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 371-380 of 601 questions.
If \(a_1=2\), \(a_2=6\), and \(a_n=a_{n-1}+a_{n-2}+5\), what is \(a_5\)?
C. (42)
पद (2,6,13,24,42) हैं इसलिए \(a_5=42\) है। पिछले दो पदों के साथ (5) भी जोड़ें। / The terms are (2,6,13,24,42), so \(a_5=42\). Exam tip: add (5) along with the previous two terms.
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If \(a_1=3\) and \(a_{n+1}=5a_n-2\), what is \(a_3\)?
C. (63)
\(a_2=5\times3-2=13\) और \(a_3=5\times13-2=63\) है। गुणा के बाद (2) घटाएँ। / \(a_2=5\times3-2=13\) and \(a_3=5\times13-2=63\). Exam tip: subtract (2) after multiplication.
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Which recursive rule is correct for the sequence \(2,5,14,37,\ldots\)?
A. \(a_1=2, a_{n+1}=2a_n+n^2\)
\(2\times2+1^2=5\) और \(2\times5+2^2=14\) मिलता है। नियम चुनते समय शुरुआती दो चरण जाँचें। / \(2\times2+1^2=5\) and \(2\times5+2^2=14\). Exam tip: check the first two steps when choosing a rule.
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Which recursive rule is correct for the sequence \(6,9,14,21,\ldots\)?
B. \(a_1=6, a_{n+1}=a_n+2n+1\)
यहाँ जोड़ (3,5,7) हैं इसलिए नियम \(a_{n+1}=a_n+2n+1\) है। पहले पद और बदलते जोड़ दोनों देखें। / The additions are (3,5,7), so the rule is \(a_{n+1}=a_n+2n+1\). Exam tip: check both first term and changing addition.
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If \(a_1=3\) and \(a_{n+1}=n a_n+2n\), what is \(a_4\)?
C. (48)
\(a_2=5\), \(a_3=14\) और \(a_4=48\) है। हर चरण में (n) से गुणा और (2n) जोड़ना है। / \(a_2=5\), \(a_3=14\), and \(a_4=48\). Exam tip: multiply by (n) and add (2n) at each step.
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If \(a_1=2\) and (a_{n+1}=(n+1)a_n-1), what is \(a_4\)?
C. (31)
\(a_2=3\), \(a_3=8\) और \(a_4=31\) है। गुणक (n+1) हर चरण में बदलता है। / \(a_2=3\), \(a_3=8\), and \(a_4=31\). Exam tip: the multiplier (n+1) changes at each step.
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If \(a_1=200\) and (a_{n+1}=a_n-\(2^n+n^2\)), what is \(a_4\)?
C. (172)
घटने वाले मान (3,8,17) हैं इसलिए \(a_4=172\) है। घात और वर्ग दोनों निकालकर घटाएँ। / The subtracted values are (3,8,17), so \(a_4=172\). Exam tip: calculate both the power and square before subtracting.
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If \(a_1=1\) and \(a_{n+1}=a_n+3^n+n\), what is \(a_4\)?
C. (46)
जुड़ने वाले मान (4,11,30) हैं इसलिए \(a_4=46\) है। \(3^n\) और (n) दोनों जोड़ें। / The added values are (4,11,30), so \(a_4=46\). Exam tip: add both \(3^n\) and (n).
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If \(a_1=2\), \(a_2=3\), and \(a_n=2a_{n-1}+3a_{n-2}\), what is \(a_4\)?
C. (33)
\(a_3=2\times3+3\times2=12\) और \(a_4=2\times12+3\times3=33\) है। गुणांकों को सही पदों पर लगाएँ। / \(a_3=2\times3+3\times2=12\) and \(a_4=2\times12+3\times3=33\). Exam tip: apply coefficients to the correct terms.
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If \(a_1=1\), \(a_2=5\), and \(a_n=2a_{n-1}-a_{n-2}+2\), what is \(a_5\)?
C. (29)
पद (1,5,11,19,29) हैं इसलिए \(a_5=29\) है। दो-पद नियम में घटाव के बाद (2) जोड़ें। / The terms are (1,5,11,19,29), so \(a_5=29\). Exam tip: subtract in the two-term rule and then add (2).
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