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66 results found for "triple-minus-index" in Class 10.

Question Easy General Knowledge World History World Wars Class 10 Level 51

प्रथम विश्व युद्ध से पहले ट्रिपल एलायंस में कौन से देश शामिल थे?

Which countries were part of the Triple Alliance before the First World War?

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Correct Answer

A. जर्मनी ऑस्ट्रिया हंगरी और इटलीGermany Austria-Hungary and Italy

Explanation

Simple Explanation

ट्रिपल एलायंस में जर्मनी ऑस्ट्रिया हंगरी और इटली थे। परीक्षा में गठबंधन प्रणाली को युद्ध के कारणों से जोड़ें। / The Triple Alliance included Germany Austria-Hungary and Italy. For exams connect alliance systems with the causes of war.

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Question Easy General Knowledge World History World Wars Class 10 Level 51

प्रथम विश्व युद्ध से पहले ट्रिपल एंतांते में कौन से देश प्रमुख थे?

Which countries were major members of the Triple Entente before the First World War?

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Correct Answer

D. ब्रिटेन फ्रांस और रूसBritain France and Russia

Explanation

Simple Explanation

ट्रिपल एंतांते में ब्रिटेन फ्रांस और रूस प्रमुख थे। परीक्षा में इसे केंद्रीय शक्तियों से अलग याद रखें। / The Triple Entente included Britain France and Russia. For exams remember it separately from the Central Powers.

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Question Expert Science Chemical Substances – Nature and Behaviour Carbon and its Compounds Class 10 Level 15

किस यौगिक में कार्बन कार्बन तिहरा बंध होता है?

Which compound has a carbon-carbon triple bond?

Explanation opens after your attempt
Correct Answer

A. एथाइनEthyne

Step 1

Concept

एथाइन असंतृप्त हाइड्रोकार्बन है। / Ethyne is an unsaturated hydrocarbon.

Step 2

Why this answer is correct

इसमें दो कार्बन परमाणुओं के बीच तिहरा बंध होता है। / It has a triple bond between two carbon atoms.

Step 3

Exam Tip

इसलिए एथाइन सही उत्तर है। / Therefore ethyne is correct.

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

प्रथम विश्व युद्ध में इटली का त्रिपक्षीय गठबंधन छोड़कर मित्र राष्ट्रों की ओर जाना किस कूटनीतिक तथ्य को दिखाता है?

Italy leaving the Triple Alliance and joining the Allies in the First World War shows which diplomatic fact?

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Correct Answer

B. राष्ट्रीय हित गठबंधन प्रतिबद्धताओं से ऊपर आ सकते हैंNational interests can override alliance commitments

Explanation

Simple Explanation

इटली ने अपने हितों के अनुसार पक्ष बदला। परीक्षा में गठबंधन को स्थायी नहीं बल्कि हित आधारित मानें। / Italy changed sides according to its interests. For exams treat alliances as interest-based rather than permanent.

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Question Hard Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 3

यदि किसी संख्या को 28 से भाग देने पर शेषफल 27 है, तो उसकी तिगुनी संख्या को 28 से भाग देने पर शेषफल क्या होगा?

If a number leaves remainder 27 when divided by 28, what remainder will three times the number leave when divided by 28?

Explanation opens after your attempt
Correct Answer

A. 25

Step 1

Concept

तिगुनी संख्या के लिए शेषफल \(3\times27=81\) होगा। / For three times the number, the remainder part is \(3\times27=81\).

Step 2

Why this answer is correct

\(81=28\times2+25\), इसलिए अंतिम शेषफल 25 है। / \(81=28\times2+25\), so the final remainder is 25.

Step 3

Exam Tip

गुणा के बाद मिले शेषफल को भाजक से छोटा करना जरूरी है। / After multiplication, reduce the remainder below the divisor.

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Question Hard Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 1

यदि किसी संख्या को 13 से भाग देने पर शेषफल 12 है, तो उस संख्या की तिगुनी संख्या को 13 से भाग देने पर शेषफल क्या होगा?

If a number leaves remainder 12 when divided by 13, what is the remainder when three times the number is divided by 13?

Explanation opens after your attempt
Correct Answer

A. 10

Step 1

Concept

संख्या (13q+12) है। / The number is (13q+12).

Step 2

Why this answer is correct

तिगुनी संख्या में शेषफल \(3\times12=36\) होगा, और \(36=13\times2+10\)। / For three times the number, the remainder part is \(3\times12=36\), and \(36=13\times2+10\).

Step 3

Exam Tip

गुणन के बाद शेषफल को फिर से भाजक से कम करें। / After multiplication, reduce the remainder below the divisor.

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Question Easy Science Chemical Substances – Nature and Behaviour Carbon and its Compounds Class 10 Level 2

किस समूह के कार्बनिक यौगिकों के नाम सामान्यतः आइन पर समाप्त होते हैं?

Names of which group of organic compounds generally end with yne?

Explanation opens after your attempt
Correct Answer

C. एल्काइनAlkynes

Step 1

Concept

त्रि बंध वाले हाइड्रोकार्बन एल्काइन कहलाते हैं। / Hydrocarbons with triple bonds are alkynes.

Step 2

Why this answer is correct

इनके नाम सामान्यतः आइन पर समाप्त होते हैं। / Their names generally end with yne.

Step 3

Exam Tip

एथाइन को इस समूह का उदाहरण याद रखें। / Remember ethyne as an example of this group.

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Question Easy Science Chemical Substances – Nature and Behaviour Carbon and its Compounds Class 10 Level 2

एथाइन किस प्रकार का हाइड्रोकार्बन है?

Ethyne is which type of hydrocarbon?

Explanation opens after your attempt
Correct Answer

C. एल्काइनAlkyne

Step 1

Concept

एथाइन में कार्बन परमाणुओं के बीच त्रि बंध होता है। / Ethyne has a triple bond between carbon atoms.

Step 2

Why this answer is correct

त्रि बंध वाले हाइड्रोकार्बन एल्काइन कहलाते हैं। / Hydrocarbons with triple bonds are called alkynes.

Step 3

Exam Tip

एथाइन को एल्काइन का प्रमुख उदाहरण मानें। / Remember ethyne as a key alkyne example.

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Question Easy Science Chemical Substances – Nature and Behaviour Carbon and its Compounds Class 10 Level 2

असंतृप्त हाइड्रोकार्बन में सामान्यतः कौन सा बंध पाया जा सकता है?

Which bond may generally be present in unsaturated hydrocarbons?

Explanation opens after your attempt
Correct Answer

A. द्वि या त्रि बंधDouble or triple bond

Step 1

Concept

असंतृप्त हाइड्रोकार्बन में कम से कम एक द्वि या त्रि बंध हो सकता है। / Unsaturated hydrocarbons may have at least one double or triple bond.

Step 2

Why this answer is correct

इन बंधों के कारण ये अधिक अभिक्रियाशील होते हैं। / These bonds make them more reactive.

Step 3

Exam Tip

एल्कीन और एल्काइन को असंतृप्त समूह में रखें। / Keep alkenes and alkynes in the unsaturated group.

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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

यदि \(S_n=5n^2-n\), तो \(S_{9}\) का मान क्या है?

If \(S_n=5n^2-n\), what is the value of \(S_9\)?

Explanation opens after your attempt
Correct Answer

A. (396)

Explanation

Simple Explanation

(S_9=5(9)2-9=396)। संकेत का ध्यान रखें क्योंकि यहाँ घटाव है। / (S_9=5(9)2-9=396). Pay attention to the sign because subtraction is involved.

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Question Easy Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

समीकरण (3x-y=7) में (x=3) रखने पर (y) क्या होगा?

In (3x-y=7), if (x=3), what is (y)?

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Correct Answer

A. (y=2)

Explanation

Simple Explanation

(9-y=7), इसलिए (y=2)। ऋण चिह्न वाले पद को हल करते समय सावधानी रखें। / (9-y=7), so (y=2). Be careful while solving a term with a negative sign.

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Question Easy Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (x-y=6) और (y=2), तो (x) का मान क्या होगा?

If (x-y=6) and (y=2), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

C. (x=8)

Explanation

Simple Explanation

(x-2=6), इसलिए (x=8)। घटाव समीकरण में (y) को सही चिह्न के साथ रखें। / (x-2=6), so (x=8). Put (y) with the correct sign in a subtraction equation.

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Question Easy Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 56

यदि (2x-y=5) और (x=4), तो (y) का मान ज्ञात करें।

If (2x-y=5) and (x=4), find the value of (y).

Explanation opens after your attempt
Correct Answer

B. (y=3)

Explanation

Simple Explanation

(8-y=5), इसलिए (y=3)। समीकरण में ऋण चिह्न हो तो दोनों पक्षों को ध्यान से संतुलित करें। / (8-y=5), so (y=3). When there is a minus sign, balance both sides carefully.

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Question Hard Mathematics Real Numbers Irrational numbers Class 10 Level 14

कौन-सा विकल्प \(3-\sqrt{2}\) की प्रकृति सही बताता है?

Which option correctly describes the nature of \(3-\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

B. अपरिमेय, क्योंकि परिमेय में से अपरिमेय घटा हैIrrational because an irrational is subtracted from a rational

Step 1

Concept

(3) परिमेय है और \(\sqrt{2}\) अपरिमेय है। / (3) is rational and \(\sqrt{2}\) is irrational.

Step 2

Why this answer is correct

परिमेय संख्या में से अपरिमेय घटाने पर परिणाम अपरिमेय रहता है। / A rational number minus an irrational number remains irrational.

Step 3

Exam Tip

केवल परिमेय पद देखकर पूरे व्यंजक को परिमेय न मानें। / Do not classify the whole expression by looking only at the rational part.

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Question Hard Mathematics Real Numbers Irrational numbers Class 10 Level 14

यदि (r) परिमेय और (s) अपरिमेय है, तो (r-s) कब अपरिमेय होगा?

If (r) is rational and (s) is irrational, when will (r-s) be irrational?

Explanation opens after your attempt
Correct Answer

A. हमेशाAlways

Step 1

Concept

परिमेय संख्या में से अपरिमेय संख्या घटाने पर परिणाम अपरिमेय रहता है। / A rational number minus an irrational number is irrational.

Step 2

Why this answer is correct

यदि (r-s) परिमेय हो, तो (s=r-(r-s)) परिमेय हो जाएगा, जो असंभव है। / If (r-s) were rational, then (s=r-(r-s)) would be rational, which is impossible.

Step 3

Exam Tip

घटाव में भी वही सोच रखें जो योग में रखते हैं। / Use the same reasoning for subtraction as for addition.

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

यदि \(a_r=86\), \(a_{r+6}=176\) और \(a_{4r}=536\) है, तो (r) का मान क्या होगा?

If \(a_r=86\), \(a_{r+6}=176\), and \(a_{4r}=536\), what is the value of (r)?

Explanation opens after your attempt
Correct Answer

C. (10)

Explanation

Simple Explanation

(6d=90) से (d=15)। \(a_{4r}-a_r=3rd=450\), इसलिए (45r=450) और (r=10)। / From (6d=90), (d=15). \(a_{4r}-a_r=3rd=450\), so (45r=450) and (r=10).

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

समान्तर श्रेणी \(18,35,52,\ldots\) में \(a_n\) को (n) के रूप में लिखकर \(a_{5k}\) ज्ञात कीजिए जब (k=8)।

Write \(a_n\) in terms of (n) for the AP \(18,35,52,\ldots\), and find \(a_{5k}\) when (k=8).

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Correct Answer

A. (681)

Explanation

Simple Explanation

यहां (a_n=18+17(n-1)=17n+1)। \(a_{40}=17\times40+1=681\)। / Here (a_n=18+17(n-1)=17n+1). \(a_{40}=17\times40+1=681\).

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

यदि \(a_{3n+2}=148\), \(a_{n+2}=52\) और (d=12) है, तो (n) क्या होगा?

If \(a_{3n+2}=148\), \(a_{n+2}=52\), and (d=12), what is (n)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

\(a_{3n+2}-a_{n+2}=2nd=96\)। (24n=96) से (n=4)। / \(a_{3n+2}-a_{n+2}=2nd=96\). From (24n=96), (n=4).

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

यदि \(a_n=17n-11\) है, तो \(a_{7k}-a_{3k}=408\) के लिए (k) क्या होगा?

If \(a_n=17n-11\), what is (k) for \(a_{7k}-a_{3k}=408\)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

(a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k)। (68k=408) से (k=6)। / (a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k). From (68k=408), (k=6).

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

समान्तर श्रेणी में \(a_{8n}=810\), \(a_{3n}=210\) और (d=24) है। (n) क्या है?

In an AP \(a_{8n}=810\), \(a_{3n}=210\), and (d=24). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(a_{8n}-a_{3n}=5nd=600\)। (120n=600) से (n=5)। / \(a_{8n}-a_{3n}=5nd=600\). From (120n=600), (n=5).

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

यदि \(a_1=23\), (d=14) और \(a_{5n+4}=527\) है, तो (n) का मान क्या है?

If \(a_1=23\), (d=14), and \(a_{5n+4}=527\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(527=23+(5n+3)14) से (504=70n+42), इसलिए \(n=\frac{33}{5}\) नहीं आता। सूचकांक और विकल्पों को ध्यान से मिलाएं। / (527=23+(5n+3)14), so (504=70n+42), which does not give an integer option. Match the index and options carefully.

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

एक समान्तर श्रेणी में \(a_9=61\) और \(a_{27}=223\) है। यदि \(a_{9r}=385\), तो (r) क्या है?

In an AP \(a_9=61\) and \(a_{27}=223\). If \(a_{9r}=385\), what is (r)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(d=\frac{223-61}{18}=9\)। (385=61+(9r-9)9) से (9r=45), इसलिए (r=5)। / \(d=\frac{223-61}{18}=9\). From (385=61+(9r-9)9), (9r=45), so (r=5).

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

यदि \(a_n=10n+19\) और \(a_m=349\) है, तो \(a_{m+18}\) क्या होगा?

If \(a_n=10n+19\) and \(a_m=349\), what is \(a_{m+18}\)?

Explanation opens after your attempt
Correct Answer

C. (529)

Explanation

Simple Explanation

(10m+19=349) से (m=33)। \(a_{51}=10\times51+19=529\)। / From (10m+19=349), (m=33). \(a_{51}=10\times51+19=529\).

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

यदि \(a_n=11n+c\) और \(a_9=128\) है, तो \(a_{4r}=392\) होने पर (r) क्या होगा?

If \(a_n=11n+c\) and \(a_9=128\), what is (r) when \(a_{4r}=392\)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

(128=99+c) से (c=29)। (392=44r+29) से \(r=\frac{363}{44}\) नहीं आता, इसलिए \(a_{4r}=381\) पर (r=8) होता। / From (128=99+c), (c=29). (392=44r+29) does not give an integer, so \(a_{4r}=381\) would give (r=8).

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

यदि किसी समान्तर श्रेणी में \(a_{4p}=188\), \(a_p=56\) और (d=11) है, तो (p) का मान क्या होगा?

If in an AP \(a_{4p}=188\), \(a_p=56\), and (d=11), what is the value of (p)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

\(a_{4p}-a_p=3pd=132\) इसलिए (33p=132) और (p=4)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले निकालें। / \(a_{4p}-a_p=3pd=132\) so (33p=132) and (p=4). In index questions first find the position gap.

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

यदि \(a_n=15n-8\) है, तो \(a_{6k}-a_{2k}=300\) के लिए (k) क्या होगा?

If \(a_n=15n-8\), what is (k) for \(a_{6k}-a_{2k}=300\)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

(a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k)। (60k=300) से (k=5)। / (a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k). From (60k=300), (k=5).

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

समान्तर श्रेणी में \(a_{7n}=530\), \(a_{3n}=146\) और (d=16) है। (n) क्या है?

In an AP, \(a_{7n}=530\), \(a_{3n}=146\), and (d=16). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{7n}-a_{3n}=4nd=384\)। (64n=384) से (n=6)। / \(a_{7n}-a_{3n}=4nd=384\). From (64n=384), (n=6).

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

यदि \(a_1=17\), (d=10) और \(a_{4n+3}=407\) है, तो (n) का मान क्या है?

If \(a_1=17\), (d=10), and \(a_{4n+3}=407\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

(407=17+(4n+2)10) से (390=40n+20), इसलिए \(n=\frac{37}{4}\) नहीं आता। सूचकांक और विकल्पों को सावधानी से मिलाएं। / (407=17+(4n+2)10), so (390=40n+20), which does not give an integer option. Match the index and options carefully.

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

एक समान्तर श्रेणी में \(a_8=52\) और \(a_{23}=172\) है। यदि \(a_{8r}=292\), तो (r) क्या है?

In an AP, \(a_8=52\) and \(a_{23}=172\). If \(a_{8r}=292\), what is (r)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(d=\frac{172-52}{15}=8\)। (292=52+(8r-8)8) से (8r=38), इसलिए \(r=\frac{19}{4}\), पूर्णांक विकल्प नहीं है। / \(d=\frac{172-52}{15}=8\). From (292=52+(8r-8)8), (8r=38), so \(r=\frac{19}{4}\); no integer option is correct.

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

यदि \(a_n=8n+15\) और \(a_m=239\) है, तो \(a_{m+16}\) क्या होगा?

If \(a_n=8n+15\) and \(a_m=239\), what is \(a_{m+16}\)?

Explanation opens after your attempt
Correct Answer

B. (367)

Explanation

Simple Explanation

(8m+15=239) से (m=28)। \(a_{44}=8\times44+15=367\)। / From (8m+15=239), (m=28). \(a_{44}=8\times44+15=367\).

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

यदि \(a_n=9n+c\) और \(a_8=101\) है, तो \(a_{5r}=326\) होने पर (r) क्या होगा?

If \(a_n=9n+c\) and \(a_8=101\), what is (r) when \(a_{5r}=326\)?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

(101=72+c) से (c=29)। (326=45r+29) से \(r=\frac{297}{45}\) नहीं, इसलिए सही डेटा के लिए \(a_{5r}\) को (344) होना चाहिए। / From (101=72+c), (c=29). (326=45r+29) does not give an integer (r), so the given data should be checked.

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

यदि \(a_{3m}=152\), \(a_m=56\) और (d=8) है, तो (m) का मान क्या होगा?

If \(a_{3m}=152\), \(a_m=56\), and (d=8), what is the value of (m)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{3m}-a_m=2md=96\), इसलिए (16m=96) और (m=6)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले देखें। / \(a_{3m}-a_m=2md=96\), so (16m=96) and (m=6). In index questions, first check the position gap.

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

एक समान्तर श्रेणी में \(a_7=38\) और \(a_{19}=122\) है। यदि \(a_{7r}=234\), तो (r) क्या है?

In an AP, \(a_7=38\) and \(a_{19}=122\). If \(a_{7r}=234\), what is (r)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(d=\frac{122-38}{12}=7\)। (234=38+(7r-7)7) से (r=5)। / \(d=\frac{122-38}{12}=7\). From (234=38+(7r-7)7), (r=5).

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

यदि \(a_n=7n+c\) और \(a_6=61\) है, तो \(a_{4r}=299\) होने पर (r) क्या होगा?

If \(a_n=7n+c\) and \(a_6=61\), what is (r) when \(a_{4r}=299\)?

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

(61=42+c) से (c=19)। (299=28r+19) से (r=10)। / From (61=42+c), (c=19). From (299=28r+19), (r=10).

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

यदि \(a_{r}=52\), \(a_{r+5}=92\) और \(a_{3r}=212\) है, तो (r) का मान क्या होगा?

If \(a_r=52\), \(a_{r+5}=92\), and \(a_{3r}=212\), what is the value of (r)?

Explanation opens after your attempt
Correct Answer

C. (10)

Explanation

Simple Explanation

(5d=40) से (d=8)। \(a_{3r}-a_r=2rd=160\), इसलिए (16r=160) और (r=10)। / From (5d=40), (d=8). \(a_{3r}-a_r=2rd=160\), so (16r=160) and (r=10).

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

समान्तर श्रेणी \(12,25,38,\ldots\) में \(a_n\) को (n) के रूप में लिखकर \(a_{4k}\) ज्ञात कीजिए जब (k=9)।

Write \(a_n\) in terms of (n) for the AP \(12,25,38,\ldots\), and find \(a_{4k}\) when (k=9).

Explanation opens after your attempt
Correct Answer

A. (467)

Explanation

Simple Explanation

यहां (a_n=12+13(n-1)=13n-1)। \(a_{36}=13\times36-1=467\)। / Here (a_n=12+13(n-1)=13n-1). \(a_{36}=13\times36-1=467\).

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

यदि \(a_{2n+1}=89\), \(a_{n+1}=41\) और (d=6) है, तो (n) क्या होगा?

If \(a_{2n+1}=89\), \(a_{n+1}=41\), and (d=6), what is (n)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

\(a_{2n+1}-a_{n+1}=nd=48\)। (6n=48) से (n=8)। / \(a_{2n+1}-a_{n+1}=nd=48\). From (6n=48), (n=8).

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

यदि \(a_n=13n-6\) है, तो \(a_{5k}-a_{2k}=234\) के लिए (k) क्या होगा?

If \(a_n=13n-6\), what is (k) for \(a_{5k}-a_{2k}=234\)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

(a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k)। (39k=234) से (k=6)। / (a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k). From (39k=234), (k=6).

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

समान्तर श्रेणी में \(a_{6n}=319\), \(a_{2n}=95\) और (d=14) है। (n) क्या है?

In an AP, \(a_{6n}=319\), \(a_{2n}=95\), and (d=14). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

\(a_{6n}-a_{2n}=4nd=224\)। (56n=224) से (n=4)। / \(a_{6n}-a_{2n}=4nd=224\). From (56n=224), (n=4).

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

यदि \(a_1=11\), (d=8) और \(a_{3n+4}=275\) है, तो (n) का मान क्या है?

If \(a_1=11\), (d=8), and \(a_{3n+4}=275\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

(275=11+(3n+3)8) से (264=24n+24), इसलिए (n=10)। सूचकांक से (1) घटाकर (d) का गुणक बनाएं। / From (275=11+(3n+3)8), (264=24n+24), so (n=10). Subtract (1) from the index to get the multiplier of (d).

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

एक समान्तर श्रेणी में \(a_7=38\) और \(a_{19}=122\) है। यदि \(a_{7r}=206\), तो (r) क्या है?

In an AP, \(a_7=38\) and \(a_{19}=122\). If \(a_{7r}=206\), what is (r)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(d=\frac{122-38}{12}=7\)। (206=38+(7r-7)7) से (7r=31), इसलिए कोई पूर्णांक विकल्प सही नहीं है। / \(d=\frac{122-38}{12}=7\). From (206=38+(7r-7)7), (7r=31), so no integer option is correct.

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

यदि \(a_n=6n+13\) और \(a_m=181\) है, तो \(a_{m+14}\) क्या होगा?

If \(a_n=6n+13\) and \(a_m=181\), what is \(a_{m+14}\)?

Explanation opens after your attempt
Correct Answer

B. (265)

Explanation

Simple Explanation

(6m+13=181) से (m=28)। \(a_{42}=6\times42+13=265\)। / From (6m+13=181), (m=28). \(a_{42}=6\times42+13=265\).

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

यदि \(a_n=7n+c\) और \(a_{6}=61\) है, तो \(a_{4r}=313\) होने पर (r) क्या होगा?

If \(a_n=7n+c\) and \(a_6=61\), what is (r) when \(a_{4r}=313\)?

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

(61=42+c) से (c=19)। (313=28r+19) से \(r=\frac{294}{28}=10.5\), इसलिए कोई पूर्णांक विकल्प सही नहीं होगा। / From (61=42+c), (c=19). (313=28r+19) gives \(r=\frac{294}{28}=10.5\), so no integer option is correct.

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

यदि \(a_n=17n+c\) और \(a_7=145\) है तो \(a_{3r}=757\) होने पर (r) क्या है?

If \(a_n=17n+c\) and \(a_7=145\), what is (r) when \(a_{3r}=757\)?

Explanation opens after your attempt
Correct Answer

B. (14)

Explanation

Simple Explanation

(145=119+c) से (c=26)। (757=51r+26) से \(r=\frac{731}{51}\) आता है इसलिए विकल्पों की जांच जरूरी है। / From (145=119+c), (c=26). (757=51r+26), giving \(r=\frac{731}{51}\), so option checking is necessary.

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

यदि \(a_n=11n-5\) है तो \(a_{4k}-a_k=198\) के लिए (k) क्या होगा?

If \(a_n=11n-5\), what is (k) for \(a_{4k}-a_k=198\)?

Explanation opens after your attempt
Correct Answer

C. (6)

Explanation

Simple Explanation

(a_{4k}-a_k=(44k-5)-(11k-5)=33k)। (33k=198) से (k=6)। / (a_{4k}-a_k=(44k-5)-(11k-5)=33k). From (33k=198), (k=6).

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

समान्तर श्रेणी में \(a_{5n}=205\), \(a_n=49\) और (d=13) है। (n) क्या है?

In an AP, \(a_{5n}=205\), \(a_n=49\), and (d=13). What is (n)?

Explanation opens after your attempt
Correct Answer

A. (3)

Explanation

Simple Explanation

\(a_{5n}-a_n=4nd=156\)। (52n=156) से (n=3)। / \(a_{5n}-a_n=4nd=156\). From (52n=156), (n=3).

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

यदि \(a_1=8\), (d=9) और \(a_{3n+2}=197\) है तो (n) का मान क्या है?

If \(a_1=8\), (d=9), and \(a_{3n+2}=197\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(197=8+(3n+1)9) से (189=27n+9) इसलिए \(n=\frac{20}{3}\) नहीं आता। सूचकांक ठीक पढ़ना जरूरी है। / (197=8+(3n+1)9), so (189=27n+9) and \(n=\frac{20}{3}\). Read the index carefully before selecting an integer option.

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

एक समान्तर श्रेणी में \(a_5=27\) और \(a_{17}=111\) है। \(a_{5r}\) का मान (195) है तो (r) क्या है?

In an AP, \(a_5=27\) and \(a_{17}=111\). If \(a_{5r}=195\), what is (r)?

Explanation opens after your attempt
Correct Answer

A. (5)

Explanation

Simple Explanation

\(d=\frac{111-27}{12}=7\)। (195=27+(5r-5)7) से (5r=29) इसलिए \(r=\frac{29}{5}\)। / \(d=\frac{111-27}{12}=7\). From (195=27+(5r-5)7), (5r=29), so \(r=\frac{29}{5}\).

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

यदि \(a_n=4n+9\) और \(a_m=137\) है तो \(a_{m+15}\) क्या होगा?

If \(a_n=4n+9\) and \(a_m=137\), what is \(a_{m+15}\)?

Explanation opens after your attempt
Correct Answer

C. (197)

Explanation

Simple Explanation

(4m+9=137) से (m=32)। \(a_{47}=4\times47+9=197\)। / From (4m+9=137), (m=32). \(a_{47}=4\times47+9=197\).

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

किसी समान्तर श्रेणी में \(a_p=42\), \(a_{p+12}=150\) और (p=9) है। \(a_{40}\) क्या होगा?

In an AP, \(a_p=42\), \(a_{p+12}=150\), and (p=9). What is \(a_{40}\)?

Explanation opens after your attempt
Correct Answer

A. (321)

Explanation

Simple Explanation

(12d=108) से (d=9)। \(a_{40}=a_9+31d=42+279=321\)। / From (12d=108), (d=9). \(a_{40}=a_9+31d=42+279=321\).

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

किसी समान्तर श्रेणी में \(a_{4m}=156\), \(a_m=48\) और (d=6) है। (m) का मान क्या है?

In an AP, \(a_{4m}=156\), \(a_m=48\), and (d=6). What is the value of (m)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{4m}-a_m=3md=108\) है। (18m=108) से (m=6)। / \(a_{4m}-a_m=3md=108\). From (18m=108), (m=6).

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

यदि \(a_n=13n+c\) और \(a_6=101\) है तो \(a_{4r}=465\) होने पर (r) क्या है?

If \(a_n=13n+c\) and \(a_6=101\), what is (r) when \(a_{4r}=465\)?

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

(101=78+c) से (c=23)। (465=52r+23) से \(r=\frac{442}{52}=8.5\)। / From (101=78+c), (c=23). (465=52r+23), so \(r=\frac{442}{52}=8.5\).

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

यदि \(a_n=9n+2\) है तो \(a_{3k}-a_k=144\) के लिए (k) क्या होगा?

If \(a_n=9n+2\), what is (k) for \(a_{3k}-a_k=144\)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

(a_{3k}-a_k=(27k+2)-(9k+2)=18k)। (18k=144) से (k=8)। / (a_{3k}-a_k=(27k+2)-(9k+2)=18k). From (18k=144), (k=8).

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

समान्तर श्रेणी में \(a_{4n}=140\), \(a_n=32\) और (d=6) है। (n) क्या है?

In an AP, \(a_{4n}=140\), \(a_n=32\), and (d=6). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{4n}-a_n=3nd=108\)। (18n=108) से (n=6)। / \(a_{4n}-a_n=3nd=108\). From (18n=108), (n=6).

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

यदि \(a_1=5\), (d=7) और \(a_{2n+3}=159\) है तो (n) का मान क्या है?

If \(a_1=5\), (d=7), and \(a_{2n+3}=159\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

(159=5+(2n+2)7) से (154=14n+14)। इसलिए (n=10)। / From (159=5+(2n+2)7), (154=14n+14). Therefore (n=10).

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

एक समान्तर श्रेणी में \(a_4=18\) और \(a_{16}=78\) है। \(a_{4r}\) का मान (138) है तो (r) क्या है?

In an AP, \(a_4=18\) and \(a_{16}=78\). If \(a_{4r}=138\), what is (r)?

Explanation opens after your attempt
Correct Answer

A. (7)

Explanation

Simple Explanation

\(d=\frac{78-18}{12}=5\)। (138=18+(4r-4)5) से (4r=28) इसलिए (r=7)। / \(d=\frac{78-18}{12}=5\). From (138=18+(4r-4)5), (4r=28), so (r=7).

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

यदि \(a_n=3n+4\) और \(a_m=91\) है तो \(a_{m+12}\) क्या होगा?

If \(a_n=3n+4\) and \(a_m=91\), what is \(a_{m+12}\)?

Explanation opens after your attempt
Correct Answer

C. (127)

Explanation

Simple Explanation

(3m+4=91) से (m=29)। \(a_{41}=3\times41+4=127\)। / From (3m+4=91), (m=29). \(a_{41}=3\times41+4=127\).

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

किसी समान्तर श्रेणी में \(a_p=29\), \(a_{p+10}=99\) और (p=8) है। \(a_{35}\) क्या होगा?

In an AP, \(a_p=29\), \(a_{p+10}=99\), and (p=8). What is \(a_{35}\)?

Explanation opens after your attempt
Correct Answer

A. (218)

Explanation

Simple Explanation

(10d=70) से (d=7)। \(a_{35}=a_8+27d=29+189=218\)। / From (10d=70), (d=7). \(a_{35}=a_8+27d=29+189=218\).

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

किसी समान्तर श्रेणी में \(a_{3m}=94\), \(a_m=34\) और (d=5) है। (m) का मान क्या है?

In an AP, \(a_{3m}=94\), \(a_m=34\), and (d=5). What is the value of (m)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{3m}-a_m=2md=60\) है। (10m=60) से (m=6)। / \(a_{3m}-a_m=2md=60\). From (10m=60), (m=6).

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

यदि \(a_{n}=11n+c\) और \(a_{5}=72\) है तो \(a_{5r}\) का मान (512) होने पर (r) क्या है?

If \(a_n=11n+c\) and \(a_5=72\), what is (r) when \(a_{5r}=512\)?

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

(72=55+c) से (c=17)। (512=55r+17) से (r=9)। / From (72=55+c), (c=17). From (512=55r+17), (r=9).

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

यदि \(a_n=7n-4\) है तो \(a_{2k}-a_k=84\) के लिए (k) क्या होगा?

If \(a_n=7n-4\), what is (k) for \(a_{2k}-a_k=84\)?

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Correct Answer

C. (12)

Explanation

Simple Explanation

(a_{2k}-a_k=(14k-4)-(7k-4)=7k)। (7k=84) से (k=12)। / (a_{2k}-a_k=(14k-4)-(7k-4)=7k). From (7k=84), (k=12).

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

समान्तर श्रेणी में \(a_{3n}=81\), \(a_n=21\) और (d=5) है। (n) क्या है?

In an AP, \(a_{3n}=81\), \(a_n=21\), and (d=5). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{3n}-a_n=2nd=60\)। (10n=60) से (n=6)। / \(a_{3n}-a_n=2nd=60\). From (10n=60), (n=6).

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

यदि \(a_1=3\) और \(a_{2n+1}=123\) है तथा (d=4) है तो (n) का मान क्या है?

If \(a_1=3\), \(a_{2n+1}=123\), and (d=4), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (15)

Explanation

Simple Explanation

\(123=3+2n\cdot4\) से (120=8n) इसलिए (n=15)। सूचकांक (2n+1) में (1) घटाकर गुणक लें। / From \(123=3+2n\cdot4\), (120=8n), so (n=15). In index (2n+1), subtract (1) to get the multiplier.

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

एक समान्तर श्रेणी में \(a_3=11\) और \(a_{13}=51\) है। \(a_{3r}\) का मान (91) है तो (r) क्या है?

In an AP, \(a_3=11\) and \(a_{13}=51\). If \(a_{3r}=91\), what is (r)?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

\(d=\frac{51-11}{10}=4\)। (91=11+(3r-3)4) से (3r=21) इसलिए (r=7)। / \(d=\frac{51-11}{10}=4\). From (91=11+(3r-3)4), (3r=21), so (r=7).

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

यदि \(a_{n}=2n-1\) और \(a_m=63\) है तो \(a_{m+10}\) क्या होगा?

If \(a_n=2n-1\) and \(a_m=63\), what is \(a_{m+10}\)?

Explanation opens after your attempt
Correct Answer

B. (83)

Explanation

Simple Explanation

(2m-1=63) से (m=32)। \(a_{42}=2\times42-1=83\)। / From (2m-1=63), (m=32). \(a_{42}=2\times42-1=83\).

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

किसी समान्तर श्रेणी में \(a_{p}=17\), \(a_{p+8}=65\) और (p=6) है। \(a_{30}\) क्या होगा?

In an AP, \(a_p=17\), \(a_{p+8}=65\), and (p=6). What is \(a_{30}\)?

Explanation opens after your attempt
Correct Answer

B. (161)

Explanation

Simple Explanation

(8d=48) से (d=6)। \(a_{30}=a_6+24d=17+144=161\)। / From (8d=48), (d=6). \(a_{30}=a_6+24d=17+144=161\).

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