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UPSC NDA II 2015 Mathematics Paper

Question : 23 of 120

Marks: +1, -0

x \in [0, 5]

x^{2} - 3x + 2 \ge 0

Solution:

Concept:

Probability = favourable unit intervals divided by total unit intervals in

[0,5]

Explanation:

Factor the quadratic:

x^2-3x+2 = (x-1)(x-2) \ge 0

This holds when

x \le 1

x \ge 2

, i.e.,

(-\infty,1] \cup [2,\infty)

Within

[0,5]

, the favourable set is

[0,1] \cup [2,5]

Divide

[0,5]

into five unit intervals:

[0,1], [1,2], [2,3], [3,4], [4,5]

The inequality is satisfied in

[0,1], [2,3], [3,4], [4,5]

— that is

4

intervals.

Total possible intervals

= 5

Required probability

= \frac{4}{5}

Answer:

\frac{4}{5}

(Option A).

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