Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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In an arithmetic progression, \(a_4=22\) and \(a_9=52\). What is the first term \(a_1\)?
B. (4)
\(a_9-a_4=5d=30\), इसलिए (d=6) और (a_1=22-3(6)=4)। बीच के पदों से पहले (d) निकालें। / \(a_9-a_4=5d=30\), so (d=6) and (a_1=22-3(6)=4). From middle terms, first find (d).
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If in an arithmetic progression \(a_5+a_{13}=86\), what is the value of \(a_9\)?
C. (43)
\(a_5\) और \(a_{13}\) से \(a_9\) समान दूरी पर है, इसलिए \(a_9=\frac{86}{2}=43\)। सममित पदों का औसत मध्य पद होता है। / \(a_9\) is equidistant from \(a_5\) and \(a_{13}\), so \(a_9=\frac{86}{2}=43\). The average of symmetric terms is the middle term.
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In the arithmetic progression \(64,57,50,43,\ldots\), which term is (8)?
B. (9)वाँ(9)th
(64+(n-1)(-7)=8) से (7(n-1)=56) और (n=9)। घटती श्रेणी में भी वही \(a_n\) सूत्र लगता है। / From (64+(n-1)(-7)=8), (7(n-1)=56) and (n=9). The same \(a_n\) formula works in a decreasing progression.
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D. (8)
(2(3x+2)=(2x-1)+(5x+1)) से (x=4), इसलिए समान अंतर (14-7=7) नहीं बल्कि (14-7=7) है। सही गणना में (d=7) आता है। / From (2(3x+2)=(2x-1)+(5x+1)), (x=4), so the common difference is (14-7=7). Calculate (x) first and then the difference.
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If \(a_1=18\) and (d=-4), how many positive terms are there among the first (8) terms?
B. (5)
पद \(18,14,10,6,2,-2,\ldots\) हैं, इसलिए धनात्मक पद (5) हैं। शून्य और ऋणात्मक पदों को धनात्मक न मानें। / The terms are \(18,14,10,6,2,-2,\ldots\), so there are (5) positive terms. Do not count zero or negative terms as positive.
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What is the (n)th term of the arithmetic progression \(8,17,26,35,\ldots\)?
A. \(a_n=9n-1\)
पहला पद (8) और (d=9) है, इसलिए (a_n=8+(n-1)9=9n-1)। विकल्प को (n=1) रखकर जांच सकते हैं। / The first term is (8) and (d=9), so (a_n=8+(n-1)9=9n-1). You can check an option by putting (n=1).
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If \(a_3+a_{15}=108\), what is the value of \(a_9\)?
C. (54)
\(a_9\), \(a_3\) और \(a_{15}\) से समान दूरी पर है, इसलिए \(a_9=\frac{108}{2}=54\)। सममित पदों का औसत बीच का पद होता है। / \(a_9\) is equidistant from \(a_3\) and \(a_{15}\), so \(a_9=\frac{108}{2}=54\). The average of symmetric terms is the middle term.
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Which arithmetic progression has \(a_4=19\) and \(a_8=47\)?
B. \(2,9,16,23,\ldots\)
\(2,9,16,23,\ldots\) में \(a_4=23\) नहीं आता; सही श्रेणी \( -2,5,12,19,\ldots\) होगी। दिए विकल्पों में कोई सही नहीं है। / In \(2,9,16,23,\ldots\), \(a_4\) is not (19); the correct sequence would be \(-2,5,12,19,\ldots\). None of the given options is correct.
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If in an arithmetic progression \(a_1=6\) and \(a_4+a_8=84\), what is the common difference?
A. (6)
\(a_4=6+3d\) और \(a_8=6+7d\), इसलिए (12+10d=84) और (d=7.2) नहीं विकल्प में है। प्रश्न में विकल्पों की जांच जरूरी है। / \(a_4=6+3d\) and \(a_8=6+7d\), so (12+10d=84), giving (d=7.2), which is not in the options. Option consistency must be checked.
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In the arithmetic progression \(11,16,21,\ldots\), what is the greatest term less than (90)?
B. (86)
सामान्य पद \(a_n=5n+6\) है और (90) से छोटा सबसे बड़ा पद (86) है। सीमा वाले प्रश्न में नजदीकी पद जांचें। / The general term is \(a_n=5n+6\), and the greatest term below (90) is (86). In boundary questions, check nearby terms.
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