Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 191-200 of 600 questions.
If \(a_1=3\) and (r=-2), what are the first four terms?
B. (3,-6,12,-24)
हर बार (-2) से गुणा करने पर (3,-6,12,-24) मिलते हैं। ऋणात्मक अनुपात से चिह्न बदलते हैं। / Multiplying by (-2) each time gives (3,-6,12,-24). A negative ratio makes the signs alternate.
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For which (x) will (8,x,18) be consecutive terms of a positive geometric progression?
B. (12)
\(x^2=8\cdot18=144\), इसलिए धनात्मक (x=12)। मध्य पद ज्यामितीय माध्य होता है। / \(x^2=8\cdot18=144\), so positive (x=12). The middle term is the geometric mean.
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What is the (n)th term of the sequence \(7,21,63,189,\ldots\)?
A. \(a_n=7\cdot3^{n-1}\)
पहला पद (7) और अनुपात (3) है, इसलिए \(a_n=7\cdot3^{n-1}\)। सामान्य पद में पहला पद और अनुपात रखें। / The first term is (7) and the ratio is (3), so \(a_n=7\cdot3^{n-1}\). Use the first term and ratio in the general term.
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If \(a_2=24\) and \(a_5=192\), and the ratio is positive, what is (r)?
A. (2)
\(a_5=a_2r^3\), इसलिए \(192=24r^3\) और \(r^3=8\), अतः (r=2)। पदों की दूरी घात तय करती है। / \(a_5=a_2r^3\), so \(192=24r^3\) and \(r^3=8\), hence (r=2). The gap between positions decides the exponent.
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In the geometric progression \(3,12,48,\ldots\), what is \(a_5\)?
C. (768)
सार्व अनुपात (4) है, इसलिए \(a_5=3\cdot4^4=768\)। (5)वें पद के लिए (4) बार अनुपात लगता है। / The common ratio is (4), so \(a_5=3\cdot4^4=768\). For the fifth term the ratio is used (4) times.
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If a geometric progression has \(a_1=2\) and \(a_3=50\), what is the positive (r)?
C. (5)
\(a_3=a_1r^2\), इसलिए \(50=2r^2\) और \(r^2=25\), अतः धनात्मक (r=5)। धनात्मक अनुपात मांगने पर धनात्मक मूल लें। / \(a_3=a_1r^2\), so \(50=2r^2\) and \(r^2=25\), hence positive (r=5). When positive ratio is asked take the positive root.
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Which statement is correct for \(12,6,3,\frac{3}{2},\ldots\)?
B. यह \(r=\frac{1}{2}\) वाली गुणोत्तर श्रेढ़ी हैIt is a geometric progression with \(r=\frac{1}{2}\)
हर पद पिछले पद का आधा है, इसलिए \(r=\frac{1}{2}\) है। अनुपात जांचने के लिए अगला पद पिछले पद से भाग दें। / Each term is half of the previous term, so \(r=\frac{1}{2}\). To check the ratio divide the next term by the previous term.
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If \(a_n=256\) in \(1,4,16,64,\ldots\), what is (n)?
B. (5)
पद (1,4,16,64,256) हैं, इसलिए (n=5)। पद-संख्या के लिए क्रम से घात पहचानें। / The terms are (1,4,16,64,256), so (n=5). For position identify powers in order.
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In the geometric progression \(2,6,18,54,\ldots\), what is \(a_3+a_4\)?
C. (72)
\(a_3=18\) और \(a_4=54\), इसलिए योग (72) है। दोनों पद अलग निकालकर जोड़ें। / \(a_3=18\) and \(a_4=54\), so the sum is (72). Find both terms separately and then add.
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C. (30)
पहले चार पद (16,8,4,2) हैं और योग (30) है। घटती गुणोत्तर श्रेढ़ी में पद क्रम से लिखें। / The first four terms are (16,8,4,2), and the sum is (30). In a decreasing geometric progression write the terms in order.
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