A parallel plate capacitor has plate area 100 m² and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF.

The value of $$\varepsilon $$₀ = 8.85 $$\times$$ 10^$$-$$12 F.m^$$-$$1.

The value of 'x' to the nearest integer is _____________.

A ball of mass 10 kg moving with a velocity 10$$\sqrt 3 $$ m/s along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30$$^\circ$$ with respect to the x-axis. The velocity of the ball moving at 30$$^\circ$$ with x-axis is x m/s. The configuration of pieces after collision is shown in the figure below. The value of x to the nearest integer is ____________.

As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s²)

The value of 'x' to the nearest integer is __________.

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is 10 m/s and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is 'x' N. The value of 'x' to the nearest integer is __________.