Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 461-470 of 600 questions.
In an arithmetic progression, \(a_3=16\) and \(a_8=41\). What is the first term \(a_1\)?
C. (6)
\(a_8-a_3=5d=25\), इसलिए (d=5) और (a_1=16-2(5)=6)। बीच के पदों से पहले (d) निकालें। / \(a_8-a_3=5d=25\), so (d=5) and (a_1=16-2(5)=6). From middle terms first find (d).
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If in an arithmetic progression \(a_4+a_8=50\), what is the value of \(a_6\)?
B. (25)
समांतर श्रेणी में \(a_4\) और \(a_8\) का औसत \(a_6\) होता है, इसलिए \(a_6=\frac{50}{2}=25\)। समान दूरी वाले पदों का औसत बीच का पद होता है। / In an arithmetic progression, the average of \(a_4\) and \(a_8\) is \(a_6\), so \(a_6=\frac{50}{2}=25\). Equidistant terms average to the middle term.
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In the arithmetic progression \(50,43,36,29,\ldots\), which term is (1)?
B. (8)वाँ(8)th
(50+(n-1)(-7)=1) से (7(n-1)=49) और (n=8)। घटती श्रेणी में भी वही \(a_n\) सूत्र लगता है। / From (50+(n-1)(-7)=1), (7(n-1)=49) and (n=8). The same \(a_n\) formula works in a decreasing progression.
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C. (6)
(2(x+2)=(x-4)+(2x-2)) से (x=8), इसलिए समान अंतर (10-4=6) है। पहले (x) निकालें फिर अंतर निकालें। / From (2(x+2)=(x-4)+(2x-2)), (x=8), so the common difference is (10-4=6). First find (x), then find the difference.
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If \(a_1=12\) and (d=-3), how many positive terms are there among the first (8) terms?
B. (4)
पद \(12,9,6,3,0,-3,\ldots\) हैं, इसलिए धनात्मक पद (4) हैं। शून्य को धनात्मक नहीं मानते। / The terms are \(12,9,6,3,0,-3,\ldots\), so there are (4) positive terms. Zero is not counted as positive.
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What is the (n)th term of the arithmetic progression \(5,14,23,32,\ldots\)?
A. \(a_n=9n-4\)
पहला पद (5) और (d=9) है, इसलिए (a_n=5+(n-1)9=9n-4)। विकल्प को (n=1) रखकर जांच सकते हैं। / The first term is (5) and (d=9), so (a_n=5+(n-1)9=9n-4). You can check an option by putting (n=1).
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If \(a_2+a_{10}=64\), what is the value of \(a_6\)?
D. (32)
\(a_2\) और \(a_{10}\) से \(a_6\) समान दूरी पर है, इसलिए \(a_6=\frac{64}{2}=32\)। सममित पदों का औसत बीच का पद होता है। / \(a_6\) is equidistant from \(a_2\) and \(a_{10}\), so \(a_6=\frac{64}{2}=32\). The average of symmetric terms is the middle term.
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Which arithmetic progression has \(a_3=12\) and \(a_7=32\)?
B. \(2,7,12,17,\ldots\)
\(2,7,12,17,\ldots\) में \(a_3=12\) और (d=5), इसलिए \(a_7=32\)। विकल्पों में दोनों शर्तें जांचें। / In \(2,7,12,17,\ldots\), \(a_3=12\) and (d=5), so \(a_7=32\). Check both conditions in the options.
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If in an arithmetic progression \(a_1=3\) and \(a_4+a_6=56\), what is the common difference?
B. (5)
\(a_4=3+3d\) और \(a_6=3+5d\), इसलिए (6+8d=56) और \(d=\frac{25}{4}\) नहीं आता; सही समीकरण से \(d=\frac{50}{8}\) है। यह विकल्प-जांच प्रश्न नहीं होना चाहिए। / Using \(a_4=3+3d\) and \(a_6=3+5d\), (6+8d=56), so \(d=\frac{25}{4}\). This result is not among the options.
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In the arithmetic progression \(7,10,13,\ldots\), what is the greatest term less than (100)?
C. (97)
सामान्य पद \(a_n=3n+4\) है और (100) से छोटा सबसे बड़ा मान (97) मिलता है। सीमा वाले प्रश्न में नजदीकी पद जांचें। / The general term is \(a_n=3n+4\), and the greatest value below (100) is (97). In boundary questions check the nearest terms.
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