Let the number of correctly answered questions be $x$ and the number of wrongly answered questions be $y$. Since the student attempted all questions, the total number of questions in the paper is $x + y$.

According to the first condition, $5$ marks are awarded for a correct answer and $2$ marks are deducted for a wrong answer, resulting in a score of $69$: $5x - 2y = 69 \quad \text{--- (Equation 1)}$

According to the second condition, if $4$ marks were awarded for a correct answer and $1$ mark deducted for a wrong answer, the score would be $84$: $4x - y = 84 \quad \text{--- (Equation 2)}$

From Equation 2, we can express $y$ in terms of $x$: $y = 4x - 84$

Substitute this value of $y$ into Equation 1: $5x - 2(4x - 84) = 69$ $5x - 8x + 168 = 69$ $-3x = 69 - 168$ $-3x = -99$ $x = 33$

Now, substitute the value of $x$ back into the expression for $y$: $y = 4(33) - 84$ $y = 132 - 84$ $y = 48$

The student answered $33$ questions correctly and $48$ questions wrongly. The total number of questions in the paper is: $x + y = 33 + 48 = 81$

Therefore, there were $81$ questions in the question paper.