Which of the following is/are EQUAL to 224 in radix-5 (i.e., base-5) notation?

Consider 4-variable functions $f1, f2, f3, f4$ expressed in sum-of-minterms form as given below.

$f1 = \sum(0,2,3,5,7,8,11,13)$

$f2 = \sum(1,3,5,7,11,13,15)$

$f3 = \sum(0,1,4,11)$

$f4 = \sum(0,2,6,13)$

With respect to the circuit given above, which of the following options is/are CORRECT?

Let p and q be the following propositions:

p: Fail grade can be given.

q: Student scores more than 50% marks.

Consider the statement: “Fail grade cannot be given when student scores more than 50% marks.”

Which one of the following is the CORRECT representation of the above statement in propositional logic?

Let $f(x)$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$ such that

$f(x) = 1 - f(2 - x)$

Which one of the following options is the CORRECT value of $\int_0^2 f(x) dx$?