The wavelength associated with a moving particle depends upon $p^{th}$power of its mass m, $q^{\mathrm{th}}$ power of its velocity v and r^th power of Planck's constant h. Then the correct set of values of p, q and r is

Given $\mathrm{\lambda } = {\mathrm{km}}^{\mathrm{p}}{\mathrm{v}}^{\mathrm{q}}{\mathrm{h}}^{\mathrm{r}},$ the dimensions of right hand side and left hand side terms should be equal.

So $\left[{\mathrm{M}}^0{\mathrm{LT}}^0\right] = {\left[\mathrm{M}\right]}^{\mathrm{p}}{\left[{\mathrm{LT}}^{-1}\right]}^{\mathrm{q}}{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]}^{\mathrm{r}}$

or $\left[{\mathrm{M}}^0{\mathrm{LT}}^0\right] = \left[{\mathrm{M}}^{p+\mathrm{r}}\right]\left[{\mathrm{L}}^{\mathrm{q}+2\mathrm{r}}\right]\left[{\mathrm{T}}^{-\mathrm{q}-\mathrm{r}}\right]$

Now, compare powers of M, L and T, we get

p+r =0..(i)    q+2r = 1  (ii), -q-r = 0    (iii)

After solving p = -1, q = -1, and r = 1 putting these values, we get

$\mathrm{\lambda } = \mathrm{k}\frac{\mathrm{h}}{\mathrm{mv}}$which is the required relation.