100 results found for "binomial-term-trend" 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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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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Which of the following is a binomial?
A. \(x^2+3\)
A polynomial with two terms is a binomial. \(x^2+3\) has two terms.
The correct answer is A. \(x^2+3\). A polynomial with two terms is a binomial. \(x^2+3\) has two terms.
दो पदों वाला बहुपद द्विपदी कहलाता है। \(x^2+3\) में दो पद हैं।
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Which polynomial is a binomial?
B. (5x-7)
A binomial has two terms. The expression (5x-7) has the two terms (5x) and (-7).
The correct answer is B. (5x-7). A binomial has two terms. The expression (5x-7) has the two terms (5x) and (-7).
द्विपदी में दो पद होते हैं। (5x-7) में (5x) और (-7) दो पद हैं।
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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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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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Which structural trend in European colonialism was made clear by the Treaty of Tordesillas?
A. यूरोपीय शक्तियां बाहरी क्षेत्रों पर दावे को वैध बनाना चाहती थींEuropean powers wanted to legitimize claims over overseas territories
This treaty divided Spanish and Portuguese claims from a European viewpoint. For exams connect it with maritime expansion and colonial claims.
The correct answer is A. यूरोपीय शक्तियां बाहरी क्षेत्रों पर दावे को वैध बनाना चाहती थीं / European powers wanted to legitimize claims over overseas territories. This treaty divided Spanish and Portuguese claims from a European viewpoint. For exams connect it with maritime expansion and colonial claims.
इस संधि ने स्पेन और पुर्तगाल के दावों को यूरोपीय दृष्टि से बांटा। परीक्षा में इसे समुद्री विस्तार और औपनिवेशिक दावे से जोड़ें।
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What trend does the Dutch East India Company show in Asian colonialism?
A. व्यापारिक कंपनी का राजनीतिक और आर्थिक नियंत्रण में बदलनाA trading company changing into political and economic control
The Dutch company expanded colonial influence along with trade. For exams remember the Netherlands and Indonesia together.
The correct answer is A. व्यापारिक कंपनी का राजनीतिक और आर्थिक नियंत्रण में बदलना / A trading company changing into political and economic control. The Dutch company expanded colonial influence along with trade. For exams remember the Netherlands and Indonesia together.
डच कंपनी ने व्यापार के साथ औपनिवेशिक प्रभाव भी बढ़ाया। परीक्षा में नीदरलैंड और इंडोनेशिया साथ याद रखें।
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The East India Company's shift from trading power to political power shows which trend?
A. व्यापारिक संस्थाएं औपनिवेशिक शासन का आधार बन सकती थींTrading bodies could become bases of colonial rule
The East India Company expanded from trade to administrative and political control. For exams understand the shift from trade to rule.
The correct answer is A. व्यापारिक संस्थाएं औपनिवेशिक शासन का आधार बन सकती थीं / Trading bodies could become bases of colonial rule. The East India Company expanded from trade to administrative and political control. For exams understand the shift from trade to rule.
ईस्ट इंडिया कंपनी ने व्यापार से प्रशासनिक और राजनीतिक नियंत्रण की ओर विस्तार किया। परीक्षा में व्यापार से शासन तक का क्रम समझें।
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What trend in Europe is understood by studying Waterloo and the Congress of Vienna together?
A. क्रांतिकारी उथल पुथल के बाद शक्ति संतुलन बहाल करने की कोशिशAttempt to restore balance of power after revolutionary upheaval
Waterloo ended the Napoleonic era and Vienna shaped a new order. For exams remember both war and diplomacy.
The correct answer is A. क्रांतिकारी उथल पुथल के बाद शक्ति संतुलन बहाल करने की कोशिश / Attempt to restore balance of power after revolutionary upheaval. Waterloo ended the Napoleonic era and Vienna shaped a new order. For exams remember both war and diplomacy.
वाटरलू ने नेपोलियन युग समाप्त किया और वियना ने नई व्यवस्था बनाई। परीक्षा में युद्ध और कूटनीति दोनों याद रखें।
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NATO and the Warsaw Pact are examples of which Cold War trend?
B. सैन्य खेमाबंदीMilitary bloc formation
NATO was linked with the western bloc and Warsaw Pact with the Soviet bloc. For exams remember both as rival military alliances.
The correct answer is B. सैन्य खेमाबंदी / Military bloc formation. NATO was linked with the western bloc and Warsaw Pact with the Soviet bloc. For exams remember both as rival military alliances.
नाटो पश्चिमी खेमे और वारसॉ संधि सोवियत खेमे से जुड़ी थी। परीक्षा में दोनों को विरोधी सैन्य गठबंधन के रूप में याद रखें।
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The Berlin Blockade showed which trend of the Cold War?
A. पूर्व और पश्चिम के बीच सीधे सैन्य युद्ध के बिना तीखा तनावSharp tension without direct military war between East and West
The Berlin Blockade increased Cold War tension in Europe. For exams connect it with the Berlin Airlift.
The correct answer is A. पूर्व और पश्चिम के बीच सीधे सैन्य युद्ध के बिना तीखा तनाव / Sharp tension without direct military war between East and West. The Berlin Blockade increased Cold War tension in Europe. For exams connect it with the Berlin Airlift.
बर्लिन नाकेबंदी ने यूरोप में शीत युद्ध का तनाव बढ़ाया। परीक्षा में इसे बर्लिन एयरलिफ्ट से जोड़ें।
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Gamal Abdel Nasser and Kwame Nkrumah were linked with which common historical trend?
A. उपनिवेश विरोधी राष्ट्रवादAnti colonial nationalism
Nasser and Nkrumah strengthened politics of independence and national dignity. Exam tip: connect them with decolonization.
The correct answer is A. उपनिवेश विरोधी राष्ट्रवाद / Anti colonial nationalism. Nasser and Nkrumah strengthened politics of independence and national dignity. Exam tip: connect them with decolonization.
नासिर और नक्रूमा दोनों ने स्वतंत्रता और राष्ट्रीय सम्मान की राजनीति को मजबूत किया। परीक्षा में इन्हें उपनिवेश मुक्ति से जोड़ें।
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Franco's rule in twentieth century Europe was linked with which trend?
A. अधिनायकवादी दक्षिणपंथी शासनAuthoritarian right wing rule
Franco was linked with long authoritarian rule in Spain. For exams connect him with politics after the Spanish Civil War.
The correct answer is A. अधिनायकवादी दक्षिणपंथी शासन / Authoritarian right wing rule. Franco was linked with long authoritarian rule in Spain. For exams connect him with politics after the Spanish Civil War.
फ्रांको स्पेन में दीर्घकालीन अधिनायकवादी शासन से जुड़े थे। परीक्षा में उन्हें स्पेनिश गृहयुद्ध के बाद की राजनीति से जोड़ें।
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Margaret Thatcher's economic policy is linked with which trend?
A. निजीकरण बाजार समर्थक सुधार और ट्रेड यूनियन शक्ति घटानाPrivatization market oriented reform and reducing trade union power
Thatcherism is linked with market oriented policies and reducing state role. For exams connect it with modern British economic change.
The correct answer is A. निजीकरण बाजार समर्थक सुधार और ट्रेड यूनियन शक्ति घटाना / Privatization market oriented reform and reducing trade union power. Thatcherism is linked with market oriented policies and reducing state role. For exams connect it with modern British economic change.
थैचरवाद बाजार समर्थक और राज्य भूमिका घटाने वाली नीतियों से जुड़ा है। परीक्षा में इसे आधुनिक ब्रिटिश आर्थिक बदलाव से जोड़ें।
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Napoleon's success and failure together show which broad historical trend?
A. क्रांतिकारी विचारों का प्रसार और साम्राज्यवादी विस्तार की सीमाSpread of revolutionary ideas and limits of imperial expansion
Napoleon spread revolutionary laws but imperial expansion was not lasting. For exams write both achievement and limitation.
The correct answer is A. क्रांतिकारी विचारों का प्रसार और साम्राज्यवादी विस्तार की सीमा / Spread of revolutionary ideas and limits of imperial expansion. Napoleon spread revolutionary laws but imperial expansion was not lasting. For exams write both achievement and limitation.
नेपोलियन ने क्रांतिकारी कानूनों को फैलाया पर साम्राज्य विस्तार टिकाऊ नहीं रहा। परीक्षा में उपलब्धि और सीमा दोनों लिखें।
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The General Agreement on Tariffs and Trade was linked with which post-war trend?
A. व्यापार बाधाएं घटाकर आर्थिक सहयोग बढ़ानाReducing trade barriers and increasing economic cooperation
In the post-war order open trade was seen as a tool of stability. For exams connect economic cooperation with peace order.
The correct answer is A. व्यापार बाधाएं घटाकर आर्थिक सहयोग बढ़ाना / Reducing trade barriers and increasing economic cooperation. In the post-war order open trade was seen as a tool of stability. For exams connect economic cooperation with peace order.
युद्धोत्तर व्यवस्था में खुला व्यापार स्थिरता का साधन माना गया। परीक्षा में आर्थिक सहयोग को शांति व्यवस्था से जोड़ें।
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Which wider trend became clear from Japan's behavior in the Manchuria crisis?
C. आक्रामक विस्तारवाद और राष्ट्र संघ की कमजोरीAggressive expansionism and League weakness
The Manchuria crisis showed that aggressive states were not being stopped easily. For exams connect Japanese expansionism with the background of the Second World War.
The correct answer is C. आक्रामक विस्तारवाद और राष्ट्र संघ की कमजोरी / Aggressive expansionism and League weakness. The Manchuria crisis showed that aggressive states were not being stopped easily. For exams connect Japanese expansionism with the background of the Second World War.
मंचूरिया संकट ने दिखाया कि आक्रामक देश आसानी से नहीं रुक रहे थे। परीक्षा में जापानी विस्तारवाद को द्वितीय विश्व युद्ध की पृष्ठभूमि से जोड़ें।
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The formation of NATO and the Warsaw Pact shows which broader trend?
A. शीत युद्ध में सैन्य गुटबंदीMilitary bloc formation in the Cold War
These alliances divided the world into two military blocs. For exams remember NATO and Warsaw Pact as opposing blocs.
The correct answer is A. शीत युद्ध में सैन्य गुटबंदी / Military bloc formation in the Cold War. These alliances divided the world into two military blocs. For exams remember NATO and Warsaw Pact as opposing blocs.
इन गठबंधनों ने विश्व को दो सैन्य गुटों में बांटा। परीक्षा में नाटो और वारसा संधि को विरोधी गुटों के रूप में याद रखें।
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The presence of Hindu Jain and Buddhist art in Badami Caves shows which cultural trend?
A. धार्मिक विविधताReligious diversity
Badami Caves show rock-cut art with religious diversity. In exams connect them with the Chalukya period.
The correct answer is A. धार्मिक विविधता / Religious diversity. Badami Caves show rock-cut art with religious diversity. In exams connect them with the Chalukya period.
बादामी गुफाएं धार्मिक विविधता वाली शैलकृत कला को दिखाती हैं। परीक्षा में इन्हें चालुक्य काल से जोड़ें।
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Jahangir's interest in naturalistic painting shows which intellectual trend of the Mughal court?
A. सूक्ष्म अवलोकन और प्रकृति के प्रति जिज्ञासाClose observation and curiosity about nature
Jahangir was famous for patronage of naturalistic paintings. Link it with art and observation.
The correct answer is A. सूक्ष्म अवलोकन और प्रकृति के प्रति जिज्ञासा / Close observation and curiosity about nature. Jahangir was famous for patronage of naturalistic paintings. Link it with art and observation.
जहांगीर प्राकृतिक चित्रों के संरक्षण के लिए प्रसिद्ध था। इसे कला और अवलोकन से जोड़ें।
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What shared trend of state defence is seen in the policies of Hyder Ali and Tipu Sultan?
A. मैसूर की सैन्य शक्ति को मजबूत कर ब्रिटिश दबाव का सामना करनाStrengthening Mysore's military power to face British pressure
Both Hyder Ali and Tipu were linked with Mysore's power and resistance to the British. Study them in the context of state defence.
The correct answer is A. मैसूर की सैन्य शक्ति को मजबूत कर ब्रिटिश दबाव का सामना करना / Strengthening Mysore's military power to face British pressure. Both Hyder Ali and Tipu were linked with Mysore's power and resistance to the British. Study them in the context of state defence.
हैदर अली और टीपू दोनों मैसूर की शक्ति और ब्रिटिश विरोध से जुड़े थे। उन्हें राज्य रक्षा के संदर्भ में पढ़ें।
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Jahangir's patronage of naturalistic painting is linked with which trend of the Mughal court?
A. सूक्ष्म अवलोकन और सौंदर्यबोधClose observation and aesthetic sense
Jahangir was famous for patronage of art and naturalistic paintings. Link it with the development of Mughal painting.
The correct answer is A. सूक्ष्म अवलोकन और सौंदर्यबोध / Close observation and aesthetic sense. Jahangir was famous for patronage of art and naturalistic paintings. Link it with the development of Mughal painting.
जहांगीर कला और प्राकृतिक चित्रों के संरक्षण के लिए प्रसिद्ध था। इसे मुगल चित्रकला के विकास से जोड़ें।
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Maharaja Chhatrasal's struggle in Bundelkhand is an example of which broader trend?
A. क्षेत्रीय शक्तियों द्वारा मुगल प्रभुत्व को चुनौतीRegional powers challenging Mughal dominance
Chhatrasal was linked with Bundela power in Bundelkhand. Link him with regional resistance against Mughal authority.
The correct answer is A. क्षेत्रीय शक्तियों द्वारा मुगल प्रभुत्व को चुनौती / Regional powers challenging Mughal dominance. Chhatrasal was linked with Bundela power in Bundelkhand. Link him with regional resistance against Mughal authority.
छत्रसाल बुंदेलखंड की बुंदेला शक्ति से जुड़े थे। उन्हें मुगल सत्ता के विरुद्ध क्षेत्रीय प्रतिरोध से जोड़ें।
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Which trend especially increased in painting during Jahangir's reign?
B. प्राकृतिक चित्रणNaturalistic depiction
Jahangir was famous for naturalistic depiction and patronage of painting. Link him with Mughal art.
The correct answer is B. प्राकृतिक चित्रण / Naturalistic depiction. Jahangir was famous for naturalistic depiction and patronage of painting. Link him with Mughal art.
जहांगीर प्राकृतिक चित्रण और चित्रकला संरक्षण के लिए प्रसिद्ध था। उसे मुगल कला से जोड़ें।
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The Wahabi Movement in India was associated with what kind of trend?
A. धार्मिक सुधार और औपनिवेशिक विरोधReligious reform and anti-colonial opposition
The Wahabi Movement was linked with religious reform and opposition to colonial rule. Place it among nineteenth-century movements in exams.
The correct answer is A. धार्मिक सुधार और औपनिवेशिक विरोध / Religious reform and anti-colonial opposition. The Wahabi Movement was linked with religious reform and opposition to colonial rule. Place it among nineteenth-century movements in exams.
वाहाबी आंदोलन धार्मिक सुधार और औपनिवेशिक शासन के विरोध से जुड़ा था। परीक्षा में इसे उन्नीसवीं शताब्दी के आंदोलनों में रखें।
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The Alipore Bomb Case was related to which revolutionary trend?
C. बंगाल की क्रांतिकारी गतिविधियाँRevolutionary activities in Bengal
The Alipore Bomb Case was linked with revolutionary activities in Bengal. Connect it with the militant nationalist phase.
The correct answer is C. बंगाल की क्रांतिकारी गतिविधियाँ / Revolutionary activities in Bengal. The Alipore Bomb Case was linked with revolutionary activities in Bengal. Connect it with the militant nationalist phase.
अलिपुर बम केस बंगाल की क्रांतिकारी गतिविधियों से जुड़ा था। इसे उग्र राष्ट्रवादी दौर से जोड़ें।
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Satara's Prati Sarkar was evidence of which trend in Quit India Movement?
A. स्थानीय समानांतर शासन की कोशिशAttempt at local parallel government
Prati Sarkar was an example of local alternative authority. Exam tip: remember Satara, Ballia and Tamluk.
The correct answer is A. स्थानीय समानांतर शासन की कोशिश / Attempt at local parallel government. Prati Sarkar was an example of local alternative authority. Exam tip: remember Satara, Ballia and Tamluk.
प्रति सरकार स्थानीय वैकल्पिक सत्ता का उदाहरण थी। परीक्षा में सतारा, बलिया और तामलुक याद रखें।
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Satara's Prati Sarkar was an example of which trend of Quit India Movement?
A. स्थानीय समानांतर शासनLocal parallel government
Prati Sarkar was an attempt of local alternative authority. Exam tip: remember examples of parallel governments.
The correct answer is A. स्थानीय समानांतर शासन / Local parallel government. Prati Sarkar was an attempt of local alternative authority. Exam tip: remember examples of parallel governments.
प्रति सरकार स्थानीय जनता की वैकल्पिक सत्ता की कोशिश थी। परीक्षा में समानांतर सरकारों के उदाहरण याद रखें।
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Satara's Prati Sarkar was an example of which broader trend in the freedom movement?
A. स्थानीय वैकल्पिक शासन और जन सत्ता की कल्पनाLocal alternative government and imagination of popular power
Prati Sarkar gave institutional form to local resistance of 1942. Exam tip: study examples of parallel governments.
The correct answer is A. स्थानीय वैकल्पिक शासन और जन सत्ता की कल्पना / Local alternative government and imagination of popular power. Prati Sarkar gave institutional form to local resistance of 1942. Exam tip: study examples of parallel governments.
प्रति सरकार ने 1942 के स्थानीय प्रतिरोध को संस्थागत रूप दिया। परीक्षा में समानांतर सरकारों के उदाहरण पढ़ें।
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The rise of organizations like Anushilan Samiti shows which trend of the Swadeshi period?
A. क्रांतिकारी राष्ट्रवाद का विकासGrowth of revolutionary nationalism
During the Swadeshi phase some youth adopted the armed path. Exam tip is to remember Bengal revolutionary networks.
The correct answer is A. क्रांतिकारी राष्ट्रवाद का विकास / Growth of revolutionary nationalism. During the Swadeshi phase some youth adopted the armed path. Exam tip is to remember Bengal revolutionary networks.
स्वदेशी काल में कुछ युवाओं ने सशस्त्र मार्ग अपनाया। परीक्षा में बंगाल के क्रांतिकारी नेटवर्क याद रखें।
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Which trend intensified in Indian politics after Direct Action Day?
A. साम्प्रदायिक ध्रुवीकरणCommunal polarisation
The violence of 1946 accelerated the move toward partition. Exam tip: connect Direct Action Day with background of partition.
The correct answer is A. साम्प्रदायिक ध्रुवीकरण / Communal polarisation. The violence of 1946 accelerated the move toward partition. Exam tip: connect Direct Action Day with background of partition.
1946 की हिंसा ने विभाजन की दिशा को और तेज किया। परीक्षा में प्रत्यक्ष कार्रवाई दिवस को विभाजन की पृष्ठभूमि से जोड़ें।
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The formation of Congress Socialist Party in 1934 shows which trend?
C. राष्ट्रीय आंदोलन में समाजवादी विचारों का प्रवेशEntry of socialist ideas into the national movement
The Congress Socialist Party linked the freedom struggle with social and economic change. Exam tip is to connect Jayaprakash Narayan with it.
The correct answer is C. राष्ट्रीय आंदोलन में समाजवादी विचारों का प्रवेश / Entry of socialist ideas into the national movement. The Congress Socialist Party linked the freedom struggle with social and economic change. Exam tip is to connect Jayaprakash Narayan with it.
कांग्रेस सोशलिस्ट पार्टी ने स्वतंत्रता संघर्ष को सामाजिक आर्थिक बदलाव से भी जोड़ा। परीक्षा में जयप्रकाश नारायण को इससे जोड़ें।
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Lal Bal Pal represented which political trend?
C. उग्रवादी राष्ट्रवादExtremist nationalism
Lala Lajpat Rai, Bal Gangadhar Tilak and Bipin Chandra Pal were the Extremist trio. Exam tip: remember all three names together.
The correct answer is C. उग्रवादी राष्ट्रवाद / Extremist nationalism. Lala Lajpat Rai, Bal Gangadhar Tilak and Bipin Chandra Pal were the Extremist trio. Exam tip: remember all three names together.
लाला लाजपत राय, बाल गंगाधर तिलक और बिपिन चंद्र पाल उग्रवादी नेताओं की त्रयी थे। परीक्षा में तीनों नाम साथ याद रखें।
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What trend became clear in the Mughal Empire after Aurangzeb?
A. केंद्रीय शक्ति का कमजोर होनाWeakening of central power
After Aurangzeb the Mughal central authority began to weaken. For exams, connect it with the rise of regional powers.
The correct answer is A. केंद्रीय शक्ति का कमजोर होना / Weakening of central power. After Aurangzeb the Mughal central authority began to weaken. For exams, connect it with the rise of regional powers.
औरंगजेब के बाद मुगल केंद्रीय सत्ता कमजोर होने लगी। परीक्षा में क्षेत्रीय शक्तियों के उभार से जोड़ें।
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Which trend especially developed in Mughal painting during Jahangir's reign?
A. प्राकृतिक चित्रणNaturalistic painting
Jahangir promoted paintings of natural objects and animals. For exams, remember him as a ruler fond of painting.
The correct answer is A. प्राकृतिक चित्रण / Naturalistic painting. Jahangir promoted paintings of natural objects and animals. For exams, remember him as a ruler fond of painting.
जहांगीर ने प्राकृतिक वस्तुओं और जीव जंतुओं के चित्रों को बढ़ावा दिया। परीक्षा में उसे चित्रकला प्रेमी शासक मानें।
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Sandstone and shrine plan in Kailasanatha temple at Kanchipuram show which Pallava trend?
A. संरचनात्मक शैव मंदिर निर्माण का विकासDevelopment of structural Shaiva temple building
Kailasanatha temple is a major example of Pallava Shaiva structural temple. For exams, connect it with Rajasimha Pallava.
The correct answer is A. संरचनात्मक शैव मंदिर निर्माण का विकास / Development of structural Shaiva temple building. Kailasanatha temple is a major example of Pallava Shaiva structural temple. For exams, connect it with Rajasimha Pallava.
कैलासनाथ मंदिर पल्लव कालीन शैव संरचनात्मक मंदिर का प्रमुख उदाहरण है। परीक्षा में इसे राजसिंह पल्लव से जोड़ें।
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Vaishnava sculpture in the Deogarh Dashavatara Temple reflects which Gupta period trend?
A. पुराणिक धार्मिक रूपों का मंदिर कला में विकासDevelopment of Puranic religious forms in temple art
Deogarh temple is an example of Gupta Vaishnava and structural temple art. For exams, study Puranic religion with temple architecture.
The correct answer is A. पुराणिक धार्मिक रूपों का मंदिर कला में विकास / Development of Puranic religious forms in temple art. Deogarh temple is an example of Gupta Vaishnava and structural temple art. For exams, study Puranic religion with temple architecture.
देवगढ़ मंदिर गुप्तकालीन वैष्णव और संरचनात्मक मंदिर कला का उदाहरण है। परीक्षा में पुराणिक धर्म और मंदिर स्थापत्य को साथ पढ़ें।
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The Nalanda tradition under Kumaragupta I shows which broader Gupta period trend?
B. शिक्षा और धार्मिक संस्थाओं का संरक्षणPatronage of education and religious institutions
Nalanda was an important centre linked with Gupta patronage of learning. For exams, connect educational institutions with royal support.
The correct answer is B. शिक्षा और धार्मिक संस्थाओं का संरक्षण / Patronage of education and religious institutions. Nalanda was an important centre linked with Gupta patronage of learning. For exams, connect educational institutions with royal support.
नालंदा गुप्तकालीन शिक्षा संरक्षण से जुड़ा महत्वपूर्ण केंद्र था। परीक्षा में शिक्षा संस्थानों को राजकीय संरक्षण से जोड़ें।
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Gupta land grant inscriptions indicate which trend?
A. राजस्व अधिकारों का हस्तांतरणTransfer of revenue rights
Land grants sometimes transferred revenue and administrative rights. For exams, connect land grants with socio-economic change.
The correct answer is A. राजस्व अधिकारों का हस्तांतरण / Transfer of revenue rights. Land grants sometimes transferred revenue and administrative rights. For exams, connect land grants with socio-economic change.
भूमि दान में कभी-कभी राजस्व और प्रशासनिक अधिकार भी दिए जाते थे। परीक्षा में भूमि दान को सामाजिक आर्थिक बदलाव से जोड़ें।
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What trend of European nationalism is shown by examples like Britannia Marianne and Germania?
A. राष्ट्रों को मानवीकृत प्रतीकों के रूप में दिखाने की प्रवृत्तिThe trend of showing nations as personified symbols
In all these examples the nation was shown through a figure.
This was a trend of giving a human form to the abstract nation.
Such visual language was influential in European nationalism. चरण 1: इन सभी उदाहरणों में राष्ट्र को किसी आकृति के माध्यम से दिखाया गया। चरण 2: यह अमूर्त राष्ट्र को मानवीय रूप देने की प्रवृत्ति थी। चरण 3: यूरोपीय राष्ट्रवाद में ऐसी दृश्य भाषा बहुत प्रभावशाली रही।
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Belgium's separation from the Netherlands was part of which wider historical trend?
A. राष्ट्रीय आत्मनिर्णय की मांगDemand for national self-determination
Belgians demanded a separate political identity.
This demand was linked with national feeling and self-determination.
Connect it with the nationalist wave after 1830. चरण 1: बेल्जियम के लोगों ने अलग राजनीतिक पहचान की मांग की। चरण 2: यह मांग राष्ट्रीय भावना और आत्मनिर्णय से जुड़ी थी। चरण 3: इसे अठारह सौ तीस के बाद फैली राष्ट्रवादी लहर से जोड़ें।
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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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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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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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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 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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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 (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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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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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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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 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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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 (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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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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