Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 251-260 of 600 questions.
If a geometric progression has first term (6) and common ratio (4), what is the third term?
C. (96)
\(a_3=6\cdot4^2=96\)। (n)वें पद में अनुपात की घात (n-1) होती है। / \(a_3=6\cdot4^2=96\). In the (n)th term the exponent of the ratio is (n-1).
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What is the common ratio of the sequence \(125,25,5,1,\ldots\)?
B. \(\frac{1}{5}\)
सार्व अनुपात \(\frac{25}{125}=\frac{1}{5}\) है। घटती गुणोत्तर श्रेढ़ी में अनुपात (1) से छोटा हो सकता है। / The common ratio is \(\frac{25}{125}=\frac{1}{5}\). In a decreasing geometric progression the ratio can be less than (1).
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If \(a_n=5\cdot3^{n-1}\), what is the value of \(a_5\)?
C. (405)
\(a_5=5\cdot3^4=405\)। घात में (n-1) का मान पहले निकालें। / \(a_5=5\cdot3^4=405\). First find the value of (n-1) in the exponent.
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In the geometric progression \(8,16,32,64,\ldots\), which term is (256)?
C. (6)वाँ(6)th
पद (8,16,32,64,128,256) हैं, इसलिए (256) छठा पद है। पद-संख्या के लिए पदों को क्रम से बनाएं। / The terms are (8,16,32,64,128,256), so (256) is the sixth term. Form the terms in order to find the position.
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If a geometric progression has (a=10) and (r=2), what are the first four terms?
B. (10,20,40,80)
पहला पद (10) है और हर बार (2) से गुणा करने पर (10,20,40,80) मिलते हैं। गुणोत्तर श्रेढ़ी में अगला पद गुणा करके बनता है। / The first term is (10), and multiplying by (2) each time gives (10,20,40,80). In a geometric progression each next term is formed by multiplication.
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What is the common ratio of the sequence \(7,-14,28,-56,\ldots\)?
B. (-2)
सार्व अनुपात \(\frac{-14}{7}=-2\) है। ऋणात्मक अनुपात से पदों के चिह्न बदलते हैं। / The common ratio is \(\frac{-14}{7}=-2\). A negative ratio changes the signs of terms.
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What is the next term in the geometric progression \(6,30,150,\ldots\)?
C. (750)
सार्व अनुपात (5) है, इसलिए अगला पद \(150\cdot5=750\) होगा। अगले पद के लिए पिछले पद को अनुपात से गुणा करें। / The common ratio is (5), so the next term is \(150\cdot5=750\). Multiply the previous term by the ratio to get the next term.
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If (9,x,81) are consecutive positive terms of a geometric progression, what is (x)?
C. (27)
\(x^2=9\cdot81=729\), इसलिए धनात्मक (x=27)। मध्य पद ज्यामितीय माध्य होता है। / \(x^2=9\cdot81=729\), so positive (x=27). The middle term is the geometric mean.
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What is the sum of the first (4) terms of the geometric progression \(8,24,72,216,\ldots\)?
C. (320)
योग (8+24+72+216=320) है। कम पद हों तो सीधे जोड़ना सुरक्षित है। / The sum is (8+24+72+216=320). For a small number of terms direct addition is safe.
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If a geometric progression has \(a_2=28\) and (r=4), what is \(a_1\)?
B. (7)
\(a_2=a_1r\), इसलिए \(28=a_1\cdot4\) और \(a_1=7\)। पीछे जाने के लिए अनुपात से भाग दें। / \(a_2=a_1r\), so \(28=a_1\cdot4\) and \(a_1=7\). Divide by the ratio to move backward.
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