Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductively. The first and third plates are maintained at temperatures 2T and 3T, respectively. The temperature of the middle (i.e. second) plate under steady state condition is

A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency $$\omega$$ = ($$\pi$$/3) rad/s. Simultaneously, at t = 0, a small pebble is projected with speed v from point P at an angle of 45$$^\circ$$ as shown in the figure. Point O is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1 s, the value of v is (take g = 10 m/s²)

Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe widths recorded are $$\beta$$_G, $$\beta$$_R and $$\beta$$_B, respectively. Then,

Consider the motion of a positive point charge in a region, there are simultaneous uniform electric and magnetic fields $$\overrightarrow E = {E_0}\widehat j$$ and $$\overrightarrow B = {B_0}\widehat j$$. At time t = 0, this charge has velocity $$\overrightarrow v $$ in the xy-plane, making an angle $$\theta$$ with the x-axis. Which of the following option(s) is(are) correct for time t > 0 ?