CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If P={xN:14xx+1(9x30x4)0},
Q={xZ:|x1|5 and |x1|2}
and R={xR:log6x+2log6x}=3, then which of the following options is (are) CORRECT?
  1. n(PQR)=10
  2. n(PQR)=1
  3. n(PQR)=1
  4. n(PQR)=1


Solution

The correct options are
A n(PQR)=10
B n(PQR)=1
C n(PQR)=1
D n(PQR)=1
For set P
14xx+1(9x30x4)0
For the inequality to be defined, x1,4
(14x256x)(9x221x30)(x+1)(x4)0
5x235x+30(x+1)(x4)0
5(x1)(x6)(x+1)(x4)0
x(1,1](4,6]
Since xN,P={1,5,6}

For set Q
|x1|5 and |x1|2
2|x1|5
5x12 or 2x15
4x1 or 3x6
x[4,1][3,6]
Since xZ,Q={4,3,2,1,3,4,5,6} 

For set R
Clearly, x>0 and x1
log6x+2log6x=3
(log6x)23log6x+2=0
(log6x1)(log6x2)=0
log6x=1 or log6x=2
x=6,36
R={6,36}

PQR={1,5,6,4,3,2,1,3,4,36}
PQR={6}
PQ={1}, PQR={1}
PQ={5,6}, PQR={5}

So, n(PQR)=10
n(PQR)=1
n(PQR)=1
n(PQR)=1

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image