100 results found for "ap-term-number-expert" in Class 10.
C. (x+82)
From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).
The correct answer is C. (x+82). From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).
(7d=35) से (d=5)। \(a_{20}=a_{12}+8d=x+42+40=x+82\)।
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If the (5)th term of an AP is (27) and the (14)th term is (90), what is the (20)th term?
C. (132)
\(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.
The correct answer is C. (132). \(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.
\(d=\frac{90-27}{14-5}=7\) और \(a_{20}=90+6\times7=132\)। पहले (d) निकालें फिर आगे बढ़ें।
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If the (4)th term of an AP is (15) and the (12)th term is (55), what is the (16)th term?
C. (75)
\(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
The correct answer is C. (75). \(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
\(d=\frac{55-15}{12-4}=5\) और \(a_{16}=55+4\times5=75\)। पहले (d) फिर वांछित पद निकालें।
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If the (3)rd term of an AP is (8) and the (8)th term is (3), what is the (11)th term?
A. (0)
\(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.
The correct answer is A. (0). \(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.
\(d=\frac{3-8}{8-3}=-1\), इसलिए (a_{11}=3+3(-1)=0)। ज्ञात पास वाले पद से आगे बढ़ना सरल है।
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If the (p)th term of an AP is (q) and the (q)th term is (p), what is its ((p+q))th term?
A. (0)
Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).
The correct answer is A. (0). Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).
संबंधों को घटाने पर (d=-1) और आगे रखने पर \(a_{p+q}=0\) मिलता है। प्रतीकात्मक AP में भी (a_n=a+(n-1)d) ही लगाएं।
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If the (5)th term of an AP is (16) and the (9)th term is (32), what is the (13)th term?
C. (48)
\(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.
The correct answer is C. (48). \(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.
\(d=\frac{32-16}{9-5}=4\), इसलिए \(a_{13}=32+4\times4=48\)। समान स्थान अंतर होने पर पदों का अंतर भी समान होता है।
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C. (x+181)
(12d=72), so (d=6). \(a_{35}=x+91+15\times6=x+181\).
The correct answer is C. (x+181). (12d=72), so (d=6). \(a_{35}=x+91+15\times6=x+181\).
(12d=72), इसलिए (d=6)। \(a_{35}=x+91+15\times6=x+181\)।
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C. नहीं, क्योंकि नए अंतर समान नहीं हैंNo, because new differences are not equal
The new terms are \(1,8,21,\ldots\), and the differences are \(7,13,\ldots\), which are not equal. Multiplying by term number does not keep (d) constant.
The correct answer is C. नहीं, क्योंकि नए अंतर समान नहीं हैं / No, because new differences are not equal. The new terms are \(1,8,21,\ldots\), and the differences are \(7,13,\ldots\), which are not equal. Multiplying by term number does not keep (d) constant.
नए पद \(1,8,21,\ldots\) हैं और अंतर \(7,13,\ldots\) हैं, जो समान नहीं हैं। पद संख्या से गुणा करना (d) को स्थिर नहीं रखता।
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C. नहीं, क्योंकि नए अंतर समान नहीं होंगेNo, because new differences will not be equal
The added squares \(1,4,9,\ldots\) have differences \(3,5,\ldots\), which are not equal, so the new sequence will not remain arithmetic. Squares of term numbers do not create equal differences.
The correct answer is C. नहीं, क्योंकि नए अंतर समान नहीं होंगे / No, because new differences will not be equal. The added squares \(1,4,9,\ldots\) have differences \(3,5,\ldots\), which are not equal, so the new sequence will not remain arithmetic. Squares of term numbers do not create equal differences.
नए जोड़े गए वर्ग \(1,4,9,\ldots\) के अंतर \(3,5,\ldots\) समान नहीं हैं, इसलिए नया अनुक्रम अंकगणितीय नहीं रहेगा। पद संख्या के वर्ग से समान अंतर नहीं बनता।
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A. (-1)
The original (d=3), and (4n) has (d=4), so the new (d=3-4=-1). In term-number based changes, change the differences too.
The correct answer is A. (-1). The original (d=3), and (4n) has (d=4), so the new (d=3-4=-1). In term-number based changes, change the differences too.
मूल (d=3) है और (4n) का (d=4) है, इसलिए नया (d=3-4=-1)। पद संख्या आधारित बदलाव में अंतरों को भी बदलें।
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B. (5)
The original (d=6), and (n) has difference (1), so the new (d=6-1=5). When subtracting term number, its difference is also subtracted.
The correct answer is B. (5). The original (d=6), and (n) has difference (1), so the new (d=6-1=5). When subtracting term number, its difference is also subtracted.
मूल (d=6) है और (n) का अंतर (1) है, इसलिए नया (d=6-1=5)। पद संख्या घटाने पर उसका अंतर भी घटता है।
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C. (-1)
The original (d=-3), and the difference of (2n) is (2), so the new (d=-3+2=-1). For term-number changes, add or subtract its difference.
The correct answer is C. (-1). The original (d=-3), and the difference of (2n) is (2), so the new (d=-3+2=-1). For term-number changes, add or subtract its difference.
मूल (d=-3) है और (2n) का अंतर (2) है, इसलिए नया (d=-3+2=-1)। पद संख्या वाले परिवर्तन में उसके अंतर को जोड़ें या घटाएं।
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B. (x+188)
From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).
The correct answer is B. (x+188). From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).
(11d=77) से (d=7)। \(a_{32}=a_{18}+14d=x+90+98=x+188\)।
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B. (x+137)
From (9d=54), (d=6). \(a_{27}=a_{15}+12d=x+65+72=x+137\).
The correct answer is B. (x+137). From (9d=54), (d=6). \(a_{27}=a_{15}+12d=x+65+72=x+137\).
(9d=54) से (d=6)। \(a_{27}=a_{15}+12d=x+65+72=x+137\)।
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The (12)th term of an AP is (71) and the common difference is (5). What is the first term?
D. (16)
From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).
The correct answer is D. (16). From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).
\(71=a+11\times5\) से (a=16)। ज्ञात पद से पहले पद तक जाने के लिए (11d) घटाएं।
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The (9)th term of an AP is (47) and the common difference is (4). What is the first term?
D. (15)
From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
The correct answer is D. (15). From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
\(47=a+8\times4\) से (a=15)। ज्ञात पद से पहले पद तक जाने के लिए (8d) घटाएं।
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The (6)th term of an AP is (23) and the common difference is (5). What is the first term?
D. (-2)
(23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
The correct answer is D. (-2). (23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
(23=a+5d=a+25), इसलिए (a=-2)। दिए गए पद से पीछे जाते समय (5d) घटाया जाता है।
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The general term of an AP is \(a_n=7n+2\). Find the (11)th term.
C. (79)
\(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.
The correct answer is C. (79). \(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.
\(a_{11}=7\times11+2=79\)। सामान्य पद में सही पद संख्या रखना ही मुख्य कदम है।
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B. (1485)
The condition gives (6+13d=3(6+3d)), so (d=3) and \(S_{30}=1485\). Convert the term condition into an equation first.
The correct answer is B. (1485). The condition gives (6+13d=3(6+3d)), so (d=3) and \(S_{30}=1485\). Convert the term condition into an equation first.
शर्त से (6+13d=3(6+3d)), इसलिए (d=3) और \(S_{30}=1485\) है। पदों की शर्त को पहले समीकरण में बदलें।
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If an AP has first term (11), last term (71), and sum (574), what is the number of terms?
C. (14)
From (\frac{n}{2}(11+71)=574), (n=14). When the last term is given, the common difference is not needed.
The correct answer is C. (14). From (\frac{n}{2}(11+71)=574), (n=14). When the last term is given, the common difference is not needed.
(\frac{n}{2}(11+71)=574) से (n=14) मिलता है। अंतिम पद दिए होने पर सार्व अंतर की जरूरत नहीं होती।
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C. अंकगणितीय श्रेणी नहीं क्योंकि नए अंतर समान नहीं होंगेNot an arithmetic progression because new differences will not be equal
The new terms are \(2,8,16,\ldots\), and the differences are \(6,8,\ldots\), which are not equal. Adding squares of term numbers does not preserve equal difference.
The correct answer is C. अंकगणितीय श्रेणी नहीं क्योंकि नए अंतर समान नहीं होंगे / Not an arithmetic progression because new differences will not be equal. The new terms are \(2,8,16,\ldots\), and the differences are \(6,8,\ldots\), which are not equal. Adding squares of term numbers does not preserve equal difference.
नए पद \(2,8,16,\ldots\) मिलते हैं और अंतर \(6,8,\ldots\) हैं, जो समान नहीं हैं। पद संख्या के वर्ग जोड़ने से समान अंतर नहीं बचता।
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If the term number is subtracted from each term of \(30,27,24,\ldots\), what will be the new (d)?
C. (-4)
The original (d=-3), and term numbers have (d=1), so the new (d=-3-1=-4). When subtracting term number, its difference is also subtracted.
The correct answer is C. (-4). The original (d=-3), and term numbers have (d=1), so the new (d=-3-1=-4). When subtracting term number, its difference is also subtracted.
मूल (d=-3) है और पद संख्या का (d=1) है, इसलिए नया (d=-3-1=-4)। पद संख्या घटाने पर उसका अंतर भी घटता है।
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B. (3)
The original (d=5), and (2n) has difference (2), so the new (d=5-2=3). In term-number subtraction, subtract its difference.
The correct answer is B. (3). The original (d=5), and (2n) has difference (2), so the new (d=5-2=3). In term-number subtraction, subtract its difference.
मूल (d=5) है और (2n) का अंतर (2) है, इसलिए नया (d=5-2=3)। पद संख्या आधारित घटाव में उसके अंतर को घटाएं।
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If the term number (n) is added to each term of \(5,9,13,\ldots\), what will be the new (d)?
C. (5)
The original (d=4), and (n) has difference (1), so the new (d=5). When adding term number, its difference is also added.
The correct answer is C. (5). The original (d=4), and (n) has difference (1), so the new (d=5). When adding term number, its difference is also added.
मूल (d=4) है और (n) का अंतर (1) है, इसलिए नया (d=5)। पद संख्या जोड़ने पर उसका अंतर भी जुड़ता है।
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A. (1)
The original (d=4), and (3n) has (d=3), so the new (d=1). In term-number changes, subtract its common difference.
The correct answer is A. (1). The original (d=4), and (3n) has (d=3), so the new (d=1). In term-number changes, subtract its common difference.
मूल (d=4) है और (3n) का (d=3) है, इसलिए नया (d=1)। पद संख्या से जुड़े परिवर्तन में उसके सार्व अंतर को घटाएं।
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C. (-4)
The original (d=-3), and term numbers have (d=1), so the new (d=-3-1=-4). When subtracting term number, its difference is also subtracted.
The correct answer is C. (-4). The original (d=-3), and term numbers have (d=1), so the new (d=-3-1=-4). When subtracting term number, its difference is also subtracted.
मूल (d=-3) है और पद संख्या का (d=1) है, इसलिए नया (d=-3-1=-4)। पद संख्या घटाने पर उसका अंतर भी घटता है।
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If each term of \(1, 4, 7, 10,\ldots\) is increased by its term number, what will be the new (d)?
B. (4)
The original (d=3), and term numbers \(1,2,3,\ldots\) have difference (1), so the new (d=4). In this transformation, add the two common differences.
The correct answer is B. (4). The original (d=3), and term numbers \(1,2,3,\ldots\) have difference (1), so the new (d=4). In this transformation, add the two common differences.
मूल (d=3) है और पद संख्या \(1,2,3,\ldots\) का अंतर (1) है, इसलिए नया (d=4)। ऐसे परिवर्तन में दोनों सार्व अंतरों को जोड़ें।
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A. (2)
The original (d=4), and the difference of (2n) is (2), so the new (d=4-2=2). In term-number transformations, subtract the difference of the change.
The correct answer is A. (2). The original (d=4), and the difference of (2n) is (2), so the new (d=4-2=2). In term-number transformations, subtract the difference of the change.
मूल (d=4) है और (2n) का अंतर (2) है, इसलिए नया (d=4-2=2)। पद संख्या पर आधारित परिवर्तन में अंतरों का अंतर घटाएं।
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A. (1050)
The condition gives (5+11d=4(5+2d)), so (d=5) and \(S_{20}=1050\). Convert the term condition into an equation first.
The correct answer is A. (1050). The condition gives (5+11d=4(5+2d)), so (d=5) and \(S_{20}=1050\). Convert the term condition into an equation first.
शर्त से (5+11d=4(5+2d)), इसलिए (d=5) और \(S_{20}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें।
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C. (1050)
The condition gives (6+8d=2(6+3d)), so (d=3) and \(S_{25}=1050\). Convert the term condition into an equation first.
The correct answer is C. (1050). The condition gives (6+8d=2(6+3d)), so (d=3) and \(S_{25}=1050\). Convert the term condition into an equation first.
शर्त से (6+8d=2(6+3d)), इसलिए (d=3) और \(S_{25}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें।
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C. (576)
The condition gives (4+7d=3(4+2d)), so (d=8) and \(S_{12}=576\). Convert the term condition into an equation first.
The correct answer is C. (576). The condition gives (4+7d=3(4+2d)), so (d=8) and \(S_{12}=576\). Convert the term condition into an equation first.
शर्त से (4+7d=3(4+2d)), इसलिए (d=8) और \(S_{12}=576\)। पदों की शर्त को पहले समीकरण में बदलें।
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The (n)th-term formula of the AP \(23,31,39,\ldots\) is \(a_n=8n+15\). What is the (36)th term?
C. (303)
\(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
The correct answer is C. (303). \(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
\(a_{36}=8\times36+15=303\)। बने हुए सूत्र में (n=36) रखकर सीधे उत्तर पाएं।
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If the (r)th term of an AP is (3r-2) and (d=4), what is the ((r+6))th term?
C. (3r+22)
The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.
The correct answer is C. (3r+22). The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.
((r+6))वां पद (r)वें पद से (6d) आगे है इसलिए (3r-2+24=3r+22)। प्रतीकात्मक प्रश्न में स्थान अंतर देखें।
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The (n)th-term formula of the AP \(19,26,33,\ldots\) is \(a_n=7n+12\). What is the (41)st term?
D. (299)
\(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
The correct answer is D. (299). \(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
\(a_{41}=7\times41+12=299\)। बने हुए सूत्र में केवल (n=41) रखें।
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If the (m)th term of an AP is (2m+3) and (d=2), what is the ((m+5))th term?
D. (2m+13)
The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.
The correct answer is D. (2m+13). The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.
((m+5))वां पद (m)वें पद से (5d) आगे है इसलिए (2m+3+10=2m+13)। प्रतीकात्मक पदों में भी स्थान अंतर देखें।
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The first term of an AP is (25) and the (18)th term is (93). What is the common difference?
C. (4)
From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
The correct answer is C. (4). From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
(93=25+17d) से (68=17d) इसलिए (d=4)। (18)वें पद के लिए गुणक (17) होता है।
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The (n)th term of the AP \(11,17,23,\ldots\) is \(a_n=6n+5\). What is its (32)nd term?
B. (197)
\(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
The correct answer is B. (197). \(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
\(a_{32}=6\times32+5=197\)। बनाए गए सूत्र में (n) का सही मान रखें।
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The first term of an AP is (18) and the (16)th term is (93). What is the common difference?
A. (5)
(93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
The correct answer is A. (5). (93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
(93=18+15d), इसलिए (75=15d) और (d=5)। (16)वें पद के लिए गुणक (15) होगा।
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If the (10)th term of an AP is (41) and the (20)th term is (81), what is its common difference?
C. (4)
\(The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
\(The correct answer is C. (4). The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
दो पदों का अंतर (81-41=40) है और पद संख्या का अंतर (10), इसलिए (d=4)। \(दो ज्ञात पदों में (d=\frac{\)पदों का अंतर}{स्थान का अंतर}) लगाएं।
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If the first term of an AP is (7) and the common difference is (4), what is its (18)th term?
A. (75)
Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
The correct answer is A. (75). Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
सूत्र (a_n=a+(n-1)d) लगाने पर \(7+17\times4=75\)। परीक्षा में (n-1) को भूलना नहीं चाहिए।
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If the (4)th term of an AP is (21) and (d=6), what is the (10)th term?
C. (57)
The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.
The correct answer is C. (57). The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.
(10)वाँ पद (4)थे पद से (6d) आगे है इसलिए (21+36=57)। पद संख्या का अंतर सीधे उपयोग करें।
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If the first term of an AP is (-12) and the common difference is (5), what is the (16)th term?
B. (63)
\(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.
The correct answer is B. (63). \(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.
\(a_{16}=-12+15\times5=63\)। पहले (15d) निकालें फिर प्रथम पद जोड़ें।
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If the first term of an AP is (9) and the common difference is (10), what is the (7)th term?
B. (69)
\(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.
The correct answer is B. (69). \(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.
\(a_7=9+6\times10=69\)। (7)वें पद के लिए (6d) जोड़ना होता है।
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If the (3)rd term of an AP is (14) and (d=5), what is the (7)th term?
C. (34)
The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.
The correct answer is C. (34). The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.
(7)वाँ पद (3)रे पद से (4d) आगे है इसलिए (14+20=34)। बीच के पदों की संख्या सही गिनें।
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If the first term of an AP is (-2) and the common difference is (6), what is the (12)th term?
B. (64)
\(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).
The correct answer is B. (64). \(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).
\(a_{12}=-2+11\times6=64\)। पहले गुणा करें फिर (-2) जोड़ें।
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If the (5)th term of an AP is (22) and (d=6), what is the (8)th term?
D. (40)
The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.
The correct answer is D. (40). The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.
(8)वाँ पद (5)वें पद से (3d) आगे है इसलिए (22+18=40)। पदों का अंतर गिनना आसान तरीका है।
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If the (7)th term of an AP is (31) and (d=4), what is the (10)th term?
C. (43)
The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.
The correct answer is C. (43). The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.
(10)वाँ पद (7)वें पद से (3d) आगे है इसलिए \(31+3\times4=43\)। पास के पदों के लिए अंतर विधि तेज होती है।
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If the first term of an AP is (15) and the common difference is (-4), what is the (8)th term?
A. (-13)
(a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
The correct answer is A. (-13). (a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
(a_8=15+7(-4)=-13)। ऋणात्मक (d) को कोष्ठक में लिखना उपयोगी है।
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If the first term of an AP is (5) and common difference is (3), what is the (8)th term?
C. (26)
Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
The correct answer is C. (26). Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
सूत्र (a_n=a+(n-1)d) लगाएं तो \(5+7\times3=26\)। परीक्षा में (n-1) लेना न भूलें।
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The (n)th term of an AP is \(a_n=2n+3\). What will be the (18)th term?
A. (39)
Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).
The correct answer is A. (39). Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).
(n=18) रखने पर \(a_{18}=2\times18+3=39\)। दिए गए \(a_n\) में सीधे पद संख्या रखें।
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The first term of an AP is (25) and the common difference is (4). What will be the (21)st term?
B. (105)
\(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
The correct answer is B. (105). \(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
\(a_{21}=25+20\times4=105\)। पद संख्या से (1) घटाना न भूलें।
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If the first term of an AP is (6) and the common difference is (7), what is the (11)th term?
D. (76)
\(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.
The correct answer is D. (76). \(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.
\(a_{11}=6+10\times7=76\)। (11)वें पद तक (10) बार अंतर जुड़ता है।
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In an AP, first term (a=4) and common difference (d=3). What is the (10)th term?
A. (31)
Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.
The correct answer is A. (31). Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.
सूत्र (a_n=a+(n-1)d) लगाने पर \(a_{10}=4+9\times3=31\)। परीक्षा में (n-1) को ध्यान से लिखें।
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The (n)th term of the AP \(73,68,63,\ldots\) is (-12). What is (n)?
C. (18)
From (-12=73+(n-1)(-5)), (85=5(n-1)) so (n=18). In a decreasing AP keep signs correct up to the negative target.
The correct answer is C. (18). From (-12=73+(n-1)(-5)), (85=5(n-1)) so (n=18). In a decreasing AP keep signs correct up to the negative target.
(-12=73+(n-1)(-5)) से (85=5(n-1)) इसलिए (n=18)। घटती AP में ऋणात्मक लक्ष्य तक चिन्ह सही रखें।
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In an AP (a=63) and (d=-4). Which term will be (-1)?
C. (17)वां(17)th
From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.
The correct answer is C. (17)वां / (17)th. From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.
(-1=63+(n-1)(-4)) से (64=4(n-1)) इसलिए (n=17)। ऋणात्मक लक्ष्य पद में चिन्हों को ध्यान से संभालें।
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Which term of the AP \(26,35,44,\ldots\) is (206)?
C. (21)वां(21)st
From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).
The correct answer is C. (21)वां / (21)st. From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).
(206=26+(n-1)9) से (180=9(n-1)) इसलिए (n=21)। पद और पहले पद का अंतर (d) से भाग दें।
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The (n)th term of the AP \(55,51,47,\ldots\) is (-17). What is (n)?
C. (19)
From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
The correct answer is C. (19). From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
(-17=55+(n-1)(-4)) से (72=4(n-1)) इसलिए (n=19)। ऋणात्मक पद तक जाते समय चिन्ह सही रखें।
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In an AP, (a=48) and (d=-3). Which term will be (0)?
C. (17)वां(17)th
From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.
The correct answer is C. (17)वां / (17)th. From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.
(0=48+(n-1)(-3)) से (3(n-1)=48) इसलिए (n=17)। शून्य पद के लिए भी सामान्य सूत्र लगाएं।
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Which term of the AP \(14,23,32,\ldots\) is (185)?
C. (20)वां(20)th
From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
The correct answer is C. (20)वां / (20)th. From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
(185=14+(n-1)9) से (171=9(n-1)) और (n=20)। अंतर को (d) से भाग देकर पद संख्या पाएं।
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The (n)th term of the AP \(27,24,21,\ldots\) is (-30). What is (n)?
C. (20)
From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
The correct answer is C. (20). From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
(-30=27+(n-1)(-3)) से (57=3(n-1)), इसलिए (n=20)। ऋणात्मक लक्ष्य पद में चिन्ह सावधानी से बदलें।
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Which term of the AP \(15,21,27,\ldots\) is (111)?
C. (17)वां(17)th
(111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).
The correct answer is C. (17)वां / (17)th. (111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).
(111=15+(n-1)6), इसलिए (96=6(n-1)) और (n=17)। पद संख्या में अंतर को (d) से भाग दें।
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In an AP \(a_{18}=111\) and \(a_{42}=351\). Which term will be (531)?
B. (60)वां(60)th
\(d=\frac{351-111}{42-18}=10\). From (531=111+(n-18)10), (n=60).
The correct answer is B. (60)वां / (60)th. \(d=\frac{351-111}{42-18}=10\). From (531=111+(n-18)10), (n=60).
\(d=\frac{351-111}{42-18}=10\)। (531=111+(n-18)10) से (n=60)।
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In an AP, \(a_{15}=88\) and \(a_{35}=248\). Which term will be (408)?
C. (55)वां(55)th
\(d=\frac{248-88}{35-15}=8\). From (408=88+(n-15)8), (n=55).
The correct answer is C. (55)वां / (55)th. \(d=\frac{248-88}{35-15}=8\). From (408=88+(n-15)8), (n=55).
\(d=\frac{248-88}{35-15}=8\)। (408=88+(n-15)8) से (n=55)।
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In an AP, \(a_{12}=70\) and \(a_{28}=198\). Which term will be (326)?
C. (44)वां(44)th
\(d=\frac{198-70}{28-12}=8\). From (326=70+(n-12)8), (n=44).
The correct answer is C. (44)वां / (44)th. \(d=\frac{198-70}{28-12}=8\). From (326=70+(n-12)8), (n=44).
\(d=\frac{198-70}{28-12}=8\)। (326=70+(n-12)8) से (n=44)।
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An AP has first term (8), last term (62), and number of terms (10). Find the sum of all terms.
A. (350)
Using (S_n=\frac{n}{2}(a+l)), the sum is (350). When the last term is given, this formula is faster.
The correct answer is A. (350). Using (S_n=\frac{n}{2}(a+l)), the sum is (350). When the last term is given, this formula is faster.
सूत्र (S_n=\frac{n}{2}(a+l)) से योग (350) आता है। जब अंतिम पद दिया हो तो यह सूत्र जल्दी काम करता है।
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How can divide and rule policy be linked with both short term control and long term crisis?
A. इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता थाIt could weaken immediate resistance but leave social distrust
This policy used division for control. For exams also write its legacy.
The correct answer is A. इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता था / It could weaken immediate resistance but leave social distrust. This policy used division for control. For exams also write its legacy.
यह नीति नियंत्रण के लिए विभाजन का उपयोग करती थी। परीक्षा में इसकी विरासत भी लिखें।
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C. (3000)
\(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.
The correct answer is C. (3000). \(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.
\(a_{21}+a_{40}=a_1+a_{60}=300\), इसलिए (20) पदों का योग (3000) है। सममित पदों का योग बराबर होता है।
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B. (2100)
\(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.
The correct answer is B. (2100). \(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.
\(a_{11}+a_{30}=a_1+a_{40}=210\), इसलिए (20) पदों का योग (2100) है। सममित पदों का योग बराबर होता है।
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B. (14)
From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.
The correct answer is B. (14). From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.
(740=10(a+60)) से (a=14) मिलता है। जब (n)वाँ पद दिया हो तो उसे अंतिम पद की तरह इस्तेमाल करें।
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What is the last term among the positive multiples of (13) less than (600)?
B. (598)
In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.
The correct answer is B. (598). In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.
(13n<600) में सबसे बड़ा (n=46) है इसलिए पद \(13\times46=598\)। सीमा से कम सबसे बड़ा पूर्णांक लें।
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If the (19)th term of the AP \(z,z+5,z+10,\ldots\) is (112), what is (z)?
C. (22)
From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.
The correct answer is C. (22). From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.
\(112=z+18\times5\) से (z=22)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।
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In the AP \(7,12,17,\ldots\), what is the last term less than (180)?
C. (177)
The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
The correct answer is C. (177). The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
पद (7+5(n-1)) हैं। (180) से कम अंतिम पद (177) है क्योंकि अगला पद (182) होगा।
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Which is the first negative term of the AP \(105,98,91,\ldots\)?
C. (17)वां(17)th
(a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.
The correct answer is C. (17)वां / (17)th. (a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.
(a_n=105+(n-1)(-7)=112-7n)। \(a_n<0\) से (n>16) इसलिए पहला ऋणात्मक पद (17)वां है।
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The (14)th term of an AP is (92) and (d=7). What is \(a_1\)?
A. (1)
From \(92=a+13\times7\), (a=1). From the (14)th term to the first term (13d) is subtracted.
The correct answer is A. (1). From \(92=a+13\times7\), (a=1). From the (14)th term to the first term (13d) is subtracted.
\(92=a+13\times7\) से (a=1)। (14)वें पद से पहले पद तक (13d) घटता है।
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Which term of the AP \(9,17,25,\ldots\) is (201)?
C. (25)वां(25)th
From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.
The correct answer is C. (25)वां / (25)th. From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.
(201=9+(n-1)8) से (192=8(n-1)) और (n=25)। पद संख्या पूर्णांक आए तो उत्तर सही दिशा में है।
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What is the last term among the positive multiples of (11) less than (500)?
B. (495)
In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
The correct answer is B. (495). In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
(11n<500) में सबसे बड़ा (n=45) है इसलिए पद \(11\times45=495\)। सीमा से कम सबसे बड़ा पूर्णांक लें।
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If the (12)th term of the AP \(y,y+6,y+12,\ldots\) is (89), what is the value of (y)?
D. (23)
From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
The correct answer is D. (23). From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
\(89=y+11\times6\) से (y=23)। चर वाले पहले पद को सीधे (a) मानें।
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In the AP \(2,6,10,\ldots\), what is the last term less than (75)?
A. (74)
The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
The correct answer is A. (74). The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
इस श्रेणी के पद (2+4(n-1)) हैं। (75) से कम अंतिम पद (74) है।
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Which is the first negative term of the AP \(72,66,60,\ldots\)?
B. (14)वां(14)th
(a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
The correct answer is B. (14)वां / (14)th. (a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
(a_n=72+(n-1)(-6)=78-6n)। \(a_n<0\) से (n>13) इसलिए पहला ऋणात्मक पद (14)वां है।
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The (10)th term of an AP is (62) and (d=5). What is \(a_1\)?
D. (17)
From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).
The correct answer is D. (17). From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).
\(62=a+9\times5\) से (a=17)। (10)वें पद से पहले पद तक (9d) घटता है।
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Which term of the AP \(21,29,37,\ldots\) is (149)?
C. (17)वां(17)th
From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
The correct answer is C. (17)वां / (17)th. From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
(149=21+(n-1)8) से (128=8(n-1)) इसलिए (n=17)। पद संख्या पूछी हो तो दिए पद को \(a_n\) मानें।
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If the (10)th term of the AP \(x, x+4, x+8,\ldots\) is (50), what is the value of (x)?
C. (14)
\(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.
The correct answer is C. (14). \(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.
\(50=x+9\times4\), इसलिए (x=14)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।
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In an AP, (a=30) and (d=-2). Which term will be (0)?
C. (16)वां(16)th
From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.
The correct answer is C. (16)वां / (16)th. From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.
(0=30+(n-1)(-2)) से (2(n-1)=30), अतः (n=16)। शून्य पद के लिए भी वही (n)वां पद सूत्र लगाएं।
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Which is the first negative term of the AP \(45,40,35,\ldots\)?
B. (11)वां(11)th
(a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.
The correct answer is B. (11)वां / (11)th. (a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.
(a_n=45+(n-1)(-5)=50-5n)। \(a_n<0\) से (n>10), इसलिए पहला ऋणात्मक पद (11)वां है।
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The (8)th term of an AP is (35) and (d=4). What is \(a_1\)?
C. (7)
\(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).
The correct answer is C. (7). \(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).
\(35=a+7\times4\), इसलिए (a=7)। (8)वें पद के लिए (7d) घटाएं।
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Which term of the AP \(3,8,13,\ldots\) is (88)?
A. (18)वां(18)th
From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).
The correct answer is A. (18)वां / (18)th. From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).
(88=3+(n-1)5) से (85=5(n-1)), अतः (n=18)। पद संख्या के प्रश्न में दिए पद को \(a_n\) मानें।
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What is the (11)th term of the AP \(200,180,160,140,\ldots\)?
D. (0)
Here (d=-20), so (a_{11}=200+10(-20)=0). In a decreasing AP, a term can also become zero.
The correct answer is D. (0). Here (d=-20), so (a_{11}=200+10(-20)=0). In a decreasing AP, a term can also become zero.
यहाँ (d=-20) है, इसलिए (a_{11}=200+10(-20)=0)। घटती श्रेढ़ी में पद शून्य भी हो सकता है।
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If \(a_n=4n+6\), what will be the (25)th term?
A. (106)
\(a_{25}=4\times25+6=106\). Put (n=25) in the given general term.
The correct answer is A. (106). \(a_{25}=4\times25+6=106\). Put (n=25) in the given general term.
\(a_{25}=4\times25+6=106\)। दिए गए सामान्य पद में (n=25) रखें।
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If (a=0) and (d=4), what is the (26)th term of the AP?
D. (100)
\(a_{26}=0+25\times4=100\). Even with zero first term, (n-1) differences are added.
The correct answer is D. (100). \(a_{26}=0+25\times4=100\). Even with zero first term, (n-1) differences are added.
\(a_{26}=0+25\times4=100\)। शून्य प्रथम पद होने पर भी (n-1) अंतर जुड़ते हैं।
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In an AP, \(a_1=13\) and (d=8). What is the (10)th term?
A. (85)
\(a_{10}=13+9\times8=85\). \(a_1\) is the first term (a).
The correct answer is A. (85). \(a_{10}=13+9\times8=85\). \(a_1\) is the first term (a).
\(a_{10}=13+9\times8=85\)। \(a_1\) ही प्रथम पद (a) होता है।
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If \(a_n=30-3n\), what will be the (6)th term?
D. (12)
\(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.
The correct answer is D. (12). \(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.
\(a_6=30-3\times6=12\)। घटते हुए सामान्य पद में घटाव सावधानी से करें।
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If \(a_n=5n-1\), what is the (20)th term of this AP?
B. (99)
\(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.
The correct answer is B. (99). \(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.
\(a_{20}=5\times20-1=99\)। जब \(a_n\) दिया हो, तो सूत्र में (n) का मान रखें।
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Which is the (18)th term of the AP \(-10,-6,-2,2,\ldots\)?
C. (58)
Here (a=-10), (d=4), so \(a_{18}=-10+17\times4=58\). The formula remains the same even when terms move from negative to positive.
The correct answer is C. (58). Here (a=-10), (d=4), so \(a_{18}=-10+17\times4=58\). The formula remains the same even when terms move from negative to positive.
यहाँ (a=-10), (d=4) है, इसलिए \(a_{18}=-10+17\times4=58\)। ऋणात्मक से धनात्मक जाने पर भी सूत्र समान रहता है।
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If the constant term of (p(x)=x-2+ax+4) is (4), which term is the constant term?
C. (4)
The constant term does not contain (x). So (4) is the constant term.
The correct answer is C. (4). The constant term does not contain (x). So (4) is the constant term.
स्थिर पद में (x) नहीं होता। इसलिए (4) स्थिर पद है।
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The first term of an arithmetic progression is (19) and \(S_{15}=810\). What is the (15)th term?
B. (89)
From (810=\frac{15}{2}(19+l)), (l=89). Exam tip: when the last term is needed, the (a+l) form is fast.
The correct answer is B. (89). From (810=\frac{15}{2}(19+l)), (l=89). Exam tip: when the last term is needed, the (a+l) form is fast.
(810=\frac{15}{2}(19+l)) से (l=89) मिलता है। परीक्षा में अंतिम पद चाहिए हो तो (a+l) वाला सूत्र तेज है।
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C. (980)
From the two terms (d=4) and (a=3). Hence \(S_{20}=980\); exam tip: find (a) and (d) before applying the sum formula.
The correct answer is C. (980). From the two terms (d=4) and (a=3). Hence \(S_{20}=980\); exam tip: find (a) and (d) before applying the sum formula.
दो पदों से (d=4) और (a=3) मिलता है इसलिए \(S_{20}=980\)। परीक्षा में पहले (a) और (d) निकालें फिर योग लगाएं।
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If the fourth term of (7, 7+d, 7+2d, 7+3d) is (34), what is the second term?
D. (16)
From (7+3d=34), (d=9), so the second term is (7+d=16). First find (d) and then form the required term.
The correct answer is D. (16). From (7+3d=34), (d=9), so the second term is (7+d=16). First find (d) and then form the required term.
(7+3d=34) से (d=9), इसलिए दूसरा पद (7+d=16) है। पहले (d) निकालकर मांगा गया पद बनाएं।
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At which mixed number position will \(-\frac{17}{5}\) lie on the number line?
B. \(-3-\frac{2}{5}\)
\(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.
The correct answer is B. \(-3-\frac{2}{5}\). \(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.
\(-\frac{17}{5}=-3-\frac{2}{5}\), इसलिए यह (-4) और (-3) के बीच है। परीक्षा में ऋणात्मक मिश्र संख्या का चिह्न ठीक रखें।
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How will \(\frac{13}{4}\) be shown as a mixed number on the number line?
A. \(3+\frac{1}{4}\)
\(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.
The correct answer is A. \(3+\frac{1}{4}\). \(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.
\(\frac{13}{4}=3+\frac{1}{4}\), इसलिए यह (3) के बाद एक चौथाई पर होगा। परीक्षा में विषम भिन्न को मिश्र संख्या में बदलें।
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Where will \(\frac{5}{4}\) be placed as a mixed number on the number line?
A. \(1+\frac{1}{4}\)
\(\frac{5}{4}=1+\frac{1}{4}\), so it is one-fourth after (1). In exams, convert an improper fraction into mixed form.
The correct answer is A. \(1+\frac{1}{4}\). \(\frac{5}{4}=1+\frac{1}{4}\), so it is one-fourth after (1). In exams, convert an improper fraction into mixed form.
\(\frac{5}{4}=1+\frac{1}{4}\), इसलिए यह (1) के बाद एक चौथाई भाग पर है। परीक्षा में अपूर्ण भिन्न को मिश्र रूप में बदलें।
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