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 221-230 of 600 questions.
If a geometric progression has \(a_3=45\) and (r=3), what is \(a_1\)?
B. (5)
\(a_3=a_1r^2\), इसलिए \(45=a_1\cdot9\) और \(a_1=5\)। दो पद पीछे जाने के लिए \(r^2\) से भाग दें। / \(a_3=a_1r^2\), so \(45=a_1\cdot9\) and \(a_1=5\). Divide by \(r^2\) to move two terms backward.
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What is the (n)th term of the sequence \(10,20,40,80,\ldots\)?
A. \(a_n=10\cdot2^{n-1}\)
पहला पद (10) और अनुपात (2) है, इसलिए \(a_n=10\cdot2^{n-1}\)। सामान्य पद में पहला पद और अनुपात दोनों रखें। / The first term is (10) and the ratio is (2), so \(a_n=10\cdot2^{n-1}\). Use both first term and ratio in the general term.
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If (a=2) and (r=3), what will be the sum of the first (5) terms?
B. (242)
पहले (5) पद (2,6,18,54,162) हैं और योग (242) है। पदों को क्रम से लिखकर जोड़ें। / The first (5) terms are (2,6,18,54,162), and their sum is (242). Write the terms in order and add.
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If \(a_1=20\) and \(r=\frac{1}{2}\), what is \(a_4\)?
B. \(\frac{5}{2}\)
(a_4=20\left\(\frac{1}{2}\right\)3=\frac{5}{2})। भिन्न अनुपात में हर बार आधा होता है। / (a_4=20\left\(\frac{1}{2}\right\)3=\frac{5}{2}). With a fractional ratio each term becomes half.
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Which value of (x) makes (6,30,x) a geometric progression?
C. (150)
सार्व अनुपात \(\frac{30}{6}=5\) है, इसलिए \(x=30\cdot5=150\)। तीसरे पद के लिए दूसरे पद को अनुपात से गुणा करें। / The common ratio is \(\frac{30}{6}=5\), so \(x=30\cdot5=150\). Multiply the second term by the ratio to get the third term.
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In the sequence \(3,15,75,375,\ldots\), which term is (1875)?
B. (5)वाँ(5)th
सार्व अनुपात (5) है और पद (3,15,75,375,1875) हैं। पद-संख्या के लिए क्रम से पद बनाएं। / The common ratio is (5), and the terms are (3,15,75,375,1875). Form terms in order to find the position.
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If a geometric progression has \(a_2=12\) and \(a_5=324\), and the ratio is positive, what is (r)?
B. (3)
\(a_5=a_2r^3\), इसलिए \(324=12r^3\) और \(r^3=27\), अतः (r=3)। पदों की दूरी घात तय करती है। / \(a_5=a_2r^3\), so \(324=12r^3\) and \(r^3=27\), hence (r=3). The gap between positions decides the exponent.
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What is the sixth term of the geometric progression \(2,-4,8,-16,\ldots\)?
C. (-64)
सार्व अनुपात (-2) है और पद (2,-4,8,-16,32,-64) हैं। ऋणात्मक अनुपात में चिह्न बदलता है। / The common ratio is (-2), and the terms are (2,-4,8,-16,32,-64). With a negative ratio signs alternate.
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Which option has the first four terms of a geometric progression with (a=12) and (r=2)?
B. (12,24,48,96)
पहला पद (12) है और हर बार (2) से गुणा करने पर (12,24,48,96) मिलते हैं। (a) और (r) दोनों को मिलाएं। / The first term is (12), and multiplying by (2) each time gives (12,24,48,96). Match both (a) and (r).
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If \(4,20,100,\ldots\) is a geometric progression, what is the product of the first three terms?
A. (8000)
गुणनफल \(4\cdot20\cdot100=8000\) है। गुणनफल में हर पद को सावधानी से गुणा करें। / The product is \(4\cdot20\cdot100=8000\). Multiply each term carefully in product questions.
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