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Question Hard General Knowledge World History Colonization and Decolonization Class 10 Level 78

फूट डालो और राज करो नीति को अल्पकालिक नियंत्रण और दीर्घकालिक संकट दोनों से कैसे जोड़ा जा सकता है?

How can divide and rule policy be linked with both short term control and long term crisis?

Explanation opens after your attempt
Correct Answer

A. इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता थाIt could weaken immediate resistance but leave social distrust

Step 1

Concept

This policy used division for control. For exams also write its legacy.

Step 2

Why this answer is correct

The correct answer is A. इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता था / It could weaken immediate resistance but leave social distrust. This policy used division for control. For exams also write its legacy.

Step 3

Exam Tip

यह नीति नियंत्रण के लिए विभाजन का उपयोग करती थी। परीक्षा में इसकी विरासत भी लिखें।

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

मोलोटोव रिबेंट्रोप संधि को अल्पकालीन लाभ और दीर्घकालीन खतरे दोनों से कैसे समझा जा सकता है?

How can the Molotov-Ribbentrop Pact be understood through both short-term benefit and long-term risk?

Explanation opens after your attempt
Correct Answer

A. जर्मनी को पूर्व से राहत मिली लेकिन सोवियत जर्मन संघर्ष अंततः टला नहींGermany got relief from the east but Soviet-German conflict was not ultimately avoided

Step 1

Concept

The pact was immediate strategy but ideological and strategic conflict remained. For exams separate short-term and long-term results.

Step 2

Why this answer is correct

The correct answer is A. जर्मनी को पूर्व से राहत मिली लेकिन सोवियत जर्मन संघर्ष अंततः टला नहीं / Germany got relief from the east but Soviet-German conflict was not ultimately avoided. The pact was immediate strategy but ideological and strategic conflict remained. For exams separate short-term and long-term results.

Step 3

Exam Tip

संधि तत्काल रणनीतिक थी पर वैचारिक और सामरिक टकराव बना रहा। परीक्षा में अल्पकालीन और दीर्घकालीन परिणाम अलग करें।

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

यदि समान्तर श्रेणी का (5)वां पद (x+7) और (12)वां पद (x+42) है तो (20)वां पद (x) के रूप में क्या होगा?

If the (5)th term of an AP is (x+7) and the (12)th term is (x+42), what is the (20)th term in terms of (x)?

Explanation opens after your attempt
Correct Answer

C. (x+82)

Step 1

Concept

From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).

Step 2

Why this answer is correct

The correct answer is C. (x+82). From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).

Step 3

Exam Tip

(7d=35) से (d=5)। \(a_{20}=a_{12}+8d=x+42+40=x+82\)।

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

यदि AP का (5)वां पद (27) और (14)वां पद (90) है तो (20)वां पद क्या होगा?

If the (5)th term of an AP is (27) and the (14)th term is (90), what is the (20)th term?

Explanation opens after your attempt
Correct Answer

C. (132)

Step 1

Concept

\(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.

Step 2

Why this answer is correct

The correct answer is C. (132). \(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.

Step 3

Exam Tip

\(d=\frac{90-27}{14-5}=7\) और \(a_{20}=90+6\times7=132\)। पहले (d) निकालें फिर आगे बढ़ें।

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

यदि समान्तर श्रेणी का (4)वां पद (15) और (12)वां पद (55) है तो (16)वां पद क्या होगा?

If the (4)th term of an AP is (15) and the (12)th term is (55), what is the (16)th term?

Explanation opens after your attempt
Correct Answer

C. (75)

Step 1

Concept

\(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.

Step 2

Why this answer is correct

The correct answer is C. (75). \(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.

Step 3

Exam Tip

\(d=\frac{55-15}{12-4}=5\) और \(a_{16}=55+4\times5=75\)। पहले (d) फिर वांछित पद निकालें।

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

यदि AP का (3)वां पद (8) और (8)वां पद (3) है, तो (11)वां पद क्या होगा?

If the (3)rd term of an AP is (8) and the (8)th term is (3), what is the (11)th term?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

\(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.

Step 2

Why this answer is correct

The correct answer is A. (0). \(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.

Step 3

Exam Tip

\(d=\frac{3-8}{8-3}=-1\), इसलिए (a_{11}=3+3(-1)=0)। ज्ञात पास वाले पद से आगे बढ़ना सरल है।

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

यदि किसी AP का (p)वां पद (q) और (q)वां पद (p) है, तो उसका ((p+q))वां पद क्या होगा?

If the (p)th term of an AP is (q) and the (q)th term is (p), what is its ((p+q))th term?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).

Step 2

Why this answer is correct

The correct answer is A. (0). Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).

Step 3

Exam Tip

संबंधों को घटाने पर (d=-1) और आगे रखने पर \(a_{p+q}=0\) मिलता है। प्रतीकात्मक AP में भी (a_n=a+(n-1)d) ही लगाएं।

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

यदि किसी समान्तर श्रेणी का (5)वां पद (16) और (9)वां पद (32) है, तो (13)वां पद क्या होगा?

If the (5)th term of an AP is (16) and the (9)th term is (32), what is the (13)th term?

Explanation opens after your attempt
Correct Answer

C. (48)

Step 1

Concept

\(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.

Step 2

Why this answer is correct

The correct answer is C. (48). \(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.

Step 3

Exam Tip

\(d=\frac{32-16}{9-5}=4\), इसलिए \(a_{13}=32+4\times4=48\)। समान स्थान अंतर होने पर पदों का अंतर भी समान होता है।

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Question Medium General Knowledge World History World Heritage Sites Class 10 Level 80

किस स्थिति में किसी स्थल को मिश्रित विश्व धरोहर माना जाता है?

In which condition is a site considered a mixed World Heritage Site?

Explanation opens after your attempt
Correct Answer

B. जब उसमें सांस्कृतिक और प्राकृतिक दोनों मूल्य होंWhen it has both cultural and natural values

Step 1

Concept

A mixed site is important by both cultural and natural criteria. For exams treat mixed heritage as a separate category.

Step 2

Why this answer is correct

The correct answer is B. जब उसमें सांस्कृतिक और प्राकृतिक दोनों मूल्य हों / When it has both cultural and natural values. A mixed site is important by both cultural and natural criteria. For exams treat mixed heritage as a separate category.

Step 3

Exam Tip

मिश्रित स्थल सांस्कृतिक और प्राकृतिक दोनों मानदंडों से महत्वपूर्ण होता है। परीक्षा में मिश्रित धरोहर को अलग श्रेणी मानें।

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Question Medium Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 17

कौन सा विकल्प \(\sqrt{3}\) की अपरिमेयता का सही संक्षिप्त प्रमाण विचार है?

Which option is the correct short proof idea for the irrationality of \(\sqrt{3}\)?

Explanation opens after your attempt
Correct Answer

A. परिमेय मानने पर अंश और हर दोनों (3) से विभाज्य मिलते हैंAssuming rational makes both numerator and denominator divisible by (3)

Step 1

Concept

Assume \(\sqrt{3}\) rational and write it in lowest form.

Step 2

Why this answer is correct

The proof shows both numerator and denominator divisible by (3).

Step 3

Exam Tip

This contradicts the condition of a lowest-form fraction. चरण 1: \(\sqrt{3}\) को परिमेय मानकर सरलतम भिन्न में लिखते हैं। चरण 2: प्रमाण से अंश और हर दोनों (3) से विभाज्य मिलते हैं। चरण 3: यह सरलतम भिन्न की शर्त से विरोधाभास है।

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Question Easy Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 18

कौन सा विकल्प \(\sqrt{2}\) की अपरिमेयता का सही छोटा कारण है?

Which option is the correct short reason for the irrationality of \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. परिमेय मानने पर सरलतम भिन्न के अंश और हर दोनों सम हो जाते हैंAssuming rational makes numerator and denominator of a lowest-form fraction both even

Step 1

Concept

Assume \(\sqrt{2}\) rational and write it in lowest form.

Step 2

Why this answer is correct

The proof gives both numerator and denominator even.

Step 3

Exam Tip

This contradicts lowest form, so \(\sqrt{2}\) is irrational. चरण 1: \(\sqrt{2}\) को परिमेय मानकर सरलतम भिन्न में लिखते हैं। चरण 2: प्रमाण से अंश और हर दोनों सम मिलते हैं। चरण 3: यह सरलतम रूप से विरोध करता है, इसलिए \(\sqrt{2}\) अपरिमेय है।

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

यदि समान्तर श्रेणी का (8)वां पद (x+19) और (20)वां पद (x+91) है, तो (35)वां पद (x) के रूप में क्या होगा?

If the (8)th term of an AP is (x+19) and the (20)th term is (x+91), what is the (35)th term in terms of (x)?

Explanation opens after your attempt
Correct Answer

C. (x+181)

Step 1

Concept

(12d=72), so (d=6). \(a_{35}=x+91+15\times6=x+181\).

Step 2

Why this answer is correct

The correct answer is C. (x+181). (12d=72), so (d=6). \(a_{35}=x+91+15\times6=x+181\).

Step 3

Exam Tip

(12d=72), इसलिए (d=6)। \(a_{35}=x+91+15\times6=x+181\)।

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

यदि समान्तर श्रेणी का (7)वां पद (x+13) और (18)वां पद (x+90) है तो (32)वां पद (x) के रूप में क्या होगा?

If the (7)th term of an AP is (x+13) and the (18)th term is (x+90), what is the (32)nd term in terms of (x)?

Explanation opens after your attempt
Correct Answer

B. (x+188)

Step 1

Concept

From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).

Step 2

Why this answer is correct

The correct answer is B. (x+188). From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).

Step 3

Exam Tip

(11d=77) से (d=7)। \(a_{32}=a_{18}+14d=x+90+98=x+188\)।

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

यदि समान्तर श्रेणी का (6)वां पद (x+11) और (15)वां पद (x+65) है तो (27)वां पद (x) के रूप में क्या होगा?

If the (6)th term of an AP is (x+11) and the (15)th term is (x+65), what is the (27)th term in terms of (x)?

Explanation opens after your attempt
Correct Answer

B. (x+137)

Step 1

Concept

From (9d=54), (d=6). \(a_{27}=a_{15}+12d=x+65+72=x+137\).

Step 2

Why this answer is correct

The correct answer is B. (x+137). From (9d=54), (d=6). \(a_{27}=a_{15}+12d=x+65+72=x+137\).

Step 3

Exam Tip

(9d=54) से (d=6)। \(a_{27}=a_{15}+12d=x+65+72=x+137\)।

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

किसी समान्तर श्रेणी का (12)वां पद (71) और सार्व अंतर (5) है। पहला पद क्या होगा?

The (12)th term of an AP is (71) and the common difference is (5). What is the first term?

Explanation opens after your attempt
Correct Answer

D. (16)

Step 1

Concept

From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).

Step 2

Why this answer is correct

The correct answer is D. (16). From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).

Step 3

Exam Tip

\(71=a+11\times5\) से (a=16)। ज्ञात पद से पहले पद तक जाने के लिए (11d) घटाएं।

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

किसी समान्तर श्रेणी का (9)वां पद (47) और सार्व अंतर (4) है। पहला पद क्या है?

The (9)th term of an AP is (47) and the common difference is (4). What is the first term?

Explanation opens after your attempt
Correct Answer

D. (15)

Step 1

Concept

From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).

Step 2

Why this answer is correct

The correct answer is D. (15). From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).

Step 3

Exam Tip

\(47=a+8\times4\) से (a=15)। ज्ञात पद से पहले पद तक जाने के लिए (8d) घटाएं।

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

एक समान्तर श्रेणी का (6)वां पद (23) और सार्व अंतर (5) है। पहला पद क्या होगा?

The (6)th term of an AP is (23) and the common difference is (5). What is the first term?

Explanation opens after your attempt
Correct Answer

D. (-2)

Step 1

Concept

(23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).

Step 2

Why this answer is correct

The correct answer is D. (-2). (23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).

Step 3

Exam Tip

(23=a+5d=a+25), इसलिए (a=-2)। दिए गए पद से पीछे जाते समय (5d) घटाया जाता है।

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

समांतर श्रेढ़ी का सामान्य पद \(a_n=7n+2\) है। (11)वाँ पद ज्ञात कीजिए।

The general term of an AP is \(a_n=7n+2\). Find the (11)th term.

Explanation opens after your attempt
Correct Answer

C. (79)

Step 1

Concept

\(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.

Step 2

Why this answer is correct

The correct answer is C. (79). \(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.

Step 3

Exam Tip

\(a_{11}=7\times11+2=79\)। सामान्य पद में सही पद संख्या रखना ही मुख्य कदम है।

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Question Expert General Knowledge World History Famous World Leaders Class 10 Level 66

अलेक्जेंडर की अल्पायु में विशाल विजय का दीर्घकालिक परिणाम क्या था?

What was the long term result of Alexander's vast conquests in a short life?

Explanation opens after your attempt
Correct Answer

A. राजनीतिक साम्राज्य टूट गया पर सांस्कृतिक प्रभाव फैलाThe political empire broke but cultural influence spread

Step 1

Concept

After Alexander's death the empire split but Hellenistic culture spread. For exams distinguish conquest and cultural diffusion.

Step 2

Why this answer is correct

The correct answer is A. राजनीतिक साम्राज्य टूट गया पर सांस्कृतिक प्रभाव फैला / The political empire broke but cultural influence spread. After Alexander's death the empire split but Hellenistic culture spread. For exams distinguish conquest and cultural diffusion.

Step 3

Exam Tip

अलेक्जेंडर की मृत्यु के बाद साम्राज्य बंटा पर हेल्लेनिस्टिक संस्कृति फैली। परीक्षा में विजय और सांस्कृतिक प्रसार अलग समझें।

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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

एक समांतर श्रेढ़ी का पहला पद (6) है और उसका (14)वाँ पद उसके (4)वें पद का (3) गुना है। पहले (30) पदों का योग क्या होगा?

The first term of an AP is (6), and its (14)th term is (3) times its (4)th term. What is the sum of the first (30) terms?

Explanation opens after your attempt
Correct Answer

B. (1485)

Step 1

Concept

The condition gives (6+13d=3(6+3d)), so (d=3) and \(S_{30}=1485\). Convert the term condition into an equation first.

Step 2

Why this answer is correct

The correct answer is B. (1485). The condition gives (6+13d=3(6+3d)), so (d=3) and \(S_{30}=1485\). Convert the term condition into an equation first.

Step 3

Exam Tip

शर्त से (6+13d=3(6+3d)), इसलिए (d=3) और \(S_{30}=1485\) है। पदों की शर्त को पहले समीकरण में बदलें।

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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

एक समांतर श्रेढ़ी का पहला पद (5) है और उसका (12)वाँ पद उसके (3)वें पद का (4) गुना है। पहले (20) पदों का योग क्या होगा?

The first term of an AP is (5), and its (12)th term is (4) times its (3)rd term. What is the sum of the first (20) terms?

Explanation opens after your attempt
Correct Answer

A. (1050)

Step 1

Concept

The condition gives (5+11d=4(5+2d)), so (d=5) and \(S_{20}=1050\). Convert the term condition into an equation first.

Step 2

Why this answer is correct

The correct answer is A. (1050). The condition gives (5+11d=4(5+2d)), so (d=5) and \(S_{20}=1050\). Convert the term condition into an equation first.

Step 3

Exam Tip

शर्त से (5+11d=4(5+2d)), इसलिए (d=5) और \(S_{20}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें।

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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

एक समांतर श्रेढ़ी का पहला पद (6) है और उसका (9)वाँ पद उसके (4)वें पद का (2) गुना है। पहले (25) पदों का योग क्या होगा?

The first term of an AP is (6), and its (9)th term is (2) times its (4)th term. What is the sum of the first (25) terms?

Explanation opens after your attempt
Correct Answer

C. (1050)

Step 1

Concept

The condition gives (6+8d=2(6+3d)), so (d=3) and \(S_{25}=1050\). Convert the term condition into an equation first.

Step 2

Why this answer is correct

The correct answer is C. (1050). The condition gives (6+8d=2(6+3d)), so (d=3) and \(S_{25}=1050\). Convert the term condition into an equation first.

Step 3

Exam Tip

शर्त से (6+8d=2(6+3d)), इसलिए (d=3) और \(S_{25}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें।

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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

एक समांतर श्रेढ़ी का पहला पद (4) है और उसका (8)वाँ पद उसके (3)वें पद का (3) गुना है। पहले (12) पदों का योग क्या होगा?

The first term of an AP is (4), and its (8)th term is (3) times its (3)rd term. What is the sum of the first (12) terms?

Explanation opens after your attempt
Correct Answer

C. (576)

Step 1

Concept

The condition gives (4+7d=3(4+2d)), so (d=8) and \(S_{12}=576\). Convert the term condition into an equation first.

Step 2

Why this answer is correct

The correct answer is C. (576). The condition gives (4+7d=3(4+2d)), so (d=8) and \(S_{12}=576\). Convert the term condition into an equation first.

Step 3

Exam Tip

शर्त से (4+7d=3(4+2d)), इसलिए (d=8) और \(S_{12}=576\)। पदों की शर्त को पहले समीकरण में बदलें।

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

समान्तर श्रेणी \(23,31,39,\ldots\) के (n)वें पद का सूत्र \(a_n=8n+15\) है। (36)वां पद क्या होगा?

The (n)th-term formula of the AP \(23,31,39,\ldots\) is \(a_n=8n+15\). What is the (36)th term?

Explanation opens after your attempt
Correct Answer

C. (303)

Step 1

Concept

\(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.

Step 2

Why this answer is correct

The correct answer is C. (303). \(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.

Step 3

Exam Tip

\(a_{36}=8\times36+15=303\)। बने हुए सूत्र में (n=36) रखकर सीधे उत्तर पाएं।

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

यदि किसी AP का (r)वां पद (3r-2) और (d=4) है तो ((r+6))वां पद क्या होगा?

If the (r)th term of an AP is (3r-2) and (d=4), what is the ((r+6))th term?

Explanation opens after your attempt
Correct Answer

C. (3r+22)

Step 1

Concept

The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.

Step 2

Why this answer is correct

The correct answer is C. (3r+22). The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.

Step 3

Exam Tip

((r+6))वां पद (r)वें पद से (6d) आगे है इसलिए (3r-2+24=3r+22)। प्रतीकात्मक प्रश्न में स्थान अंतर देखें।

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

समान्तर श्रेणी \(19,26,33,\ldots\) के (n)वें पद का सूत्र \(a_n=7n+12\) है। (41)वां पद क्या होगा?

The (n)th-term formula of the AP \(19,26,33,\ldots\) is \(a_n=7n+12\). What is the (41)st term?

Explanation opens after your attempt
Correct Answer

D. (299)

Step 1

Concept

\(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.

Step 2

Why this answer is correct

The correct answer is D. (299). \(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.

Step 3

Exam Tip

\(a_{41}=7\times41+12=299\)। बने हुए सूत्र में केवल (n=41) रखें।

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

यदि किसी समान्तर श्रेणी का (m)वां पद (2m+3) और (d=2) है तो ((m+5))वां पद क्या होगा?

If the (m)th term of an AP is (2m+3) and (d=2), what is the ((m+5))th term?

Explanation opens after your attempt
Correct Answer

D. (2m+13)

Step 1

Concept

The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.

Step 2

Why this answer is correct

The correct answer is D. (2m+13). The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.

Step 3

Exam Tip

((m+5))वां पद (m)वें पद से (5d) आगे है इसलिए (2m+3+10=2m+13)। प्रतीकात्मक पदों में भी स्थान अंतर देखें।

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

समान्तर श्रेणी का पहला पद (25) है और (18)वां पद (93) है। सार्व अंतर क्या है?

The first term of an AP is (25) and the (18)th term is (93). What is the common difference?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).

Step 2

Why this answer is correct

The correct answer is C. (4). From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).

Step 3

Exam Tip

(93=25+17d) से (68=17d) इसलिए (d=4)। (18)वें पद के लिए गुणक (17) होता है।

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

समान्तर श्रेणी \(11,17,23,\ldots\) का (n)वां पद \(a_n=6n+5\) है। इसका (32)वां पद क्या होगा?

The (n)th term of the AP \(11,17,23,\ldots\) is \(a_n=6n+5\). What is its (32)nd term?

Explanation opens after your attempt
Correct Answer

B. (197)

Step 1

Concept

\(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.

Step 2

Why this answer is correct

The correct answer is B. (197). \(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.

Step 3

Exam Tip

\(a_{32}=6\times32+5=197\)। बनाए गए सूत्र में (n) का सही मान रखें।

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

एक समान्तर श्रेणी का पहला पद (18) और (16)वां पद (93) है। सार्व अंतर क्या है?

The first term of an AP is (18) and the (16)th term is (93). What is the common difference?

Explanation opens after your attempt
Correct Answer

A. (5)

Step 1

Concept

(93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).

Step 2

Why this answer is correct

The correct answer is A. (5). (93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).

Step 3

Exam Tip

(93=18+15d), इसलिए (75=15d) और (d=5)। (16)वें पद के लिए गुणक (15) होगा।

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

यदि किसी समान्तर श्रेणी का (10)वां पद (41) और (20)वां पद (81) है, तो उसका सार्व अंतर क्या है?

If the (10)th term of an AP is (41) and the (20)th term is (81), what is its common difference?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

\(The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).

Step 2

Why this answer is correct

\(The correct answer is C. (4). The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).

Step 3

Exam Tip

दो पदों का अंतर (81-41=40) है और पद संख्या का अंतर (10), इसलिए (d=4)। \(दो ज्ञात पदों में (d=\frac{\)पदों का अंतर}{स्थान का अंतर}) लगाएं।

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

यदि किसी समान्तर श्रेणी का पहला पद (7) और सार्व अंतर (4) है, तो उसका (18)वां पद क्या होगा?

If the first term of an AP is (7) and the common difference is (4), what is its (18)th term?

Explanation opens after your attempt
Correct Answer

A. (75)

Step 1

Concept

Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).

Step 2

Why this answer is correct

The correct answer is A. (75). Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).

Step 3

Exam Tip

सूत्र (a_n=a+(n-1)d) लगाने पर \(7+17\times4=75\)। परीक्षा में (n-1) को भूलना नहीं चाहिए।

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

यदि एपी का (4)था पद (21) और (d=6) है तो (10)वाँ पद क्या होगा?

If the (4)th term of an AP is (21) and (d=6), what is the (10)th term?

Explanation opens after your attempt
Correct Answer

C. (57)

Step 1

Concept

The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.

Step 2

Why this answer is correct

The correct answer is C. (57). The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.

Step 3

Exam Tip

(10)वाँ पद (4)थे पद से (6d) आगे है इसलिए (21+36=57)। पद संख्या का अंतर सीधे उपयोग करें।

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

यदि एपी का प्रथम पद (-12) और सार्व अंतर (5) है तो (16)वाँ पद क्या होगा?

If the first term of an AP is (-12) and the common difference is (5), what is the (16)th term?

Explanation opens after your attempt
Correct Answer

B. (63)

Step 1

Concept

\(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.

Step 2

Why this answer is correct

The correct answer is B. (63). \(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.

Step 3

Exam Tip

\(a_{16}=-12+15\times5=63\)। पहले (15d) निकालें फिर प्रथम पद जोड़ें।

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

यदि किसी एपी का प्रथम पद (9) और सार्व अंतर (10) है तो (7)वाँ पद क्या होगा?

If the first term of an AP is (9) and the common difference is (10), what is the (7)th term?

Explanation opens after your attempt
Correct Answer

B. (69)

Step 1

Concept

\(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.

Step 2

Why this answer is correct

The correct answer is B. (69). \(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.

Step 3

Exam Tip

\(a_7=9+6\times10=69\)। (7)वें पद के लिए (6d) जोड़ना होता है।

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

यदि किसी एपी का (3)रा पद (14) और (d=5) है तो (7)वाँ पद क्या होगा?

If the (3)rd term of an AP is (14) and (d=5), what is the (7)th term?

Explanation opens after your attempt
Correct Answer

C. (34)

Step 1

Concept

The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.

Step 2

Why this answer is correct

The correct answer is C. (34). The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.

Step 3

Exam Tip

(7)वाँ पद (3)रे पद से (4d) आगे है इसलिए (14+20=34)। बीच के पदों की संख्या सही गिनें।

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

यदि एपी का प्रथम पद (-2) और सार्व अंतर (6) है तो (12)वाँ पद क्या होगा?

If the first term of an AP is (-2) and the common difference is (6), what is the (12)th term?

Explanation opens after your attempt
Correct Answer

B. (64)

Step 1

Concept

\(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).

Step 2

Why this answer is correct

The correct answer is B. (64). \(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).

Step 3

Exam Tip

\(a_{12}=-2+11\times6=64\)। पहले गुणा करें फिर (-2) जोड़ें।

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

यदि किसी एपी का (5)वाँ पद (22) और (d=6) है तो (8)वाँ पद क्या है?

If the (5)th term of an AP is (22) and (d=6), what is the (8)th term?

Explanation opens after your attempt
Correct Answer

D. (40)

Step 1

Concept

The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.

Step 2

Why this answer is correct

The correct answer is D. (40). The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.

Step 3

Exam Tip

(8)वाँ पद (5)वें पद से (3d) आगे है इसलिए (22+18=40)। पदों का अंतर गिनना आसान तरीका है।

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

यदि एपी का (7)वाँ पद (31) है और (d=4) है तो (10)वाँ पद क्या होगा?

If the (7)th term of an AP is (31) and (d=4), what is the (10)th term?

Explanation opens after your attempt
Correct Answer

C. (43)

Step 1

Concept

The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.

Step 2

Why this answer is correct

The correct answer is C. (43). The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.

Step 3

Exam Tip

(10)वाँ पद (7)वें पद से (3d) आगे है इसलिए \(31+3\times4=43\)। पास के पदों के लिए अंतर विधि तेज होती है।

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

यदि एपी का प्रथम पद (15) और सार्व अंतर (-4) है तो (8)वाँ पद क्या होगा?

If the first term of an AP is (15) and the common difference is (-4), what is the (8)th term?

Explanation opens after your attempt
Correct Answer

A. (-13)

Step 1

Concept

(a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.

Step 2

Why this answer is correct

The correct answer is A. (-13). (a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.

Step 3

Exam Tip

(a_8=15+7(-4)=-13)। ऋणात्मक (d) को कोष्ठक में लिखना उपयोगी है।

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

यदि किसी एपी का प्रथम पद (5) और सार्व अंतर (3) है तो (8)वाँ पद क्या होगा?

If the first term of an AP is (5) and common difference is (3), what is the (8)th term?

Explanation opens after your attempt
Correct Answer

C. (26)

Step 1

Concept

Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).

Step 2

Why this answer is correct

The correct answer is C. (26). Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).

Step 3

Exam Tip

सूत्र (a_n=a+(n-1)d) लगाएं तो \(5+7\times3=26\)। परीक्षा में (n-1) लेना न भूलें।

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

किसी समांतर श्रेढ़ी का (n)वाँ पद \(a_n=2n+3\) है। (18)वाँ पद क्या होगा?

The (n)th term of an AP is \(a_n=2n+3\). What will be the (18)th term?

Explanation opens after your attempt
Correct Answer

A. (39)

Step 1

Concept

Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).

Step 2

Why this answer is correct

The correct answer is A. (39). Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).

Step 3

Exam Tip

(n=18) रखने पर \(a_{18}=2\times18+3=39\)। दिए गए \(a_n\) में सीधे पद संख्या रखें।

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

एक समांतर श्रेढ़ी का प्रथम पद (25) और सार्व अंतर (4) है। (21)वाँ पद क्या होगा?

The first term of an AP is (25) and the common difference is (4). What will be the (21)st term?

Explanation opens after your attempt
Correct Answer

B. (105)

Step 1

Concept

\(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.

Step 2

Why this answer is correct

The correct answer is B. (105). \(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.

Step 3

Exam Tip

\(a_{21}=25+20\times4=105\)। पद संख्या से (1) घटाना न भूलें।

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

यदि समांतर श्रेढ़ी का प्रथम पद (6) और सार्व अंतर (7) है, तो (11)वाँ पद क्या है?

If the first term of an AP is (6) and the common difference is (7), what is the (11)th term?

Explanation opens after your attempt
Correct Answer

D. (76)

Step 1

Concept

\(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.

Step 2

Why this answer is correct

The correct answer is D. (76). \(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.

Step 3

Exam Tip

\(a_{11}=6+10\times7=76\)। (11)वें पद तक (10) बार अंतर जुड़ता है।

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

समांतर श्रेढ़ी में प्रथम पद (a=4) और सार्व अंतर (d=3) है। इसका (10)वाँ पद क्या होगा?

In an AP, first term (a=4) and common difference (d=3). What is the (10)th term?

Explanation opens after your attempt
Correct Answer

A. (31)

Step 1

Concept

Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.

Step 2

Why this answer is correct

The correct answer is A. (31). Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.

Step 3

Exam Tip

सूत्र (a_n=a+(n-1)d) लगाने पर \(a_{10}=4+9\times3=31\)। परीक्षा में (n-1) को ध्यान से लिखें।

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Question Expert General Knowledge World History World Heritage Sites Class 10 Level 84

फुजि पर्वत को केवल प्राकृतिक पर्वत नहीं बल्कि सांस्कृतिक स्थल क्यों माना जाता है?

Why is Mount Fuji considered a cultural site and not only a natural mountain?

Explanation opens after your attempt
Correct Answer

A. क्योंकि यह कला तीर्थ और धार्मिक प्रतीकवाद से जुड़ा हैBecause it is linked with art pilgrimage and religious symbolism

Step 1

Concept

Mount Fuji is a strong symbol of Japanese art and spiritual tradition. For exams remember source of inspiration.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि यह कला तीर्थ और धार्मिक प्रतीकवाद से जुड़ा है / Because it is linked with art pilgrimage and religious symbolism. Mount Fuji is a strong symbol of Japanese art and spiritual tradition. For exams remember source of inspiration.

Step 3

Exam Tip

फुजि पर्वत जापानी कला और आध्यात्मिक परंपरा का मजबूत प्रतीक है। परीक्षा में प्रेरणा स्रोत याद रखें।

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Question Hard General Knowledge World History World Heritage Sites Class 10 Level 80

हिरोशिमा शांति स्मारक को केवल स्थापत्य नहीं बल्कि स्मृति स्थल क्यों माना जाता है?

Why is Hiroshima Peace Memorial considered a memory site and not only architecture?

Explanation opens after your attempt
Correct Answer

A. क्योंकि यह परमाणु युद्ध की मानवीय त्रासदी और शांति संदेश से जुड़ा हैBecause it is linked with human tragedy of nuclear war and message of peace

Step 1

Concept

Hiroshima Peace Memorial reminds us of war warning and peace. For exams understand memory heritage.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि यह परमाणु युद्ध की मानवीय त्रासदी और शांति संदेश से जुड़ा है / Because it is linked with human tragedy of nuclear war and message of peace. Hiroshima Peace Memorial reminds us of war warning and peace. For exams understand memory heritage.

Step 3

Exam Tip

हिरोशिमा शांति स्मारक युद्ध की चेतावनी और शांति की याद दिलाता है। परीक्षा में स्मृति धरोहर समझें।

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Question Hard General Knowledge World History World Heritage Sites Class 10 Level 80

बफर जोन की विफलता किसी विश्व धरोहर स्थल को किस प्रकार प्रभावित कर सकती है?

How can failure of a buffer zone affect a World Heritage Site?

Explanation opens after your attempt
Correct Answer

A. मुख्य क्षेत्र पर बाहरी दबाव बढ़ा सकती हैIt can increase external pressure on the core area

Step 1

Concept

A buffer zone protects the core heritage area. For exams remember the different roles of core and buffer.

Step 2

Why this answer is correct

The correct answer is A. मुख्य क्षेत्र पर बाहरी दबाव बढ़ा सकती है / It can increase external pressure on the core area. A buffer zone protects the core heritage area. For exams remember the different roles of core and buffer.

Step 3

Exam Tip

बफर जोन मुख्य धरोहर क्षेत्र की रक्षा करता है। परीक्षा में कोर और बफर का कार्य अलग याद रखें।

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Question Medium General Knowledge World History World Heritage Sites Class 10 Level 82

बेतलेहम का जन्मस्थान स्थल किस धार्मिक परंपरा से जुड़ा है?

The birthplace site in Bethlehem is linked with which religious tradition?

Explanation opens after your attempt
Correct Answer

C. ईसाई परंपराChristian tradition

Step 1

Concept

Bethlehem is a Christian heritage site linked with the birthplace of Jesus. For exams remember religious site and location together.

Step 2

Why this answer is correct

The correct answer is C. ईसाई परंपरा / Christian tradition. Bethlehem is a Christian heritage site linked with the birthplace of Jesus. For exams remember religious site and location together.

Step 3

Exam Tip

बेतलेहम यीशु के जन्मस्थान से जुड़ा ईसाई धरोहर स्थल है। परीक्षा में धार्मिक स्थल और स्थान साथ याद रखें।

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Question Easy General Knowledge World History World Heritage Sites Class 10 Level 83

नेमरत दाग किस देश का प्रसिद्ध पुरातात्विक पर्वतीय स्थल है?

Nemrut Dag is a famous archaeological mountain site of which country?

Explanation opens after your attempt
Correct Answer

B. तुर्कीTurkey

Step 1

Concept

Nemrut Dag is famous for giant statues in Turkey. For exams remember mountain monument.

Step 2

Why this answer is correct

The correct answer is B. तुर्की / Turkey. Nemrut Dag is famous for giant statues in Turkey. For exams remember mountain monument.

Step 3

Exam Tip

नेमरत दाग तुर्की में स्थित विशाल मूर्तियों के लिए प्रसिद्ध है। परीक्षा में पर्वतीय स्मारक याद रखें।

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Question Easy General Knowledge World History World Heritage Sites Class 10 Level 82

बेतलेहम में यीशु के जन्मस्थान से जुड़ा स्थल किस परंपरा से संबंधित है?

The site linked with the birthplace of Jesus in Bethlehem is related to which tradition?

Explanation opens after your attempt
Correct Answer

C. ईसाई परंपराChristian tradition

Step 1

Concept

The birthplace site in Bethlehem is linked with Christian tradition. For exams remember the context of religious sites.

Step 2

Why this answer is correct

The correct answer is C. ईसाई परंपरा / Christian tradition. The birthplace site in Bethlehem is linked with Christian tradition. For exams remember the context of religious sites.

Step 3

Exam Tip

बेतलेहम का जन्मस्थान ईसाई परंपरा से जुड़ा है। परीक्षा में धार्मिक स्थलों का संदर्भ याद रखें।

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Question Easy General Knowledge World History World Heritage Sites Class 10 Level 82

वेटिकन सिटी किस प्रकार का विश्व धरोहर स्थल है?

Vatican City is what type of World Heritage Site?

Explanation opens after your attempt
Correct Answer

B. सांस्कृतिक और धार्मिक केंद्रCultural and religious center

Step 1

Concept

Vatican City is a site of cultural and religious importance. For exams remember Saint Peter Basilica.

Step 2

Why this answer is correct

The correct answer is B. सांस्कृतिक और धार्मिक केंद्र / Cultural and religious center. Vatican City is a site of cultural and religious importance. For exams remember Saint Peter Basilica.

Step 3

Exam Tip

वेटिकन सिटी सांस्कृतिक और धार्मिक महत्व वाला स्थल है। परीक्षा में सेंट पीटर बेसिलिका याद रखें।

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Question Easy General Knowledge World History World Heritage Sites Class 10 Level 81

मसादा किस देश का प्रसिद्ध पुरातात्विक स्थल है?

Masada is a famous archaeological site of which country?

Explanation opens after your attempt
Correct Answer

C. इजराइलIsrael

Step 1

Concept

Masada is an ancient fortress like archaeological site in Israel. For exams remember desert fortress.

Step 2

Why this answer is correct

The correct answer is C. इजराइल / Israel. Masada is an ancient fortress like archaeological site in Israel. For exams remember desert fortress.

Step 3

Exam Tip

मसादा इजराइल में स्थित प्राचीन किले जैसा पुरातात्विक स्थल है। परीक्षा में रेगिस्तानी किला याद रखें।

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Question Easy General Knowledge World History World Heritage Sites Class 10 Level 81

गोबेकली तेपे किस देश में स्थित प्राचीन स्थल है?

Gobekli Tepe is an ancient site located in which country?

Explanation opens after your attempt
Correct Answer

A. तुर्कीTurkey

Step 1

Concept

Gobekli Tepe is an ancient archaeological site in Turkey. For exams remember prehistoric ritual site.

Step 2

Why this answer is correct

The correct answer is A. तुर्की / Turkey. Gobekli Tepe is an ancient archaeological site in Turkey. For exams remember prehistoric ritual site.

Step 3

Exam Tip

गोबेकली तेपे तुर्की में स्थित प्राचीन पुरातात्विक स्थल है। परीक्षा में प्रागैतिहासिक पूजा स्थल याद रखें।

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Question Easy General Knowledge World History World Heritage Sites Class 10 Level 80

विश्व धरोहर स्थल के संरक्षण में बफर जोन क्यों उपयोगी होता है?

Why is a buffer zone useful in protecting a World Heritage Site?

Explanation opens after your attempt
Correct Answer

A. मुख्य स्थल को बाहरी दबावों से बचाने के लिएTo protect the main site from external pressures

Step 1

Concept

A buffer zone helps protect the main heritage area. For exams remember the difference between core area and buffer zone.

Step 2

Why this answer is correct

The correct answer is A. मुख्य स्थल को बाहरी दबावों से बचाने के लिए / To protect the main site from external pressures. A buffer zone helps protect the main heritage area. For exams remember the difference between core area and buffer zone.

Step 3

Exam Tip

बफर जोन मुख्य धरोहर क्षेत्र की सुरक्षा में मदद करता है। परीक्षा में कोर क्षेत्र और बफर जोन का अंतर याद रखें।

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Question Expert General Knowledge World History World Heritage Sites Class 10 Level 80

बफर जोन विश्व धरोहर स्थल प्रबंधन में क्यों बनाया जाता है?

Why is a buffer zone created in World Heritage site management?

Explanation opens after your attempt
Correct Answer

A. मुख्य धरोहर क्षेत्र को बाहरी दबावों से संरक्षण देने के लिएTo protect the core heritage area from external pressures

Step 1

Concept

A buffer zone is a supporting area for protecting the core site. For exams remember the difference between core area and buffer zone.

Step 2

Why this answer is correct

The correct answer is A. मुख्य धरोहर क्षेत्र को बाहरी दबावों से संरक्षण देने के लिए / To protect the core heritage area from external pressures. A buffer zone is a supporting area for protecting the core site. For exams remember the difference between core area and buffer zone.

Step 3

Exam Tip

बफर जोन मुख्य स्थल की सुरक्षा में सहायक क्षेत्र होता है। परीक्षा में कोर एरिया और बफर जोन का अंतर याद रखें।

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Question Expert General Knowledge World History World Heritage Sites Class 10 Level 80

विश्व धरोहर स्थल के लिए अखंडता की शर्त किस बात से संबंधित है?

The condition of integrity for a World Heritage Site is related to what?

Explanation opens after your attempt
Correct Answer

A. स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थितिWholeness of the site and condition supporting its value

Step 1

Concept

Integrity shows whether the site's value is sufficiently represented and protected. For exams keep integrity and authenticity separate.

Step 2

Why this answer is correct

The correct answer is A. स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value. Integrity shows whether the site's value is sufficiently represented and protected. For exams keep integrity and authenticity separate.

Step 3

Exam Tip

अखंडता बताती है कि स्थल का मूल्य सुरक्षित और पर्याप्त रूप से प्रतिनिधित है या नहीं। परीक्षा में अखंडता और प्रामाणिकता अलग रखें।

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Question Medium General Knowledge Indian History Historical Monuments of India Class 10 Level 37

धमेख स्तूप किस बौद्ध स्थल पर स्थित है?

Dhamek Stupa is located at which Buddhist site?

Explanation opens after your attempt
Correct Answer

B. सारनाथSarnath

Step 1

Concept

Dhamek Stupa is located at Sarnath which is traditionally linked with Buddha's first sermon. For exams remember special events of Buddhist sites.

Step 2

Why this answer is correct

The correct answer is B. सारनाथ / Sarnath. Dhamek Stupa is located at Sarnath which is traditionally linked with Buddha's first sermon. For exams remember special events of Buddhist sites.

Step 3

Exam Tip

धमेख स्तूप सारनाथ में स्थित है जहां बुद्ध के प्रथम उपदेश की परंपरा जुड़ी है। परीक्षा में बौद्ध तीर्थों की विशेष घटनाएं याद रखें।

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Question Expert General Knowledge World History Ancient Civilizations Class 10 Level 49

कार्थेज में टोपेट शब्द किस प्रकार के पुरातात्विक स्थल से जुड़ा है?

The term tophet in Carthage is associated with what type of archaeological site?

Explanation opens after your attempt
Correct Answer

B. अनुष्ठानिक दफन क्षेत्रRitual burial area

Step 1

Concept

The tophet at Carthage is a debated site linked with ritual and burial. For exams interpret sensitive evidence carefully.

Step 2

Why this answer is correct

The correct answer is B. अनुष्ठानिक दफन क्षेत्र / Ritual burial area. The tophet at Carthage is a debated site linked with ritual and burial. For exams interpret sensitive evidence carefully.

Step 3

Exam Tip

टोपेट कार्थेज में अनुष्ठान और दफन से जुड़ा विवादित स्थल है। परीक्षा में संवेदनशील प्रमाणों की व्याख्या सावधानी से करें।

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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

किसी समांतर श्रेढ़ी के पहले पद और (60)वें पद का योग (300) है। (21)वें पद से (40)वें पद तक का योग ज्ञात कीजिए।

The sum of the first term and the (60)th term of an AP is (300). Find the sum from the (21)st term to the (40)th term.

Explanation opens after your attempt
Correct Answer

C. (3000)

Step 1

Concept

\(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.

Step 2

Why this answer is correct

The correct answer is C. (3000). \(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.

Step 3

Exam Tip

\(a_{21}+a_{40}=a_1+a_{60}=300\), इसलिए (20) पदों का योग (3000) है। सममित पदों का योग बराबर होता 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

किसी समांतर श्रेढ़ी के पहले पद और (40)वें पद का योग (210) है। (11)वें पद से (30)वें पद तक का योग ज्ञात कीजिए।

The sum of the first term and the (40)th term of an AP is (210). Find the sum from the (11)th term to the (30)th term.

Explanation opens after your attempt
Correct Answer

B. (2100)

Step 1

Concept

\(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.

Step 2

Why this answer is correct

The correct answer is B. (2100). \(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.

Step 3

Exam Tip

\(a_{11}+a_{30}=a_1+a_{40}=210\), इसलिए (20) पदों का योग (2100) है। सममित पदों का योग बराबर होता 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 67

किसी समांतर श्रेढ़ी में पहले (20) पदों का योग (740) है और (20)वाँ पद (60) है। पहला पद ज्ञात कीजिए।

In an AP, the sum of the first (20) terms is (740), and the (20)th term is (60). Find the first term.

Explanation opens after your attempt
Correct Answer

B. (14)

Step 1

Concept

From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.

Step 2

Why this answer is correct

The correct answer is B. (14). From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.

Step 3

Exam Tip

(740=10(a+60)) से (a=14) मिलता है। जब (n)वाँ पद दिया हो तो उसे अंतिम पद की तरह इस्तेमाल करें।

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

(600) से कम (13) के धनात्मक गुणजों में अंतिम पद क्या है?

What is the last term among the positive multiples of (13) less than (600)?

Explanation opens after your attempt
Correct Answer

B. (598)

Step 1

Concept

In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.

Step 2

Why this answer is correct

The correct answer is B. (598). In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.

Step 3

Exam Tip

(13n<600) में सबसे बड़ा (n=46) है इसलिए पद \(13\times46=598\)। सीमा से कम सबसे बड़ा पूर्णांक लें।

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

समान्तर श्रेणी \(73,68,63,\ldots\) का (n)वां पद (-12) है। (n) क्या है?

The (n)th term of the AP \(73,68,63,\ldots\) is (-12). What is (n)?

Explanation opens after your attempt
Correct Answer

C. (18)

Step 1

Concept

From (-12=73+(n-1)(-5)), (85=5(n-1)) so (n=18). In a decreasing AP keep signs correct up to the negative target.

Step 2

Why this answer is correct

The correct answer is C. (18). From (-12=73+(n-1)(-5)), (85=5(n-1)) so (n=18). In a decreasing AP keep signs correct up to the negative target.

Step 3

Exam Tip

(-12=73+(n-1)(-5)) से (85=5(n-1)) इसलिए (n=18)। घटती AP में ऋणात्मक लक्ष्य तक चिन्ह सही रखें।

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

यदि AP \(z,z+5,z+10,\ldots\) का (19)वां पद (112) है तो (z) क्या होगा?

If the (19)th term of the AP \(z,z+5,z+10,\ldots\) is (112), what is (z)?

Explanation opens after your attempt
Correct Answer

C. (22)

Step 1

Concept

From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.

Step 2

Why this answer is correct

The correct answer is C. (22). From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.

Step 3

Exam Tip

\(112=z+18\times5\) से (z=22)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।

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

समान्तर श्रेणी \(7,12,17,\ldots\) में (180) से कम अंतिम पद क्या है?

In the AP \(7,12,17,\ldots\), what is the last term less than (180)?

Explanation opens after your attempt
Correct Answer

C. (177)

Step 1

Concept

The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).

Step 2

Why this answer is correct

The correct answer is C. (177). The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).

Step 3

Exam Tip

पद (7+5(n-1)) हैं। (180) से कम अंतिम पद (177) है क्योंकि अगला पद (182) होगा।

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

एक AP में (a=63) और (d=-4) है। कौन-सा पद (-1) होगा?

In an AP (a=63) and (d=-4). Which term will be (-1)?

Explanation opens after your attempt
Correct Answer

C. (17)वां(17)th

Step 1

Concept

From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.

Step 2

Why this answer is correct

The correct answer is C. (17)वां / (17)th. From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.

Step 3

Exam Tip

(-1=63+(n-1)(-4)) से (64=4(n-1)) इसलिए (n=17)। ऋणात्मक लक्ष्य पद में चिन्हों को ध्यान से संभालें।

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

समान्तर श्रेणी \(105,98,91,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?

Which is the first negative term of the AP \(105,98,91,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (17)वां(17)th

Step 1

Concept

(a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.

Step 2

Why this answer is correct

The correct answer is C. (17)वां / (17)th. (a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.

Step 3

Exam Tip

(a_n=105+(n-1)(-7)=112-7n)। \(a_n<0\) से (n>16) इसलिए पहला ऋणात्मक पद (17)वां 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 \(26,35,44,\ldots\) का कौन-सा पद (206) है?

Which term of the AP \(26,35,44,\ldots\) is (206)?

Explanation opens after your attempt
Correct Answer

C. (21)वां(21)st

Step 1

Concept

From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).

Step 2

Why this answer is correct

The correct answer is C. (21)वां / (21)st. From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).

Step 3

Exam Tip

(206=26+(n-1)9) से (180=9(n-1)) इसलिए (n=21)। पद और पहले पद का अंतर (d) से भाग दें।

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

किसी समान्तर श्रेणी का (14)वां पद (92) और (d=7) है। \(a_1\) क्या होगा?

The (14)th term of an AP is (92) and (d=7). What is \(a_1\)?

Explanation opens after your attempt
Correct Answer

A. (1)

Step 1

Concept

From \(92=a+13\times7\), (a=1). From the (14)th term to the first term (13d) is subtracted.

Step 2

Why this answer is correct

The correct answer is A. (1). From \(92=a+13\times7\), (a=1). From the (14)th term to the first term (13d) is subtracted.

Step 3

Exam Tip

\(92=a+13\times7\) से (a=1)। (14)वें पद से पहले पद तक (13d) घटता 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 \(9,17,25,\ldots\) का कौन-सा पद (201) है?

Which term of the AP \(9,17,25,\ldots\) is (201)?

Explanation opens after your attempt
Correct Answer

C. (25)वां(25)th

Step 1

Concept

From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.

Step 2

Why this answer is correct

The correct answer is C. (25)वां / (25)th. From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.

Step 3

Exam Tip

(201=9+(n-1)8) से (192=8(n-1)) और (n=25)। पद संख्या पूर्णांक आए तो उत्तर सही दिशा में है।

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

(500) से कम (11) के धनात्मक गुणजों में अंतिम पद क्या है?

What is the last term among the positive multiples of (11) less than (500)?

Explanation opens after your attempt
Correct Answer

B. (495)

Step 1

Concept

In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.

Step 2

Why this answer is correct

The correct answer is B. (495). In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.

Step 3

Exam Tip

(11n<500) में सबसे बड़ा (n=45) है इसलिए पद \(11\times45=495\)। सीमा से कम सबसे बड़ा पूर्णांक 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 \(55,51,47,\ldots\) का (n)वां पद (-17) है। (n) क्या है?

The (n)th term of the AP \(55,51,47,\ldots\) is (-17). What is (n)?

Explanation opens after your attempt
Correct Answer

C. (19)

Step 1

Concept

From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.

Step 2

Why this answer is correct

The correct answer is C. (19). From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.

Step 3

Exam Tip

(-17=55+(n-1)(-4)) से (72=4(n-1)) इसलिए (n=19)। ऋणात्मक पद तक जाते समय चिन्ह सही रखें।

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

यदि समान्तर श्रेणी \(y,y+6,y+12,\ldots\) का (12)वां पद (89) है तो (y) का मान क्या है?

If the (12)th term of the AP \(y,y+6,y+12,\ldots\) is (89), what is the value of (y)?

Explanation opens after your attempt
Correct Answer

D. (23)

Step 1

Concept

From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).

Step 2

Why this answer is correct

The correct answer is D. (23). From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).

Step 3

Exam Tip

\(89=y+11\times6\) से (y=23)। चर वाले पहले पद को सीधे (a) मानें।

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

समान्तर श्रेणी \(2,6,10,\ldots\) में (75) से कम अंतिम पद क्या है?

In the AP \(2,6,10,\ldots\), what is the last term less than (75)?

Explanation opens after your attempt
Correct Answer

A. (74)

Step 1

Concept

The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).

Step 2

Why this answer is correct

The correct answer is A. (74). The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).

Step 3

Exam Tip

इस श्रेणी के पद (2+4(n-1)) हैं। (75) से कम अंतिम पद (74) है।

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

एक समान्तर श्रेणी में (a=48) और (d=-3) है। कौन-सा पद (0) होगा?

In an AP, (a=48) and (d=-3). Which term will be (0)?

Explanation opens after your attempt
Correct Answer

C. (17)वां(17)th

Step 1

Concept

From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.

Step 2

Why this answer is correct

The correct answer is C. (17)वां / (17)th. From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.

Step 3

Exam Tip

(0=48+(n-1)(-3)) से (3(n-1)=48) इसलिए (n=17)। शून्य पद के लिए भी सामान्य सूत्र लगाएं।

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

समान्तर श्रेणी \(72,66,60,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?

Which is the first negative term of the AP \(72,66,60,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (14)वां(14)th

Step 1

Concept

(a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.

Step 2

Why this answer is correct

The correct answer is B. (14)वां / (14)th. (a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.

Step 3

Exam Tip

(a_n=72+(n-1)(-6)=78-6n)। \(a_n<0\) से (n>13) इसलिए पहला ऋणात्मक पद (14)वां है।

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

समान्तर श्रेणी \(14,23,32,\ldots\) का कौन-सा पद (185) है?

Which term of the AP \(14,23,32,\ldots\) is (185)?

Explanation opens after your attempt
Correct Answer

C. (20)वां(20)th

Step 1

Concept

From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.

Step 2

Why this answer is correct

The correct answer is C. (20)वां / (20)th. From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.

Step 3

Exam Tip

(185=14+(n-1)9) से (171=9(n-1)) और (n=20)। अंतर को (d) से भाग देकर पद संख्या पाएं।

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

किसी समान्तर श्रेणी का (10)वां पद (62) और (d=5) है। \(a_1\) क्या होगा?

The (10)th term of an AP is (62) and (d=5). What is \(a_1\)?

Explanation opens after your attempt
Correct Answer

D. (17)

Step 1

Concept

From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).

Step 2

Why this answer is correct

The correct answer is D. (17). From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).

Step 3

Exam Tip

\(62=a+9\times5\) से (a=17)। (10)वें पद से पहले पद तक (9d) घटता है।

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

समान्तर श्रेणी \(21,29,37,\ldots\) का कौन-सा पद (149) है?

Which term of the AP \(21,29,37,\ldots\) is (149)?

Explanation opens after your attempt
Correct Answer

C. (17)वां(17)th

Step 1

Concept

From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).

Step 2

Why this answer is correct

The correct answer is C. (17)वां / (17)th. From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).

Step 3

Exam Tip

(149=21+(n-1)8) से (128=8(n-1)) इसलिए (n=17)। पद संख्या पूछी हो तो दिए पद को \(a_n\) मानें।

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

समान्तर श्रेणी \(27,24,21,\ldots\) का (n)वां पद (-30) है। (n) क्या है?

The (n)th term of the AP \(27,24,21,\ldots\) is (-30). What is (n)?

Explanation opens after your attempt
Correct Answer

C. (20)

Step 1

Concept

From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.

Step 2

Why this answer is correct

The correct answer is C. (20). From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.

Step 3

Exam Tip

(-30=27+(n-1)(-3)) से (57=3(n-1)), इसलिए (n=20)। ऋणात्मक लक्ष्य पद में चिन्ह सावधानी से बदलें।

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

यदि समान्तर श्रेणी \(x, x+4, x+8,\ldots\) का (10)वां पद (50) है, तो (x) का मान क्या है?

If the (10)th term of the AP \(x, x+4, x+8,\ldots\) is (50), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

C. (14)

Step 1

Concept

\(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.

Step 2

Why this answer is correct

The correct answer is C. (14). \(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.

Step 3

Exam Tip

\(50=x+9\times4\), इसलिए (x=14)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।

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

एक समान्तर श्रेणी में (a=30) और (d=-2) है। कौन-सा पद (0) होगा?

In an AP, (a=30) and (d=-2). Which term will be (0)?

Explanation opens after your attempt
Correct Answer

C. (16)वां(16)th

Step 1

Concept

From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.

Step 2

Why this answer is correct

The correct answer is C. (16)वां / (16)th. From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.

Step 3

Exam Tip

(0=30+(n-1)(-2)) से (2(n-1)=30), अतः (n=16)। शून्य पद के लिए भी वही (n)वां पद सूत्र लगाएं।

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

समान्तर श्रेणी \(45,40,35,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?

Which is the first negative term of the AP \(45,40,35,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (11)वां(11)th

Step 1

Concept

(a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.

Step 2

Why this answer is correct

The correct answer is B. (11)वां / (11)th. (a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.

Step 3

Exam Tip

(a_n=45+(n-1)(-5)=50-5n)। \(a_n<0\) से (n>10), इसलिए पहला ऋणात्मक पद (11)वां है।

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

समान्तर श्रेणी \(15,21,27,\ldots\) का कौन-सा पद (111) है?

Which term of the AP \(15,21,27,\ldots\) is (111)?

Explanation opens after your attempt
Correct Answer

C. (17)वां(17)th

Step 1

Concept

(111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).

Step 2

Why this answer is correct

The correct answer is C. (17)वां / (17)th. (111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).

Step 3

Exam Tip

(111=15+(n-1)6), इसलिए (96=6(n-1)) और (n=17)। पद संख्या में अंतर को (d) से भाग दें।

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

किसी समान्तर श्रेणी का (8)वां पद (35) और (d=4) है। \(a_1\) क्या होगा?

The (8)th term of an AP is (35) and (d=4). What is \(a_1\)?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

\(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).

Step 2

Why this answer is correct

The correct answer is C. (7). \(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).

Step 3

Exam Tip

\(35=a+7\times4\), इसलिए (a=7)। (8)वें पद के लिए (7d) घटाएं।

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

समान्तर श्रेणी \(3,8,13,\ldots\) का कौन-सा पद (88) है?

Which term of the AP \(3,8,13,\ldots\) is (88)?

Explanation opens after your attempt
Correct Answer

A. (18)वां(18)th

Step 1

Concept

From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).

Step 2

Why this answer is correct

The correct answer is A. (18)वां / (18)th. From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).

Step 3

Exam Tip

(88=3+(n-1)5) से (85=5(n-1)), अतः (n=18)। पद संख्या के प्रश्न में दिए पद को \(a_n\) मानें।

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

समांतर श्रेढ़ी \(200,180,160,140,\ldots\) का (11)वाँ पद क्या है?

What is the (11)th term of the AP \(200,180,160,140,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. (0)

Step 1

Concept

Here (d=-20), so (a_{11}=200+10(-20)=0). In a decreasing AP, a term can also become zero.

Step 2

Why this answer is correct

The correct answer is D. (0). Here (d=-20), so (a_{11}=200+10(-20)=0). In a decreasing AP, a term can also become zero.

Step 3

Exam Tip

यहाँ (d=-20) है, इसलिए (a_{11}=200+10(-20)=0)। घटती श्रेढ़ी में पद शून्य भी हो सकता है।

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

यदि \(a_n=4n+6\) है, तो (25)वाँ पद क्या होगा?

If \(a_n=4n+6\), what will be the (25)th term?

Explanation opens after your attempt
Correct Answer

A. (106)

Step 1

Concept

\(a_{25}=4\times25+6=106\). Put (n=25) in the given general term.

Step 2

Why this answer is correct

The correct answer is A. (106). \(a_{25}=4\times25+6=106\). Put (n=25) in the given general term.

Step 3

Exam Tip

\(a_{25}=4\times25+6=106\)। दिए गए सामान्य पद में (n=25) रखें।

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

यदि (a=0) और (d=4) है, तो समांतर श्रेढ़ी का (26)वाँ पद क्या है?

If (a=0) and (d=4), what is the (26)th term of the AP?

Explanation opens after your attempt
Correct Answer

D. (100)

Step 1

Concept

\(a_{26}=0+25\times4=100\). Even with zero first term, (n-1) differences are added.

Step 2

Why this answer is correct

The correct answer is D. (100). \(a_{26}=0+25\times4=100\). Even with zero first term, (n-1) differences are added.

Step 3

Exam Tip

\(a_{26}=0+25\times4=100\)। शून्य प्रथम पद होने पर भी (n-1) अंतर जुड़ते हैं।

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

एक समांतर श्रेढ़ी में \(a_1=13\) और (d=8) है। (10)वाँ पद क्या है?

In an AP, \(a_1=13\) and (d=8). What is the (10)th term?

Explanation opens after your attempt
Correct Answer

A. (85)

Step 1

Concept

\(a_{10}=13+9\times8=85\). \(a_1\) is the first term (a).

Step 2

Why this answer is correct

The correct answer is A. (85). \(a_{10}=13+9\times8=85\). \(a_1\) is the first term (a).

Step 3

Exam Tip

\(a_{10}=13+9\times8=85\)। \(a_1\) ही प्रथम पद (a) होता है।

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

यदि \(a_n=30-3n\) है, तो (6)वाँ पद क्या होगा?

If \(a_n=30-3n\), what will be the (6)th term?

Explanation opens after your attempt
Correct Answer

D. (12)

Step 1

Concept

\(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.

Step 2

Why this answer is correct

The correct answer is D. (12). \(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.

Step 3

Exam Tip

\(a_6=30-3\times6=12\)। घटते हुए सामान्य पद में घटाव सावधानी से करें।

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

यदि \(a_n=5n-1\) हो, तो इस समांतर श्रेढ़ी का (20)वाँ पद क्या है?

If \(a_n=5n-1\), what is the (20)th term of this AP?

Explanation opens after your attempt
Correct Answer

B. (99)

Step 1

Concept

\(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.

Step 2

Why this answer is correct

The correct answer is B. (99). \(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.

Step 3

Exam Tip

\(a_{20}=5\times20-1=99\)। जब \(a_n\) दिया हो, तो सूत्र में (n) का मान रखें।

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

समांतर श्रेढ़ी \(-10,-6,-2,2,\ldots\) का (18)वाँ पद कौन सा है?

Which is the (18)th term of the AP \(-10,-6,-2,2,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (58)

Step 1

Concept

Here (a=-10), (d=4), so \(a_{18}=-10+17\times4=58\). The formula remains the same even when terms move from negative to positive.

Step 2

Why this answer is correct

The correct answer is C. (58). Here (a=-10), (d=4), so \(a_{18}=-10+17\times4=58\). The formula remains the same even when terms move from negative to positive.

Step 3

Exam Tip

यहाँ (a=-10), (d=4) है, इसलिए \(a_{18}=-10+17\times4=58\)। ऋणात्मक से धनात्मक जाने पर भी सूत्र समान रहता है।

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-2+ax+4) का स्थिर पद (4) है, तो स्थिर पद कौन-सा है?

If the constant term of (p(x)=x-2+ax+4) is (4), which term is the constant term?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

The constant term does not contain (x). So (4) is the constant term.

Step 2

Why this answer is correct

The correct answer is C. (4). The constant term does not contain (x). So (4) is the constant term.

Step 3

Exam Tip

स्थिर पद में (x) नहीं होता। इसलिए (4) स्थिर पद है।

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Question Expert Art Education Fundamentals of Visual Arts Line Class 10 Level 8

रेखीय संतुलन में मोटी छोटी रेखा और पतली लंबी रेखा का संबंध कैसे देखा जाता है?

How is the relation between a thick short line and a thin long line seen in linear balance?

Explanation opens after your attempt
Correct Answer

B. दोनों का दृश्य भार अलग तरीके से संतुलित हो सकता हैTheir visual weights can balance in different ways

Step 1

Concept

Visual weight comes not only from length but also thickness and placement. Exam tip: consider multiple qualities together.

Step 2

Why this answer is correct

The correct answer is B. दोनों का दृश्य भार अलग तरीके से संतुलित हो सकता है / Their visual weights can balance in different ways. Visual weight comes not only from length but also thickness and placement. Exam tip: consider multiple qualities together.

Step 3

Exam Tip

दृश्य भार केवल लंबाई नहीं, मोटाई और स्थिति से भी बनता है। परीक्षा में कई गुण साथ देखें।

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Question Hard General Knowledge Indian History Historical Monuments of India Class 10 Level 36

राजघाट पर महात्मा गांधी की समाधि पर कौन सा छोटा वाक्य अंकित है?

Which short phrase is inscribed on Mahatma Gandhi's memorial at Raj Ghat?

Explanation opens after your attempt
Correct Answer

A. हे रामHey Ram

Step 1

Concept

The phrase Hey Ram at Raj Ghat is linked with Mahatma Gandhi's memory. For exams remember symbols and phrases of national memorials.

Step 2

Why this answer is correct

The correct answer is A. हे राम / Hey Ram. The phrase Hey Ram at Raj Ghat is linked with Mahatma Gandhi's memory. For exams remember symbols and phrases of national memorials.

Step 3

Exam Tip

राजघाट पर हे राम वाक्य महात्मा गांधी की स्मृति से जुड़ा है। परीक्षा में राष्ट्रीय स्मारकों के प्रतीक और वाक्य याद रखें।

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Question Expert Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 18

यदि \(\sqrt{2}\) की जगह \(\sqrt{8}\) पर विचार किया जाए, तो \(\sqrt{8}\) के अपरिमेय होने का सबसे सही छोटा तर्क क्या है?

If \(\sqrt{8}\) is considered instead of \(\sqrt{2}\), what is the best short reason that \(\sqrt{8}\) is irrational?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{8}=2\sqrt{2}\), और परिमेय (2) को अपरिमेय \(\sqrt{2}\) से गुणा करने पर अपरिमेय संख्या मिलती है\(\sqrt{8}=2\sqrt{2}\), and multiplying irrational \(\sqrt{2}\) by nonzero rational (2) gives an irrational number

Step 1

Concept

\(\sqrt{8}=\sqrt{4\cdot2}=2\sqrt{2}\).

Step 2

Why this answer is correct

\(\sqrt{2}\) is irrational and (2) is a nonzero rational number, so \(2\sqrt{2}\) remains irrational.

Step 3

Exam Tip

Separate perfect-square factors while simplifying roots. चरण 1: \(\sqrt{8}=\sqrt{4\cdot2}=2\sqrt{2}\)। चरण 2: \(\sqrt{2}\) अपरिमेय है और (2) शून्येतर परिमेय है, इसलिए \(2\sqrt{2}\) अपरिमेय रहेगा। चरण 3: सरलीकरण में पूर्ण वर्ग गुणनखंड अलग करें।

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Question Medium Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 16

कौन सा विकल्प \(\sqrt{2}\) की सिद्धि का सही संक्षिप्त ढांचा देता है?

Which option gives the correct short structure of the proof of \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. परिमेय मानें, वर्ग करें, दोनों सम पाएं, सहअभाज्य से विरोधाभासAssume rational, square, find both even, contradict coprime

Step 1

Concept

Assume \(\sqrt{2}\) rational and write it as \(\frac{p}{q}\).

Step 2

Why this answer is correct

Squaring leads to both (p) and (q) being even.

Step 3

Exam Tip

Both even contradict the coprime condition. चरण 1: \(\sqrt{2}\) को परिमेय मानकर \(\frac{p}{q}\) लिखते हैं। चरण 2: वर्ग करने पर दोनों (p) और (q) सम निकलते हैं। चरण 3: दोनों सम होना सहअभाज्य शर्त से विरोधाभास देता है।

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Question Easy Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 17

कौन सा विकल्प \(\sqrt{5}\) की अपरिमेयता का सही संक्षिप्त कारण है?

Which option is the correct short reason for the irrationality of \(\sqrt{5}\)?

Explanation opens after your attempt
Correct Answer

A. परिमेय मानने पर अंश और हर दोनों (5) से विभाज्य हो जाते हैंAssuming rational makes both numerator and denominator divisible by (5)

Step 1

Concept

We assume \(\sqrt{5}\) rational and write it in lowest form.

Step 2

Why this answer is correct

The proof shows numerator and denominator both divisible by (5).

Step 3

Exam Tip

This contradicts lowest form, so \(\sqrt{5}\) is irrational. चरण 1: \(\sqrt{5}\) को परिमेय मानकर सरलतम भिन्न में लिखते हैं। चरण 2: प्रमाण से अंश और हर दोनों (5) से विभाज्य मिलते हैं। चरण 3: यह सरलतम रूप के विरुद्ध है, इसलिए \(\sqrt{5}\) अपरिमेय है।

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