100 results found for "fourth term" in Class 10.
If (a=17) and (d=0), what will be the fourth term?
B. (17)
(d=0) होने पर सभी पद (17) रहते हैं। स्थिर श्रेणी में कोई वृद्धि या कमी नहीं होती। / When (d=0), all terms remain (17). In a constant progression there is no increase or decrease.
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If (a=10) and (d=0), what will be the fourth term?
D. (10)
(d=0) होने पर सभी पद (10) रहते हैं। स्थिर श्रेणी में कोई वृद्धि या कमी नहीं होती। / When (d=0), all terms remain (10). In a constant progression there is no increase or decrease.
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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 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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The importance of China's May Fourth Movement was linked with what?
A. राष्ट्रवाद और सांस्कृतिक बौद्धिक जागरणNationalism and cultural intellectual awakening
मई चौथी आंदोलन ने चीनी युवाओं में राष्ट्रवाद और आधुनिक विचारों को बढ़ाया। परीक्षा में इसे चीन के बौद्धिक परिवर्तन से जोड़ें। / The May Fourth Movement increased nationalism and modern ideas among Chinese youth. For exams, connect it with China's intellectual change.
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The May Fourth Movement in China strengthened which tendency after the 1911 Revolution?
A. राष्ट्रवाद और नई सांस्कृतिक चेतनाNationalism and new cultural awareness
मई चौथी आंदोलन ने युवाओं और बुद्धिजीवियों में राष्ट्रवादी चेतना बढ़ाई। परीक्षा में इसे आधुनिक चीनी राजनीति की पृष्ठभूमि से जोड़ें। / The May Fourth Movement increased nationalist awareness among youth and intellectuals. For exams connect it with the background of modern Chinese politics.
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The Fourth Buddhist Council is associated with which ruler?
B. कनिष्कKanishka
चौथी बौद्ध संगीति कनिष्क से जुड़ी मानी जाती है। उसे बौद्ध धर्म के संरक्षण के लिए याद करें। / The Fourth Buddhist Council is associated with Kanishka. Remember him for patronage of Buddhism.
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What is the fourth term in \(\frac{5}{4},\frac{7}{4},\frac{9}{4},\frac{11}{4},\ldots\)?
D. \(\frac{11}{4}\)
लिखे क्रम में चौथा पद \(\frac{11}{4}\) है। पद संख्या गिनते समय पहला पद शामिल करें। / In the written order, the fourth term is \(\frac{11}{4}\). Include the first term while counting positions.
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What is the fourth term in \(16,22,28,34,\ldots\)?
D. (34)
लिखे हुए क्रम में चौथा पद (34) है। ऐसे प्रश्न में सूत्र की जगह सीधी गिनती करें। / In the written order, the fourth term is (34). In such questions, count directly instead of using a formula.
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What is the fourth term in the sequence \(6,12,18,24,\ldots\)?
C. (24)
दिए गए पदों में चौथा पद (24) है। क्रम गिनते समय पहला पद (6) से शुरू करें। / The fourth term in the given terms is (24). Start counting from (6) as the first term.
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What is the fourth term in \(14,18,22,26,\ldots\)?
C. (26)
चौथा पद सीधे (26) है। पद क्रम गिनते समय पहला पद (14) से शुरू करें। / The fourth term is directly (26). While counting positions, start from the first term (14).
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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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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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B. (-5)
चौथे और पहले पद के बीच (3) अंतर हैं, इसलिए (3d=-15) और (d=-5)। घटती श्रेणी में (d) ऋणात्मक रखें। / There are (3) gaps between the fourth and first terms, so (3d=-15) and (d=-5). Keep (d) negative for a decreasing progression.
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What is the difference between the third and fourth terms of \(75,69,63,57,\ldots\)?
B. (-6)
तीसरा पद (63) और चौथा (57) है इसलिए अंतर (57-63=-6) है। अंतर निकालते समय अगला पद घटा पिछला पद करें। / The third term is (63) and the fourth is (57), so the difference is (57-63=-6). While finding difference subtract the previous term from the next term.
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What is the difference between the third and fourth terms of \(42,39,36,33,\ldots\)?
B. (-3)
तीसरा पद (36) और चौथा (33) है इसलिए (33-36=-3)। अंतर निकालते समय बाद वाला पद घटा पहले वाला पद करें। / The third term is (36) and the fourth is (33), so (33-36=-3). While finding the difference subtract the previous term from 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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In which year was the Seventy-fourth Constitutional Amendment passed?
C. 19921992
चौहत्तरवां संशोधन 1992 में पारित हुआ था। इसे नगर निकायों और शहरी स्थानीय शासन से जोड़ें। / The Seventy-fourth Amendment was passed in 1992. Link it with municipalities and urban local governance.
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In which year was the Fourth Anglo-Mysore War fought?
A. 1799 ईस्वी1799 CE
चतुर्थ आंग्ल मैसूर युद्ध 1799 ईस्वी में हुआ। इसी युद्ध में टीपू सुल्तान की मृत्यु हुई। / The Fourth Anglo-Mysore War was fought in 1799 CE. Tipu Sultan died in this war.
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Kanishka's association with the Fourth Buddhist Council shows which feature of his rule?
A. बौद्ध धर्म का संरक्षण और सांस्कृतिक प्रभावPatronage of Buddhism and cultural influence
कनिष्क कुषाण शासक था और बौद्ध धर्म के संरक्षण के लिए प्रसिद्ध था। उसे धार्मिक संरक्षण से याद करें। / Kanishka was a Kushan ruler famous for patronage of Buddhism. Remember him with religious patronage.
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What was the effect of the Fourth Anglo-Mysore War on British power in South India?
C. अंग्रेजों के प्रमुख विरोधी मैसूर की शक्ति टूट गईThe power of Mysore, a major British opponent, was broken
1799 में टीपू की मृत्यु से मैसूर की चुनौती समाप्त हो गई। परीक्षा में मैसूर युद्धों को ब्रिटिश विस्तार से जोड़ें। / Tipu's death in 1799 ended Mysore's challenge. Exam tip: connect Mysore wars with British expansion.
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What was the biggest political result of the Fourth Anglo-Mysore War?
C. टीपू सुल्तान की मृत्यु और मैसूर की शक्ति का पतनDeath of Tipu Sultan and decline of Mysore power
1799 में टीपू सुल्तान की मृत्यु से मैसूर की अंग्रेज विरोधी शक्ति कमजोर हुई। परीक्षा में मैसूर युद्धों का क्रम याद रखें। / Tipu Sultan's death in 1799 weakened Mysore's anti-British power. Exam tip: remember the sequence of Mysore Wars.
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What was the main result of the Fourth Mysore War in 1799?
A. टीपू सुल्तान की मृत्यु और मैसूर शक्ति का पतनDeath of Tipu Sultan and decline of Mysore power
1799 में श्रीरंगपट्टनम में टीपू सुल्तान मारे गए। परीक्षा में मैसूर युद्धों का अंत अंग्रेजी प्रभुत्व से जोड़ें। / Tipu Sultan died at Seringapatam in 1799. Exam tip is to link the end of Mysore Wars with British dominance.
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Kanishka's so called Fourth Buddhist Council is more associated with which Buddhist tradition?
A. सर्वास्तिवाद महायान संदर्भSarvastivada Mahayana context
कनिष्क की परिषद कश्मीर और बौद्ध शास्त्रीय परंपरा से जोड़ी जाती है। परीक्षा में परिषदों के विवरणों में परंपरागत भिन्नता याद रखें। / Kanishka's council is linked with Kashmir and Buddhist scholastic tradition. For exams, remember variations in council traditions.
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A. महायानMahayana
कनिष्क के संरक्षण से महायान बौद्ध धर्म के विकास को बल मिला माना जाता है। परीक्षा में कुषाण और महायान संबंध याद रखें। / Kanishka's patronage is considered to have strengthened Mahayana Buddhism. For exams, remember the Kushana and Mahayana link.
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C. कनिष्कKanishka
चौथी बौद्ध संगीति को कनिष्क के संरक्षण से जोड़ा जाता है। परीक्षा में इसे कुषाण काल और बौद्ध धर्म के विकास से जोड़ें। / The Fourth Buddhist Council is associated with Kanishka's patronage. For exams, connect it with the Kushana period and the development of Buddhism.
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Mahavira was the twenty-fourth Tirthankara of which religion?
A. जैन धर्मJainism
महावीर स्वामी जैन धर्म के चौबीसवें तीर्थंकर थे। परीक्षा में तीर्थंकर शब्द जैन धर्म से जोड़ें। / Mahavira was the twenty-fourth Tirthankara of Jainism. In exams, connect the term Tirthankara with Jainism.
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The Fourth Buddhist Council is generally associated with which Kushan ruler?
A. कनिष्कKanishka
चौथी बौद्ध संगीति कनिष्क से जुड़ी मानी जाती है। परीक्षा में कनिष्क और बौद्ध धर्म के महायान रूप को साथ याद करें। / The Fourth Buddhist Council is considered associated with Kanishka. For exams, remember Kanishka with the Mahayana form of Buddhism.
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In a similar segment, what is the fourth equal point from (2) when each part is \(\frac{1}{2}\)?
C. (4)
चौथा बिंदु \(2+4\times\frac{1}{2}=4\) है। बराबर भागों में आरंभिक बिंदु में कुल कदम जोड़ें। / The fourth point is \(2+4\times\frac{1}{2}=4\). Add the total step length to the starting point.
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A. 11
\(12^2=144\), और 144 को 19 से भाग देने पर शेषफल 11 है। / \(12^2=144\), and 144 leaves remainder 11 when divided by 19.
\(12^4\) के लिए \(11^2=121\) देखें। / For \(12^4\), check \(11^2=121\).
\(121=19\times6+7\), इसलिए शेषफल 7 है। / \(121=19\times6+7\), so the remainder is 7.
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C. 4
\(10^2=100\), और 100 को 17 से भाग देने पर शेषफल 15 है। / \(10^2=100\), and 100 leaves remainder 15 when divided by 17.
\(10^4\) के लिए \(15^2=225\) देखें। / For \(10^4\), check \(15^2=225\).
\(225=17\times13+4\), इसलिए शेषफल 4 है। / \(225=17\times13+4\), so the remainder is 4.
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D. 9
\(7^2=49\), और 49 को 13 से भाग देने पर शेषफल 10 है। / \(7^2=49\), and 49 leaves remainder 10 when divided by 13.
\(7^4\) के लिए \(10^2=100\) देखें। / For \(7^4\), check \(10^2=100\).
\(100=13\times7+9\), इसलिए शेषफल 9 है। / \(100=13\times7+9\), so the remainder is 9.
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B. 4
\(7^2=49\), और 49 को 9 से भाग देने पर शेषफल 4 है। / \(7^2=49\), which leaves remainder 4 on division by 9.
\(7^4\) के लिए \(4^2=16\), और 16 का 9 से शेषफल 7 नहीं, बल्कि 7 है; इसलिए सही शेषफल 7 होगा। / For \(7^4\), use \(4^2=16\), and 16 leaves remainder 7 on division by 9.
बड़ी घातों में हर चरण के बाद शेषफल घटाना जरूरी है। / In higher powers, reduce the remainder after each step.
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D. 4
चौथे घात के लिए \(4^4\) का शेषफल देखें। / For the fourth power, look at the remainder of \(4^4\).
\(4^2=16\), जिसका 7 से शेषफल 2 है; फिर \(4^4\) का शेषफल \(2^2=4\) होगा। / \(4^2=16\), which leaves remainder 2 when divided by 7; then \(4^4\) leaves the same remainder as \(2^2=4\).
बड़ी घातों में छोटे-छोटे चरणों में शेषफल निकालें। / For higher powers, reduce remainders step by step.
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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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The (10)th term of an AP is (62) and (d=5). What is \(a_1\)?
D. (17)
\(62=a+9\times5\) से (a=17)। (10)वें पद से पहले पद तक (9d) घटता है। / From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).
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Which term of the AP \(21,29,37,\ldots\) is (149)?
C. (17)वां(17)th
(149=21+(n-1)8) से (128=8(n-1)) इसलिए (n=17)। पद संख्या पूछी हो तो दिए पद को \(a_n\) मानें। / From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
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The (n)th term of the AP \(27,24,21,\ldots\) is (-30). What is (n)?
C. (20)
(-30=27+(n-1)(-3)) से (57=3(n-1)), इसलिए (n=20)। ऋणात्मक लक्ष्य पद में चिन्ह सावधानी से बदलें। / From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
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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)
\(50=x+9\times4\), इसलिए (x=14)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं। / \(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.
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In an AP, (a=30) and (d=-2). Which term will be (0)?
C. (16)वां(16)th
(0=30+(n-1)(-2)) से (2(n-1)=30), अतः (n=16)। शून्य पद के लिए भी वही (n)वां पद सूत्र लगाएं। / From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.
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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)। \(a_n<0\) से (n>10), इसलिए पहला ऋणात्मक पद (11)वां है। / (a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.
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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), इसलिए (96=6(n-1)) और (n=17)। पद संख्या में अंतर को (d) से भाग दें। / (111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).
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The (8)th term of an AP is (35) and (d=4). What is \(a_1\)?
C. (7)
\(35=a+7\times4\), इसलिए (a=7)। (8)वें पद के लिए (7d) घटाएं। / \(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).
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