A. क्योंकि बहुजातीय साम्राज्य टूट रहा था और तुर्की राष्ट्रीय राज्य की जरूरत उभरी/Because the multi ethnic empire was breaking and need for a Turkish nation state emerged
Step 1
Concept
The fall of empire made a new national framework important. For exams connect the Turkish Revolution with nation state building.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि बहुजातीय साम्राज्य टूट रहा था और तुर्की राष्ट्रीय राज्य की जरूरत उभरी / Because the multi ethnic empire was breaking and need for a Turkish nation state emerged. The fall of empire made a new national framework important. For exams connect the Turkish Revolution with nation state building.
Step 3
Exam Tip
साम्राज्य के पतन ने नए राष्ट्रीय ढांचे को महत्वपूर्ण बनाया। परीक्षा में तुर्की क्रांति को राष्ट्र राज्य निर्माण से जोड़ें।
A. क्योंकि नए राष्ट्र को राजवंश से अलग पहचान चाहिए थी/Because the new nation needed an identity separate from the dynasty
Step 1
Concept
Old symbols were linked with monarchy and privilege.
Step 2
Why this answer is correct
New symbols created the identity of a civic nation.
Step 3
Exam Tip
Connect symbolic change with political change. चरण 1: पुराने प्रतीक राजशाही और विशेषाधिकार से जुड़े थे। चरण 2: नए प्रतीकों ने नागरिक राष्ट्र की पहचान बनाई। चरण 3: प्रतीक परिवर्तन को सत्ता परिवर्तन से जोड़ें।
A. क्योंकि पुराने प्रतीक राजवंश और असमान सत्ता की याद दिलाते थे/Because old symbols reminded people of dynasty and unequal power
Step 1
Concept
Old symbols were linked with monarchy and privileges.
Step 2
Why this answer is correct
New symbols created a new identity of the civic nation.
Step 3
Exam Tip
Replacing symbols signals a change in political thinking. चरण 1: पुराने प्रतीक राजसत्ता और विशेषाधिकारों से जुड़े थे। चरण 2: नए प्रतीकों ने नागरिक राष्ट्र की नई पहचान बनाई। चरण 3: प्रतीक बदलना राजनीतिक सोच बदलने का संकेत होता है।
The two terms give (d=4) and (a=13), so \(S_{60}=7860\). Finding the common difference from distant terms is the first step.
Step 2
Why this answer is correct
The correct answer is D. (7860). The two terms give (d=4) and (a=13), so \(S_{60}=7860\). Finding the common difference from distant terms is the first step.
Step 3
Exam Tip
दो पदों से (d=4) और (a=13) मिलते हैं, इसलिए \(S_{60}=7860\) है। दूर के पदों से सार्व अंतर निकालना पहला कदम है।
The two terms give (d=4) and (a=0), so \(S_{40}=3120\). Finding the common difference from distant terms is the first step.
Step 2
Why this answer is correct
The correct answer is D. (3120). The two terms give (d=4) and (a=0), so \(S_{40}=3120\). Finding the common difference from distant terms is the first step.
Step 3
Exam Tip
दो पदों से (d=4) और (a=0) मिलते हैं, इसलिए \(S_{40}=3120\) है। दूर के पदों से सार्व अंतर निकालना पहला कदम है।
From (S_{15}=\frac{15}{2}(a+68)), (a=12), then (d=4) and \(S_{30}=2100\). Treat the given (n)th term as the last term.
Step 2
Why this answer is correct
The correct answer is C. (2100). From (S_{15}=\frac{15}{2}(a+68)), (a=12), then (d=4) and \(S_{30}=2100\). Treat the given (n)th term as the last term.
Step 3
Exam Tip
(S_{15}=\frac{15}{2}(a+68)) से (a=12), फिर (d=4) और \(S_{30}=2100\) है। दिए गए (n)वें पद को अंतिम पद की तरह लें।
The two terms give (d=3) and (a=8), so \(S_{50}=4075\). Finding the common difference from distant terms is the first step.
Step 2
Why this answer is correct
The correct answer is D. (4075). The two terms give (d=3) and (a=8), so \(S_{50}=4075\). Finding the common difference from distant terms is the first step.
Step 3
Exam Tip
दो पदों से (d=3) और (a=8) मिलता है, इसलिए \(S_{50}=4075\)। दूर के पदों से सार्व अंतर निकालना पहला कदम है।
From (S_{10}=5\(a+a_{10}\)), (a=3), then (d=4) and \(S_{20}=820\). When a last-like term is given, the average method helps.
Step 2
Why this answer is correct
The correct answer is C. (820). From (S_{10}=5\(a+a_{10}\)), (a=3), then (d=4) and \(S_{20}=820\). When a last-like term is given, the average method helps.
Step 3
Exam Tip
(S_{10}=5\(a+a_{10}\)) से (a=3), फिर (d=4) और \(S_{20}=820\)। अंतिम पद जैसा दिया हो तो औसत विधि काम आती है।
A. उन्हें हिंदू समाज के और विभाजन की आशंका थी/He feared further division of Hindu society
Step 1
Concept
Gandhi opposed separate electorates but a compromise was made on representation. Exam tip: remember Poona Pact.
Step 2
Why this answer is correct
The correct answer is A. उन्हें हिंदू समाज के और विभाजन की आशंका थी / He feared further division of Hindu society. Gandhi opposed separate electorates but a compromise was made on representation. Exam tip: remember Poona Pact.
Step 3
Exam Tip
गांधीजी ने पृथक निर्वाचन का विरोध किया लेकिन प्रतिनिधित्व के प्रश्न पर समझौता हुआ। परीक्षा में पूना समझौता याद रखें।
A. इससे भारत की एकता और भविष्य का संघ कमजोर हो सकता था/It could weaken India's unity and future federation
Step 1
Concept
This condition of Cripps proposals was linked with fear of partition. Exam tip: remember terms of proposals.
Step 2
Why this answer is correct
The correct answer is A. इससे भारत की एकता और भविष्य का संघ कमजोर हो सकता था / It could weaken India's unity and future federation. This condition of Cripps proposals was linked with fear of partition. Exam tip: remember terms of proposals.
Step 3
Exam Tip
क्रिप्स प्रस्तावों की यह शर्त विभाजन की आशंका से जुड़ी थी। परीक्षा में प्रस्ताव की शर्तें याद रखें।
A. यह युद्ध के बाद का वादा था और तत्काल सत्ता हस्तांतरण नहीं था/It was a post-war promise and not immediate transfer of power
Step 1
Concept
Cripps Mission could not meet the demand for immediate national government. Exam tip: remember proposal and reason for rejection.
Step 2
Why this answer is correct
The correct answer is A. यह युद्ध के बाद का वादा था और तत्काल सत्ता हस्तांतरण नहीं था / It was a post-war promise and not immediate transfer of power. Cripps Mission could not meet the demand for immediate national government. Exam tip: remember proposal and reason for rejection.
Step 3
Exam Tip
क्रिप्स मिशन तत्काल राष्ट्रीय सरकार की मांग पूरी नहीं कर सका। परीक्षा में प्रस्ताव और अस्वीकृति का कारण याद रखें।
The first term is (3), and the (80)th term is (556), so the sum is (22360). Finding the first and last terms from \(a_n\) is an easy method.
Step 2
Why this answer is correct
The correct answer is C. (22360). The first term is (3), and the (80)th term is (556), so the sum is (22360). Finding the first and last terms from \(a_n\) is an easy method.
Step 3
Exam Tip
पहला पद (3) और (80)वाँ पद (556) है, इसलिए योग (22360) है। \(a_n\) से पहला और अंतिम पद निकालना आसान तरीका है।
The numbers are \(111,124,\ldots,995\), and their sum is (38157). A remainder-based AP has common difference equal to the divisor.
Step 2
Why this answer is correct
The correct answer is D. (38157). The numbers are \(111,124,\ldots,995\), and their sum is (38157). A remainder-based AP has common difference equal to the divisor.
Step 3
Exam Tip
संख्याएँ \(111,124,\ldots,995\) हैं और उनका योग (38157) है। शेष वाली श्रेढ़ी का सार्व अंतर भाजक के बराबर होता है।
The first multiple is (209), the last is (1197), and there are (53) terms, so the sum is (37259). Choose the first multiple within the range correctly.
Step 2
Why this answer is correct
The correct answer is A. (37259). The first multiple is (209), the last is (1197), and there are (53) terms, so the sum is (37259). Choose the first multiple within the range correctly.
Step 3
Exam Tip
पहला गुणज (209), अंतिम (1197) और (53) पद हैं, इसलिए योग (37259) है। सीमा के अंदर पहला गुणज सही चुनें।
Subtracting the sum of multiples of (48) from the sum of multiples of (24) gives (1027752). In but-not cases, subtract the stricter condition.
Step 2
Why this answer is correct
The correct answer is D. (1027752). Subtracting the sum of multiples of (48) from the sum of multiples of (24) gives (1027752). In but-not cases, subtract the stricter condition.
Step 3
Exam Tip
(24) के गुणजों के योग से (48) के गुणजों का योग घटाने पर (1027752) मिलता है। but not में बड़ी शर्त को घटाना होता है।
The first number is (1036), the last is (9990), and there are (243) terms, so the sum is (1339659). Choose the first and last multiples carefully.
Step 2
Why this answer is correct
The correct answer is A. (1339659). The first number is (1036), the last is (9990), and there are (243) terms, so the sum is (1339659). Choose the first and last multiples carefully.
Step 3
Exam Tip
पहली संख्या (1036), अंतिम (9990) और कुल (243) पद हैं, इसलिए योग (1339659) है। पहला और अंतिम गुणज सावधानी से चुनें।
Subtracting the sum of multiples of (\operatorname{lcm}(18,30)) from the sum of multiples of (18) gives (83664). In a but-not condition, remove the overlap.
Step 2
Why this answer is correct
The correct answer is B. (83664). Subtracting the sum of multiples of (\operatorname{lcm}(18,30)) from the sum of multiples of (18) gives (83664). In a but-not condition, remove the overlap.
Step 3
Exam Tip
(18) के गुणजों के योग से (\operatorname{lcm}(18,30)) के गुणजों का योग घटाने पर (83664) मिलता है। but not वाली शर्त में overlap हटाएँ।
Subtracting the sum of multiples of (36) from the sum of multiples of (9) gives (93753). Numbers divisible by both are multiples of (\operatorname{lcm}(9,12)).
Step 2
Why this answer is correct
The correct answer is A. (93753). Subtracting the sum of multiples of (36) from the sum of multiples of (9) gives (93753). Numbers divisible by both are multiples of (\operatorname{lcm}(9,12)).
Step 3
Exam Tip
(9) के गुणजों के योग से (36) के गुणजों का योग घटाने पर (93753) मिलता है। दोनों से विभाज्य संख्याएँ (\operatorname{lcm}(9,12)) की गुणज होती हैं।
Subtracting the sum of multiples of (72) from the sum of multiples of (18) gives (28278). Use the least common multiple to remove overlap.
Step 2
Why this answer is correct
The correct answer is D. (28278). Subtracting the sum of multiples of (72) from the sum of multiples of (18) gives (28278). Use the least common multiple to remove overlap.
Step 3
Exam Tip
(18) के गुणजों के योग से (72) के गुणजों का योग घटाने पर (28278) मिलता है। overlap हटाने के लिए लघुत्तम समापवर्त्य लें।
The numbers are \(17,28,\ldots,94\), and the sum of (8) terms is (444). A remainder-based AP has common difference equal to the divisor.
Step 2
Why this answer is correct
The correct answer is A. (444). The numbers are \(17,28,\ldots,94\), and the sum of (8) terms is (444). A remainder-based AP has common difference equal to the divisor.
Step 3
Exam Tip
संख्याएँ \(17,28,\ldots,94\) हैं और (8) पदों का योग (444) है। शेष वाली श्रेढ़ी का अंतर भाजक के बराबर होता है।
Adding sums of multiples of (5) and (8), then subtracting multiples of (40), gives (150500). Avoiding double counting is important.
Step 2
Why this answer is correct
The correct answer is B. (150500). Adding sums of multiples of (5) and (8), then subtracting multiples of (40), gives (150500). Avoiding double counting is important.
Step 3
Exam Tip
(5) और (8) के गुणजों के योग जोड़कर (40) के गुणजों का योग घटाने से (150500) मिलता है। दोहरी गिनती से बचना जरूरी है।
Subtracting the sum of multiples of (50) from the sum of multiples of (10) gives (39600). Remove the common multiples of both conditions.
Step 2
Why this answer is correct
The correct answer is A. (39600). Subtracting the sum of multiples of (50) from the sum of multiples of (10) gives (39600). Remove the common multiples of both conditions.
Step 3
Exam Tip
(10) के गुणजों के योग से (50) के गुणजों का योग घटाने पर (39600) मिलता है। दोनों शर्तों के साझा गुणजों को हटाएँ।
The sum of all three-digit numbers is (494550), and the sum of multiples of (11) is (44550), so the answer is (450000). For not divisible, the complement method is fast.
Step 2
Why this answer is correct
The correct answer is C. (450000). The sum of all three-digit numbers is (494550), and the sum of multiples of (11) is (44550), so the answer is (450000). For not divisible, the complement method is fast.
Step 3
Exam Tip
तीन अंकों की सभी संख्याओं का योग (494550) है और (11) के गुणजों का योग (44550), इसलिए उत्तर (450000) है। विभाज्य नहीं में पूरक विधि तेज होती है।
The selected terms are \(a_5,a_{10},\ldots,a_{50}\), and their sum is (1875). In position-based questions, form the new AP of selected terms.
Step 2
Why this answer is correct
The correct answer is B. (1875). The selected terms are \(a_5,a_{10},\ldots,a_{50}\), and their sum is (1875). In position-based questions, form the new AP of selected terms.
Step 3
Exam Tip
चुने गए पद \(a_5,a_{10},\ldots,a_{50}\) हैं और उनका योग (1875) है। क्रमांक आधारित प्रश्न में चुने गए पदों की नई श्रेढ़ी बनाएँ।
The first term is (3), and the (70)th term is (348), so the sum is (12285). Finding the first and last terms from \(a_n\) is an easy method.
Step 2
Why this answer is correct
The correct answer is D. (12285). The first term is (3), and the (70)th term is (348), so the sum is (12285). Finding the first and last terms from \(a_n\) is an easy method.
Step 3
Exam Tip
पहला पद (3) और (70)वाँ पद (348) है, इसलिए योग (12285) है। \(a_n\) से पहले और अंतिम पद निकालना आसान तरीका है।
The numbers are \(13,22,\ldots,94\), and the sum of (10) terms is (535). In remainder questions, the common difference equals the divisor.
Step 2
Why this answer is correct
The correct answer is D. (535). The numbers are \(13,22,\ldots,94\), and the sum of (10) terms is (535). In remainder questions, the common difference equals the divisor.
Step 3
Exam Tip
संख्याएँ \(13,22,\ldots,94\) हैं और (10) पदों का योग (535) है। शेष वाले प्रश्न में सार्व अंतर भाजक के बराबर होता है।
The first multiple is (128), the last is (896), and there are (49) terms, so the sum is (25088). Choose the first term according to the range carefully.
Step 2
Why this answer is correct
The correct answer is A. (25088). The first multiple is (128), the last is (896), and there are (49) terms, so the sum is (25088). Choose the first term according to the range carefully.
Step 3
Exam Tip
पहला गुणज (128), अंतिम (896) और कुल (49) पद हैं, इसलिए योग (25088) है। सीमा के अनुसार पहला पद ध्यान से चुनें।
The numbers are \(105,147,\ldots,987\), and their sum is (12012). In this condition, the new AP has common difference (42).
Step 2
Why this answer is correct
The correct answer is D. (12012). The numbers are \(105,147,\ldots,987\), and their sum is (12012). In this condition, the new AP has common difference (42).
Step 3
Exam Tip
संख्याएँ \(105,147,\ldots,987\) हैं और उनका योग (12012) है। ऐसी शर्त में नई श्रेढ़ी का अंतर (42) हो जाता है।
The first number is (114), the last is (988), and there are (47) terms, so the sum is (25897). In divisibility questions, choose the first and last values carefully.
Step 2
Why this answer is correct
The correct answer is A. (25897). The first number is (114), the last is (988), and there are (47) terms, so the sum is (25897). In divisibility questions, choose the first and last values carefully.
Step 3
Exam Tip
पहली संख्या (114), अंतिम (988) और कुल (47) पद हैं, इसलिए योग (25897) है। विभाज्यता वाले प्रश्नों में पहला और अंतिम मान सावधानी से चुनें।
The numbers are \(153,170,\ldots,748\), and their sum is (16218). Choose the first and last multiples within the limits correctly.
Step 2
Why this answer is correct
The correct answer is B. (16218). The numbers are \(153,170,\ldots,748\), and their sum is (16218). Choose the first and last multiples within the limits correctly.
Step 3
Exam Tip
संख्याएँ \(153,170,\ldots,748\) हैं और उनका योग (16218) है। सीमा के अंदर पहला और अंतिम गुणज सही चुनें।
Subtracting the sum of multiples of (30) from the sum of multiples of (6) gives (66336). Numbers divisible by both (6) and (15) are multiples of (30).
Step 2
Why this answer is correct
The correct answer is C. (66336). Subtracting the sum of multiples of (30) from the sum of multiples of (6) gives (66336). Numbers divisible by both (6) and (15) are multiples of (30).
Step 3
Exam Tip
(6) के गुणजों के योग से (30) के गुणजों का योग घटाने पर (66336) मिलता है। (6) और (15) दोनों से विभाज्य संख्याएँ (30) की गुणज होती हैं।
Subtracting the sum of multiples of (36) from the sum of multiples of (12) gives (26460). Use the least common multiple to remove overlap.
Step 2
Why this answer is correct
The correct answer is A. (26460). Subtracting the sum of multiples of (36) from the sum of multiples of (12) gives (26460). Use the least common multiple to remove overlap.
Step 3
Exam Tip
(12) के गुणजों के योग से (36) के गुणजों का योग घटाने पर (26460) मिलता है। overlap हटाने के लिए लघुत्तम समापवर्त्य लें।
The numbers are \(11,17,\ldots,95\), and the sum of (15) terms is (795). A remainder-based AP has common difference equal to the divisor.
Step 2
Why this answer is correct
The correct answer is B. (795). The numbers are \(11,17,\ldots,95\), and the sum of (15) terms is (795). A remainder-based AP has common difference equal to the divisor.
Step 3
Exam Tip
संख्याएँ \(11,17,\ldots,95\) हैं और (15) पदों का योग (795) है। remainder वाली श्रेढ़ी का अंतर भाजक के बराबर होता है।
Adding sums of multiples of (4) and (7), then subtracting multiples of (28), gives (87850). Avoiding double counting is important.
Step 2
Why this answer is correct
The correct answer is A. (87850). Adding sums of multiples of (4) and (7), then subtracting multiples of (28), gives (87850). Avoiding double counting is important.
Step 3
Exam Tip
(4) और (7) के गुणजों के योग जोड़कर (28) के गुणजों का योग घटाने से (87850) मिलता है। दोहरी गिनती से बचना जरूरी है।
Subtracting the sum of multiples of (24) from the sum of multiples of (8) gives (33368). In a but-not condition, subtract the complement.
Step 2
Why this answer is correct
The correct answer is C. (33368). Subtracting the sum of multiples of (24) from the sum of multiples of (8) gives (33368). In a but-not condition, subtract the complement.
Step 3
Exam Tip
(8) के गुणजों के योग से (24) के गुणजों का योग घटाने पर (33368) मिलता है। but not वाली शर्त में पूरक घटाएँ।
The sum of all three-digit numbers is (494550), and the sum of multiples of (9) is (55350), so the answer is (439200). For not divisible, the complement method is fast.
Step 2
Why this answer is correct
The correct answer is B. (439200). The sum of all three-digit numbers is (494550), and the sum of multiples of (9) is (55350), so the answer is (439200). For not divisible, the complement method is fast.
Step 3
Exam Tip
तीन अंकों की सभी संख्याओं का योग (494550) है और (9) के गुणजों का योग (55350), इसलिए उत्तर (439200) है। not divisible में पूरक विधि तेज होती है।
The selected terms are \(a_4,a_8,\ldots,a_{40}\), and their sum is (1060). In position-based questions, form the new AP of selected terms.
Step 2
Why this answer is correct
The correct answer is A. (1060). The selected terms are \(a_4,a_8,\ldots,a_{40}\), and their sum is (1060). In position-based questions, form the new AP of selected terms.
Step 3
Exam Tip
चुने गए पद \(a_4,a_8,\ldots,a_{40}\) हैं और उनका योग (1060) है। क्रमांक आधारित प्रश्न में चुने गए पदों की नई श्रेढ़ी बनाएँ।
The first term is (11), and the (60)th term is (365), so the sum is (11280). Finding the first and last terms from \(a_n\) is an easy method.
Step 2
Why this answer is correct
The correct answer is A. (11280). The first term is (11), and the (60)th term is (365), so the sum is (11280). Finding the first and last terms from \(a_n\) is an easy method.
Step 3
Exam Tip
पहला पद (11) और (60)वाँ पद (365) है, इसलिए योग (11280) है। \(a_n\) से पहले और अंतिम पद निकालना आसान तरीका है।
The numbers are \(11,19,\ldots,99\), and the sum of (12) terms is (660). In remainder questions, the common difference equals the divisor.
Step 2
Why this answer is correct
The correct answer is A. (660). The numbers are \(11,19,\ldots,99\), and the sum of (12) terms is (660). In remainder questions, the common difference equals the divisor.
Step 3
Exam Tip
संख्याएँ \(11,19,\ldots,99\) हैं और (12) पदों का योग (660) है। शेष वाले प्रश्न में सार्व अंतर भाजक के बराबर होता है।
The first multiple is (91), the last is (598), and there are (40) terms, so the sum is (13780). Choose the first term according to the range carefully.
Step 2
Why this answer is correct
The correct answer is C. (13780). The first multiple is (91), the last is (598), and there are (40) terms, so the sum is (13780). Choose the first term according to the range carefully.
Step 3
Exam Tip
पहला गुणज (91), अंतिम (598) और कुल (40) पद हैं, इसलिए योग (13780) है। सीमा के अनुसार पहला पद ध्यान से चुनें।
The numbers are \(105,135,\ldots,975\), and their sum is (16200). In this condition, the new AP has common difference (30).
Step 2
Why this answer is correct
The correct answer is B. (16200). The numbers are \(105,135,\ldots,975\), and their sum is (16200). In this condition, the new AP has common difference (30).
Step 3
Exam Tip
संख्याएँ \(105,135,\ldots,975\) हैं और उनका योग (16200) है। ऐसी शर्त में नई श्रेढ़ी का अंतर (30) हो जाता है।
