Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 571-580 of 600 questions.
If \(a_n=63-5n\), what is the value of \(a_4+a_9\)?
B. (81)
\(a_4=43\) और \(a_9=18\), इसलिए योग (61) नहीं बल्कि (61) है। सही विकल्पों में (61) होना चाहिए। / \(a_4=43\) and \(a_9=18\), so the sum is (61). The correct option should include (61).
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In an arithmetic progression, \(a_8=45\) and \(a_{13}=80\). What is \(a_1\)?
A. (-4)
\(a_{13}-a_8=5d=35\), इसलिए (d=7) और (a_1=45-7(7)=-4)। पहले (d) निकालकर पीछे जाएं। / \(a_{13}-a_8=5d=35\), so (d=7) and (a_1=45-7(7)=-4). First find (d), then move backward.
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If (p+2), (2p+5), (4p+1) are three consecutive terms of an arithmetic progression, what is (p)?
A. (5)
(2(2p+5)=(p+2)+(4p+1)) से (4p+10=5p+3) और (p=7) आता है। सही विकल्प (7) होना चाहिए। / From (2(2p+5)=(p+2)+(4p+1)), (4p+10=5p+3), so (p=7). The correct option should be (7).
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What is the sum of the first (9) terms of the arithmetic progression \(5,13,21,29,\ldots\)?
C. (333)
पहला और नौवाँ पद (5) और (69) हैं, इसलिए योग (\frac{9(5+69)}{2}=333)। सममित जोड़ से गणना तेज होती है। / The first and ninth terms are (5) and (69), so the sum is (\frac{9(5+69)}{2}=333). Pairing symmetric terms makes calculation quick.
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If the (n)th term of an arithmetic progression is \(a_n=24-4n\), which term is zero?
C. (6)वाँ(6)th
(24-4n=0) से (n=6)। शून्य पद के लिए \(a_n\) को (0) के बराबर रखें। / From (24-4n=0), (n=6). For a zero term, set \(a_n\) equal to (0).
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In an arithmetic progression, \(a_6=31\) and \(a_{14}=79\). What is \(a_{10}\)?
B. (55)
आठ अंतरों में वृद्धि (48) है, इसलिए (d=6) और (a_{10}=31+4(6)=55)। \(a_{10}\) दोनों दिए पदों के बीच आता है। / The increase over eight gaps is (48), so (d=6) and (a_{10}=31+4(6)=55). \(a_{10}\) lies between the two given terms.
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Which arithmetic progression has \(a_1=36\) and \(a_9=4\)?
A. \(36,32,28,24,\ldots\)
\(36,32,28,24,20,16,12,8,4,\ldots\) में पहला पद (36) और नौवाँ पद (4) है। विकल्पों में नौवें पद तक जांच करें। / In \(36,32,28,24,20,16,12,8,4,\ldots\), the first term is (36) and the ninth term is (4). Check options up to the ninth term.
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If \(a_1=6\) and (d=9), what is the value of \(a_{16}-a_7\)?
B. (81)
\(a_{16}\) और \(a_7\) के बीच (9) अंतर हैं, इसलिए अंतर \(9\times9=81\) है। पदों का अंतर सीधे (d) से निकाला जा सकता है। / There are (9) gaps between \(a_{16}\) and \(a_7\), so the difference is \(9\times9=81\). Term differences can be found directly using (d).
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In the arithmetic progression \(17,23,29,\ldots\), what is the first term greater than (100)?
C. (107)
सामान्य पद \(a_n=6n+11\) है और \(a_{16}=107\) पहला पद है जो (100) से बड़ा है। सीमा वाले प्रश्न में पास के पद जांचें। / The general term is \(a_n=6n+11\), and \(a_{16}=107\) is the first term greater than (100). In boundary questions, check nearby terms.
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If in an arithmetic progression \(a_5+a_{15}=150\), what is \(a_{10}\)?
C. (75)
\(a_{10}\), \(a_5\) और \(a_{15}\) से समान दूरी पर है, इसलिए \(a_{10}=\frac{150}{2}=75\)। सममित पदों का औसत मध्य पद होता है। / \(a_{10}\) is equidistant from \(a_5\) and \(a_{15}\), so \(a_{10}=\frac{150}{2}=75\). The average of symmetric terms is the middle term.
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