KCET2019MathematicsBasics of Mathematics
On the set of positive rationals, a binary operation * is defined by ( a^ * b= 2 a b 5 ). If ( 2^ * x=3⁻¹ ) then ( x= )
Options
- A( 5 12 )
- B( 125 48 )
- C( 1 6 )
- D( 2 5 )
Correct answer
B. ( 125 48 )
Step-by-step solution
(B) [ array l a^ * e=a a^ * e=a 2 a e 5 =a e= 5 2 a^ * a⁻¹=e 2 a a⁻¹ 5 = 5 2 a⁻¹= 25 4 a 2^ * x=3⁻¹ 2(2 x) 5 = 25 4(3) x= 125 48 array ]