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NIMCET 2012 Question Paper with solutions
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© examsnet.com
Question : 14
Total: 120
Coefficients of quadratic equation
a
x
2
+ bx + c = 0 are chosen by tossing three faircoins, where ‘head’ means one and ‘tail’ meanstwo. Then the probability that roots of theequation are imaginary, is
7
8
5
8
3
8
1
8
Validate
Solution:
Total sample events n(S) =
(
2
)
3
= 8
Cases
Value
Condition for imaginary roots
b
2
- 4ac = 0
H,T,T
1,2,2
(
2
)
2
- 4 (1) (2) < 0
H, H, T
1, 1,2
(
1
)
2
- 4(1) (2) <0
H, T, H
1,2,1
(
2
)
2
- 4 (1) (1) = 0
H, H, H
1,1,1
(
1
)
2
— 4 (1) (1)< 0
T, H,H
2, 1,1
(
1
)
2
— 4 (2) (1) < 0
T, T, H
2, 2, 1
(
2
)
2
— 4 (2) (1) < 0
T, H, T
2, 1,2
(
1
)
2
- 4 (2)(2)< 0
T, T, T
2, 2, 2
(
2
)
2
- 4 (2) (2) < 0
∴ Total favourable events n(E) = 7
∴ Required probability =
n
(
E
)
n
(
S
)
=
7
8
© examsnet.com
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