Consider the following two functions
p
:
R
→
R
p:R→R
p
(
t
)
=
{
4
e
(
t
−
8
)
−
4
t
−
8
if
0
≤
t
<
8
,
4
t
=
8
4
(
t
2
−
64
)
1
ln
(
t
−
8
)
if
t
>
8
p(t)=
⎩
⎨
⎧
t−8
4e
(t−8)
−4
4
4(t
2
−64)
ln(t−8)
1
if 0≤t<8,
t=8
if t>8
and
q
:
R
→
R
q:R→R
q
(
t
)
=
∣
t
(
t
−
2
)
(
t
−
8
)
∣
q(t)=∣t(t−2)(t−8)∣ and the following statements (a function is said to be continuous (respectively differentiable) if it is continuous (respectively differentiable) at all the points in the domain of the function).
Statement
P:
Statement P: Both the functions
p
(
t
)
p(t) and
q
(
t
)
q(t) are continuous.
Statement
Q:
Statement Q: Both the functions
p
(
t
)
p(t) and
q
(
t
)
q(t) are not differentiable.
Statement
R:
Statement R:
p
(
t
)
p(t) is continuous,
q
(
t
)
q(t) is differentiable.
Statement
S:
Statement S:
q
(
t
)
q(t) is continuous,
p
(
t
)
p(t) is not differentiable.
Statement
T:
Statement T: Neither
p
(
t
)
p(t) nor
q
(
t
)
q(t) is continuous.
Find the number of correct statements.
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