Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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What is the common difference of the arithmetic progression \(-10,-6,-2,2,\ldots\)?
B. (4)
यहाँ (-6-(-10)=4) है। ऋणात्मक संख्याओं के साथ घटाव सावधानी से करें। / Here (-6-(-10)=4). Subtract carefully when negative numbers are involved.
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A. (5)
सार्व अंतर दूसरा पद घटा पहला पद होता है। इसलिए (23-18=5)। / The common difference is the second term minus the first term. Therefore, (23-18=5).
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Is the sequence \(4,8,13,19,\ldots\) an arithmetic progression or not?
C. नहीं क्योंकि अंतर समान नहीं हैंNo because differences are not equal
इसके अंतर (4,5,6) हैं। समान अंतर न होने से यह समांतर श्रेढ़ी नहीं है। / Its differences are (4,5,6). Since the differences are not equal, it is not an arithmetic progression.
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C. (3)
हर अगला पद पिछले पद से (3) अधिक है। यही इस श्रेढ़ी का सार्व अंतर है। / Each next term is (3) greater than the previous term. This is the common difference of the sequence.
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If (a=2) and (d=5), what are the first three terms?
B. (2,7,12)
पहला पद (2) है और हर बार (5) जोड़ना है। इसलिए पहले तीन पद (2,7,12) हैं। / The first term is (2), and (5) is added each time. Therefore, the first three terms are (2,7,12).
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Which sequence starts with (a=9) and (d=2)?
A. \(9,11,13,15,\ldots\)
पहला पद (9) है और हर बार (2) जोड़ना है। इसलिए सही अनुक्रम \(9,11,13,15,\ldots\) है। / The first term is (9), and (2) is added each time. Hence the correct sequence is \(9,11,13,15,\ldots\).
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What will be the next two terms in \(40,35,30,25,\ldots\)?
C. (20,15)
यहाँ सार्व अंतर (-5) है। इसलिए (25-5=20) और (20-5=15)। / The common difference is (-5). Therefore, (25-5=20) and (20-5=15).
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Which term is not given in the arithmetic progression \(18,21,24,27,\ldots\)?
D. (30)
लिखे हुए पद (18,21,24,27) हैं। (30) अगला पद हो सकता है पर दिए गए पदों में नहीं है। / The written terms are (18,21,24,27). (30) can be the next term but is not among the given terms.
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If a sequence is \(5,5,5,5,\ldots\), what type of arithmetic progression is it?
C. समान पदों वालीConstant terms
सभी पद समान हैं इसलिए (d=0) है। इसे समान पदों वाली समांतर श्रेढ़ी कह सकते हैं। / All terms are equal, so (d=0). It can be called an arithmetic progression with constant terms.
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B. (2)
हर अगली पंक्ति में (2) सीटें बढ़ती हैं। इसलिए सार्व अंतर (2) है। / Each next row increases by (2) seats. Therefore, the common difference is (2).
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