Assertion: The buffer $HCOOH/HCOONa$ will have $pH$ lesser than $7.$
Reason: Conjugate base of a weak acid is a strong base.
(A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(B) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(C) Assertion is true but Reason is false
(D) Assertion is false but Reason is true
(E) Both Assertion and Reason are false.

Hint:
The buffer $HCOOH/HCOONa$ is an acidic buffer solution containing weak acid formic acid and its salt solution formate with strong base $NaOH$.

Complete step by step answer:
A buffer solution is one which resists changes in $pH$ when small quantities of an acid or an alkaline are added to it. An acidic buffer solution is simply one which has a $pH$ less than $7$. Acidic buffer solutions are commonly made from a weak and one of its salts-often a sodium salt.
A buffer is a mixture of a weak base and its conjugate acid. They act to moderate gross changes in $pH$. So, approx. equal concentrations of a weak base with its conjugate acid or addition of half an equivalent of strong acid to weak base, will generate a buffer.
In the given question, buffer solutions formic acid, $HCOOH$(weak acid) and sodium formate, $HCOONa$ (its conjugate base) $HCO{O^ - }$ formate anion.
The Henderson-Hasselbalch equation allows you to calculate the $pH$ of the buffer by using the ${p^{ka}}$ of the weak acid and the ratio that exists between the concentrations of the weak acid and conjugate base.
${p^{ka}}$ of formic acid is $3.75$
\[{p^H}\, = \,\,{p^{ka}} + \,\log \left( {\dfrac{{\left[ {{\text{conjugate base}}} \right]}}{{\left[ {{\text{weak acid}}} \right]}}} \right)\]
At equal concentrations of weak acid and conjugate base, the \[\log \] term is equal to zero.
So, \[{p^H}\, = \,\,{p^{ka}} = 3.75\]
If you have more conjugate base than weak acid, then \[\log \] term will be a positive value.
\[{p^H}\, = \,\,{p^{ka}} + \,\mathop {\log \left( {} \right)}\limits_{{\text{ + ve value}}} \]
We can see here,
The $pH$ of the buffer is higher than the \[{p^{ka}}\] of the acid.
\[{p^H}\, = \,3.75 + \,{\text{something}}\]
\[{p^H}\, < 7\]
So, it will have $pH$ less than \[7\] as the solution will be acidic.

Hence the correct answer is option, A.

Note: A conjugate acid, within the Brønsted–Lowry acid–base theory, is a chemical compound formed when an acid donates a proton to a base—in other words, it is a base with a hydrogen ion added to it, as in the reverse reaction it loses a hydrogen ion.