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NIMCET 2012 — Mathematics PYQ

NIMCET | Mathematics | 2012

Coefficients of quadratic equation $ax^2 + bx + c = 0$ are chosen by tossing three fair coins, where 'head' means one and 'tail' means two. Then the probability that roots of the equation are imaginary, is:

Choose the correct answer:

A.
$\frac{7}{8}$

Same Topic Questions

NIMCET

If $α$ and $β$ are roots of $x^{2} - x - 1 = 0$ , and $A_{n} = α^{n} + β^{n}$ , then the ar…

(Correct Answer)

B.
$\frac{5}{8}$

C.
$\frac{3}{8}$

D.
$\frac{1}{8}$

Correct Answer:
$\frac{7}{8}$

Explanation

Calculation:

If $b = 1$ : $b^2 = 1$ .

Possible $(a, c)$ pairs are $(1,1), (1,2), (2,1), (2,2)$ .

In all 4 cases, $1 < 4ac$ is true. (4 favorable cases)

If $b = 2$ : $b^2 = 4$ .

Case $(1,1)$ : $4 < 4(1)(1) \implies 4 < 4$ (False)

Case $(1,2)$ : $4 < 4(1)(2) \implies 4 < 8$ (True)

Case $(2,1)$ : $4 < 4(2)(1) \implies 4 < 8$ (True)

Case $(2,2)$ : $4 < 4(2)(2) \implies 4 < 16$ (True)

(3 favorable cases)

Total Favorable Cases: $4 + 3 = 7$ .

Probability:

$P = \frac{7}{8}$

Correct Option: (a)

Explanation

Correct Option: (a)

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