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 441-450 of 601 questions.
If \(a_1=3\) and \(a_{n+1}=n a_n+4\), what is \(a_3\)?
B. (18)
\(a_2=1\times3+4=7\) और \(a_3=2\times7+4=18\) है। (n) का मान हर चरण में बदलें। / \(a_2=1\times3+4=7\) and \(a_3=2\times7+4=18\). Exam tip: change the value of (n) at each step.
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Which recursive rule is correct for the sequence \(5,16,49,148,\ldots\)?
A. \(a_1=5, a_{n+1}=3a_n+1\)
\(3\times5+1=16\) और \(3\times16+1=49\) है। नियम चुनते समय शुरुआती दो चरण जाँचें। / \(3\times5+1=16\) and \(3\times16+1=49\). Exam tip: check the first two steps when choosing a rule.
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Which recursive rule is correct for the sequence \(20,15,7,-8,\ldots\)?
A. (a_1=20, a_{n+1}=a_n-(3n+2))
घटाव (5,8,11) हैं इसलिए (3n+2) घटता है। पहला पद और घटाव दोनों मिलाने चाहिए। / The subtractions are (5,8,11), so (3n+2) is subtracted. Exam tip: match both the first term and the subtraction pattern.
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If \(a_1=7\) and \(a_{n+1}=a_n+n^2+n\), which term is (47)?
B. (5)वाँ(5)th
पद (7,9,15,27,47) हैं इसलिए (47) पाँचवाँ पद है। बदलते जोड़ लिखकर पद संख्या जाँचें। / The terms are (7,9,15,27,47), so (47) is the fifth term. Exam tip: write changing additions to check the position.
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If \(a_1=150\) and (a_{n+1}=a_n-\(n^2+n\)), which term is (110)?
B. (5)वाँ(5)th
पद (150,148,142,130,110) हैं इसलिए (110) पाँचवाँ पद है। घटते हुए पदों को क्रमांक सहित लिखें। / The terms are (150,148,142,130,110), so (110) is the fifth term. Exam tip: write decreasing terms with positions.
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If \(a_1=2\), \(a_2=8\), and \(a_n=a_{n-1}+2a_{n-2}+n\), what is \(a_5\)?
A. (66)
\(a_3=15\), \(a_4=35\) और \(a_5=70\) है। सही विकल्पों में (70) होना चाहिए। / \(a_3=15\), \(a_4=35\), and \(a_5=70\). Exam tip: multiply \(a_{n-2}\) by (2) and add current (n).
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If \(a_1=2\), \(a_2=8\), and \(a_n=a_{n-1}+2a_{n-2}+n\), what is \(a_4\)?
C. (35)
\(a_3=8+2\times2+3=15\) और \(a_4=15+2\times8+4=35\) है। वर्तमान (n) भी जोड़ना न भूलें। / \(a_3=8+2\times2+3=15\) and \(a_4=15+2\times8+4=35\). Exam tip: do not forget to add current (n).
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If \(a_1=6\) and \(a_{n+1}=a_n+a_1+n^2\), what is \(a_4\)?
B. (37)
पद (6,13,23,38) हैं इसलिए \(a_4=38\) है। सही विकल्पों में (38) होना चाहिए। / The terms are (6,13,23,38), so \(a_4=38\). Exam tip: \(a_1\) stays fixed while \(n^2\) changes.
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If \(a_1=6\) and \(a_{n+1}=a_n+a_1+n^2\), what is \(a_3\)?
C. (23)
\(a_2=6+6+1=13\) और \(a_3=13+6+4=23\) है। \(a_1\) स्थिर रहता है। / \(a_2=6+6+1=13\) and \(a_3=13+6+4=23\). Exam tip: \(a_1\) remains fixed.
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If \(a_1=5\) and (a_{n+1}=a_n+(n+1)!), what is \(a_4\)?
B. (39)
जुड़ने वाले मान (2!,3!,4!) यानी (2,6,24) हैं इसलिए \(a_4=37\) है। सही विकल्पों में (37) होना चाहिए। / The added values (2!,3!,4!) are (2,6,24), so \(a_4=37\). Exam tip: calculate factorial increments in order.
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