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Search Class 10 Questions

75 results found for "triple-plus-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 Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

एक कक्षा में कुल (74) विद्यार्थी हैं। लड़कों की संख्या का (3) गुना और लड़कियों की संख्या का (2) गुना मिलाकर (186) है। लड़कियों की संख्या क्या है?

In a class, there are (74) students. Three times the number of boys plus twice the number of girls is (186). What is the number of girls?

Explanation opens after your attempt
Correct Answer

A. (36)

Explanation

Simple Explanation

लड़के (x) और लड़कियां (y) मानें। (x+y=74) और (3x+2y=186) से (x=38), इसलिए (y=36)। / Let boys be (x) and girls be (y). From (x+y=74) and (3x+2y=186), (x=38), so (y=36).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 57

दो संख्याओं का योग (52) है। बड़ी संख्या का (3) गुना और छोटी संख्या का (2) गुना मिलाकर (136) है। बड़ी संख्या क्या है?

The sum of two numbers is (52). Three times the larger number plus twice the smaller number is (136). What is the larger number?

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Correct Answer

C. (32)

Explanation

Simple Explanation

मान लें बड़ी संख्या (x) और छोटी (y) है। (x+y=52) और (3x+2y=136) से (x=32)। / Let the larger number be (x) and the smaller be (y). From (x+y=52) and (3x+2y=136), (x=32).

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Question Hard Mathematics Pair of Linear Equations in Two Variables Algebraic methods: Substitution method and Elimination method. Class 10 Level 55

एक कक्षा में लड़कों और लड़कियों की कुल संख्या (68) है। लड़कों की संख्या का (2) गुना और लड़कियों की संख्या मिलाकर (112) है। लड़कियों की संख्या क्या है?

In a class, the total number of boys and girls is (68). Twice the number of boys plus the number of girls is (112). What is the number of girls?

Explanation opens after your attempt
Correct Answer

D. (24)

Explanation

Simple Explanation

लड़के (x) और लड़कियां (y) मानें। (x+y=68) और (2x+y=112) से (x=44), इसलिए (y=24)। / Let boys be (x) and girls be (y). From (x+y=68) and (2x+y=112), (x=44), so (y=24).

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Question Easy Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

किसी संख्या (x) के वर्ग में उसके (3) गुने को जोड़ने पर (10) मिलता है। सही समीकरण कौन-सा है?

The square of a number (x) plus (3) times the number is (10). Which equation is correct?

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Correct Answer

B. \(x^2+3x=10\)

Explanation

Simple Explanation

वर्ग का अर्थ \(x^2\) और (3) गुना का अर्थ (3x) है। शब्द प्रश्न में वाक्य को धीरे-धीरे समीकरण में बदलें। / Square means \(x^2\) and (3) times means (3x). In word problems, convert the sentence slowly into an equation.

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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?

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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?

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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) Introduction to APs and common difference. Class 10 Level 63

अनुक्रम \(9,16,23,30,\ldots\) में (a+2d) का मान क्या है?

In the sequence \(9,16,23,30,\ldots\), what is the value of (a+2d)?

Explanation opens after your attempt
Correct Answer

C. (23)

Explanation

Simple Explanation

यहां (a=9) और (d=7), इसलिए (a+2d=9+14=23)। (a+2d) तीसरे पद के बराबर होता है। / Here (a=9) and (d=7), so (a+2d=9+14=23). (a+2d) equals the third term.

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

अनुक्रम \(21,26,31,36,\ldots\) में (a+d) का मान क्या है?

In the sequence \(21,26,31,36,\ldots\), what is the value of (a+d)?

Explanation opens after your attempt
Correct Answer

B. (26)

Explanation

Simple Explanation

यहां (a=21) और (d=5), इसलिए (a+d=26) है। (a+d) दूसरा पद होता है। / Here (a=21) and (d=5), so (a+d=26). (a+d) is the second term.

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

अनुक्रम \(3,8,13,18,\ldots\) में (a+2d) का मान क्या है?

In the sequence \(3,8,13,18,\ldots\), what is the value of (a+2d)?

Explanation opens after your attempt
Correct Answer

C. (13)

Explanation

Simple Explanation

यहां (a=3) और (d=5), इसलिए (a+2d=3+10=13)। (a+2d) तीसरे पद के बराबर होता है। / Here (a=3) and (d=5), so (a+2d=3+10=13). (a+2d) equals the third term.

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

अनुक्रम \(16,20,24,28,\ldots\) में (a+d) का मान क्या है?

In the sequence \(16,20,24,28,\ldots\), what is the value of (a+d)?

Explanation opens after your attempt
Correct Answer

C. (20)

Explanation

Simple Explanation

यहां (a=16) और (d=4), इसलिए (a+d=20)। (a+d) वास्तव में दूसरा पद होता है। / Here (a=16) and (d=4), so (a+d=20). (a+d) is actually the second term.

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Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

किस विकल्प में परिमेय और अपरिमेय संख्या का योग अपरिमेय है?

In which option is the sum of a rational and an irrational number irrational?

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Correct Answer

A. \(4+\sqrt{13}\)

Explanation

Simple Explanation

(4) परिमेय है और \(\sqrt{13}\) अपरिमेय है, इसलिए योग अपरिमेय है। परीक्षा में पूर्ण वर्ग के वर्गमूल को पहले पहचानें। / (4) is rational and \(\sqrt{13}\) is irrational, so the sum is irrational. In exams identify square roots of perfect squares first.

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Question Expert Mathematics Real Numbers Irrational numbers Class 10 Level 15

कौन सा विकल्प सिद्ध करता है कि \(\frac{3}{2}+\sqrt{5}\) अपरिमेय है?

Which option proves that \(\frac{3}{2}+\sqrt{5}\) is irrational?

Explanation opens after your attempt
Correct Answer

B. क्योंकि परिमेय संख्या में अपरिमेय संख्या जोड़ने पर परिणाम अपरिमेय होता हैBecause adding an irrational number to a rational number gives an irrational result

Step 1

Concept

\(\frac{3}{2}\) परिमेय संख्या है और \(\sqrt{5}\) अपरिमेय संख्या है। / \(\frac{3}{2}\) is rational and \(\sqrt{5}\) is irrational.

Step 2

Why this answer is correct

यदि उनका योग परिमेय मानें तो \(\sqrt{5}\) को दो परिमेय संख्याओं के अंतर के रूप में लिखना पड़ेगा जो असंभव है। / If their sum were rational, then \(\sqrt{5}\) would become the difference of two rational numbers, which is impossible.

Step 3

Exam Tip

परिमेय और अपरिमेय के योग वाले प्रश्नों में विरोधाभास विधि बहुत उपयोगी है। / For rational-plus-irrational questions, contradiction is a very useful method.

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Question Expert Mathematics Real Numbers Irrational numbers Class 10 Level 15

यदि \(x=3+\sqrt{2}\) है तो (x) के बारे में क्या सही है?

If \(x=3+\sqrt{2}\) then what is true about (x)?

Explanation opens after your attempt
Correct Answer

B. (x) अपरिमेय है(x) is irrational

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 और अपरिमेय का योग अपरिमेय होता है। / The sum of a rational and an irrational number is irrational.

Step 3

Exam Tip

किसी पूर्णांक में अपरिमेय संख्या जोड़ने से वह पूर्णांक नहीं रहता। / Adding an irrational number to an integer does not give an integer.

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Question Hard Mathematics Real Numbers Irrational numbers Class 10 Level 14

यदि \(a=3+\sqrt{2}\), तो (a) की प्रकृति क्या है?

If \(a=3+\sqrt{2}\), what is the nature of (a)?

Explanation opens after your attempt
Correct Answer

B. अपरिमेयIrrational

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 और अपरिमेय का योग अपरिमेय होता है। / The sum of a rational and an irrational number is irrational.

Step 3

Exam Tip

पूर्णांक जोड़ने से मूल की अपरिमेयता समाप्त नहीं होती। / Adding an integer does not remove the irrational nature of the surd.

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Question Hard Mathematics Real Numbers Irrational numbers Class 10 Level 14

यदि (x) अपरिमेय है, तो (x+3) के परिमेय होने की संभावना के बारे में सही कथन क्या है?

If (x) is irrational, what is correct about the possibility of (x+3) being rational?

Explanation opens after your attempt
Correct Answer

B. यह कभी परिमेय नहीं हो सकताIt can never be rational

Step 1

Concept

(3) एक परिमेय संख्या है। / (3) is rational.

Step 2

Why this answer is correct

यदि (x+3) परिमेय हो, तो (x=(x+3)-3) भी परिमेय होगा, जो दी गई बात के विरुद्ध है। / If (x+3) were rational, then (x=(x+3)-3) would also be rational, contradicting the given fact.

Step 3

Exam Tip

ऐसे प्रश्नों में विरोध विधि तेज काम करती है। / The contradiction method is useful in such questions.

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Question Hard Mathematics Real Numbers Irrational numbers Class 10 Level 14

यदि \(x=\sqrt{5}-2\), तो (x) के बारे में सही कथन कौन-सा है?

If \(x=\sqrt{5}-2\), which statement about (x) is correct?

Explanation opens after your attempt
Correct Answer

B. (x) अपरिमेय है(x) is irrational

Step 1

Concept

\(\sqrt{5}\) अपरिमेय है और (2) परिमेय है। / \(\sqrt{5}\) is irrational and (2) is rational.

Step 2

Why this answer is correct

अपरिमेय संख्या में से परिमेय संख्या घटाने पर परिणाम अपरिमेय रहता है। / Subtracting a rational number from an irrational number gives an irrational number.

Step 3

Exam Tip

किसी मूल से पूर्णांक घटाने पर भी मूल की प्रकृति पर ध्यान दें। / When an integer is subtracted from a surd, focus on the nature of the surd.

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Question Easy Mathematics Real Numbers Euclid’s Division Lemma Class 10 Level 2

यदि कोई संख्या (12q+5) के रूप में है, तो उसे (12) से भाग देने पर शेषफल क्यों (5) होगा?

If a number is of the form (12q+5), why will its remainder be (5) when divided by (12)?

Explanation opens after your attempt
Correct Answer

A. क्योंकि (12q), (12) का गुणज है और (5<12)Because (12q) is a multiple of (12) and (5<12)

Step 1

Concept

(12q), (12) से पूर्णतः विभाजित होता है। / (12q) is exactly divisible by (12).

Step 2

Why this answer is correct

बचा हुआ (5) है और यह (12) से छोटा है, इसलिए वही शेषफल है। / The leftover part is (5), and it is less than (12), so it is the remainder.

Step 3

Exam Tip

(bq+r) में (bq) गुणज और (r) शेषफल होता है। / In (bq+r), (bq) is the multiple and (r) is the remainder.

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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).

Explanation opens after your attempt
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 \(a_{2k}-a_k=84\)?

Explanation opens after your attempt
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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