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 21-30 of 600 questions.
If \(a_n=3\cdot2^{n-1}\), what first three terms does it give?
A. (3,6,12)
(n=1,2,3) रखने पर (3,6,12) मिलते हैं। परीक्षा में (n-1) वाले घातांक को ध्यान से लगाएँ। / Putting (n=1,2,3) gives (3,6,12). In exams, apply the exponent (n-1) carefully.
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What is the general term of the geometric progression \(8,24,72,216,\ldots\)?
A. \(a_n=8\cdot3^{n-1}\)
पहला पद (8) और अनुपात (3) है, इसलिए \(a_n=8\cdot3^{n-1}\) है। परीक्षा में पहला पद और अनुपात दोनों मिलाएँ। / The first term is (8) and the ratio is (3), so \(a_n=8\cdot3^{n-1}\). In exams, match both the first term and the ratio.
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If \(2,10,50,\Box,\ldots\) is a geometric progression, what term fills the blank?
D. (250)
सामान्य अनुपात (5) है, इसलिए रिक्त पद \(50\times5=250\) है। परीक्षा में समान अनुपात जारी रखें। / The common ratio is (5), so the missing term is \(50\times5=250\). In exams, continue the same ratio.
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What is the common ratio in the geometric progression \(32,16,8,4,\ldots\)?
B. \(\frac{1}{2}\)
लगातार पदों का अनुपात \(16\div32=\frac{1}{2}\) है। परीक्षा में घटती गुणोत्तर श्रेणी में भिन्न अनुपात लिखें। / The ratio of consecutive terms is \(16\div32=\frac{1}{2}\). 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 \(6,18,54,162,\ldots\)?
B. (486)
पाँचवाँ पद (486) और छठा पद (1458) नहीं; दिए चार पदों के बाद पाँचवाँ (486) है। परीक्षा में पद संख्या गिनते समय पहला पद शामिल करें। / The fifth term is (486), not the sixth; the asked term should be counted carefully. In exams, include the first term while counting.
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Is \(10,20,40,80,\ldots\) a geometric progression?
A. हाँ, सामान्य अनुपात (2) हैYes, common ratio is (2)
हर लगातार पद का अनुपात (2) है। परीक्षा में समान अनुपात दिखे तो गुणोत्तर श्रेणी मानें। / Each consecutive term has ratio (2). In exams, if equal ratio appears, treat it as a geometric progression.
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If (a=2) and (r=5), what are the first four terms?
B. (2,10,50,250)
हर बार (5) से गुणा करने पर (2,10,50,250) मिलते हैं। परीक्षा में पहला पद न बदलें। / Multiplying by (5) each time gives (2,10,50,250). In exams, do not change the first term.
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Which is the general term of the geometric progression \(27,9,3,1,\ldots\)?
B. (a_n=27\cdot\left\(\frac{1}{3}\right\)^{n-1})
पहला पद (27) और अनुपात \(\frac{1}{3}\) है, इसलिए (a_n=27\cdot\left\(\frac{1}{3}\right\)^{n-1}) है। परीक्षा में घटती श्रेणी में भिन्न अनुपात लगाएँ। / The first term is (27) and the ratio is \(\frac{1}{3}\), so (a_n=27\cdot\left\(\frac{1}{3}\right\)^{n-1}). In exams, use the fractional ratio in a decreasing sequence.
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If \(a_n=16\cdot\left(\frac{1}{2}\right)^{n-1}\), what is the value of \(a_4\)?
B. (2)
\(a_4=16\cdot\left(\frac{1}{2}\right)^3=2\) है। परीक्षा में (n-1) वाले घातांक को सही रखें। / \(a_4=16\cdot\left(\frac{1}{2}\right)^3=2\). In exams, keep the exponent (n-1) correct.
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What are (a) and (r) in the geometric progression \(1,5,25,125,\ldots\)?
A. (a=1,r=5)
पहला पद (1) है और अनुपात \(5\div1=5\) है। परीक्षा में (a) और (r) अलग-अलग पहचानें। / The first term is (1), and the ratio is \(5\div1=5\). In exams, identify (a) and (r) separately.
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