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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B. \(a_n=\frac{2n}{3n+2}\)
अंश (2n) और हर (3n+2) है इसलिए \(a_n=\frac{2n}{3n+2}\)। हर की बढ़त को ध्यान से देखें। / The numerator is (2n) and the denominator is (3n+2), so \(a_n=\frac{2n}{3n+2}\). Observe the denominator growth carefully.
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If \(a_n=11n-6\), what is \(a_7-a_2\)?
B. (55)
\(a_7=71\) और \(a_2=16\), इसलिए अंतर (55) है। घटाने से पहले दोनों पदों की अलग गणना करें। / \(a_7=71\) and \(a_2=16\), so the difference is (55). Calculate both terms separately before subtracting.
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What is the general term of the sequence \(5,-10,15,-20,\ldots\)?
D. (a_n=(-1)^{n+1}5n)
परिमाण (5n) है और चिह्न धन से शुरू होकर बदलता है इसलिए (a_n=(-1)^{n+1}5n)। पहले पद का चिह्न देखकर ((-1)) की शक्ति चुनें। / The magnitude is (5n) and signs start positive and alternate, so (a_n=(-1)^{n+1}5n). Choose the power of ((-1)) by checking the first term sign.
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Which is the correct rule for the sequence \(7,18,37,64,\ldots\)?
B. \(a_n=3n^2+4n\)
\(3n^2+4n\) से (7,20,39,64) नहीं आता; सही नियम \(4n^2+3\) है। विकल्पों को पहले चार पदों से मिलाना चाहिए। / \(3n^2+4n\) does not give the sequence; the correct rule is \(4n^2+3\). Options should be matched with the first four terms.
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If \(a_n=n^2+dn+2\) and \(a_4=34\), what is the value of (d)?
C. (4)
(16+4d+2=34) से (4d=16) और (d=4)। अज्ञात स्थिरांक के लिए दिया पद नियम में रखें। / From (16+4d+2=34), (4d=16) and (d=4). Substitute the given term in the rule to find the unknown constant.
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If \(a_n=15-3n\), which will be the first negative term?
C. (6)वाँ(6)th
\(a_5=0\) और \(a_6=-3\) है, इसलिए पहला ऋणात्मक पद (6)वाँ है। शून्य को ऋणात्मक न मानें। / \(a_5=0\) and \(a_6=-3\), so the first negative term is the (6)th. Do not count zero as negative.
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In an arithmetic sequence, \(a_4=17\) and \(a_9=42\). What is the value of \(a_{12}\)?
C. (57)
पाँच अंतरों में वृद्धि (25) है इसलिए (d=5), अतः (a_{12}=42+3(5)=57)। समान अंतर को आगे बढ़ाकर पद निकालें। / The increase over five gaps is (25), so (d=5), hence (a_{12}=42+3(5)=57). Extend the terms using the common difference.
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Which is the correct general term for the sequence \(10,21,34,49,\ldots\)?
D. \(a_n=n^2+8n+1\)
\(n^2+8n+1\) से (10,21,34,49) मिलते हैं। बढ़ते अंतर दिखें तो द्विघात नियम जांचें। / \(n^2+8n+1\) gives (10,21,34,49). When differences increase, check a quadratic rule.
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If (a_n=(2n-1)2+2), what is the value of \(a_5\)?
C. (83)
(a_5=(9)2+2=83)। पहले कोष्ठक का मान निकालें फिर वर्ग करें। / (a_5=(9)2+2=83). First find the value inside the bracket and then square it.
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In an arithmetic sequence, \(a_5=6\) and \(a_{10}=-9\). What will be its explicit rule?
A. \(a_n=21-3n\)
पाँच अंतरों में परिवर्तन (-15) है इसलिए (d=-3), अतः \(a_n=21-3n\)। दो दिए पदों से पहले समान अंतर निकालें। / The change over five gaps is (-15), so (d=-3), hence \(a_n=21-3n\). From two given terms first find the common difference.
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