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### Daily Question Banks for Engineering Entrance and Board Exams

Questions
Physics
A long horizontal wire AB, which is free to move in a vertical plane and carries a steady current of 20A, is in equilibrium at a height of 0.01 m over another parallel long wire CD which is fixed in a horizontal plane and carries a steady current of 30 A, as shown in figure. Show that when AB is slightly depressed, it executes simple harmonic motion. Find the period of oscillations.

Chemistry
At 380oC, the half-life period for the first order decomposition of H2O2 is 360 min. The energy of activation of the reaction is 200 kJ mol -1. Calculate the time required for 75% decomposition at 450oC.

Mathematics
There are n urns, each of these contain n + 1 balls. The ith urn contains i white balls and (n + 1 - i) red balls. Let ui be the event of selecting ith urn, i = 1, 2, 3............., n and w the event of getting a white ball.
 Let if n even and E denotes the event of choosing even numbered urn, then the value of P(w / E) is
 (a) (b) (c) (d)
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