Which organism is this?
This is an insect in the order Neuroptera, definitely neither a dragonfly (order Odonata) nor a grasshopper (Order Orthoptera).  The name of that order means "nerve-wing", which referes to the intricate network of veins throughout the wings, which have a very different appearance and pattern than the wings of either dragonflies or grasshoppers.  I'm not familiar with Indian fauna per se, but the long antennae with slightly curved/hooked tips make it look more like an antlion (family Myrmeleontidae within the Neuroptera) than an owlfly (family Ascalaphidae within the Neuroptera; their antennae have small clubs at the ends), though it's a bit hard to tell from the photo.