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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 Topic Quiz

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Question 1/150 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 2/150 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 3/150 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 4/150 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 5/150 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 6/150 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 7/150 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 8/150 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 9/150 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 10/150 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 11/150 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 12/150 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 13/150 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 14/150 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 15/150 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 16/150 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 17/150 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 18/150 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 19/150 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 20/150 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 21/150 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 22/150 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 23/150 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 24/150 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 25/150 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 26/150 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 27/150 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 28/150 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 29/150 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 30/150 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 31/150 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 32/150 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 33/150 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 34/150 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 35/150 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 36/150 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 37/150 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 38/150 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 39/150 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 40/150 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 41/150 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 42/150 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 43/150 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 44/150 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 45/150 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 46/150 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 47/150 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 48/150 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 49/150 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 50/150 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 51/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में \(a_8=46\) और \(a_{22}=144\) है। \(a_{40}\) का मान क्या होगा?

In an AP, \(a_8=46\) and \(a_{22}=144\). What is the value of \(a_{40}\)?

Explanation opens after your attempt
Correct Answer

C. (270)

Explanation

Simple Explanation

\(d=\frac{144-46}{22-8}=7\), इसलिए \(a_{40}=144+18\times7=270\)। निकट ज्ञात पद से आगे बढ़ना तेज तरीका है। / \(d=\frac{144-46}{22-8}=7\), so \(a_{40}=144+18\times7=270\). Moving from the nearer known term is faster.

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Question 52/150 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 53/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_n=kn+17\) और \(a_{20}-a_7=104\) है, तो \(a_{31}\) क्या होगा?

If \(a_n=kn+17\) and \(a_{20}-a_7=104\), what is \(a_{31}\)?

Explanation opens after your attempt
Correct Answer

B. (265)

Explanation

Simple Explanation

(13k=104) से (k=8)। इसलिए \(a_{31}=8\times31+17=265\)। पहले (k) निकालें फिर पद संख्या रखें। / From (13k=104), (k=8). Therefore \(a_{31}=8\times31+17=265\). First find (k), then substitute the term number.

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Question 54/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी \(210,197,184,\ldots\) में (0) से छोटा पहला पद कौन-सा है?

In the AP \(210,197,184,\ldots\), which is the first term less than (0)?

Explanation opens after your attempt
Correct Answer

A. (-11)

Explanation

Simple Explanation

यहां (d=-13) है और (2) के बाद (-11) आता है। इसलिए (0) से छोटा पहला पद (-11) है। / Here (d=-13), and after (2), (-11) comes. Therefore the first term less than (0) is (-11).

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Question 55/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_9=x+25\) और \(a_{23}=x+109\) है, तो \(a_{41}\) (x) के रूप में क्या होगा?

If \(a_9=x+25\) and \(a_{23}=x+109\), what is \(a_{41}\) in terms of (x)?

Explanation opens after your attempt
Correct Answer

C. (x+217)

Explanation

Simple Explanation

(14d=84), इसलिए (d=6)। \(a_{41}=x+109+18\times6=x+217\)। / (14d=84), so (d=6). \(a_{41}=x+109+18\times6=x+217\).

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Question 56/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक AP में \(a_{12}=3a_5+4\) और \(a_5=19\) है। \(a_{26}\) क्या होगा?

In an AP, \(a_{12}=3a_5+4\) and \(a_5=19\). What is \(a_{26}\)?

Explanation opens after your attempt
Correct Answer

A. (143)

Explanation

Simple Explanation

\(a_{12}=61\) और (7d=42), इसलिए (d=6)। \(a_{26}=61+14\times6=145\) नहीं, \(a_{26}=19+21\times6=145\); सही विकल्पों में (145) नहीं है। / \(a_{12}=61\) and (7d=42), so (d=6). \(a_{26}=19+21\times6=145\); the correct value is not in the listed options.

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Question 57/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी में \(a_{15}=88\) और \(a_{35}=248\) है। कौन-सा पद (408) होगा?

In an AP, \(a_{15}=88\) and \(a_{35}=248\). Which term will be (408)?

Explanation opens after your attempt
Correct Answer

C. (55)वां(55)th

Explanation

Simple Explanation

\(d=\frac{248-88}{35-15}=8\)। (408=88+(n-15)8) से (n=55)। / \(d=\frac{248-88}{35-15}=8\). From (408=88+(n-15)8), (n=55).

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Question 58/150 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 59/150 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 60/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी \(27,40,53,\ldots\) में (850) से बड़ा पहला पद कौन-सा है?

What is the first term greater than (850) in the AP \(27,40,53,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (859)

Explanation

Simple Explanation

पद (27+13(n-1)) के रूप में हैं। (850) से बड़ा पहला पद (859) है क्योंकि पिछला पद (846) है। / The terms are of the form (27+13(n-1)). The first term greater than (850) is (859) because the previous term is (846).

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Question 61/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_6+a_{20}=190\) है, तो \(a_{13}\) का मान क्या होगा?

If \(a_6+a_{20}=190\), what is the value of \(a_{13}\)?

Explanation opens after your attempt
Correct Answer

B. (95)

Explanation

Simple Explanation

\(a_{13}\), \(a_6\) और \(a_{20}\) के बीच समान दूरी पर है। इसलिए \(a_{13}=\frac{190}{2}=95\)। / \(a_{13}\) is equally spaced between \(a_6\) and \(a_{20}\). Therefore \(a_{13}=\frac{190}{2}=95\).

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Question 62/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में \(a_4+a_{12}+a_{20}=300\) है। \(a_{12}\) का मान क्या होगा?

In an AP, \(a_4+a_{12}+a_{20}=300\). What is the value of \(a_{12}\)?

Explanation opens after your attempt
Correct Answer

C. (100)

Explanation

Simple Explanation

तीनों पद समान दूरी पर हैं, इसलिए मध्य पद औसत होगा। \(a_{12}=\frac{300}{3}=100\)। / The three terms are equally spaced, so the middle term is the average. \(a_{12}=\frac{300}{3}=100\).

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Question 63/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_1=41\) और \(a_{21}=a_1+220\) है, तो \(a_{51}\) क्या होगा?

If \(a_1=41\) and \(a_{21}=a_1+220\), what is \(a_{51}\)?

Explanation opens after your attempt
Correct Answer

B. (591)

Explanation

Simple Explanation

(20d=220) से (d=11)। \(a_{51}=41+50\times11=591\)। / From (20d=220), (d=11). \(a_{51}=41+50\times11=591\).

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Question 64/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी \(11,\frac{31}{2},20,\ldots\) का (44)वां पद क्या होगा?

What will be the (44)th term of the AP \(11,\frac{31}{2},20,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{407}{2}\)

Explanation

Simple Explanation

यहां \(d=\frac{9}{2}\)। \(a_{44}=11+43\cdot\frac{9}{2}=\frac{409}{2}\), इसलिए विकल्पों को फिर जांचना चाहिए। / Here \(d=\frac{9}{2}\). \(a_{44}=11+43\cdot\frac{9}{2}=\frac{409}{2}\), so the options should be rechecked.

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Question 65/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में \(a_{20}=0\) और \(a_{50}=-270\) है। \(a_1\) क्या होगा?

In an AP, \(a_{20}=0\) and \(a_{50}=-270\). What is \(a_1\)?

Explanation opens after your attempt
Correct Answer

B. (171)

Explanation

Simple Explanation

(30d=-270) से (d=-9)। \(a_1=a_{20}-19d=171\)। / From (30d=-270), (d=-9). \(a_1=a_{20}-19d=171\).

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Question 66/150 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 67/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी \(221,204,187,\ldots\) में (50) से छोटा पहला पद कौन-सा है?

In the AP \(221,204,187,\ldots\), what is the first term less than (50)?

Explanation opens after your attempt
Correct Answer

B. (34)

Explanation

Simple Explanation

यहां (d=-17) है। (51) के बाद (34) आता है, इसलिए (50) से छोटा पहला पद (34) है। / Here (d=-17). After (51), (34) comes, so the first term less than (50) is (34).

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Question 68/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि किसी समान्तर श्रेणी में \(a_{31}=a_9+198\) है, तो सार्व अंतर क्या है?

If in an AP \(a_{31}=a_9+198\), what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (9)

Explanation

Simple Explanation

\(a_{31}-a_9=22d=198\), इसलिए (d=9)। पदों के स्थान अंतर को (d) से गुणा करें। / \(a_{31}-a_9=22d=198\), so (d=9). Multiply the position gap by (d).

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Question 69/150 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 70/150 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 71/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि समान्तर श्रेणी में \(a_6=6x-5\), \(a_{13}=13x-33\) और \(a_{20}=20x-61\) हैं, तो \(a_{27}\) क्या होगा?

If in an AP \(a_6=6x-5\), \(a_{13}=13x-33\), and \(a_{20}=20x-61\), what is \(a_{27}\)?

Explanation opens after your attempt
Correct Answer

C. (27x-89)

Explanation

Simple Explanation

समान दूरी वाले पदों का समूह अंतर (7x-28) है। \(a_{27}=a_{20}+7x-28=27x-89\)। / The group difference of equally spaced terms is (7x-28). \(a_{27}=a_{20}+7x-28=27x-89\).

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Question 72/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी \(43,60,77,\ldots\) में (1200) और (1300) के बीच सबसे बड़ा पद क्या है?

In the AP \(43,60,77,\ldots\), what is the greatest term between (1200) and (1300)?

Explanation opens after your attempt
Correct Answer

B. (1284)

Explanation

Simple Explanation

पद (43+17(n-1)) के रूप में हैं। (1300) से कम सबसे बड़ा उपयुक्त पद (1284) है। / The terms are of the form (43+17(n-1)). The greatest suitable term less than (1300) is (1284).

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Question 73/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_{n+6}-a_n=96\) है और \(a_{18}=157\) है, तो \(a_{48}\) क्या होगा?

If \(a_{n+6}-a_n=96\) and \(a_{18}=157\), what is \(a_{48}\)?

Explanation opens after your attempt
Correct Answer

C. (637)

Explanation

Simple Explanation

(6d=96), इसलिए (d=16)। \(a_{48}=157+30\times16=637\)। / (6d=96), so (d=16). \(a_{48}=157+30\times16=637\).

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Question 74/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में \(a_5+a_{11}=138\) और \(a_{18}=165\) है। \(a_{36}\) क्या होगा?

In an AP, \(a_5+a_{11}=138\) and \(a_{18}=165\). What is \(a_{36}\)?

Explanation opens after your attempt
Correct Answer

A. (327)

Explanation

Simple Explanation

(2a+14d=138) और (a+17d=165)। हल करने पर (d=9) और \(a_{36}=327\)। / (2a+14d=138) and (a+17d=165). Solving gives (d=9) and \(a_{36}=327\).

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Question 75/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_9=43\) और \(a_{14}=2a_9+17\) है, तो \(a_{34}\) क्या होगा?

If \(a_9=43\) and \(a_{14}=2a_9+17\), what is \(a_{34}\)?

Explanation opens after your attempt
Correct Answer

A. (283)

Explanation

Simple Explanation

\(a_{14}=103\) और (5d=60), इसलिए (d=12)। \(a_{34}=43+25\times12=343\), इसलिए दिए विकल्पों में सही उत्तर नहीं है। / \(a_{14}=103\) and (5d=60), so (d=12). \(a_{34}=43+25\times12=343\), so the correct answer is not in the options.

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Question 76/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी \(-17,\frac{-15}{2},2,\ldots\) का (35)वां पद क्या होगा?

What will be the (35)th term of the AP \(-17,\frac{-15}{2},2,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (272)

Explanation

Simple Explanation

यहां \(d=\frac{19}{2}\)। \(a_{35}=-17+34\cdot\frac{19}{2}=306\), इसलिए विकल्पों को फिर जांचें। / Here \(d=\frac{19}{2}\). \(a_{35}=-17+34\cdot\frac{19}{2}=306\), so recheck the options.

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Question 77/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_{28}=7a_{12}\) और \(a_{12}=44\) है, तो \(a_{44}\) क्या होगा?

If \(a_{28}=7a_{12}\) and \(a_{12}=44\), what is \(a_{44}\)?

Explanation opens after your attempt
Correct Answer

B. (572)

Explanation

Simple Explanation

\(a_{28}=308\), इसलिए (16d=264) और \(d=\frac{33}{2}\)। \(a_{44}=308+16\cdot\frac{33}{2}=572\)। / \(a_{28}=308\), so (16d=264) and \(d=\frac{33}{2}\). \(a_{44}=308+16\cdot\frac{33}{2}=572\).

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Question 78/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में \(a_{25}=a_{10}+180\) और \(a_{10}=70\) है। \(a_{65}\) क्या होगा?

In an AP, \(a_{25}=a_{10}+180\) and \(a_{10}=70\). What is \(a_{65}\)?

Explanation opens after your attempt
Correct Answer

B. (730)

Explanation

Simple Explanation

(15d=180), इसलिए (d=12)। \(a_{65}=a_{10}+55d=70+660=730\)। / (15d=180), so (d=12). \(a_{65}=a_{10}+55d=70+660=730\).

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Question 79/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_n=an+b\), \(a_{10}=97\) और \(a_{32}=317\) है, तो \(a_{54}\) क्या होगा?

If \(a_n=an+b\), \(a_{10}=97\) and \(a_{32}=317\), what is \(a_{54}\)?

Explanation opens after your attempt
Correct Answer

B. (537)

Explanation

Simple Explanation

(22a=220), इसलिए (a=10)। \(a_{54}=a_{32}+22\times10=537\)। / (22a=220), so (a=10). \(a_{54}=a_{32}+22\times10=537\).

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Question 80/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी \(156,142,128,\ldots\) में (-120) से बड़ा अंतिम पद कौन-सा है?

In the AP \(156,142,128,\ldots\), which is the last term greater than (-120)?

Explanation opens after your attempt
Correct Answer

B. (-112)

Explanation

Simple Explanation

(d=-14) है। (-110) इस श्रेणी में नहीं है, जबकि (-112) के बाद (-126) आता है। / (d=-14). (-110) is not in this AP, while after (-112), (-126) comes.

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Question 81/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक मशीन में पहले चरण पर भार (980) इकाई है और हर अगले चरण में (45) इकाई घटता है। किस चरण में भार (305) इकाई होगा?

In a machine, the load is (980) units at the first stage and decreases by (45) units at each next stage. At which stage will the load be (305) units?

Explanation opens after your attempt
Correct Answer

C. (16)वां(16)th

Explanation

Simple Explanation

(305=980+(n-1)(-45)) से (675=45(n-1)), इसलिए (n=16)। घटती स्थिति में (d) ऋणात्मक लें। / From (305=980+(n-1)(-45)), (675=45(n-1)), so (n=16). In a decreasing situation, take (d) as negative.

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Question 82/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक विद्यार्थी पहले दिन (55) प्रश्न हल करता है और प्रतिदिन (12) प्रश्न अधिक हल करता है। किस दिन वह (367) प्रश्न हल करेगा?

A student solves (55) questions on the first day and (12) more questions each day. On which day will he solve (367) questions?

Explanation opens after your attempt
Correct Answer

C. (27)वां(27)th

Explanation

Simple Explanation

(367=55+(n-1)12) से (312=12(n-1)), इसलिए (n=27)। दैनिक संख्या पद है कुल योग नहीं। / From (367=55+(n-1)12), (312=12(n-1)), so (n=27). Daily count is a term, not a total sum.

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Question 83/150 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 84/150 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 85/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_{20}=6a_8-13\) और \(a_8=37\) है, तो \(a_{32}\) क्या होगा?

If \(a_{20}=6a_8-13\) and \(a_8=37\), what is \(a_{32}\)?

Explanation opens after your attempt
Correct Answer

C. (399)

Explanation

Simple Explanation

\(a_{20}=209\) और (12d=172), इसलिए \(d=\frac{43}{3}\)। \(a_{32}=209+12\cdot\frac{43}{3}=381\), विकल्पों में यह नहीं है। / \(a_{20}=209\) and (12d=172), so \(d=\frac{43}{3}\). \(a_{32}=209+12\cdot\frac{43}{3}=381\), which is not in the options.

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Question 86/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में \(a_{18}=135\) और \(a_{46}=443\) है। \(a_{32}\) क्या होगा?

In an AP, \(a_{18}=135\) and \(a_{46}=443\). What is \(a_{32}\)?

Explanation opens after your attempt
Correct Answer

C. (289)

Explanation

Simple Explanation

\(a_{32}\), \(a_{18}\) और \(a_{46}\) के बीच समान दूरी पर है। इसलिए \(a_{32}=\frac{135+443}{2}=289\)। / \(a_{32}\) is equally spaced between \(a_{18}\) and \(a_{46}\). Therefore \(a_{32}=\frac{135+443}{2}=289\).

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Question 87/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि समान्तर श्रेणी \(v-12,v-3,v+6,\ldots\) का (31)वां पद (438) है, तो (v) का मान क्या होगा?

If the (31)st term of the AP \(v-12,v-3,v+6,\ldots\) is (438), what is the value of (v)?

Explanation opens after your attempt
Correct Answer

B. (180)

Explanation

Simple Explanation

यहां (d=9)। \(438=v-12+30\times9=v+258\), इसलिए (v=180)। / Here (d=9). \(438=v-12+30\times9=v+258\), so (v=180).

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Question 88/150 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 89/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

किसी समान्तर श्रेणी में \(a_1=167\) और (d=-9) है। \(a_n\) ऋणात्मक होने वाला पहला (n) क्या है?

In an AP, \(a_1=167\) and (d=-9). What is the first (n) for which \(a_n\) is negative?

Explanation opens after your attempt
Correct Answer

B. (20)

Explanation

Simple Explanation

(a_n=167-9(n-1)=176-9n)। \(a_n<0\) से \(n>\frac{176}{9}\), इसलिए पहला (n=20)। / (a_n=167-9(n-1)=176-9n). From \(a_n<0\), \(n>\frac{176}{9}\), so the first (n=20).

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Question 90/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

(3600) से कम (37) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?

What will be the last term in the AP of positive multiples of (37) less than (3600)?

Explanation opens after your attempt
Correct Answer

C. (3589)

Explanation

Simple Explanation

(37n<3600) में सबसे बड़ा (n=97) है। अंतिम पद \(37\times97=3589\) होगा। / In (37n<3600), the greatest (n=97). The last term will be \(37\times97=3589\).

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Question 91/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

(1200) से बड़े (31) के गुणजों की AP \(1209,1240,1271,\ldots\) है। इसका (29)वां पद क्या होगा?

The AP of multiples of (31) greater than (1200) is \(1209,1240,1271,\ldots\). What will be its (29)th term?

Explanation opens after your attempt
Correct Answer

A. (2077)

Explanation

Simple Explanation

यहां (a=1209) और (d=31)। \(a_{29}=1209+28\times31=2077\)। / Here (a=1209) and (d=31). \(a_{29}=1209+28\times31=2077\).

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Question 92/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक AP में \(a_8+a_{24}=320\) और \(a_{14}+a_{30}=512\) है। \(a_{46}\) क्या होगा?

In an AP, \(a_8+a_{24}=320\) and \(a_{14}+a_{30}=512\). What is \(a_{46}\)?

Explanation opens after your attempt
Correct Answer

D. (752)

Explanation

Simple Explanation

पहले योग से (2a+30d=320) और दूसरे से (2a+42d=512)। (d=16) और \(a_{46}=752\)। / The first sum gives (2a+30d=320) and the second gives (2a+42d=512). (d=16) and \(a_{46}=752\).

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Question 93/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_7=36\) और \(a_{13}=4a_7-12\) है, तो \(a_{37}\) क्या होगा?

If \(a_7=36\) and \(a_{13}=4a_7-12\), what is \(a_{37}\)?

Explanation opens after your attempt
Correct Answer

D. (480)

Explanation

Simple Explanation

\(a_{13}=132\) और (6d=96), इसलिए (d=16)। \(a_{37}=36+30\times16=516\), इसलिए विकल्पों में सही उत्तर नहीं है। / \(a_{13}=132\) and (6d=96), so (d=16). \(a_{37}=36+30\times16=516\), so the correct answer is not in the options.

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Question 94/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी \(56,73,90,\ldots\) में कितने पद (1500) से कम हैं?

In the AP \(56,73,90,\ldots\), how many terms are less than (1500)?

Explanation opens after your attempt
Correct Answer

B. (85)

Explanation

Simple Explanation

(56+17(n-1)<1500) से (17(n-1)<1444)। सबसे बड़ा (n=85) है। / From (56+17(n-1)<1500), (17(n-1)<1444). The greatest (n=85).

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Question 95/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_{18}=a+17d=176\) और \(a_{48}=a+47d=596\) है, तो \(a_{78}\) क्या होगा?

If \(a_{18}=a+17d=176\) and \(a_{48}=a+47d=596\), what is \(a_{78}\)?

Explanation opens after your attempt
Correct Answer

B. (1016)

Explanation

Simple Explanation

(30d=420), इसलिए (d=14)। \(a_{78}=596+30\times14=1016\)। / (30d=420), so (d=14). \(a_{78}=596+30\times14=1016\).

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Question 96/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि समान्तर श्रेणी में \(a_5=31\) और \(a_{12}+a_{19}=272\) है, तो \(a_{33}\) क्या होगा?

If in an AP \(a_5=31\) and \(a_{12}+a_{19}=272\), what is \(a_{33}\)?

Explanation opens after your attempt
Correct Answer

C. (311)

Explanation

Simple Explanation

\(a_{12}+a_{19}=62+21d=272\), इसलिए (d=10)। \(a_{33}=31+28\times10=311\)। / \(a_{12}+a_{19}=62+21d=272\), so (d=10). \(a_{33}=31+28\times10=311\).

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Question 97/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि AP में \(a_6=42\) और \(a_{14}+a_{22}=420\) है, तो \(a_{38}\) क्या होगा?

If in an AP \(a_6=42\) and \(a_{14}+a_{22}=420\), what is \(a_{38}\)?

Explanation opens after your attempt
Correct Answer

B. (462)

Explanation

Simple Explanation

(a_{14}+a_{22}=\(a_6+8d\)+\(a_6+16d\)=84+24d=420), इसलिए (d=14)। \(a_{38}=42+32d=490\), विकल्पों में यह नहीं है। / (a_{14}+a_{22}=\(a_6+8d\)+\(a_6+16d\)=84+24d=420), so (d=14). \(a_{38}=42+32d=490\), which is not in the options.

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Question 98/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी \(-68,-49,-30,\ldots\) में (700) से बड़ा पहला पद कौन-सा है?

In the AP \(-68,-49,-30,\ldots\), what is the first term greater than (700)?

Explanation opens after your attempt
Correct Answer

B. (711)

Explanation

Simple Explanation

(a_n=-68+19(n-1))। (700) के बाद आने वाला पहला पद (711) है। / (a_n=-68+19(n-1)). The first term after (700) is (711).

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Question 99/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_n=10n+q\) और \(a_{7n}-a_{3n}=520\) है, तो (n) का मान क्या है?

If \(a_n=10n+q\) and \(a_{7n}-a_{3n}=520\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (13)

Explanation

Simple Explanation

(a_{7n}-a_{3n}=(70n+q)-(30n+q)=40n)। (40n=520) से (n=13)। / (a_{7n}-a_{3n}=(70n+q)-(30n+q)=40n). From (40n=520), (n=13).

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Question 100/150 Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में \(a_{12}=40\) और \(a_{36}=-224\) है। \(a_{60}\) क्या होगा?

In an AP, \(a_{12}=40\) and \(a_{36}=-224\). What is \(a_{60}\)?

Explanation opens after your attempt
Correct Answer

B. (-488)

Explanation

Simple Explanation

\(d=\frac{-224-40}{36-12}=-11\)। (a_{60}=-224+24(-11)=-488)। / \(d=\frac{-224-40}{36-12}=-11\). (a_{60}=-224+24(-11)=-488).

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Question 101/150 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 102/150 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 103/150 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 104/150 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 105/150 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 106/150 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 107/150 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 108/150 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 109/150 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 110/150 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 111/150 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 112/150 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 113/150 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 114/150 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 115/150 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 116/150 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 117/150 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 118/150 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 119/150 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 120/150 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 121/150 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 122/150 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 123/150 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 124/150 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 125/150 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 126/150 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 127/150 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 128/150 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 129/150 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?

Explanation opens after your attempt
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 130/150 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?

Explanation opens after your attempt
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 131/150 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 132/150 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 133/150 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 \(a_{39}\)?

Explanation opens after your attempt
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 134/150 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 135/150 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 136/150 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 137/150 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?

Explanation opens after your attempt
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 138/150 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)?

Explanation opens after your attempt
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 139/150 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?

Explanation opens after your attempt
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 140/150 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 141/150 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 142/150 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)?

Explanation opens after your attempt
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 143/150 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 \(a_{92}\)?

Explanation opens after your attempt
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 144/150 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 145/150 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)?

Explanation opens after your attempt
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 146/150 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 147/150 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 148/150 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 149/150 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 150/150 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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