CAT Previous Year Questions | Trigonometry

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CAT 2019 QA Slot 1 | Geometry - Trigonometry CAT Question
The number of the real roots of the equation 2cos(x(x + 1)) = 2^x + 2^–x is

(a) 0

(b) 2

(d) 1

EXPLANATION

Given: 2 cos (x(x + 1)) = 2^x + 2^–x

Now, by AM – GM inequality, we get

∴ 2 cos (x(x + 1)) ≥ 2

We know, –1 ≤ cosθ ≤ 1

∴ 2 cos(x(x + 1)) = 2

Hence, the expression is valid only if 2x + 2–x = 2, which is true for only one value of x i.e. 0. Therefore, the expression has only one real solution.

Question 1 of 5

Q1CAT 2004

A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on th same straight line. The father observes that the shadows of his head and his son's head are incident at the same point on the ground. If the heights o the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the pos then how far (in metres) is the son standing from his father?

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