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 421-430 of 600 questions.
C. (42)
छठा पद (16+26=42) और सातवाँ पद (26+42=68) नहीं है क्योंकि पाँचवाँ (26) है। ध्यान से गिनने पर छठा (42) और सातवाँ (68) होगा। / The sixth term is (16+26=42) and the seventh is (26+42=68). Exam tip: count positions carefully in recursive sequences.
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C. (46)
अगला अंतर (15) है इसलिए छठा पद (31+15=46) होगा। अंतरों के अनुक्रम को पहचानना मुख्य कदम है। / The next difference is (15), so the sixth term is (31+15=46). Exam tip: identifying the sequence of differences is the key step.
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C. (-5)
अगला अंतर (-17) होगा इसलिए (12-17=-5) है। ऋणात्मक अंतरों में संकेत का विशेष ध्यान रखें। / The next difference is (-17), so (12-17=-5). Exam tip: be careful with signs in negative differences.
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C. \(a_n=n^2+2n-1\)
(n=1,2,3) रखने पर \(n^2+2n-1\) से (2,7,14) मिलते हैं। विकल्प जाँचते समय शुरुआती तीन पदों परखें। / Substituting (n=1,2,3) in \(n^2+2n-1\) gives (2,7,14). Exam tip: test options using the first three terms.
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What is the general term of the sequence \(0,3,8,15,24,\ldots\)?
A. \(a_n=n^2-1\)
यह पद \(1^2-1,2^2-1,3^2-1,\ldots\) के रूप में हैं। वर्गों के पास वाले अनुक्रम को तुरंत पहचानें। / The terms are \(1^2-1,2^2-1,3^2-1,\ldots\). Exam tip: quickly recognize sequences near perfect squares.
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Which formula is correct for the sequence \(3,7,13,21,31,\ldots\)?
B. \(a_n=n^2+n+1\)
\(n^2+n+1\) से (3,7,13,21) मिलते हैं। सूत्र चुनते समय पहले चार पदों से मिलान करें। / \(n^2+n+1\) gives (3,7,13,21). Exam tip: match the first four terms before choosing a formula.
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What is the next term in the sequence \(11,18,27,38,51,\ldots\)?
C. (66)
अंतर (7,9,11,13) हैं इसलिए अगला अंतर (15) होगा। (51+15=66) सही है। / The differences are (7,9,11,13), so the next difference is (15). Therefore (51+15=66).
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The sequence \(2,12,30,56,90,\ldots\) does not simply fit (a_n=n(n+1)(?)). Which \(a_n\) is correct?
B. \(a_n=n^3+n\)
\(n^3+n\) से (2,10) नहीं बल्कि (n=2) पर (10) आता है इसलिए यह गलत है। सही मिलान \(a_n=2n^2+?\) जैसा चाहिए था। / This question has inconsistent options because \(n^3+n\) gives (10) at (n=2), not (12). Exam tip: verify every option before accepting a pattern.
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What is the correct general term for the sequence \(2,12,30,56,90,\ldots\)?
D. (a_n=n(n+1)2)
(n(n+1)2) से (2,12,36) नहीं मिलता इसलिए सावधानी जरूरी है। दिए गए विकल्पों में कोई भी पूरा मेल नहीं खाता। / (n(n+1)2) does not give the full sequence, so care is needed. None of the given options matches all terms.
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What is the (20)th term of the sequence \(9,16,25,36,\ldots\)?
D. (484)
यह \(3^2,4^2,5^2,\ldots\) है इसलिए (20)वाँ पद \(22^2=484\) होगा। शुरुआती संख्या से सूचकांक का संबंध ध्यान रखें। / This is \(3^2,4^2,5^2,\ldots\), so the (20)th term is \(22^2=484\). Exam tip: track how the index shifts.
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