Explanation

(c)
As $a,\ b,\ c,\ d$ are in HP. So, $b$ is HM between $a$ and $c$. Also, GM between $a$ and $c = \sqrt{ac}.$
Now, GM > HM
$\Rightarrow \ \sqrt{ac} > b$
$\Rightarrow \ ac > b^{2}$ …(i)
Again, $a,\ b,c,d$ are in HP. So $c$ is HM between $b$ and $d$.
Therefore, $bd > c^{2}$ …(ii)
On multiplying relations (i) and (ii), we get
$abcd > b^{2}c^{2} \Rightarrow ad > bc$
Hence, option (b) is true.
Now, AM between $a$ and $c$ $= \frac{1}{2}(a + c)$
Now, as AM > HM
So, here $a + c > 2b$ …(iii)
And $c$ is HM between $b$ and $d$
$\Rightarrow \ b + d > 2c$ …(iv)
On adding relations (iii) and (iv), we get
$(a + c) + (b + d) > 2(b + c)$
$\Rightarrow a + d > b + c$
So, both (a) and (b) are correct.