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 121-130 of 600 questions.
If \(a_n=6\cdot2^{n-1}\) what first three terms does it give?
A. (6,12,24)
(n=1,2,3) रखने पर (6,12,24) मिलते हैं। परीक्षा में (n-1) वाले घातांक को ध्यान से लगाएँ। / Putting (n=1,2,3) gives (6,12,24). In exams apply the exponent (n-1) carefully.
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What is the general term of the geometric progression \(7,28,112,448,\ldots\)?
A. \(a_n=7\cdot4^{n-1}\)
पहला पद (7) और अनुपात (4) है इसलिए \(a_n=7\cdot4^{n-1}\) है। परीक्षा में पहला पद और अनुपात दोनों मिलाएँ। / The first term is (7) and the ratio is (4) so \(a_n=7\cdot4^{n-1}\). In exams match both the first term and the ratio.
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If \(4,20,100,\Box,\ldots\) is a geometric progression what term fills the blank?
C. (500)
सामान्य अनुपात (5) है इसलिए रिक्त पद \(100\times5=500\) है। परीक्षा में समान अनुपात जारी रखें। / The common ratio is (5) so the missing term is \(100\times5=500\). In exams continue the same ratio.
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What is the common ratio in the geometric progression \(72,24,8,\frac{8}{3},\ldots\)?
B. \(\frac{1}{3}\)
लगातार पदों का अनुपात \(24\div72=\frac{1}{3}\) है। परीक्षा में घटती गुणोत्तर श्रेणी में भिन्न अनुपात लिखें। / The ratio of consecutive terms is \(24\div72=\frac{1}{3}\). In exams write the fractional ratio for a decreasing geometric progression.
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What will be the sixth term in the geometric progression \(2,8,32,128,\ldots\)?
D. (2048)
चौथे पद (128) के बाद पाँचवाँ (512) और छठा (2048) है। परीक्षा में पद संख्या गिनते समय पहला पद शामिल करें। / After the fourth term (128) the fifth is (512) and the sixth is (2048). In exams include the first term while counting.
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Is \(14,42,126,378,\ldots\) a geometric progression?
A. हाँ सामान्य अनुपात (3) हैYes common ratio is (3)
हर लगातार पद का अनुपात (3) है। परीक्षा में समान अनुपात दिखे तो गुणोत्तर श्रेणी मानें। / Each consecutive term has ratio (3). In exams if equal ratio appears treat it as a geometric progression.
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If (a=4) and (r=7) what are the first four terms?
B. (4,28,196,1372)
हर बार (7) से गुणा करने पर (4,28,196,1372) मिलते हैं। परीक्षा में पहला पद न बदलें। / Multiplying by (7) each time gives (4,28,196,1372). In exams do not change the first term.
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Which is the general term of the geometric progression \(100,20,4,\frac{4}{5},\ldots\)?
B. \(a_n=100\cdot\left(\frac{1}{5}\right)^{n-1}\)
पहला पद (100) और अनुपात \(\frac{1}{5}) है इसलिए \(a_n=100\cdot\left(\frac{1}{5}\right)^{n-1}\) है। परीक्षा में घटती श्रेणी में भिन्न अनुपात लगाएँ। / The first term is (100) and the ratio is \(\frac{1}{5}\) so \(a_n=100\cdot\left(\frac{1}{5}\right)^{n-1}\). In exams use the fractional ratio in a decreasing sequence.
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If \(a_n=64\cdot\left(\frac{1}{2}\right)^{n-1}\) what is the value of \(a_5\)?
B. (4)
\(a_5=64\cdot\left(\frac{1}{2}\right)^4=4\) है। परीक्षा में (n-1) वाले घातांक को सही रखें। / \(a_5=64\cdot\left(\frac{1}{2}\right)^4=4\). In exams keep the exponent (n-1) correct.
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What are (a) and (r) in the geometric progression \(3,18,108,648,\ldots\)?
A. (a=3,r=6)
पहला पद (3) है और अनुपात \(18\div3=6\) है। परीक्षा में (a) और (r) अलग-अलग पहचानें। / The first term is (3) and the ratio is \(18\div3=6\). In exams identify (a) and (r) separately.
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