$$\int_\limits0^\pi x \sin x \cos ^4 x d x=$$

The equation of the plane which passes through (2, $$-$$3, 1) and is normal to the line joining the points (3, 4, $$-$$1) and (2, $$-$$1, 5) is given by

A committee of 5 is to be formed out of 6 men and 4 ladies. The number of ways this can be done, when at most 2 ladies are included, is

In a triangle ABC with usual notations a = 2, b = 3, then value of $$\frac{\cos 2 \mathrm{~A}}{\mathrm{a}^2}-\frac{\cos 2 \mathrm{~B}}{\mathrm{~b}^2}$$ is