Bodhee Prep-Online CAT Coaching | Online CAT Preparation | CAT Online Courses

Get 30% OFF on CAT Crash Course. Code: LASTLAP. Course starts from 18th Sept Enroll Now

CAT 2019 Quant Question with Solution 36

Question:
If x is a real number, then $\sqrt{\log _{e} \frac{4 x-x^{2}}{3}}$ is a real number if and only if

  1. $1 \leq x \leq 2$
  2. $-3 \leq x \leq 3$
  3. $1 \leq x \leq 3$
  4. $-1 \leq x \leq 3$
Show Answer

Correct Answer: Option: 3

The expression will be real only if ${{\log }_{e}}\frac{4x-{{x}^{2}}}{3}\ge 0$

Or $\frac{4x-{{x}^{2}}}{3}\ge {{e}^{0}}$

$\Rightarrow \frac{4x-{{x}^{2}}}{3}\ge 1$

$\Rightarrow 4x-{{x}^{2}}\ge 3$

$\Rightarrow {{x}^{2}}-4x+3\le 0$

$\Rightarrow \left( x-1 \right)\left( x-3 \right)\le 0$

$1 \leq x \leq 3$


CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions

CAT 2019 Slot-1


CAT 2019 Slot-2

CAT online Courses

CAT 2023 Mock Test Series

  • 400+ Topic Tests
  • 45 Sectional tests
  • 20 Mock Tests (Video Solutions)
  • Only at INR 2499

20% Discount Code: GET20

FREE CAT Prep Whatsapp Group

CAT 2023 Online Course at affordable price