Design an active bandpass filter to get 1.5MHz peak frequency and 300KHz band
It won't make a very sharp or precise filter using the configuration shown but, to make life simpler (given that it is a really sloppy filter) you can regard C1 and R1 as forming a high-pass network and C2 and R2 as forming a low-pass network. 

The two filter points need to be different to obtain a 300 kHz bandwidth so, 


make the low-pass network cut-off at 1.5 MHz + 150 kHz (1.65 MHz) and 
make the high-pass network cut-off at 1.5 MHz - 150 kHz (1.35 MHz).


That allows you to calculate both resistors based on both capacitors being 1 uF. However, what you will find is that 1 uF is too high in value for an op-amp to work with at circa 1.5 MHz and you will need to choose a much lower default value.

For instance, using a 100 pF capacitor, it will form a 3 dB point at 1.65 MHz when R = 964 ohms. 

If you'd have used 1 uF, R would be 0.096 ohms and that isn't practical for any op-amp.

However, you will never get a centre frequency to bandwidth ratio as required by the question using a simple op-amp and high-pass and low-pass networks. To get a centre frequency if 1.5 MHz and a bandwidth of 300 kHz implies a Q factor of 1500/300 = 5. This cannot be achieved by the op-amp configuration shown because the maximum Q factor is limited to 0.5. You can try it of course, but you'll get just a sloppy band pass filter like this: -



It just won't deliver what you want. Bandwidth is approximately 3.53 MHz - 610 kHz = 2.92 MHz and centre frequency is 1.47 MHz hence, Q = 0.503.