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If [x] denotes the greatest integer less...

If [x] denotes the greatest integer less than or equal to x, then the solution set of inequation `([x]-2)/(4-[x]) > 0,` is ...

A

`(2, 3]`

B

`[3, 4)`

C

`[2, 3]`

D

`[3, 4]`

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`([x]-2)/(4-[x]) gt 0`
`rArr ([x]-2)/([x]-4) lt 0 rArr 2 lt [x] lt 4 rArr [x] = 3 rArr x in [3, 4)`
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OBJECTIVE RD SHARMA ENGLISH-ALGEBRAIC INEQUATIONS-Section I - Solved Mcqs
  1. The solution set of the inequation (x-1)/(x-2) gt 2, is

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  2. The complete set of values of 'x' which satisfy the inequations: 5x+2...

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  3. The solution set of the inequation |2x-3| lt x-1, is

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  4. Write the solution set of the inequation |x-1|geq|x-3|dot

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  5. The solution set of the inequation |x|-1 lt 1-x, is

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  6. The set of all real numbers x for which x^2-|x+2|+x >0 is (-oo,-2) b. ...

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  7. The solution set of the inequation (|x+3|+x)/(x+2) gt 1, is

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  8. The set of values of x for which the inequality |x-1|+|x+1|lt 4 always...

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  9. The solution set of the inequation |[|x|-7]|-5< 0, is ... ([*] denote...

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  10. If [x] denotes the greatest integer less than or equal to x, then the ...

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  11. The area of the region represented by |x-y| le 3 " and " |x+y|le 3, is

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  12. The total number of integral points i.e. points having integral coordi...

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  13. The solution set of the inequation |(1)/(x)-2| lt 4, is

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  14. The set of real values of x satisfying the inequality |x^(2) + x -6| l...

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  15. The set of real values of x satisfying ||x-1|-1|le 1, is

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  16. The largest interval for whichx^(12)+x^9+x^4-x+1>0 -4<xlt=0 b. 0<x<1 ...

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  17. The number of integral solutions of x^2+9<(x+3)^2<8x+25 is

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  18. If x^2-ax+1-2a^2 > 0 for all x in R, then ....

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  19. The least integral value of 'k' for which (k -2)x^2 +8x+k+4>0 for all ...

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  20. If 9^(x+1) + (a^(2)-4a-2) 3^(x) + 1 lt 0 "for all" x in R, then

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