Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 471-480 of 600 questions.
If \(a_n=5\cdot2^{n-1}-3\), what is the value of \(a_6\)?
B. (157)
\(a_6=5\cdot2^5-3=157\) है। परीक्षा में (n-1) वाले घातांक पर ध्यान दें। / \(a_6=5\cdot2^5-3=157\). In exams, pay attention to the exponent (n-1).
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Which general term is correct for the sequence \(2,7,17,37,\ldots\)?
A. \(a_n=5\cdot2^{n-1}-3\)
\(5\cdot2^{n-1}-3\) से (2,7,17,37) मिलते हैं। परीक्षा में गुणोत्तर रूप में स्थिर घटाव भी जाँचें। / \(5\cdot2^{n-1}-3\) gives (2,7,17,37). In exams, also check constant subtraction in geometric forms.
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If \(a_n=3n^2+n-2\), what is the sum of the first three terms?
C. (40)
पहले तीन पद (2,12,26) हैं और योग (40) है। परीक्षा में योग से पहले सभी पद लिखें। / The first three terms are (2,12,26), and the sum is (40). In exams, write all terms before adding.
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What is the general term of the sequence \(2,12,26,44,\ldots\)?
A. \(a_n=3n^2+n-2\)
\(3n^2+n-2\) से (2,12,26,44) मिलते हैं। परीक्षा में दूसरे अंतर देखकर वर्गीय नियम चुनें। / \(3n^2+n-2\) gives (2,12,26,44). In exams, choose a quadratic rule by checking second differences.
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If \(a_n=2n^3-n\), what is the value of \(a_4\)?
C. (124)
\(a_4=2\times64-4=124\) है। परीक्षा में घन और रैखिक घटाव अलग-अलग करें। / \(a_4=2\times64-4=124\). In exams, handle the cube and linear subtraction separately.
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Which explicit rule is correct for the sequence \(1,14,51,124,\ldots\)?
B. \(a_n=2n^3-n\)
\(2n^3-n\) से (1,14,51,124) मिलते हैं। परीक्षा में घन आधारित नियमों को छोटे (n) से जाँचें। / \(2n^3-n\) gives (1,14,51,124). In exams, test cube-based rules with small (n).
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If \(a_n=n^3+n^2\), what is \(a_5:a_3\)?
B. (25:6)
\(a_5=150\) और \(a_3=36\), इसलिए सरल अनुपात (25:6) है। परीक्षा में अनुपात को सरल जरूर करें। / \(a_5=150\) and \(a_3=36\), so the simplified ratio is (25:6). In exams, always simplify the ratio.
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What is the general term of the sequence \(2,12,36,80,\ldots\)?
A. \(a_n=n^3+n^2\)
\(n^3+n^2\) से (2,12,36,80) मिलते हैं। परीक्षा में घन और वर्ग वाले संयुक्त नियम जाँचें। / \(n^3+n^2\) gives (2,12,36,80). In exams, check combined cube-and-square rules.
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If \(a_n=90-6n\), what is the value of \(a_3+a_{10}\)?
C. (102)
\(a_3=72\) और \(a_{10}=30\), इसलिए योग (102) है। परीक्षा में घटते सूत्र में दोनों पद सावधानी से निकालें। / \(a_3=72\) and \(a_{10}=30\), so the sum is (102). In exams, find both terms carefully in a decreasing formula.
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What is the general term of the sequence \(84,78,72,66,\ldots\)?
B. \(a_n=90-6n\)
(n=1) पर (84) और (n=2) पर (78) मिलता है, इसलिए \(a_n=90-6n\) है। परीक्षा में घटते अनुक्रम के पहले दो पद जाँचें। / At (n=1) it gives (84), and at (n=2) it gives (78), so \(a_n=90-6n\). In exams, check the first two terms of a decreasing sequence.
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