defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Differential Calculus Differentiability
Let f : \(\mathbb{R}\) - {0} → \(\mathbb{R}\) be a function satisfying \(f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}\) for all x, y, f(y) ≠ 0. If f' (1) = 2024, then
1
xf' (x) - 2024 f(x) = 0
2
xf' (x) + 2024f(x) = 0
3
xf' (x) + f(x) = 2024
4
xf' (x) - 2023f(x) = 0