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 481-490 of 601 questions.
If \(a_1=210\) and (a_{n+1}=a_n-(7n+6)), what is \(a_4\)?
A. (150)
घटने वाले मान (13,20,27) हैं इसलिए \(a_4=150\) है। घटाने से पहले (7n+6) निकालें। / The subtracted values are (13,20,27), so \(a_4=150\). Exam tip: calculate (7n+6) before subtracting.
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If \(a_1=2\), \(a_2=3\), and \(a_n=5a_{n-1}-4a_{n-2}+3\), what is \(a_4\)?
C. (41)
\(a_3=10\) और \(a_4=41\) है। दोनों पिछले पदों के गुणांक सावधानी से लगाएँ। / \(a_3=10\) and \(a_4=41\). Exam tip: apply the coefficients of both previous terms carefully.
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If \(a_1=7\) and \(a_{n+1}=a_n+\frac{7n}{2}\), what is \(a_5\)?
B. (42)
कुल जोड़ (\frac{7(1+2+3+4)}{2}=35) है इसलिए \(a_5=42\) है। भिन्न जोड़ में कुल जोड़ पहले निकालें। / The total addition is (\frac{7(1+2+3+4)}{2}=35), so \(a_5=42\). Exam tip: find total fractional addition first.
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If \(a_1=80\) and \(a_{n+1}=a_n-\frac{7n}{2}\), what is \(a_5\)?
A. (45)
कुल घटाव (\frac{7(1+2+3+4)}{2}=35) है इसलिए \(a_5=45\) है। भिन्न घटावों को पहले जोड़ें। / The total subtraction is (\frac{7(1+2+3+4)}{2}=35), so \(a_5=45\). Exam tip: add fractional subtractions first.
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If \(a_1=4\) and \(a_{n+1}=n a_n+5\), what is \(a_4\)?
D. (74)
\(a_2=9\), \(a_3=23\) और \(a_4=74\) है। गुणक (n) हर चरण में बदलता है। / \(a_2=9\), \(a_3=23\), and \(a_4=74\). Exam tip: the multiplier (n) changes at each step.
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If \(a_1=5\) and (a_{n+1}=(n+2)a_n-1), what is \(a_4\)?
B. (274)
\(a_2=14\), \(a_3=55\) और \(a_4=274\) है। गुणक (n+2) बदलता है। / \(a_2=14\), \(a_3=55\), and \(a_4=274\). Exam tip: the multiplier (n+2) changes.
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Which recursive rule is correct for the sequence \(4,14,44,134,\ldots\)?
C. \(a_1=4, a_{n+1}=3a_n+2\)
\(3\times4+2=14\) और \(3\times14+2=44\) है। नियम चुनते समय पहला पद भी जाँचें। / \(3\times4+2=14\) and \(3\times14+2=44\). Exam tip: check the first term too when selecting a rule.
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Which recursive rule is correct for the sequence \(6,11,19,30,\ldots\)?
D. \(a_1=6, a_{n+1}=a_n+3n+2\)
जोड़ (5,8,11) हैं इसलिए (3n+2) जुड़ता है। पहला पद और बदलते जोड़ दोनों मिलाएँ। / The additions are (5,8,11), so (3n+2) is added. Exam tip: match both the first term and changing additions.
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If \(a_1=5\) and \(a_{n+1}=a_n+n^2\), which term is (60)?
A. (6)वाँ(6)th
पद (5,6,10,19,35,60) हैं इसलिए (60) छठा पद है। वर्ग जोड़ते समय क्रमांक साथ लिखें। / The terms are (5,6,10,19,35,60), so (60) is the sixth term. Exam tip: write positions while adding squares.
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If \(a_1=5\) and \(a_{n+1}=a_n+n!+2^n\), what is \(a_5\)?
B. (68)
जुड़ने वाले मान (3,6,14,40) हैं इसलिए \(a_5=68\) है। फैक्टोरियल और घात दोनों निकालें। / The added values are (3,6,14,40), so \(a_5=68\). Exam tip: calculate both the factorial and the power.
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