Which of the following statement is correct'? (Take, earth as a sphere of uniform density)  

Acceleration due to gravity at altitude h,

$g_h=\frac{g}{(1+h/R{)}^2}\approx g\left(1-\frac{2h}{\dot{R}}\right)$                                     …(i)

At depth d,

$g_d=g\left(1-\frac{d}{R}\right)$                                                             …(ii)

In both Eqs. (i) and (ii), if  h  and d increases, g decreases.

At latitude  $\varphi ,g_{\varphi }=g-{\omega }^{2}R{\cos }^2\varphi$

As, $\varphi$ increases, $g_{\varphi }$ also increases.
Thus, option (4) is correct but rest are incorrect.