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 211-220 of 600 questions.
If a geometric progression has \(a_2=21\) and (r=3), what is \(a_1\)?
D. (7)
\(a_2=a_1r\), इसलिए \(21=a_1\cdot3\) और \(a_1=7\)। पीछे जाने के लिए अनुपात से भाग दें। / \(a_2=a_1r\), so \(21=a_1\cdot3\) and \(a_1=7\). Divide by the ratio to move backward.
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If a geometric progression has \(a_1=2\) and \(a_5=162\), and the ratio is positive, what is (r)?
B. (3)
\(a_5=a_1r^4\), इसलिए \(162=2r^4\) और \(r^4=81\), अतः (r=3)। पद-संख्या का अंतर घात तय करता है। / \(a_5=a_1r^4\), so \(162=2r^4\) and \(r^4=81\), hence (r=3). The position gap decides the exponent.
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What is the (6)th term of the sequence \(\frac{3}{4},\frac{3}{2},3,6,\ldots\)?
B. (24)
सार्व अनुपात (2) है और पद \(\frac{3}{4},\frac{3}{2},3,6,12,24\) हैं। क्रम से गुणा करते जाएं। / The common ratio is (2), and the terms are \(\frac{3}{4},\frac{3}{2},3,6,12,24\). Keep multiplying in order.
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What is the sixth term of the geometric progression \(128,64,32,16,\ldots\)?
A. (4)
सार्व अनुपात \(\frac{1}{2}\) है, इसलिए पद (128,64,32,16,8,4) होंगे। घटती श्रेढ़ी में बार-बार अनुपात से गुणा करें। / The common ratio is \(\frac{1}{2}\), so the terms are (128,64,32,16,8,4). In a decreasing progression multiply by the ratio repeatedly.
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If (a=2) and (r=6), what is \(a_4\)?
C. (432)
\(a_4=2\cdot6^3=432\)। (n)वें पद में घात (n-1) होती है। / \(a_4=2\cdot6^3=432\). In the (n)th term the exponent is (n-1).
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Which option has common ratio \(\frac{1}{5}\)?
C. \(100,20,4,\frac{4}{5},\ldots\)
\(100,20,4,\frac{4}{5},\ldots\) में \(\frac{20}{100}=\frac{1}{5}\) है। अनुपात के लिए लगातार पदों को भाग दें। / In \(100,20,4,\frac{4}{5},\ldots\), \(\frac{20}{100}=\frac{1}{5}\). Divide consecutive terms to find the ratio.
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In the geometric progression \(2,6,18,54,\ldots\), which term is (486)?
C. (6)वाँ(6)th
पद (2,6,18,54,162,486) हैं, इसलिए (486) छठा पद है। पद-संख्या के लिए क्रम से पद बनाएं। / The terms are (2,6,18,54,162,486), so (486) is the sixth term. Form terms in order to find the position.
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If \(a_n=16\left(\frac{1}{2}\right)^{n-1}\), what is \(a_4\)?
B. (2)
\(a_4=16\left(\frac{1}{2}\right)^3=2\)। भिन्न अनुपात में घात की गणना सावधानी से करें। / \(a_4=16\left(\frac{1}{2}\right)^3=2\). Calculate powers of fractional ratios carefully.
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If (3,12,x,192) is a geometric progression, what is (x)?
C. (48)
सार्व अनुपात \(\frac{12}{3}=4\) है, इसलिए \(x=12\cdot4=48\)। समान अनुपात को हर अगले पद पर लगाएं। / The common ratio is \(\frac{12}{3}=4\), so \(x=12\cdot4=48\). Apply the same ratio to each next term.
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What is the sum of the first (4) terms of the geometric progression \(12,24,48,96,\ldots\)?
A. (180)
योग (12+24+48+96=180) है। कम पद हों तो सीधे जोड़ना आसान है। / The sum is (12+24+48+96=180). For a small number of terms direct addition is easy.
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