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 331-340 of 600 questions.
If \(a_1=5\) and (r=-2), what is \(a_6\)?
A. (-160)
(a_6=5(-2)5=-160) है। परीक्षा में ऋणात्मक अनुपात की विषम घात ऋणात्मक रहती है। / (a_6=5(-2)5=-160). In exams an odd power of a negative ratio remains negative.
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What is the sum of the first (5) terms of the geometric progression \(3,15,75,375,\ldots\)?
B. (2343)
(S_5=3\(5^5-1\)/(5-1)=2343) है। परीक्षा में बड़े अनुपात में सूत्र से समय बचता है। / (S_5=3\(5^5-1\)/(5-1)=2343). In exams the formula saves time for large ratios.
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If \(a_4=80\) and (r=2), what is the value of \(a_9\)?
C. (2560)
चौथे से नौवें पद तक (5) कदम हैं इसलिए \(a_9=80\cdot2^5=2560\) है। परीक्षा में पद-संख्या का अंतर गिनें। / There are (5) steps from the fourth to the ninth term, so \(a_9=80\cdot2^5=2560\). In exams count the position gap.
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In the geometric progression \(512,256,128,\ldots\), which term is (4)?
B. आठवाँ पद(8)th term
(512\left\(\frac{1}{2}\right\)^{n-1}=4) से (\left\(\frac{1}{2}\right\)^{n-1}=\frac{1}{128}) इसलिए (n=8) है। परीक्षा में आधा करते हुए पद गिनें। / From (512\left\(\frac{1}{2}\right\)^{n-1}=4), (\left\(\frac{1}{2}\right\)^{n-1}=\frac{1}{128}), so (n=8). In exams count terms while halving.
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If (a=6), \(S_4=240\), and (r=3), what is the statement?
A. सही क्योंकि \(S_4=240\)True because \(S_4=240\)
(S_4=6\(3^4-1\)/(3-1)=240) है। परीक्षा में कथन-प्रकार प्रश्न में सूत्र से पुष्टि करें। / (S_4=6\(3^4-1\)/(3-1)=240). 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 \(8,24,72,\ldots\)?
C. (1080)
\(a_5=648\) और \(a_6=1944\) नहीं बल्कि \(a_5=648\) तथा \(a_6=1944\) का योग (2592) होता है। दिए विकल्पों में सही उत्तर नहीं है। / \(a_5=648\) and \(a_6=1944\), so their sum is (2592). None of the given options is correct.
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If \(a_n=100\left(\frac{1}{2}\right)^{n-1}\), which term will be equal to \(\frac{25}{2}\)?
B. चौथा पद(4)th term
\(100\left(\frac{1}{2}\right)^{n-1}=\frac{25}{2}\) से \(\left(\frac{1}{2}\right)^{n-1}=\frac{1}{8}\) इसलिए (n=4) है। परीक्षा में भिन्नों को पहले सरल करें। / From \(100\left(\frac{1}{2}\right)^{n-1}=\frac{25}{2}\), \(\left(\frac{1}{2}\right)^{n-1}=\frac{1}{8}\), so (n=4). In exams simplify fractions first.
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What is the sum of the first (10) terms of the geometric progression \(4,8,16,\ldots\)?
A. (4092)
(S_{10}=4\(2^{10}-1\)=4092) है। परीक्षा में \(2^{10}=1024\) याद रखना उपयोगी है। / (S_{10}=4\(2^{10}-1\)=4092). In exams remembering \(2^{10}=1024\) is useful.
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If a geometric progression has \(a_4=54\) and \(a_7=1458\), what is the positive value of (r)?
B. (3)
\(\frac{1458}{54}=27=r^3\) इसलिए (r=3) है। परीक्षा में पद-संख्या का अंतर (3) होने पर \(r^3\) मिलेगा। / \(\frac{1458}{54}=27=r^3\), so (r=3). In exams a position gap of (3) gives \(r^3\).
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What is \(a_{11}\) in the geometric progression \(6,12,24,\ldots\)?
C. (6144)
\(a_{11}=6\cdot2^{10}=6144\) है। परीक्षा में ग्यारहवें पद के लिए \(r^{10}\) लगाएँ। / \(a_{11}=6\cdot2^{10}=6144\). In exams use \(r^{10}\) for the eleventh term.
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