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 51-60 of 600 questions.
What is the common ratio in the sequence \(4,12,36,108,\ldots\)?
B. (3)
लगातार पदों का अनुपात \(12\div4=3\) है। परीक्षा में दूसरे पद को पहले पद से भाग दें। / The ratio of consecutive terms is \(12\div4=3\). In exams divide the second term by the first term.
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What will be the next term of the geometric progression \(7,14,28,56,\ldots\)?
C. (112)
हर बार (2) से गुणा हो रहा है इसलिए अगला पद \(56\times2=112\) है। परीक्षा में पहले सामान्य अनुपात पहचानें। / Each term is multiplied by (2) so the next term is \(56\times2=112\). In exams first identify the common ratio.
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If a geometric progression has first term (5) and common ratio (3) what is the second term?
D. (15)
दूसरा पद \(5\times3=15\) होगा। परीक्षा में अगले पद के लिए सामान्य अनुपात से गुणा करें। / The second term is \(5\times3=15\). In exams multiply by the common ratio to get the next term.
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What is the common ratio in the sequence \(125,25,5,1,\ldots\)?
B. \(\frac{1}{5}\)
लगातार पदों का अनुपात \(25\div125=\frac{1}{5}\) है। परीक्षा में घटती गुणोत्तर श्रेणी में अनुपात भिन्न हो सकता है। / The ratio of consecutive terms is \(25\div125=\frac{1}{5}\). In exams a decreasing geometric progression can have a fractional ratio.
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Is the sequence \(2,8,32,128,\ldots\) a geometric progression?
B. हाँ सामान्य अनुपात (4) हैYes common ratio is (4)
सभी लगातार पदों का अनुपात (4) है। परीक्षा में गुणोत्तर श्रेणी के लिए समान अनुपात जाँचें। / All consecutive terms have ratio (4). In exams check equal ratios for a geometric progression.
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Why is the sequence \(3,6,9,12,\ldots\) not a geometric progression?
C. अनुपात समान नहीं हैंRatios are not equal
अनुपात \(6\div3=2\) और \(9\div6=\frac{3}{2}\) समान नहीं हैं। परीक्षा में लगातार अनुपात जाँचें। / The ratios \(6\div3=2\) and \(9\div6=\frac{3}{2}\) are not equal. In exams check consecutive ratios.
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What is the first term in the geometric progression \(9,27,81,243,\ldots\)?
B. (9)
अनुक्रम का पहला लिखा हुआ पद (9) है। परीक्षा में पहला पद (a) सीधे पहले पद से लें। / The first written term of the sequence is (9). In exams take the first term (a) directly from the sequence.
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If (a=4) and (r=5) what is the third term of the geometric progression?
C. (100)
तीसरा पद \(ar^2=4\times5^2=100\) है। परीक्षा में तीसरे पद के लिए अनुपात का वर्ग लगाएँ। / The third term is \(ar^2=4\times5^2=100\). 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 \(162,54,18,6,\ldots\)?
B. (2)
हर बार \(\frac{1}{3}\) से गुणा हो रहा है इसलिए अगला पद \(6\times\frac{1}{3}=2\) है। परीक्षा में घटती श्रेणी में भिन्न अनुपात पहचानें। / Each term is multiplied by \(\frac{1}{3}\) so the next term is \(6\times\frac{1}{3}=2\). In exams identify fractional ratios in decreasing sequences.
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What is the fifth term in the geometric progression \(3,12,48,192,\ldots\)?
C. (768)
सामान्य अनुपात (4) है इसलिए पाँचवाँ पद \(192\times4=768\) है। परीक्षा में अंतिम ज्ञात पद को अनुपात से गुणा करें। / The common ratio is (4) so the fifth term is \(192\times4=768\). In exams multiply the last known term by the ratio.
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