The infinite series $${\,f\left( x \right) = x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - \,\,}$$ Converges to

The value of the integral $$\int\limits_{ - a}^a {{{dx} \over {1 + {x^2}}}} $$

A box contains $$2$$ washers, $$3$$ nuts and $$4$$ bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing $$2$$ washers first followed by $$3$$ nuts and subsequently the $$4$$ bolts is

A lightly loaded full journal bearing has a journal of $$50mm,$$ bush bore of $$50.50mm$$ and bush length of $$20mm.$$ if rotational speed of journal is $$1200rpm$$ and average viscosity of liquid lubricant is $$0.03$$ $$Pa$$- $$sec,$$ the power loss (in Watt) will be :