CAT 2019 Question Paper | Quants Slot 1

CAT Questions

Here is a slightly tough question in CAT 2019. It combines the topics of trigonometry and algebra. It is very important to have done a solid CAT Preparation to be sure about the concepts and trigonometry formula to even attempt this question. Once you are clear with the concepts & formulas, it would be prudent to practice them from CAT previous year paper.

Question 17 : The number of the real roots of the equation 2cos(x(x + 1)) = 2^x + 2^-x is

1. 0
2. Infinite
3. 1
4. 2

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Video Explanation

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Explanatory Answer

2cos (x(x + 1)) = 2^x + 2^-x
Consider RHS, 2^x + 2^-x
This is of the form,
We know that when y is positive and when y is negative
Here, since we are dealing with 2^x, is considered
So, 2cos (x (x + 1))
Substitute x = 0, 2^x + 2^-x = 2⁰ + 2⁰ = 2
2cos (x (x + 1)) = 2cos (0(0 + 1)) = 2cos (0) = 2 x = 0 is a valid solution
Any value other than this wont work.
Therefore, only x = 0 works and there is only one real solution

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The question is "The number of the real roots of the equation 2cos(x(x + 1)) = 2^x + 2^-x is "

Hence, the answer is 1

Choice C is the correct answer.