If set A `={x|(x^2(x-5)(2x-1))/((5x+1)(x+2)) lt 0 }` and
Set `B={x|(3x+1)/(6x^3+x^2-x) gt 0 } " then " A cap B` does not contain (a) (1,4) (b) (5,11) (c) `( − 3/ 2 , − 1/ 2 )` (d) None of these

Options

A. (1,4)
B. (5,11)
C. `(-3/2,(-1)/2)`
D. None of these

Answer

B

Explanation

we have `(x^2(x-5)(2x-1))/((5x+1)(x+2)) lt 0 ` ltbgt
from the sign scheme , solution is `(-2,-1/5) cup (1/5,5)`
Now `(3x+1)/(6x^3+x^2-x) gt 0 `
`rArr (3x+1)/(x(3x-1)(2x+1)) gt 0 `

form the sign scheme solution is
`(-oo,-1/2) cup (-1/3,0) cup (1/3 , oo)`
Clearly from (i) and (ii) options ( s) (1) and ( 3) and correct