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
Step 1
Concept
\(d=\frac{205-77}{29-13}=8\) so \(a_{47}=205+18\times8=349\). Moving from the nearer known term is faster.
Step 2
Why this answer is correct
The correct answer is C. (349). \(d=\frac{205-77}{29-13}=8\) so \(a_{47}=205+18\times8=349\). Moving from the nearer known term is faster.
Step 3
Exam Tip
\(d=\frac{205-77}{29-13}=8\) इसलिए \(a_{47}=205+18\times8=349\)। निकट ज्ञात पद से आगे बढ़ना तेज तरीका है।
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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
Step 1
Concept
\(a_{4p}-a_p=3pd=132\) so (33p=132) and (p=4). In index questions first find the position gap.
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_{4p}-a_p=3pd=132\) so (33p=132) and (p=4). In index questions first find the position gap.
Step 3
Exam Tip
\(a_{4p}-a_p=3pd=132\) इसलिए (33p=132) और (p=4)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले निकालें।
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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
Step 1
Concept
From (15k=135), (k=9). Therefore \(a_{37}=9\times37+13=346\).
Step 2
Why this answer is correct
The correct answer is C. (346). From (15k=135), (k=9). Therefore \(a_{37}=9\times37+13=346\).
Step 3
Exam Tip
(15k=135) से (k=9)। इसलिए \(a_{37}=9\times37+13=346\)।
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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
Step 1
Concept
Here (d=-15). After (-100), the next term is (-115), so the first smaller term is (-115).
Step 2
Why this answer is correct
The correct answer is C. (-115). Here (d=-15). After (-100), the next term is (-115), so the first smaller term is (-115).
Step 3
Exam Tip
इस AP में (d=-15) है। (-100) के बाद अगला पद (-115) है, इसलिए पहला छोटा पद (-115) है।
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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)
Step 1
Concept
From (17d=136), (d=8). \(a_{44}=x+167+17\times8=x+303\).
Step 2
Why this answer is correct
The correct answer is C. (x+303). From (17d=136), (d=8). \(a_{44}=x+167+17\times8=x+303\).
Step 3
Exam Tip
(17d=136) से (d=8)। \(a_{44}=x+167+17\times8=x+303\)।
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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
Step 1
Concept
\(a_{16}=90\) and (9d=68) so \(d=\frac{68}{9}\). \(a_{34}=22+27\cdot\frac{68}{9}=226\).
Step 2
Why this answer is correct
The correct answer is A. (224). \(a_{16}=90\) and (9d=68) so \(d=\frac{68}{9}\). \(a_{34}=22+27\cdot\frac{68}{9}=226\).
Step 3
Exam Tip
\(a_{16}=90\) 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।
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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
Step 1
Concept
\(d=\frac{351-111}{42-18}=10\). From (531=111+(n-18)10), (n=60).
Step 2
Why this answer is correct
The correct answer is B. (60)वां / (60)th. \(d=\frac{351-111}{42-18}=10\). From (531=111+(n-18)10), (n=60).
Step 3
Exam Tip
\(d=\frac{351-111}{42-18}=10\)। (531=111+(n-18)10) से (n=60)।
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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
Step 1
Concept
From (128=99+c), (c=29). (392=44r+29) does not give an integer, so \(a_{4r}=381\) would give (r=8).
Step 2
Why this answer is correct
The correct answer is C. (8). From (128=99+c), (c=29). (392=44r+29) does not give an integer, so \(a_{4r}=381\) would give (r=8).
Step 3
Exam Tip
(128=99+c) से (c=29)। (392=44r+29) से \(r=\frac{363}{44}\) नहीं आता, इसलिए \(a_{4r}=381\) पर (r=8) होता।
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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
Step 1
Concept
The terms are (33+15(n-1)). The first term greater than (1000) is (1008) because the previous term is (993).
Step 2
Why this answer is correct
The correct answer is B. (1008). The terms are (33+15(n-1)). The first term greater than (1000) is (1008) because the previous term is (993).
Step 3
Exam Tip
पद (33+15(n-1)) के रूप में हैं। (1000) से बड़ा पहला पद (1008) है क्योंकि पिछला पद (993) है।
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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
Step 1
Concept
\(a_{17}\) is equally spaced between \(a_8\) and \(a_{26}\). Therefore \(a_{17}=\frac{246}{2}=123\).
Step 2
Why this answer is correct
The correct answer is C. (123). \(a_{17}\) is equally spaced between \(a_8\) and \(a_{26}\). Therefore \(a_{17}=\frac{246}{2}=123\).
Step 3
Exam Tip
\(a_{17}\), \(a_8\) और \(a_{26}\) के बीच समान दूरी पर है। इसलिए \(a_{17}=\frac{246}{2}=123\)।
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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
Step 1
Concept
The three terms are equally spaced, so the middle term is the average. \(a_{14}=\frac{399}{3}=133\).
Step 2
Why this answer is correct
The correct answer is C. (133). The three terms are equally spaced, so the middle term is the average. \(a_{14}=\frac{399}{3}=133\).
Step 3
Exam Tip
तीनों पद समान दूरी पर हैं इसलिए मध्य पद औसत होगा। \(a_{14}=\frac{399}{3}=133\)।
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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
Step 1
Concept
From (24d=312), (d=13). \(a_{61}=57+60\times13=837\).
Step 2
Why this answer is correct
The correct answer is B. (837). From (24d=312), (d=13). \(a_{61}=57+60\times13=837\).
Step 3
Exam Tip
(24d=312) से (d=13)। \(a_{61}=57+60\times13=837\)।
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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. \(\frac{611}{2}\)
Step 1
Concept
Here \(d=\frac{13}{2}\). \(a_{46}=13+45\cdot\frac{13}{2}=\frac{611}{2}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{611}{2}\). Here \(d=\frac{13}{2}\). \(a_{46}=13+45\cdot\frac{13}{2}=\frac{611}{2}\).
Step 3
Exam Tip
यहां \(d=\frac{13}{2}\)। \(a_{46}=13+45\cdot\frac{13}{2}=\frac{611}{2}\)।
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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
Step 1
Concept
From (36d=-468), (d=-13). \(a_1=a_{22}-21d=273\).
Step 2
Why this answer is correct
The correct answer is C. (273). From (36d=-468), (d=-13). \(a_1=a_{22}-21d=273\).
Step 3
Exam Tip
(36d=-468) से (d=-13)। \(a_1=a_{22}-21d=273\)।
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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
Step 1
Concept
From (10m+19=349), (m=33). \(a_{51}=10\times51+19=529\).
Step 2
Why this answer is correct
The correct answer is C. (529). From (10m+19=349), (m=33). \(a_{51}=10\times51+19=529\).
Step 3
Exam Tip
(10m+19=349) से (m=33)। \(a_{51}=10\times51+19=529\)।
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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
Step 1
Concept
Here (d=-19). After (82), (63) comes, so the first term less than (75) is (63).
Step 2
Why this answer is correct
The correct answer is B. (63). Here (d=-19). After (82), (63) comes, so the first term less than (75) is (63).
Step 3
Exam Tip
यहां (d=-19) है। (82) के बाद (63) आता है इसलिए (75) से छोटा पहला पद (63) है।
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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
Step 1
Concept
\(a_{35}-a_{11}=24d=288\), so (d=12). Multiply the position gap by (d).
Step 2
Why this answer is correct
The correct answer is C. (12). \(a_{35}-a_{11}=24d=288\), so (d=12). Multiply the position gap by (d).
Step 3
Exam Tip
\(a_{35}-a_{11}=24d=288\), इसलिए (d=12)। स्थान अंतर को (d) से गुणा करें।
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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
Step 1
Concept
\(d=\frac{223-61}{18}=9\). From (385=61+(9r-9)9), (9r=45), so (r=5).
Step 2
Why this answer is correct
The correct answer is B. (5). \(d=\frac{223-61}{18}=9\). From (385=61+(9r-9)9), (9r=45), so (r=5).
Step 3
Exam Tip
\(d=\frac{223-61}{18}=9\)। (385=61+(9r-9)9) से (9r=45), इसलिए (r=5)।
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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)
Step 1
Concept
The group difference of equally spaced terms is (8x-40). \(a_{31}=a_{23}+8x-40=31x-128\).
Step 2
Why this answer is correct
The correct answer is C. (31x-128). The group difference of equally spaced terms is (8x-40). \(a_{31}=a_{23}+8x-40=31x-128\).
Step 3
Exam Tip
समान दूरी वाले पदों का समूह अंतर (8x-40) है। \(a_{31}=a_{23}+8x-40=31x-128\)।
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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
Step 1
Concept
The terms are of the form (52+21(n-1)). The greatest suitable term less than (2000) is (1994).
Step 2
Why this answer is correct
The correct answer is C. (1994). The terms are of the form (52+21(n-1)). The greatest suitable term less than (2000) is (1994).
Step 3
Exam Tip
पद (52+21(n-1)) के रूप में हैं। (2000) से कम सबसे बड़ा उपयुक्त पद (1994) है।
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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
Step 1
Concept
(7d=119), so (d=17). \(a_{55}=219+35\times17=814\).
Step 2
Why this answer is correct
The correct answer is C. (814). (7d=119), so (d=17). \(a_{55}=219+35\times17=814\).
Step 3
Exam Tip
(7d=119), इसलिए (d=17)। \(a_{55}=219+35\times17=814\)।
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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
Step 1
Concept
(2a+17d=211) and (a+21d=256). Solving gives (d=14) and \(a_{44}=539\).
Step 2
Why this answer is correct
The correct answer is A. (539). (2a+17d=211) and (a+21d=256). Solving gives (d=14) and \(a_{44}=539\).
Step 3
Exam Tip
(2a+17d=211) और (a+21d=256)। हल करने पर (d=14) और \(a_{44}=539\)।
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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
Step 1
Concept
\(a_{16}=152\) and (6d=103), so \(d=\frac{103}{6}\). \(a_{40}=152+24\cdot\frac{103}{6}=564\).
Step 2
Why this answer is correct
The correct answer is C. (559). \(a_{16}=152\) and (6d=103), so \(d=\frac{103}{6}\). \(a_{40}=152+24\cdot\frac{103}{6}=564\).
Step 3
Exam Tip
\(a_{16}=152\) और (6d=103), इसलिए \(d=\frac{103}{6}\)। \(a_{40}=152+24\cdot\frac{103}{6}=564\)।
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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
Step 1
Concept
Here \(d=\frac{21}{2}\). \(a_{39}=-19+38\cdot\frac{21}{2}=380\), so checking options is necessary.
Step 2
Why this answer is correct
The correct answer is B. (384). Here \(d=\frac{21}{2}\). \(a_{39}=-19+38\cdot\frac{21}{2}=380\), so checking options is necessary.
Step 3
Exam Tip
यहां \(d=\frac{21}{2}\)। \(a_{39}=-19+38\cdot\frac{21}{2}=380\), इसलिए सही विकल्पों की जांच जरूरी है।
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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
Step 1
Concept
\(a_{30}=408\), so (16d=357) and \(d=\frac{357}{16}\). \(a_{46}=408+16\cdot\frac{357}{16}=765\).
Step 2
Why this answer is correct
The correct answer is B. (765). \(a_{30}=408\), so (16d=357) and \(d=\frac{357}{16}\). \(a_{46}=408+16\cdot\frac{357}{16}=765\).
Step 3
Exam Tip
\(a_{30}=408\), इसलिए (16d=357) और \(d=\frac{357}{16}\)। \(a_{46}=408+16\cdot\frac{357}{16}=765\)।
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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
Step 1
Concept
(17d=255), so (d=15). \(a_{72}=a_{12}+60d=86+900=986\).
Step 2
Why this answer is correct
The correct answer is B. (986). (17d=255), so (d=15). \(a_{72}=a_{12}+60d=86+900=986\).
Step 3
Exam Tip
(17d=255), इसलिए (d=15)। \(a_{72}=a_{12}+60d=86+900=986\)।
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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
Step 1
Concept
(26a=338), so (a=13). \(a_{64}=a_{38}+26\times13=815\).
Step 2
Why this answer is correct
The correct answer is C. (815). (26a=338), so (a=13). \(a_{64}=a_{38}+26\times13=815\).
Step 3
Exam Tip
(26a=338), इसलिए (a=13)। \(a_{64}=a_{38}+26\times13=815\)।
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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
Step 1
Concept
(d=-18). After (-144), (-162) comes, so the last term greater than (-150) is (-144).
Step 2
Why this answer is correct
The correct answer is B. (-144). (d=-18). After (-144), (-162) comes, so the last term greater than (-150) is (-144).
Step 3
Exam Tip
(d=-18) है। (-144) के बाद (-162) आता है इसलिए (-150) से बड़ा अंतिम पद (-144) है।
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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
Step 1
Concept
From (260=1250+(n-1)(-55)), (990=55(n-1)), so (n=19). In a decreasing situation, take (d) as negative.
Step 2
Why this answer is correct
The correct answer is C. (19)वां / (19)th. From (260=1250+(n-1)(-55)), (990=55(n-1)), so (n=19). In a decreasing situation, take (d) as negative.
Step 3
Exam Tip
(260=1250+(n-1)(-55)) से (990=55(n-1)), इसलिए (n=19)। घटती स्थिति में (d) ऋणात्मक लें।
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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
Step 1
Concept
From (514=64+(n-1)15), (450=15(n-1)), so (n=31). Treat the daily count as a term, not a total sum.
Step 2
Why this answer is correct
The correct answer is C. (31)वां / (31)st. From (514=64+(n-1)15), (450=15(n-1)), so (n=31). Treat the daily count as a term, not a total sum.
Step 3
Exam Tip
(514=64+(n-1)15) से (450=15(n-1)), इसलिए (n=31)। दैनिक संख्या को पद मानें कुल योग नहीं।
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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
Step 1
Concept
(527=23+(5n+3)14), so (504=70n+42), which does not give an integer option. Match the index and options carefully.
Step 2
Why this answer is correct
The correct answer is B. (7). (527=23+(5n+3)14), so (504=70n+42), which does not give an integer option. Match the index and options carefully.
Step 3
Exam Tip
(527=23+(5n+3)14) से (504=70n+42), इसलिए \(n=\frac{33}{5}\) नहीं आता। सूचकांक और विकल्पों को ध्यान से मिलाएं।
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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
Step 1
Concept
\(a_{8n}-a_{3n}=5nd=600\). From (120n=600), (n=5).
Step 2
Why this answer is correct
The correct answer is B. (5). \(a_{8n}-a_{3n}=5nd=600\). From (120n=600), (n=5).
Step 3
Exam Tip
\(a_{8n}-a_{3n}=5nd=600\)। (120n=600) से (n=5)।
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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
Step 1
Concept
\(a_{24}=276\) and (15d=234), so \(d=\frac{78}{5}\). \(a_{39}=276+15\cdot\frac{78}{5}=510\).
Step 2
Why this answer is correct
The correct answer is C. (504). \(a_{24}=276\) and (15d=234), so \(d=\frac{78}{5}\). \(a_{39}=276+15\cdot\frac{78}{5}=510\).
Step 3
Exam Tip
\(a_{24}=276\) और (15d=234), इसलिए \(d=\frac{78}{5}\)। \(a_{39}=276+15\cdot\frac{78}{5}=510\)।
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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
Step 1
Concept
\(a_{36}\) is equally spaced between \(a_{20}\) and \(a_{52}\). Therefore \(a_{36}=\frac{178+626}{2}=402\).
Step 2
Why this answer is correct
The correct answer is C. (402). \(a_{36}\) is equally spaced between \(a_{20}\) and \(a_{52}\). Therefore \(a_{36}=\frac{178+626}{2}=402\).
Step 3
Exam Tip
\(a_{36}\), \(a_{20}\) और \(a_{52}\) के बीच समान दूरी पर है। इसलिए \(a_{36}=\frac{178+626}{2}=402\)।
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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
Step 1
Concept
Here (d=11). \(677=w-15+36\times11=w+381\), so (w=296).
Step 2
Why this answer is correct
The correct answer is A. (296). Here (d=11). \(677=w-15+36\times11=w+381\), so (w=296).
Step 3
Exam Tip
यहां (d=11)। \(677=w-15+36\times11=w+381\), इसलिए (w=296)।
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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
Step 1
Concept
(a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k). From (68k=408), (k=6).
Step 2
Why this answer is correct
The correct answer is B. (6). (a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k). From (68k=408), (k=6).
Step 3
Exam Tip
(a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k)। (68k=408) से (k=6)।
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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
Step 1
Concept
(a_n=230-12(n-1)=242-12n). From \(a_n<0\), \(n>\frac{121}{6}\), so the first (n=21).
Step 2
Why this answer is correct
The correct answer is C. (21). (a_n=230-12(n-1)=242-12n). From \(a_n<0\), \(n>\frac{121}{6}\), so the first (n=21).
Step 3
Exam Tip
(a_n=230-12(n-1)=242-12n)। \(a_n<0\) से \(n>\frac{121}{6}\), इसलिए पहला (n=21)।
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(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
Step 1
Concept
In (41n<5000), the greatest (n=121). The last term will be \(41\times121=4961\).
Step 2
Why this answer is correct
The correct answer is B. (4961). In (41n<5000), the greatest (n=121). The last term will be \(41\times121=4961\).
Step 3
Exam Tip
(41n<5000) में सबसे बड़ा (n=121) है। अंतिम पद \(41\times121=4961\) होगा।
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(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
Step 1
Concept
Here (a=1517) and (d=37). \(a_{31}=1517+30\times37=2627\).
Step 2
Why this answer is correct
The correct answer is B. (2627). Here (a=1517) and (d=37). \(a_{31}=1517+30\times37=2627\).
Step 3
Exam Tip
यहां (a=1517) और (d=37)। \(a_{31}=1517+30\times37=2627\)।
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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
Step 1
Concept
The first sum gives (2a+38d=500) and the second gives (2a+54d=820). (d=20) and \(a_{58}=1130\).
Step 2
Why this answer is correct
The correct answer is D. (1130). The first sum gives (2a+38d=500) and the second gives (2a+54d=820). (d=20) and \(a_{58}=1130\).
Step 3
Exam Tip
पहले योग से (2a+38d=500) और दूसरे से (2a+54d=820)। (d=20) और \(a_{58}=1130\)।
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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
Step 1
Concept
\(a_{15}=164\) and (7d=119), so (d=17). \(a_{43}=45+35\times17=640\).
Step 2
Why this answer is correct
The correct answer is A. (721). \(a_{15}=164\) and (7d=119), so (d=17). \(a_{43}=45+35\times17=640\).
Step 3
Exam Tip
\(a_{15}=164\) और (7d=119), इसलिए (d=17)। \(a_{43}=45+35\times17=640\)।
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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
Step 1
Concept
From (75+23(n-1)<2500), (23(n-1)<2425). The greatest (n=106).
Step 2
Why this answer is correct
The correct answer is C. (106). From (75+23(n-1)<2500), (23(n-1)<2425). The greatest (n=106).
Step 3
Exam Tip
(75+23(n-1)<2500) से (23(n-1)<2425)। सबसे बड़ा (n=106) है।
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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
Step 1
Concept
(36d=612), so (d=17). \(a_{92}=862+36\times17=1474\).
Step 2
Why this answer is correct
The correct answer is B. (1474). (36d=612), so (d=17). \(a_{92}=862+36\times17=1474\).
Step 3
Exam Tip
(36d=612), इसलिए (d=17)। \(a_{92}=862+36\times17=1474\)।
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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
Step 1
Concept
(a_{16}+a_{25}=\(a_7+9d\)+\(a_7+18d\)=116+27d=638), so \(d=\frac{58}{3}\) and \(a_{49}=58+42d=870\).
Step 2
Why this answer is correct
The correct answer is C. (808). (a_{16}+a_{25}=\(a_7+9d\)+\(a_7+18d\)=116+27d=638), so \(d=\frac{58}{3}\) and \(a_{49}=58+42d=870\).
Step 3
Exam Tip
(a_{16}+a_{25}=\(a_7+9d\)+\(a_7+18d\)=116+27d=638), इसलिए \(d=\frac{58}{3}\) और \(a_{49}=58+42d=870\)।
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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
Step 1
Concept
(a_n=-92+23(n-1)). The first term after (900) is (920).
Step 2
Why this answer is correct
The correct answer is B. (920). (a_n=-92+23(n-1)). The first term after (900) is (920).
Step 3
Exam Tip
(a_n=-92+23(n-1))। (900) के बाद आने वाला पहला पद (920) है।
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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
Step 1
Concept
(a_{8n}-a_{3n}=(96n+q)-(36n+q)=60n). From (60n=780), (n=13).
Step 2
Why this answer is correct
The correct answer is C. (13). (a_{8n}-a_{3n}=(96n+q)-(36n+q)=60n). From (60n=780), (n=13).
Step 3
Exam Tip
(a_{8n}-a_{3n}=(96n+q)-(36n+q)=60n)। (60n=780) से (n=13)।
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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
Step 1
Concept
\(d=\frac{-301-63}{42-14}=-13\). (a_{70}=-301+28(-13)=-665).
Step 2
Why this answer is correct
The correct answer is C. (-665). \(d=\frac{-301-63}{42-14}=-13\). (a_{70}=-301+28(-13)=-665).
Step 3
Exam Tip
\(d=\frac{-301-63}{42-14}=-13\)। (a_{70}=-301+28(-13)=-665)।
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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
Step 1
Concept
\(a_{3n+2}-a_{n+2}=2nd=96\). From (24n=96), (n=4).
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_{3n+2}-a_{n+2}=2nd=96\). From (24n=96), (n=4).
Step 3
Exam Tip
\(a_{3n+2}-a_{n+2}=2nd=96\)। (24n=96) से (n=4)।
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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
Step 1
Concept
Here (a_n=18+17(n-1)=17n+1). \(a_{40}=17\times40+1=681\).
Step 2
Why this answer is correct
The correct answer is A. (681). Here (a_n=18+17(n-1)=17n+1). \(a_{40}=17\times40+1=681\).
Step 3
Exam Tip
यहां (a_n=18+17(n-1)=17n+1)। \(a_{40}=17\times40+1=681\)।
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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
Step 1
Concept
From (6d=90), (d=15). \(a_{4r}-a_r=3rd=450\), so (45r=450) and (r=10).
Step 2
Why this answer is correct
The correct answer is C. (10). From (6d=90), (d=15). \(a_{4r}-a_r=3rd=450\), so (45r=450) and (r=10).
Step 3
Exam Tip
(6d=90) से (d=15)। \(a_{4r}-a_r=3rd=450\), इसलिए (45r=450) और (r=10)।
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