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 301-310 of 600 questions.
What is the twelfth term of the geometric progression \(3,6,12,24,\ldots\)?
B. (6144)
यहाँ (a=3) और (r=2) है इसलिए \(a_{12}=3\cdot2^{11}=6144\) है। परीक्षा में \(a_n=ar^{n-1}\) लगाएँ। / Here (a=3) and (r=2) so \(a_{12}=3\cdot2^{11}=6144\). In exams use \(a_n=ar^{n-1}\).
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If a geometric progression has (a=5) and (r=3) what is the value of \(a_8\)?
C. (10935)
\(a_8=5\cdot3^7=10935\) है। परीक्षा में आठवें पद के लिए \(r^7\) लगाएँ। / \(a_8=5\cdot3^7=10935\). In exams use \(r^7\) for the eighth term.
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What is the ninth term of the geometric progression \(256,128,64,32,\ldots\)?
A. (1)
यहाँ \(r=\frac{1}{2}\) है इसलिए (a_9=256\cdot\left\(\frac{1}{2}\right\)8=1) है। परीक्षा में घटती श्रेणी में भिन्न अनुपात लगाएँ। / Here \(r=\frac{1}{2}\) so (a_9=256\cdot\left\(\frac{1}{2}\right\)8=1). In exams use the fractional ratio in decreasing progressions.
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If \(a_n=4\cdot3^{n-1}\) which term will be (2916)?
B. सातवाँ पद(7)th term
\(4\cdot3^{n-1}=2916\) से \(3^{n-1}=729=3^6\) इसलिए (n=7) है। परीक्षा में पहले दिए पद को \(a_n\) के बराबर रखें। / From \(4\cdot3^{n-1}=2916\), \(3^{n-1}=729=3^6\) so (n=7). In exams first equate the given term to \(a_n\).
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B. (3)
\(486=6r^4\) से \(r^4=81\) और (r=3) है। परीक्षा में पाँचवें पद के लिए \(r^4\) याद रखें। / From \(486=6r^4\), \(r^4=81\) and (r=3). In exams remember \(r^4\) for the fifth term.
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What is the general term of the geometric progression \(10,30,90,270,\ldots\)?
A. \(a_n=10\cdot3^{n-1}\)
पहला पद (10) और अनुपात (3) है इसलिए \(a_n=10\cdot3^{n-1}\) है। परीक्षा में \(ar^{n-1}\) में (a) और (r) सही रखें। / The first term is (10) and the ratio is (3) so \(a_n=10\cdot3^{n-1}\). In exams keep (a) and (r) correct in \(ar^{n-1}\).
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What is the sum of the first (6) terms of the geometric progression \(2,6,18,54,\ldots\)?
C. (728)
पहले (6) पदों का योग (2\(3^6-1\)/(3-1)=728) है। परीक्षा में (r>1) के लिए (S_n=\frac{a\(r^n-1\)}{r-1}) लगाएँ। / The sum of the first (6) terms is (2\(3^6-1\)/(3-1)=728). In exams use (S_n=\frac{a\(r^n-1\)}{r-1}) for (r>1).
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If (8,x,72) are in geometric progression and (x>0), what is (x)?
C. (24)
मध्य पद के लिए \(x^2=8\cdot72=576\) इसलिए (x=24) है। परीक्षा में तीन GP पदों में मध्य पद का वर्ग बाहरी पदों के गुणनफल के बराबर होता है। / For the middle term \(x^2=8\cdot72=576\), so (x=24). In exams the square of the middle GP term equals the product of outer terms.
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What is the sum of the first (8) terms of the geometric progression \(5,10,20,40,\ldots\)?
A. (1275)
(S_8=5\(2^8-1\)=1275) है। परीक्षा में अनुपात (2) हो तो घात जल्दी निकालें। / (S_8=5\(2^8-1\)=1275). In exams calculate powers quickly when the ratio is (2).
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If \(a_4=135\) and (r=3), what is the first term (a)?
B. (5)
\(a_4=ar^3\) इसलिए \(135=a\cdot27\) और (a=5) है। परीक्षा में चौथे पद से \(r^3\) भाग दें। / \(a_4=ar^3\), so \(135=a\cdot27\) and (a=5). In exams divide the fourth term by \(r^3\).
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