An ideal voltmeter and an ideal ammeter are connected as shown. The amount of heat produced in $10\mathrm{\Omega }$ and $5 \mathrm{\Omega }$ resistors are _____ respectively

An ideal voltmeter offers infinite resistance, then it acts as open circuit. Therefore current through $10\mathrm{\Omega }$ is zero 
$\therefore$no heat is generated at $10\mathrm{\Omega }$ an ideal ammeter offers zero resistance therefore ammeter acts as short circuit . So no current passes through $5\mathrm{\Omega }$ resistor.
$\therefore$no heat is generated at $5\mathrm{\Omega }$.