2016 · Q36
Consider the following statements :
- 1There exists a positive real number m such that cos x = 2^(m + 1).
- 2mn ≥ m + n for all m, n belonging to set of natural numbers.
Which of the above statements is/are correct?
Elementary MathematicsNumber System
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Statement 1 is impossible since |cos x| ≤ 1 < 2 < 2^{m+1} for every positive real m. Statement 2 fails already at m = n = 1 (1 < 2). Hence neither, option D.