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| # | Question | Subject and topic | Difficulty |
|---|---|---|---|
| 4301 | For AX = B, suppose |A| = 0 and (adj A)B ≠ O. Then the system | Mathematics/Applied Mathematics Solving systems of linear equations |
Medium |
| 4302 | For which value of k does the system kx + 2y = 3, 2x + y = 5 have no solution? | Mathematics/Applied Mathematics Solving systems of linear equations |
Medium |
| 4303 | The system x + y + z = 6, y + 3z = 11, x − 2y + z = 0 has the solution | Mathematics/Applied Mathematics Solving systems of linear equations |
Hard |
| 4304 | If f(x) = kx + 1 for x ≤ 2 and f(x) = 3x − 1 for x > 2, for which value of k is f continuous at x = 2? | Mathematics/Applied Mathematics Continuity and differentiability |
Easy |
| 4305 | At x = 0, the function f(x) = |x| is | Mathematics/Applied Mathematics Continuity and differentiability |
Easy |
| 4306 | The derivative of sin(x²) with respect to x is | Mathematics/Applied Mathematics Continuity and differentiability |
Medium |
| 4307 | If f(x) = x² for x ≤ 1 and f(x) = ax + b for x > 1 is differentiable at x = 1, then (a, b) equals | Mathematics/Applied Mathematics Continuity and differentiability |
Medium |
| 4308 | At how many points is f(x) = |x − 1| + |x − 2| not differentiable? | Mathematics/Applied Mathematics Continuity and differentiability |
Hard |
| 4309 | The derivative of tan⁻¹x with respect to x is | Mathematics/Applied Mathematics Derivatives of special functions |
Easy |
| 4310 | The derivative of log(sin x) is | Mathematics/Applied Mathematics Derivatives of special functions |
Easy |
| 4311 | If x = at² and y = 2at, then dy/dx equals | Mathematics/Applied Mathematics Derivatives of special functions |
Medium |
| 4312 | For the curve x² + y² = 25, the value of dy/dx at the point (3, 4) is | Mathematics/Applied Mathematics Derivatives of special functions |
Medium |
| 4313 | If y = x^x for x > 0, then dy/dx equals | Mathematics/Applied Mathematics Derivatives of special functions |
Hard |
| 4314 | If y = x³ − 2x, then d²y/dx² equals | Mathematics/Applied Mathematics Second-order derivatives |
Easy |
| 4315 | The second derivative of y = sin x is | Mathematics/Applied Mathematics Second-order derivatives |
Easy |
| 4316 | The function y = e^(3x) satisfies which of the following? | Mathematics/Applied Mathematics Second-order derivatives |
Medium |
| 4317 | If y = log x, the value of d²y/dx² at x = 2 is | Mathematics/Applied Mathematics Second-order derivatives |
Medium |
| 4318 | If x = a cos t and y = a sin t, then d²y/dx² equals | Mathematics/Applied Mathematics Second-order derivatives |
Hard |
| 4319 | The rate of change of the area of a circle with respect to its radius r, when r = 5 cm, is | Mathematics/Applied Mathematics Rate of change |
Easy |
| 4320 | A particle moves so that s = t³ − 3t metres after t seconds. Its velocity at t = 2 s is | Mathematics/Applied Mathematics Rate of change |
Easy |