Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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In an arithmetic progression, (a=3) and (d=0). What are the first three terms?
C. (3,3,3)
(d=0) होने पर हर पद समान रहता है। इसलिए पहले तीन पद (3,3,3) हैं। / When (d=0), every term remains equal. Therefore, the first three terms are (3,3,3).
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If (a=15) and (d=-4), what are the first four terms?
B. (15,11,7,3)
पहला पद (15) है और हर बार (4) घटता है। इसलिए पद (15,11,7,3) होंगे। / The first term is (15), and (4) is subtracted each time. Hence the terms are (15,11,7,3).
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What is the common difference of \(2k,2k+3,2k+6,2k+9,\ldots\)?
B. (3)
लगातार पदों का अंतर ((2k+3)-2k=3) है। बीजीय पदों में समान पद काट दें। / The difference of consecutive terms is ((2k+3)-2k=3). In algebraic terms, cancel like terms.
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If an arithmetic progression has (d=-1.5) and first term (10), what is the second term?
A. (8.5)
दूसरा पद (10+(-1.5)=8.5) है। दशमलव और ऋणात्मक चिन्ह दोनों का ध्यान रखें। / The second term is (10+(-1.5)=8.5). Take care of both decimals and negative signs.
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What is (d) in the arithmetic progression \(\frac{1}{3},\frac{2}{3},1,\frac{4}{3},\ldots\)?
A. \(\frac{1}{3}\)
\(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\) है। भिन्नों में पहले दो पदों का अंतर निकालें। / \(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\). For fractions, find the difference of the first two terms.
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Rooms on the floors of a building increase as \(18,22,26,30,\ldots\). What is the common difference?
B. (4)
हर अगली मंजिल पर (4) कमरे बढ़ रहे हैं। इसलिए सार्व अंतर (4) है। / Each next floor has (4) more rooms. Therefore, the common difference is (4).
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What will be the fifth term in \(64,57,50,43,\ldots\)?
A. (36)
यहाँ (d=-7) है। पाँचवाँ पद (43-7=36) होगा। / Here (d=-7). The fifth term will be (43-7=36).
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If (a=4) and (a+d=13), what is the value of (d)?
B. (9)
(d=13-4=9) है। दूसरे पद से पहले पद को घटाने पर सार्व अंतर मिलता है। / (d=13-4=9). Subtracting the first term from the second term gives the common difference.
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Which sequence is an arithmetic progression with (d=0.25)?
B. \(0.25,0.5,0.75,1.0,\ldots\)
(0.5-0.25=0.25) और आगे भी यही अंतर है। इसलिए यह सही समांतर श्रेढ़ी है। / (0.5-0.25=0.25), and the same difference continues. Hence this is the correct arithmetic progression.
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What is the common difference in \(7,7.5,8,8.5,\ldots\)?
B. (0.5)
सार्व अंतर (7.5-7=0.5) है। दशमलव पदों में भी नियमित अंतर देखें। / The common difference is (7.5-7=0.5). For decimal terms also, check the regular difference.
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