Consider the equation $${{du} \over {dt}} = 3{t^2} + 1$$ with $$u=0$$ at $$t=0.$$ This is numerically solved by using the forward Euler method with a step size. $$\,\Delta t = 2.$$ The absolute error in the solution at the end of the first time step is __________

A particle of mass 2 kg is traveling at a velocity of 1.5 m/s. A force f(t)=3t² (in N) is applied to it in the direction of motion for a duration of 2 seconds, where t denotes time in seconds. The velocity (in m/s, up to one decimal place) of the particle immediately after the removal of the force is________

According to $$IS$$ $$456$$- $$2000,$$ which one of the following statements about the depth of natural axis $${x_u},\,\,bal$$ for a balanced reinforced concrete section is correct?

A pre-tensioned rectangular concrete beam $$150$$ $$mm$$ wide and $$300$$ $$mm$$ depth is prestressed with three straight tendones, each having a cross-sectional area of $$50$$ $$m{m^2},$$ to an initial stress of $$1200$$ $$N/m{m^2}.$$ The tendons are located at $$100$$ $$mm$$ from the soffit of the beam. If the modular ratio is $$6,$$ the loss of prestressing force (in $$kN,$$ up to one decimal place) due to the elastic deformation of concrete only is ________