Govt. Exams
Entrance Exams
Displacement = √(30² + 40²) = √(900 + 1600) = √2500 = 50 km
This is a geometric series with a = 2, r = 2, n = 10. Sum = a(r^n - 1)/(r-1) = 2(2¹⁰ - 1)/(2-1) = 2(1024 - 1) = 2046
Using sin²θ + cos²θ = 1: sin²θ = 1 - 9/25 = 16/25, so sin θ = 4/5 (positive in first quadrant)
Area of sector = (θ/360°) × πr² = (60/360) × π × 49 = (1/6) × 22/7 × 49 = 25.67 cm²
Number of arrangements of 5 people = 5! = 5 × 4 × 3 × 2 × 1 = 120.
Distance = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.
Simple Interest = (P × R × T)/100 = (5000 × 8 × 3)/100 = 1200.
For ax² + bx + c = 0, sum of roots = -b/a = -(-5)/1 = 5.
Prime numbers on a die: 2, 3, 5 (total 3). Total outcomes = 6. Probability = 3/6 = 1/2.
Using dividend = divisor × quotient + remainder: Number = 7 × 12 + 3 = 84 + 3 = 87.
