The logic gate equivalent to the given logic circuit is :-

A very long solenoid of radius R is carrying current I(t) = kte^–at(k > 0), as a function of time (t $$ \ge $$ 0). counter clockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by :-

A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '$$\lambda $$_x' and '$$\lambda $$_y' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

The position of a particle as a function of time t, is given by
x(t) = at + bt² – ct³
where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be :