Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 101-110 of 600 questions.
What is the common ratio in the sequence \(6,18,54,162,\ldots\)?
C. (3)
लगातार पदों का अनुपात \(18\div6=3\) है। परीक्षा में दूसरे पद को पहले पद से भाग दें। / The ratio of consecutive terms is \(18\div6=3\). In exams divide the second term by the first term.
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What will be the next term of the geometric progression \(4,16,64,256,\ldots\)?
C. (1024)
हर बार (4) से गुणा हो रहा है इसलिए अगला पद \(256\times4=1024\) है। परीक्षा में पहले सामान्य अनुपात पहचानें। / Each term is multiplied by (4) so the next term is \(256\times4=1024\). In exams first identify the common ratio.
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If a geometric progression has first term (7) and common ratio (4) what is the second term?
C. (28)
दूसरा पद \(7\times4=28\) होगा। परीक्षा में अगले पद के लिए सामान्य अनुपात से गुणा करें। / The second term is \(7\times4=28\). In exams multiply by the common ratio to get the next term.
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What is the common ratio in the sequence \(243,81,27,9,\ldots\)?
B. \(\frac{1}{3}\)
लगातार पदों का अनुपात \(81\div243=\frac{1}{3}\) है। परीक्षा में घटती गुणोत्तर श्रेणी में अनुपात भिन्न हो सकता है। / The ratio of consecutive terms is \(81\div243=\frac{1}{3}\). In exams a decreasing geometric progression can have a fractional ratio.
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Is the sequence \(5,25,125,625,\ldots\) a geometric progression?
A. हाँ सामान्य अनुपात (5) हैYes common ratio is (5)
सभी लगातार पदों का अनुपात (5) है। परीक्षा में गुणोत्तर श्रेणी के लिए समान अनुपात जाँचें। / All consecutive terms have ratio (5). In exams check equal ratios for a geometric progression.
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Why is the sequence \(2,6,12,20,\ldots\) not a geometric progression?
C. अनुपात समान नहीं हैंRatios are not equal
अनुपात \(6\div2=3\) और \(12\div6=2\) समान नहीं हैं। परीक्षा में लगातार अनुपात जाँचें। / The ratios \(6\div2=3\) and \(12\div6=2\) are not equal. In exams check consecutive ratios.
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What is the first term in the geometric progression \(12,36,108,324,\ldots\)?
B. (12)
अनुक्रम का पहला लिखा हुआ पद (12) है। परीक्षा में पहला पद (a) सीधे पहले पद से लें। / The first written term of the sequence is (12). In exams take the first term (a) directly from the sequence.
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If (a=2) and (r=6) what is the third term of the geometric progression?
C. (72)
तीसरा पद \(ar^2=2\times6^2=72\) है। परीक्षा में तीसरे पद के लिए अनुपात का वर्ग लगाएँ। / The third term is \(ar^2=2\times6^2=72\). 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 \(128,64,32,16,\ldots\)?
B. (8)
हर बार \(\frac{1}{2}\) से गुणा हो रहा है इसलिए अगला पद \(16\times\frac{1}{2}=8\) है। परीक्षा में घटती श्रेणी में भिन्न अनुपात पहचानें। / Each term is multiplied by \(\frac{1}{2}\) so the next term is \(16\times\frac{1}{2}=8\). In exams identify fractional ratios in decreasing sequences.
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What is the fifth term in the geometric progression \(4,12,36,108,\ldots\)?
B. (324)
सामान्य अनुपात (3) है इसलिए पाँचवाँ पद \(108\times3=324\) है। परीक्षा में अंतिम ज्ञात पद को अनुपात से गुणा करें। / The common ratio is (3) so the fifth term is \(108\times3=324\). In exams multiply the last known term by the ratio.
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