A BATTERY OF EMF 10 V AND INTERNAL RESISTANCE OF 0.5 OHM IS CONNECTED ACROSS A VARIABLE RESISTANCE R.THE MAXIMUM VALUE OF R IS GIVEN BY

1. 0.5 OHM
2. 1.00 OHM
3. 2.0 OHM
4. 0.25 OHM

First of all, you must be awared with the Maximum Power transfer theorem..in which, the power delivered would be maximum across the external resistance, if internal resistance of the circuit equal to the external resistance.
so r = R
Now, P= i²R = (V/r+R)2R...Differentiate the relation w.r.t. R and get the value of R in terms of r=== 0.5ohm

GOOD LUCK..........