A lot of quest give you exp lamps. You can also check the reward of the quest before you start it.
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The Smithing Quest
Try Imp Catcher. Its the simplest one.
These following quests will give you fishing exp. Free-player quests. None Member quests. The Fishing Contest: 2437exp. Land of the Goblins:3000exp. Rum Deal:7000exp. Sea Slug:7175exp. Swan Song:10000exp. Tai Bwo Wannai Trio:5000exp. The Fremennik Trials:2812exp. Check out Sal's Realm of Runescape for Quest Guides.
276 - Wolf Whistle1,000 - Spirit of Summer1,500 - Summer's End4,000 - The Curse of ArravTotal: 6,776 Experience
400 exp.
Just create a new account and do quests that give you defence exp and train just defence skill, then train attack skill.
Exp and ability to wear a Rune Platebody and Dragonhide.
75 exp each.
There is a quest called "The Digsite" .It gives you at least 15,000 exp. Its an intermediate kind of quest and its a lot of fun http://runescape.wikia.com/wiki/The_Dig_Site
by completing certain quests or acheivment diaries for example i got a lamp from begginer lumbridge acheivment. hope that helps ------------------------------------------------------------------------------------ here are the real ways to get lamp 1:members toturial island get free 250 exp lamp 2.sir vant in lumby dundeon gives u 2 exp lamps for 200 exp 31complete the secrurity of player security stronghold at end(pass exam with 100%) the teacher will give u 2 lamps containing 500 exp 4.random school event at end u will receive a book containing 1-1000 exp 5. genie random event giving 100-1000 exp 6.there are many more ways but those are jsut the starting ones -internetlord
Lunar Diplomacy
920 each