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JEE Main 9 Apr 2024 Shift 1 Solved Paper
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© examsnet.com
Question : 21
Total: 90
Let
a
,
b
and
c
denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked
1
,
2
,
3
,
4
. If the probability that
a
x
2
+
b
x
+
c
=
0
has all real roots is
m
n
,
gcd
(
m
,
n
)
=
1
, then
m
+
n
is equal to ______.
[9 Apr 2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
a, b, c
∈
{
1
,
2
,
3
,
4
}
Tetrahedral dice
ax
2
+
bx
+
c
=
0
has all real roots
⇒
D
≥
0
⇒
b
2
−
4
ac
≥
0
Let
b
=
1
⇒
1
−
4
ac
≥
0
(Not feasible)
b
=
2
⇒
4
−
4
ac
≥
0
1
≥
ac
⇒
a
=
1
,
c
=
1
b
=
3
⇒
9
−
4
ac
≥
0
9
4
≥
ac
⇒
a
=
1
,
c
=
1
⇒
a
=
1
,
c
=
2
⇒
a
=
2
,
c
=
1
b
=
4
⇒
16
−
4
ac
≥
0
4
≥
ac
⇒
a
=
1
,
c
=
1
⇒
a
=
1
,
c
=
2
⇒
a
=
2
,
c
=
1
⇒
a
=
1
,
c
=
3
⇒
a
=
3
,
c
=
1
⇒
a
=
1
,
c
=
4
⇒
a
=
4
,
c
=
1
⇒
a
=
2
,
c
=
2
Probability
=
12
(
4
)
(
4
)
(
4
)
=
3
16
=
m
m
m
+
n
=
19
© examsnet.com
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