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| # | Question | Subject and topic | Difficulty |
|---|---|---|---|
| 4341 | ∫ dx/[x(x + 1)] equals | Mathematics/Applied Mathematics Methods of integration |
Medium |
| 4342 | ∫ log x dx equals | Mathematics/Applied Mathematics Methods of integration |
Medium |
| 4343 | ∫ dx/(x² − 9) equals | Mathematics/Applied Mathematics Methods of integration |
Hard |
| 4344 | The value of ∫₀² x dx is | Mathematics/Applied Mathematics Definite integrals |
Easy |
| 4345 | The value of ∫ from −1 to 1 of x³ dx is | Mathematics/Applied Mathematics Definite integrals |
Easy |
| 4346 | The value of ∫₀^(π/2) cos x dx is | Mathematics/Applied Mathematics Definite integrals |
Medium |
| 4347 | The value of ∫₀^(π/2) sin x/(sin x + cos x) dx is | Mathematics/Applied Mathematics Definite integrals |
Medium |
| 4348 | The value of ∫₀¹ x(1 − x)⁴ dx is | Mathematics/Applied Mathematics Definite integrals |
Hard |
| 4349 | The area bounded by the line y = x, the x-axis and the line x = 4 is | Mathematics/Applied Mathematics Applications of integrals |
Easy |
| 4350 | The area enclosed by the ellipse x²/a² + y²/b² = 1 is | Mathematics/Applied Mathematics Applications of integrals |
Easy |
| 4351 | The area under y = x² from x = 0 to x = 3, above the x-axis, is | Mathematics/Applied Mathematics Applications of integrals |
Medium |
| 4352 | The area of the part of the circle x² + y² = 16 lying in the first quadrant is | Mathematics/Applied Mathematics Applications of integrals |
Medium |
| 4353 | The area of the region bounded by the parabola y² = 4x and the line x = 4 is | Mathematics/Applied Mathematics Applications of integrals |
Hard |
| 4354 | The order of the differential equation d³y/dx³ + 2 d²y/dx² + dy/dx = 0 is | Mathematics/Applied Mathematics Differential equations: basics |
Easy |
| 4355 | The degree of (d²y/dx²)² + (dy/dx)³ + y = 0 is | Mathematics/Applied Mathematics Differential equations: basics |
Easy |
| 4356 | The degree of the differential equation d²y/dx² + sin(dy/dx) = 0 is | Mathematics/Applied Mathematics Differential equations: basics |
Medium |
| 4357 | How many arbitrary constants appear in the general solution of a differential equation of order 3? | Mathematics/Applied Mathematics Differential equations: basics |
Medium |
| 4358 | The family y = Aeˣ + Be⁻ˣ, with A and B arbitrary constants, is the general solution of | Mathematics/Applied Mathematics Differential equations: basics |
Hard |
| 4359 | The solution of dy/dx = 2x with y(0) = 1 is | Mathematics/Applied Mathematics Solving differential equations |
Easy |
| 4360 | The integrating factor of dy/dx + 2y = eˣ is | Mathematics/Applied Mathematics Solving differential equations |
Easy |