CAT 2019 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Quants Questions | Question 17

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)) = 2x + 2-x is

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

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

2cos (x(x + 1)) = 2x + 2-x
Consider RHS, 2x + 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 2x, is considered
So, 2cos (x (x + 1))
Substitute x = 0, 2x + 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


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

Hence, the answer is 1

Choice C is the correct answer.

 

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com