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 481-490 of 600 questions.
If \(a_n=5\cdot2^{n-1}\), what will (n) be for \(a_n=320\)?
C. (7)
\(5\cdot2^{n-1}=320\), इसलिए \(2^{n-1}=64=2^6\) और (n=7)। घातों की तुलना करें। / \(5\cdot2^{n-1}=320\), so \(2^{n-1}=64=2^6\) and (n=7). Compare powers.
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The consecutive terms of a geometric progression are (x,3x,27). What is the positive (x)?
C. (3)
((3x)2=x\cdot27), इसलिए \(9x^2=27x\) और धनात्मक (x=3)। शून्य को धनात्मक हल में नहीं लें। / ((3x)2=x\cdot27), so \(9x^2=27x\) and positive (x=3). Do not take zero as a positive solution.
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If \(a_1=6\) and (r=3), what is \(a_6-a_4\)?
C. (1296)
\(a_4=162\) और \(a_6=1458\), इसलिए अंतर (1296) है। पहले दोनों पद सही घात से निकालें। / \(a_4=162\) and \(a_6=1458\), so the difference is (1296). First find both terms using the correct powers.
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Which statement correctly describes the geometric progression \(18,6,2,\frac{2}{3},\ldots\)?
B. \(r=\frac{1}{3}\) और श्रेढ़ी घटती है\(r=\frac{1}{3}\) and the progression decreases
हर पद पिछले पद का \(\frac{1}{3}\) है, इसलिए श्रेढ़ी घटती है। अनुपात की दिशा और मान दोनों देखें। / Each term is \(\frac{1}{3}\) of the previous term, so the progression decreases. Check both the value and direction of the ratio.
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If \(a_2=24\) and \(r=\frac{1}{2}\), what will be \(a_5\)?
B. (3)
(a_5=a_2r-3=24\left\(\frac{1}{2}\right\)3=3)। तीन पद आगे जाने पर \(r^3\) लगता है। / (a_5=a_2r-3=24\left\(\frac{1}{2}\right\)3=3). Moving three positions forward uses \(r^3\).
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In the geometric progression \(2,10,50,\ldots\), what is the greatest term less than (6000)?
A. (1250)
पद (2,10,50,250,1250,6250) हैं, इसलिए (6000) से छोटा सबसे बड़ा पद (1250) है। अगला पद सीमा पार करता है। / The terms are (2,10,50,250,1250,6250), so the greatest term below (6000) is (1250). The next term crosses the limit.
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If \(a_3=12\) and \(a_6=96\), and the ratio is positive, what will \(a_8\) be?
C. (384)
\(a_6=a_3r^3\), इसलिए (r=2), अतः \(a_8=96\cdot2^2=384\)। पहले अनुपात निकालकर आगे बढ़ें। / \(a_6=a_3r^3\), so (r=2), hence \(a_8=96\cdot2^2=384\). First find the ratio and then move forward.
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If \(a_1=1\) and (r=4), what will be the product of the first (4) terms?
C. (4096)
पहले चार पद (1,4,16,64) हैं और गुणनफल (4096) है। गुणनफल में हर पद को सावधानी से गुणा करें। / The first four terms are (1,4,16,64), and their product is (4096). Multiply each term carefully in product questions.
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A. (2)
\(a_4=a_1r^3\), इसलिए \(72=9r^3\) और \(r^3=8\), अतः (r=2)। पदों की दूरी को घात बनाएं। / \(a_4=a_1r^3\), so \(72=9r^3\) and \(r^3=8\), hence (r=2). Use the position gap as the exponent.
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If \(a_n=7\cdot3^{n-1}\), what is the value of \(\frac{a_5}{a_3}\)?
C. (9)
\(\frac{a_5}{a_3}=r^2=3^2=9\)। समान श्रेढ़ी में पदों का अनुपात पद-संख्या के अंतर पर निर्भर करता है। / \(\frac{a_5}{a_3}=r^2=3^2=9\). In the same progression, the ratio of terms depends on the difference of positions.
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