If temp. gets cold resistance in thermostat increases so voltage across it increases and led lights brighter. i understand everything except that for led. it emits light when current passes through it, but if resistance increases how can current

Normally, when something gets colder, its electrical resistance gets smaller.  This is true of component-A in the drawing ... a simple resistor.

The component labeled 'B' has a strange and unusual symbol, and it's not a simple resistor.  It's a "thermistor".  The word "thermal" always has something to do with heat, and "thermistor" comes from "thermal resistor.  These things can be manufactured either way ... using different materials, a thermistor can be manufactured so that its resistance goes UP, or goes DOWN, or doesn'tchange when it gets colder.  I'm pretty sure that's what's going on here.

When this circuit gets colder, resistance-A gets smaller, but resistance-B either gets bigger OR doesn't change.  Either way, the voltage across B increases.  Since the LED is connected directly across B, the current through it depends on that voltage, so the LED gets more current, and becomes brighter, when A and B both get colder.

This circuit could actually be a very useful device.  If you took out the LED and put a voltmeter in its place, then the reading on the voltmeter would tell you the temperature of wherever you put the two components A and B.

the answer is a)

mark brainliest