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 471-480 of 600 questions.
If \(a_1=\frac{3}{2}\) and (r=4), what will be \(a_5\)?
B. (384)
\(a_5=\frac{3}{2}\cdot4^4=384\)। भिन्न पहले पद के साथ घात का गुणा ध्यान से करें। / \(a_5=\frac{3}{2}\cdot4^4=384\). Multiply the power carefully with the fractional first term.
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In the geometric progression \(1,3,9,27,\ldots\), what is the greatest term less than (1000)?
B. (729)
पद (1,3,9,27,81,243,729,2187) हैं, इसलिए (1000) से छोटा सबसे बड़ा पद (729) है। सीमा वाले प्रश्न में अगला पद भी जांचें। / The terms are (1,3,9,27,81,243,729,2187), so the greatest term below (1000) is (729). In boundary questions, check the next term too.
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If in a geometric progression \(a_1=7\), \(a_4+a_5=756\), and (r=3), which statement is correct?
C. सही योग (756) नहीं बल्कि (945) हैThe correct sum is (945), not (756)
\(a_4=7\cdot3^3=189\) और \(a_5=567\), इसलिए योग (756) है। इसलिए दिया योग सही है। / \(a_4=7\cdot3^3=189\) and \(a_5=567\), so the sum is (756). Therefore the given sum is correct.
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If \(6,18,54,\ldots\) is a geometric progression, what is the value of \(a_5-a_3\)?
A. (432)
\(a_3=54\) और \(a_5=486\), इसलिए अंतर (432) है। दोनों पद अलग निकालकर घटाएं। / \(a_3=54\) and \(a_5=486\), so the difference is (432). Find both terms separately and subtract.
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In the geometric progression \(a,ar,ar^2,\ldots\), \(a_2=8\) and \(a_4=128\). What will be \(a_6\)?
C. (2048)
\(a_4=a_2r^2\), इसलिए \(r^2=16\) और धनात्मक क्रम में \(a_6=128\cdot16=2048\)। समान दूरी पर वही \(r^2\) फिर लगता है। / \(a_4=a_2r^2\), so \(r^2=16\), and for the positive sequence \(a_6=128\cdot16=2048\). The same \(r^2\) applies over the same gap.
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If \(a_n=81\left(\frac{1}{3}\right)^{n-1}\), what is \(a_2+a_5\)?
A. (28)
\(a_2=27\) और \(a_5=1\), इसलिए योग (28) है। भिन्न अनुपात में हर पद तेजी से घटता है। / \(a_2=27\) and \(a_5=1\), so the sum is (28). With a fractional ratio, terms decrease quickly.
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If \(a_1=4\) and (r=-2), what will be the sum of the first (5) terms?
D. (44)
पद (4,-8,16,-32,64) हैं और योग (44) है। ऋणात्मक अनुपात में चिह्नों को ध्यान से जोड़ें। / The terms are (4,-8,16,-32,64), and their sum is (44). Add signs carefully with a negative ratio.
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If \(a_3=45\) and \(a_7=3645\), and (r) is positive, what is (r)?
B. (3)
\(a_7=a_3r^4\), इसलिए \(3645=45r^4\) और \(r^4=81\), अतः (r=3)। चार पदों की दूरी पर \(r^4\) लगता है। / \(a_7=a_3r^4\), so \(3645=45r^4\) and \(r^4=81\), hence (r=3). A four-position gap uses \(r^4\).
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Which geometric progression has common ratio \(-\frac{1}{2}\)?
A. \(32,-16,8,-4,\ldots\)
\(32,-16,8,-4,\ldots\) में हर बार \(-\frac{1}{2}\) से गुणा होता है। अनुपात के लिए अगला पद पिछले पद से भाग दें। / In \(32,-16,8,-4,\ldots\), each term is multiplied by \(-\frac{1}{2}\). Divide the next term by the previous term to find the ratio.
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If a geometric progression has \(a_2=6\) and \(a_4=54\), what will be the value of \(a_1+a_5\)?
A. (164)
\(a_4=a_2r^2\), इसलिए (r=3), \(a_1=2\) और \(a_5=162\), अतः योग (164) है। पहले (r) निकालें। / \(a_4=a_2r^2\), so (r=3), \(a_1=2\), and \(a_5=162\), hence the sum is (164). Find (r) first.
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