Govt. Exams
Entrance Exams
Using Pythagorean theorem: h² + 5² = 13². So h² = 169 - 25 = 144. Therefore h = 12 m.
In a right-angled triangle, the sum of acute angles is 90°. Therefore, other angle = 90° - 35° = 55°.
Surface area of sphere = 4πr² = 616. So 4 × (22/7) × r² = 616. Thus r² = 49, r = 7 cm.
Amount = P(1 + r/100)ⁿ = 10000(1.1)² = 10000 × 1.21 = 12100. Compound interest = 12100 - 10000 = ₹2,100.
Let numbers be 3k and 4k. LCM(3k, 4k) = 12k = 180. So k = 15. Numbers are 45 and 60. Greater number is 60.
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.
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).
Sum of angles in a triangle = 180°. So ∠C = 180° - 60° - 80° = 40°
Arranging in order: {1,2,3,5,7,8,9}. Median is the middle value = 5
Area of parallelogram = base × height = 15 × 8 = 120 cm²
