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 $$\left( {D = {\raise0.5ex\hbox{$\scriptstyle d$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {dt}$}}} \right)$$

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

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