For positive non-zero real variables $p$ and $q$, if

$\log \left(p^2 + q^2\right) = \log p + \log q + 2 \log 3$,

then, the value of $\frac{p^4 + q^4}{p^2 q^2}$ is

In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks.

Steve was advised to keep his head _____ (i) _____ before heading _____ (ii) _____ to bat; for, while he had a head _____ (iii) _____ batting, he could only do so with a cool head _____ (iv) _____ his shoulders.

A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken.

Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person.

Macronutrient energy contribution

The typical energy density (kcal/g) of these macronutrients is given in the table:

The total fat (all three types), in grams, this person consumes is