Classes: Freestyle wrestling has multiple weight classes to ensure fair competition, allowing wrestlers to compete against others of similar size and weight.

Additional Information

• Freestyle wrestling is a style of competitive grappling where wrestlers can use a variety of holds, throws, and techniques to gain control over their opponent.
• Unlike Greco-Roman wrestling, athletes in freestyle can attack their opponent's legs and use both upper and lower body techniques.

The correct answer is Methanamine.

Key Points

• Methylamine (CH₃NH₂) is a simple amine, which is a derivative of ammonia (NH₃) where one hydrogen atom is replaced by a methyl group (CH₃).
• Methylamine is a colorless gas at room temperature with a strong, fishy odor.
• It is highly soluble in water due to its ability to form hydrogen bonds.
• Methylamine is used in the production of various chemicals, including pharmaceuticals, pesticides, and surfactants. It is also involved in the synthesis of other amines and is used in organic chemistry as a reagent.
• As an amine, methylamine can act as a base and can participate in nucleophilic substitution reactions, making it an important building block in organic synthesis.
• Methylamine is flammable and can be toxic if inhaled or ingested.

Additional Information

The correct answer is Cuba.

Key Points

• In 2023, Praveen Chithravel participated in the ‘Prueba de Confrontacion’ athletics meet in Cuba, where he excelled in the men’s triple jump event.
• The ‘Prueba de Confrontacion’ is an athletics competition that brings together athletes from various countries to compete in multiple track and field events.

Additional Information

The correct answer is Turgor pressure.

Key Points

• Enlargement and extension growth of cells is primarily caused by cell turgor pressure and cell wall expansion.
• In plants, this growth is driven by water uptake, which increases turgor pressure within the cells, leading to expansion.
• Additionally, the synthesis of new cell wall materials allows for cell elongation.
• Other factors, such as hormonal regulation (e.g., auxins), also play a role in promoting cell growth and elongation.

Additional Information

• Imbibition
• It is the process by which a substance (usually a solid, like seeds or plant tissues) absorbs water and swells.
• This occurs due to the affinity of water molecules for the polar surfaces of the solid. In seeds, imbibition triggers metabolic activities, leading to germination.
• Example: When dry seeds are placed in water, they absorb water, swell, and become turgid, preparing for germination.
• Pressure Potential
• Pressure potential is the physical pressure exerted by the fluid (usually water) within the cell against the cell wall.
• In plant cells, when water enters the cell through osmosis, it creates turgor pressure that pushes the plasma membrane against the cell wall, contributing to the overall water potential.
• Pressure potential is essential for maintaining cell structure and rigidity, allowing plants to stand upright and grow.
• Osmotic Pressure
• It is the pressure required to prevent the flow of water across a semipermeable membrane due to osmotic potential (the tendency of water to move into a solution).
• It results from differences in solute concentration on either side of a membrane. Water moves from an area of lower solute concentration (higher water potential) to an area of higher solute concentration (lower water potential).
• It is crucial for processes like nutrient uptake, cell hydration, and overall water balance in cells and organisms.

The correct answer is Article 30.

Key Points

• Article 30 specifically states that all minorities, whether based on religion or language, have the right to establish and administer educational institutions of their choice.
• The article not only grants the right to establish educational institutions but also ensures that minorities can administer these institutions according to their own management and governance structures.
• Article 30 serves as a safeguard against any discriminatory policies that might hinder the establishment or functioning of educational institutions by minorities.
• The Supreme Court of India has elaborated on the scope of Article 30 in various judgments, affirming the right of minorities to manage their institutions without undue interference from the state.

Additional Information

The correct answer is Nagaland.

Key Points

• According to the Census of India 2011, Nagaland experienced the lowest population -0.58% growth rate among Indian states.
• Nagaland is the only state in India that has recorded a Negative population growth as per the 2011 census.
• It shows that Nagaland recorded Negative Growth in Population Minus 0.47% Decadal Population Growth.
• As per the census 2001, 19,88,602 (total population) now that has declined to 19,80,602 (census 2011).
• It is bordered by the state of Assam to the West, Manipur to the South, Arunachal Pradesh to the North, and the Sagaing Region of Myanmar to the East. Kohima is the capital of Nagaland state.

Additional Information

• The Population growth rate of Jharkhand was 22.42% over the decade 2001-2011.
• The Population growth rate of Punjab was 13.89% over the decade 2001-2011.
• The Population growth rate of Uttar Pradesh was 20.09% over the decade 2001-2011.

The correct answer is Both (a) and (b).

Key Points

• The market attains equilibrium when the market supply and market demand of a commodity become equal.
• The term supply refers to how much of a certain product, item, commodity, or service suppliers are willing to make available at a particular price
• Demand refers to how much of that product, item, commodity, or service consumers are willing and able to purchase at a particular price
• Supply and demand are economic forces of the free market that control what suppliers are willing to produce and what consumers are willing and able to purchase.

Additional Information

• If the market price is above the equilibrium value, there is an excess supply in the market (a surplus), which means there is more supply than demand.
• If the market price is below the equilibrium value, then there is an excess in demand (supply shortage).

The correct answer is 1926.

Key Points

• This School was founded by Vishnu Narayan Bhatkhande in Lucknow.
• Named after Rai Umanath Bali who was known as Marris.
• It became a University in 2000 and was renamed as Bhatkhande Music Institute University.
• This institute has been a significant center for Hindustani Classical music.

Additional Information

• Kalakshetra Foundation (Chennai) was founded by Rukmini Devi Arundale in 1936.
• Sangeet Natak Akademi (New Delhi) was founded in 1952.
• Swarnabhoomi Academy of Music (Chennai) was founded in 2010.
• Prayaag Sangeet Samiti(Allahabad) was founded in 1926.
• Rabindra Bharti University(Kolkata) was founded in 1962.
• Bhartiya Vidya Bhavan(Mumbai) was founded by K.M. Munshi in 1938.

The correct answer is Windows Operating System.

Key Points

• Windows operating system is owned by Microsoft.
• The first operating system Windows 1.0 was released on November 20, 1985.
• The latest operating system windows 11 was launched in 2021.
• Other examples of system software are Device Drivers, Utility programs, NTFS, FAT32, Hyper-V etc.

Additional Information

• Adobe Photoshop is a powerful and widely used editing software. It was first released in 1990.
• Google Chrome was released on September 2, 2008. Initially released only on Microsoft Windows.
• Chrome is based on the open-source project Chromium and it uses the V8 JavaScript engine.
• Microsoft Word was first released in 1983 under the name Multi-Tool Word.
• The main types of Software are System software, Application Software, Programming Software, Driver Software, Firmware, Utility software.