Search: ap-decreasing-limit-expert

Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

एक घटती समान्तर श्रेणी में प्रथम पद (72) और सार्व अंतर (-4) है। पहले (24) पदों का योग कितना होगा?

In a decreasing arithmetic progression the first term is (72) and the common difference is (-4). What is the sum of the first (24) terms?

Explanation opens after your attempt

Correct Answer

D. (624)

Step 1

Concept

(S_{24}=\frac{24}{2}[144+23(-4)]=624). Exam tip: handle the negative common difference carefully.

Step 2

Why this answer is correct

The correct answer is D. (624). (S_{24}=\frac{24}{2}[144+23(-4)]=624). Exam tip: handle the negative common difference carefully.

Step 3

Exam Tip

(S_{24}=\frac{24}{2}[144+23(-4)]=624) है। परीक्षा में ऋणात्मक सार्व अंतर का चिन्ह सावधानी से रखें।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 68

एक घटती समान्तर श्रेणी में प्रथम पद (65) और सार्व अंतर (-5) है। पहले (15) पदों का योग कितना होगा?

In a decreasing arithmetic progression the first term is (65) and the common difference is (-5). What is the sum of the first (15) terms?

Explanation opens after your attempt

Correct Answer

A. (450)

Step 1

Concept

(S_{15}=\frac{15}{2}[130+14(-5)]=450). Exam tip: handle the negative common difference carefully.

Step 2

Why this answer is correct

The correct answer is A. (450). (S_{15}=\frac{15}{2}[130+14(-5)]=450). Exam tip: handle the negative common difference carefully.

Step 3

Exam Tip

(S_{15}=\frac{15}{2}[130+14(-5)]=450) है। परीक्षा में ऋणात्मक सार्व अंतर का चिन्ह सावधानी से रखें।

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Question Medium Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 63

किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-4) नहीं है?

In which sequence are terms decreasing by an equal amount but (d) is not (-4)?

Explanation opens after your attempt

Correct Answer

B. $45,40,35,30,\ldots$

Step 1

Concept

In $45,40,35,30,\ldots$, (d=-5), not (-4). Check both value and sign in the options.

Step 2

Why this answer is correct

The correct answer is B. $45,40,35,30,\ldots$. In $45,40,35,30,\ldots$, (d=-5), not (-4). Check both value and sign in the options.

Step 3

Exam Tip

$45,40,35,30,\ldots$ में (d=-5) है, (-4) नहीं। विकल्पों में मान और चिह्न दोनों जांचें।

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Question Medium Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 61

किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-2) नहीं है?

In which sequence are the terms decreasing by an equal amount but (d) is not (-2)?

Explanation opens after your attempt

Correct Answer

A. $20,17,14,11,\ldots$

Step 1

Concept

In $20,17,14,11,\ldots$, (d=-3), not (-2). Check both sign and value in options.

Step 2

Why this answer is correct

The correct answer is A. $20,17,14,11,\ldots$. In $20,17,14,11,\ldots$, (d=-3), not (-2). Check both sign and value in options.

Step 3

Exam Tip

$20,17,14,11,\ldots$ में (d=-3) है, (-2) नहीं। विकल्पों में चिह्न और मान दोनों जांचें।

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Question Easy Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

निम्न में से कौन सा अनुक्रम घटती अंकगणितीय श्रेणी है?

Which of the following is a decreasing arithmetic progression?

Explanation opens after your attempt

Correct Answer

A. $50,45,40,35,\ldots$

Step 1

Concept

In $50,45,40,35,\ldots$, the equal difference is (-5). A decreasing arithmetic progression has negative (d).

Step 2

Why this answer is correct

The correct answer is A. $50,45,40,35,\ldots$. In $50,45,40,35,\ldots$, the equal difference is (-5). A decreasing arithmetic progression has negative (d).

Step 3

Exam Tip

$50,45,40,35,\ldots$ में समान अंतर (-5) है। घटती अंकगणितीय श्रेणी का (d) ऋणात्मक होता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $240,222,204,\ldots$ में (-150) से बड़ा अंतिम पद कौन-सा है?

In the AP $240,222,204,\ldots$, which is the last term greater than (-150)?

Explanation opens after your attempt

Correct Answer

B. (-144)

Step 1

Concept

(d=-18). After (-144), (-162) comes, so the last term greater than (-150) is (-144).

Step 2

Why this answer is correct

The correct answer is B. (-144). (d=-18). After (-144), (-162) comes, so the last term greater than (-150) is (-144).

Step 3

Exam Tip

(d=-18) है। (-144) के बाद (-162) आता है इसलिए (-150) से बड़ा अंतिम पद (-144) है।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $156,142,128,\ldots$ में (-120) से बड़ा अंतिम पद कौन-सा है?

In the AP $156,142,128,\ldots$, which is the last term greater than (-120)?

Explanation opens after your attempt

Correct Answer

B. (-112)

Step 1

Concept

(d=-14). (-110) is not in this AP, while after (-112), (-126) comes.

Step 2

Why this answer is correct

The correct answer is B. (-112). (d=-14). (-110) is not in this AP, while after (-112), (-126) comes.

Step 3

Exam Tip

(d=-14) है। (-110) इस श्रेणी में नहीं है, जबकि (-112) के बाद (-126) आता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी $121,109,97,\ldots$ में (-75) से बड़ा अंतिम पद कौन-सा है?

In the AP $121,109,97,\ldots$, which is the last term greater than (-75)?

Explanation opens after your attempt

Correct Answer

A. (-71)

Step 1

Concept

(d=-12). After (-71), the next term is (-83), so the last term greater than (-75) is (-71).

Step 2

Why this answer is correct

The correct answer is A. (-71). (d=-12). After (-71), the next term is (-83), so the last term greater than (-75) is (-71).

Step 3

Exam Tip

(d=-12) है। (-71) के बाद (-83) आता है, इसलिए (-75) से बड़ा अंतिम पद (-71) है।

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Question Expert Mathematics Arithmetic Progressions (AP) Introduction to APs and common difference. Class 10 Level 62

किस विकल्प में समांतर श्रेणी घट रही है?

Which option shows a decreasing AP?

Explanation opens after your attempt

Correct Answer

C. $20,17,14,11,\ldots$

Step 1

Concept

Here the common difference is (-3), so the terms are decreasing. In exams, a decreasing AP has negative (d).

Step 2

Why this answer is correct

The correct answer is C. $20,17,14,11,\ldots$. Here the common difference is (-3), so the terms are decreasing. In exams, a decreasing AP has negative (d).

Step 3

Exam Tip

यहां सामान्य अंतर (-3) है, इसलिए पद घट रहे हैं। परीक्षा में घटती समांतर श्रेणी का (d) ऋणात्मक होता है।

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Question Expert General Knowledge Indian History Indian Freedom Movement Class 10 Level 21

भारतीय सिविल सेवा परीक्षा की आयु सीमा घटाने के विरोध का राष्ट्रीय महत्व क्या था?

What was the national importance of opposing the reduction of age limit for the Indian Civil Service exam?

Explanation opens after your attempt

Correct Answer

A. इसने प्रशासन में भारतीयों के समान अवसर की मांग को राजनीतिक मुद्दा बनायाIt made equal opportunity for Indians in administration a political issue

Step 1

Concept

The ICS agitation was linked with political awareness of educated Indians. Exam tip is to remember Surendranath Banerjee.

Step 2

Why this answer is correct

The correct answer is A. इसने प्रशासन में भारतीयों के समान अवसर की मांग को राजनीतिक मुद्दा बनाया / It made equal opportunity for Indians in administration a political issue. The ICS agitation was linked with political awareness of educated Indians. Exam tip is to remember Surendranath Banerjee.

Step 3

Exam Tip

आई सी एस आंदोलन शिक्षित भारतीयों की राजनीतिक चेतना से जुड़ा था। परीक्षा में सुरेन्द्रनाथ बनर्जी को याद रखें।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $104,95,86,\ldots$ में (-50) से बड़ा अंतिम पद कौन-सा है?

In the AP $104,95,86,\ldots$, which is the last term greater than (-50)?

Explanation opens after your attempt

Correct Answer

A. (-41)

Step 1

Concept

(d=-9). The last term greater than (-50) is (-40) if it appears, so always verify actual terms before choosing.

Step 2

Why this answer is correct

The correct answer is A. (-41). (d=-9). The last term greater than (-50) is (-40) if it appears, so always verify actual terms before choosing.

Step 3

Exam Tip

(d=-9) है। (-50) से बड़ा अंतिम पद (-40) नहीं बल्कि (-40) श्रेणी में नहीं आता इसलिए (-40) से पहले सही पद (-40) जांचना चाहिए।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $85,77,69,\ldots$ में (-35) से बड़ा अंतिम पद कौन-सा है?

In the AP $85,77,69,\ldots$, which is the last term greater than (-35)?

Explanation opens after your attempt

Correct Answer

C. (-31)

Step 1

Concept

(d=-8). The last term greater than (-35) is (-27) because the next term is (-35).

Step 2

Why this answer is correct

The correct answer is C. (-31). (d=-8). The last term greater than (-35) is (-27) because the next term is (-35).

Step 3

Exam Tip

(d=-8) है। (-35) से बड़ा अंतिम पद (-27) है क्योंकि अगला पद (-35) है।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी $64,57,50,\ldots$ में (-20) से बड़ा अंतिम पद कौन-सा है?

In the AP $64,57,50,\ldots$, which is the last term greater than (-20)?

Explanation opens after your attempt

Correct Answer

A. (-13)

Step 1

Concept

(d=-7). The last term greater than (-20) is (-13) because the next term is (-20).

Step 2

Why this answer is correct

The correct answer is A. (-13). (d=-7). The last term greater than (-20) is (-13) because the next term is (-20).

Step 3

Exam Tip

(d=-7) है। (-20) से बड़ा अंतिम पद (-13) है क्योंकि अगला पद (-20) है।

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Question Expert General Knowledge World History Colonization and Decolonization Class 10 Level 77

नवउपनिवेशवाद में मुद्रा और वित्तीय निर्भरता किस प्रकार नीति स्वायत्तता को सीमित कर सकती है?

How can currency and financial dependence limit policy autonomy in neo colonialism?

Explanation opens after your attempt

Correct Answer

A. बाहरी ऋण विनिमय दबाव और निवेश शर्तें आर्थिक निर्णयों को प्रभावित कर सकती हैंExternal debt exchange pressure and investment conditions can affect economic decisions

Step 1

Concept

Financial dependence can create influence even without direct rule. For exams understand neo colonialism.

Step 2

Why this answer is correct

The correct answer is A. बाहरी ऋण विनिमय दबाव और निवेश शर्तें आर्थिक निर्णयों को प्रभावित कर सकती हैं / External debt exchange pressure and investment conditions can affect economic decisions. Financial dependence can create influence even without direct rule. For exams understand neo colonialism.

Step 3

Exam Tip

वित्तीय निर्भरता प्रत्यक्ष शासन के बिना भी प्रभाव पैदा कर सकती है। परीक्षा में नवउपनिवेशवाद समझें।

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Question Expert General Knowledge World History Colonization and Decolonization Class 10 Level 75

असमान व्यापारिक शर्तें नवस्वतंत्र देशों की विकास नीति को कैसे सीमित कर सकती थीं?

How could unequal trade terms limit development policy of newly independent countries?

Explanation opens after your attempt

Correct Answer

A. कच्चे माल के कम मूल्य और तैयार माल के अधिक मूल्य से निर्भरता बढ़ाकरBy increasing dependence through low raw material prices and high finished goods prices

Step 1

Concept

Unequal trade could increase economic dependence. For exams remember difference between raw materials and finished goods.

Step 2

Why this answer is correct

The correct answer is A. कच्चे माल के कम मूल्य और तैयार माल के अधिक मूल्य से निर्भरता बढ़ाकर / By increasing dependence through low raw material prices and high finished goods prices. Unequal trade could increase economic dependence. For exams remember difference between raw materials and finished goods.

Step 3

Exam Tip

असमान व्यापार आर्थिक निर्भरता को बढ़ा सकता था। परीक्षा में कच्चा माल और तैयार माल का अंतर याद रखें।

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Question Expert General Knowledge World History Colonization and Decolonization Class 10 Level 75

इंडोचीन संघर्ष को केवल वियतनाम तक सीमित करना क्यों गलत है?

Why is it wrong to limit the Indochina struggle only to Vietnam?

Explanation opens after your attempt

Correct Answer

A. क्योंकि फ्रांसीसी इंडोचीन में वियतनाम लाओस और कंबोडिया जुड़े थेBecause French Indochina included Vietnam Laos and Cambodia

Step 1

Concept

Indochina was an example of regional colonial control. For exams remember Laos and Cambodia with Vietnam.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि फ्रांसीसी इंडोचीन में वियतनाम लाओस और कंबोडिया जुड़े थे / Because French Indochina included Vietnam Laos and Cambodia. Indochina was an example of regional colonial control. For exams remember Laos and Cambodia with Vietnam.

Step 3

Exam Tip

इंडोचीन क्षेत्रीय औपनिवेशिक नियंत्रण का उदाहरण था। परीक्षा में वियतनाम के साथ लाओस और कंबोडिया भी याद रखें।

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Question Hard General Knowledge World History Colonization and Decolonization Class 10 Level 75

उपनिवेश मुक्ति को केवल स्वतंत्रता दिवस तक सीमित करना गलत क्यों है?

Why is it wrong to limit decolonization only to independence day?

Explanation opens after your attempt

Correct Answer

A. क्योंकि स्वतंत्रता के बाद राष्ट्र निर्माण आर्थिक निर्भरता और पहचान की चुनौतियां जारी रहींBecause nation building economic dependence and identity challenges continued after independence

Step 1

Concept

Decolonization is a process not only a date. For exams write post independence challenges.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि स्वतंत्रता के बाद राष्ट्र निर्माण आर्थिक निर्भरता और पहचान की चुनौतियां जारी रहीं / Because nation building economic dependence and identity challenges continued after independence. Decolonization is a process not only a date. For exams write post independence challenges.

Step 3

Exam Tip

उपनिवेश मुक्ति एक प्रक्रिया है केवल एक तारीख नहीं। परीक्षा में स्वतंत्रता बाद की चुनौतियां लिखें।

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Question Expert General Knowledge World History Important Historical Events Class 10 Level 74

प्राग स्प्रिंग के दमन ने सुधारवादी समाजवाद की कौन सी सीमा दिखाई?

What limit of reformist socialism did the suppression of Prague Spring show?

Explanation opens after your attempt

Correct Answer

A. मॉस्को नियंत्रण के बाहर स्वतंत्र सुधार स्वीकार्य नहीं थेIndependent reforms outside Moscow control were not acceptable

Step 1

Concept

Prague Spring showed conflict between reform and Soviet control. For exams remember the Brezhnev Doctrine.

Step 2

Why this answer is correct

The correct answer is A. मॉस्को नियंत्रण के बाहर स्वतंत्र सुधार स्वीकार्य नहीं थे / Independent reforms outside Moscow control were not acceptable. Prague Spring showed conflict between reform and Soviet control. For exams remember the Brezhnev Doctrine.

Step 3

Exam Tip

प्राग स्प्रिंग ने सुधार और सोवियत नियंत्रण का टकराव दिखाया। परीक्षा में ब्रेझनेव सिद्धांत याद रखें।

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Question Expert General Knowledge World History Important Historical Events Class 10 Level 74

फ्रांसीसी क्रांति में टेरर के दौर से क्रांतिकारी आदर्शों की कौन सी सीमा स्पष्ट होती है?

What limit of revolutionary ideals becomes clear from the Reign of Terror in the French Revolution?

Explanation opens after your attempt

Correct Answer

A. आदर्शों की रक्षा के नाम पर दमनकारी सत्ता बन सकती हैRepressive power can emerge in the name of protecting ideals

Step 1

Concept

The Terror showed tension between liberty and repression. For exams analyze the revolution in a balanced way.

Step 2

Why this answer is correct

The correct answer is A. आदर्शों की रक्षा के नाम पर दमनकारी सत्ता बन सकती है / Repressive power can emerge in the name of protecting ideals. The Terror showed tension between liberty and repression. For exams analyze the revolution in a balanced way.

Step 3

Exam Tip

टेरर ने स्वतंत्रता और दमन के बीच तनाव दिखाया। परीक्षा में क्रांति का संतुलित विश्लेषण करें।

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Question Expert General Knowledge World History Important Historical Events Class 10 Level 72

प्राग स्प्रिंग के दमन से सुधारवादी समाजवाद की कौन सी सीमा सामने आई?

What limit of reformist socialism became clear from the suppression of Prague Spring?

Explanation opens after your attempt

Correct Answer

A. सोवियत खेमे में सुधार तभी तक संभव थे जब तक मॉस्को नियंत्रण स्वीकार रहेReforms were possible in the Soviet bloc only while Moscow control was accepted

Step 1

Concept

Prague Spring showed conflict between desire for reform and Soviet control. For exams remember the Brezhnev Doctrine.

Step 2

Why this answer is correct

The correct answer is A. सोवियत खेमे में सुधार तभी तक संभव थे जब तक मॉस्को नियंत्रण स्वीकार रहे / Reforms were possible in the Soviet bloc only while Moscow control was accepted. Prague Spring showed conflict between desire for reform and Soviet control. For exams remember the Brezhnev Doctrine.

Step 3

Exam Tip

प्राग स्प्रिंग ने सुधार की इच्छा और सोवियत नियंत्रण का टकराव दिखाया। परीक्षा में ब्रेझनेव सिद्धांत याद रखें।

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Question Expert General Knowledge World History Important Historical Events Class 10 Level 72

हैती क्रांति ने यूरोपीय उदार आदर्शों की किस सीमा को उजागर किया?

Which limit of European liberal ideals did the Haitian Revolution expose?

Explanation opens after your attempt

Correct Answer

A. स्वतंत्रता की भाषा के साथ उपनिवेशों में दासता जारी रहने का विरोधाभासContradiction of slavery continuing in colonies alongside language of liberty

Step 1

Concept

The Haitian Revolution linked the ideal of liberty with anti slavery struggle. For exams distinguish it within Atlantic revolutions.

Step 2

Why this answer is correct

The correct answer is A. स्वतंत्रता की भाषा के साथ उपनिवेशों में दासता जारी रहने का विरोधाभास / Contradiction of slavery continuing in colonies alongside language of liberty. The Haitian Revolution linked the ideal of liberty with anti slavery struggle. For exams distinguish it within Atlantic revolutions.

Step 3

Exam Tip

हैती क्रांति ने स्वतंत्रता के आदर्श को दासता विरोधी संघर्ष से जोड़ा। परीक्षा में इसे अटलांटिक क्रांतियों में अलग पहचानें।

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Question Expert General Knowledge World History Important Historical Events Class 10 Level 70

वियतनाम युद्ध ने कंटेनमेंट नीति की व्यवहारिक सीमा क्यों दिखायी?

Why did the Vietnam War show the practical limit of containment policy?

Explanation opens after your attempt

Correct Answer

A. स्थानीय राष्ट्रवाद और गुरिल्ला युद्ध को बाहरी सैन्य शक्ति से रोकना कठिन थाLocal nationalism and guerrilla war were hard to stop with external military power

Step 1

Concept

The Vietnam War showed conflict between local context and superpower strategy. For exams remember Domino Theory.

Step 2

Why this answer is correct

The correct answer is A. स्थानीय राष्ट्रवाद और गुरिल्ला युद्ध को बाहरी सैन्य शक्ति से रोकना कठिन था / Local nationalism and guerrilla war were hard to stop with external military power. The Vietnam War showed conflict between local context and superpower strategy. For exams remember Domino Theory.

Step 3

Exam Tip

वियतनाम युद्ध ने स्थानीय संदर्भ और महाशक्ति रणनीति के टकराव को दिखाया। परीक्षा में डोमिनो सिद्धांत याद रखें।

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Question Expert General Knowledge World History Important Historical Events Class 10 Level 70

म्यूनिख समझौता अंतरराष्ट्रीय कूटनीति में तुष्टीकरण की सीमा कैसे दिखाता है?

How does the Munich Agreement show the limit of appeasement in international diplomacy?

Explanation opens after your attempt

Correct Answer

A. आक्रामक विस्तारवाद को रोकने के बजाय समय दिया गयाAggressive expansionism was given time instead of being stopped

Step 1

Concept

The Munich Agreement failed to stop Hitler's aggression. For exams connect it with the background of World War II.

Step 2

Why this answer is correct

The correct answer is A. आक्रामक विस्तारवाद को रोकने के बजाय समय दिया गया / Aggressive expansionism was given time instead of being stopped. The Munich Agreement failed to stop Hitler's aggression. For exams connect it with the background of World War II.

Step 3

Exam Tip

म्यूनिख समझौता हिटलर की आक्रामकता रोकने में सफल नहीं हुआ। परीक्षा में इसे द्वितीय विश्व युद्ध की पृष्ठभूमि से जोड़ें।

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Question Expert General Knowledge World History Important Historical Events Class 10 Level 71

शीत युद्ध में परमाणु प्रतिरोध ने प्रत्यक्ष महाशक्ति युद्ध को क्यों सीमित किया?

Why did nuclear deterrence limit direct superpower war during the Cold War?

Explanation opens after your attempt

Correct Answer

A. जवाबी परमाणु विनाश के डर ने सावधानी पैदा कीFear of retaliatory nuclear destruction created caution

Step 1

Concept

Nuclear fear prevented direct war but proxy wars increased. Exam tip: understand deterrence and proxy wars together.

Step 2

Why this answer is correct

The correct answer is A. जवाबी परमाणु विनाश के डर ने सावधानी पैदा की / Fear of retaliatory nuclear destruction created caution. Nuclear fear prevented direct war but proxy wars increased. Exam tip: understand deterrence and proxy wars together.

Step 3

Exam Tip

परमाणु भय ने प्रत्यक्ष युद्ध को रोका लेकिन प्रतिनिधि युद्ध बढ़े। परीक्षा में प्रतिरोध और प्रतिनिधि युद्ध को साथ समझें।

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Question Hard General Knowledge World History Important Historical Events Class 10 Level 73

म्यूनिख समझौता तुष्टिकरण नीति की सीमा क्यों दिखाता है?

Why does the Munich Agreement show the limit of appeasement policy?

Explanation opens after your attempt

Correct Answer

A. हिटलर की मांग मानने से आक्रमणकारी नीति नहीं रुकीAccepting Hitler's demand did not stop aggressive policy

Step 1

Concept

The Munich Agreement tried to avoid war but did not stop aggression. Exam tip: study appeasement in the background of World War II.

Step 2

Why this answer is correct

The correct answer is A. हिटलर की मांग मानने से आक्रमणकारी नीति नहीं रुकी / Accepting Hitler's demand did not stop aggressive policy. The Munich Agreement tried to avoid war but did not stop aggression. Exam tip: study appeasement in the background of World War II.

Step 3

Exam Tip

म्यूनिख समझौता युद्ध टालने की कोशिश था लेकिन इससे आक्रामकता नहीं रुकी। परीक्षा में तुष्टिकरण को द्वितीय विश्व युद्ध की पृष्ठभूमि में पढ़ें।

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Question Medium General Knowledge World History Important Historical Events Class 10 Level 74

प्राग स्प्रिंग का दमन सोवियत खेमे में किस सीमा को दिखाता है?

The suppression of Prague Spring showed which limit within the Soviet bloc?

Explanation opens after your attempt

Correct Answer

B. स्वतंत्र समाजवादी सुधारों की सीमाLimits of independent socialist reforms

Step 1

Concept

Prague Spring tried reform but Soviet intervention stopped it. For exams connect it with the Brezhnev Doctrine.

Step 2

Why this answer is correct

The correct answer is B. स्वतंत्र समाजवादी सुधारों की सीमा / Limits of independent socialist reforms. Prague Spring tried reform but Soviet intervention stopped it. For exams connect it with the Brezhnev Doctrine.

Step 3

Exam Tip

प्राग स्प्रिंग ने सुधार की कोशिश की पर सोवियत हस्तक्षेप ने उसे रोक दिया। परीक्षा में इसे ब्रेझनेव सिद्धांत से जोड़ें।

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Question Expert General Knowledge World History Famous World Leaders Class 10 Level 69

ब्रेझनेव सिद्धांत ने समाजवादी देशों की संप्रभुता को कैसे सीमित किया?

How did the Brezhnev Doctrine limit the sovereignty of socialist countries?

Explanation opens after your attempt

Correct Answer

A. सोवियत हित के नाम पर हस्तक्षेप को सही ठक्षेप को सही ठहराकरBy justifying intervention in the name of Soviet interests

Step 1

Concept

The Brezhnev Doctrine was a justification of Soviet control over Eastern Europe. For exams connect it with the Prague Spring.

Step 2

Why this answer is correct

The correct answer is A. सोवियत हित के नाम पर हस्तक्षेप को सही ठक्षेप को सही ठहराकर / By justifying intervention in the name of Soviet interests. The Brezhnev Doctrine was a justification of Soviet control over Eastern Europe. For exams connect it with the Prague Spring.

Step 3

Exam Tip

ब्रेझनेव सिद्धांत पूर्वी यूरोप पर सोवियत नियंत्रण का तर्क था। परीक्षा में इसे प्राग स्प्रिंग से जोड़ें।

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Question Expert General Knowledge World History Famous World Leaders Class 10 Level 67

ओटो वॉन बिस्मार्क ने किस नीति से समाजवादी प्रभाव को सीमित करने और मजदूरों को आकर्षित करने का प्रयास किया?

With which policy did Otto von Bismarck try to limit socialist influence and attract workers?

Explanation opens after your attempt

Correct Answer

B. सामाजिक बीमा नीतिSocial Insurance Policy

Step 1

Concept

Bismarck used plans like social insurance to attract workers. For exams connect him not only with war but also with state policy.

Step 2

Why this answer is correct

The correct answer is B. सामाजिक बीमा नीति / Social Insurance Policy. Bismarck used plans like social insurance to attract workers. For exams connect him not only with war but also with state policy.

Step 3

Exam Tip

बिस्मार्क ने सामाजिक बीमा जैसी योजनाओं से मजदूरों को आकर्षित किया। परीक्षा में उसे केवल युद्ध नहीं बल्कि राज्य नीति से भी जोड़ें।

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Question Medium General Knowledge World History Revolutions of the World Class 10 Level 55

अधिकार विधेयक सोलह सौ नवासी ने इंग्लैंड में क्या सीमित किया?

What did the Bill of Rights 1689 limit in England?

Explanation opens after your attempt

Correct Answer

B. राजा की मनमानी शक्तिArbitrary power of the king

Step 1

Concept

The Bill of Rights placed constitutional limits on royal power. For exams connect it with parliamentary rights.

Step 2

Why this answer is correct

The correct answer is B. राजा की मनमानी शक्ति / Arbitrary power of the king. The Bill of Rights placed constitutional limits on royal power. For exams connect it with parliamentary rights.

Step 3

Exam Tip

अधिकार विधेयक ने राजा की शक्ति को संवैधानिक सीमाओं में रखा। परीक्षा में इसे संसद के अधिकारों से जोड़ें।

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Question Easy General Knowledge World History Revolutions of the World Class 10 Level 59

यंग तुर्क आंदोलन किस शासन व्यवस्था को सीमित करना चाहता था?

The Young Turk movement wanted to limit which type of rule?

Explanation opens after your attempt

Correct Answer

B. सुल्तान की निरंकुश सत्ताSultan's autocratic power

Step 1

Concept

The Young Turks wanted constitutional limits on the Sultan's autocratic power. For exams connect it with Ottoman reform movements.

Step 2

Why this answer is correct

The correct answer is B. सुल्तान की निरंकुश सत्ता / Sultan's autocratic power. The Young Turks wanted constitutional limits on the Sultan's autocratic power. For exams connect it with Ottoman reform movements.

Step 3

Exam Tip

यंग तुर्क सुल्तान की निरंकुश सत्ता पर संवैधानिक नियंत्रण चाहते थे। परीक्षा में इसे ओटोमन सुधार आंदोलन से जोड़ें।

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Question Expert General Knowledge World History World Wars Class 10 Level 54

इम्फाल कोहिमा की लड़ाइयों में भूगोल और रसद ने जापानी अभियान को कैसे सीमित किया?

How did geography and logistics limit the Japanese campaign at Imphal-Kohima?

Explanation opens after your attempt

Correct Answer

A. कठिन terrain और लंबी आपूर्ति रेखाओं ने आक्रमण को कमजोर कियाDifficult terrain and long supply lines weakened the offensive

Step 1

Concept

The geography of northeast India and Burma was difficult for the campaign. For exams study the Asian front with maps.

Step 2

Why this answer is correct

The correct answer is A. कठिन terrain और लंबी आपूर्ति रेखाओं ने आक्रमण को कमजोर किया / Difficult terrain and long supply lines weakened the offensive. The geography of northeast India and Burma was difficult for the campaign. For exams study the Asian front with maps.

Step 3

Exam Tip

पूर्वोत्तर भारत और बर्मा क्षेत्र का भूगोल अभियान के लिए कठिन था। परीक्षा में एशियाई मोर्चे को मानचित्र से पढ़ें।

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Question Expert General Knowledge World History World Wars Class 10 Level 52

नूर्नबर्ग सिद्धांतों ने आदेश पालन की दलील को क्यों सीमित किया?

Why did the Nuremberg Principles limit the defense of following orders?

Explanation opens after your attempt

Correct Answer

A. क्योंकि गंभीर अंतरराष्ट्रीय अपराधों में व्यक्ति की जिम्मेदारी भी मानी गईBecause individual responsibility was recognized in grave international crimes

Step 1

Concept

Nuremberg showed that state orders are not a complete defense for crimes. For exams remember individual accountability.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि गंभीर अंतरराष्ट्रीय अपराधों में व्यक्ति की जिम्मेदारी भी मानी गई / Because individual responsibility was recognized in grave international crimes. Nuremberg showed that state orders are not a complete defense for crimes. For exams remember individual accountability.

Step 3

Exam Tip

नूर्नबर्ग ने बताया कि राज्य आदेश अपराध से पूर्ण बचाव नहीं है। परीक्षा में व्यक्तिगत जवाबदेही याद रखें।

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Question Expert General Knowledge World History World Wars Class 10 Level 50

युद्ध योजनाओं की समय सारिणी ने 1914 की कूटनीति को कैसे सीमित किया?

How did military timetables limit diplomacy in 1914?

Explanation opens after your attempt

Correct Answer

C. उन्होंने लामबंदी को तेज किया और समझौते के लिए समय घटायाThey accelerated mobilization and reduced time for compromise

Step 1

Concept

Rapid military preparation pressured leaders to decide quickly. For exams understand the relation between military planning and diplomacy.

Step 2

Why this answer is correct

The correct answer is C. उन्होंने लामबंदी को तेज किया और समझौते के लिए समय घटाया / They accelerated mobilization and reduced time for compromise. Rapid military preparation pressured leaders to decide quickly. For exams understand the relation between military planning and diplomacy.

Step 3

Exam Tip

तेज सैन्य तैयारी ने नेताओं पर जल्दी निर्णय लेने का दबाव डाला। परीक्षा में सैन्य योजना और कूटनीति का संबंध समझें।

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Question Hard General Knowledge World History World Wars Class 10 Level 53

मॉस्को के पास जर्मन रुकावट ने ब्लिट्जक्रिग की कौन सी सीमा दिखायी?

What limit of Blitzkrieg was shown by the German halt near Moscow?

Explanation opens after your attempt

Correct Answer

A. तेज आक्रमण लंबी दूरी मौसम और रसद के सामने कमजोर पड़ सकता थाRapid attack could weaken before distance weather and logistics

Step 1

Concept

The Moscow campaign showed that speed was not enough when supply and weather were difficult. For exams connect geography with strategy.

Step 2

Why this answer is correct

The correct answer is A. तेज आक्रमण लंबी दूरी मौसम और रसद के सामने कमजोर पड़ सकता था / Rapid attack could weaken before distance weather and logistics. The Moscow campaign showed that speed was not enough when supply and weather were difficult. For exams connect geography with strategy.

Step 3

Exam Tip

मॉस्को अभियान ने दिखाया कि गति पर्याप्त नहीं जब आपूर्ति और मौसम कठिन हों। परीक्षा में भूगोल को रणनीति से जोड़ें।

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Question Expert General Knowledge Indian History Modern Indian History Class 10 Level 14

1857 के विद्रोह में धार्मिक आशंका को केवल कारतूस तक सीमित मानना क्यों अधूरा है?

Why is it incomplete to limit religious fear in 1857 only to cartridges?

Explanation opens after your attempt

Correct Answer

A. क्योंकि सामाजिक सुधारों और मिशनरी गतिविधियों से भी संदेह बढ़े थेBecause social reforms and missionary activities also increased suspicion

Step 1

Concept

Cartridges were the immediate cause but religious and cultural insecurity had already grown. Exam tip: understand causes as multi-layered.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि सामाजिक सुधारों और मिशनरी गतिविधियों से भी संदेह बढ़े थे / Because social reforms and missionary activities also increased suspicion. Cartridges were the immediate cause but religious and cultural insecurity had already grown. Exam tip: understand causes as multi-layered.

Step 3

Exam Tip

कारतूस तत्काल कारण था पर धार्मिक और सांस्कृतिक असुरक्षा पहले से बढ़ रही थी। परीक्षा में कारणों को बहुस्तरीय समझें।

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Question Expert General Knowledge Indian History Medieval Indian History Class 10 Level 9

अलाउद्दीन खिलजी ने उलेमा के राजनीतिक प्रभाव को सीमित करने की कोशिश क्यों की?

Why did Alauddin Khalji try to limit the political influence of the ulema?

Explanation opens after your attempt

Correct Answer

A. सुल्तान की निरंकुश सत्ता को मजबूत करने के लिएTo strengthen the Sultan's absolute authority

Step 1

Concept

Alauddin wanted state policy to remain separate from clerical control. Exam tip is to connect it with his strong central rule.

Step 2

Why this answer is correct

The correct answer is A. सुल्तान की निरंकुश सत्ता को मजबूत करने के लिए / To strengthen the Sultan's absolute authority. Alauddin wanted state policy to remain separate from clerical control. Exam tip is to connect it with his strong central rule.

Step 3

Exam Tip

अलाउद्दीन ने राज्य नीति को धार्मिक वर्ग के नियंत्रण से अलग रखना चाहा। परीक्षा में इसे उसके मजबूत केंद्रीय शासन से जोड़ें।

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Question Hard General Knowledge Indian History Ancient Indian History Class 10 Level 1

सुत्कागेंडोर को सिंधु सभ्यता के किस भौगोलिक छोर से जोड़ा जाता है?

Sutkagendor is associated with which geographical limit of the Indus Civilization?

Explanation opens after your attempt

Correct Answer

B. पश्चिमी सीमाWestern limit

Step 1

Concept

Sutkagendor is linked with the western limit of the Indus Civilization. For exams, remember frontier sites with directions.

Step 2

Why this answer is correct

The correct answer is B. पश्चिमी सीमा / Western limit. Sutkagendor is linked with the western limit of the Indus Civilization. For exams, remember frontier sites with directions.

Step 3

Exam Tip

सुत्कागेंडोर को सिंधु सभ्यता के पश्चिमी छोर से जोड़ा जाता है। परीक्षा में सीमांत स्थलों को दिशा सहित याद रखें।

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Question Expert Social Science Chapter 2: Nationalism in India The Sense of Collective Belonging Class 10 Level 27

राष्ट्रीय आंदोलन में लोक संस्कृति को महत्व देने से इतिहास लेखन की कौन सी सीमा टूटती थी?

Giving importance to folk culture in the national movement challenged which limit of history writing?

Explanation opens after your attempt

Correct Answer

A. इतिहास को केवल राजाओं और युद्धों तक सीमित रखनाLimiting history only to kings and wars

Step 1

Concept

Older history often focused on kings and wars.

Step 2

Why this answer is correct

Folk culture made ordinary people part of the national story.

Step 3

Exam Tip

When a question asks about a limitation, identify the old framework. चरण 1: पुराना इतिहास अक्सर राजाओं और युद्धों पर केंद्रित था। चरण 2: लोक संस्कृति ने आम लोगों को राष्ट्रीय कथा का हिस्सा बनाया। चरण 3: प्रश्न में सीमा पूछी जाए तो पुराने ढांचे को पहचानें।

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Question Hard Social Science Chapter 2: Nationalism in India Towards Civil Disobedience Class 10 Level 22

साइमन आयोग के विरोध को केवल प्रतिनिधित्व की कमी तक सीमित करना क्यों अधूरा होगा?

Why would it be incomplete to limit the protest against the Simon Commission only to lack of representation?

Explanation opens after your attempt

Correct Answer

A. क्योंकि इसने भारतीय आत्मसम्मान और स्वशासन की मांग को भी तेज कियाBecause it also sharpened Indian self-respect and the demand for self-rule

Step 1

Concept

The absence of Indian members showed lack of representation.

Step 2

Why this answer is correct

It strengthened the feeling that Indians should control their own future.

Step 3

Exam Tip

In exams connect it with self-respect and demand for self-rule. चरण 1: आयोग में भारतीय सदस्य न होना प्रतिनिधित्व की कमी दिखाता था। चरण 2: इससे भारतीयों में अपने भविष्य पर अपना अधिकार चाहने की भावना मजबूत हुई। चरण 3: परीक्षा में इसे आत्मसम्मान और स्वशासन की मांग से जोड़ें।

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Question Medium Social Science Chapter 2: Nationalism in India Differing Strands within the Movement Class 10 Level 19

आंतरिक प्रवासन कानून ने बागान मजदूरों की स्वतंत्रता को कैसे सीमित किया?

How did the Inland Emigration Act limit the freedom of plantation workers?

Explanation opens after your attempt

Correct Answer

A. वे बिना अनुमति बागान छोड़ नहीं सकते थेThey could not leave plantations without permission

Step 1

Concept

This law controlled the movement of plantation workers.

Step 2

Why this answer is correct

It was difficult for them to leave plantations without permission.

Step 3

Exam Tip

Remember this law with the lack of freedom of plantation workers. चरण 1: यह कानून बागान मजदूरों की आवाजाही पर नियंत्रण रखता था। चरण 2: बिना अनुमति बागान छोड़ना उनके लिए कठिन था। चरण 3: इस कानून को बागान मजदूरों की अस्वतंत्रता से जोड़कर याद करें।

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Question Expert Social Science Chapter 2: Nationalism in India The First World War, Khilafat, and Non-Cooperation Class 10 Level 18

बागान मजदूरों पर लागू नियमों ने उनकी स्वतंत्रता को कैसे सीमित किया?

How did rules applied to plantation workers limit their freedom?

Explanation opens after your attempt

Correct Answer

A. वे बिना अनुमति बागान छोड़ नहीं सकते थेThey could not leave plantations without permission

Step 1

Concept

The plantation labour system controlled workers' movement.

Step 2

Why this answer is correct

Leaving the plantation without permission was difficult.

Step 3

Exam Tip

So swaraj meant personal freedom to them. चरण 1: बागान श्रम व्यवस्था में मजदूरों की आवाजाही नियंत्रित थी। चरण 2: बिना अनुमति बागान छोड़ना कठिन था। चरण 3: इसलिए स्वराज उनके लिए निजी आजादी का अर्थ रखता था।

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Question Hard Science Chemical Substances – Nature and Behaviour Acids, Bases, and Salts Class 10 Level 14

दाँतों के इनेमल को घुलने से बचाने के लिए मुँह का पीएच किस सीमा से ऊपर रखना बेहतर है?

To protect tooth enamel from dissolving, it is better to keep mouth pH above which limit?

Explanation opens after your attempt

Correct Answer

B. लगभग पाँच दशमलव पाँचAbout 5.5

Step 1

Concept

Tooth enamel is affected at low pH.

Step 2

Why this answer is correct

Below about 5.5, enamel can start dissolving.

Step 3

Exam Tip

So keeping mouth pH above this limit is better for teeth. चरण 1: दाँतों का इनेमल कम पीएच पर प्रभावित होता है। चरण 2: लगभग पाँच दशमलव पाँच से नीचे इनेमल घुलना शुरू हो सकता है। चरण 3: इसलिए मुँह का पीएच इस सीमा से ऊपर रखना दाँतों के लिए बेहतर है।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 68

एक सीढ़ी में सबसे नीचे (45) ईंटें हैं और हर ऊपर वाली पंक्ति में (3) ईंटें कम हैं। (12) पंक्तियों में कुल कितनी ईंटें होंगी?

A stair pattern has (45) bricks in the bottom row and (3) fewer bricks in each upper row. How many bricks are there in (12) rows?

Explanation opens after your attempt

Correct Answer

C. (342)

Step 1

Concept

This is the AP $45,42,39,\ldots$, and (S_{12}=6[90+11(-3)]=342). Exam tip: treat the decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is C. (342). This is the AP $45,42,39,\ldots$, and (S_{12}=6[90+11(-3)]=342). Exam tip: treat the decrease as a negative common difference.

Step 3

Exam Tip

यह $45,42,39,\ldots$ श्रेणी है और (S_{12}=6[90+11(-3)]=342)। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 68

एक समान्तर श्रेणी में प्रथम पद (25) और सार्व अंतर (-2) है। पहले (20) पदों का औसत क्या होगा?

In an arithmetic progression the first term is (25) and the common difference is (-2). What is the average of the first (20) terms?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

The last term is (25+19(-2)=-13), so the average is $\frac{25-13}{2}=6$. Exam tip: the average is the average of first and last terms.

Step 2

Why this answer is correct

The correct answer is B. (6). The last term is (25+19(-2)=-13), so the average is $\frac{25-13}{2}=6$. Exam tip: the average is the average of first and last terms.

Step 3

Exam Tip

अंतिम पद (25+19(-2)=-13) है इसलिए औसत $\frac{25-13}{2}=6$ है। परीक्षा में औसत प्रथम और अंतिम पद का औसत होता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 68

एक समान्तर श्रेणी में (a=18) और (d=-4) है। पहले कितने पदों का योग (144) होगा?

In an arithmetic progression (a=18) and (d=-4). How many first terms have sum (144)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

Using the sum formula gives (n=9). Exam tip: even in a decreasing AP, take the positive value of (n).

Step 2

Why this answer is correct

The correct answer is B. (9). Using the sum formula gives (n=9). Exam tip: even in a decreasing AP, take the positive value of (n).

Step 3

Exam Tip

योग सूत्र रखने पर समीकरण से (n=9) मिलता है। परीक्षा में घटती श्रेणी में भी धनात्मक (n) ही लें।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी $81,75,69,\ldots$ के कितने आरम्भिक पदों का योग (315) होगा?

How many initial terms of the arithmetic progression $81,75,69,\ldots$ have sum (315)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

Solving (\frac{n}{2}[162-6(n-1)]=315) gives (n=7). Exam tip: the same sum formula works for decreasing progressions too.

Step 2

Why this answer is correct

The correct answer is C. (7). Solving (\frac{n}{2}[162-6(n-1)]=315) gives (n=7). Exam tip: the same sum formula works for decreasing progressions too.

Step 3

Exam Tip

(\frac{n}{2}[162-6(n-1)]=315) हल करने पर (n=7) मिलता है। परीक्षा में घटती श्रेणी में भी वही योग सूत्र लागू होता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $310,291,272,\ldots$ में (75) से छोटा पहला पद कौन-सा है?

In the AP $310,291,272,\ldots$, what is the first term less than (75)?

Explanation opens after your attempt

Correct Answer

B. (63)

Step 1

Concept

Here (d=-19). After (82), (63) comes, so the first term less than (75) is (63).

Step 2

Why this answer is correct

The correct answer is B. (63). Here (d=-19). After (82), (63) comes, so the first term less than (75) is (63).

Step 3

Exam Tip

यहां (d=-19) है। (82) के बाद (63) आता है इसलिए (75) से छोटा पहला पद (63) है।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $221,204,187,\ldots$ में (50) से छोटा पहला पद कौन-सा है?

In the AP $221,204,187,\ldots$, what is the first term less than (50)?

Explanation opens after your attempt

Correct Answer

B. (34)

Step 1

Concept

Here (d=-17). After (51), (34) comes, so the first term less than (50) is (34).

Step 2

Why this answer is correct

The correct answer is B. (34). Here (d=-17). After (51), (34) comes, so the first term less than (50) is (34).

Step 3

Exam Tip

यहां (d=-17) है। (51) के बाद (34) आता है, इसलिए (50) से छोटा पहला पद (34) है।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी $169,154,139,\ldots$ में (40) से छोटा पहला पद कौन-सा है?

In the AP $169,154,139,\ldots$, what is the first term less than (40)?

Explanation opens after your attempt

Correct Answer

B. (34)

Step 1

Concept

Here (d=-15). After (49), the next term is (34), so the first term less than (40) is (34).

Step 2

Why this answer is correct

The correct answer is B. (34). Here (d=-15). After (49), the next term is (34), so the first term less than (40) is (34).

Step 3

Exam Tip

यहां (d=-15) है। (49) के बाद (34) आता है, इसलिए (40) से छोटा पहला पद (34) है।

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Question Expert Science Chemical Substances – Nature and Behaviour Chemical Reactions and Equations Class 10 Level 5

धातु क धातु ख को और धातु ख धातु ग को उनके लवणों से हटाती है। क्रियाशीलता का सही घटता क्रम क्या है?

Metal A displaces metal B and metal B displaces metal C from their salts. What is the correct decreasing order of reactivity?

Explanation opens after your attempt

Correct Answer

A. क फिर ख फिर गA then B then C

Step 1

Concept

A metal that displaces another is more reactive.

Step 2

Why this answer is correct

A is more reactive than B and B is more reactive than C.

Step 3

Exam Tip

Therefore decreasing order is A then B then C. चरण 1: जो धातु दूसरी को हटाती है वह अधिक क्रियाशील होती है। चरण 2: क ख से अधिक और ख ग से अधिक है। चरण 3: इसलिए घटता क्रम क फिर ख फिर ग होगा।

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Question Expert Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 72

एक सीढ़ीनुमा दीवार में नीचे की पंक्ति में (210) पत्थर हैं और हर ऊपर की पंक्ति में (10) पत्थर कम हैं। किस पंक्ति में (70) पत्थर होंगे?

A stepped wall has (210) stones in the bottom row and (10) fewer stones in each upper row. Which row will have (70) stones?

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

From (210+(n-1)(-10)=70), (n=15). Exam tip: keep (d) negative in a decreasing AP.

Step 2

Why this answer is correct

The correct answer is C. (15). From (210+(n-1)(-10)=70), (n=15). Exam tip: keep (d) negative in a decreasing AP.

Step 3

Exam Tip

(210+(n-1)(-10)=70) से (n=15) मिलता है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक रखें।

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Question Expert Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 72

एक कारखाना पहले दिन (720) इकाइयां बनाता है और हर अगले दिन (24) इकाइयां कम बनाता है। पहले (16) दिनों में कुल उत्पादन कितना होगा?

A factory makes (720) units on the first day and (24) fewer units each next day. What is the total production in the first (16) days?

Explanation opens after your attempt

Correct Answer

D. (8640)

Step 1

Concept

The production is the decreasing AP $720,696,672,\ldots$ and $S_{16}=8640$. Exam tip: treat decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is D. (8640). The production is the decreasing AP $720,696,672,\ldots$ and $S_{16}=8640$. Exam tip: treat decrease as a negative common difference.

Step 3

Exam Tip

उत्पादन $720,696,672,\ldots$ घटती समान्तर श्रेणी है और $S_{16}=8640$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Expert Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 71

एक सीढ़ी में नीचे की पंक्ति में (180) टाइलें हैं और हर ऊपर की पंक्ति में (8) टाइलें कम हैं। किस पंक्ति में (68) टाइलें होंगी?

A staircase has (180) tiles in the bottom row and (8) fewer tiles in each upper row. Which row will have (68) tiles?

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

From (180+(n-1)(-8)=68), (n=15). Exam tip: handle the sign carefully in a decreasing AP.

Step 2

Why this answer is correct

The correct answer is C. (15). From (180+(n-1)(-8)=68), (n=15). Exam tip: handle the sign carefully in a decreasing AP.

Step 3

Exam Tip

(180+(n-1)(-8)=68) से (n=15) मिलता है। परीक्षा में घटती श्रेणी में चिन्ह सावधानी से रखें।

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Question Expert Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 71

एक फैक्टरी पहले दिन (600) इकाइयां बनाती है और हर अगले दिन (22) इकाइयां कम बनाती है। पहले (18) दिनों में कुल उत्पादन कितना होगा?

A factory makes (600) units on the first day and (22) fewer units each next day. What is the total production in the first (18) days?

Explanation opens after your attempt

Correct Answer

D. (7434)

Step 1

Concept

The production is the decreasing AP $600,578,556,\ldots$ and $S_{18}=7434$. Exam tip: treat a decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is D. (7434). The production is the decreasing AP $600,578,556,\ldots$ and $S_{18}=7434$. Exam tip: treat a decrease as a negative common difference.

Step 3

Exam Tip

उत्पादन $600,578,556,\ldots$ घटती समान्तर श्रेणी है और $S_{18}=7434$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Expert Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक वेबसाइट पर पहले दिन (900) विजिट आए और हर अगले दिन (50) विजिट कम हुए। (10) दिनों में कुल कितने विजिट आएंगे?

A website gets (900) visits on the first day and (50) fewer visits each next day. How many visits are received in (10) days?

Explanation opens after your attempt

Correct Answer

C. (6750)

Step 1

Concept

The visits form the decreasing AP $900,850,800,\ldots$ and $S_{10}=6750$. Exam tip: keep (d) negative for decreasing numbers.

Step 2

Why this answer is correct

The correct answer is C. (6750). The visits form the decreasing AP $900,850,800,\ldots$ and $S_{10}=6750$. Exam tip: keep (d) negative for decreasing numbers.

Step 3

Exam Tip

विजिट $900,850,800,\ldots$ घटती समान्तर श्रेणी हैं और $S_{10}=6750$। परीक्षा में घटती संख्या के लिए (d) ऋणात्मक रखें।

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Question Expert Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक मशीन पर पहले दिन (1000) रुपये खर्च हुए और हर अगले दिन (45) रुपये कम खर्च हुए। (12) दिनों में कुल खर्च कितना होगा?

A machine costs (1000) rupees on the first day and (45) rupees less each next day. What is the total cost in (12) days?

Explanation opens after your attempt

Correct Answer

D. (9030)

Step 1

Concept

The costs form the decreasing AP $1000,955,910,\ldots$ and $S_{12}=9030$. Exam tip: take (d) negative for decreasing costs.

Step 2

Why this answer is correct

The correct answer is D. (9030). The costs form the decreasing AP $1000,955,910,\ldots$ and $S_{12}=9030$. Exam tip: take (d) negative for decreasing costs.

Step 3

Exam Tip

खर्च $1000,955,910,\ldots$ घटती समान्तर श्रेणी है और $S_{12}=9030$। परीक्षा में घटते खर्च के लिए (d) ऋणात्मक लें।

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Question Expert Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक मंच सजावट में पहली पंक्ति में (96) लाइटें हैं और हर अगली पंक्ति में (4) लाइटें कम हैं। (18) पंक्तियों में कुल कितनी लाइटें होंगी?

In a stage decoration the first row has (96) lights and each next row has (4) fewer lights. How many lights are there in (18) rows?

Explanation opens after your attempt

Correct Answer

C. (1116)

Step 1

Concept

The lights form the decreasing AP $96,92,88,\ldots$ and $S_{18}=1116$. Exam tip: in decreasing rows the common difference is negative.

Step 2

Why this answer is correct

The correct answer is C. (1116). The lights form the decreasing AP $96,92,88,\ldots$ and $S_{18}=1116$. Exam tip: in decreasing rows the common difference is negative.

Step 3

Exam Tip

लाइटें $96,92,88,\ldots$ घटती समान्तर श्रेणी हैं और $S_{18}=1116$। परीक्षा में घटती पंक्ति में सार्व अंतर ऋणात्मक होता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक गोदाम में पहले दिन (500) पैकेट रखे गए और हर अगले दिन (25) पैकेट कम रखे गए। (14) दिनों में कुल कितने पैकेट रखे गए?

In a warehouse (500) packets are stored on the first day and (25) fewer packets are stored each next day. How many packets are stored in (14) days?

Explanation opens after your attempt

Correct Answer

C. (4725)

Step 1

Concept

The packet numbers form a decreasing AP and $S_{14}=4725$. Exam tip: take a decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is C. (4725). The packet numbers form a decreasing AP and $S_{14}=4725$. Exam tip: take a decrease as a negative common difference.

Step 3

Exam Tip

पैकेटों की संख्या घटती समान्तर श्रेणी है और $S_{14}=4725$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Expert Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक फैक्टरी पहले दिन (420) इकाइयां बनाती है और हर अगले दिन (18) इकाइयां कम बनाती है। पहले (15) दिनों में कुल उत्पादन कितना होगा?

A factory makes (420) units on the first day and (18) fewer units each next day. What is the total production in the first (15) days?

Explanation opens after your attempt

Correct Answer

D. (4410)

Step 1

Concept

The production is the decreasing AP $420,402,384,\ldots$ and $S_{15}=4410$. Exam tip: treat a decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is D. (4410). The production is the decreasing AP $420,402,384,\ldots$ and $S_{15}=4410$. Exam tip: treat a decrease as a negative common difference.

Step 3

Exam Tip

उत्पादन $420,402,384,\ldots$ घटती समान्तर श्रेणी है और $S_{15}=4410$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Hard Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 72

एक सीढ़ी में नीचे की पंक्ति में (132) टाइलें हैं और हर ऊपर की पंक्ति में (6) टाइलें कम हैं। किस पंक्ति में (54) टाइलें होंगी?

A staircase has (132) tiles in the bottom row and (6) fewer tiles in each upper row. Which row will have (54) tiles?

Explanation opens after your attempt

Correct Answer

D. (14)

Step 1

Concept

From (132+(n-1)(-6)=54), (n=14). Exam tip: handle the sign carefully in a decreasing AP.

Step 2

Why this answer is correct

The correct answer is D. (14). From (132+(n-1)(-6)=54), (n=14). Exam tip: handle the sign carefully in a decreasing AP.

Step 3

Exam Tip

(132+(n-1)(-6)=54) से (n=14) मिलता है। परीक्षा में घटती श्रेणी में चिन्ह सावधानी से रखें।

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Question Hard Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 72

एक फैक्टरी पहले दिन (360) इकाइयां बनाती है और हर अगले दिन (15) इकाइयां कम बनाती है। पहले (16) दिनों में कुल उत्पादन कितना होगा?

A factory makes (360) units on the first day and (15) fewer units each next day. What is the total production in the first (16) days?

Explanation opens after your attempt

Correct Answer

D. (3960)

Step 1

Concept

The production is the decreasing AP $360,345,330,\ldots$ and $S_{16}=3960$. Exam tip: treat a decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is D. (3960). The production is the decreasing AP $360,345,330,\ldots$ and $S_{16}=3960$. Exam tip: treat a decrease as a negative common difference.

Step 3

Exam Tip

उत्पादन $360,345,330,\ldots$ घटती समान्तर श्रेणी है और $S_{16}=3960$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Hard Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 71

एक सीढ़ी में नीचे की पंक्ति में (110) टाइलें हैं और हर ऊपर की पंक्ति में (5) टाइलें कम हैं। किस पंक्ति में (55) टाइलें होंगी?

A staircase has (110) tiles in the bottom row and (5) fewer tiles in each upper row. Which row will have (55) tiles?

Explanation opens after your attempt

Correct Answer

C. (12)

Step 1

Concept

From (110+(n-1)(-5)=55), (n=12). Exam tip: handle the sign carefully in a decreasing AP.

Step 2

Why this answer is correct

The correct answer is C. (12). From (110+(n-1)(-5)=55), (n=12). Exam tip: handle the sign carefully in a decreasing AP.

Step 3

Exam Tip

(110+(n-1)(-5)=55) से (n=12) मिलता है। परीक्षा में घटती श्रेणी में चिन्ह सावधानी से रखें।

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Question Hard Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 71

एक फैक्टरी पहले दिन (300) इकाइयां बनाती है और हर अगले दिन (20) इकाइयां कम बनाती है। पहले (12) दिनों में कुल उत्पादन कितना होगा?

A factory makes (300) units on the first day and (20) fewer units each next day. What is the total production in the first (12) days?

Explanation opens after your attempt

Correct Answer

D. (2280)

Step 1

Concept

The production is the decreasing AP $300,280,260,\ldots$ and $S_{12}=2280$. Exam tip: treat a decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is D. (2280). The production is the decreasing AP $300,280,260,\ldots$ and $S_{12}=2280$. Exam tip: treat a decrease as a negative common difference.

Step 3

Exam Tip

उत्पादन $300,280,260,\ldots$ घटती समान्तर श्रेणी है और $S_{12}=2280$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Hard Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक मशीन पहले घंटे (150) पैकेट बनाती है और हर अगले घंटे (10) पैकेट कम बनाती है। किस घंटे में उत्पादन (60) पैकेट होगा?

A machine makes (150) packets in the first hour and (10) fewer packets each next hour. In which hour will the production be (60) packets?

Explanation opens after your attempt

Correct Answer

D. (10)

Step 1

Concept

From (150+(n-1)(-10)=60), (n=10). Exam tip: write (d) as negative in a decreasing sequence.

Step 2

Why this answer is correct

The correct answer is D. (10). From (150+(n-1)(-10)=60), (n=10). Exam tip: write (d) as negative in a decreasing sequence.

Step 3

Exam Tip

(150+(n-1)(-10)=60) से (n=10) मिलता है। परीक्षा में घटती श्रेणी में (d) को ऋणात्मक लिखें।

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Question Hard Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक सीढ़ी में सबसे नीचे (96) ईंटें हैं और हर ऊपर वाली पंक्ति में (6) ईंटें कम हैं। (12) पंक्तियों में कुल कितनी ईंटें होंगी?

A staircase has (96) bricks in the bottom row and (6) fewer bricks in each upper row. How many bricks are there in (12) rows?

Explanation opens after your attempt

Correct Answer

C. (756)

Step 1

Concept

This is the decreasing AP $96,90,84,\ldots$, and $S_{12}=756$. Exam tip: treat a decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is C. (756). This is the decreasing AP $96,90,84,\ldots$, and $S_{12}=756$. Exam tip: treat a decrease as a negative common difference.

Step 3

Exam Tip

यह घटती समान्तर श्रेणी $96,90,84,\ldots$ है और $S_{12}=756$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Medium Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 72

एक सीढ़ीनुमा सजावट में नीचे की पंक्ति में (72) बल्ब हैं और हर ऊपर की पंक्ति में (6) बल्ब कम हैं। (10)वीं पंक्ति में कितने बल्ब होंगे?

In a stair-like decoration the bottom row has (72) bulbs and each upper row has (6) fewer bulbs. How many bulbs are in the (10)th row?

Explanation opens after your attempt

Correct Answer

C. (18)

Step 1

Concept

The bulb numbers are $72,66,60,\ldots$ and $a_{10}=18$. Exam tip: keep the difference negative when moving upward.

Step 2

Why this answer is correct

The correct answer is C. (18). The bulb numbers are $72,66,60,\ldots$ and $a_{10}=18$. Exam tip: keep the difference negative when moving upward.

Step 3

Exam Tip

बल्बों की संख्या $72,66,60,\ldots$ है और $a_{10}=18$। परीक्षा में ऊपर जाते समय अंतर ऋणात्मक रखें।

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Question Medium Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 72

एक मशीन पहले घंटे (120) पैकेट बनाती है और हर अगले घंटे (8) पैकेट कम बनाती है। पहले (11) घंटों में कुल उत्पादन कितना होगा?

A machine makes (120) packets in the first hour and (8) fewer packets each next hour. What is the total production in the first (11) hours?

Explanation opens after your attempt

Correct Answer

B. (880)

Step 1

Concept

The production is the decreasing AP $120,112,104,\ldots$ and $S_{11}=880$. Exam tip: treat a decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is B. (880). The production is the decreasing AP $120,112,104,\ldots$ and $S_{11}=880$. Exam tip: treat a decrease as a negative common difference.

Step 3

Exam Tip

उत्पादन $120,112,104,\ldots$ घटती समान्तर श्रेणी है और $S_{11}=880$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Medium Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 71

एक सीढ़ीनुमा सजावट में नीचे की पंक्ति में (60) बल्ब हैं और हर ऊपर की पंक्ति में (5) बल्ब कम हैं। (9)वीं पंक्ति में कितने बल्ब होंगे?

In a stair-like decoration the bottom row has (60) bulbs and each upper row has (5) fewer bulbs. How many bulbs are in the (9)th row?

Explanation opens after your attempt

Correct Answer

B. (20)

Step 1

Concept

The bulb numbers are $60,55,50,\ldots$ and $a_9=20$. Exam tip: keep the difference negative when moving upward.

Step 2

Why this answer is correct

The correct answer is B. (20). The bulb numbers are $60,55,50,\ldots$ and $a_9=20$. Exam tip: keep the difference negative when moving upward.

Step 3

Exam Tip

बल्बों की संख्या $60,55,50,\ldots$ है और $a_9=20$। परीक्षा में ऊपर जाते समय अंतर ऋणात्मक रखें।

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Question Medium Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 71

एक मशीन पहले घंटे (95) पैकेट बनाती है और हर अगले घंटे (5) पैकेट कम बनाती है। पहले (9) घंटों में कुल उत्पादन कितना होगा?

A machine makes (95) packets in the first hour and (5) fewer packets each next hour. What is the total production in the first (9) hours?

Explanation opens after your attempt

Correct Answer

A. (675)

Step 1

Concept

The production is the decreasing AP $95,90,85,\ldots$ and $S_9=675$. Exam tip: treat a decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is A. (675). The production is the decreasing AP $95,90,85,\ldots$ and $S_9=675$. Exam tip: treat a decrease as a negative common difference.

Step 3

Exam Tip

उत्पादन $95,90,85,\ldots$ घटती समान्तर श्रेणी है और $S_9=675$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Medium Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक सीढ़ीनुमा सजावट में नीचे की पंक्ति में (45) बल्ब हैं और हर ऊपर की पंक्ति में (3) बल्ब कम हैं। (8)वीं पंक्ति में कितने बल्ब होंगे?

In a stair-like decoration the bottom row has (45) bulbs and each upper row has (3) fewer bulbs. How many bulbs are in the (8)th row?

Explanation opens after your attempt

Correct Answer

B. (24)

Step 1

Concept

The bulb numbers are $45,42,39,\ldots$ and $a_8=24$. Exam tip: keep the difference negative when moving upward.

Step 2

Why this answer is correct

The correct answer is B. (24). The bulb numbers are $45,42,39,\ldots$ and $a_8=24$. Exam tip: keep the difference negative when moving upward.

Step 3

Exam Tip

बल्बों की संख्या $45,42,39,\ldots$ है और $a_8=24$। परीक्षा में ऊपर जाते समय अंतर ऋणात्मक रखें।

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Question Medium Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक सीढ़ी में सबसे नीचे (52) ईंटें हैं और हर ऊपर वाली पंक्ति में (4) ईंटें कम हैं। (10) पंक्तियों में कुल कितनी ईंटें होंगी?

A staircase has (52) bricks in the bottom row and (4) fewer bricks in each upper row. How many bricks are there in (10) rows?

Explanation opens after your attempt

Correct Answer

A. (340)

Step 1

Concept

This is the decreasing AP $52,48,44,\ldots$ and $S_{10}=340$. Exam tip: treat the decrease as a negative common difference.

Step 2

Why this answer is correct

The correct answer is A. (340). This is the decreasing AP $52,48,44,\ldots$ and $S_{10}=340$. Exam tip: treat the decrease as a negative common difference.

Step 3

Exam Tip

यह घटती समान्तर श्रेणी $52,48,44,\ldots$ है और $S_{10}=340$। परीक्षा में कमी को ऋणात्मक सार्व अंतर मानें।

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Question Easy Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 72

एक सीढ़ी में सबसे नीचे (50) टाइलें हैं और हर ऊपर वाली पंक्ति में (4) टाइलें कम हैं। (9) पंक्तियों में कुल कितनी टाइलें होंगी?

A staircase has (50) tiles in the bottom row and (4) fewer tiles in each upper row. How many tiles are there in (9) rows?

Explanation opens after your attempt

Correct Answer

A. (306)

Step 1

Concept

This is the decreasing AP $50,46,42,\ldots$. $S_9=306$, so there are (306) tiles.

Step 2

Why this answer is correct

The correct answer is A. (306). This is the decreasing AP $50,46,42,\ldots$. $S_9=306$, so there are (306) tiles.

Step 3

Exam Tip

यह घटती समान्तर श्रेणी $50,46,42,\ldots$ है। $S_9=306$ इसलिए कुल (306) टाइलें होंगी।

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Question Easy Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 71

एक सीढ़ी में सबसे नीचे (40) टाइलें हैं और हर ऊपर वाली पंक्ति में (3) टाइलें कम हैं। (8) पंक्तियों में कुल कितनी टाइलें होंगी?

A staircase has (40) tiles in the bottom row and (3) fewer tiles in each upper row. How many tiles are there in (8) rows?

Explanation opens after your attempt

Correct Answer

A. (236)

Step 1

Concept

This is the decreasing AP $40,37,34,\ldots$. $S_8=236$ so there are (236) tiles.

Step 2

Why this answer is correct

The correct answer is A. (236). This is the decreasing AP $40,37,34,\ldots$. $S_8=236$ so there are (236) tiles.

Step 3

Exam Tip

यह घटती समान्तर श्रेणी $40,37,34,\ldots$ है। $S_8=236$ इसलिए कुल (236) टाइलें होंगी।

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Question Easy Mathematics Arithmetic Progressions (AP) Word problems based on APs Class 10 Level 70

एक जलाशय में पहले दिन (1000) लीटर पानी है और हर दिन (50) लीटर पानी कम हो जाता है। (8)वें दिन कितना पानी बचेगा?

A reservoir has (1000) litres of water on the first day and (50) litres less each day. How much water remains on the (8)th day?

Explanation opens after your attempt

Correct Answer

B. (650) लीटर

Step 1

Concept

This is a decreasing AP. (a_8=1000+7(-50)=650).

Step 2

Why this answer is correct

The correct answer is B. (650) लीटर. This is a decreasing AP. (a_8=1000+7(-50)=650).

Step 3

Exam Tip

यह घटती समान्तर श्रेणी है। (a_8=1000+7(-50)=650)।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समांतर श्रेढ़ी $250,238,226,\ldots$ के पहले (30) पदों का योग ज्ञात कीजिए।

Find the sum of the first (30) terms of the AP $250,238,226,\ldots$.

Explanation opens after your attempt

Correct Answer

D. (2280)

Step 1

Concept

The last term is (-98), and $S_{30}=2280$. Once the last term is found, (S_n=\frac{n}{2}(a+l)) is faster.

Step 2

Why this answer is correct

The correct answer is D. (2280). The last term is (-98), and $S_{30}=2280$. Once the last term is found, (S_n=\frac{n}{2}(a+l)) is faster.

Step 3

Exam Tip

अंतिम पद (-98) है और $S_{30}=2280$ है। अंतिम पद मिल जाए तो (S_n=\frac{n}{2}(a+l)) तेज रहता है।

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समांतर श्रेढ़ी $300,287,274,\ldots$ के पहले (35) पदों का योग ज्ञात कीजिए।

Find the sum of the first (35) terms of the AP $300,287,274,\ldots$.

Explanation opens after your attempt

Correct Answer

D. (2765)

Step 1

Concept

Here (d=-13), and $S_{35}=2765$. Do not forget the negative sign of the common difference in a decreasing AP.

Step 2

Why this answer is correct

The correct answer is D. (2765). Here (d=-13), and $S_{35}=2765$. Do not forget the negative sign of the common difference in a decreasing AP.

Step 3

Exam Tip

यहाँ (d=-13) है और $S_{35}=2765$ आता है। घटती श्रेढ़ी में सार्व अंतर का ऋणात्मक चिह्न न भूलें।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $140,132,124,\ldots$ के पहले (25) पदों का योग ज्ञात कीजिए।

Find the sum of the first (25) terms of the AP $140,132,124,\ldots$.

Explanation opens after your attempt

Correct Answer

D. (1100)

Step 1

Concept

The last term is (-52), and $S_{25}=1100$. Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.

Step 2

Why this answer is correct

The correct answer is D. (1100). The last term is (-52), and $S_{25}=1100$. Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.

Step 3

Exam Tip

अंतिम पद (-52) है और $S_{25}=1100$ है। घटती श्रेढ़ी में भी (S_n=\frac{n}{2}(a+l)) उपयोगी है।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $160,151,142,\ldots$ के पहले (22) पदों का योग ज्ञात कीजिए।

Find the sum of the first (22) terms of the AP $160,151,142,\ldots$.

Explanation opens after your attempt

Correct Answer

D. (1441)

Step 1

Concept

Here (d=-9), and the formula gives $S_{22}=1441$. In a decreasing AP, write the common difference as negative.

Step 2

Why this answer is correct

The correct answer is D. (1441). Here (d=-9), and the formula gives $S_{22}=1441$. In a decreasing AP, write the common difference as negative.

Step 3

Exam Tip

यहाँ (d=-9) है और सूत्र से $S_{22}=1441$ मिलता है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखें।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 68

समांतर श्रेढ़ी $95,89,83,\ldots$ के पहले (20) पदों का योग ज्ञात कीजिए।

Find the sum of the first (20) terms of the AP $95,89,83,\ldots$.

Explanation opens after your attempt

Correct Answer

B. (760)

Step 1

Concept

The last term is (-19), and $S_{20}=760$. Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.

Step 2

Why this answer is correct

The correct answer is B. (760). The last term is (-19), and $S_{20}=760$. Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.

Step 3

Exam Tip

अंतिम पद (-19) है और $S_{20}=760$ है। घटती श्रेढ़ी में भी (S_n=\frac{n}{2}(a+l)) उपयोगी है।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 68

समांतर श्रेढ़ी $120,113,106,\ldots$ के पहले (25) पदों का योग ज्ञात कीजिए।

Find the sum of the first (25) terms of the AP $120,113,106,\ldots$.

Explanation opens after your attempt

Correct Answer

C. (900)

Step 1

Concept

Here (d=-7), and the formula gives $S_{25}=900$. In a decreasing AP, write the common difference as negative.

Step 2

Why this answer is correct

The correct answer is C. (900). Here (d=-7), and the formula gives $S_{25}=900$. In a decreasing AP, write the common difference as negative.

Step 3

Exam Tip

यहाँ (d=-7) है और सूत्र से $S_{25}=900$ मिलता है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखें।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समांतर श्रेढ़ी $50,47,44,\ldots$ में (6)वें पद से (20)वें पद तक का योग क्या है?

In the AP $50,47,44,\ldots$, what is the sum from the (6)th term to the (20)th term?

Explanation opens after your attempt

Correct Answer

C. (210)

Step 1

Concept

The required sum is $S_{20}-S_5=210$. The same partial-sum method works for a decreasing AP.

Step 2

Why this answer is correct

The correct answer is C. (210). The required sum is $S_{20}-S_5=210$. The same partial-sum method works for a decreasing AP.

Step 3

Exam Tip

आवश्यक योग $S_{20}-S_5=210$ है। घटती श्रेढ़ी में भी आंशिक योग का वही तरीका लागू होता है।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $24,21,18,\ldots$ के पहले (16) पदों का योग कितना है?

What is the sum of the first (16) terms of the AP $24,21,18,\ldots$?

Explanation opens after your attempt

Correct Answer

C. (24)

Step 1

Concept

The last term is (-21), and (S_{16}=\frac{16}{2}(24-21)=24). Positive and negative terms can greatly reduce the sum.

Step 2

Why this answer is correct

The correct answer is C. (24). The last term is (-21), and (S_{16}=\frac{16}{2}(24-21)=24). Positive and negative terms can greatly reduce the sum.

Step 3

Exam Tip

अंतिम पद (-21) है और (S_{16}=\frac{16}{2}(24-21)=24)। धनात्मक और ऋणात्मक पद एक-दूसरे को काफी घटा सकते हैं।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $100,95,90,\ldots$ के पहले (12) पदों का योग ज्ञात कीजिए।

Find the sum of the first (12) terms of the AP $100,95,90,\ldots$.

Explanation opens after your attempt

Correct Answer

A. (870)

Step 1

Concept

The last term is (45), so (S_{12}=\frac{12}{2}(100+45)=870). Once the last term is found, the sum is quick.

Step 2

Why this answer is correct

The correct answer is A. (870). The last term is (45), so (S_{12}=\frac{12}{2}(100+45)=870). Once the last term is found, the sum is quick.

Step 3

Exam Tip

अंतिम पद (45) है, इसलिए (S_{12}=\frac{12}{2}(100+45)=870)। अंतिम पद मिल जाए तो योग तेजी से निकलेगा।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $31,28,25,\ldots$ के पहले (20) पदों का योग ज्ञात कीजिए।

Find the sum of the first (20) terms of the AP $31,28,25,\ldots$.

Explanation opens after your attempt

Correct Answer

A. (50)

Step 1

Concept

Here the last term is (-26), and $S_{20}=50$. In a decreasing AP, the sum can become quite small.

Step 2

Why this answer is correct

The correct answer is A. (50). Here the last term is (-26), and $S_{20}=50$. In a decreasing AP, the sum can become quite small.

Step 3

Exam Tip

यहाँ अंतिम पद (-26) है और $S_{20}=50$ मिलता है। घटती श्रेढ़ी में योग बहुत छोटा भी हो सकता है।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 69

समांतर श्रेढ़ी $50,47,44,\ldots$ के पहले (18) पदों का योग ज्ञात कीजिए।

Find the sum of the first (18) terms of the AP $50,47,44,\ldots$.

Explanation opens after your attempt

Correct Answer

A. (441)

Step 1

Concept

Here (d=-3), and the formula gives $S_{18}=441$. In a decreasing AP, write the common difference as negative.

Step 2

Why this answer is correct

The correct answer is A. (441). Here (d=-3), and the formula gives $S_{18}=441$. In a decreasing AP, write the common difference as negative.

Step 3

Exam Tip

यहाँ (d=-3) है और सूत्र से $S_{18}=441$ मिलता है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखें।

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Question Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first (n) terms of an AP Class 10 Level 68

यदि (S_n=\frac{n}{2}(a+l)), (a=25), (l=5), और (n=7) है, तो योग क्या होगा?

If (S_n=\frac{n}{2}(a+l)), (a=25), (l=5), and (n=7), what is the sum?

Explanation opens after your attempt

Correct Answer

C. (105)

Step 1

Concept

(S_7=\frac{7}{2}(25+5)=105). The first term may be larger, but the formula remains the same.

Step 2

Why this answer is correct

The correct answer is C. (105). (S_7=\frac{7}{2}(25+5)=105). The first term may be larger, but the formula remains the same.

Step 3

Exam Tip

(S_7=\frac{7}{2}(25+5)=105)। पहला पद बड़ा हो सकता है, फिर भी सूत्र वही रहता है।

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Question Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी $60,54,48,\ldots$ के पहले (5) पदों का योग क्या होगा?

What will be the sum of the first (5) terms of the AP $60,54,48,\ldots$?

Explanation opens after your attempt

Correct Answer

B. (240)

Step 1

Concept

The fifth term is (36). (S_5=\frac{5}{2}(60+36)=240).

Step 2

Why this answer is correct

The correct answer is B. (240). The fifth term is (36). (S_5=\frac{5}{2}(60+36)=240).

Step 3

Exam Tip

पांचवां पद (36) है। (S_5=\frac{5}{2}(60+36)=240)।

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Question Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी $50,45,40,\ldots$ के पहले (9) पदों का योग क्या है?

What is the sum of the first (9) terms of the AP $50,45,40,\ldots$?

Explanation opens after your attempt

Correct Answer

B. (270)

Step 1

Concept

The ninth term is (10). (S_9=\frac{9}{2}(50+10)=270).

Step 2

Why this answer is correct

The correct answer is B. (270). The ninth term is (10). (S_9=\frac{9}{2}(50+10)=270).

Step 3

Exam Tip

नौवां पद (10) है। (S_9=\frac{9}{2}(50+10)=270)।

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Question Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी $100,90,80,\ldots$ के पहले (6) पदों का योग क्या है?

What is the sum of the first (6) terms of the AP $100,90,80,\ldots$?

Explanation opens after your attempt

Correct Answer

C. (450)

Step 1

Concept

The sixth term is (50). (S_6=\frac{6}{2}(100+50)=450).

Step 2

Why this answer is correct

The correct answer is C. (450). The sixth term is (50). (S_6=\frac{6}{2}(100+50)=450).

Step 3

Exam Tip

छठा पद (50) है। (S_6=\frac{6}{2}(100+50)=450)।

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Question Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

यदि (a=25), (d=-2), (n=15) है तो $S_{15}$ क्या होगा?

If (a=25), (d=-2), (n=15), what is $S_{15}$?

Explanation opens after your attempt

Correct Answer

C. (165)

Step 1

Concept

In a decreasing AP use (d=-2). (S_{15}=\frac{15}{2}[50+14(-2)]=165).

Step 2

Why this answer is correct

The correct answer is C. (165). In a decreasing AP use (d=-2). (S_{15}=\frac{15}{2}[50+14(-2)]=165).

Step 3

Exam Tip

घटती AP में (d=-2) रखें। (S_{15}=\frac{15}{2}[50+14(-2)]=165)।

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Question Easy Mathematics Arithmetic Progressions (AP) Finding the sum of the first $n$ terms of an AP Class 10 Level 67

समान्तर श्रेणी $20,18,16,\ldots$ के पहले (8) पदों का योग क्या है?

What is the sum of the first (8) terms of the AP $20,18,16,\ldots$?

Explanation opens after your attempt

Correct Answer

B. (104)

Step 1

Concept

This is a decreasing AP with (d=-2). (S_8=\frac{8}{2}[40+7(-2)]=104).

Step 2

Why this answer is correct

The correct answer is B. (104). This is a decreasing AP with (d=-2). (S_8=\frac{8}{2}[40+7(-2)]=104).

Step 3

Exam Tip

यह घटती AP है जिसमें (d=-2) है। (S_8=\frac{8}{2}[40+7(-2)]=104)।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $143,130,117,\ldots$ में (25) से छोटा पहला पद कौन-सा है?

In the AP $143,130,117,\ldots$, what is the first term less than (25)?

Explanation opens after your attempt

Correct Answer

A. (13)

Step 1

Concept

In this AP, (d=-13). After (26), the next term is (13), so the first term less than (25) is (13).

Step 2

Why this answer is correct

The correct answer is A. (13). In this AP, (d=-13). After (26), the next term is (13), so the first term less than (25) is (13).

Step 3

Exam Tip

इस AP में (d=-13) है। (26) के बाद (13) आता है इसलिए (25) से छोटा पहला पद (13) है।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $112,101,90,\ldots$ में (15) से छोटा पहला पद कौन-सा है?

In the AP $112,101,90,\ldots$, what is the first term less than (15)?

Explanation opens after your attempt

Correct Answer

A. (13)

Step 1

Concept

In this AP, (d=-11). After (24), the next term is (13), so the first term less than (15) is (13).

Step 2

Why this answer is correct

The correct answer is A. (13). In this AP, (d=-11). After (24), the next term is (13), so the first term less than (15) is (13).

Step 3

Exam Tip

इस AP में (d=-11) है। (24) के बाद (13) आता है इसलिए (15) से छोटा पहला पद (13) है।

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी $97,88,79,\ldots$ में (20) से छोटा पहला पद कौन-सा है?

In the AP $97,88,79,\ldots$, what is the first term less than (20)?

Explanation opens after your attempt

Correct Answer

A. (16)

Step 1

Concept

In this AP, (d=-9). After the term (25), the next term is (16), so the first term less than (20) is (16).

Step 2

Why this answer is correct

The correct answer is A. (16). In this AP, (d=-9). After the term (25), the next term is (16), so the first term less than (20) is (16).

Step 3

Exam Tip

इस AP में (d=-9)। पद (25) के बाद (16) आता है इसलिए (20) से छोटा पहला पद (16) है।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $128,119,110,\ldots$ में (30) से बड़ा अंतिम पद कौन-सा है?

In the AP $128,119,110,\ldots$, which is the last term greater than (30)?

Explanation opens after your attempt

Correct Answer

C. (38)

Step 1

Concept

(d=-9) and the terms go $128,119,110,\ldots,38,29$. The last term greater than (30) is (38).

Step 2

Why this answer is correct

The correct answer is C. (38). (d=-9) and the terms go $128,119,110,\ldots,38,29$. The last term greater than (30) is (38).

Step 3

Exam Tip

(d=-9) है और पद $128,119,110,\ldots,38,29$ आते हैं। (30) से बड़ा अंतिम पद (38) है।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक टंकी में पहले घंटे (240) लीटर पानी है और हर घंटे (18) लीटर पानी घटता है। (9)वें घंटे में पानी कितना होगा?

A tank has (240) litres of water in the first hour and (18) litres decrease every hour. How much water will be there in the (9)th hour?

Explanation opens after your attempt

Correct Answer

A. (96) लीटर(96) litres

Step 1

Concept

This is a decreasing AP with (a=240) and (d=-18). (a_9=240+8(-18)=96) litres.

Step 2

Why this answer is correct

The correct answer is A. (96) लीटर / (96) litres. This is a decreasing AP with (a=240) and (d=-18). (a_9=240+8(-18)=96) litres.

Step 3

Exam Tip

यह घटती AP है जिसमें (a=240) और (d=-18) है। (a_9=240+8(-18)=96) लीटर।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि $a_n=95-5n$ है तो (26)वां पद क्या होगा?

If $a_n=95-5n$, what will be the (26)th term?

Explanation opens after your attempt

Correct Answer

A. (-35)

Step 1

Concept

$a_{26}=95-5\times26=-35$. In a decreasing formula check the sign after subtraction.

Step 2

Why this answer is correct

The correct answer is A. (-35). $a_{26}=95-5\times26=-35$. In a decreasing formula check the sign after subtraction.

Step 3

Exam Tip

$a_{26}=95-5\times26=-35$। घटते सूत्र में घटाव के बाद चिन्ह जांचें।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $120,109,98,\ldots$ का (13)वां पद क्या होगा?

What will be the (13)th term of the AP $120,109,98,\ldots$?

Explanation opens after your attempt

Correct Answer

C. (-12)

Step 1

Concept

(d=-11) so (a_{13}=120+12(-11)=-12). With a large negative difference multiply first.

Step 2

Why this answer is correct

The correct answer is C. (-12). (d=-11) so (a_{13}=120+12(-11)=-12). With a large negative difference multiply first.

Step 3

Exam Tip

(d=-11) है इसलिए (a_{13}=120+12(-11)=-12)। बड़े ऋणात्मक अंतर में गुणा पहले करें।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी $84,78,72,\ldots$ का (18)वां पद ज्ञात कीजिए।

Find the (18)th term of the AP $84,78,72,\ldots$.

Explanation opens after your attempt

Correct Answer

B. (-18)

Step 1

Concept

Here (d=-6) so (a_{18}=84+17(-6)=-18). In a decreasing AP take the common difference as negative.

Step 2

Why this answer is correct

The correct answer is B. (-18). Here (d=-6) so (a_{18}=84+17(-6)=-18). In a decreasing AP take the common difference as negative.

Step 3

Exam Tip

यहां (d=-6) है इसलिए (a_{18}=84+17(-6)=-18)। घटती AP में सार्व अंतर को ऋणात्मक लें।

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Question Medium Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी $90,83,76,\ldots$ में (20) से बड़ा अंतिम पद कौन-सा है?

In the AP $90,83,76,\ldots$, which is the last term greater than (20)?

Explanation opens after your attempt

Correct Answer

D. (27)

Step 1

Concept

(d=-7) and the terms go $90,83,76,\ldots,27,20$. The last term greater than (20) is (27).

Step 2

Why this answer is correct

The correct answer is D. (27). (d=-7) and the terms go $90,83,76,\ldots,27,20$. The last term greater than (20) is (27).

Step 3

Exam Tip

(d=-7) है और पद $90,83,76,\ldots,27,20$ आते हैं। (20) से बड़ा अंतिम पद (27) है।

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एक घटती समान्तर श्रेणी में प्रथम पद (72) और सार्व अंतर (-4) है। पहले (24) पदों का योग कितना होगा?

Concept

Why this answer is correct

Exam Tip

एक घटती समान्तर श्रेणी में प्रथम पद (65) और सार्व अंतर (-5) है। पहले (15) पदों का योग कितना होगा?

Concept

Why this answer is correct

Exam Tip

किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-4) नहीं है?

Concept

Why this answer is correct

Exam Tip

किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-2) नहीं है?

Concept

Why this answer is correct

Exam Tip

निम्न में से कौन सा अनुक्रम घटती अंकगणितीय श्रेणी है?

Concept

Why this answer is correct

Exam Tip

समान्तर श्रेणी \(240,222,204,\ldots\) में (-150) से बड़ा अंतिम पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

समान्तर श्रेणी \(156,142,128,\ldots\) में (-120) से बड़ा अंतिम पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

समान्तर श्रेणी \(121,109,97,\ldots\) में (-75) से बड़ा अंतिम पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

किस विकल्प में समांतर श्रेणी घट रही है?

Concept

Why this answer is correct

Exam Tip

भारतीय सिविल सेवा परीक्षा की आयु सीमा घटाने के विरोध का राष्ट्रीय महत्व क्या था?

Concept

Why this answer is correct

Exam Tip

समान्तर श्रेणी \(104,95,86,\ldots\) में (-50) से बड़ा अंतिम पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

समान्तर श्रेणी \(85,77,69,\ldots\) में (-35) से बड़ा अंतिम पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

समान्तर श्रेणी \(64,57,50,\ldots\) में (-20) से बड़ा अंतिम पद कौन-सा है?

Concept

Why this answer is correct

Exam Tip

नवउपनिवेशवाद में मुद्रा और वित्तीय निर्भरता किस प्रकार नीति स्वायत्तता को सीमित कर सकती है?

Concept

Why this answer is correct

Exam Tip

असमान व्यापारिक शर्तें नवस्वतंत्र देशों की विकास नीति को कैसे सीमित कर सकती थीं?

Concept

Why this answer is correct

Exam Tip

इंडोचीन संघर्ष को केवल वियतनाम तक सीमित करना क्यों गलत है?

Concept

Why this answer is correct

Exam Tip

उपनिवेश मुक्ति को केवल स्वतंत्रता दिवस तक सीमित करना गलत क्यों है?

Concept

Why this answer is correct

Exam Tip

प्राग स्प्रिंग के दमन ने सुधारवादी समाजवाद की कौन सी सीमा दिखाई?

Concept

Why this answer is correct

Exam Tip

फ्रांसीसी क्रांति में टेरर के दौर से क्रांतिकारी आदर्शों की कौन सी सीमा स्पष्ट होती है?

Concept

Why this answer is correct

Exam Tip

प्राग स्प्रिंग के दमन से सुधारवादी समाजवाद की कौन सी सीमा सामने आई?

Concept

Why this answer is correct