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The set of values of x satisfying simultaneously the inequalities ( x − 8 ) ( 2 − x ) l o g 0 . 3 ( 1 0 7 ( l o g 2 5 − 1 ) ) ≥ 0 a n d     2 x − 3 − 3 1 > 0     i s :

Option 1 -

A singleton set

Option 2 -

An empty set

Option 3 -

An infinite set

Option 4 -

A set consisting of exactly two elements

0 3 Views | Posted 3 weeks ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 weeks ago
    Correct Option - 1


    Detailed Solution:

    Note that Dr < 0, hence given inequality (1) is true only if N r ≥ 0  

      i.e.   ( x − 8 ) ( x − 2 ) ≤ 0       a n d     2 x − 3 > 3 1

    i.e.    2 ≤ x ≤ 8       a n d     2 x − 3 ≥ 3 1

    only x = 8 satisfies both the inequality.

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