Govt Exams
(x + 1/x)² = x² + 2 + 1/x² = 7 + 2 = 9. So x + 1/x = ±3
(2.5)² - (1.5)² / 2 = [6.25 - 2.25] / 2 = 4/2 = 2
Using set theory: n(M∪S) = n(M) + n(S) - n(M∩S). 50 = 30 + 25 - n(M∩S). n(M∩S) = 5
a:b = 3:4, b:c = 5:6. Multiply first by 5 and second by 4: a:b = 15:20, b:c = 20:24. So a:b:c = 15:20:24
Series follows n(n+1): 1×2=2, 2×3=6, 3×4=12, 4×5=20, 5×6=30, 6×7=42
Profit = 520 - 400 = 120. Profit% = (120/400) × 100 = 30%
Work = 5 × 12 = 60 worker-days. Days for 8 workers = 60/8 = 7.5 days
CI = P[(1 + r/100)^n - 1] = 10000[(1.1)^2 - 1] = 10000[0.21] = Rs. 2,100
LCM of 12 and 18 = 36. Any number divisible by both 12 and 18 must be divisible by their LCM, which is 36
Total distance = 120 + 150 = 270 km. Total time = 2 + 3 = 5 hours. Average speed = 270/5 = 54 km/h