2015 · Q74
Consider the following statements :
- 1There exists no value of x such that 1/1- x=4+2{3},\;0
- 2x = 3^{² x} does not hold good for any real x.
Which of the above statements is/are correct?
Elementary MathematicsTrigonometry
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Statement 1: 1/(1−sinx) = 4 + 2√3 gives sinx = √3/2 (x = π/3 exists), so 'no such x' is false. Statement 2: 3^{2t} > t for every real t (the minimum of 3^{2t}−t is ≈0.81 > 0), so the equation has no real solution — true. Hence '2 only' (option B).