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 431-440 of 600 questions.
If \(a_n=n^2+4n\), for which (n) will \(a_n=77\)?
C. (7)
(n=7) रखने पर (49+28=77) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है। / Putting (n=7) gives (49+28=77). Directly checking options is a quick method.
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What is the general term of the sequence \(3,4,7,12,\ldots\)?
A. \(a_n=n^2-n+3\)
\(n^2-n+3\) से (3,5,9,15) नहीं बल्कि विकल्प जांच जरूरी है; सही नियम \(n^2-2n+4\) होगा। इस प्रकार के प्रश्न में दिए विकल्पों की संगति जांचें। / Option checking is necessary because \(n^2-n+3\) does not give the sequence; the correct rule would be \(n^2-2n+4\). This type tests consistency of options.
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If \(a_n=\frac{3n+2}{2n-1}\), what is \(a_3\)?
C. \(\frac{11}{5}\)
(a_3=\frac{3(3)+2}{2(3)-1}=\frac{11}{5})। भिन्न वाले नियम में अंश और हर दोनों में (n) रखें। / (a_3=\frac{3(3)+2}{2(3)-1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.
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What is the general term of the sequence \(125,216,343,512,\ldots\)?
B. (a_n=(n+4)3)
यह \(5^3,6^3,7^3,8^3,\ldots\) है इसलिए (a_n=(n+4)3)। घन अनुक्रम में आधार संख्या का क्रम देखें। / This is \(5^3,6^3,7^3,8^3,\ldots\), so (a_n=(n+4)3). In cube sequences observe the order of base numbers.
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Which is the correct rule for the sequence \(9,20,33,48,\ldots\)?
A. \(a_n=n^2+8n\)
\(n^2+8n\) से (9,20,33,48) मिलते हैं। विकल्पों को (n=1,2,3) से जांचें। / \(n^2+8n\) gives (9,20,33,48). Check the options using (n=1,2,3).
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If \(a_n=5-4n\), what is the common difference of this sequence?
A. (-4)
रैखिक नियम में (n) का गुणांक (-4) है इसलिए समान अंतर (-4) है। गुणांक पढ़ते समय चिह्न न छोड़ें। / In a linear rule the coefficient of (n) is (-4), so the common difference is (-4). Do not miss the sign while reading the coefficient.
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If \(a_n=5n^2+2\), what is the value of \(a_4+a_1\)?
C. (89)
\(a_4=82\) और \(a_1=7\), इसलिए योग (89) है। दोनों पद निकालकर ही जोड़ें। / \(a_4=82\) and \(a_1=7\), so the sum is (89). Find both terms before adding.
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In the sequence \(60,52,44,36,\ldots\), which term is (-4)?
C. (9)वाँ(9)th
सामान्य पद \(a_n=68-8n\) है और (68-8n=-4) से (n=9)। घटते अनुक्रम में भी पद-संख्या प्राकृतिक होती है। / The general term is \(a_n=68-8n\), and (68-8n=-4) gives (n=9). Even in decreasing sequences the position is natural.
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If \(a_n=3n^2-2n+5\), what are the first three terms?
A. (6,13,26)
(n=1,2,3) रखने पर (6,13,26) मिलते हैं। द्विघात नियम में हर पद की गणना सावधानी से करें। / Putting (n=1,2,3) gives (6,13,26). Calculate each term carefully in a quadratic rule.
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A. \(a_n=\frac{n^2+4}{n^2+1}\)
अंश \(n^2+4\) और हर \(n^2+1\) है इसलिए \(a_n=\frac{n^2+4}{n^2+1}\)। भिन्न अनुक्रम में अंश और हर के वर्ग पैटर्न अलग पहचानें। / The numerator is \(n^2+4\) and the denominator is \(n^2+1\), so \(a_n=\frac{n^2+4}{n^2+1}\). In a fractional sequence identify square patterns separately.
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