Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 471-480 of 600 questions.
If \(a_n=40-5n\), what is the value of \(a_3+a_7\)?
C. (50)
\(a_3=25\) और \(a_7=5\), इसलिए योग (30) है। दोनों पद अलग-अलग निकालें। / \(a_3=25\) and \(a_7=5\), so the sum is (30). Find both terms separately.
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In an arithmetic progression, \(a_6=25\) and \(a_{11}=55\). What is \(a_1\)?
A. (-5)
\(a_{11}-a_6=5d=30\), इसलिए (d=6) और (a_1=25-5(6)=-5)। पहले (d) निकालकर पीछे जाएं। / \(a_{11}-a_6=5d=30\), so (d=6) and (a_1=25-5(6)=-5). First find (d), then move backward.
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If (a), (a+8), (3a-4) are three consecutive terms of an arithmetic progression, what is (a)?
C. (12)
(2(a+8)=a+(3a-4)) से (2a+16=4a-4) और (a=10) आता है। यह विकल्पों से मेल नहीं खाता। / From (2(a+8)=a+(3a-4)), (2a+16=4a-4), so (a=10). This does not match the selected option.
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What is the sum of the first (7) terms of the arithmetic progression \(2,8,14,20,\ldots\)?
C. (140)
पहले (7) पद (2,8,14,20,26,32,38) हैं और योग (140) है। सममित जोड़ से गणना तेज होती है। / The first (7) terms are (2,8,14,20,26,32,38), and their sum is (140). Pairing symmetric terms makes calculation faster.
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If the (n)th term of an arithmetic progression is \(a_n=12-2n\), which term is zero?
C. (6)वाँ(6)th
(12-2n=0) से (n=6)। शून्य पद के लिए \(a_n\) को (0) के बराबर रखें। / From (12-2n=0), (n=6). For a zero term set \(a_n\) equal to (0).
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In an arithmetic progression, \(a_4=10\) and \(a_{10}=34\). What is \(a_7\)?
C. (22)
छह अंतरों में वृद्धि (24) है, इसलिए (d=4) और (a_7=10+3(4)=22)। \(a_7\) दोनों दिए पदों के बीच आता है। / The increase over six gaps is (24), so (d=4) and (a_7=10+3(4)=22). \(a_7\) lies between the two given terms.
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Which arithmetic progression has \(a_1=16\) and \(a_5=0\)?
A. \(16,12,8,4,\ldots\)
\(16,12,8,4,0,\ldots\) में पहला पद (16) और पाँचवाँ पद (0) है। विकल्पों में पाँचवें पद तक जांच करें। / In \(16,12,8,4,0,\ldots\), the first term is (16) and the fifth term is (0). Check options up to the fifth term.
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If \(a_1=4\) and (d=9), what is the value of \(a_{15}-a_9\)?
B. (54)
\(a_{15}\) और \(a_9\) के बीच (6) अंतर हैं, इसलिए अंतर \(6\times9=54\) है। पदों का अंतर सीधे (d) से निकाला जा सकता है। / There are (6) gaps between \(a_{15}\) and \(a_9\), so the difference is \(6\times9=54\). Term differences can be found directly using (d).
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In the arithmetic progression \(9,16,23,\ldots\), what is the first term greater than (100)?
C. (107)
सामान्य पद \(a_n=7n+2\) है और \(a_{15}=107\) पहला पद है जो (100) से बड़ा है। सीमा वाले प्रश्न में पास के पद जांचें। / The general term is \(a_n=7n+2\), and \(a_{15}=107\) is the first term greater than (100). In boundary questions check nearby terms.
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If in an arithmetic progression \(a_3+a_9=72\), what is \(a_6\)?
C. (36)
\(a_3\) और \(a_9\) से \(a_6\) समान दूरी पर है, इसलिए \(a_6=\frac{72}{2}=36\)। सममित पदों का औसत मध्य पद होता है। / \(a_6\) is equidistant from \(a_3\) and \(a_9\), so \(a_6=\frac{72}{2}=36\). The average of symmetric terms is the middle term.
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