⇒ H = 2R

Volume of first hemisphere = (2/3)π(6)³ = 144π

Volume of second hemisphere = (2/3)π(8)³ = 341.33π

Total volume = 144π + 341.33π = 485.33π

(2/3)πR³ = 485.33π ⇒ R³ = (3 × 485.33) ÷ 2 = 728

R = ∛728 ≈ 9 cm

Volume of pyramid = 1/3 × Base area × Height

Half of base side = 12 ÷ 2 = 6 cm

Using right triangle:

Height2 = Slant height2 − (half base)2

⇒ Height2 = 102 − 62

⇒ Height2 = 100 − 36 = 64

⇒ Height = 8 cm

Base area = 12 × 12 = 144 cm2

Volume = 1/3 × 144 × 8

⇒ Volume = 384 cm3

∴ The volume of the pyramid is 384 cm3.

Area of circle ∝ (radius)2

Ratio of areas = (1)2 : (√2)2

⇒ Ratio of areas = 1 : 2

Let area of smaller tyre = 1 part = 100

⇒ Area of larger tyre = 2 parts = 2 × 100

⇒ Area of larger tyre = 200 cm2

∴ The area of the larger tyre is 200 cm2.

Formula used:

∠BIC = 90° + 1/2 ∠BAC

125 = 90 + 1/2 ∠BAC

⇒ 1/2 ∠BAC = 125 − 90

⇒ 1/2 ∠BAC = 35

⇒ ∠BAC = 35 × 2

⇒ ∠BAC = 70°

∴ The value of ∠BAC is 70°.

Consider △ABC and △CDA

AB ∥ CD

⇒ ∠BAC = ∠ACD (alternate interior angles)

AC = AC (common side)

AB = CD (given)

⇒ △ABC ≅ △CDA (by SAS)

∴ Triangles ABC and CDA are congruent.

Distance of DE from A = 2/3 of height of ΔABC

⇒ Side ratio = 2/3

⇒ Area(ΔADE) : Area(ΔABC) = (2/3)2 = 4/9

⇒ Area(DECB) : Area(ΔABC) = 1 − 4/9 = 5/9

⇒ Area(ΔADE) : Area(DECB) = (4/9) : (5/9)

⇒ 4 : 5

∴ Required ratio = 4 : 5

√[ d2 − (r₁ + r₂)2 ]

⇒ r₁ + r₂ = 9 + 5 = 14

⇒ d2 − (r₁ + r₂)2

⇒ 172 − 142

⇒ 289 − 196

⇒ 93

⇒ Length of internal common tangent = √93 cm

√[ d2 − (r1 + r2)2 ]

⇒ r1 + r2 = 7 + 3 = 10

⇒ d2 − (r1 + r2)2

⇒ 202 − 102

⇒ 400 − 100

⇒ 300

⇒ Length of transverse common tangent = √300 

∴ The required length is √300 cm.

⇒ 9 cm > 7 cm

⇒ Distance of 9 cm chord = 4 cm

⇒ Shorter chord (7 cm) will be farther than 4 cm from center

∴ The distance of the 7 cm chord from the center is more than 4 cm.

Side opposite angle = 2 × R × sin(angle)

⇒ Required side = 2 × r × sin120°

⇒ sin120° = √3 / 2

⇒ Required side = 2 × r × (√3 / 2)

⇒ Required side =  r√3

∴ The length of the side opposite the 120° angle is  r√3.

LCM of 8 and 16 = 16

⇒ \\(\\frac{1}{8}=\\frac{2}{16}\\)

⇒ \\(\\frac{2}{16}+\\frac{1}{16}=\\frac{3}{16}\\)

⇒ \\(\\frac{3}{16}=0.1875\\)

∴ The required decimal value is 0.1875.

The correct answer is: Stubborn. The word \"Intransigent\" refers to a person who is unwilling or refusing to change one's views or to agree about something. The meanings of the other words are: Willing: Ready to do something; Compliant: Yielding to others; Submissive: Ready to conform to authority.

The correct answer is: In a state of depression or inactivity. Meaning: The idiom \"in the doldrums\" refers to a state of stagnation, low spirits, or lack of progress, originating from the nautical term for calm equatorial waters where ships often became stranded.

The correct answer is: Hallucinogenic. Meaning: Relating to or denoting drugs that cause hallucinations. The word is derived from \"hallucinogen\" + the suffix \"-ic\".

The correct answer is: Apostate. It refers to a person who renounces a religious or political belief. The meanings of the rest of the words are: Renegade: A person who deserts a cause; Atheist: A person who does not believe in God; Heretic: A person with beliefs contrary to orthodox doctrine.

The correct answer is: Schism. It refers to a formal split within a religious organization. The meanings of the rest of the words are: Sedition: Inciting rebellion against authority; Heresy: Belief contrary to orthodox doctrine; Apostasy: Renunciation of a belief.

The correct answer is: A. The current was unusually strong near the bridge.. Meaning: In the original sentence, \"current\" means \"present\" or \"most recent.\" In option A, \"current\" refers to a body of water or air moving in a definite direction. Options B, C, and D use \"current\" with the same meaning as the original sentence (present/contemporary).

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The tone of the author is best captured as Analytical, as the passage involves a detailed examination of the options provided.
\n\t
• Option 1 (Dogmatic) implies a rigid or authoritative tone, which is not evident in the passage.
\n\t
• Option 2 (Reverent) suggests a tone of deep respect, which does not align with the analytical evaluation of the options.
\n\t
• Option 4 (Indifferent) reflects a lack of interest or concern, which is not consistent with the passage's tone.
\n

Additional Information

\n\t
• An analytical tone is characterized by an objective and detailed examination of information or arguments.
\n\t
• In this context, the author evaluates the options provided to determine the correct tone for the passage.
\n\t
• This careful and reasoned approach aligns with the definition of an analytical tone.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The sentence "Smartness devoid of rigor often culminates in superficiality..." highlights the limitation of relying solely on smart work.
\n\t
• It emphasizes that while smart work is beneficial, it needs to be complemented by rigor and thoroughness to avoid superficial outcomes.
\n\t
• This contrasts with other sentences that focus on different aspects of work without directly addressing this limitation.
\n

Additional Information

\n\t
• Option 1: Focuses on the historical valorization of hard work, which is a separate concept.
\n\t
• Option 2: Describes transcending repetitive efforts without directly addressing the limitation of smart work.
\n\t
• Option 4: Discusses the attributes of a sagacious worker but does not pinpoint the drawback of smart work alone.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• From a philosophical standpoint, hard work and smart work are not inherently opposed to one another but should function in harmony to yield sustainable and effective results.
\n\t
• The argument emphasizes the balance between the two approaches rather than favoring one over the other.
\n\t
• While hard work provides consistency and effort, smart work enhances efficiency by leveraging tools, strategies, and innovation.
\n

Additional Information

\n\t
• Hard Work: Refers to putting in consistent effort and dedication over time to achieve goals.
\n\t
• Smart Work: Involves using innovative techniques, tools, and strategies to achieve goals more efficiently.
\n\t
• Neither approach is superior on its own; combining both leads to sustainable success.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The phrase "minimize entropy in labor" implies reducing randomness and inefficiency in effort.
\n\t
• Entropy, in this context, refers to disorganization or disorder in work processes.
\n\t
• Smart work involves creating streamlined, efficient workflows to achieve maximum productivity with minimal wasted effort.
\n

Additional Information

\n\t
• Option 1: "Reduce physical strain through technology" – While technology can reduce physical strain, it doesn't directly address inefficiency in effort.
\n\t
• Option 3: "Avoid structured systems of work" – This is the opposite of minimizing entropy, as structured systems reduce disorder.
\n\t
• Option 4: "Increase workload to achieve results faster" – Increasing workload doesn't necessarily minimize inefficiency and randomness.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The metaphor "Treadmill" is often used to describe unidirectional exertion, symbolizing repetitive motion with no change in direction or outcome.
\n\t
• It conveys the idea of continuous effort without significant progress or variation.
\n\t
• Other options like "Algorithmic precision" or "Social capital" do not align with the concept of unidirectional exertion.
\n\t
• Thus, the correct metaphor is "Treadmill," making Option 1 the right choice.
\n

Additional Information

\n\t
• Option 2: Algorithmic precision – This refers to accuracy and systematic execution, not unidirectional exertion.
\n\t
• Option 3: Crucible of challenges – This refers to a severe test or trial, which is unrelated to the concept of unidirectional exertion.
\n\t
• Option 4: Social capital – This relates to the networks and relationships that enable society to function effectively, not unidirectional exertion.
\n\t
• Treadmill aptly describes the repetitive and unidirectional nature of exertion, which is why it is the correct answer.
\n

वाक्य में व्यंजन से शुरू होने वाले शब्द: Italy is a beautiful village and China is a big building

इस प्रकार, 5 शब्द हैं जो व्यंजन से शुरू होते हैं। 

इस प्रकार, विकल्प 4 दिए गए पते के ठीक समान है। 

I: A < O → असत्य (चूँकि, A ≤ T < D ≥ O है, A और O के बीच कोई सीधा संबंध नहीं है)
\nII: C < G → सत्य (C= A ≤ T < D ≤ G, यह C < G देता है)

इस प्रकार, केवल निष्कर्ष II अनुसरण करता है।

तर्क: a # b = a ÷ b

1. 10 # 5 = 5 ⇒ 10 ÷ 5 ≠ 2

I. जीन संपादन तकनीकें संभावित रूप से आनुवंशिक विकारों को ठीक कर सकती हैं। - निहित है (यह कथन स्पष्ट रूप से इंगित करता है कि इन प्रौद्योगिकियों में आनुवंशिक विकारों को ठीक करने की अपार क्षमता है। यदि यह सच नहीं होता, तो कथन गलत हो जाता)

II. नैतिक चिंताएँ जीन संपादन तकनीकों के विकास का एक स्वाभाविक परिणाम हैं। - निहित है (कथन का तात्पर्य है कि उन्नति से नैतिक चिंताएं बढ़ती हैं। इसके मान्य होने के लिए, हमें यह मानना ​​होगा कि ऐसी तकनीकी प्रगति से नैतिक मुद्दे सामने आते हैं)

III. आनुवंशिक विकारों को ठीक करने के लिए जीन संपादन की क्षमता नैतिक चिंताओं से अधिक है। - निहित नहीं है (कथन यह तुलना नहीं करता है कि कौन सा अधिक है। यह केवल संभावित और चिंताओं दोनों का उल्लेख करता है — कोई निर्णय नहीं लिया गया है)

इसलिए, केवल I और II निहित हैं।

I. बैंक सुरक्षा में सुधार करना चाहता है। - सत्य (क्योंकि बायोमेट्रिक लॉगिन सिस्टम आमतौर पर सुरक्षा बढ़ाने और धोखाधड़ी को कम करने के लिए पेश किए जाते हैं। इसलिए यह निष्कर्ष निकालना उचित है कि बैंक का इरादा सुरक्षा में सुधार करना है)।
\n
\nII. ग्राहकों को बायोमेट्रिक आईडी ले जानी चाहिए। - असत्य (क्योंकि बायोमेट्रिक लॉगिन आमतौर पर उंगलियों के निशान, चेहरे की पहचान आदि का उपयोग करता है - इसके लिए ग्राहकों को अलग से बायोमेट्रिक आईडी ले जाने की आवश्यकता नहीं होती है)।

इसलिए, केवल निष्कर्ष I अनुसरण करता है।

यहाँ अनुसरित तर्क निम्न है: अक्षरों को उनके विपरीत अक्षरों के रूप में कूटबद्ध किया गया है।

निष्कर्ष:

I. कुछ जानवर जंगली हैं। - असत्य (क्योंकि, जानवरों और जंगली के बीच कोई निश्चित संबंध नहीं दिया गया है, इसलिए यह संभव हो सकता है)।

II. सभी जंगली जानवर हैं। - असत्य (क्योंकि, जानवरों और जंगली के बीच कोई निश्चित संबंध नहीं दिया गया है, इसलिए यह संभव हो सकता है)

इसलिए, न तो I और न ही II अनुसरण करता है। 

1. AIR → QUARRELSOME → नहीं बनाया जा सकता है क्योंकि यहाँ 'I' लुप्त है।

छठा पद = a × r^(6-1)

48 = 1.5 × r⁵

r = (48 ÷ 1.5)^1/5 = 32^1/5 = 2.0

मनमोहन सिंह को छोड़कर सभी विकल्प भारत के स्वतंत्रता सेनानी हैं।

P, R की माता है।

PLANE को 74851 के रूप में कूटबद्ध किया गया है।

DOG को 392 के रूप में कूटबद्ध किया गया है।

इसी प्रकार,

√144 = 144^1/2 = 12

³√27 = 27^1/3 = 3

√144 + ³√27 = 12 + 3 = 15

तर्क: a # b = ab

⇒ कुल बिल = (5 × ₹8) + (3 × ₹25)

⇒ कुल बिल = ₹40 + ₹75

⇒ कुल बिल = ₹115

स्पष्ट रूप से, P, R के पिता हैं।

2. 10 + 2 - 4 × 1 = 8

चिह्नों को उनके अर्थ से प्रतिस्थापित करने के बाद, हमें मिलता है:

⇒ 10 ÷ 2 + 4 - 1 = 8

⇒ 5 + 4 - 1 = 8

⇒ 9 - 1 = 8

⇒ 8 = 8

⇒ 25 ÷ 5 + 3 × 2 - 4 = ?

⇒ 5 + 3 × 2 - 4 = ?

⇒ 5 + 6 - 4 = ?

⇒ 11 - 4 = ?

⇒ 7 = ?

चिह्नों को उनके अर्थों से प्रतिस्थापित करने के बाद, हमें मिलता है:

= 5 ^ 2 - 3 × 1   =  52 - 3 × 1  = 25 - 3 × 1

= 25 - 3  = 22

⇒ योग = 11 + 40

⇒ योग = 51

⇒ परिणाम = 51 × 5

⇒ परिणाम = 255

सही उत्तर है विकल्प 1: A → 3, B → 4, C → 1, D → 2।

मुख्य बिंदु

\n\t
• गुर्जर-प्रतिहार: इस राजवंश ने मुख्य रूप से वर्तमान गुजरात और राजस्थान के क्षेत्रों पर शासन किया, जो उनके शासनकाल के दौरान व्यापार और संस्कृति के महत्वपूर्ण केंद्र थे।
\n\t
• राष्ट्रकूट: उन्होंने पश्चिमी दक्कन क्षेत्र पर प्रभुत्व स्थापित किया, जिसमें महाराष्ट्र और कर्नाटक के कुछ हिस्से शामिल थे। राष्ट्रकूट कला और वास्तुकला में अपने योगदान के लिए जाने जाते थे, विशेष रूप से एलोरा में रॉक-कट मंदिर।
\n\t
• पाल: पाल राजवंश ने बंगाल और बिहार के कुछ हिस्सों पर शासन किया। वे बौद्ध धर्म के संरक्षक थे और उन्होंने दक्षिण पूर्व एशिया में धर्म के प्रसार में बहुत योगदान दिया।
\n\t
• चोल: चोल राजवंश तमिलनाडु में केंद्रित था, जो अपने समुद्री व्यापार और नौसैनिक प्रभुत्व के लिए जाना जाता था। वे अपने मंदिर वास्तुकला और सांस्कृतिक योगदान के लिए प्रसिद्ध थे, जिसमें बृहदेश्वर मंदिर भी शामिल है।
\n\t
• उपरोक्त मिलान इन राजवंशों के भौगोलिक प्रभुत्व के संबंध में ऐतिहासिक और पुरातात्विक साक्ष्यों के अनुरूप हैं।
\n

अतिरिक्त जानकारी

\n\t
• गुर्जर-प्रतिहार:\n\t
  \n\t\t
  • गुर्जर-प्रतिहार 8वीं शताब्दी के दौरान भारत में अरब आक्रमणों का विरोध करने में सहायक थे।
  \n\t\t
  • उनका साम्राज्य उत्तरी भारत में फैला हुआ था, लेकिन गुजरात और राजस्थान उनके मूल क्षेत्र थे।
  \n\t\t
  • वे हिंदू मंदिर वास्तुकला के संरक्षण के लिए जाने जाते थे।
  \n\t
  \n\t
\n\t
• राष्ट्रकूट:\n\t
  \n\t\t
  • राष्ट्रकूट मध्यकाल के दौरान प्रायद्वीपीय भारत में सबसे शक्तिशाली राजवंशों में से एक के रूप में उभरे।
  \n\t\t
  • उनका शासन एलोरा में कैलाशनाथ मंदिर के निर्माण द्वारा चिह्नित है, जो यूनेस्को की विश्व धरोहर स्थल है।
  \n\t\t
  • वे कन्नड़ और संस्कृत में साहित्य में अपने योगदान के लिए जाने जाते थे।
  \n\t
  \n\t
\n\t
• पाल:\n\t
  \n\t\t
  • पालों ने बंगाल और बिहार पर शासन किया, और उनका साम्राज्य 8वीं और 12वीं शताब्दी ईस्वी के बीच फला-फूला।
  \n\t\t
  • वे महायान बौद्ध धर्म के कट्टर समर्थक थे और उन्होंने नालंदा और विक्रमशिला सहित कई मठों और विश्वविद्यालयों की स्थापना की।
  \n\t\t
  • पाल कला और वास्तुकला ने भारत से परे क्षेत्रों को प्रभावित किया, विशेष रूप से तिब्बत और दक्षिण पूर्व एशिया में।
  \n\t
  \n\t
\n\t
• चोल:\n\t
  \n\t\t
  • चोल अपनी प्रशासनिक दक्षता और नौसैनिक शक्ति के लिए जाने जाते थे, जिसने दक्षिण पूर्व एशिया में उनके विदेशी अभियानों को सुविधाजनक बनाया।
  \n\t\t
  • उनके शासनकाल में बृहदेश्वर मंदिर जैसे स्मारकीय मंदिरों का निर्माण हुआ, जो यूनेस्को की विश्व धरोहर स्थल है।
  \n\t\t
  • उन्होंने तमिल साहित्य और संस्कृति के विकास को बढ़ावा दिया, जिससे क्षेत्र पर स्थायी प्रभाव पड़ा।
  \n\t
  \n\t
\n

सही उत्तर ग्लासगो है।

मुख्य बिंदु

\n\t
• ग्लासगो लागत संबंधी चिंताओं और लॉजिस्टिक मुद्दों के कारण ऑस्ट्रेलिया के मेजबानी से हटने के बाद 2026 राष्ट्रमंडल खेलों की मेजबानी करने के लिए तैयार है।
\n\t
• राष्ट्रमंडल खेल महासंघ (सीजीएफ) ने ग्लासगो को नए मेजबान के रूप में घोषित किया क्योंकि उसके पास 2014 राष्ट्रमंडल खेलों सहित प्रमुख अंतरराष्ट्रीय खेल आयोजनों की मेजबानी करने का पूर्व अनुभव है।
\n\t
• ग्लासगो के पास एक अच्छी तरह से विकसित बुनियादी ढांचा है, जिसमें खेल सुविधाएं और परिवहन नेटवर्क शामिल हैं, जो इस परिमाण के आयोजन की मेजबानी के लिए उपयुक्त हैं।
\n\t
• शहर से उम्मीद है कि वह अतिरिक्त व्यय को कम करने के लिए एमिरेट्स एरिना और हैम्पडेन पार्क जैसे अपने मौजूदा स्थानों का लाभ उठाएगा।
\n\t
• ग्लासगो को खेलों का आवंटन करने का निर्णय सीजीएफ के भविष्य के मेजबान शहरों के लिए स्थिरता और वित्तीय व्यवहार्यता सुनिश्चित करने के प्रयासों के अनुरूप है।
\n

अतिरिक्त जानकारी

\n\t
• बर्मिंघम:\n\n\t
  \n\t\t
  • बर्मिंघम ने 2022 राष्ट्रमंडल खेलों की मेजबानी की, जिसमें 19 खेल शामिल थे और 72 देशों और क्षेत्रों के प्रतिभागियों ने भाग लिया।
  \n\t\t
  • इस कार्यक्रम को अपनी समावेशिता के लिए बहुत सराहा गया, क्योंकि यह पुरुषों की तुलना में महिलाओं के लिए अधिक पदक कार्यक्रमों को प्रदर्शित करने वाला पहला राष्ट्रमंडल खेल बन गया।
  \n\t\t
  • शहर की सुविधाओं, जैसे कि अलेक्जेंडर स्टेडियम, को कार्यक्रम की मेजबानी के लिए महत्वपूर्ण रूप से उन्नत किया गया।
  \n\t
  \n\t
\n\t
• विक्टोरिया:\n\t
  \n\t\t
  • ऑस्ट्रेलिया का एक राज्य विक्टोरिया को शुरू में 2026 राष्ट्रमंडल खेलों की मेजबानी करनी थी, लेकिन 2023 में बढ़ते खर्चों के कारण वापस ले लिया गया जो इसकी बजटीय अपेक्षाओं से अधिक हो गया था।
  \n\t\t
  • वापस लेने के निर्णय ने इस तरह के बड़े पैमाने पर अंतरराष्ट्रीय कार्यक्रमों की मेजबानी से जुड़ी वित्तीय चुनौतियों पर प्रकाश डाला।
  \n\t
  \n\t
\n\t
• टोरंटो:\n\t
  \n\t\t
  • टोरंटो, कनाडा ने राष्ट्रमंडल खेलों की मेजबानी नहीं की है, लेकिन यह एक प्रमुख शहर है जो 2015 पैन अमेरिकन गेम्स जैसे अंतरराष्ट्रीय खेल आयोजनों की मेजबानी के लिए जाना जाता है।
  \n\t\t
  • शहर में खेल और सांस्कृतिक कार्यक्रमों के लिए एक मजबूत बुनियादी ढांचा है, जो इसे भविष्य के खेलों के लिए एक संभावित उम्मीदवार बनाता है।
  \n\t
  \n\t
\n

सही उत्तर है एक पेड़ माँ के नाम 2.0 वृक्षारोपण।

मुख्य बिंदु

\n\t
• विश्व पर्यावरण दिवस 2025 पर, शिक्षा मंत्री धर्मेंद्र प्रधान ने माताओं को श्रद्धांजलि के रूप में वृक्षारोपण को प्रोत्साहित करने के लिए एक पेड़ माँ के नाम 2.0 अभियान को बढ़ावा दिया।
\n\t
• यह अभियान पर्यावरणीय स्थिरता और माताओं को पेड़ समर्पित करके कृतज्ञता की संस्कृति को बढ़ावा देने पर जोर देता है।
\n\t
• यह पहले के एक पेड़ माँ के नाम पहल की निरंतरता है, जिसने अपने पहले चरण में महत्वपूर्ण सार्वजनिक भागीदारी हासिल की।
\n\t
• यह पहल जलवायु परिवर्तन का मुकाबला करने और जैव विविधता के संरक्षण पर सरकार के व्यापक ध्यान के अनुरूप है।
\n\t
• इस अभियान के तहत, नागरिकों को अपने घरों, स्कूलों और सार्वजनिक स्थानों पर पेड़ लगाने के लिए प्रोत्साहित किया जाता है, साथ ही उनके पर्यावरणीय लाभों के बारे में जागरूकता बढ़ाई जाती है।
\n

अतिरिक्त जानकारी

\n\t
• प्लास्टिक-मुक्त भारत अभियान:\n\n\t
  \n\t\t
  • यह अभियान एकल-उपयोग प्लास्टिक को खत्म करने और प्लास्टिक प्रदूषण को कम करने के लिए स्थायी विकल्पों को बढ़ावा देने पर केंद्रित है।
  \n\t\t
  • भारत ने 2025 तक एकल-उपयोग प्लास्टिक को चरणबद्ध तरीके से समाप्त करने और स्वच्छ भारत अभियान जैसी पहलों के माध्यम से सार्वजनिक जागरूकता बढ़ाने का संकल्प लिया है।
  \n\t\t
  • अभियान में प्लास्टिक कचरे को कम करने और पुनर्चक्रण को बढ़ावा देने के लिए उद्योगों, शैक्षणिक संस्थानों और गैर सरकारी संगठनों की सक्रिय भागीदारी देखी गई है।
  \n\t
  \n\t
\n\t
• स्वच्छ गंगा युवा आंदोलन:\n\t
  \n\t\t
  • यह पहल बड़े नमामि गंगे कार्यक्रम का हिस्सा है, जिसका उद्देश्य गंगा नदी को फिर से जीवंत और संरक्षित करना है।
  \n\t\t
  • यह युवाओं को नदी के किनारों की सफाई, प्रदूषण को रोकने और स्वच्छ जल निकायों के महत्व के बारे में जागरूकता फैलाने जैसी गतिविधियों में शामिल करता है।
  \n\t\t
  • यह आंदोलन पर्यावरणीय संरक्षण और जल संसाधन प्रबंधन में युवा नागरिकों की भूमिका पर प्रकाश डालता है।
  \n\t
  \n\t
\n\t
• राष्ट्रीय तटीय सफाई अभियान:\n\t
  \n\t\t
  • यह कार्यक्रम तटीय क्षेत्रों की सफाई और मानवीय गतिविधियों के कारण होने वाले समुद्री प्रदूषण को संबोधित करने पर केंद्रित है।
  \n\t\t
  • इसमें समुद्र तटों से कचरा हटाने और समुद्री पारिस्थितिक तंत्र को बहाल करने के लिए स्वयंसेवक, स्थानीय समुदाय और पर्यावरण संगठन शामिल हैं।
  \n\t\t
  • यह अभियान समुद्री जैव विविधता की रक्षा और समुद्री प्रदूषण के प्रभावों को कम करने के लिए महत्वपूर्ण है।
  \n\t
  \n\t
\n

सही उत्तर 30 टन है।

मुख्य बिंदु

\n\t
• भारत के नेक्स्ट जनरेशन लॉन्च व्हीकल (NGLV) को भारतीय अंतरिक्ष अनुसंधान संगठन (ISRO) द्वारा अंतरिक्ष मिशनों के लिए भविष्य की भारी पेलोड मांगों को पूरा करने के लिए विकसित किया जा रहा है।
\n\t
• NGLV को एक मॉड्यूलर आर्किटेक्चर के साथ डिज़ाइन किया गया है और यह लो अर्थ ऑर्बिट (LEO) में 30 टन तक पेलोड ले जाने में सक्षम है।
\n\t
• यह क्षमता सुनिश्चित करती है कि NGLV उपग्रह प्रक्षेपण, मानव अंतरिक्ष यान मिशन और इंटरप्लेनेटरी मिशन सहित अंतरिक्ष अनुप्रयोगों की एक विस्तृत श्रृंखला का समर्थन कर सकता है।
\n\t
• NGLV को पोलर सैटेलाइट लॉन्च व्हीकल (PSLV) और जियोसिंक्रोनस सैटेलाइट लॉन्च व्हीकल (GSLV) परिवारों के उत्तराधिकारी के रूप में देखा गया है, जो उच्च पेलोड क्षमता और बेहतर विश्वसनीयता प्रदान करता है।
\n\t
• NGLV का विकास वैश्विक अंतरिक्ष प्रक्षेपण बाजार में प्रतिस्पर्धी बने रहने के साथ-साथ घरेलू आवश्यकताओं को पूरा करने की भारत की दीर्घकालिक रणनीति का हिस्सा है।
\n

अतिरिक्त जानकारी

\n\t
• लो अर्थ ऑर्बिट (LEO)\n\n\t
  \n\t\t
  • LEO पृथ्वी के चारों ओर 160 किमी और 2,000 किमी के बीच की ऊंचाई वाली कक्षा को संदर्भित करता है।
  \n\t\t
  • यह आमतौर पर पृथ्वी अवलोकन उपग्रहों, संचार उपग्रहों और अंतर्राष्ट्रीय अंतरिक्ष स्टेशन (ISS) के लिए उपयोग किया जाता है।
  \n\t\t
  • LEO मिशनों के लिए सटीक नेविगेशन और मिशन उद्देश्यों को पूरा करने के लिए पर्याप्त पेलोड क्षमता वाले लॉन्च वाहनों की आवश्यकता होती है।
  \n\t
  \n\t
\n

सही उत्तर है यह BWF सुपर 750 टियर के भाग के रूप में 14 से 19 जनवरी, 2025 तक के.डी. जाधव इंडोर हॉल, आईजी स्टेडियम, नई दिल्ली में आयोजित किया गया था।.

मुख्य बिंदु

\n\t
• योनेक्स-सनराइज इंडिया ओपन 2025 को BWF सुपर 750 टूर्नामेंट के रूप में वर्गीकृत किया गया है, जो प्रतिष्ठित BWF वर्ल्ड टूर का हिस्सा है।
\n\t
• टूर्नामेंट के.डी. जाधव इंडोर हॉल में आयोजित किया गया था, जो आईजी स्टेडियम, नई दिल्ली के भीतर स्थित है।
\n\t
• कार्यक्रम का आधिकारिक कार्यक्रम 14 से 19 जनवरी, 2025 तक चला, जिसमें शीर्ष अंतरराष्ट्रीय बैडमिंटन खिलाड़ियों का प्रदर्शन किया गया।
\n\t
• BWF सुपर 750 टियर बैडमिंटन टूर्नामेंट पदानुक्रम में उच्चतम स्तरों में से एक है, जो सुपर 1000 टूर्नामेंट के बाद दूसरा है।
\n\t
• यह टूर्नामेंट वैश्विक प्रतिभागियों को आकर्षित करता है और महत्वपूर्ण रैंकिंग अंक और पुरस्कार राशि प्रदान करता है, जो बैडमिंटन कैलेंडर में इसके महत्व में योगदान देता है।
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अतिरिक्त जानकारी

\n\t
• योनेक्स-सनराइज इंडिया ओपन\n\n\t
  \n\t\t
  • योनेक्स-सनराइज इंडिया ओपन भारत में आयोजित एक वार्षिक बैडमिंटन टूर्नामेंट है, जिसमें एकल और युगल श्रेणियों में प्रतिस्पर्धा करने वाले अंतरराष्ट्रीय खिलाड़ी शामिल होते हैं।
  \n\t\t
  • यह BWF वर्ल्ड टूर का हिस्सा है और पुरस्कार राशि और रैंकिंग अंकों के आधार पर विभिन्न स्तरों के तहत वर्गीकृत किया गया है।
  \n\t\t
  • टूर्नामेंट भारत में बैडमिंटन को बढ़ावा देने और वैश्विक प्रतिस्पर्धी मानकों को बढ़ावा देने में महत्वपूर्ण भूमिका निभाता है।
  \n\t
  \n\t
\n

सही उत्तर है विकल्प 3: A सत्य है, लेकिन R असत्य है।

मुख्य बिंदु

\n\t
• खुशी सूचकांक विभिन्न कारकों को मापता है, जिसमें राजनीतिक स्वतंत्रता, सामाजिक समर्थन, आय, स्वास्थ्य, जीवन प्रत्याशा और उदारता शामिल हैं।
\n\t
• खुशी सूचकांक को आधिकारिक तौर पर विश्व खुशी रिपोर्ट के रूप में जाना जाता है, जो इन मानदंडों के आधार पर देशों को रैंक करता है।
\n\t
• राजनीतिक स्वतंत्रता और सामाजिक समर्थन इस सूचकांक में मूल्यांकन किए गए महत्वपूर्ण घटक हैं ताकि समाज में व्यक्तियों की भलाई का आकलन किया जा सके।
\n\t
• विश्व खुशी रिपोर्ट यूएनडीपी द्वारा प्रकाशित नहीं की जाती है; इसके बजाय, इसे संयुक्त राष्ट्र के तत्वावधान में सतत विकास समाधान नेटवर्क (एसडीएसएन) द्वारा तैयार किया जाता है।
\n\t
• यह रिपोर्ट गैलप वर्ल्ड पोल जैसे वैश्विक सर्वेक्षणों से एकत्र किए गए डेटा पर आधारित है, जो देशों में व्यक्तिपरक कल्याण और खुशी के स्तर पर जोर देती है।
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अतिरिक्त जानकारी

\n\t
• यूएनडीपी के प्रमुख सूचकांक:\n\n\t
  \n\t\t
  • मानव विकास सूचकांक (एचडीआई): औसत उपलब्धि का एक सारांश उपाय:\n\n\t\t
    \n\t\t\t
    • एक लंबा और स्वस्थ जीवन (जन्म के समय जीवन प्रत्याशा)।
    \n\t\t\t
    • ज्ञान तक पहुंच (स्कूलिंग के औसत वर्ष और स्कूलिंग के अपेक्षित वर्ष)।
    \n\t\t\t
    • जीवन स्तर (प्रति व्यक्ति सकल राष्ट्रीय आय)।
    \n\t\t
    \n\t\t
  \n\t\t
  • बहुआयामी गरीबी सूचकांक (एमपीआई): व्यक्तियों के लिए स्वास्थ्य, शिक्षा और जीवन स्तर (जैसे पोषण, स्वच्छता, बिजली, खाना पकाने का ईंधन, आदि) में अतिव्यापी अभावों की पहचान करता है।
  \n\t\t
  • लैंगिक असमानता सूचकांक (जीआईआई): प्रजनन स्वास्थ्य, सशक्तिकरण और आर्थिक गतिविधि में लैंगिक असमानताओं को मापता है।
  \n\t\t
  • असमानता-समायोजित मानव विकास सूचकांक (आईएचडीआई): असमानता के स्तर के अनुपात में एचडीआई को \"छूट\" देकर देशों के भीतर असमानता के लिए जिम्मेदार है, संयुक्त राष्ट्र विकास कार्यक्रम नोट करता है।
  \n\t\t
  • लैंगिक विकास सूचकांक (जीडीआई): पुरुषों और महिलाओं के लिए एचडीआई की तुलना करता है।
  \n\t\t
  • ग्रहों के दबाव-समायोजित एचडीआई (पीएचडीआई): पर्यावरणीय प्रभाव के लिए एचडीआई को समायोजित करता है।
  \n\t\t
  • लैंगिक सामाजिक मानदंड सूचकांक (जीएसएनआई): लैंगिक समानता को प्रतिबंधित करने वाले सामाजिक मानदंडों को मापता है।
  \n\t
  \n\t
\n

3.375 = 3375 ÷ 1000

⇒ 3375 ÷ 125 = 27, 1000 ÷ 125 = 8

⇒ 3.375 = 27/8

a का 15% = b का 25%

⇒ a ÷ b = 25 ÷ 15

⇒ a ÷ b = 5 ÷ 3

मान लीजिए कि प्रत्येक संख्या में से x घटाया जाना है।

(7 − x)(11 − x) = (9 − x)(8 − x)

77 − 18x + x² = 72 − 17x + x²

77 − 72 = 18x − 17x

x = 5

6.4 = 32/5

2 5/8 = 21/8, 1.75 = 7/4

⇒ 32/5 − (21/8 + 7/4)

⇒ 32/5 − (21/8 + 14/8)

⇒ 32/5 − 35/8

5 और 8 का लघुत्तम समापवर्त्य = 40

⇒ 32/5 = 256/40, 35/8 = 175/40

⇒ 256/40 − 175/40

⇒ 81/40

⇒ 81 ÷ 40 = 2.025

आलोक (पहले 6 महीने) ⇒ 90,000 x 6 = 5,40,000

आलोक (अगले 6 महीने) ⇒ 1,20,000 x 6 = 7,20,000

कुल (आलोक) ⇒ 5,40,000 + 7,20,000 = 12,60,000

दीपक (6 महीने) ⇒ 1,20,000 x 6 = 7,20,000

अनुपात ⇒ 12,60,000 : 7,20,000

⇒ 126 : 72

⇒ 7 : 4

आयु का पुराना कुल योग = 17 × 19

⇒ पुराना कुल योग = 323

आयु का नया कुल योग = 18 × 20

⇒ नया कुल योग = 360

शिक्षक की आयु = 360 − 323

⇒ शिक्षक की आयु = 37

कुल वेतन = 62,000 × 80 ⇒ ₹49,60,000

30 कर्मचारियों का कुल वेतन = 72,000 × 30 ⇒ ₹21,60,000

शेष कर्मचारियों का कुल वेतन = 49,60,000 − 21,60,000 ⇒ ₹28,00,000

शेष कर्मचारी = 80 − 30 ⇒ 50

शेष कर्मचारियों का औसत वेतन = 28,00,000 ÷ 50 ⇒ ₹56,000

मान लीजिए कि मूल मूलधन P है।

4 = (1 + r/100)⁶

16 = (1 + r/100)^t

16 = 4², t = 6 x 2 = 12 वर्ष

माना कि क्रय मूल्य (C.P.) = ₹10x, हानि = ₹1x

विक्रय मूल्य (S.P.) = क्रय मूल्य (C.P.) − हानि

⇒ विक्रय मूल्य (S.P.) = 10x − 1x = 9x

विक्रय मूल्य (S.P.) और क्रय मूल्य (C.P.) का अनुपात ⇒ विक्रय मूल्य (S.P.) : क्रय मूल्य (C.P.) = 9x : 10x = 9 : 10

विक्रय मूल्य = 150 × (1 − 10/100)

⇒ विक्रय मूल्य = 150 × 0.9

⇒ विक्रय मूल्य = ₹135

क्रय मूल्य = 135 ÷ (1 + 25/100)

⇒ क्रय मूल्य = 135 ÷ 1.25

⇒ क्रय मूल्य = ₹108

माना कि अंकित मूल्य ₹x है।

छूट के बाद मूल्य = x x 0.8

इंस्टॉलेशन और सपोर्ट शुल्क = x x 0.8 x 0.15 = x x 0.12

पुनर्विक्रेता के लिए क्रय मूल्य = x x 0.8 + x x 0.12 = x x 0.92

पुनर्विक्रेता का विक्रय मूल्य = x x 0.92 x 1.25

x x 0.92 x 1.25 = x x 0.92 + ₹7800

x x (1.15 − 0.92) = ₹7800

x = ₹7800 ÷ 0.23

x = ₹33,913.04

कुल मिश्रण = 90 लीटर

दूध = (7/9) × 90 = 70 लीटर

पानी = (2/9) × 90 = 20 लीटर

(70 + x) / (20 + x) = 5/2

⇒ 2 × (70 + x) = 5 × (20 + x)

⇒ 140 + 2x = 100 + 5x

⇒ 40 = 3x

⇒ x = 40 ÷ 3 ≈ 13.33 लीटर

माना कि गोले की त्रिज्या = r

(4/3)πr³ = 36π ⇒ r³ = 27 ⇒ r = 3 सेमी

बेलन की ऊँचाई = 2r = 6 सेमी

बेलन का आयतन = π x 3² x 6 = 54π सेमी³

खाली स्थान = 54π − 36π = 18π सेमी³

अर्धगोले का आयतन = शंकु का आयतन

\\(\\frac{2}{3}\\pi R³ = \\frac{1}{3}\\pi R²H\\)

⇒ 23R=13H\" id=\"MathJax-Element-79-Frame\" role=\"presentation\" style=\"position: relative;\" tabindex=\"0\">23R=13H23R=13H\" id=\"MathJax-Element-10-Frame\" role=\"presentation\" style=\"position: relative;\" tabindex=\"0\">23R=13H\n\n

⇒ H = 2R

पहले गोलार्ध का आयतन = (2/3)π(6)³ = 144π

दूसरे गोलार्ध का आयतन = (2/3)π(8)³ = 341.33π

कुल आयतन = 144π + 341.33π = 485.33π

(2/3)πR³ = 485.33π ⇒ R³ = (3 x 485.33) ÷ 2 = 728

R = ∛728 ≈ 9 सेमी

पिरामिड का आयतन = 1/3 x आधार का क्षेत्रफल x ऊँचाई

आधार भुजा का आधा = 12 ÷ 2 = 6 सेमी

समकोण त्रिभुज का उपयोग करने पर:

ऊँचाई2 = तिर्यक ऊँचाई2 − (आधा आधार)2

⇒ ऊँचाई2 = 102 − 62

⇒ ऊँचाई2 = 100 − 36 = 64

⇒ ऊँचाई = 8 सेमी

आधार का क्षेत्रफल = 12 x 12 = 144 सेमी2

आयतन = 1/3 x 144 x 8

⇒ आयतन = 384 सेमी3

∴ पिरामिड का आयतन 384 सेमी3 है।

वृत्त का क्षेत्रफल ∝ (त्रिज्या)2

क्षेत्रफलों का अनुपात = (1)2 : (√2)2

⇒ क्षेत्रफलों का अनुपात = 1 : 2

माना कि छोटे टायर का क्षेत्रफल = 1 भाग = 100

⇒ बड़े टायर का क्षेत्रफल = 2 भाग = 2 x 100

⇒ बड़े टायर का क्षेत्रफल = 200 सेमी2

∴ बड़े टायर का क्षेत्रफल 200 सेमी2 है।

प्रयुक्त सूत्र:

∠BIC = 90° + 1/2 ∠BAC

125 = 90 + 1/2 ∠BAC

⇒ 1/2 ∠BAC = 125 − 90

⇒ 1/2 ∠BAC = 35

⇒ ∠BAC = 35 x 2

⇒ ∠BAC = 70°

∴ ∠BAC का मान 70° है।

△ABC और △CDA पर विचार करें

AB ∥ CD

⇒ ∠BAC = ∠ACD (एकांतर आंतरिक कोण)

AC = AC (उभयनिष्ठ भुजा)

AB = CD (दिया गया है)

⇒ △ABC ≅ △CDA (SAS द्वारा)

∴ त्रिभुज ABC और CDA सर्वांगसम हैं।

A से DE की दूरी = ΔABC की ऊँचाई का 2/3

⇒ भुजा अनुपात = 2/3

⇒ क्षेत्रफल(ΔADE) : क्षेत्रफल(ΔABC) = (2/3)2 = 4/9

⇒ क्षेत्रफल(DECB) : क्षेत्रफल(ΔABC) = 1 − 4/9 = 5/9

⇒ क्षेत्रफल(ΔADE) : क्षेत्रफल(DECB) = (4/9) : (5/9)

⇒ 4 : 5

∴ अभीष्ट अनुपात = 4 : 5

√[ d2 − (r₁ + r₂)2 ]

⇒ r₁ + r₂ = 9 + 5 = 14

⇒ d2 − (r₁ + r₂)2

⇒ 172 − 142

⇒ 289 − 196

⇒ 93

⇒ आंतरिक उभयनिष्ठ स्पर्श रेखा की लंबाई = √93 सेमी

√[ d2 − (r1 + r2)2 ]

⇒ r1 + r2 = 7 + 3 = 10

⇒ d2 − (r1 + r2)2

⇒ 202 − 102

⇒ 400 − 100

⇒ 300

⇒ अनुप्रस्थ उभयनिष्ठ स्पर्शरेखा की लंबाई = √300

∴ अभीष्ट लंबाई √300 सेमी है।

⇒ 9 सेमी > 7 सेमी

⇒ 9 सेमी जीवा की दूरी = 4 सेमी

⇒ छोटी जीवा (7 सेमी) केंद्र से 4 सेमी से अधिक दूर होगी

∴ केंद्र से 7 सेमी जीवा की दूरी 4 सेमी से अधिक है।

कोण के विपरीत भुजा = 2 x R x sin(कोण)

⇒ अभीष्ट भुजा = 2 x r x sin120°

⇒ sin120° = √3 / 2

⇒ अभीष्ट भुजा = 2 x r x (√3 / 2)

⇒ अभीष्ट भुजा = r√3

∴ 120° कोण के विपरीत भुजा की लंबाई r√3 है।

8 और 16 का LCM = 16

⇒ \\(\\frac{1}{8}=\\frac{2}{16}\\)

⇒ \\(\\frac{2}{16}+\\frac{1}{16}=\\frac{3}{16}\\)

⇒ \\(\\frac{3}{16}=0.1875\\)

∴ अभीष्ट दशमलव मान 0.1875 है।

The correct answer is: Stubborn. The word \"Intransigent\" refers to a person who is unwilling or refusing to change one's views or to agree about something. The meanings of the other words are: Willing: Ready to do something; Compliant: Yielding to others; Submissive: Ready to conform to authority.

The correct answer is: In a state of depression or inactivity. Meaning: The idiom \"in the doldrums\" refers to a state of stagnation, low spirits, or lack of progress, originating from the nautical term for calm equatorial waters where ships often became stranded.

The correct answer is: Hallucinogenic. Meaning: Relating to or denoting drugs that cause hallucinations. The word is derived from \"hallucinogen\" + the suffix \"-ic\".

The correct answer is: Apostate. It refers to a person who renounces a religious or political belief. The meanings of the rest of the words are: Renegade: A person who deserts a cause; Atheist: A person who does not believe in God; Heretic: A person with beliefs contrary to orthodox doctrine.

The correct answer is: Schism. It refers to a formal split within a religious organization. The meanings of the rest of the words are: Sedition: Inciting rebellion against authority; Heresy: Belief contrary to orthodox doctrine; Apostasy: Renunciation of a belief.

The correct answer is: A. The current was unusually strong near the bridge.. Meaning: In the original sentence, \"current\" means \"present\" or \"most recent.\" In option A, \"current\" refers to a body of water or air moving in a definite direction. Options B, C, and D use \"current\" with the same meaning as the original sentence (present/contemporary).

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

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• The tone of the author is best captured as Analytical, as the passage involves a detailed examination of the options provided.
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• Option 1 (Dogmatic) implies a rigid or authoritative tone, which is not evident in the passage.
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• Option 2 (Reverent) suggests a tone of deep respect, which does not align with the analytical evaluation of the options.
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• Option 4 (Indifferent) reflects a lack of interest or concern, which is not consistent with the passage's tone.
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Additional Information

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• An analytical tone is characterized by an objective and detailed examination of information or arguments.
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• In this context, the author evaluates the options provided to determine the correct tone for the passage.
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• This careful and reasoned approach aligns with the definition of an analytical tone.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The sentence "Smartness devoid of rigor often culminates in superficiality..." highlights the limitation of relying solely on smart work.
\n\t
• It emphasizes that while smart work is beneficial, it needs to be complemented by rigor and thoroughness to avoid superficial outcomes.
\n\t
• This contrasts with other sentences that focus on different aspects of work without directly addressing this limitation.
\n

Additional Information

\n\t
• Option 1: Focuses on the historical valorization of hard work, which is a separate concept.
\n\t
• Option 2: Describes transcending repetitive efforts without directly addressing the limitation of smart work.
\n\t
• Option 4: Discusses the attributes of a sagacious worker but does not pinpoint the drawback of smart work alone.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• From a philosophical standpoint, hard work and smart work are not inherently opposed to one another but should function in harmony to yield sustainable and effective results.
\n\t
• The argument emphasizes the balance between the two approaches rather than favoring one over the other.
\n\t
• While hard work provides consistency and effort, smart work enhances efficiency by leveraging tools, strategies, and innovation.
\n

Additional Information

\n\t
• Hard Work: Refers to putting in consistent effort and dedication over time to achieve goals.
\n\t
• Smart Work: Involves using innovative techniques, tools, and strategies to achieve goals more efficiently.
\n\t
• Neither approach is superior on its own; combining both leads to sustainable success.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The phrase "minimize entropy in labor" implies reducing randomness and inefficiency in effort.
\n\t
• Entropy, in this context, refers to disorganization or disorder in work processes.
\n\t
• Smart work involves creating streamlined, efficient workflows to achieve maximum productivity with minimal wasted effort.
\n

Additional Information

\n\t
• Option 1: "Reduce physical strain through technology" – While technology can reduce physical strain, it doesn't directly address inefficiency in effort.
\n\t
• Option 3: "Avoid structured systems of work" – This is the opposite of minimizing entropy, as structured systems reduce disorder.
\n\t
• Option 4: "Increase workload to achieve results faster" – Increasing workload doesn't necessarily minimize inefficiency and randomness.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The metaphor "Treadmill" is often used to describe unidirectional exertion, symbolizing repetitive motion with no change in direction or outcome.
\n\t
• It conveys the idea of continuous effort without significant progress or variation.
\n\t
• Other options like "Algorithmic precision" or "Social capital" do not align with the concept of unidirectional exertion.
\n\t
• Thus, the correct metaphor is "Treadmill," making Option 1 the right choice.
\n

Additional Information

\n\t
• Option 2: Algorithmic precision – This refers to accuracy and systematic execution, not unidirectional exertion.
\n\t
• Option 3: Crucible of challenges – This refers to a severe test or trial, which is unrelated to the concept of unidirectional exertion.
\n\t
• Option 4: Social capital – This relates to the networks and relationships that enable society to function effectively, not unidirectional exertion.
\n\t
• Treadmill aptly describes the repetitive and unidirectional nature of exertion, which is why it is the correct answer.
\n

Words in the sentence that begin with a consonant: Italy is a beautiful village and China is a big building

Thus, there are 5 words that begin with a consonant

Thus, option 4 is exactly the same as the one given.

A statement is given followed by two conclusions. Find which conclusion is TRUE based on the given statement.
\nStatement:
\nC= A ≤ T < D ≥ O; G ≥ D < S; T ≥ A
\nConclusions:
\nI: A < O
\nII: C < G

I: A < O - False (As, A ≤ T < D ≥ O, there is no direct relationship between A and O)
\nII: C < G - True (C= A ≤ T < D ≤ G, it gives C < G)

Thus, only Conclusion II follows.

Logic: a # b = a ÷ b

1. 10 # 5 = 5 ⇒ 10 ÷ 5 ≠ 2

I. Gene editing technologies can potentially cure genetic disorders. - Implicit (The statement clearly implies these technologies offer immense potential for curing genetic disorders. If this were not true, the statement would collapse)

II. Ethical concerns are a natural consequence of advancing gene editing technologies - Implicit (The statement implies advancement raises ethical concerns. For this to be valid, we must assume that such technological progress leads to ethical issues)

III. The potential for gene editing to cure genetic disorders outweighs the ethical concerns - Not Implicit (The statement does not compare which is greater. It simply mentions both potential and concerns — no judgment is made)

So, only I and II are implicit.

I. The bank wants to improve security. - True (Because biometric login systems are generally introduced to enhance security and reduce fraud. So it is reasonable to conclude that the bank’s intention is to improve security).
\n
\nII. Customers must carry biometric IDs. - False (Because biometric login usually uses fingerprints, face recognition, etc. — it does not necessarily require customers to carry separate biometric IDs).

So, only Conclusion I follows.

The logic followed here is: Letter are coded as their opposite letters.

Conclusions:

I. Some animals are wild. - False (Because, no definite relation given between animals and wild, so it can be possible).

II. All wild are animals. - False (Because, no definite relation given between animals and wild, so it can be possible)

So, neither I nor II follows

1. AIR → QUARRELSOME → Cannot be formed as 'I' is missing

6th term = a × r^(6-1)

48 = 1.5 × r⁵

r = (48 ÷ 1.5)^1/5 = 32^1/5 = 2.0

All options except Manmohan Singh are freedom fighters of India.

P is mother of R.

PLANE is coded as 74851.

DOG is coded as 392.

Similarly,

√144 = 144^1/2 = 12

³√27 = 27^1/3 = 3

√144 + ³√27 = 12 + 3 = 15

Logic: a # b = ab

⇒ Total bill = (5 × ₹8) + (3 × ₹25)

⇒ Total bill = ₹40 + ₹75

⇒ Total bill = ₹115

Clearly, P is R's father.

2. 10 + 2 - 4 × 1 = 8

After replacing the symbols by their meaning, we get:

⇒ 10 ÷ 2 + 4 - 1 = 8

⇒ 5 + 4 - 1 = 8

⇒ 9 - 1 = 8

⇒ 8 = 8

⇒ 25 ÷ 5 + 3 × 2 - 4 = ?

⇒ 5 + 3 × 2 - 4 = ?

⇒ 5 + 6 - 4 = ?

⇒ 11 - 4 = ?

⇒ 7 = ?

After replacing the symbols by their meaning, we get:

= 5 ^ 2 - 3 × 1   =  52 - 3 × 1  = 25 - 3 × 1

= 25 - 3  = 22

⇒ Sum = 11 + 40

⇒ Sum = 51

⇒ Result = 51 × 5

⇒ Result = 255

The correct answer is Glasgow.

Key Points

\n\t
• Glasgow is set to host the 2026 Commonwealth Games after Australia withdrew from hosting due to cost concerns and logistical issues.
\n\t
• The Commonwealth Games Federation (CGF) announced Glasgow as the new host due to its prior experience in hosting major international sporting events, including the 2014 Commonwealth Games.
\n\t
• Glasgow has a well-developed infrastructure, including sports facilities and transportation networks, suitable for hosting an event of this magnitude.
\n\t
• The city is expected to leverage its existing venues, such as the Emirates Arena and Hampden Park, to minimize additional expenditure.
\n\t
• The decision to allocate the Games to Glasgow aligns with the CGF's efforts to ensure sustainability and financial viability for future host cities.
\n

Additional Information

\n\t
• Birmingham:\n\n\t
  \n\t\t
  • Birmingham hosted the 2022 Commonwealth Games, which featured 19 sports and drew participants from 72 nations and territories.
  \n\t\t
  • The event was highly praised for its inclusivity, as it became the first Commonwealth Games to feature more medal events for women than men.
  \n\t\t
  • The city's facilities, such as the Alexander Stadium, underwent significant upgrades to host the event.
  \n\t
  \n\t
\n\t
• Victoria:\n\t
  \n\t\t
  • Victoria, a state in Australia, was initially set to host the 2026 Commonwealth Games but withdrew in 2023 due to escalating costs that exceeded its budgetary expectations.
  \n\t\t
  • The decision to withdraw highlighted the financial challenges associated with hosting such large-scale international events.
  \n\t
  \n\t
\n\t
• Toronto:\n\t
  \n\t\t
  • Toronto, Canada, has not hosted the Commonwealth Games but is a prominent city known for hosting international sports events, such as the 2015 Pan American Games.
  \n\t\t
  • The city has a strong infrastructure for sports and cultural events, making it a potential candidate for future Games.
  \n\t
  \n\t
\n

The correct answer is Ek Ped Maa Ke Naam 2.0 tree-planting.

Key Points

\n\t
• On World Environment Day 2025, Education Minister Dharmendra Pradhan promoted the Ek Ped Maa Ke Naam 2.0 campaign to encourage tree plantation as a tribute to mothers.
\n\t
• The campaign emphasizes environmental sustainability and fostering a culture of gratitude by dedicating trees to mothers.
\n\t
• It is a continuation of the earlier Ek Ped Maa Ke Naam initiative, which gained significant public participation in its first phase.
\n\t
• The initiative aligns with the government’s broader focus on combating climate change and conserving biodiversity.
\n\t
• Under this campaign, citizens are encouraged to plant trees in their homes, schools, and public spaces while promoting awareness about their environmental benefits.
\n

Additional Information

\n\t
• Plastic-Free India Campaign:\n\n\t
  \n\t\t
  • This campaign focuses on eliminating single-use plastics and promoting sustainable alternatives to reduce plastic pollution.
  \n\t\t
  • India has pledged to phase out single-use plastics by 2025 and aims to increase public awareness through initiatives like Swachh Bharat Abhiyan.
  \n\t\t
  • The campaign has seen active participation from industries, educational institutions, and NGOs to reduce plastic waste and promote recycling.
  \n\t
  \n\t
\n\t
• Clean Ganga Youth Movement:\n\t
  \n\t\t
  • This initiative is part of the larger Namami Gange Programme, aiming to rejuvenate and conserve the Ganga river.
  \n\t\t
  • It engages youth in activities like cleaning riverbanks, preventing pollution, and spreading awareness about the importance of clean water bodies.
  \n\t\t
  • The movement highlights the role of young citizens in environmental conservation and water resource management.
  \n\t
  \n\t
\n\t
• National Coastal Cleanup Drive:\n\t
  \n\t\t
  • This program focuses on cleaning coastal areas and addressing marine pollution caused by human activities.
  \n\t\t
  • It involves volunteers, local communities, and environmental organizations to remove waste from beaches and restore marine ecosystems.
  \n\t\t
  • The drive is crucial for protecting marine biodiversity and mitigating the impacts of ocean pollution.
  \n\t
  \n\t
\n

The correct answer is 30 tonnes.

Key Points

\n\t
• India's Next Generation Launch Vehicle (NGLV) is being developed by the Indian Space Research Organisation (ISRO) to meet future heavy payload demands for space missions.
\n\t
• The NGLV is designed with a modular architecture and is capable of carrying up to 30 tonnes of payload to Low Earth Orbit (LEO).
\n\t
• This capability ensures that the NGLV can support a wide range of space applications, including satellite launches, human spaceflight missions, and interplanetary missions.
\n\t
• The NGLV is envisioned as a successor to the Polar Satellite Launch Vehicle (PSLV) and Geosynchronous Satellite Launch Vehicle (GSLV) families, offering higher payload capacities and enhanced reliability.
\n\t
• The development of the NGLV is part of India's long-term strategy to remain competitive in the global space launch market while also addressing domestic requirements.
\n

Additional Information

\n\t
• Low Earth Orbit (LEO)\n\n\t
  \n\t\t
  • LEO refers to an orbit around Earth with an altitude between 160 km and 2,000 km.
  \n\t\t
  • It is commonly used for Earth observation satellites, communication satellites, and the International Space Station (ISS).
  \n\t\t
  • LEO missions require launch vehicles capable of precise navigation and sufficient payload capacity to meet mission objectives.
  \n\t
  \n\t
\n

The correct answer is It was hosted at the K.D. Jadhav Indoor Hall, IG Stadium, New Delhi, from January 14 to 19, 2025, as part of the BWF Super 750 tier..

Key Points

\n\t
• The Yonex-Sunrise India Open 2025 is classified as a BWF Super 750 tournament, which is part of the prestigious BWF World Tour.
\n\t
• The tournament was hosted at the K.D. Jadhav Indoor Hall, located within IG Stadium, New Delhi.
\n\t
• The event's official schedule spanned from January 14 to 19, 2025, showcasing top international badminton players.
\n\t
• The BWF Super 750 tier is among the highest levels in the badminton tournament hierarchy, second only to Super 1000 tournaments.
\n\t
• This tournament attracts global participants and offers significant ranking points and prize money, contributing to its importance in the badminton calendar.
\n

Additional Information

\n\t
• Yonex-Sunrise India Open\n\n\t
  \n\t\t
  • The Yonex-Sunrise India Open is an annual badminton tournament held in India, featuring international players competing in singles and doubles categories.
  \n\t\t
  • It forms part of the BWF World Tour and is classified under different tiers based on prize money and ranking points.
  \n\t\t
  • The tournament plays a vital role in promoting badminton in India and fostering global competitive standards.
  \n\t
  \n\t
\n

The correct answer is Option 3: A is true, but R is false.

Key Points

\n\t
• The Happiness Index measures various factors, including political freedom, social support, income, health, life expectancy, and generosity.
\n\t
• The Happiness Index is officially known as the World Happiness Report, which ranks countries based on these criteria.
\n\t
• Political freedom and social support are significant components assessed in this index to evaluate the well-being of individuals in a society.
\n\t
• The World Happiness Report is not published by the UNDP; instead, it is prepared by the Sustainable Development Solutions Network (SDSN) under the auspices of the United Nations.
\n\t
• The report is based on data collected from global surveys like the Gallup World Poll, emphasizing subjective well-being and happiness levels across countries.
\n

Additional Information

\n\t
• Key UNDP Indices:\n\n\t
  \n\t\t
  • Human Development Index (HDI): A summary measure of average achievement in:\n\n\t\t
    \n\t\t\t
    • A long and healthy life (Life Expectancy at Birth).
    \n\t\t\t
    • Access to knowledge (Mean Years of Schooling & Expected Years of Schooling).
    \n\t\t\t
    • A decent standard of living (Gross National Income per Capita).
    \n\t\t
    \n\t\t
  \n\t\t
  • Multidimensional Poverty Index (MPI): Identifies overlapping deprivations in health, education, and living standards (like nutrition, sanitation, electricity, cooking fuel, etc.) for individuals.
  \n\t\t
  • Gender Inequality Index (GII): Measures gender disparities in reproductive health, empowerment, and economic activity.
  \n\t\t
  • Inequality-adjusted Human Development Index (IHDI): Accounts for inequality within countries by "discounting" the HDI in proportion to the level of inequality, notes United Nations Development Programme.
  \n\t\t
  • Gender Development Index (GDI): Compares HDI for men and women.
  \n\t\t
  • Planetary Pressures-adjusted HDI (PHDI): Adjusts the HDI for environmental impact.
  \n\t\t
  • Gender Social Norms Index (GSNI): Measures social norms restricting gender equality. 
  \n\t
  \n\t
\n

3.375 = 3375 ÷ 1000

⇒ 3375 ÷ 125 = 27, 1000 ÷ 125 = 8

⇒ 3.375 = 27/8

15% of a = 25% of b

⇒ a ÷ b = 25 ÷ 15

⇒ a ÷ b = 5 ÷ 3

Let the number to be subtracted from each be x.

(7 − x)(11 − x) = (9 − x)(8 − x)

77 − 18x + x² = 72 − 17x + x²

77 − 72 = 18x − 17x

x = 5

6.4 = 32/5

2 5/8 = 21/8, 1.75 = 7/4

⇒ 32/5 − (21/8 + 7/4)

⇒ 32/5 − (21/8 + 14/8)

⇒ 32/5 − 35/8

LCM of 5 and 8 = 40

⇒ 32/5 = 256/40, 35/8 = 175/40

⇒ 256/40 − 175/40

⇒ 81/40

⇒ 81 ÷ 40 = 2.025

Old total sum of ages = 17 × 19

⇒ Old total sum = 323

New total sum of ages = 18 × 20

⇒ New total sum = 360

Teacher’s age = 360 − 323

⇒ Teacher’s age = 37

Total salary = 62,000 × 80 ⇒ ₹49,60,000

Total salary of 30 employees = 72,000 × 30 ⇒ ₹21,60,000

Total salary of remaining employees = 49,60,000 − 21,60,000 ⇒ ₹28,00,000

Remaining employees = 80 − 30 ⇒ 50

Average salary of remaining employees = 28,00,000 ÷ 50 ⇒ ₹56,000

Let the original principal be P.

4 = (1 + r/100)⁶

16 = (1 + r/100)^t

16 = 4², t = 6 × 2 = 12 years

Let Cost Price (C.P.) = ₹10x, Loss = ₹1x

S.P. = C.P. − Loss

⇒ S.P. = 10x − 1x = 9x

Ratio of S.P. to C.P. ⇒ S.P. : C.P. = 9x : 10x = 9 : 10

SP = 150 × (1 − 10/100)

⇒ SP = 150 × 0.9

⇒ SP = ₹135

CP = 135 ÷ (1 + 25/100)

⇒ CP = 135 ÷ 1.25

⇒ CP = ₹108

Total mixture = 90 litres

Milk = (7/9) × 90 = 70 litres

Water = (2/9) × 90 = 20 litres

(70 + x) / (20 + x) = 5/2

⇒ 2 × (70 + x) = 5 × (20 + x)

⇒ 140 + 2x = 100 + 5x

⇒ 40 = 3x

⇒ x = 40 ÷ 3 ≈ 13.33 litres

Let the radius of the sphere = r

(4/3)πr³ = 36π ⇒ r³ = 27 ⇒ r = 3 cm

Height of the cylinder = 2r = 6 cm

Volume of cylinder = π × 3² × 6 = 54π cm³

Vacant space = 54π − 36π = 18π cm³

Volume of hemisphere = Volume of cone

\\(\\frac{2}{3}\\pi R³ = \\frac{1}{3}\\pi R²H\\)

⇒ 23R=13H\" id=\"MathJax-Element-77-Frame\" role=\"presentation\" style=\"position: relative;\" tabindex=\"0\">23R=13H23R=13H\" id=\"MathJax-Element-8-Frame\" role=\"presentation\" style=\"position: relative;\" tabindex=\"0\">23R=13H\n\n

⇒ H = 2R

Volume of first hemisphere = (2/3)π(6)³ = 144π

Volume of second hemisphere = (2/3)π(8)³ = 341.33π

Total volume = 144π + 341.33π = 485.33π

(2/3)πR³ = 485.33π ⇒ R³ = (3 × 485.33) ÷ 2 = 728

R = ∛728 ≈ 9 cm

Volume of pyramid = 1/3 × Base area × Height

Half of base side = 12 ÷ 2 = 6 cm

Using right triangle:

Height2 = Slant height2 − (half base)2

⇒ Height2 = 102 − 62

⇒ Height2 = 100 − 36 = 64

⇒ Height = 8 cm

Base area = 12 × 12 = 144 cm2

Volume = 1/3 × 144 × 8

⇒ Volume = 384 cm3

∴ The volume of the pyramid is 384 cm3.

Area of circle ∝ (radius)2

Ratio of areas = (1)2 : (√2)2

⇒ Ratio of areas = 1 : 2

Let area of smaller tyre = 1 part = 100

⇒ Area of larger tyre = 2 parts = 2 × 100

⇒ Area of larger tyre = 200 cm2

∴ The area of the larger tyre is 200 cm2.

Formula used:

∠BIC = 90° + 1/2 ∠BAC

125 = 90 + 1/2 ∠BAC

⇒ 1/2 ∠BAC = 125 − 90

⇒ 1/2 ∠BAC = 35

⇒ ∠BAC = 35 × 2

⇒ ∠BAC = 70°

∴ The value of ∠BAC is 70°.

Consider △ABC and △CDA

AB ∥ CD

⇒ ∠BAC = ∠ACD (alternate interior angles)

AC = AC (common side)

AB = CD (given)

⇒ △ABC ≅ △CDA (by SAS)

∴ Triangles ABC and CDA are congruent.

Distance of DE from A = 2/3 of height of ΔABC

⇒ Side ratio = 2/3

⇒ Area(ΔADE) : Area(ΔABC) = (2/3)2 = 4/9

⇒ Area(DECB) : Area(ΔABC) = 1 − 4/9 = 5/9

⇒ Area(ΔADE) : Area(DECB) = (4/9) : (5/9)

⇒ 4 : 5

∴ Required ratio = 4 : 5

√[ d2 − (r₁ + r₂)2 ]

⇒ r₁ + r₂ = 9 + 5 = 14

⇒ d2 − (r₁ + r₂)2

⇒ 172 − 142

⇒ 289 − 196

⇒ 93

⇒ Length of internal common tangent = √93 cm

√[ d2 − (r1 + r2)2 ]

⇒ r1 + r2 = 7 + 3 = 10

⇒ d2 − (r1 + r2)2

⇒ 202 − 102

⇒ 400 − 100

⇒ 300

⇒ Length of transverse common tangent = √300 

∴ The required length is √300 cm.

⇒ 9 cm > 7 cm

⇒ Distance of 9 cm chord = 4 cm

⇒ Shorter chord (7 cm) will be farther than 4 cm from center

∴ The distance of the 7 cm chord from the center is more than 4 cm.

Side opposite angle = 2 × R × sin(angle)

⇒ Required side = 2 × r × sin120°

⇒ sin120° = √3 / 2

⇒ Required side = 2 × r × (√3 / 2)

⇒ Required side =  r√3

∴ The length of the side opposite the 120° angle is  r√3.

LCM of 8 and 16 = 16

⇒ \\(\\frac{1}{8}=\\frac{2}{16}\\)

⇒ \\(\\frac{2}{16}+\\frac{1}{16}=\\frac{3}{16}\\)

⇒ \\(\\frac{3}{16}=0.1875\\)

∴ The required decimal value is 0.1875.

The correct answer is: Stubborn. The word \"Intransigent\" refers to a person who is unwilling or refusing to change one's views or to agree about something. The meanings of the other words are: Willing: Ready to do something; Compliant: Yielding to others; Submissive: Ready to conform to authority.

The correct answer is: In a state of depression or inactivity. Meaning: The idiom \"in the doldrums\" refers to a state of stagnation, low spirits, or lack of progress, originating from the nautical term for calm equatorial waters where ships often became stranded.

The correct answer is: Hallucinogenic. Meaning: Relating to or denoting drugs that cause hallucinations. The word is derived from \"hallucinogen\" + the suffix \"-ic\".

The correct answer is: Apostate. It refers to a person who renounces a religious or political belief. The meanings of the rest of the words are: Renegade: A person who deserts a cause; Atheist: A person who does not believe in God; Heretic: A person with beliefs contrary to orthodox doctrine.

The correct answer is: Schism. It refers to a formal split within a religious organization. The meanings of the rest of the words are: Sedition: Inciting rebellion against authority; Heresy: Belief contrary to orthodox doctrine; Apostasy: Renunciation of a belief.

The correct answer is: A. The current was unusually strong near the bridge.. Meaning: In the original sentence, \"current\" means \"present\" or \"most recent.\" In option A, \"current\" refers to a body of water or air moving in a definite direction. Options B, C, and D use \"current\" with the same meaning as the original sentence (present/contemporary).

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The tone of the author is best captured as Analytical, as the passage involves a detailed examination of the options provided.
\n\t
• Option 1 (Dogmatic) implies a rigid or authoritative tone, which is not evident in the passage.
\n\t
• Option 2 (Reverent) suggests a tone of deep respect, which does not align with the analytical evaluation of the options.
\n\t
• Option 4 (Indifferent) reflects a lack of interest or concern, which is not consistent with the passage's tone.
\n

Additional Information

\n\t
• An analytical tone is characterized by an objective and detailed examination of information or arguments.
\n\t
• In this context, the author evaluates the options provided to determine the correct tone for the passage.
\n\t
• This careful and reasoned approach aligns with the definition of an analytical tone.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The sentence "Smartness devoid of rigor often culminates in superficiality..." highlights the limitation of relying solely on smart work.
\n\t
• It emphasizes that while smart work is beneficial, it needs to be complemented by rigor and thoroughness to avoid superficial outcomes.
\n\t
• This contrasts with other sentences that focus on different aspects of work without directly addressing this limitation.
\n

Additional Information

\n\t
• Option 1: Focuses on the historical valorization of hard work, which is a separate concept.
\n\t
• Option 2: Describes transcending repetitive efforts without directly addressing the limitation of smart work.
\n\t
• Option 4: Discusses the attributes of a sagacious worker but does not pinpoint the drawback of smart work alone.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• From a philosophical standpoint, hard work and smart work are not inherently opposed to one another but should function in harmony to yield sustainable and effective results.
\n\t
• The argument emphasizes the balance between the two approaches rather than favoring one over the other.
\n\t
• While hard work provides consistency and effort, smart work enhances efficiency by leveraging tools, strategies, and innovation.
\n

Additional Information

\n\t
• Hard Work: Refers to putting in consistent effort and dedication over time to achieve goals.
\n\t
• Smart Work: Involves using innovative techniques, tools, and strategies to achieve goals more efficiently.
\n\t
• Neither approach is superior on its own; combining both leads to sustainable success.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The phrase "minimize entropy in labor" implies reducing randomness and inefficiency in effort.
\n\t
• Entropy, in this context, refers to disorganization or disorder in work processes.
\n\t
• Smart work involves creating streamlined, efficient workflows to achieve maximum productivity with minimal wasted effort.
\n

Additional Information

\n\t
• Option 1: "Reduce physical strain through technology" – While technology can reduce physical strain, it doesn't directly address inefficiency in effort.
\n\t
• Option 3: "Avoid structured systems of work" – This is the opposite of minimizing entropy, as structured systems reduce disorder.
\n\t
• Option 4: "Increase workload to achieve results faster" – Increasing workload doesn't necessarily minimize inefficiency and randomness.
\n

Read the following passage and answer the questions based on the passage :

In the relentless pursuit of excellence, the dichotomy between hard work and smart work emerges not merely as a matter of preference but as a nuanced dialectic in the broader schema of human productivity. Hard work—often equated with sheer diligence, indefatigable endurance, and linear perseverance—has historically been valorized as the cornerstone of achievement. The laboring individual, armed with nothing but obstinacy and time, is celebrated in folklore and biographies alike. However, in an era punctuated by algorithmic precision and cognitive economy, such traditional notions increasingly invite scrutiny. Contrastingly, smart work embodies a strategic orchestration of effort—an application of metacognition, resource optimization, and situational analysis. It seeks to minimize entropy in labor while maximizing the return on cognitive and physical investment. Smart workers interrogate systems, deconstruct inefficiencies, and leverage available tools—be they digital frameworks or social capital—to expedite outcomes. They transcend the treadmill of unidirectional exertion by inserting intelligence into execution. Nevertheless, the glorification of smart work without the substratum of hard work yields its own inadequacies. Smartness devoid of rigor often culminates in superficiality—a veneer of competence that collapses under sustained demand. Likewise, unmitigated hard work, devoid of strategic redirection, can lead to burnout and inefficiency. Hence, the contemporary paradigm necessitates a confluence: the sagacious worker is one who tempers grit with guile, who labors not just with effort but with efficacy. The juxtaposition, then, is not binary but complementary. To romanticize either extreme is to overlook the variegated realities of performance. In the crucible of modern challenges, the symbiotic blend of persistence and precision is what renders output sustainable and impact magnified. In essence, success is not the fruit of blind toil or cunning alone, but the synthesis of intelligent perseverance. 

Key Points

\n\t
• The metaphor "Treadmill" is often used to describe unidirectional exertion, symbolizing repetitive motion with no change in direction or outcome.
\n\t
• It conveys the idea of continuous effort without significant progress or variation.
\n\t
• Other options like "Algorithmic precision" or "Social capital" do not align with the concept of unidirectional exertion.
\n\t
• Thus, the correct metaphor is "Treadmill," making Option 1 the right choice.
\n

Additional Information

\n\t
• Option 2: Algorithmic precision – This refers to accuracy and systematic execution, not unidirectional exertion.
\n\t
• Option 3: Crucible of challenges – This refers to a severe test or trial, which is unrelated to the concept of unidirectional exertion.
\n\t
• Option 4: Social capital – This relates to the networks and relationships that enable society to function effectively, not unidirectional exertion.
\n\t
• Treadmill aptly describes the repetitive and unidirectional nature of exertion, which is why it is the correct answer.
\n