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 151-160 of 600 questions.
What is the common ratio in the sequence \(3,6,12,24,\ldots\)?
A. (2)
सार्व अनुपात \(\frac{6}{3}=2\) है। गुणोत्तर श्रेढ़ी में दूसरा पद पहले पद से भाग दें। / The common ratio is \(\frac{6}{3}=2\). In a geometric progression divide the second term by the first term.
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If a geometric progression has first term (5) and common ratio (3), what is the fourth term?
C. (135)
\(a_4=5\cdot3^3=135\)। (n)वें पद के लिए \(a_n=ar^{n-1}\) याद रखें। / \(a_4=5\cdot3^3=135\). Remember \(a_n=ar^{n-1}\) for the (n)th term.
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Which sequence is a geometric progression?
B. \(4,12,36,108,\ldots\)
\(4,12,36,108,\ldots\) में हर बार (3) से गुणा हो रहा है। गुणोत्तर श्रेढ़ी में लगातार अनुपात समान होता है। / In \(4,12,36,108,\ldots\), each term is multiplied by (3). In a geometric progression consecutive ratios are equal.
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What is the common ratio of the sequence \(81,27,9,3,\ldots\)?
B. \(\frac{1}{3}\)
सार्व अनुपात \(\frac{27}{81}=\frac{1}{3}\) है। घटती गुणोत्तर श्रेढ़ी में अनुपात (1) से छोटा हो सकता है। / The common ratio is \(\frac{27}{81}=\frac{1}{3}\). In a decreasing geometric progression the ratio can be less than (1).
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If \(a_n=2\cdot4^{n-1}\), what is the value of \(a_5\)?
C. (512)
\(a_5=2\cdot4^4=512\)। घात में (n-1) का मान पहले निकालें। / \(a_5=2\cdot4^4=512\). First find the value of (n-1) in the exponent.
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In the geometric progression \(7,14,28,56,\ldots\), which term is (224)?
C. (6)वाँ(6)th
पद (7,14,28,56,112,224) हैं, इसलिए (224) छठा पद है। छोटे प्रश्नों में पद लिखकर जांचना तेज है। / The terms are (7,14,28,56,112,224), so (224) is the sixth term. For small questions listing terms is quick.
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Which sequence is not a geometric progression?
C. \(2,4,8,15,\ldots\)
\(2,4,8,15,\ldots\) में अनुपात \(2,2,\frac{15}{8}\) बराबर नहीं हैं। गुणोत्तर श्रेढ़ी में अनुपात स्थिर होना चाहिए। / In \(2,4,8,15,\ldots\), the ratios \(2,2,\frac{15}{8}\) are not equal. A geometric progression must have a constant ratio.
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If a geometric progression has (a=6) and (r=2), what are the first four terms?
B. (6,12,24,48)
पहला पद (6) है और हर बार (2) से गुणा करने पर (6,12,24,48) मिलते हैं। गुणोत्तर श्रेढ़ी में अगला पद गुणा करके बनता है। / The first term is (6), and multiplying by (2) each time gives (6,12,24,48). In a geometric progression each next term is formed by multiplication.
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What is the common ratio of the sequence \(2,-6,18,-54,\ldots\)?
B. (-3)
सार्व अनुपात \(\frac{-6}{2}=-3\) है। ऋणात्मक अनुपात होने पर चिह्न बारी-बारी से बदलते हैं। / The common ratio is \(\frac{-6}{2}=-3\). With a negative ratio the signs alternate.
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What is the next term in the geometric progression \(4,12,36,\ldots\)?
D. (108)
सार्व अनुपात (3) है, इसलिए अगला पद \(36\cdot3=108\) होगा। अगले पद के लिए पिछले पद को अनुपात से गुणा करें। / The common ratio is (3), so the next term is \(36\cdot3=108\). Multiply the previous term by the ratio for the next term.
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