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Class 10 Mathematics - Arithmetic Progressions (AP) - Finding the $n$th term of an AP Expert Quiz

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

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Question 1/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक समान्तर श्रेणी में \(a_{13}=77\) और \(a_{29}=205\) है। \(a_{47}\) का मान क्या होगा?

In an AP \(a_{13}=77\) and \(a_{29}=205\). What is the value of \(a_{47}\)?

Explanation opens after your attempt
Correct Answer

C. (349)

Explanation

Simple Explanation

\(d=\frac{205-77}{29-13}=8\) इसलिए \(a_{47}=205+18\times8=349\)। निकट ज्ञात पद से आगे बढ़ना तेज तरीका है। / \(d=\frac{205-77}{29-13}=8\) so \(a_{47}=205+18\times8=349\). Moving from the nearer known term is faster.

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Question 2/50 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 3/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_n=kn+13\) और \(a_{24}-a_9=135\) है, तो \(a_{37}\) क्या होगा?

If \(a_n=kn+13\) and \(a_{24}-a_9=135\), what is \(a_{37}\)?

Explanation opens after your attempt
Correct Answer

C. (346)

Explanation

Simple Explanation

(15k=135) से (k=9)। इसलिए \(a_{37}=9\times37+13=346\)। / From (15k=135), (k=9). Therefore \(a_{37}=9\times37+13=346\).

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Question 4/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी \(260,245,230,\ldots\) में (-100) से छोटा पहला पद कौन-सा है?

In the AP \(260,245,230,\ldots\), which is the first term less than (-100)?

Explanation opens after your attempt
Correct Answer

C. (-115)

Explanation

Simple Explanation

इस AP में (d=-15) है। (-100) के बाद अगला पद (-115) है, इसलिए पहला छोटा पद (-115) है। / Here (d=-15). After (-100), the next term is (-115), so the first smaller term is (-115).

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Question 5/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_{10}=x+31\) और \(a_{27}=x+167\) है, तो \(a_{44}\) (x) के रूप में क्या होगा?

If \(a_{10}=x+31\) and \(a_{27}=x+167\), what is \(a_{44}\) in terms of (x)?

Explanation opens after your attempt
Correct Answer

C. (x+303)

Explanation

Simple Explanation

(17d=136) से (d=8)। \(a_{44}=x+167+17\times8=x+303\)। / From (17d=136), (d=8). \(a_{44}=x+167+17\times8=x+303\).

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Question 6/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक AP में \(a_{16}=4a_7+2\) और \(a_7=22\) है। \(a_{34}\) क्या होगा?

In an AP \(a_{16}=4a_7+2\) and \(a_7=22\). What is \(a_{34}\)?

Explanation opens after your attempt
Correct Answer

A. (224)

Explanation

Simple Explanation

\(a_{16}=90\) और (9d=68) इसलिए \(d=\frac{68}{9}\)। \(a_{34}=a_{16}+18d=90+136=226\) नहीं बल्कि \(a_{34}=22+27\cdot\frac{68}{9}=226\) होगा। / \(a_{16}=90\) and (9d=68) so \(d=\frac{68}{9}\). \(a_{34}=22+27\cdot\frac{68}{9}=226\).

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Question 7/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी में \(a_{18}=111\) और \(a_{42}=351\) है। कौन-सा पद (531) होगा?

In an AP \(a_{18}=111\) and \(a_{42}=351\). Which term will be (531)?

Explanation opens after your attempt
Correct Answer

B. (60)वां(60)th

Explanation

Simple Explanation

\(d=\frac{351-111}{42-18}=10\)। (531=111+(n-18)10) से (n=60)। / \(d=\frac{351-111}{42-18}=10\). From (531=111+(n-18)10), (n=60).

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Question 8/50 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 9/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी \(33,48,63,\ldots\) में (1000) से बड़ा पहला पद कौन-सा है?

What is the first term greater than (1000) in the AP \(33,48,63,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (1008)

Explanation

Simple Explanation

पद (33+15(n-1)) के रूप में हैं। (1000) से बड़ा पहला पद (1008) है क्योंकि पिछला पद (993) है। / The terms are (33+15(n-1)). The first term greater than (1000) is (1008) because the previous term is (993).

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Question 10/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_8+a_{26}=246\) है, तो \(a_{17}\) का मान क्या होगा?

If \(a_8+a_{26}=246\), what is the value of \(a_{17}\)?

Explanation opens after your attempt
Correct Answer

C. (123)

Explanation

Simple Explanation

\(a_{17}\), \(a_8\) और \(a_{26}\) के बीच समान दूरी पर है। इसलिए \(a_{17}=\frac{246}{2}=123\)। / \(a_{17}\) is equally spaced between \(a_8\) and \(a_{26}\). Therefore \(a_{17}=\frac{246}{2}=123\).

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Question 11/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक समान्तर श्रेणी में \(a_5+a_{14}+a_{23}=399\) है। \(a_{14}\) का मान क्या होगा?

In an AP \(a_5+a_{14}+a_{23}=399\). What is the value of \(a_{14}\)?

Explanation opens after your attempt
Correct Answer

C. (133)

Explanation

Simple Explanation

तीनों पद समान दूरी पर हैं इसलिए मध्य पद औसत होगा। \(a_{14}=\frac{399}{3}=133\)। / The three terms are equally spaced, so the middle term is the average. \(a_{14}=\frac{399}{3}=133\).

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Question 12/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_1=57\) और \(a_{25}=a_1+312\) है, तो \(a_{61}\) क्या होगा?

If \(a_1=57\) and \(a_{25}=a_1+312\), what is \(a_{61}\)?

Explanation opens after your attempt
Correct Answer

B. (837)

Explanation

Simple Explanation

(24d=312) से (d=13)। \(a_{61}=57+60\times13=837\)। / From (24d=312), (d=13). \(a_{61}=57+60\times13=837\).

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Question 13/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी \(13,\frac{39}{2},26,\ldots\) का (46)वां पद क्या होगा?

What will be the (46)th term of the AP \(13,\frac{39}{2},26,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{611}{2}\)

Explanation

Simple Explanation

यहां \(d=\frac{13}{2}\)। \(a_{46}=13+45\cdot\frac{13}{2}=\frac{611}{2}\)। / Here \(d=\frac{13}{2}\). \(a_{46}=13+45\cdot\frac{13}{2}=\frac{611}{2}\).

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Question 14/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक समान्तर श्रेणी में \(a_{22}=0\) और \(a_{58}=-468\) है। \(a_1\) क्या होगा?

In an AP \(a_{22}=0\) and \(a_{58}=-468\). What is \(a_1\)?

Explanation opens after your attempt
Correct Answer

C. (273)

Explanation

Simple Explanation

(36d=-468) से (d=-13)। \(a_1=a_{22}-21d=273\)। / From (36d=-468), (d=-13). \(a_1=a_{22}-21d=273\).

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Question 15/50 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 16/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

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

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

Explanation opens after your attempt
Correct Answer

B. (63)

Explanation

Simple Explanation

यहां (d=-19) है। (82) के बाद (63) आता है इसलिए (75) से छोटा पहला पद (63) है। / Here (d=-19). After (82), (63) comes, so the first term less than (75) is (63).

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Question 17/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि किसी समान्तर श्रेणी में \(a_{35}=a_{11}+288\) है, तो सार्व अंतर क्या है?

If in an AP \(a_{35}=a_{11}+288\), what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (12)

Explanation

Simple Explanation

\(a_{35}-a_{11}=24d=288\), इसलिए (d=12)। स्थान अंतर को (d) से गुणा करें। / \(a_{35}-a_{11}=24d=288\), so (d=12). Multiply the position gap by (d).

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Question 18/50 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 19/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि समान्तर श्रेणी में \(a_7=7x-8\), \(a_{15}=15x-48\) और \(a_{23}=23x-88\) हैं, तो \(a_{31}\) क्या होगा?

If in an AP \(a_7=7x-8\), \(a_{15}=15x-48\), and \(a_{23}=23x-88\), what is \(a_{31}\)?

Explanation opens after your attempt
Correct Answer

C. (31x-128)

Explanation

Simple Explanation

समान दूरी वाले पदों का समूह अंतर (8x-40) है। \(a_{31}=a_{23}+8x-40=31x-128\)। / The group difference of equally spaced terms is (8x-40). \(a_{31}=a_{23}+8x-40=31x-128\).

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Question 20/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी \(52,73,94,\ldots\) में (1800) और (2000) के बीच सबसे बड़ा पद क्या है?

In the AP \(52,73,94,\ldots\), what is the greatest term between (1800) and (2000)?

Explanation opens after your attempt
Correct Answer

C. (1994)

Explanation

Simple Explanation

पद (52+21(n-1)) के रूप में हैं। (2000) से कम सबसे बड़ा उपयुक्त पद (1994) है। / The terms are of the form (52+21(n-1)). The greatest suitable term less than (2000) is (1994).

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Question 21/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_{n+7}-a_n=119\) है और \(a_{20}=219\) है, तो \(a_{55}\) क्या होगा?

If \(a_{n+7}-a_n=119\) and \(a_{20}=219\), what is \(a_{55}\)?

Explanation opens after your attempt
Correct Answer

C. (814)

Explanation

Simple Explanation

(7d=119), इसलिए (d=17)। \(a_{55}=219+35\times17=814\)। / (7d=119), so (d=17). \(a_{55}=219+35\times17=814\).

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Question 22/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक समान्तर श्रेणी में \(a_6+a_{13}=211\) और \(a_{22}=256\) है। \(a_{44}\) क्या होगा?

In an AP \(a_6+a_{13}=211\) and \(a_{22}=256\). What is \(a_{44}\)?

Explanation opens after your attempt
Correct Answer

A. (539)

Explanation

Simple Explanation

(2a+17d=211) और (a+21d=256)। हल करने पर (d=14) और \(a_{44}=539\)। / (2a+17d=211) and (a+21d=256). Solving gives (d=14) and \(a_{44}=539\).

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Question 23/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_{10}=49\) और \(a_{16}=3a_{10}+5\) है, तो \(a_{40}\) क्या होगा?

If \(a_{10}=49\) and \(a_{16}=3a_{10}+5\), what is \(a_{40}\)?

Explanation opens after your attempt
Correct Answer

C. (559)

Explanation

Simple Explanation

\(a_{16}=152\) और (6d=103), इसलिए \(d=\frac{103}{6}\)। \(a_{40}=152+24\cdot\frac{103}{6}=564\)। / \(a_{16}=152\) and (6d=103), so \(d=\frac{103}{6}\). \(a_{40}=152+24\cdot\frac{103}{6}=564\).

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Question 24/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी \(-19,\frac{-17}{2},2,\ldots\) का (39)वां पद क्या होगा?

What will be the (39)th term of the AP \(-19,\frac{-17}{2},2,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (384)

Explanation

Simple Explanation

यहां \(d=\frac{21}{2}\)। \(a_{39}=-19+38\cdot\frac{21}{2}=380\), इसलिए सही विकल्पों की जांच जरूरी है। / Here \(d=\frac{21}{2}\). \(a_{39}=-19+38\cdot\frac{21}{2}=380\), so checking options is necessary.

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Question 25/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_{30}=8a_{14}\) और \(a_{14}=51\) है, तो \(a_{46}\) क्या होगा?

If \(a_{30}=8a_{14}\) and \(a_{14}=51\), what is \(a_{46}\)?

Explanation opens after your attempt
Correct Answer

B. (765)

Explanation

Simple Explanation

\(a_{30}=408\), इसलिए (16d=357) और \(d=\frac{357}{16}\)। \(a_{46}=408+16\cdot\frac{357}{16}=765\)। / \(a_{30}=408\), so (16d=357) and \(d=\frac{357}{16}\). \(a_{46}=408+16\cdot\frac{357}{16}=765\).

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Question 26/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक समान्तर श्रेणी में \(a_{29}=a_{12}+255\) और \(a_{12}=86\) है। \(a_{72}\) क्या होगा?

In an AP \(a_{29}=a_{12}+255\) and \(a_{12}=86\). What is \(a_{72}\)?

Explanation opens after your attempt
Correct Answer

B. (986)

Explanation

Simple Explanation

(17d=255), इसलिए (d=15)। \(a_{72}=a_{12}+60d=86+900=986\)। / (17d=255), so (d=15). \(a_{72}=a_{12}+60d=86+900=986\).

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Question 27/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_n=an+b\), \(a_{12}=139\) और \(a_{38}=477\) है, तो \(a_{64}\) क्या होगा?

If \(a_n=an+b\), \(a_{12}=139\) and \(a_{38}=477\), what is \(a_{64}\)?

Explanation opens after your attempt
Correct Answer

C. (815)

Explanation

Simple Explanation

(26a=338), इसलिए (a=13)। \(a_{64}=a_{38}+26\times13=815\)। / (26a=338), so (a=13). \(a_{64}=a_{38}+26\times13=815\).

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Question 28/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

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

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

Explanation opens after your attempt
Correct Answer

B. (-144)

Explanation

Simple Explanation

(d=-18) है। (-144) के बाद (-162) आता है इसलिए (-150) से बड़ा अंतिम पद (-144) है। / (d=-18). After (-144), (-162) comes, so the last term greater than (-150) is (-144).

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Question 29/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक परीक्षण में पहले चरण पर मान (1250) इकाई है और हर अगले चरण में (55) इकाई घटता है। किस चरण में मान (260) इकाई होगा?

In a test, the value is (1250) units at the first stage and decreases by (55) units at each next stage. At which stage will the value be (260) units?

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Correct Answer

C. (19)वां(19)th

Explanation

Simple Explanation

(260=1250+(n-1)(-55)) से (990=55(n-1)), इसलिए (n=19)। घटती स्थिति में (d) ऋणात्मक लें। / From (260=1250+(n-1)(-55)), (990=55(n-1)), so (n=19). In a decreasing situation, take (d) as negative.

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Question 30/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक विद्यार्थी पहले दिन (64) प्रश्न हल करता है और प्रतिदिन (15) प्रश्न अधिक हल करता है। किस दिन वह (514) प्रश्न हल करेगा?

A student solves (64) questions on the first day and (15) more questions each day. On which day will he solve (514) questions?

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Correct Answer

C. (31)वां(31)st

Explanation

Simple Explanation

(514=64+(n-1)15) से (450=15(n-1)), इसलिए (n=31)। दैनिक संख्या को पद मानें कुल योग नहीं। / From (514=64+(n-1)15), (450=15(n-1)), so (n=31). Treat the daily count as a term, not a total sum.

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Question 31/50 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 32/50 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 33/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_{24}=7a_{9}-18\) और \(a_9=42\) है, तो \(a_{39}\) क्या होगा?

If \(a_{24}=7a_9-18\) and \(a_9=42\), what is \(a_{39}\)?

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Correct Answer

C. (504)

Explanation

Simple Explanation

\(a_{24}=276\) और (15d=234), इसलिए \(d=\frac{78}{5}\)। \(a_{39}=276+15\cdot\frac{78}{5}=510\)। / \(a_{24}=276\) and (15d=234), so \(d=\frac{78}{5}\). \(a_{39}=276+15\cdot\frac{78}{5}=510\).

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Question 34/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक समान्तर श्रेणी में \(a_{20}=178\) और \(a_{52}=626\) है। \(a_{36}\) क्या होगा?

In an AP \(a_{20}=178\) and \(a_{52}=626\). What is \(a_{36}\)?

Explanation opens after your attempt
Correct Answer

C. (402)

Explanation

Simple Explanation

\(a_{36}\), \(a_{20}\) और \(a_{52}\) के बीच समान दूरी पर है। इसलिए \(a_{36}=\frac{178+626}{2}=402\)। / \(a_{36}\) is equally spaced between \(a_{20}\) and \(a_{52}\). Therefore \(a_{36}=\frac{178+626}{2}=402\).

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Question 35/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि समान्तर श्रेणी \(w-15,w-4,w+7,\ldots\) का (37)वां पद (677) है, तो (w) का मान क्या होगा?

If the (37)th term of the AP \(w-15,w-4,w+7,\ldots\) is (677), what is the value of (w)?

Explanation opens after your attempt
Correct Answer

A. (296)

Explanation

Simple Explanation

यहां (d=11)। \(677=w-15+36\times11=w+381\), इसलिए (w=296)। / Here (d=11). \(677=w-15+36\times11=w+381\), so (w=296).

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Question 36/50 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 37/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

किसी समान्तर श्रेणी में \(a_1=230\) और (d=-12) है। \(a_n\) ऋणात्मक होने वाला पहला (n) क्या है?

In an AP \(a_1=230\) and (d=-12). What is the first (n) for which \(a_n\) is negative?

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Correct Answer

C. (21)

Explanation

Simple Explanation

(a_n=230-12(n-1)=242-12n)। \(a_n<0\) से \(n>\frac{121}{6}\), इसलिए पहला (n=21)। / (a_n=230-12(n-1)=242-12n). From \(a_n<0\), \(n>\frac{121}{6}\), so the first (n=21).

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Question 38/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

(5000) से कम (41) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?

What will be the last term in the AP of positive multiples of (41) less than (5000)?

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Correct Answer

B. (4961)

Explanation

Simple Explanation

(41n<5000) में सबसे बड़ा (n=121) है। अंतिम पद \(41\times121=4961\) होगा। / In (41n<5000), the greatest (n=121). The last term will be \(41\times121=4961\).

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Question 39/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

(1500) से बड़े (37) के गुणजों की AP \(1517,1554,1591,\ldots\) है। इसका (31)वां पद क्या होगा?

The AP of multiples of (37) greater than (1500) is \(1517,1554,1591,\ldots\). What will be its (31)st term?

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Correct Answer

B. (2627)

Explanation

Simple Explanation

यहां (a=1517) और (d=37)। \(a_{31}=1517+30\times37=2627\)। / Here (a=1517) and (d=37). \(a_{31}=1517+30\times37=2627\).

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Question 40/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक AP में \(a_{10}+a_{30}=500\) और \(a_{18}+a_{38}=820\) है। \(a_{58}\) क्या होगा?

In an AP \(a_{10}+a_{30}=500\) and \(a_{18}+a_{38}=820\). What is \(a_{58}\)?

Explanation opens after your attempt
Correct Answer

D. (1130)

Explanation

Simple Explanation

पहले योग से (2a+38d=500) और दूसरे से (2a+54d=820)। (d=20) और \(a_{58}=1130\)। / The first sum gives (2a+38d=500) and the second gives (2a+54d=820). (d=20) and \(a_{58}=1130\).

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Question 41/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_8=45\) और \(a_{15}=4a_8-16\) है, तो \(a_{43}\) क्या होगा?

If \(a_8=45\) and \(a_{15}=4a_8-16\), what is \(a_{43}\)?

Explanation opens after your attempt
Correct Answer

A. (721)

Explanation

Simple Explanation

\(a_{15}=164\) और (7d=119), इसलिए (d=17)। \(a_{43}=45+35\times17=640\)। / \(a_{15}=164\) and (7d=119), so (d=17). \(a_{43}=45+35\times17=640\).

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Question 42/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी \(75,98,121,\ldots\) में कितने पद (2500) से कम हैं?

In the AP \(75,98,121,\ldots\), how many terms are less than (2500)?

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Correct Answer

C. (106)

Explanation

Simple Explanation

(75+23(n-1)<2500) से (23(n-1)<2425)। सबसे बड़ा (n=106) है। / From (75+23(n-1)<2500), (23(n-1)<2425). The greatest (n=106).

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Question 43/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_{20}=a+19d=250\) और \(a_{56}=a+55d=862\) है, तो \(a_{92}\) क्या होगा?

If \(a_{20}=a+19d=250\) and \(a_{56}=a+55d=862\), what is \(a_{92}\)?

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Correct Answer

B. (1474)

Explanation

Simple Explanation

(36d=612), इसलिए (d=17)। \(a_{92}=862+36\times17=1474\)। / (36d=612), so (d=17). \(a_{92}=862+36\times17=1474\).

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Question 44/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि AP में \(a_7=58\) और \(a_{16}+a_{25}=638\) है, तो \(a_{49}\) क्या होगा?

If in an AP \(a_7=58\) and \(a_{16}+a_{25}=638\), what is \(a_{49}\)?

Explanation opens after your attempt
Correct Answer

C. (808)

Explanation

Simple Explanation

(a_{16}+a_{25}=\(a_7+9d\)+\(a_7+18d\)=116+27d=638), इसलिए \(d=\frac{58}{3}\) और \(a_{49}=58+42d=870\)। / (a_{16}+a_{25}=\(a_7+9d\)+\(a_7+18d\)=116+27d=638), so \(d=\frac{58}{3}\) and \(a_{49}=58+42d=870\).

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Question 45/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी \(-92,-69,-46,\ldots\) में (900) से बड़ा पहला पद कौन-सा है?

In the AP \(-92,-69,-46,\ldots\), what is the first term greater than (900)?

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Correct Answer

B. (920)

Explanation

Simple Explanation

(a_n=-92+23(n-1))। (900) के बाद आने वाला पहला पद (920) है। / (a_n=-92+23(n-1)). The first term after (900) is (920).

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Question 46/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_n=12n+q\) और \(a_{8n}-a_{3n}=780\) है, तो (n) का मान क्या है?

If \(a_n=12n+q\) and \(a_{8n}-a_{3n}=780\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (13)

Explanation

Simple Explanation

(a_{8n}-a_{3n}=(96n+q)-(36n+q)=60n)। (60n=780) से (n=13)। / (a_{8n}-a_{3n}=(96n+q)-(36n+q)=60n). From (60n=780), (n=13).

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Question 47/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक समान्तर श्रेणी में \(a_{14}=63\) और \(a_{42}=-301\) है। \(a_{70}\) क्या होगा?

In an AP \(a_{14}=63\) and \(a_{42}=-301\). What is \(a_{70}\)?

Explanation opens after your attempt
Correct Answer

C. (-665)

Explanation

Simple Explanation

\(d=\frac{-301-63}{42-14}=-13\)। (a_{70}=-301+28(-13)=-665)। / \(d=\frac{-301-63}{42-14}=-13\). (a_{70}=-301+28(-13)=-665).

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Question 48/50 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 49/50 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 50/50 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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