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 31-40 of 600 questions.
If a geometric progression has (a=7) and (r=2), what is the fifth term?
C. (112)
\(a_5=7\cdot2^4=112\) है। परीक्षा में पाँचवें पद के लिए \(r^4\) लगाएँ। / \(a_5=7\cdot2^4=112\). In exams, use \(r^4\) for the fifth term.
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In the sequence \(4,8,16,32,\ldots\), which term is (64)?
B. पाँचवाँ पद(5)th term
पद (4,8,16,32,64) हैं, इसलिए (64) पाँचवाँ पद है। परीक्षा में पहला पद भी गिनें। / The terms are (4,8,16,32,64), so (64) is the fifth term. In exams, count the first term too.
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If a geometric progression has \(a_1=6\) and \(a_2=18\), what is the common ratio?
B. (3)
सामान्य अनुपात \(a_2\div a_1=18\div6=3\) है। परीक्षा में दो लगातार पदों का अनुपात लें। / The common ratio is \(a_2\div a_1=18\div6=3\). In exams, take the ratio of two consecutive terms.
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What is the next term of the geometric progression \(9,18,36,72,\ldots\)?
C. (144)
सामान्य अनुपात (2) है, इसलिए अगला पद \(72\times2=144\) है। परीक्षा में अंतिम ज्ञात पद में अनुपात से गुणा करें। / The common ratio is (2), so the next term is \(72\times2=144\). In exams, multiply the last known term by the ratio.
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Which option shows a geometric progression?
C. (3,6,12,24)
(3,6,12,24) में लगातार अनुपात (2) है। परीक्षा में विकल्पों में समान अनुपात खोजें। / In (3,6,12,24), the consecutive ratio is (2). In exams, look for equal ratios in the options.
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What is the fifth term in the geometric progression \(200,100,50,25,\ldots\)?
A. \(\frac{25}{2}\)
सामान्य अनुपात \(\frac{1}{2}\) है, इसलिए पाँचवाँ पद \(25\times\frac{1}{2}=\frac{25}{2}\) है। परीक्षा में भिन्न अनुपात ध्यान से लगाएँ। / The common ratio is \(\frac{1}{2}\), so the fifth term is \(25\times\frac{1}{2}=\frac{25}{2}\). In exams, apply fractional ratios carefully.
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If \(x,,3x,,9x,\ldots\) is a geometric progression, what is the common ratio?
C. (3)
दूसरे पद और पहले पद का अनुपात \(3x\div x=3\) है। परीक्षा में बीजीय पदों में भी भाग करें। / The ratio of the second term to the first term is \(3x\div x=3\). In exams, divide even with algebraic terms.
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What is the common ratio in the geometric progression \(5,5,5,5,\ldots\)?
B. (1)
लगातार पद समान हैं, इसलिए अनुपात \(5\div5=1\) है। परीक्षा में स्थिर शून्येतर श्रेणी भी गुणोत्तर श्रेणी हो सकती है। / Consecutive terms are equal, so the ratio is \(5\div5=1\). In exams, a non-zero constant sequence can also be a geometric progression.
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If (a=11) and (r=1), what are the first three terms?
C. (11,11,11)
सामान्य अनुपात (1) होने पर सभी पद (11) रहेंगे। परीक्षा में (r=1) का मतलब स्थिर गुणोत्तर श्रेणी है। / When the common ratio is (1), all terms remain (11). In exams, (r=1) means a constant geometric progression.
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What is the missing term in the geometric progression \(3,\Box,27,81,\ldots\)?
B. (9)
(27) और (81) का अनुपात (3) है, इसलिए रिक्त पद \(27\div3=9\) है। परीक्षा में पीछे की ओर भी सामान्य अनुपात लगाएँ। / The ratio of (27) and (81) is (3), so the missing term is \(27\div3=9\). In exams, apply the common ratio backward too.
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