Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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What is the common ratio in the sequence \(2,6,18,54,\ldots\)?
B. (3)
लगातार पदों का अनुपात \(6\div2=3\) है। परीक्षा में दूसरे पद को पहले पद से भाग दें। / The ratio of consecutive terms is \(6\div2=3\). In exams, divide the second term by the first term.
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What will be the next term of the geometric progression \(5,10,20,40,\ldots\)?
D. (80)
हर बार (2) से गुणा हो रहा है, इसलिए अगला पद \(40\times2=80\) है। परीक्षा में पहले सामान्य अनुपात पहचानें। / Each term is multiplied by (2), so the next term is \(40\times2=80\). In exams, first identify the common ratio.
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If a geometric progression has first term (4) and common ratio (2), what is the second term?
C. (8)
दूसरा पद \(4\times2=8\) होगा। परीक्षा में अगले पद के लिए सामान्य अनुपात से गुणा करें। / The second term is \(4\times2=8\). In exams, multiply by the common ratio to get the next term.
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What is the common ratio in the sequence \(81,27,9,3,\ldots\)?
B. \(\frac{1}{3}\)
लगातार पदों का अनुपात \(27\div81=\frac{1}{3}\) है। परीक्षा में घटती गुणोत्तर श्रेणी में अनुपात भिन्न हो सकता है। / The ratio of consecutive terms is \(27\div81=\frac{1}{3}\). In exams, a decreasing geometric progression can have a fractional ratio.
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Is the sequence \(3,6,12,24,\ldots\) a geometric progression?
A. हाँ, सामान्य अनुपात (2) हैYes, common ratio is (2)
सभी लगातार पदों का अनुपात (2) है। परीक्षा में गुणोत्तर श्रेणी के लिए समान अनुपात जाँचें। / All consecutive terms have ratio (2). In exams, check equal ratios for a geometric progression.
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Why is the sequence \(2,4,6,8,\ldots\) not a geometric progression?
C. अनुपात समान नहीं हैंRatios are not equal
अनुपात \(4\div2=2\) और \(6\div4=\frac{3}{2}\) समान नहीं हैं। परीक्षा में लगातार अनुपात जाँचें। / The ratios \(4\div2=2\) and \(6\div4=\frac{3}{2}\) are not equal. In exams, check consecutive ratios.
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What is the first term in the geometric progression \(7,21,63,189,\ldots\)?
B. (7)
अनुक्रम का पहला लिखा हुआ पद (7) है। परीक्षा में पहला पद (a) सीधे पहले पद से लें। / The first written term of the sequence is (7). In exams, take the first term (a) directly from the sequence.
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If (a=3) and (r=4), what is the third term of the geometric progression?
C. (48)
तीसरा पद \(ar^2=3\times4^2=48\) है। परीक्षा में तीसरे पद के लिए अनुपात का वर्ग लगाएँ। / The third term is \(ar^2=3\times4^2=48\). In exams, use the square of the ratio for the third term.
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What is the next term of the geometric progression \(64,32,16,8,\ldots\)?
C. (4)
हर बार \(\frac{1}{2}\) से गुणा हो रहा है, इसलिए अगला पद \(8\times\frac{1}{2}=4\) है। परीक्षा में घटती श्रेणी में भिन्न अनुपात पहचानें। / Each term is multiplied by \(\frac{1}{2}\), so the next term is \(8\times\frac{1}{2}=4\). In exams, identify fractional ratios in decreasing sequences.
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What is the fifth term in the geometric progression \(2,6,18,54,\ldots\)?
C. (162)
सामान्य अनुपात (3) है, इसलिए पाँचवाँ पद \(54\times3=162\) है। परीक्षा में अंतिम ज्ञात पद को अनुपात से गुणा करें। / The common ratio is (3), so the fifth term is \(54\times3=162\). In exams, multiply the last known term by the ratio.
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