NIMCET 2012 Question Paper with solutions

Question : 14 of 120

Marks: +1, -0

Coefficients of quadratic equation

ax^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

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