Govt Exams
A = P(1 + r/100)ⁿ = 8000(1.1)² = 8000 × 1.21 = 9680. CI = 9680 - 8000 = 1680.
Area of rhombus = (1/2) × d₁ × d₂ = (1/2) × 6 × 8 = 24 cm².
log₁₀ 200 = log₁₀(2 × 100) = log₁₀ 2 + log₁₀ 100 = 0.301 + 2 = 2.301.
Sum of 5 numbers = 35 × 5 = 175. New sum = 38 × 5 = 190. Difference = 190 - 175 = 15. Original number = 50 - 15 = 35.
cos θ = 7/25 means adjacent = 7, hypotenuse = 25. Using Pythagoras, opposite = 24. tan θ = opposite/adjacent = 24/7.
One angle = 90°. Other two in ratio 1:2. Let them be x and 2x. x + 2x + 90 = 180 → 3x = 90 → x = 30°. Angles are 30°, 60°, 90°.
Volume of cone = (1/3)πr²h = (1/3) × (22/7) × 25 × 12 = (1/3) × (22/7) × 300 = 314.29 cm³.
Quadratic equation is x² - (sum of roots)x + (product of roots) = 0, which gives x² - 7x + 10 = 0.
Let numbers be 3x and 5x. 3x + 5x = 64 → 8x = 64 → x = 8. Larger number = 5 × 8 = 40.
x³ - 8 = (x-2)(x² + 2x + 4), so (x³ - 8)/(x - 2) = x² + 2x + 4