In a manufacturing plant, the probability of making a defective bolts is $$0.1$$. The mean and standard deviation of defective bolts in a total of $$900$$ bolts are respectively

Find the solution of the differential equation $$\,{{{d^2}u} \over {d{t^2}}} + {\lambda ^2}y = \cos \left( {wt + k} \right)$$ with initial conditions $$\,y\left( 0 \right) = 0,\,\,{{dy\left( 0 \right)} \over {dt}} = 0.$$ Here $$\lambda ,$$ $$w$$ and $$k$$ are constants. Use either the method of undetermined coefficients (or) the operator $$\left( {D = {\raise0.5ex\hbox{$\scriptstyle d$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {dt}$}}} \right)$$

The ratio of tension on the tight side to that on the slack side in a flat belt drive is

A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in N, necessary to roll the wheel along the rail is