Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 491-500 of 600 questions.
If \(a_3=7\) and \(a_{12}=61\), what is \(a_1\)?
A. (-5)
\(a_{12}-a_3=9d=54\), इसलिए (d=6) और (a_1=7-2(6)=-5)। पहले समान अंतर निकालें। / \(a_{12}-a_3=9d=54\), so (d=6) and (a_1=7-2(6)=-5). Find the common difference first.
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What is the sum of the first (9) terms of the arithmetic progression \(1,6,11,16,\ldots\)?
B. (189)
पहला और नौवाँ पद (1) और (41) हैं, इसलिए योग (\frac{9(1+41)}{2}=189)। योग में पहला और अंतिम पद उपयोग करें। / The first and ninth terms are (1) and (41), so the sum is (\frac{9(1+41)}{2}=189). Use the first and last terms for the sum.
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If \(a_n=25-3n\), which is the first negative term?
C. (9)वाँ(9)th
\(a_8=1\) और \(a_9=-2\), इसलिए पहला ऋणात्मक पद (9)वाँ है। शून्य से नीचे जाने वाला पहला पद देखें। / \(a_8=1\) and \(a_9=-2\), so the first negative term is the (9)th. Look for the first term below zero.
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If in an arithmetic progression \(a_2+a_6=40\), what is \(a_4\)?
C. (20)
\(a_4\), \(a_2\) और \(a_6\) से समान दूरी पर है, इसलिए \(a_4=\frac{40}{2}=20\)। सममित पदों का औसत मध्य पद होता है। / \(a_4\) is equidistant from \(a_2\) and \(a_6\), so \(a_4=\frac{40}{2}=20\). The average of symmetric terms is the middle term.
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Which option can be three consecutive terms of an arithmetic progression?
B. (6,12,18)
(6,12,18) में दोनों अंतर (6) हैं। लगातार तीन पदों के लिए दोनों अंतर बराबर होने चाहिए। / In (6,12,18), both differences are (6). For three consecutive terms, the two differences must be equal.
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If \(a_1=9\) and (d=4), what is the value of \(a_3+a_9\)?
C. (60)
\(a_3=17\) और \(a_9=41\), इसलिए योग (58) है। यह विकल्पों से मेल नहीं खाता। / \(a_3=17\) and \(a_9=41\), so the sum is (58). This does not match the options.
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In an arithmetic progression, \(a_5=30\) and (d=7). What is \(a_1\)?
A. (2)
\(a_5=a_1+4d\), इसलिए \(30=a_1+28\) और \(a_1=2\)। दिए पद से पीछे जाने के लिए समान अंतर घटाएं। / \(a_5=a_1+4d\), so \(30=a_1+28\) and \(a_1=2\). To move backward from a given term subtract common differences.
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In the arithmetic progression \(8,15,22,\ldots\), what is the value of \(a_{10}+a_2\)?
D. (86)
\(a_{10}=71\) और \(a_2=15\), इसलिए योग (86) है। दोनों पद अलग-अलग निकालें। / \(a_{10}=71\) and \(a_2=15\), so the sum is (86). Find both terms separately.
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If an arithmetic progression has \(a_4=18\) and \(a_9=48\), what is \(a_{12}\)?
C. (66)
पाँच अंतरों में वृद्धि (30) है, इसलिए (d=6) और (a_{12}=48+3(6)=66)। पहले (d) निकालें फिर आगे बढ़ें। / The increase over five gaps is (30), so (d=6) and (a_{12}=48+3(6)=66). First find (d), then move forward.
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What is the (20)th term of the arithmetic progression \(13,18,23,28,\ldots\)?
B. (108)
यहाँ (a=13) और (d=5), इसलिए (a_{20}=13+19(5)=108)। बड़े पद के लिए भी (a_n=a+(n-1)d) लगाएं। / Here (a=13) and (d=5), so (a_{20}=13+19(5)=108). Use (a_n=a+(n-1)d) even for larger terms.
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