Home
Class 12
MATHS
Find the number of distinct rational num...

Find the number of distinct rational numbers `x` such that `0 lt x lt1` and `x=p//q` , where `p ,q in {1,2,3,4,5,6}` .

A

15

B

13

C

12

D

11

Text Solution

Verified by Experts

The correct Answer is:
D
As `0 lt x lt 1`, we have `p lt q`
The number of rational numbers=5+4+3+2+1=15
When p,q have a common factor, we get some rational numbers which are not different from those already counted.
There are 4 such numbers `(2)/(4),(2)/(6),(3)/(6),(4)/(6)`.
`therefore` The required of rational numbers=15-4=11
Promotional Banner

Similar Questions

Explore conceptually related problems

The number of distinct real roots of x^4 - 4 x^3 + 12 x^2 + x - 1 = 0 is :

The number of real solutions of the equation log_(a)x=|x|,0 lt a lt 1 , is

Write down the contrapositive of the following statements.:if x is a real number such that 0ltxlt1 , then x^(2)lt1

Is zero a rational number ? Can you write it in the form (p)/(q) , where p and q are integers and q ne 0 ?

Find the unit vector in the direction of vector vec(PQ) , where P and Q are the points (1,2,3) and (4,5,6) , respectively.

Let p(x) be a polynomial of degree 4 such that P(1)=P(3)=P(5)=P'(7)=0. If the real number ane1,3,5 is such that P(a)=0 can be expressed as a=(p)/(q) , where p and q are relatively prime, then (p-8q) is……….

Show that 3.142678 is a rational number In other words express 3.142678 in the form (p)/(q) where p and q are integer and q ne 0

If sec x cos 5x=-1 and 0 lt x lt (pi)/(4) , then x is equal to

If |x - 2| lt 3 then -1 lt x lt 5 .