The first difference is (12-5=7), and the second is (26-19=7). Equal differences confirm an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. (7) और (7) / (7) and (7). The first difference is (12-5=7), and the second is (26-19=7). Equal differences confirm an arithmetic progression.
Step 3
Exam Tip
पहला अंतर (12-5=7) और दूसरा (26-19=7) है। समान अंतर समांतर श्रेढ़ी की पुष्टि करता है।
The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.
Step 2
Why this answer is correct
The correct answer is B. (2d). The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.
Step 3
Exam Tip
नए अनुक्रम में दो-दो मूल पदों की छलांग है, इसलिए अंतर (2d) है। परीक्षा में पद-संख्या की छलांग को (d) से गुणा करें।
The new sequence jumps three original terms each time, so its difference is (3d=12). In exams, count the gap between selected term numbers.
Step 2
Why this answer is correct
The correct answer is C. (12). The new sequence jumps three original terms each time, so its difference is (3d=12). In exams, count the gap between selected term numbers.
Step 3
Exam Tip
नए अनुक्रम में हर बार तीन पदों की छलांग है, इसलिए अंतर (3d=12) है। परीक्षा में चुने गए पदों के बीच की दूरी गिनें।
Multiplying by \(\frac{1}{3}\) changes the difference from (-9) to (-3), and adding (5) does not change it. In exams, separate the effects of addition and multiplication.
Step 2
Why this answer is correct
The correct answer is C. (-3). Multiplying by \(\frac{1}{3}\) changes the difference from (-9) to (-3), and adding (5) does not change it. In exams, separate the effects of addition and multiplication.
Step 3
Exam Tip
\(\frac{1}{3}\) से गुणा करने पर अंतर (-9) से (-3) हो जाता है, और (5) जोड़ने से अंतर नहीं बदलता। परीक्षा में जोड़ और गुणन के प्रभाव अलग करें।
Multiplying terms by (2) multiplies the difference by (2), so it becomes (8). In exams, adding or subtracting a constant does not change the difference, but multiplication does.
Step 2
Why this answer is correct
The correct answer is D. (8). Multiplying terms by (2) multiplies the difference by (2), so it becomes (8). In exams, adding or subtracting a constant does not change the difference, but multiplication does.
Step 3
Exam Tip
पदों को (2) से गुणा करने पर अंतर भी (2) गुना हो जाता है, इसलिए (8)। परीक्षा में जोड़ना-घटाना अंतर नहीं बदलता, गुणा बदलता है।
The first sequence has (d=4) and the second has (d=6), so the difference sequence has (d=4-6=-2). In termwise difference, take the difference of common differences.
Step 2
Why this answer is correct
The correct answer is A. (-2). The first sequence has (d=4) and the second has (d=6), so the difference sequence has (d=4-6=-2). In termwise difference, take the difference of common differences.
Step 3
Exam Tip
पहले अनुक्रम का (d=4) और दूसरे का (d=6) है, इसलिए अंतर अनुक्रम का (d=4-6=-2)। पद-दर-पद अंतर में सार्व अंतरों का अंतर लें।
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.
Step 2
Why this answer is correct
The correct answer is B. (-6). 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.
Step 3
Exam Tip
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 (36) and the fourth is (33), so (33-36=-3). While finding the difference subtract the previous term from the next term.
Step 2
Why this answer is correct
The correct answer is B. (-3). 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.
Step 3
Exam Tip
तीसरा पद (36) और चौथा (33) है इसलिए (33-36=-3)। अंतर निकालते समय बाद वाला पद घटा पहले वाला पद करें।
B. दृश्य रचना को समझना बनाना मूल्यांकन करना और सुधारना/Understand create evaluate and improve visual composition
Step 1
Concept
Art elements are basis of both creation and criticism. Exam tip: write both creation and evaluation.
Step 2
Why this answer is correct
The correct answer is B. दृश्य रचना को समझना बनाना मूल्यांकन करना और सुधारना / Understand create evaluate and improve visual composition. Art elements are basis of both creation and criticism. Exam tip: write both creation and evaluation.
Step 3
Exam Tip
कला तत्व रचना और आलोचना दोनों के आधार हैं। परीक्षा में creation और evaluation दोनों लिखें।
A. दृश्य रचना को समझना बनाना जांचना और सुधारना/To understand create evaluate and improve visual composition
Step 1
Concept
Learning art elements helps in both creation and criticism. Exam tip: write both creation and evaluation.
Step 2
Why this answer is correct
The correct answer is A. दृश्य रचना को समझना बनाना जांचना और सुधारना / To understand create evaluate and improve visual composition. Learning art elements helps in both creation and criticism. Exam tip: write both creation and evaluation.
Step 3
Exam Tip
कला तत्व सीखना रचना और आलोचना दोनों में मदद करता है। परीक्षा में creation और evaluation दोनों लिखें।
A. क्योंकि उसका धर्म और संस्कृति पर भी प्रभाव पड़ता था/Because it also affected religion and culture
Step 1
Concept
Missionary education created cultural influence along with education. For exams understand cultural colonialism.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि उसका धर्म और संस्कृति पर भी प्रभाव पड़ता था / Because it also affected religion and culture. Missionary education created cultural influence along with education. For exams understand cultural colonialism.
Step 3
Exam Tip
मिशनरी शिक्षा ने शिक्षा के साथ सांस्कृतिक प्रभाव भी डाला। परीक्षा में सांस्कृतिक उपनिवेशवाद समझें।
A. आधुनिक नागरिक और कुशल कर्मी तैयार करना/Preparing modern citizens and skilled workers
Step 1
Concept
Educational reforms provided human resources for a modern state and industry. For exams connect education with modernization.
Step 2
Why this answer is correct
The correct answer is A. आधुनिक नागरिक और कुशल कर्मी तैयार करना / Preparing modern citizens and skilled workers. Educational reforms provided human resources for a modern state and industry. For exams connect education with modernization.
Step 3
Exam Tip
शिक्षा सुधारों ने आधुनिक राज्य और उद्योग को मानव संसाधन दिया। परीक्षा में शिक्षा को आधुनिकीकरण से जोड़ें।
A. प्रश्नों से आलोचनात्मक सोच विकसित करना/Developing critical thinking through questions
Step 1
Concept
Socrates deepened thinking through questions and dialogue. Connect it with the method of Greek philosophy.
Step 2
Why this answer is correct
The correct answer is A. प्रश्नों से आलोचनात्मक सोच विकसित करना / Developing critical thinking through questions. Socrates deepened thinking through questions and dialogue. Connect it with the method of Greek philosophy.
Step 3
Exam Tip
सुकरात प्रश्न और संवाद से सोच को गहरा करते थे। परीक्षा में इसे यूनानी दर्शन की पद्धति से जोड़ें।
A. प्रश्नों से आलोचनात्मक सोच बढ़ाना/Increasing critical thinking through questions
Step 1
Concept
Socrates deepened thinking through questions. Link it with the dialogic method in exams.
Step 2
Why this answer is correct
The correct answer is A. प्रश्नों से आलोचनात्मक सोच बढ़ाना / Increasing critical thinking through questions. Socrates deepened thinking through questions. Link it with the dialogic method in exams.
Step 3
Exam Tip
सुकरात प्रश्नों के माध्यम से सोच को गहरा करते थे। परीक्षा में इसे संवादात्मक विधि से जोड़ें।
Plato made the philosophical tradition of the Academy famous. In exams, remember him as a link between Socrates and Aristotle.
Step 2
Why this answer is correct
The correct answer is A. अकादमी / Academy. Plato made the philosophical tradition of the Academy famous. In exams, remember him as a link between Socrates and Aristotle.
Step 3
Exam Tip
प्लेटो ने अकादमी से जुड़ी दार्शनिक परंपरा को प्रसिद्ध किया। परीक्षा में उसे सुकरात और अरस्तू के बीच की कड़ी मानें।
A. प्रकृति के बीच स्वतंत्र सीखना/Free learning amid nature
Step 1
Concept
Santiniketan is linked with Tagore's nature-centred educational vision. In exams connect it with Visva-Bharati and cultural renaissance.
Step 2
Why this answer is correct
The correct answer is A. प्रकृति के बीच स्वतंत्र सीखना / Free learning amid nature. Santiniketan is linked with Tagore's nature-centred educational vision. In exams connect it with Visva-Bharati and cultural renaissance.
Step 3
Exam Tip
शांतिनिकेतन टैगोर की प्रकृति केंद्रित शिक्षा दृष्टि से जुड़ा है। परीक्षा में इसे विश्वभारती और सांस्कृतिक पुनर्जागरण से जोड़ें।
Hauz Khas complex is linked with the Hauz-i-Alai reservoir and madrasa tradition. For exams identify monuments of urban water management.
Step 2
Why this answer is correct
The correct answer is A. हौज ए अलाई / Hauz-i-Alai. Hauz Khas complex is linked with the Hauz-i-Alai reservoir and madrasa tradition. For exams identify monuments of urban water management.
Step 3
Exam Tip
हौज खास परिसर हौज ए अलाई जलाशय और मदरसा परंपरा से जुड़ा है। परीक्षा में शहरी जल प्रबंधन स्मारकों को पहचानें।
A. आवासीय उच्च शिक्षा केंद्र/Residential higher learning centre
Step 1
Concept
Nalanda was a residential higher learning centre of ancient India. For exams remember the nature and state of learning centres.
Step 2
Why this answer is correct
The correct answer is A. आवासीय उच्च शिक्षा केंद्र / Residential higher learning centre. Nalanda was a residential higher learning centre of ancient India. For exams remember the nature and state of learning centres.
Step 3
Exam Tip
नालंदा प्राचीन भारत का आवासीय उच्च शिक्षा केंद्र था। परीक्षा में शिक्षा केंद्रों की प्रकृति और राज्य याद रखें।
A. प्राचीन आवासीय विश्वविद्यालय परंपरा/Ancient residential university tradition
Step 1
Concept
Nalanda was an ancient residential learning centre. In exams connect it with Buddhist studies and Bihar.
Step 2
Why this answer is correct
The correct answer is A. प्राचीन आवासीय विश्वविद्यालय परंपरा / Ancient residential university tradition. Nalanda was an ancient residential learning centre. In exams connect it with Buddhist studies and Bihar.
Step 3
Exam Tip
नालंदा प्राचीन आवासीय शिक्षा केंद्र था। परीक्षा में इसे बौद्ध अध्ययन और बिहार से जोड़ें।
Santiniketan is linked with Rabindranath Tagore. In exams connect it with education and cultural renaissance.
Step 2
Why this answer is correct
The correct answer is A. रवींद्रनाथ टैगोर / Rabindranath Tagore. Santiniketan is linked with Rabindranath Tagore. In exams connect it with education and cultural renaissance.
Step 3
Exam Tip
शांतिनिकेतन रवींद्रनाथ टैगोर से जुड़ा है। परीक्षा में इसे शिक्षा और सांस्कृतिक पुनर्जागरण से जोड़ें।
Kumaragupta I is associated with the founding of Nalanda University. For exams connect the Gupta period with growth in education and culture.
Step 2
Why this answer is correct
The correct answer is A. नालंदा विश्वविद्यालय / Nalanda University. Kumaragupta I is associated with the founding of Nalanda University. For exams connect the Gupta period with growth in education and culture.
Step 3
Exam Tip
कुमारगुप्त प्रथम को नालंदा विश्वविद्यालय की स्थापना से जोड़ा जाता है। परीक्षा में गुप्तकाल को शिक्षा और संस्कृति के उत्कर्ष से जोड़ें।
A. वैदिक आदर्शों और आधुनिक शिक्षा का संयोजन/Combination of Vedic ideals and modern education
Step 1
Concept
DAV institutions promoted social reform through education. Exam tip: remember institutional reforms.
Step 2
Why this answer is correct
The correct answer is A. वैदिक आदर्शों और आधुनिक शिक्षा का संयोजन / Combination of Vedic ideals and modern education. DAV institutions promoted social reform through education. Exam tip: remember institutional reforms.
Step 3
Exam Tip
डी ए वी संस्थाओं ने शिक्षा के माध्यम से सामाजिक सुधार को बढ़ाया। परीक्षा में संस्थागत सुधारों को याद रखें।
The Aligarh Movement was linked with promoting modern education. Exam tip is to connect Sir Syed Ahmad Khan with it.
Step 2
Why this answer is correct
The correct answer is A. अलीगढ़ आंदोलन / Aligarh Movement. The Aligarh Movement was linked with promoting modern education. Exam tip is to connect Sir Syed Ahmad Khan with it.
Step 3
Exam Tip
अलीगढ़ आंदोलन आधुनिक शिक्षा को बढ़ावा देने से जुड़ा था। परीक्षा में सर सैयद अहमद खान को इससे जोड़ें।
A. प्रवेश जांच और वाद विवाद की विद्वत परंपरा/Admission scrutiny and scholarly debate tradition
Step 1
Concept
Gate scholars were linked with debate and examination in higher Buddhist learning. For exams, understand Mahaviharas as organized institutions.
Step 2
Why this answer is correct
The correct answer is A. प्रवेश जांच और वाद विवाद की विद्वत परंपरा / Admission scrutiny and scholarly debate tradition. Gate scholars were linked with debate and examination in higher Buddhist learning. For exams, understand Mahaviharas as organized institutions.
Step 3
Exam Tip
द्वारपंडित उच्च बौद्ध शिक्षा में वाद विवाद और परीक्षा की परंपरा से जुड़े थे। परीक्षा में महाविहारों को संगठित संस्थान समझें।
A. वे कठिन राष्ट्रीय विचार को सरल उदाहरणों में समझाते थे/They explained difficult national ideas through simple examples
Step 1
Concept
An idea like nationalism can be hard to understand directly.
Step 2
Why this answer is correct
Symbols make it simple and memorable.
Step 3
Exam Tip
In exams treat symbols as explanatory tools. चरण 1: राष्ट्रवाद जैसे विचार को सीधे समझना कठिन हो सकता है। चरण 2: प्रतीक उसे सरल और यादगार बनाते हैं। चरण 3: परीक्षा में प्रतीकों को समझाने वाले साधन मानें।
A. औपनिवेशिक संस्थाओं के बहिष्कार का विरोध/Protest through boycott of colonial institutions
Step 1
Concept
One method of Non-Cooperation was to keep away from government institutions.
Step 2
Why this answer is correct
Students challenged colonial education by leaving schools.
Step 3
Exam Tip
In exams, remember boycott as a major strategy of the movement. चरण 1: असहयोग का एक तरीका सरकारी संस्थाओं से दूरी बनाना था। चरण 2: विद्यार्थियों ने स्कूल छोड़कर औपनिवेशिक शिक्षा व्यवस्था को चुनौती दी। चरण 3: परीक्षा में बहिष्कार को आंदोलन की प्रमुख रणनीति के रूप में याद रखें।
Subtracting the same number from every term does not change the difference. In exams, treat uniform subtraction as changing only the first term.
Step 2
Why this answer is correct
The correct answer is B. (7). Subtracting the same number from every term does not change the difference. In exams, treat uniform subtraction as changing only the first term.
Step 3
Exam Tip
हर पद से समान संख्या घटाने पर अंतर नहीं बदलता। परीक्षा में समान घटाव को केवल पहला पद बदलने वाला समझें।
Multiplication scales all differences by the same factor, so the new difference is (-3d). In exams, apply the transformation to the difference.
Step 2
Why this answer is correct
The correct answer is B. (-3d). Multiplication scales all differences by the same factor, so the new difference is (-3d). In exams, apply the transformation to the difference.
Step 3
Exam Tip
गुणन से सभी अंतर उसी गुणक से गुणा होते हैं, इसलिए नया अंतर (-3d) है। परीक्षा में रूपांतरण का असर अंतर पर लगाएं।
The selected sequence is \(5,19,33,\ldots\), and its difference is (14). Selecting every second term makes the new (d) twice the original (d).
Step 2
Why this answer is correct
The correct answer is C. (14). The selected sequence is \(5,19,33,\ldots\), and its difference is (14). Selecting every second term makes the new (d) twice the original (d).
Step 3
Exam Tip
चुना गया अनुक्रम \(5,19,33,\ldots\) होगा और इसका अंतर (14) है। हर दूसरा पद लेने पर नया (d) मूल (d) का (2) गुना होता है।
The first sequence has (d=5) and the second has (d=6), so the difference sequence has (d=5-6=-1). In termwise difference, take the difference of common differences.
Step 2
Why this answer is correct
The correct answer is A. (-1). The first sequence has (d=5) and the second has (d=6), so the difference sequence has (d=5-6=-1). In termwise difference, take the difference of common differences.
Step 3
Exam Tip
पहले अनुक्रम का (d=5) और दूसरे का (d=6) है, इसलिए अंतर अनुक्रम का (d=5-6=-1)। पद-दर-पद अंतर में सार्व अंतरों का अंतर लें।
The new terms are (a+3,a+d+6,a+2d+9), and both differences are (d+3). The difference of the added numbers is added to (d).
Step 2
Why this answer is correct
The correct answer is C. (d+3). The new terms are (a+3,a+d+6,a+2d+9), and both differences are (d+3). The difference of the added numbers is added to (d).
Step 3
Exam Tip
नए पद (a+3,a+d+6,a+2d+9) हैं और दोनों अंतर (d+3) हैं। क्रमशः बढ़ते जोड़ का अंतर (d) में जुड़ता है।
From the first to the fifth term there are (4) gaps, so (4d=-20) and (d=-5). In a decreasing progression, (d) is negative.
Step 2
Why this answer is correct
The correct answer is B. (-5). From the first to the fifth term there are (4) gaps, so (4d=-20) and (d=-5). In a decreasing progression, (d) is negative.
Step 3
Exam Tip
पहले से पांचवें पद तक (4) अंतर हैं, इसलिए (4d=-20) और (d=-5)। घटती श्रेणी में (d) ऋणात्मक होता है।
Adding the same number to all terms does not change the common difference. The original (d=20-24=-4), so the new (d) remains (-4).
Step 2
Why this answer is correct
The correct answer is B. (-4). Adding the same number to all terms does not change the common difference. The original (d=20-24=-4), so the new (d) remains (-4).
Step 3
Exam Tip
सभी पदों में समान संख्या जोड़ने से सार्व अंतर नहीं बदलता। मूल (d=20-24=-4) है, इसलिए नया (d=-4) ही रहेगा।
The new terms are (a+2, a+d+4, a+2d+6), and both differences are (d+2). The difference (2) of the added numbers is also added to (d).
Step 2
Why this answer is correct
The correct answer is C. (d+2). The new terms are (a+2, a+d+4, a+2d+6), and both differences are (d+2). The difference (2) of the added numbers is also added to (d).
Step 3
Exam Tip
नए पद (a+2, a+d+4, a+2d+6) हैं और दोनों अंतर (d+2) हैं। क्रमशः बढ़ते जोड़ का अंतर (2) भी (d) में जुड़ता है।
From the second to the fifth term there are (3) gaps, so (3d=-18) and (d=-6). In a decreasing progression, (d) remains negative.
Step 2
Why this answer is correct
The correct answer is B. (-6). From the second to the fifth term there are (3) gaps, so (3d=-18) and (d=-6). In a decreasing progression, (d) remains negative.
Step 3
Exam Tip
दूसरे से पांचवें पद तक (3) अंतर हैं, इसलिए (3d=-18) और (d=-6)। घटती श्रेणी में (d) ऋणात्मक रहता है।
(-1-\left\(-\frac{7}{4}\right\)=\frac{3}{4}), and the next difference is also \(\frac{3}{4}\). Be careful while subtracting negative fractions.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{4}\). (-1-\left\(-\frac{7}{4}\right\)=\frac{3}{4}), and the next difference is also \(\frac{3}{4}\). Be careful while subtracting negative fractions.
Step 3
Exam Tip
(-1-\left\(-\frac{7}{4}\right\)=\frac{3}{4}) और अगला अंतर भी \(\frac{3}{4}\) है। ऋणात्मक भिन्नों में घटाव सावधानी से करें।
Each next term is (4) less than the previous one, so (d=-4). A decreasing arithmetic progression has a negative common difference.
Step 2
Why this answer is correct
The correct answer is B. (-4), ऋणात्मक / (-4), negative. Each next term is (4) less than the previous one, so (d=-4). A decreasing arithmetic progression has a negative common difference.
Step 3
Exam Tip
हर अगला पद पिछले से (4) कम है, इसलिए (d=-4). घटती समांतर श्रेणी में सामान्य अंतर ऋणात्मक होता है।
In the first option, every consecutive difference is \(\frac{3}{4}\). With fractions, using common denominators is the safer method.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{4}, 1, \frac{7}{4}, \frac{5}{2}\). In the first option, every consecutive difference is \(\frac{3}{4}\). With fractions, using common denominators is the safer method.
Step 3
Exam Tip
पहले विकल्प में हर लगातार अंतर \(\frac{3}{4}\) है। भिन्नों में हर को समान बनाकर अंतर निकालना सुरक्षित तरीका है।
From (2y=9+(2y+6)), we get (0=15), so it never forms an arithmetic progression. None of the listed values can be its common difference.
Step 2
Why this answer is correct
The correct answer is B. (15). From (2y=9+(2y+6)), we get (0=15), so it never forms an arithmetic progression. None of the listed values can be its common difference.
Step 3
Exam Tip
(2y=9+(2y+6)) से (0=15) नहीं, इसलिए यह कभी समांतर श्रेणी नहीं बनती। सही विकल्पों में ऐसा कोई सामान्य अंतर नहीं है।
In (20,16,12,8), (4) is subtracted each time, so (d=-4). Do not just see decreasing order; check equal differences too.
Step 2
Why this answer is correct
The correct answer is B. (20, 16, 12, 8). In (20,16,12,8), (4) is subtracted each time, so (d=-4). Do not just see decreasing order; check equal differences too.
Step 3
Exam Tip
(20,16,12,8) में हर बार (4) घटता है, इसलिए (d=-4). केवल घटते क्रम को देखकर नहीं, बराबर अंतर भी जांचें।
A. (d=-1) वाली अंकगणितीय श्रेणी/Arithmetic progression with (d=-1)
Step 1
Concept
The first has (d=4) and the second has (d=5), so the difference sequence has (d=4-5=-1). The termwise difference of two arithmetic progressions is also an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is A. (d=-1) वाली अंकगणितीय श्रेणी / Arithmetic progression with (d=-1). The first has (d=4) and the second has (d=5), so the difference sequence has (d=4-5=-1). The termwise difference of two arithmetic progressions is also an arithmetic progression.
Step 3
Exam Tip
पहले (d=4) और दूसरे (d=5) हैं, इसलिए अंतर अनुक्रम का (d=4-5=-1)। दो अंकगणितीय श्रेणियों का पद-दर-पद अंतर भी अंकगणितीय श्रेणी होता है।
The new terms are (a+1, a+d+2, a+2d+3), and both differences are (d+1). Adding increasing numbers respectively adds (1) to (d).
Step 2
Why this answer is correct
The correct answer is C. (d+1). The new terms are (a+1, a+d+2, a+2d+3), and both differences are (d+1). Adding increasing numbers respectively adds (1) to (d).
Step 3
Exam Tip
नए पद (a+1, a+d+2, a+2d+3) हैं और दोनों अंतर (d+1) हैं। क्रमशः बढ़ती हुई जोड़ से (d) में (1) जुड़ता है।
The two common differences are (3) and (5), so the sum sequence has (d=3+5=8). In termwise addition, common differences add.
Step 2
Why this answer is correct
The correct answer is C. (8). The two common differences are (3) and (5), so the sum sequence has (d=3+5=8). In termwise addition, common differences add.
Step 3
Exam Tip
दोनों सार्व अंतर (3) और (5) हैं, इसलिए योग अनुक्रम का (d=3+5=8)। पद-दर-पद योग में सार्व अंतरों का योग होता है।
The first three options have (d=-8), but \(81,72,63,54,\ldots\) has (d=-9). Check both value and sign in the options.
Step 2
Why this answer is correct
The correct answer is D. \(81,72,63,54,\ldots\). The first three options have (d=-8), but \(81,72,63,54,\ldots\) has (d=-9). Check both value and sign in the options.
Step 3
Exam Tip
पहले तीन विकल्पों में (d=-8) है, लेकिन \(81,72,63,54,\ldots\) में (d=-9) है। विकल्पों में मान और चिह्न दोनों देखें।
There are (3) gaps between the fourth and first terms, so (3d=-15) and (d=-5). Keep (d) negative for a decreasing progression.
Step 2
Why this answer is correct
The correct answer is B. (-5). There are (3) gaps between the fourth and first terms, so (3d=-15) and (d=-5). Keep (d) negative for a decreasing progression.
Step 3
Exam Tip
चौथे और पहले पद के बीच (3) अंतर हैं, इसलिए (3d=-15) और (d=-5)। घटती श्रेणी में (d) ऋणात्मक रखें।
From the second to the fifth term there are (3) gaps, so (3d=18) and (d=6). Convert distance between terms into number of gaps.
Step 2
Why this answer is correct
The correct answer is B. (6). From the second to the fifth term there are (3) gaps, so (3d=18) and (d=6). Convert distance between terms into number of gaps.
Step 3
Exam Tip
दूसरे से पांचवें पद तक (3) अंतर होते हैं, इसलिए (3d=18) और (d=6)। पदों की दूरी को अंतरों की संख्या में बदलें।
The original common difference is (5), so after multiplying by (3), the new (d=15). When all terms are multiplied by the same factor, (d) is multiplied by that factor too.
Step 2
Why this answer is correct
The correct answer is C. (15). The original common difference is (5), so after multiplying by (3), the new (d=15). When all terms are multiplied by the same factor, (d) is multiplied by that factor too.
Step 3
Exam Tip
मूल सार्व अंतर (5) है, इसलिए (3) से गुणा करने पर नया (d=15) होगा। सभी पदों को समान गुणक से गुणा करने पर (d) भी उसी गुणक से गुणा होता है।
Adding the same (5) to all terms does not change (d), so (d=-4) remains. Equal addition or subtraction keeps the common difference unchanged.
Step 2
Why this answer is correct
The correct answer is B. (-4). Adding the same (5) to all terms does not change (d), so (d=-4) remains. Equal addition or subtraction keeps the common difference unchanged.
Step 3
Exam Tip
सभी पदों में समान (5) जोड़ने से (d) नहीं बदलता, इसलिए (d=-4) रहेगा। समान जोड़ या घटाव से सार्व अंतर अपरिवर्तित रहता है।
Equating differences gives ((3x+10)-(5x+2)=(x+18)-(3x+10)), which is an identity, so (d=8-2x). Therefore it is an arithmetic progression for every (x), but (d) is not fixed.
Step 2
Why this answer is correct
The correct answer is C. (4). Equating differences gives ((3x+10)-(5x+2)=(x+18)-(3x+10)), which is an identity, so (d=8-2x). Therefore it is an arithmetic progression for every (x), but (d) is not fixed.
Step 3
Exam Tip
दोनों अंतर बराबर रखने पर ((3x+10)-(5x+2)=(x+18)-(3x+10)), जिससे पहचान समानता बनती है और (d=8-2x)। इसलिए यह हर (x) पर अंकगणितीय श्रेणी है, लेकिन (d) निश्चित नहीं है।
\(\frac{7}{10}-\frac{2}{5}=\frac{3}{10}\) and \(1-\frac{7}{10}=\frac{3}{10}\). Do not forget to use common denominators in fractions.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{10}\). \(\frac{7}{10}-\frac{2}{5}=\frac{3}{10}\) and \(1-\frac{7}{10}=\frac{3}{10}\). Do not forget to use common denominators in fractions.
Step 3
Exam Tip
\(\frac{7}{10}-\frac{2}{5}=\frac{3}{10}\) और \(1-\frac{7}{10}=\frac{3}{10}\) है। भिन्नों में हर समान करना न भूलें।
\(\frac{7}{6}-\frac{5}{6}=\frac{1}{3}\) and \(\frac{3}{2}-\frac{7}{6}=\frac{1}{3}\). For fractions subtract using common denominators.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{3}\). \(\frac{7}{6}-\frac{5}{6}=\frac{1}{3}\) and \(\frac{3}{2}-\frac{7}{6}=\frac{1}{3}\). For fractions subtract using common denominators.
Step 3
Exam Tip
\(\frac{7}{6}-\frac{5}{6}=\frac{1}{3}\) और \(\frac{3}{2}-\frac{7}{6}=\frac{1}{3}\) है। भिन्नों में हर समान करके घटाएं।
\(1-\frac{3}{4}=\frac{1}{4}\) and \(\frac{5}{4}-1=\frac{1}{4}\). For fractions subtract using common denominators.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{1}{4}\). \(1-\frac{3}{4}=\frac{1}{4}\) and \(\frac{5}{4}-1=\frac{1}{4}\). For fractions subtract using common denominators.
Step 3
Exam Tip
\(1-\frac{3}{4}=\frac{1}{4}\) और \(\frac{5}{4}-1=\frac{1}{4}\) है। भिन्नों में समान हर बनाकर घटाएं।
The common difference is (23-18=5), and the same difference continues. In exams always check the difference of consecutive terms.
Step 2
Why this answer is correct
The correct answer is B. (5). The common difference is (23-18=5), and the same difference continues. In exams always check the difference of consecutive terms.
Step 3
Exam Tip
सार्व अंतर (23-18=5) है और आगे भी यही अंतर है। परीक्षा में दो क्रमागत पदों का अंतर जरूर जांचें।
\(\frac{6}{7}-\frac{4}{7}=\frac{2}{7}\). For fractions with the same denominator, quickly check the difference of numerators.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{2}{7}\). \(\frac{6}{7}-\frac{4}{7}=\frac{2}{7}\). For fractions with the same denominator, quickly check the difference of numerators.
Step 3
Exam Tip
\(\frac{6}{7}-\frac{4}{7}=\frac{2}{7}\) है। समान हर वाले भिन्नों में अंशों का अंतर जल्दी जाँचें।
The difference of consecutive terms is (42-36=6). Always subtract the previous term from the next term to find the common difference.
Step 2
Why this answer is correct
The correct answer is C. (6). The difference of consecutive terms is (42-36=6). Always subtract the previous term from the next term to find the common difference.
Step 3
Exam Tip
लगातार पदों का अंतर (42-36=6) है। सार्व अंतर निकालते समय हमेशा अगले पद से पिछले पद को घटाएँ।
The common difference is second term minus first term, so (11-7=4). In exams do not reverse the order of subtraction.
Step 2
Why this answer is correct
The correct answer is B. (11-7=4). The common difference is second term minus first term, so (11-7=4). In exams do not reverse the order of subtraction.
Step 3
Exam Tip
सार्व अंतर दूसरा पद घटा पहला पद होता है इसलिए (11-7=4) है। परीक्षा में घटाव का क्रम न बदलें।
