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.
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If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+3n\), what is \(a_5\)?
B. (50)
\(a_3=17\), \(a_4=35\) और \(a_5=67\) है। सही विकल्पों में (67) होना चाहिए। / \(a_3=17\), \(a_4=35\), and \(a_5=67\). Exam tip: add current (3n) with the previous two terms.
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If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+3n\), what is \(a_4\)?
D. (35)
\(a_3=6+2+9=17\) और \(a_4=17+6+12=35\) है। वर्तमान (n) का सही मान रखें। / \(a_3=6+2+9=17\) and \(a_4=17+6+12=35\). Exam tip: use the correct current value of (n).
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If \(a_1=3\) and \(a_{n+1}=a_n^2-2a_n+3\), what is \(a_3\)?
B. (34)
\(a_2=9-6+3=6\) और \(a_3=36-12+3=27\) है। सही विकल्पों में (27) होना चाहिए। / \(a_2=9-6+3=6\) and \(a_3=36-12+3=27\). Exam tip: square first, then subtract and add.
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If \(a_1=4\) and \(a_{n+1}=a_n^2-a_n+1\), what is \(a_2\)?
B. (13)
\(a_2=4^2-4+1=13\) है। वर्ग लेकर वही पद घटाएँ और (1) जोड़ें। / \(a_2=4^2-4+1=13\). Exam tip: square the term, subtract the same term, and add (1).
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If \(a_1=11\) and \(a_{n+1}=a_n+7\), which term is (74)?
C. (10)वाँ(10)th
(74-11=63) और \(63\div7=9\) चरण हैं इसलिए पद संख्या (10) है। चरणों में (1) जोड़कर पद संख्या मिलती है। / (74-11=63), and \(63\div7=9\) steps, so the term number is (10). Exam tip: add (1) to the number of steps.
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If \(a_1=9\) and \(a_{n+1}=a_n+8\), what is \(a_{12}\)?
C. (97)
\(a_{12}\) के लिए (8) को (11) बार जोड़ा जाता है इसलिए (9+88=97) है। पद संख्या से एक कम बार नियम लगता है। / For \(a_{12}\), (8) is added (11) times, so (9+88=97). Exam tip: the rule is applied one less time than the term number.
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If \(a_1=4\) and \(a_{n+1}=2a_n+7\), what is the value of \(a_4-a_2\)?
C. (70)
पद (4,15,37,81) हैं इसलिए \(a_4-a_2=66\) है। सही विकल्पों में (66) होना चाहिए। / The terms are (4,15,37,81), so \(a_4-a_2=66\). Exam tip: find both terms first and subtract.
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If \(a_1=4\) and \(a_{n+1}=2a_n+7\), what is the value of \(a_3-a_2\)?
C. (22)
पद (4,15,37) हैं इसलिए \(a_3-a_2=22\) है। पहले दोनों पद निकालें फिर अंतर लें। / The terms are (4,15,37), so \(a_3-a_2=22\). Exam tip: find both terms before taking the difference.
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If \(a_1=4\), \(a_2=8\), and \(a_n=a_{n-1}+a_{n-2}+6\), what is \(a_5\)?
A. (54)
पद (4,8,18,32,56) हैं इसलिए \(a_5=56\) है। सही विकल्पों में (56) होना चाहिए। / The terms are (4,8,18,32,56), so \(a_5=56\). Exam tip: add (6) along with the previous two terms.
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If \(a_1=4\), \(a_2=8\), and \(a_n=a_{n-1}+a_{n-2}+6\), what is \(a_4\)?
D. (32)
\(a_3=8+4+6=18\) और \(a_4=18+8+6=32\) है। अतिरिक्त स्थिरांक हर चरण में जोड़ें। / \(a_3=8+4+6=18\) and \(a_4=18+8+6=32\). Exam tip: add the extra constant at every step.
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