Well, if you're analyzing a beam, then the quickest and easiest way is hands down, the moment - area method. Students often overlook it and delve into complex methods while the problem may be solved a lot easily.

Other than this, there are often other quick methods depending on the question. For example sometimes the conjugate beam method is not such a bad choice. If you can write the moment curvature equation and are quick at differentiation, you can use that.

I for one, never get into slope deflection method unless it is strictly needed. I stick to moment area, conjugate beam and the 4th order differential equation.

Also, a friendly tip : just have a look at the options especially in the IES paper. They never push you into long calculations. You could sense that some options just have to be wrong and are nowhere close to be correct. In GATE, this approach doesn't fare well though.

Hope it helps.