edited by
2,044 views
5 votes
5 votes

If $x > y > 1,$ which of the following must be true$?$

  1. $\ln x > \ln y$
  2. $e^{x} > e^{y} $
  3. $y^x > x^y $
  4. $\cos x > \cos y$
  1. (i) and (ii)
  2. (i) and (iii)
  3. (iii) and (iv)
  4. (ii) and (iv)
edited by

2 Answers

Best answer
4 votes
4 votes
Both $\ln$ and $e^x$ are monotonically (continuously) increasing functions. So, (i) and (ii) are TRUE.

If we take $x = 3, y = 2;y^x = 8, x^y = 9.$ So, (iii) is false

$\cos x$ is not a monotonically increasing function. So, (iv) is false.

Correct Option: A
edited by
0 votes
0 votes

Let x=Π & y=Π/2  then cosx=-1 & cosy=0

i.e cosx<cosy

so (iv) is incorrect & option (C) & (D) are not possible

considering (ii) for the base e to be same & the value of exponent x>y>1 ,the value e> ey  holds true

So option (A) is correct 

Answer:

Related questions

1 votes
1 votes
2 answers
1
Akash Kanase asked Feb 12, 2016
893 views
Find the missing sequence in the letter series below:$A, CD, GHI, ?, UVWXY$$LMN$ $MNO$ $MNOP$$NOPQ$
0 votes
0 votes
2 answers
2
9 votes
9 votes
1 answer
3
Akash Kanase asked Feb 12, 2016
1,674 views
$\log \tan 1^o + \log \tan 2^o + \dots + \log \tan 89^o$ is $\ldots$$1$$1/\sqrt{2}$$0$$−1$
9 votes
9 votes
1 answer
4
Akash Kanase asked Feb 12, 2016
5,827 views
From a circular sheet of paper of radius $30$ cm, a sector of $10\%$ area is removed. If the remaining part is used to make a conical surface, then the ratio of the radiu...