Join WhatsApp Icon CAT WhatsApp Group
Question 78

If x is a real number, then $$\sqrt{\log_{e}{\dfrac{4x - x^2}{3}}}$$ is a real number if and only if

Solution

Share

$$\sqrt{\log_{e}{\dfrac{4x - x^2}{3}}}$$ will be real if $$\log_e\ \dfrac{\ 4x-x^2}{3}\ \ge\ 0$$

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

$$\ 4x-x^2-3\ \ge\ 0$$

$$\ x^2-4x+3\ \le\ 0$$

$$1\le\ x\le\ 3$$

Video Solution

video
View More Questions From Inequalities

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 41+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Time, Speed and Distance QuestionsCAT Data Sufficiency QuestionsCAT Venn Diagrams QuestionsCAT Quadratic Equations QuestionsCAT Profit and Loss Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Puzzles QuestionsCAT Quant Based DI QuestionsCAT Maxima-Minima QuestionsCAT Data Interpretation Basics QuestionsCAT Games and Tournamnents Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Vocabulary QuestionsCAT Verbal Ability QuestionsCAT Para Jumbles QuestionsCAT Critical Reasoning QuestionsCAT Reading Comprehension Questions

Free CAT Quant Questions

CAT Data Sufficiency

CAT Linear Equations

CAT Profit and Loss

CAT Profit And Loss

CAT Algebra

CAT Inequalities

CAT Geometry

CAT Logarithms, Surds and Indices

CAT Averages, Ratio and Proportion

CAT Time, Speed and Distance

CAT Simple Interest Compound Interest

CAT Percentages

CAT Averages

CAT Averages Mixtures Alligations

CAT Logarithms

CAT Mensuration

CAT Functions, Graphs and Statistics

CAT Arithmetic

CAT Coordinate Geometry

CAT Remainders

CAT Time Speed Distance

CAT Probability, Combinatorics

CAT Number Systems

CAT Number Series

CAT Venn Diagrams

CAT Quadratic Equations

CAT Time And Work

CAT Miscellaneous

CAT Progressions and Series