Mathematics

The series is a geometric series with first term a = 2 and common ratio r = 1/5. The sum to infinity is a / (1 - r) = 2 / (1 - 1/5) = 2 / (4/5) = 2 * 5/4 = 5/2. However, the terms given are 2 + 2/5 + 2/25 + 2/125 + ..., which matches the ratio 1/5. The sum is 2 / (1 - 1/5) = 2 / (4/5) = 2 * 5/4 = 5/2. Therefore, the correct answer is 5/2, which corresponds to option B. The original correct_answer was B, which is correct. The explanation was missing and has been added. The difficulty is set to easy as this is a basic geometric series sum problem.

The population increases by 700 each year for 5 years, so total increase = 700 × 5 = 3500. Given the population after 5 years is 25000, the initial population = 25000 - 3500 = 21500.

According to the factor theorem, if (z - a) is a factor of polynomial P(z), then P(a) = 0. None of the options A (z), B (o), or C (a) represent zero, so the correct answer is D (None of these).

The multiplicative inverse of a complex number a + bi is given by (a - bi) / (a^2 + b^2). For 6 - 5i, the inverse is (6 + 5i) / (6^2 + (-5)^2) = (6 + 5i) / 61. The imaginary part is therefore 5/61.

In a triangle, the largest angle is opposite the longest side. Here, side a = 60 is the longest, so the largest angle is opposite side a.

The total number of balls is 9 + 8 + 3 = 20. The number of balls that are not orange is 9 + 8 = 17. Therefore, the probability of selecting a ball that is not orange is 17/20.

The total number of ways to dress is the product of the number of choices for each clothing item: 6 coats × 3 shirts × 5 trousers = 90 ways.

The number 1 is the only number whose square (1² = 1) and cube (1³ = 1) are the same as the number itself. Other numbers do not satisfy this condition.

Each boy runs 60 km in 6 hours, so the distance covered in 1 hour is 60 km ÷ 6 hours = 10 km. However, the question asks for the distance covered by 1 boy in 1 hour, and since the question states '4th boys ran 60 km each in 6 hours,' it likely means 4 boys each ran 60 km in 6 hours. The distance per boy per hour is 60 km ÷ 6 = 10 km, so the correct answer is 10 km, which corresponds to option B. The initial calculation is correct, so the correct answer is B.

The principle of moments states that for the scale to balance, the moments on both sides must be equal. Moment is calculated as force (weight) multiplied by the distance (arm length) from the pivot. Given 100 kg on the 90 cm arm, the moment is 100 × 90 = 9000 kg·cm. To balance, the moment on the 100 cm arm must also be 9000 kg·cm. Therefore, the weight on the 100 cm arm should be 9000 / 100 = 90 kg. Hence, the correct answer is 90 kg (option B).