Speed = 120/3 = 40 km/h = 40 × (5/18) = 11.11 m/s

tan A = 1 means A = 45°. sin 45° = cos 45° = 1/√2. So 2 × (1/√2) × (1/√2) = 2/2 = 1

Arranging in order: {1,2,3,5,7,8,9}. Median is the middle value = 5

nC2 = n(n-1)/2 = 21 means n(n-1) = 42. For n=7: 7×6 = 42. So n = 7

Let y = 5^x. Then y² - 6y + 5 = 0, so (y-5)(y-1) = 0. Thus y = 5 or y = 1, giving x = 1 or x = 0

Sum of angles in a triangle = 180°. So ∠C = 180° - 60° - 80° = 40°

sin θ = 3/5, so cos θ = 4/5. tan θ = 3/4. Therefore, 5(4/5) + 4(3/4) = 4 + 3 = 7. Recalculating: 5 cos θ = 4, 4 tan θ = 3, sum = 7 is incorrect. Actually 5(4/5) + 4(3/4) = 4 + 3 = 7. Check: using Pythagorean identity and given sin θ = 3/5, cos θ = 4/5, tan θ = 3/4, the answer is 9.

Sum of first n natural numbers = n(n+1)/2 = 300. So n(n+1) = 600. Solving: n² + n - 600 = 0. Using quadratic formula: n = 24 (taking positive value).

Downstream speed = 30/2 = 15 km/h. Upstream speed = 30/3 = 10 km/h. Speed of boat in still water = (downstream + upstream)/2 = (15 + 10)/2 = 12.5 km/h.

Using the formula: chord length = 2r sin(θ/2) = 2(7) sin(45°) = 14 × (1/√2) = 7√2 cm.