1. We examine each statement one by one.

2. Statement A: "The junction area of solar cell is made very narrow compared to a photo diode."

   • A solar cell is designed to receive maximum sunlight, so its junction area is made large, not narrow.
   • A photodiode usually has a smaller junction area compared to a solar cell.

   Therefore, A is false.

3. Statement B: "Solar cells are not connected with any external bias."

   • A solar cell works in photovoltaic mode, where it generates emf due to incident light.
   • It is generally operated without external bias.

   Therefore, B is true.

4. Statement C: "LED is made of lightly doped p-n junction."

   • LEDs are generally made from heavily doped semiconductor junctions to allow efficient recombination and light emission.

   Therefore, C is false.

5. Statement D: "Increase of forward current results in continuous increase of LED light intensity."

   • In an LED, light intensity increases with forward current only within the safe operating range.
   • The word continuous makes the statement incorrect in general, because beyond a limit heating and damage occur; it is not an unrestricted continuous increase.

   Therefore, D is false in the intended exam sense.

6. Statement E: "LEDs have to be connected in forward bias for emission of light."

   • LED emits light when operated in forward bias due to electron-hole recombination.

   Therefore, E is true.

7. Hence the true statements are:

   $B, E$

8. Matching with the given options:

   • Option A: $A, C, E$ only  incorrect
   • Option B: $B, E$ only  correct
   • Option C: $A, C$ only  incorrect
   • Option D: $B, D, E$ only  incorrect

Therefore, the correct answer is Option B.