can we use last year central government ST caste certificate for jee advanced 2021? If NO then for how many months the central government caste certificate is valid?

A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of ________pJ. (Assume no friction)
Option: 1 864
Option: 2 34
Option: 3 28
Option: 4 76

The radius in kilometer to which the present radius of earth (R=6400 km) to be compressed so that the escape velocity is increased 10 times is ________.
Option: 1 64
Option: 2 45
Option: 3 24
Option: 4 98

For VHF signal broadcasting, _________km² of maximum service area will be covered by an antenna tower of height 30 m , if the receiving antenna is placed at ground. Let radius of the earth be 6400 km. (Round off to the Nearest Integer) (Take as 3.14)
Option: 1 1206
Option: 2 13
Option: 3 45
Option: 4 56

Four identical rectangular plates with length, and breadth, are arranged as shown in figure. The equivalent capacitance between A and C is The value of x is _________. (Round off to the Nearest Integer)
Option: 1 2
Option: 2 3
Option: 3 4
Option: 4 5

The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere of same mass 'm' and radius 'R' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is _______. [Mark the body as per their respective numbering given in the question]
Option: 1 4
Option: 2 3
Option: 3 2
Option: 4 1