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The pitch of a screw gauge is 1 mm and there are 100 "divisions" on circular scale. When faces A and B are just touching each without putting anything between the studs 32nd divisions of the circular scale (below its Zero) coincides with the reference line. When a glass plate is placed between the studs, the linear scale reads 4 divisions and the circular reads 16 divisions. Find the thickness of the glass plate. Zero of linnear scale is not hidden from circular scale when A and B touches each other.

If the number of permutations of n different things taken 4 at a time in which one particular thing does not occur is equal to that in which it does occur,find n .

In how many ways 12 different things can be divided equally among 3 persons? Also find in how many ways can these 12 things be divided in three sets each having 4 things.

Monochromatic light of lamba=5000Å is incident on two slits separately by a distance of 5xx10^(-4)m . The interference patteren is seen on a screen placed at a distance of 1m form the slits. A thing glass plate of thicknes 1.5xx10^(-6)m and refractive index mu=1.5 is placed between one of the slits and the screen. Find the intensity at the centre of the screen if the density there is I_(0) in the absence of the plate. Also find the lateral shift of the central maximum. '

The energy levels of a hypothetical one electron atom are shown in the figure. (a)Find the ionization potential of this atom. (b) Find the short wavelength limit of the series terminating at n=2 (c ) Find the excitaion potential for the state n=3. (d) find wave number of the photon emitted for the transiton n=3 to n=1 prop _______________ 0eV n=5 __________________ -0.80 eV n=4 ______________ -1.45 eV n=3__________________ -3.08 eV n=2_______________ -5.30 eV n=1 ____________________ -15.6 eV .