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 91-100 of 600 questions.
What is \(a_5\) of the geometric progression \(14,42,126,378,\ldots\)?
C. (1134)
(r=3) है इसलिए \(a_5=378\times3=1134\) है। परीक्षा में (n-1) बार अनुपात से गुणा करें। / (r=3) so \(a_5=378\times3=1134\). In exams multiply by the ratio (n-1) times.
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If a geometric progression has \(a_1=5\) and (r=4) what is \(a_3\)?
C. (80)
\(a_3=5\cdot4^2=80\) है। परीक्षा में तीसरे पद के लिए \(r^2\) लगाएँ। / \(a_3=5\cdot4^2=80\). In exams use \(r^2\) for the third term.
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Which sequence has common ratio \(\frac{1}{3}\)?
B. (81,27,9,3)
(81,27,9,3) में हर बार \(\frac{1}{3}\) से गुणा होता है। परीक्षा में घटती गुणोत्तर श्रेणी का अनुपात भिन्न लिखें। / In (81,27,9,3) each term is multiplied by \(\frac{1}{3}\). In exams write the ratio of a decreasing geometric progression as a fraction.
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What is the tenth term of the geometric progression \(4,8,16,32,\ldots\)?
B. (2048)
यह \(4\cdot2^{n-1}\) के रूप में है इसलिए दसवाँ पद \(4\cdot2^9=2048\) है। परीक्षा में घात पहचानकर जल्दी हल करें। / This is of the form \(4\cdot2^{n-1}\) so the tenth term is \(4\cdot2^9=2048\). In exams identify powers to solve quickly.
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If \(a_n=4^n\) what is the value of \(a_3\)?
C. (64)
\(a_3=4^3=64\) है। परीक्षा में घात का मान ध्यान से निकालें। / \(a_3=4^3=64\). In exams calculate the power carefully.
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What is the general term of the geometric progression \(36,18,9,\frac{9}{2},\ldots\)?
A. \(a_n=36\cdot\left(\frac{1}{2}\right)^{n-1}\)
पहला पद (36) और अनुपात \(\frac{1}{2}\) है। परीक्षा में \(ar^{n-1}\) में सही भिन्न अनुपात रखें। / The first term is (36) and the ratio is \(\frac{1}{2}\). In exams put the correct fractional ratio in \(ar^{n-1}\).
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If (8,,x,,72) is a geometric progression what is the positive value of (x)?
C. (24)
मध्य पद का वर्ग \(8\times72=576\) है इसलिए धनात्मक (x=24) है। परीक्षा में तीन पदों वाली गुणोत्तर श्रेणी में मध्य पद का वर्ग बाहरी पदों के गुणनफल के बराबर होता है। / The square of the middle term is \(8\times72=576\) so the positive (x=24). In exams for three GP terms the square of the middle term equals the product of the outer terms.
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What will be the fifth term in the geometric progression \(12,48,192,768,\ldots\)?
C. (3072)
सामान्य अनुपात (4) है इसलिए पाँचवाँ पद \(768\times4=3072\) है। परीक्षा में अंतिम ज्ञात पद को अनुपात से गुणा करें। / The common ratio is (4) so the fifth term is \(768\times4=3072\). In exams multiply the last known term by the ratio.
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Which geometric progression has first term (6) and common ratio (4)?
A. \(6,24,96,384,\ldots\)
पहला पद (6) है और हर बार (4) से गुणा हो रहा है। परीक्षा में पहला पद और अनुपात दोनों मिलाएँ। / The first term is (6) and each term is multiplied by (4). In exams match both the first term and the ratio.
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If (a=9) and (r=2) what will be the sixth term of the geometric progression?
D. (288)
छठा पद \(a r^5=9\cdot2^5=288\) है। परीक्षा में (n)वें पद के लिए \(r^{n-1}\) लगाएँ। / The sixth term is \(a r^5=9\cdot2^5=288\). In exams use \(r^{n-1}\) for the (n)th term.
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