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Mathematics · JEE | SEQUENCES AND SERIES
हिन्दीMatch List-I with List-II: List-I List-II A Common ratio of \( 2, 2\sqrt{2}, 4, \dots \) I \( \frac{1}{3} \) B Common ratio of \( \sqrt{7}, \sqrt{21}, 3\sqrt{7}, \dots \) II \( \sqrt{3} \) C Common ratio of \( \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \dots \) III \( \sqrt{2} \) D Sum of infinite G.P. \( 1 + \frac{1}{2} + \frac{1}{4} + \dots \) IV 2 Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I | List-II | ||
|---|---|---|---|
| A | Common ratio of \( 2, 2\sqrt{2}, 4, \dots \) | I | \( \frac{1}{3} \) |
| B | Common ratio of \( \sqrt{7}, \sqrt{21}, 3\sqrt{7}, \dots \) | II | \( \sqrt{3} \) |
| C | Common ratio of \( \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \dots \) | III | \( \sqrt{2} \) |
| D | Sum of infinite G.P. \( 1 + \frac{1}{2} + \frac{1}{4} + \dots \) | IV | 2 |
Choose the correct answer from the options given below:
View Answer & Solution
Correct answer · Option B
A-(III), B-(II), C-(I), D-(IV)
Explanation
Computing common ratios: A gives \( \frac{2\sqrt{2}}{2} = \sqrt{2} \) (III); B gives \( \frac{\sqrt{21}}{\sqrt{7}} = \sqrt{3} \) (II); C gives \( \frac{1/9}{1/3} = \frac{1}{3} \) (I); D gives \( \frac{1}{1-1/2} = 2 \) (IV).
