Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 511-520 of 600 questions.
What is the (n)th term of the sequence \(64,125,216,343,\ldots\)?
B. (a_n=(n+3)3)
यह \(4^3,5^3,6^3,7^3,\ldots\) है इसलिए (a_n=(n+3)3)। घन अनुक्रम में आधार संख्या पहचानें। / This is \(4^3,5^3,6^3,7^3,\ldots\), so (a_n=(n+3)3). In cube sequences identify the base number.
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If \(a_n=4n-1\) and \(b_n=n^2+2n\), what is \(a_6+b_4\)?
B. (47)
\(a_6=23\) और \(b_4=24\), इसलिए योग (47) है। दो नियमों में पद-संख्या अलग हो सकती है इसलिए ध्यान रखें। / \(a_6=23\) and \(b_4=24\), so the sum is (47). With two rules the term numbers may differ, so use them carefully.
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What will be the (10)th term of the sequence \(11,24,43,68,\ldots\)?
C. (331)
इसका नियम \(a_n=3n^2+4n+4\) है इसलिए \(a_{10}=300+40+4=344\) नहीं बल्कि विकल्पों से मिलान गलत है; सही (10)वाँ पद (344) है। विकल्पों की संगति भी परीक्षा में जांचें। / Its rule is \(a_n=3n^2+4n+4\), so the (10)th term is (344), not any listed option. In exams also check the consistency of options.
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Which is the correct rule for the sequence \(8,17,28,41,\ldots\)?
A. \(a_n=n^2+6n+1\)
\(n^2+6n+1\) से (8,17,28,41) मिलते हैं। बढ़ते अंतर दिखें तो द्विघात नियम की जांच करें। / \(n^2+6n+1\) gives (8,17,28,41). When differences increase, check a quadratic rule.
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Which statement about (93) is correct for the sequence \(13,21,29,37,\ldots\)?
B. (93) ग्यारहवाँ पद है(93) is the eleventh term
सामान्य पद \(a_n=8n+5\) है और (8n+5=93) से (n=11)। यदि (n) प्राकृतिक संख्या हो तो दिया पद अनुक्रम में आता है। / The general term is \(a_n=8n+5\), and (8n+5=93) gives (n=11). If (n) is a natural number, the given term belongs to the sequence.
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What is the general term of the sequence \(9,49,121,225,\ldots\)?
A. (a_n=(4n-1)2)
यह \(3^2,7^2,11^2,15^2,\ldots\) है इसलिए (a_n=(4n-1)2)। वर्गों में आधारों का अंतर देखें। / This is \(3^2,7^2,11^2,15^2,\ldots\), so (a_n=(4n-1)2). In square sequences observe the difference between bases.
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If \(a_n=6^n-3n\), what is the value of \(a_3\)?
C. (207)
(a_3=63-3(3)=216-9=207)। घात निकालने के बाद रैखिक भाग घटाएं। / (a_3=63-3(3)=216-9=207). Evaluate the power first and then subtract the linear part.
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A. \(a_n=\frac{3n+2}{4n+2}\)
अंश (3n+2) और हर (4n+2) है इसलिए \(a_n=\frac{3n+2}{4n+2}\)। भिन्न अनुक्रम में दोनों भागों का अलग नियम बनाएं। / The numerator is (3n+2) and the denominator is (4n+2), so \(a_n=\frac{3n+2}{4n+2}\). In a fractional sequence form separate rules for both parts.
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In an arithmetic sequence, \(a_4=23\) and \(a_9=58\). What is its general term?
B. \(a_n=7n-5\)
पाँच अंतरों में वृद्धि (35) है इसलिए (d=7), फिर \(a_n=7n-5\)। दो दिए पदों से पहले समान अंतर निकालें। / The increase over five gaps is (35), so (d=7), then \(a_n=7n-5\). From two given terms first find the common difference.
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Which option contains the first three terms formed by \(a_n=3n^2-2n+6\)?
A. (7,14,27)
(n=1,2,3) रखने पर (7,14,27) मिलते हैं। विकल्प जांचने के लिए शुरुआती पद निकालें। / Putting (n=1,2,3) gives (7,14,27). To check options, find the initial terms.
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