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 431-440 of 600 questions.
If \(a_1=6\) and (r=-2), what is \(a_7\)?
A. (384)
(a_7=6(-2)6=384) है। परीक्षा में ऋणात्मक अनुपात की सम घात धनात्मक होती है। / (a_7=6(-2)6=384). In exams, an even power of a negative ratio is positive.
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What is the sum of the first (4) terms of the geometric progression \(3,18,108,648,\ldots\)?
A. (777)
पहले चार पदों का योग (3+18+108+648=777) है। परीक्षा में पद कम हों तो सीधे जोड़ना सुरक्षित है। / The sum of the first four terms is (3+18+108+648=777). In exams, direct addition is safe when the number of terms is small.
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If \(a_4=96\) and (r=2), what is the value of \(a_{10}\)?
B. (6144)
चौथे से दसवें पद तक (6) कदम हैं, इसलिए \(a_{10}=96\cdot2^6=6144\) है। परीक्षा में पद-संख्या का अंतर गिनें। / There are (6) steps from the fourth to the tenth term, so \(a_{10}=96\cdot2^6=6144\). In exams, count the position gap.
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In the geometric progression \(810,270,90,\ldots\), which term is (10)?
B. पाँचवाँ पद(5)th term
हर बार \(\frac{1}{3}\) से गुणा होता है, इसलिए पद (810,270,90,30,10) हैं। परीक्षा में घटती GP को क्रम से भी जाँच सकते हैं। / Each term is multiplied by \(\frac{1}{3}\), so the terms are (810,270,90,30,10). In exams, you can also check a decreasing GP in order.
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If (a=10), (r=3), and \(S_5=1210\), what is the statement?
A. सही क्योंकि \(S_5=1210\)True because \(S_5=1210\)
(S_5=\frac{10\(3^5-1\)}{3-1}=1210) है। परीक्षा में कथन-प्रकार प्रश्न में सूत्र से पुष्टि करें। / (S_5=\frac{10\(3^5-1\)}{3-1}=1210). In exams, confirm statement-type questions with the formula.
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What is the value of \(a_5+a_6\) for the geometric progression \(4,16,64,\ldots\)?
B. (5120)
\(a_5=1024\) और \(a_6=4096\), इसलिए योग (5120) है। परीक्षा में दोनों पद अलग-अलग निकालकर जोड़ें। / \(a_5=1024\) and \(a_6=4096\), so the sum is (5120). In exams, find both terms separately and add.
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If \(a_n=162\left(\frac{1}{3}\right)^{n-1}\), which term will be equal to (2)?
B. पाँचवाँ पद(5)th term
\(162\left(\frac{1}{3}\right)^{n-1}=2\) से \(\left(\frac{1}{3}\right)^{n-1}=\frac{1}{81}\), इसलिए (n=5) है। परीक्षा में भिन्नों को पहले सरल करें। / From \(162\left(\frac{1}{3}\right)^{n-1}=2\), \(\left(\frac{1}{3}\right)^{n-1}=\frac{1}{81}\), so (n=5). In exams, simplify fractions first.
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What is the sum of the first (9) terms of the geometric progression \(7,14,28,\ldots\)?
A. (3577)
(S_9=7\(2^9-1\)=3577) है। परीक्षा में \(2^9=512\) याद रखना उपयोगी है। / (S_9=7\(2^9-1\)=3577). In exams, remembering \(2^9=512\) is useful.
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If a geometric progression has \(a_5=96\) and \(a_9=1536\), what is the positive value of (r)?
A. (2)
\(\frac{1536}{96}=16=r^4\), इसलिए (r=2) है। परीक्षा में पद-संख्या का अंतर (4) होने पर \(r^4\) मिलेगा। / \(\frac{1536}{96}=16=r^4\), so (r=2). In exams, a position gap of (4) gives \(r^4\).
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What is \(a_8\) in the geometric progression \(15,45,135,\ldots\)?
A. (32805)
\(a_8=15\cdot3^7=32805\) है। परीक्षा में आठवें पद के लिए \(r^7\) लगाएँ। / \(a_8=15\cdot3^7=32805\). In exams, use \(r^7\) for the eighth term.
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