The beetle used as a biocontrol agent for aphids and mosquitoes is:

The correct option is Ladybird.

Biological Control (Biocontrol):
Biocontrol is a method of controlling pests, weeds, and plant diseases using other living organisms (natural predators or parasites) instead of harmful chemical pesticides. This approach helps protect the environment and maintains a natural ecological balance.

Why Ladybird is the correct option:
1. Beetle Classification: The ladybird (commonly known as a ladybug) is a beetle belonging to the insect order Coleoptera.
2. Control of Aphids: Ladybirds are highly beneficial predators in gardens and agricultural fields because both their larvae and adults feed voraciously on aphids, which are small sap-sucking pests that damage crops.
3. Relation to Mosquito Control: In biological pest control, ladybirds and dragonflies are often grouped together as common insect predators. Ladybirds are used to control aphids, while dragonflies (which are not beetles) are used to target and control mosquito populations.

Analysis of the Other Options:
- Trichoderma: This is a genus of free-living fungi found in soil and root ecosystems. It is used as a biocontrol agent against plant pathogens but is a fungus, not a beetle.
- Dragonflies: These insects are biocontrol agents that feed on mosquitoes. However, they belong to the order Odonata and are not classified as beetles.
- Silver fish: Silverfish are wingless, nocturnal pests that consume household items containing starch or cellulose (such as paper and clothing). They do not act as biocontrol agents.