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 491-500 of 600 questions.
If \(a_n=kn+2\) and \(a_5=27\), what will be the value of \(a_9\)?
C. (47)
(5k+2=27) से (k=5) और \(a_9=47\) मिलता है। पहले अज्ञात स्थिरांक निकालें। / From (5k+2=27), (k=5), and \(a_9=47\). Exam tip: find the unknown constant first.
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If \(a_n=pn^2+q\), \(a_1=5\) and \(a_2=14\), what will be \(a_4\)?
B. (50)
(p+q=5) और (4p+q=14) से (p=3) और (q=2) मिलता है। फिर \(a_4=50\) होगा। / From (p+q=5) and (4p+q=14), we get (p=3) and (q=2). Then \(a_4=50\).
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If \(a_n=n^2+cn\) and \(a_4=32\), what will be the value of \(a_9\)?
D. (117)
(16+4c=32) से (c=4) है। इसलिए \(a_9=81+36=117\) होगा। / From (16+4c=32), (c=4). Therefore \(a_9=81+36=117\).
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In the sequence \(2,6,12,20,\ldots\), how many terms are less than (100)?
A. (9)
यहाँ (a_n=n(n+1)) है और \(9\times10=90\) जबकि \(10\times11=110\) है। इसलिए (9) पद (100) से छोटे हैं। / Here (a_n=n(n+1)), and \(9\times10=90\) while \(10\times11=110\). So (9) terms are less than (100).
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If \(a_n=2^n+n^2\), what will be the value of \(a_5\)?
C. (57)
\(a_5=2^5+5^2=32+25=57\) है। घात और वर्ग दोनों अलग-अलग निकालें। / \(a_5=2^5+5^2=32+25=57\). Exam tip: calculate the power and square separately.
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What will be the (12)th term in the sequence \(3,5,9,15,23,\ldots\)?
B. (135)
यहाँ \(a_n=n^2-n+3\) है इसलिए \(a_{12}=144-12+3=135\) है। शुरुआती अंतरों से सूत्र पहचानें। / Here \(a_n=n^2-n+3\), so \(a_{12}=144-12+3=135\). Exam tip: identify the formula from initial differences.
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If (a_n=\frac{n(n+3)}{2}), which term is (65)?
D. (10)वाँ(10)th
\(\frac{10\times13}{2}=65\) इसलिए यह (10)वाँ पद है। विकल्पों को सीधे सूत्र में रखकर जाँच सकते हैं। / Since \(\frac{10\times13}{2}=65\), it is the (10)th term. Exam tip: substitute options directly into the formula.
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If (a_n=n(n+2)), what will be the value of \(a_{11}-a_8\)?
A. (63)
\(a_{11}=143\) और \(a_8=80\) है इसलिए अंतर (63) है। पदों को अलग निकालकर घटाएँ। / \(a_{11}=143\) and \(a_8=80\), so the difference is (63). Exam tip: find the terms separately and then subtract.
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C. (47)
अंतर (3,4,7,12) हैं और अगला अंतर (19) होगा। इसलिए (28+19=47) है। / The differences are (3,4,7,12), and the next difference will be (19). Therefore (28+19=47).
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What will be the (10)th term in the sequence \(1,4,2,8,3,16,4,\ldots\)?
B. (64)
सम स्थानों पर \(4,8,16,32,64,\ldots\) हैं। (10)वाँ पद पाँचवाँ सम-स्थान पद है इसलिए (64) है। / Even positions are \(4,8,16,32,64,\ldots\). The (10)th term is the fifth even-position term, so it is (64).
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