100 results found for "second-term" in Class 10.
If the fourth term of (4,4+d,4+2d,4+3d) is (31), what is the second term?
B. (13)
(4+3d=31) से (d=9), इसलिए दूसरा पद (4+d=13)। पहले (d) निकालकर मांगा गया पद बनाएं। / From (4+3d=31), (d=9), so the second term is (4+d=13). First find (d) and then form the required term.
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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)
(7+3d=34) से (d=9), इसलिए दूसरा पद (7+d=16) है। पहले (d) निकालकर मांगा गया पद बनाएं। / From (7+3d=34), (d=9), so the second term is (7+d=16). First find (d) and then form the required term.
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If the fourth term of (3, 3+d, 3+2d, 3+3d) is (24), what is the second term?
C. (10)
(3+3d=24) से (d=7), इसलिए दूसरा पद (3+d=10)। पहले (d) निकालकर संबंधित पद बनाएं। / From (3+3d=24), (d=7), so the second term is (3+d=10). First find (d) and then form the required term.
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If (d=4) and the first term is (1), what will be the second term?
B. (5)
दूसरा पद (1+4=5) होगा। पहले पद में सार्व अंतर जोड़ें। / The second term is (1+4=5). Add the common difference to the first term.
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If (a=5) and the second term is (17), what is (d)?
C. (12)
(d=17-5=12) है। दूसरे पद में से पहले पद को घटाकर सार्व अंतर पाएं। / (d=17-5=12). Find the common difference by subtracting the first term from the second term.
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If (a=3.5) and (d=2.5), what is the second term?
C. (6.0)
दूसरा पद (a+d=3.5+2.5=6.0) है। दशमलव जोड़ते समय अंकों को सही स्थान पर रखें। / The second term is (a+d=3.5+2.5=6.0). While adding decimals keep digits in proper places.
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If (a=3) and the second term is (10), what is (d)?
C. (7)
(d=10-3=7) है। दूसरे पद में से पहले पद को घटाकर सार्व अंतर पाएं। / (d=10-3=7). Find the common difference by subtracting the first term from the second term.
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If (a=2.5) and (d=1.5), what is the second term?
C. (4.0)
दूसरा पद (a+d=2.5+1.5=4.0) है। दशमलव जोड़ते समय अंकों को ठीक से मिलाएं। / The second term is (a+d=2.5+1.5=4.0). Align digits carefully when adding decimals.
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If (a=7) and (d=4), what is the second term?
A. (11)
दूसरा पद (a+d) होता है। इसलिए (7+4=11) सही है। / The second term is (a+d). So (7+4=11) is correct.
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In an arithmetic progression \(a,a+d,a+2d,\ldots\), which is the second term?
D. (a+d)
दूसरा पद (a+d) होता है। सामान्य रूप में पदों का क्रम याद रखें। / The second term is (a+d). Remember the order of terms in the general form.
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In an arithmetic progression, (d=9) and the second term is (20). What is the first term?
B. (11)
पहला पद (20-9=11) है। दूसरे पद से (d) घटाकर पहला पद मिलता है। / The first term is (20-9=11). Subtract (d) from the second term to get the first term.
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In an arithmetic progression, (d=4) and the second term is (11). What is the first term?
A. (7)
पहला पद (11-4=7) है। दूसरे पद से (d) घटाकर पहला पद मिलता है। / The first term is (11-4=7). Subtract (d) from the second term to get the first term.
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C. (x+82)
(7d=35) से (d=5)। \(a_{20}=a_{12}+8d=x+42+40=x+82\)। / From (7d=35), (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)
\(d=\frac{90-27}{14-5}=7\) और \(a_{20}=90+6\times7=132\)। पहले (d) निकालें फिर आगे बढ़ें। / \(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.
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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)
\(d=\frac{55-15}{12-4}=5\) और \(a_{16}=55+4\times5=75\)। पहले (d) फिर वांछित पद निकालें। / \(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
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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)
\(d=\frac{3-8}{8-3}=-1\), इसलिए (a_{11}=3+3(-1)=0)। ज्ञात पास वाले पद से आगे बढ़ना सरल है। / \(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.
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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)
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। / Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).
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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)
\(d=\frac{32-16}{9-5}=4\), इसलिए \(a_{13}=32+4\times4=48\)। समान स्थान अंतर होने पर पदों का अंतर भी समान होता है। / \(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.
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If the second term is (11) and the fourth term is (21) in (6, 6+d, 6+2d, 6+3d), what is (d)?
B. (5)
(6+d=11) से (d=5), और (6+3d=21) इसकी पुष्टि करता है। दो शर्तें हों तो दोनों से उत्तर जांचें। / From (6+d=11), (d=5), and (6+3d=21) confirms it. When two conditions are given, verify the answer with both.
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In an arithmetic progression, the first term is (22) and the second term is (16). What is (d)?
B. (-6)
(d=16-22=-6) है। दूसरा पद छोटा हो तो (d) ऋणात्मक होता है। / (d=16-22=-6). If the second term is smaller, (d) is negative.
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B. (7)
सार्व अंतर (18-11=7) है। (d) के लिए दूसरा पद घटा पहला पद करें। / The common difference is (18-11=7). For (d), subtract the first term from the second term.
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If an arithmetic progression has (d=-1.5) and first term (10), what is the second term?
A. (8.5)
दूसरा पद (10+(-1.5)=8.5) है। दशमलव और ऋणात्मक चिन्ह दोनों का ध्यान रखें। / The second term is (10+(-1.5)=8.5). Take care of both decimals and negative signs.
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In an arithmetic progression, the first term is (13) and the second term is (8). What is (d)?
B. (-5)
(d=8-13=-5) है। दूसरा पद छोटा हो तो (d) ऋणात्मक होगा। / (d=8-13=-5). If the second term is smaller, (d) will be negative.
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A. (8)
दूसरा पद (a+d) होता है। इसलिए (5+3=8) है। / The second term is (a+d). Therefore, (5+3=8).
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C. (x+181)
(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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B. (x+188)
(11d=77) से (d=7)। \(a_{32}=a_{18}+14d=x+90+98=x+188\)। / From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).
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B. (x+137)
(9d=54) से (d=6)। \(a_{27}=a_{15}+12d=x+65+72=x+137\)। / From (9d=54), (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)
\(71=a+11\times5\) से (a=16)। ज्ञात पद से पहले पद तक जाने के लिए (11d) घटाएं। / From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).
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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)
\(47=a+8\times4\) से (a=15)। ज्ञात पद से पहले पद तक जाने के लिए (8d) घटाएं। / From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
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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), इसलिए (a=-2)। दिए गए पद से पीछे जाते समय (5d) घटाया जाता है। / (23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
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The general term of an AP is \(a_n=7n+2\). Find the (11)th term.
C. (79)
\(a_{11}=7\times11+2=79\)। सामान्य पद में सही पद संख्या रखना ही मुख्य कदम है। / \(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.
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D. (9)
दूसरा पद (7+2=9) होगा। अगला पद पाने के लिए सार्व अंतर जोड़ें। / The second term is (7+2=9). Add the common difference to get the next term.
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B. (1485)
शर्त से (6+13d=3(6+3d)), इसलिए (d=3) और \(S_{30}=1485\) है। पदों की शर्त को पहले समीकरण में बदलें। / The condition gives (6+13d=3(6+3d)), so (d=3) and \(S_{30}=1485\). Convert the term condition into an equation first.
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A. (1050)
शर्त से (5+11d=4(5+2d)), इसलिए (d=5) और \(S_{20}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें। / The condition gives (5+11d=4(5+2d)), so (d=5) and \(S_{20}=1050\). Convert the term condition into an equation first.
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C. (1050)
शर्त से (6+8d=2(6+3d)), इसलिए (d=3) और \(S_{25}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें। / The condition gives (6+8d=2(6+3d)), so (d=3) and \(S_{25}=1050\). Convert the term condition into an equation first.
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C. (576)
शर्त से (4+7d=3(4+2d)), इसलिए (d=8) और \(S_{12}=576\)। पदों की शर्त को पहले समीकरण में बदलें। / The condition gives (4+7d=3(4+2d)), so (d=8) and \(S_{12}=576\). Convert the term condition into an equation first.
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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)
\(a_{36}=8\times36+15=303\)। बने हुए सूत्र में (n=36) रखकर सीधे उत्तर पाएं। / \(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
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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)
((r+6))वां पद (r)वें पद से (6d) आगे है इसलिए (3r-2+24=3r+22)। प्रतीकात्मक प्रश्न में स्थान अंतर देखें। / 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.
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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)
\(a_{41}=7\times41+12=299\)। बने हुए सूत्र में केवल (n=41) रखें। / \(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
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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)
((m+5))वां पद (m)वें पद से (5d) आगे है इसलिए (2m+3+10=2m+13)। प्रतीकात्मक पदों में भी स्थान अंतर देखें। / 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.
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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)
(93=25+17d) से (68=17d) इसलिए (d=4)। (18)वें पद के लिए गुणक (17) होता है। / From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
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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)
\(a_{32}=6\times32+5=197\)। बनाए गए सूत्र में (n) का सही मान रखें। / \(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
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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), इसलिए (75=15d) और (d=5)। (16)वें पद के लिए गुणक (15) होगा। / (93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
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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)
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। \(/ The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
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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)
सूत्र (a_n=a+(n-1)d) लगाने पर \(7+17\times4=75\)। परीक्षा में (n-1) को भूलना नहीं चाहिए। / Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
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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)
(10)वाँ पद (4)थे पद से (6d) आगे है इसलिए (21+36=57)। पद संख्या का अंतर सीधे उपयोग करें। / The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.
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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)
\(a_{16}=-12+15\times5=63\)। पहले (15d) निकालें फिर प्रथम पद जोड़ें। / \(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.
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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)
\(a_7=9+6\times10=69\)। (7)वें पद के लिए (6d) जोड़ना होता है। / \(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.
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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)
(7)वाँ पद (3)रे पद से (4d) आगे है इसलिए (14+20=34)। बीच के पदों की संख्या सही गिनें। / The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.
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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)
\(a_{12}=-2+11\times6=64\)। पहले गुणा करें फिर (-2) जोड़ें। / \(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).
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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)
(8)वाँ पद (5)वें पद से (3d) आगे है इसलिए (22+18=40)। पदों का अंतर गिनना आसान तरीका है। / The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.
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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)
(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। / The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.
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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)। ऋणात्मक (d) को कोष्ठक में लिखना उपयोगी है। / (a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
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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)
सूत्र (a_n=a+(n-1)d) लगाएं तो \(5+7\times3=26\)। परीक्षा में (n-1) लेना न भूलें। / Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
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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)
(n=18) रखने पर \(a_{18}=2\times18+3=39\)। दिए गए \(a_n\) में सीधे पद संख्या रखें। / Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).
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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)
\(a_{21}=25+20\times4=105\)। पद संख्या से (1) घटाना न भूलें। / \(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
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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)
\(a_{11}=6+10\times7=76\)। (11)वें पद तक (10) बार अंतर जुड़ता है। / \(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.
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In an AP, first term (a=4) and common difference (d=3). What is the (10)th term?
A. (31)
सूत्र (a_n=a+(n-1)d) लगाने पर \(a_{10}=4+9\times3=31\)। परीक्षा में (n-1) को ध्यान से लिखें। / Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.
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The Second World War in Europe began with which event?
A. जर्मनी का पोलैंड पर आक्रमणGermany's invasion of Poland
जर्मनी ने 1 सितंबर 1939 को पोलैंड पर आक्रमण किया और युद्ध शुरू हुआ। परीक्षा में 1939 को द्वितीय विश्व युद्ध की शुरुआत मानें। / Germany invaded Poland on 1 September 1939 and the war began. For exams, remember 1939 as the start of the Second World War.
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When did the Second World War end?
D. उन्नीस सौ पैंतालीस1945
द्वितीय विश्व युद्ध उन्नीस सौ पैंतालीस में समाप्त हुआ। परीक्षा में इसे संयुक्त राष्ट्र की स्थापना से जोड़ें। / The Second World War ended in 1945. For exams connect it with the founding of the United Nations.
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Before the French Revolution the Second Estate was mainly linked with whom?
A. कुलीन वर्गNobility
दूसरा एस्टेट कुलीन वर्ग से जुड़ा था। परीक्षा में विशेषाधिकार प्राप्त वर्गों को पहले और दूसरे एस्टेट से जोड़ें। / The Second Estate was linked with nobility. For exams connect privileged groups with the First and Second Estates.
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How did the Treaty of Versailles help create the background of the Second World War?
D. उसकी कठोर शर्तों से जर्मनी में असंतोष बढ़ाIts harsh terms increased resentment in Germany
वर्साय संधि की क्षतिपूर्ति और युद्ध दोष धारा से जर्मनी में नाराजगी बढ़ी। परीक्षा में इसे नाजीवाद के उदय से जोड़ें। / Reparations and the war guilt clause increased anger in Germany. For exams connect it with the rise of Nazism.
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Which countries were the main Axis Powers in the Second World War?
A. जर्मनी इटली और जापानGermany Italy and Japan
धुरी शक्तियों में जर्मनी इटली और जापान प्रमुख थे। परीक्षा में इन्हें मित्र राष्ट्रों से अलग रखें। / The main Axis Powers were Germany Italy and Japan. For exams keep them separate from the Allied Powers.
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In which year did the Second World War end?
D. 1945
द्वितीय विश्व युद्ध 1945 में समाप्त हुआ था। परीक्षा में 1939 से 1945 इसकी अवधि याद रखें। / The Second World War ended in 1945. For exams remember its period as 1939 to 1945.
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In which year did the Second World War begin?
C. 1939
द्वितीय विश्व युद्ध 1939 में शुरू हुआ था। परीक्षा में जर्मनी द्वारा पोलैंड पर आक्रमण को शुरुआत से जोड़ें। / The Second World War began in 1939. For exams connect its start with Germany's invasion of Poland.
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In which year was the Second Round Table Conference held?
B. 19311931
द्वितीय गोलमेज सम्मेलन 1931 में हुआ था। इसमें गांधीजी ने कांग्रेस की ओर से भाग लिया था। / The Second Round Table Conference was held in 1931. Gandhi attended it on behalf of Congress.
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The Second Five-Year Plan began in which year?
B. सन् 19561956
दूसरी पंचवर्षीय योजना 1956 में शुरू हुई थी। परीक्षा में भारी उद्योगों पर इसका जोर याद रखें। / The Second Five-Year Plan began in 1956. In exams remember its focus on heavy industries.
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The Second Battle of Panipat took place in which year?
C. 1556 ईस्वी1556 CE
पानीपत का दूसरा युद्ध 1556 में हुआ और अकबर की सत्ता मजबूत हुई। परीक्षा में तीनों पानीपत युद्धों की तिथियां अलग रखें। / The Second Battle of Panipat took place in 1556 and strengthened Akbar's power. For exams keep the dates of all three Panipat battles separate.
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Who represented the Congress at the Second Round Table Conference?
D. महात्मा गांधीMahatma Gandhi
दूसरे गोलमेज सम्मेलन में गांधीजी ने कांग्रेस का प्रतिनिधित्व किया। परीक्षा में सम्मेलन और प्रतिनिधि याद रखें। / Gandhi represented the Congress at the Second Round Table Conference. Exam tip: remember conferences and representatives.
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The Second Buddhist Council at Vaishali was mainly connected with what?
B. संघ अनुशासन पर मतभेदDisputes over monastic discipline
द्वितीय संगीति संघ के अनुशासन संबंधी विवादों से जुड़ी मानी जाती है। परीक्षा में बौद्ध परिषदों के कारण याद रखें। / The Second Council is considered connected with disputes over monastic discipline. For exams, remember reasons for Buddhist councils.
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What does increased repression in the second phase of the Civil Disobedience Movement show?
A. औपनिवेशिक शासन जन आंदोलन से भयभीत थाColonial rule was afraid of mass mobilisation
Repression often increases when a regime feels seriously challenged.
Arrests and strict measures showed the strength of the movement.
Link repression with colonial anxiety.
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Gandhiji's participation in the Second Round Table Conference happened after what?
A. गांधी इरविन समझौते के बादAfter the Gandhi-Irwin Pact
गांधी इरविन समझौते में बातचीत की सहमति बनी। / The Gandhi-Irwin Pact created agreement for talks.
इसी के बाद गांधीजी दूसरे गोलमेज सम्मेलन में गए। / After this, Gandhiji attended the Second Round Table Conference.
घटना क्रम को समयरेखा की तरह याद करें। / Remember the sequence like a timeline.
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What situation does the term Vichy France show in the Second World War?
C. नाजी प्रभाव के अधीन सहयोगी फ्रांसीसी शासनA collaborationist French regime under Nazi influence
विची फ्रांस जर्मन कब्जे के बाद बनी सहयोगी शासन व्यवस्था थी। परीक्षा में इसे फ्री फ्रेंच आंदोलन से अलग रखें। / Vichy France was a collaborationist regime after German occupation. For exams keep it separate from the Free French movement.
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The term ghetto in the Second World War was linked with what context?
D. यहूदियों को अलग क्षेत्रों में बंद करनाConfining Jews in separate areas
नाजी शासन ने यहूदियों को गेटो में अलग और नियंत्रित रखा। परीक्षा में इसे नाजी उत्पीड़न से जोड़ें। / The Nazi regime isolated and controlled Jews in ghettos. For exams connect it with Nazi persecution.
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C. (14)
चुना गया अनुक्रम \(5,19,33,\ldots\) होगा और इसका अंतर (14) है। हर दूसरा पद लेने पर नया (d) मूल (d) का (2) गुना होता है। / The selected sequence is \(5,19,33,\ldots\), and its difference is (14). Selecting every second term makes the new (d) twice the original (d).
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If (2a+3, 5a-1, 11a-13) are in an arithmetic progression, what is the second term?
C. (14)
(2(5a-1)=(2a+3)+(11a-13)) से (a=3). दूसरा पद (5a-1=14) है। / From (2(5a-1)=(2a+3)+(11a-13)), (a=3). The second term is (5a-1=14).
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If an arithmetic progression has (a=28) and second term (19), what is the common difference?
B. (-9)
सार्व अंतर (19-28=-9) है। दूसरे पद से पहले पद को घटाकर (d) निकालें। / The common difference is (19-28=-9). Find (d) by subtracting the first term from the second term.
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If (a=6) and the second term is (10), what is the common difference?
C. (4)
दूसरा पद (a+d) होता है। इसलिए (d=10-6=4) है। / The second term is (a+d). Therefore, (d=10-6=4).
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If (a=20) and (d=-5), what is the second term?
A. (15)
दूसरा पद (a+d=20+(-5)=15) है। ऋणात्मक (d) जोड़ते समय चिन्ह सावधानी से लगाएँ। / The second term is (a+d=20+(-5)=15). Use signs carefully while adding negative (d).
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If (a=9) and (d=-2), what is the second term of the arithmetic progression?
A. (7)
दूसरा पद (a+d=9+(-2)=7) है। ऋणात्मक अंतर जोड़ते समय चिन्ह सावधानी से लगाएँ। / The second term is (a+d=9+(-2)=7). Use signs carefully while adding a negative difference.
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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
यह नीति नियंत्रण के लिए विभाजन का उपयोग करती थी। परीक्षा में इसकी विरासत भी लिखें। / This policy used division for control. For exams also write its legacy.
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C. (3000)
\(a_{21}+a_{40}=a_1+a_{60}=300\), इसलिए (20) पदों का योग (3000) है। सममित पदों का योग बराबर होता है। / \(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.
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B. (2100)
\(a_{11}+a_{30}=a_1+a_{40}=210\), इसलिए (20) पदों का योग (2100) है। सममित पदों का योग बराबर होता है। / \(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.
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B. (14)
(740=10(a+60)) से (a=14) मिलता है। जब (n)वाँ पद दिया हो तो उसे अंतिम पद की तरह इस्तेमाल करें। / 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.
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What is the last term among the positive multiples of (13) less than (600)?
B. (598)
(13n<600) में सबसे बड़ा (n=46) है इसलिए पद \(13\times46=598\)। सीमा से कम सबसे बड़ा पूर्णांक लें। / In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.
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The (n)th term of the AP \(73,68,63,\ldots\) is (-12). What is (n)?
C. (18)
(-12=73+(n-1)(-5)) से (85=5(n-1)) इसलिए (n=18)। घटती AP में ऋणात्मक लक्ष्य तक चिन्ह सही रखें। / 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.
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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)
\(112=z+18\times5\) से (z=22)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं। / From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.
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In the AP \(7,12,17,\ldots\), what is the last term less than (180)?
C. (177)
पद (7+5(n-1)) हैं। (180) से कम अंतिम पद (177) है क्योंकि अगला पद (182) होगा। / The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
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In an AP (a=63) and (d=-4). Which term will be (-1)?
C. (17)वां(17)th
(-1=63+(n-1)(-4)) से (64=4(n-1)) इसलिए (n=17)। ऋणात्मक लक्ष्य पद में चिन्हों को ध्यान से संभालें। / From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.
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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)। \(a_n<0\) से (n>16) इसलिए पहला ऋणात्मक पद (17)वां है। / (a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.
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Which term of the AP \(26,35,44,\ldots\) is (206)?
C. (21)वां(21)st
(206=26+(n-1)9) से (180=9(n-1)) इसलिए (n=21)। पद और पहले पद का अंतर (d) से भाग दें। / From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).
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The (14)th term of an AP is (92) and (d=7). What is \(a_1\)?
A. (1)
\(92=a+13\times7\) से (a=1)। (14)वें पद से पहले पद तक (13d) घटता है। / From \(92=a+13\times7\), (a=1). From the (14)th term to the first term (13d) is subtracted.
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Which term of the AP \(9,17,25,\ldots\) is (201)?
C. (25)वां(25)th
(201=9+(n-1)8) से (192=8(n-1)) और (n=25)। पद संख्या पूर्णांक आए तो उत्तर सही दिशा में है। / 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.
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What is the last term among the positive multiples of (11) less than (500)?
B. (495)
(11n<500) में सबसे बड़ा (n=45) है इसलिए पद \(11\times45=495\)। सीमा से कम सबसे बड़ा पूर्णांक लें। / In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
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The (n)th term of the AP \(55,51,47,\ldots\) is (-17). What is (n)?
C. (19)
(-17=55+(n-1)(-4)) से (72=4(n-1)) इसलिए (n=19)। ऋणात्मक पद तक जाते समय चिन्ह सही रखें। / From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
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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)
\(89=y+11\times6\) से (y=23)। चर वाले पहले पद को सीधे (a) मानें। / From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
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In the AP \(2,6,10,\ldots\), what is the last term less than (75)?
A. (74)
इस श्रेणी के पद (2+4(n-1)) हैं। (75) से कम अंतिम पद (74) है। / The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
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In an AP, (a=48) and (d=-3). Which term will be (0)?
C. (17)वां(17)th
(0=48+(n-1)(-3)) से (3(n-1)=48) इसलिए (n=17)। शून्य पद के लिए भी सामान्य सूत्र लगाएं। / From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.
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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)। \(a_n<0\) से (n>13) इसलिए पहला ऋणात्मक पद (14)वां है। / (a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
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Which term of the AP \(14,23,32,\ldots\) is (185)?
C. (20)वां(20)th
(185=14+(n-1)9) से (171=9(n-1)) और (n=20)। अंतर को (d) से भाग देकर पद संख्या पाएं। / From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
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