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 531-540 of 600 questions.
What is the (40)th term of the sequence \(15,24,33,42,\ldots\)?
B. (366)
सामान्य पद \(a_n=9n+6\) है इसलिए \(a_{40}=366\)। बड़े पद के लिए भी वही सामान्य नियम लगाएं। / The general term is \(a_n=9n+6\), so \(a_{40}=366\). Use the same general rule even for a large term.
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In an arithmetic sequence, \(a_2=19\) and \(a_8=-17\). What is its explicit rule?
A. \(a_n=31-6n\)
छह अंतरों में परिवर्तन (-36) है इसलिए (d=-6), अतः \(a_n=31-6n\)। दो दिए पदों से पहले समान अंतर निकालें। / The change over six gaps is (-36), so (d=-6), hence \(a_n=31-6n\). From two given terms first find the common difference.
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If \(a_n=n^2+5n\), for which (n) will \(a_n=126\)?
B. (9)
(n=9) रखने पर (81+45=126) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है। / Putting (n=9) gives (81+45=126). Directly checking options is a quick method.
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What is the general term of the sequence \(4,8,14,22,\ldots\)?
A. \(a_n=n^2+n+2\)
\(n^2+n+2\) से (4,8,14,22) मिलते हैं। दूसरे अंतर समान हों तो द्विघात नियम देखें। / \(n^2+n+2\) gives (4,8,14,22). If second differences are equal, check a quadratic rule.
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If \(a_n=\frac{4n+1}{3n-1}\), what is \(a_4\)?
C. \(\frac{17}{11}\)
(a_4=\frac{4(4)+1}{3(4)-1}=\frac{17}{11})। भिन्न वाले नियम में अंश और हर दोनों में (n) रखें। / (a_4=\frac{4(4)+1}{3(4)-1}=\frac{17}{11}). In a fractional rule substitute (n) in both numerator and denominator.
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What is the general term of the sequence \(216,343,512,729,\ldots\)?
B. (a_n=(n+5)3)
यह \(6^3,7^3,8^3,9^3,\ldots\) है इसलिए (a_n=(n+5)3)। घन अनुक्रम में आधार संख्या का क्रम देखें। / This is \(6^3,7^3,8^3,9^3,\ldots\), so (a_n=(n+5)3). In cube sequences observe the order of base numbers.
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Which is the correct rule for the sequence \(14,31,54,83,\ldots\)?
A. \(a_n=3n^2+8n+3\)
\(3n^2+8n+3\) से (14,31,54,83) मिलते हैं। विकल्पों को शुरुआती पदों से मिलाएं। / \(3n^2+8n+3\) gives (14,31,54,83). Match options with the initial terms.
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If \(a_n=11-5n\), what is the common difference of this sequence?
A. (-5)
रैखिक नियम में (n) का गुणांक (-5) है इसलिए समान अंतर (-5) है। गुणांक पढ़ते समय चिह्न न छोड़ें। / In a linear rule the coefficient of (n) is (-5), so the common difference is (-5). Do not miss the sign while reading the coefficient.
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If \(a_n=6n^2-1\), what is the value of \(a_4+a_2\)?
B. (120)
\(a_4=95\) और \(a_2=23\), इसलिए योग (118) है। सही विकल्प (118) है और दोनों पद अलग निकालें। / \(a_4=95\) and \(a_2=23\), so the sum is (118). The correct option is (118), and both terms should be found separately.
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In the sequence \(70,61,52,43,\ldots\), which term is (-2)?
C. (9)वाँ(9)th
सामान्य पद \(a_n=79-9n\) है और (79-9n=-2) से (n=9)। घटते अनुक्रम में भी पद-संख्या प्राकृतिक होती है। / The general term is \(a_n=79-9n\), and (79-9n=-2) gives (n=9). Even in decreasing sequences the position is natural.
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