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Quantity I: Let the original number be x. First, the number is multiplied by 3: 3x. Then, it is increased by 25%, so the result is 3x × 1.25 = 375. Solving for x: 3x × 1.25 = 375, 3x = 375 / 1.25 = 300, x = 300 / 3 = 100. Quantity II: Let the speed of the stream be x. The speed of the boat downstream is 18 + x, and the speed of the boat upstream is 18 - x. The time taken for downstream = 48 / (18 + x), The time taken for upstream = 36 / (18 - x). Since the time taken to travel both distances is equal, we equate the two expressions: 48 / (18 + x) = 36 / (18 - x). Cross-multiplying, we get: 48(18 - x) = 36(18 + x). Simplifying: 864 - 48x = 648 + 36x, 864 - 648 = 48x + 36x, 216 = 84x, x = 216 / 84 = 2.57 km/h. Quantity III: Using the compound interest formula: Amount = Principal × (1 + Rate / 100) ^ Time. Amount = 10,000 × (1 + 5/100)^3. Amount = 10,000 × (1.05)^3 ≈ 10,000 × 1.157625 = ₹11,576.25. Comparing the quantities: Quantity I = 100, Quantity II ≈ 2.57 km/h, Quantity III ≈ 11,576.25. Answer: (B) Quantity II < Quantity I < Quantity III
For the study purpose, the mean of the observations is 148 gm and standard deviation is 17.4 gm. Approximately, the coefficient of variation equals to:
Following two statements are related to regression coefficient
(I) Independent of the change of origin
(II) Independent of the change of scale
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For the recorded observation, the coefficient of variation is 0.2 and the variance is 16. The arithmetic mean is:
If the random sample of size n is drawn without replacement from a finite population of size N, the correction factor for standard error of sample mean...
Two data set of size 9 and 6 have standard deviation 3 and 4 respectively and arithmetic means 3 and 3 respectively. The standard deviation of combined...
The arithmetic mean of the following frequency distribution of number of accidents X on week working days is:
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The grouped data for the observation are as follows.
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Five persons A, B, C, D and E occupy seats in a row at random. The probability that A and B sit next to each other is: