I gave it a little complexity!

$Given : \quad Q=\{ 1,7,2,9 \} \\ P(Q)=\color{#D61F06}{\{} \phi, \{1\},\{ 7\}, \{ 2\}, \{9 \}, \{1,7 \}, \\ \{1,2 \}, \{1,9 \}, \{7,2 \}, \{7,9 \}, \\ \{2,9 \}, \{1,7,2 \}, \{1,7,9 \}, \\ \{ 1,2,9\}, \{7,2,9 \}, \{1,7,2,9 \} \color{#D61F06}{\}}$

$\boxed{ \text{No. of elements in the set } Q=4 \\ \text{No. of elements in the set } P(Q)=16 \\ \text{Total no. of subsets of the set } Q=2^4=16 \\ \text{Total no. of subsets of the set } P(Q)=2^{\left( 2^4 \right)}}$

a). Total no. of subsets of $P(Q)=2^{\left( 2^4 \right)}$ which is more than $1729$ . Hence this statement is correct.

b). No. of subsets of $Q$ = Cardinal no. of $P(Q)$ = $2^4$ . Hence this statement is correct.

c). $\phi \in P(Q) \ \text{and} \ \phi \subseteq P(Q)$ . Hence there exists some $t$ and $t=\phi$ . Hence this statement is correct.

d). $P(Q)$ is the set of all the subsets of $Q$ . Hence if $y \in P(Q) \implies y \subseteq Q$ . So this statement is correct.

e). There is no elements common in $Q$ and $P(Q)$ . Hence the statement is correct.

f). $\phi$ is the subset of both $Q$ and $P(Q)$ . So, no. of set(s) which is(are) subsets of both $Q$ and $P(Q)$ is $1$ , not zero. Hence this statement is incorrect.

From the above explanations, one can easily say that the correct statements are $\boxed{a), \ b), \ c), \ d), \ e)}$

enjoy !