Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 411-420 of 600 questions.
In the sequence \(4,7,12,19,28,\ldots\), \(a_n=n^2+3\). Which term is (84)?
B. (9)वाँ(9)th
\(n^2+3=84\) से \(n^2=81\) और (n=9) मिलता है। वर्ग संख्या पहचानना समय बचाता है। / From \(n^2+3=84\), \(n^2=81\) and (n=9). Exam tip: recognizing perfect squares saves time.
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Find the next term in the sequence \(6,13,24,39,58,\ldots\).
D. (81)
अंतर (7,11,15,19) हैं इसलिए अगला अंतर (23) होगा। (58+23=81) मिलता है। / The differences are (7,11,15,19), so the next difference is (23). Thus (58+23=81).
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A. (91)
\(6^3-5^3=216-125=91\) है। घन अनुक्रम में सीधे घन निकालकर घटाएँ। / \(6^3-5^3=216-125=91\). Exam tip: in cube sequences, calculate the two cubes and subtract.
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In the sequence \(10,8,11,9,12,10,\ldots\), two subsequences are hidden. What is the next term?
B. (13)
विषम स्थानों पर \(10,11,12,\ldots\) है इसलिए अगला विषम स्थान (13) होगा। वैकल्पिक अनुक्रम में स्थानों को अलग करें। / Odd positions are \(10,11,12,\ldots\), so the next odd-position term is (13). Exam tip: separate positions in alternating sequences.
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What is the next term in the sequence \(2,9,4,16,6,25,\ldots\)?
A. (8)
विषम स्थानों पर \(2,4,6,\ldots\) हैं इसलिए अगला विषम पद (8) है। वैकल्पिक पैटर्न में दोनों धाराएँ अलग देखें। / Odd positions are \(2,4,6,\ldots\), so the next odd-position term is (8). Exam tip: split the two patterns in alternating sequences.
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In the sequence \(3,6,11,18,27,\ldots\), \(a_n=n^2+2\). What is \(a_9\)?
C. (83)
\(a_9=9^2+2=83\) है। सामान्य पद मिलने पर अनुमान नहीं लगाना चाहिए। / \(a_9=9^2+2=83\). Exam tip: when the general term is given, avoid guessing.
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How many terms of the sequence \(12,17,22,27,\ldots\) are less than (60)?
C. (10)
यहाँ (a_n=12+5(n-1)) और (12+5(n-1)<60) से (n<10.6) मिलता है। इसलिए (10) पद छोटे हैं। / Here (a_n=12+5(n-1)), and (12+5(n-1)<60) gives (n<10.6). So (10) terms are less than (60).
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In the sequence \(100,93,86,79,\ldots\), how many positive terms are there?
C. (15)
(a_n=100-7(n-1)>0) से (n<15.28) मिलता है। अतः धनात्मक पदों की संख्या (15) है। / (a_n=100-7(n-1)>0) gives (n<15.28). Therefore the number of positive terms is (15).
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In the sequence \(5,10,20,40,\ldots\), which term is (320)?
C. (7)वाँ(7)th
पद \(5\times2^{n-1}\) हैं और \(5\times2^6=320\) है। इसलिए यह (7)वाँ पद है। / The terms are \(5\times2^{n-1}\), and \(5\times2^6=320\). Hence it is the (7)th term.
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B. (34)
आगे के पद (21,34) हैं इसलिए आठवाँ पद (34) है। पुनरावर्ती अनुक्रम में पद छोड़ना नहीं चाहिए। / The next terms are (21,34), so the eighth term is (34). Exam tip: do not skip steps in recursive sequences.
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