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 181-190 of 600 questions.
What is the fifth term of the geometric progression \(1,-2,4,-8,\ldots\)?
B. (16)
सार्व अनुपात (-2) है, इसलिए पाँचवाँ पद ((-8)(-2)=16) है। ऋणात्मक अनुपात में चिह्न बदलता है। / The common ratio is (-2), so the fifth term is ((-8)(-2)=16). With a negative ratio signs alternate.
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Which option has the first four terms of a geometric progression with (a=9) and (r=3)?
C. (9,27,81,243)
पहला पद (9) है और हर बार (3) से गुणा करने पर (9,27,81,243) मिलते हैं। (a) और (r) दोनों को मिलाएं। / The first term is (9), and multiplying by (3) each time gives (9,27,81,243). Match both (a) and (r).
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If \(5,15,45,\ldots\) is a geometric progression, what is the product of the first three terms?
A. (3375)
गुणनफल \(5\cdot15\cdot45=3375\) है। गुणनफल में हर पद को सावधानी से गुणा करें। / The product is \(5\cdot15\cdot45=3375\). Multiply each term carefully in product questions.
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What is the next term in the geometric progression \(100,50,25,\ldots\)?
B. \(\frac{25}{2}\)
सार्व अनुपात \(\frac{1}{2}\) है, इसलिए अगला पद \(25\cdot\frac{1}{2}=\frac{25}{2}\) होगा। अनुपात से गुणा करें। / The common ratio is \(\frac{1}{2}\), so the next term is \(25\cdot\frac{1}{2}=\frac{25}{2}\). Multiply by the ratio.
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If \(a_n=4\cdot2^{n-1}\), which sequence does it form?
C. \(4,8,16,32,\ldots\)
(n=1,2,3,4) रखने पर (4,8,16,32) मिलते हैं। नियम से शुरू के पद बनाकर विकल्प मिलाएं। / Putting (n=1,2,3,4) gives (4,8,16,32). Form the initial terms from the rule and match the option.
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If (x,12,36) are consecutive terms of a geometric progression, what is (x)?
C. (4)
\(\frac{36}{12}=3\), इसलिए \(\frac{12}{x}=3\) और (x=4)। लगातार अनुपात बराबर रखें। / \(\frac{36}{12}=3\), so \(\frac{12}{x}=3\) and (x=4). Keep consecutive ratios equal.
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What is the (6)th term of the geometric progression \(8,24,72,\ldots\)?
C. (1944)
यहाँ (r=3), इसलिए \(a_6=8\cdot3^5=1944\)। (6)वें पद में (5) बार अनुपात लगता है। / Here (r=3), so \(a_6=8\cdot3^5=1944\). The sixth term uses the ratio (5) times.
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Which sequence has common ratio (5)?
B. \(2,10,50,250,\ldots\)
\(2,10,50,250,\ldots\) में हर बार (5) से गुणा हो रहा है। अनुपात के लिए अगले पद को पिछले पद से भाग दें। / In \(2,10,50,250,\ldots\), each term is multiplied by (5). For the ratio divide the next term by the previous term.
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If \(a_1= \frac{3}{4}\) and (r=2), what is \(a_4\)?
C. (6)
\(a_4=\frac{3}{4}\cdot2^3=6\)। भिन्न पहले पद के साथ घात को सावधानी से गुणा करें। / \(a_4=\frac{3}{4}\cdot2^3=6\). Multiply the power carefully with the fractional first term.
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What is the sum of the first (5) terms of the geometric progression \(2,4,8,16,\ldots\)?
C. (62)
पहले (5) पद (2,4,8,16,32) हैं और योग (62) है। पदों को क्रम से लिखकर जोड़ें। / The first (5) terms are (2,4,8,16,32), and the sum is (62). Write the terms in order and add.
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