Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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What is the common difference in the arithmetic progression \(25,20,15,10,\ldots\)?
B. (-5)
यहाँ (20-25=-5) है। सार्व अंतर में चिन्ह का ध्यान रखना जरूरी है। / Here (20-25=-5). It is important to take care of the sign in the common difference.
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If each next term of a sequence is (7) more than the previous term, what is its common difference?
C. (7)
हर बार (7) जोड़ने का अर्थ सार्व अंतर (7) है। ऐसी श्रेढ़ी समांतर श्रेढ़ी होगी। / Adding (7) each time means the common difference is (7). Such a sequence will be an arithmetic progression.
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What is the common difference of \(1.5,2.0,2.5,3.0,\ldots\)?
B. (0.5)
लगातार पदों का अंतर (2.0-1.5=0.5) है। दशमलव पदों में भी समान अंतर जाँचना होता है। / The difference of consecutive terms is (2.0-1.5=0.5). Even for decimal terms, equal differences must be checked.
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What is the common difference of \(\frac{1}{2},1,\frac{3}{2},2,\ldots\)?
A. \(\frac{1}{2}\)
यहाँ \(1-\frac{1}{2}=\frac{1}{2}\) है। भिन्नों में भी सार्व अंतर लगातार पदों से ही निकलेगा। / Here \(1-\frac{1}{2}=\frac{1}{2}\). For fractions also, the common difference is found from consecutive terms.
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Which sequence is an arithmetic progression with (d=3)?
B. \(4,7,10,13,\ldots\)
\(4,7,10,13,\ldots\) में हर बार (3) जुड़ता है। इसलिए इसका सार्व अंतर (3) है। / In \(4,7,10,13,\ldots\), (3) is added each time. Hence its common difference is (3).
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If the arithmetic progression is \(a,a+2,a+4,a+6,\ldots\), what is the common difference?
C. (2)
लगातार पदों का अंतर ((a+2)-a=2) है। अक्षर वाले पदों में भी घटाकर अंतर निकालें। / The difference of consecutive terms is ((a+2)-a=2). For algebraic terms also, subtract to find the difference.
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What will be the next term in \(30,27,24,21,\ldots\)?
C. (18)
यहाँ सार्व अंतर (-3) है। इसलिए अगला पद (21-3=18) होगा। / The common difference is (-3). Therefore, the next term is (21-3=18).
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Which is the third term in the arithmetic progression \(2,5,8,11,\ldots\)?
C. (8)
तीसरा लिखा हुआ पद (8) है। आसान प्रश्नों में पद की स्थिति ध्यान से गिनें। / The third written term is (8). In easy questions, count the position of the term carefully.
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Which option states the correct property of an arithmetic progression?
B. हर दो लगातार पदों का अंतर समान होता हैThe difference between every two consecutive terms is equal
समांतर श्रेढ़ी में लगातार पदों का अंतर स्थिर होता है। यही इसकी मुख्य पहचान है। / In an arithmetic progression, the difference between consecutive terms is constant. This is its main identity.
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Why is \(3,6,12,24,\ldots\) not an arithmetic progression?
C. क्योंकि लगातार अंतर समान नहीं हैंBecause consecutive differences are not equal
अंतर (3,6,12) हैं जो समान नहीं हैं। इसलिए यह समांतर श्रेढ़ी नहीं है। / The differences are (3,6,12), which are not equal. Hence it is not an arithmetic progression.
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