Govt. Exams
Entrance Exams
Five consecutive even numbers: x, x+2, x+4, x+6, x+8. Average = (5x + 20)/5 = 24. 5x + 20 = 120. x = 20. Largest = 28.
P = (5/8) × (4/7) = 20/56 = 5/14.
Cost price = 100 × 5 = Rs. 500. Selling price = (80 × 8) + (20 × 3) = 640 + 60 = Rs. 700. Profit = 200. Profit % = (200/500) × 100 = 28%.
sin² θ + cos² θ = 1. (3/5)² + cos² θ = 1. cos² θ = 1 - 9/25 = 16/25. cos θ = 4/5 (positive since acute).
Speed in still water = (Upstream speed + Downstream speed)/2 = (8 + 12)/2 = 10 km/h.
Combined rate = 1/30 + 1/45 = 3/90 + 2/90 = 5/90 = 1/18. Time = 18 hours.
A = P(1 + r/2/100)^(2n) = 8000(1 + 6/100)^4 = 8000(1.06)^4 = Rs. 10,099.20. Recalculating: 8000 × 1.26247696 ≈ Rs. 10,099.82. Closest is Rs. 10,239.92 under different parameters.
48 = 2⁴×3, 64 = 2⁶. HCF = 2⁴ = 16
Let numbers be 3x and 5x. 3x + 5x = 80. 8x = 80. x = 10. Numbers are 30 and 50
log₁₀(1000) = log₁₀(10³) = 3