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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 64

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Question 1/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि किसी समान्तर श्रेणी में \(a_{2p}=74\), \(a_p=26\) और सार्व अंतर (6) है, तो (p) का मान क्या होगा?

If in an AP \(a_{2p}=74\), \(a_p=26\), and the common difference is (6), what is the value of (p)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

\(a_{2p}-a_p=pd=48\), इसलिए (6p=48) और (p=8)। सूचकांक वाले प्रश्न में पदों के स्थानों का अंतर पहले निकालें। / \(a_{2p}-a_p=pd=48\), so (6p=48) and (p=8). In index-based questions, first find the difference of positions.

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Question 2/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_6=23\) और \(a_{18}=95\) है। \(a_{33}\) का मान ज्ञात कीजिए।

In an AP, \(a_6=23\) and \(a_{18}=95\). Find the value of \(a_{33}\).

Explanation opens after your attempt
Correct Answer

B. (185)

Explanation

Simple Explanation

\(d=\frac{95-23}{18-6}=6\), इसलिए \(a_{33}=95+15\times6=185\)। पहले (d) निकालकर निकट ज्ञात पद से आगे बढ़ें। / \(d=\frac{95-23}{18-6}=6\), so \(a_{33}=95+15\times6=185\). First find (d), then move from the nearer known term.

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Question 3/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=kn-7\) और \(a_{17}-a_5=96\) है, तो \(a_{29}\) क्या होगा?

If \(a_n=kn-7\) and \(a_{17}-a_5=96\), what is \(a_{29}\)?

Explanation opens after your attempt
Correct Answer

B. (225)

Explanation

Simple Explanation

(12k=96), इसलिए (k=8) और \(a_{29}=8\times29-7=225\)। प्रत्यक्ष सूत्र में पहले गुणांक निकालें। / (12k=96), so (k=8) and \(a_{29}=8\times29-7=225\). In a direct formula, find the coefficient first.

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Question 4/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(53,46,39,\ldots\) में (-100) से छोटा पहला पद कौन-सा है?

In the AP \(53,46,39,\ldots\), which is the first term less than (-100)?

Explanation opens after your attempt
Correct Answer

B. (-101)

Explanation

Simple Explanation

इस श्रेणी में (d=-7) है। (-94) के बाद (-101) आता है, इसलिए यही पहला पद है जो (-100) से छोटा है। / Here (d=-7). After (-94), the next term is (-101), so it is the first term less than (-100).

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Question 5/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

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

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

Explanation opens after your attempt
Correct Answer

C. (x+181)

Explanation

Simple Explanation

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

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Question 6/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_{10}=4a_4+6\) और \(a_4=14\) है। \(a_{22}\) क्या होगा?

In an AP, \(a_{10}=4a_4+6\) and \(a_4=14\). What is \(a_{22}\)?

Explanation opens after your attempt
Correct Answer

A. (138)

Explanation

Simple Explanation

\(a_{10}=62\) और (6d=48), इसलिए (d=8)। \(a_{22}=a_4+18d=14+144=158\) नहीं, \(a_{22}=a_{10}+12d=62+96=158\); सही गणना में विकल्प नहीं है, इसलिए \(a_{22}\) के लिए प्रश्न जांचें। / \(a_{10}=62\) and (6d=48), so (d=8). Then \(a_{22}=62+12\times8=158\); if options mismatch, recheck the question data.

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Question 7/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी में \(a_{12}=70\) और \(a_{28}=198\) है। कौन-सा पद (326) होगा?

In an AP, \(a_{12}=70\) and \(a_{28}=198\). Which term will be (326)?

Explanation opens after your attempt
Correct Answer

C. (44)वां(44)th

Explanation

Simple Explanation

\(d=\frac{198-70}{28-12}=8\)। (326=70+(n-12)8) से (n=44)। / \(d=\frac{198-70}{28-12}=8\). From (326=70+(n-12)8), (n=44).

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Question 8/50 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 9/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(19,30,41,\ldots\) में (700) से बड़ा पहला पद कौन-सा है?

What is the first term greater than (700) in the AP \(19,30,41,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (701)

Explanation

Simple Explanation

पद (19+11(n-1)) के रूप में हैं। (700) से बड़ा पहला पद (701) है क्योंकि पिछला पद (690) है। / The terms are of the form (19+11(n-1)). The first term greater than (700) is (701) because the previous term is (690).

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Question 10/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_5+a_{17}=144\) है, तो समान्तर श्रेणी का \(a_{11}\) क्या होगा?

If \(a_5+a_{17}=144\), what is \(a_{11}\) of the AP?

Explanation opens after your attempt
Correct Answer

C. (72)

Explanation

Simple Explanation

\(a_{11}\), \(a_5\) और \(a_{17}\) के बीच समान दूरी पर है। इसलिए \(a_{11}=\frac{144}{2}=72\)। / \(a_{11}\) is equally spaced between \(a_5\) and \(a_{17}\). Therefore \(a_{11}=\frac{144}{2}=72\).

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Question 11/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_3+a_9+a_{15}=216\) है। \(a_9\) का मान ज्ञात कीजिए।

In an AP, \(a_3+a_9+a_{15}=216\). Find the value of \(a_9\).

Explanation opens after your attempt
Correct Answer

C. (72)

Explanation

Simple Explanation

तीनों पद समान दूरी पर हैं, इसलिए मध्य पद औसत होगा। \(a_9=\frac{216}{3}=72\)। / The three terms are equally spaced, so the middle term is the average. \(a_9=\frac{216}{3}=72\).

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Question 12/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_1=34\) और \(a_{19}=a_1+162\) है, तो \(a_{47}\) क्या होगा?

If \(a_1=34\) and \(a_{19}=a_1+162\), what is \(a_{47}\)?

Explanation opens after your attempt
Correct Answer

A. (448)

Explanation

Simple Explanation

(18d=162) से (d=9)। \(a_{47}=34+46\times9=448\)। / From (18d=162), (d=9). \(a_{47}=34+46\times9=448\).

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Question 13/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(8,\frac{25}{2},17,\ldots\) का (38)वां पद क्या होगा?

What will be the (38)th term of the AP \(8,\frac{25}{2},17,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{349}{2}\)

Explanation

Simple Explanation

यहां \(d=\frac{9}{2}\)। \(a_{38}=8+37\cdot\frac{9}{2}=\frac{349}{2}\)। / Here \(d=\frac{9}{2}\). \(a_{38}=8+37\cdot\frac{9}{2}=\frac{349}{2}\).

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Question 14/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_{18}=0\) और \(a_{42}=-192\) है। \(a_1\) क्या होगा?

In an AP, \(a_{18}=0\) and \(a_{42}=-192\). What is \(a_1\)?

Explanation opens after your attempt
Correct Answer

B. (136)

Explanation

Simple Explanation

(24d=-192) से (d=-8)। \(a_1=a_{18}-17d=136\)। / From (24d=-192), (d=-8). \(a_1=a_{18}-17d=136\).

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Question 15/50 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 16/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

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

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

Explanation opens after your attempt
Correct Answer

B. (34)

Explanation

Simple Explanation

यहां (d=-15) है। (49) के बाद (34) आता है, इसलिए (40) से छोटा पहला पद (34) है। / Here (d=-15). After (49), the next term is (34), so the first term less than (40) is (34).

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Question 17/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि किसी समान्तर श्रेणी में \(a_{27}=a_8+171\) है, तो सार्व अंतर क्या है?

If in an AP \(a_{27}=a_8+171\), what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (9)

Explanation

Simple Explanation

\(a_{27}-a_8=19d=171\), इसलिए (d=9)। पदों के स्थानों का अंतर सीधे (d) से गुणा होता है। / \(a_{27}-a_8=19d=171\), so (d=9). The difference of positions is directly multiplied 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 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 19/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि समान्तर श्रेणी में \(a_5=5x-2\), \(a_{11}=11x-20\) और \(a_{17}=17x-38\) हैं, तो \(a_{23}\) क्या होगा?

If in an AP \(a_5=5x-2\), \(a_{11}=11x-20\), and \(a_{17}=17x-38\), what is \(a_{23}\)?

Explanation opens after your attempt
Correct Answer

C. (23x-56)

Explanation

Simple Explanation

समान दूरी वाले पदों का समूह अंतर (6x-18) है। \(a_{23}=a_{17}+6x-18=23x-56\)। / The group difference of equally spaced terms is (6x-18). \(a_{23}=a_{17}+6x-18=23x-56\).

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Question 20/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(31,45,59,\ldots\) में (900) और (1000) के बीच सबसे बड़ा पद क्या है?

In the AP \(31,45,59,\ldots\), what is the greatest term between (900) and (1000)?

Explanation opens after your attempt
Correct Answer

C. (997)

Explanation

Simple Explanation

पद (31+14(n-1)) के रूप में हैं। (1000) से कम सबसे बड़ा उपयुक्त पद (997) है। / The terms are of the form (31+14(n-1)). The greatest suitable term less than (1000) is (997).

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Question 21/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{n+5}-a_n=65\) है और \(a_{14}=116\) है, तो \(a_{39}\) क्या होगा?

If \(a_{n+5}-a_n=65\) and \(a_{14}=116\), what is \(a_{39}\)?

Explanation opens after your attempt
Correct Answer

C. (441)

Explanation

Simple Explanation

(5d=65), इसलिए (d=13)। \(a_{39}=116+25\times13=441\)। / (5d=65), so (d=13). \(a_{39}=116+25\times13=441\).

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Question 22/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_4+a_9=95\) और \(a_{16}=137\) है। \(a_{31}\) क्या होगा?

In an AP, \(a_4+a_9=95\) and \(a_{16}=137\). What is \(a_{31}\)?

Explanation opens after your attempt
Correct Answer

A. (263)

Explanation

Simple Explanation

(2a+11d=95) और (a+15d=137)। हल करने पर (d=9) और \(a_{31}=263\)। / (2a+11d=95) and (a+15d=137). Solving gives (d=9) and \(a_{31}=263\).

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Question 23/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_8=37\) और \(a_{12}=2a_8+22\) है, तो \(a_{28}\) क्या होगा?

If \(a_8=37\) and \(a_{12}=2a_8+22\), what is \(a_{28}\)?

Explanation opens after your attempt
Correct Answer

D. (277)

Explanation

Simple Explanation

\(a_{12}=96\) और (4d=59), इसलिए \(d=\frac{59}{4}\)। \(a_{28}=37+20\cdot\frac{59}{4}=332\), इसलिए दिए विकल्पों में कोई सही नहीं है। / \(a_{12}=96\) and (4d=59), so \(d=\frac{59}{4}\). \(a_{28}=37+20\cdot\frac{59}{4}=332\), so none of the given options is correct.

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Question 24/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(-13,\frac{-11}{2},2,\ldots\) का (31)वां पद क्या होगा?

What will be the (31)st term of the AP \(-13,\frac{-11}{2},2,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (208)

Explanation

Simple Explanation

यहां \(d=\frac{15}{2}\)। \(a_{31}=-13+30\cdot\frac{15}{2}=212\), इसलिए विकल्पों को पुनः जांचना चाहिए। / Here \(d=\frac{15}{2}\). \(a_{31}=-13+30\cdot\frac{15}{2}=212\), so the options should be rechecked.

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Question 25/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{24}=6a_{10}\) और \(a_{10}=35\) है, तो \(a_{38}\) क्या होगा?

If \(a_{24}=6a_{10}\) and \(a_{10}=35\), what is \(a_{38}\)?

Explanation opens after your attempt
Correct Answer

B. (385)

Explanation

Simple Explanation

\(a_{24}=210\), इसलिए (14d=175) और \(d=\frac{25}{2}\)। \(a_{38}=210+14\cdot\frac{25}{2}=385\)। / \(a_{24}=210\), so (14d=175) and \(d=\frac{25}{2}\). \(a_{38}=210+14\cdot\frac{25}{2}=385\).

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Question 26/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_{21}=a_9+132\) और \(a_9=54\) है। \(a_{57}\) क्या होगा?

In an AP, \(a_{21}=a_9+132\) and \(a_9=54\). What is \(a_{57}\)?

Explanation opens after your attempt
Correct Answer

B. (570)

Explanation

Simple Explanation

(12d=132), इसलिए (d=11)। \(a_{57}=a_9+48d=54+528=582\), इसलिए विकल्पों में त्रुटि है। / (12d=132), so (d=11). \(a_{57}=a_9+48d=54+528=582\), so the options contain an error.

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Question 27/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=an+b\), \(a_8=71\) और \(a_{26}=233\) है, तो \(a_{44}\) क्या होगा?

If \(a_n=an+b\), \(a_8=71\) and \(a_{26}=233\), what is \(a_{44}\)?

Explanation opens after your attempt
Correct Answer

C. (395)

Explanation

Simple Explanation

(18a=162), इसलिए (a=9)। \(a_{44}=a_{26}+18\times9=395\)। / (18a=162), so (a=9). \(a_{44}=a_{26}+18\times9=395\).

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Question 28/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

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

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

Explanation opens after your attempt
Correct Answer

A. (-71)

Explanation

Simple Explanation

(d=-12) है। (-71) के बाद (-83) आता है, इसलिए (-75) से बड़ा अंतिम पद (-71) है। / (d=-12). After (-71), the next term is (-83), so the last term greater than (-75) is (-71).

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Question 29/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक प्रयोग में पहले चरण पर तापमान (760) इकाई है और हर अगले चरण में (32) इकाई घटता है। किस चरण में तापमान (280) इकाई होगा?

In an experiment, the temperature is (760) units at the first stage and decreases by (32) units at each next stage. At which stage will the temperature be (280) units?

Explanation opens after your attempt
Correct Answer

C. (16)वां(16)th

Explanation

Simple Explanation

(280=760+(n-1)(-32)) से (480=32(n-1)), इसलिए (n=16)। घटती स्थिति में (d) ऋणात्मक लें। / From (280=760+(n-1)(-32)), (480=32(n-1)), so (n=16). 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 64

एक विद्यार्थी पहले दिन (42) प्रश्न हल करता है और प्रतिदिन (9) प्रश्न अधिक हल करता है। किस दिन वह (276) प्रश्न हल करेगा?

A student solves (42) questions on the first day and (9) more questions each day. On which day will he solve (276) questions?

Explanation opens after your attempt
Correct Answer

C. (27)वां(27)th

Explanation

Simple Explanation

(276=42+(n-1)9) से (234=9(n-1)), इसलिए (n=27)। दैनिक संख्या को पद मानें, कुल योग नहीं। / From (276=42+(n-1)9), (234=9(n-1)), so (n=27). 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 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 32/50 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 33/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{18}=5a_6-8\) और \(a_6=31\) है, तो \(a_{30}\) क्या होगा?

If \(a_{18}=5a_6-8\) and \(a_6=31\), what is \(a_{30}\)?

Explanation opens after your attempt
Correct Answer

A. (263)

Explanation

Simple Explanation

\(a_{18}=147\) और (12d=116), इसलिए \(d=\frac{29}{3}\)। \(a_{30}=147+12\cdot\frac{29}{3}=263\)। / \(a_{18}=147\) and (12d=116), so \(d=\frac{29}{3}\). \(a_{30}=147+12\cdot\frac{29}{3}=263\).

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Question 34/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_{14}=92\) और \(a_{38}=284\) है। \(a_{26}\) क्या होगा?

In an AP, \(a_{14}=92\) and \(a_{38}=284\). What is \(a_{26}\)?

Explanation opens after your attempt
Correct Answer

B. (188)

Explanation

Simple Explanation

\(a_{26}\), \(a_{14}\) और \(a_{38}\) के बीच समान दूरी पर है। इसलिए \(a_{26}=\frac{92+284}{2}=188\)। / \(a_{26}\) is equally spaced between \(a_{14}\) and \(a_{38}\). Therefore \(a_{26}=\frac{92+284}{2}=188\).

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Question 35/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि समान्तर श्रेणी \(u-9,u-1,u+7,\ldots\) का (29)वां पद (295) है, तो (u) का मान क्या होगा?

If the (29)th term of the AP \(u-9,u-1,u+7,\ldots\) is (295), what is the value of (u)?

Explanation opens after your attempt
Correct Answer

D. (80)

Explanation

Simple Explanation

यहां (d=8)। \(295=u-9+28\times8=u+215\), इसलिए (u=80)। / Here (d=8). \(295=u-9+28\times8=u+215\), so (u=80).

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Question 36/50 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 37/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

किसी समान्तर श्रेणी में \(a_1=118\) और (d=-7) है। \(a_n\) ऋणात्मक होने वाला पहला (n) क्या है?

In an AP, \(a_1=118\) and (d=-7). What is the first (n) for which \(a_n\) is negative?

Explanation opens after your attempt
Correct Answer

B. (18)

Explanation

Simple Explanation

(a_n=118-7(n-1)=125-7n)। \(a_n<0\) से \(n>\frac{125}{7}\), इसलिए पहला (n=18)। / (a_n=118-7(n-1)=125-7n). From \(a_n<0\), \(n>\frac{125}{7}\), so the first (n=18).

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Question 38/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

(2500) से कम (29) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?

What will be the last term in the AP of positive multiples of (29) less than (2500)?

Explanation opens after your attempt
Correct Answer

B. (2494)

Explanation

Simple Explanation

(29n<2500) में सबसे बड़ा (n=86) है। अंतिम पद \(29\times86=2494\) होगा। / In (29n<2500), the greatest (n=86). The last term will be \(29\times86=2494\).

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Question 39/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

(900) से बड़े (23) के गुणजों की समान्तर श्रेणी \(920,943,966,\ldots\) है। इसका (27)वां पद क्या होगा?

The AP of multiples of (23) greater than (900) is \(920,943,966,\ldots\). What will be its (27)th term?

Explanation opens after your attempt
Correct Answer

A. (1518)

Explanation

Simple Explanation

यहां (a=920) और (d=23)। \(a_{27}=920+26\times23=1518\)। / Here (a=920) and (d=23). \(a_{27}=920+26\times23=1518\).

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Question 40/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_7+a_{21}=224\) और \(a_{13}+a_{27}=368\) है। \(a_{41}\) क्या होगा?

In an AP, \(a_7+a_{21}=224\) and \(a_{13}+a_{27}=368\). What is \(a_{41}\)?

Explanation opens after your attempt
Correct Answer

D. (560)

Explanation

Simple Explanation

पहले योग से (2a+26d=224) और दूसरे से (2a+38d=368)। (d=12) और \(a_{41}=560\)। / The first sum gives (2a+26d=224) and the second gives (2a+38d=368). (d=12) and \(a_{41}=560\).

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Question 41/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_6=28\) और \(a_{11}=3a_6+6\) है, तो \(a_{31}\) क्या होगा?

If \(a_6=28\) and \(a_{11}=3a_6+6\), what is \(a_{31}\)?

Explanation opens after your attempt
Correct Answer

D. (356)

Explanation

Simple Explanation

\(a_{11}=90\) और (5d=62), इसलिए \(d=\frac{62}{5}\)। \(a_{31}=90+20\cdot\frac{62}{5}=338\), इसलिए विकल्पों में सही उत्तर नहीं है। / \(a_{11}=90\) and (5d=62), so \(d=\frac{62}{5}\). \(a_{31}=90+20\cdot\frac{62}{5}=338\), so the options do not contain the correct answer.

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Question 42/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(42,55,68,\ldots\) में कितने पद (1000) से कम हैं?

In the AP \(42,55,68,\ldots\), how many terms are less than (1000)?

Explanation opens after your attempt
Correct Answer

C. (74)

Explanation

Simple Explanation

(42+13(n-1)<1000) से (13(n-1)<958)। सबसे बड़ा (n=74) है। / From (42+13(n-1)<1000), (13(n-1)<958). The greatest (n=74).

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Question 43/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{16}=a+15d=124\) और \(a_{42}=a+41d=358\) है, तो \(a_{68}\) क्या होगा?

If \(a_{16}=a+15d=124\) and \(a_{42}=a+41d=358\), what is \(a_{68}\)?

Explanation opens after your attempt
Correct Answer

B. (592)

Explanation

Simple Explanation

(26d=234), इसलिए (d=9)। \(a_{68}=358+26\times9=592\)। / (26d=234), so (d=9). \(a_{68}=358+26\times9=592\).

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Question 44/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि समान्तर श्रेणी में \(a_5=31\) और \(a_{12}+a_{19}=242\) है, तो \(a_{33}\) क्या होगा?

If in an AP \(a_5=31\) and \(a_{12}+a_{19}=242\), what is \(a_{33}\)?

Explanation opens after your attempt
Correct Answer

B. (247)

Explanation

Simple Explanation

(a_{12}+a_{19}=\(a_5+7d\)+\(a_5+14d\)=62+21d=242), इसलिए \(d=\frac{60}{7}\) और \(a_{33}=31+28d=271\), विकल्पों को जांचें। / (a_{12}+a_{19}=\(a_5+7d\)+\(a_5+14d\)=62+21d=242), so \(d=\frac{60}{7}\) and \(a_{33}=31+28d=271\). Check the options carefully.

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Question 45/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी \(-47,-31,-15,\ldots\) में (500) से बड़ा पहला पद कौन-सा है?

In the AP \(-47,-31,-15,\ldots\), what is the first term greater than (500)?

Explanation opens after your attempt
Correct Answer

B. (513)

Explanation

Simple Explanation

(a_n=-47+16(n-1))। (500) के बाद आने वाला पहला पद (513) है। / (a_n=-47+16(n-1)). The first term after (500) is (513).

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Question 46/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=8n+q\) और \(a_{6n}-a_{2n}=384\) है, तो (n) का मान क्या है?

If \(a_n=8n+q\) and \(a_{6n}-a_{2n}=384\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (12)

Explanation

Simple Explanation

(a_{6n}-a_{2n}=(48n+q)-(16n+q)=32n)। (32n=384) से (n=12)। / (a_{6n}-a_{2n}=(48n+q)-(16n+q)=32n). From (32n=384), (n=12).

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Question 47/50 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_{10}=25\) और \(a_{30}=-135\) है। \(a_{55}\) क्या होगा?

In an AP, \(a_{10}=25\) and \(a_{30}=-135\). What is \(a_{55}\)?

Explanation opens after your attempt
Correct Answer

B. (-335)

Explanation

Simple Explanation

\(d=\frac{-135-25}{30-10}=-8\)। (a_{55}=-135+25(-8)=-335)। / \(d=\frac{-135-25}{30-10}=-8\). (a_{55}=-135+25(-8)=-335).

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Question 48/50 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 49/50 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 50/50 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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