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Physics
A long horizontal rod has a bead which can slide along its length and initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with constant angular acceleration . If the coefficient of friction between the rod and the bead is , and gravity is neglected, then the time after which the bed starts slipping is d) Infinitesimal
Chemistry
(Subjective Type) Nitrobenzene is formed as the major product along with a minor product in the reaction of benzene with a hot mixture of nitric acid and sulphuric acid. The minor product consists of carbon: 42.86%, hydrogen: 2.40%, nitrogen: 16.67% and oxygen: 38.07% (i) Calculate the empirical formula of the minor product. (ii) When 5.5g of the minor product is dissolved in 45g of benzene, the boiling point of the solution is 1.84 ⁰C higher than that of pure benzene. Calculate the molar mass of the minor product and determine its molecular and structural formula. (Molal boiling point elevation constant of benzene is 2.53 K kg mol^-1). (IIT 1999)
Mathematics
Show that the area of the triangle on the Argand diagram formed by the complex numbers Z, iZ and Z + iZ is . (IIT 1986)

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