Solution:

Degree of a polynomial is the highest power of the variable in the polynomial.

(i) $5 x^{3}+4 x^{2}+7 x$

This is a polynomial in variable $x$ and the highest power of variable $x$ is 3 . Therefore, the degree of this polynomial is $3 .$

(ii) $4-y^{2}$

This is a polynomial in variable $y$ and the highest power of variable $y$ is 2 . Therefore, the degree of this polynomial is 2 .

(iii) $5 t-\sqrt{7}$

This is a polynomial in variable $t$ and the highest power of variable $t$ is 1 . Therefore, the degree of this polynomial is $1 .$

(iv) 3

This is a constant polynomial. Degree of a constant polynomial is always 0 .