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 571-580 of 600 questions.
If \(a_n=2n!+1\), what will be the value of \(a_5\)?
C. (241)
\(a_5=2\times5!+1=2\times120+1=241\) है। पहले फैक्टोरियल निकालें फिर गुणा करें। / \(a_5=2\times5!+1=2\times120+1=241\). Exam tip: calculate the factorial first and then multiply.
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In the sequence \(3,6,12,24,\ldots\), which is the first term greater than (500)?
B. (9)वाँ(9)th
\(a_8=384\) और \(a_9=768\) है इसलिए पहला बड़ा पद (9)वाँ है। सीमा के दोनों ओर के पद जाँचें। / \(a_8=384\) and \(a_9=768\), so the first greater term is the (9)th. Exam tip: check terms on both sides of the boundary.
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C. (65)
\(2\times33-1=65\) है। पुनरावर्ती नियम में गुणा और घटाव का क्रम न बदलें। / \(2\times33-1=65\). Exam tip: do not change the order of multiplication and subtraction in recurrence rules.
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If \(a_n=\frac{3n-1}{2n+5}\), what will be the simplified value of \(a_7\)?
A. \(\frac{20}{19}\)
\(a_7=\frac{21-1}{14+5}=\frac{20}{19}\) है। अंश और हर अलग-अलग सावधानी से निकालें। / \(a_7=\frac{21-1}{14+5}=\frac{20}{19}\). Exam tip: calculate numerator and denominator separately.
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What will be the (10)th term in the sequence \(1,5,2,10,4,20,8,\ldots\)?
D. (80)
सम स्थानों पर \(5,10,20,40,80,\ldots\) हैं। (10)वाँ पद पाँचवाँ सम-स्थान पद है इसलिए (80) है। / Even positions are \(5,10,20,40,80,\ldots\). The (10)th term is the fifth even-position term, so it is (80).
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B. (6)
बराबर अंतर से (2x+3-(x-1)=4x+1-(2x+3)) मिलता है। इससे (x=6) आता है। / Equal differences give (2x+3-(x-1)=4x+1-(2x+3)). This gives (x=6).
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If \(a_n=kn^2+2n\) and \(a_4=56\), what will be the value of \(a_7\)?
A. (161)
(16k+8=56) से (k=3) है। इसलिए \(a_7=3\times49+14=161\) होगा। / From (16k+8=56), (k=3). Therefore \(a_7=3\times49+14=161\).
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If \(a_n=pn+q\), \(a_5=31\) and \(a_{12}=80\), what will \(a_1\) be?
C. (3)
\(p=\frac{80-31}{12-5}=7\) और (q=-4) है। इसलिए \(a_1=7-4=3\) है। / \(p=\frac{80-31}{12-5}=7\) and (q=-4). Therefore \(a_1=7-4=3\).
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B. (76)
पहले अंतर (4,7,12,19) हैं इसलिए अगला अंतर (28) होगा। (48+28=76) है। / The first differences are (4,7,12,19), so the next difference is (28). Therefore (48+28=76).
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If \(a_n=2^n+3^n\), what will be the value of \(a_4\)?
C. (97)
\(a_4=2^4+3^4=16+81=97\) है। दोनों घात अलग-अलग निकालकर जोड़ें। / \(a_4=2^4+3^4=16+81=97\). Exam tip: calculate both powers separately and add.
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