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A short circuit occurs in a telephone cable having a resistance of 0.45 Omega m^(-1) . The circuit is tested with a Wheatstone bridge network have values of 100 Omega and 1110 Omega respectively. A balance condition is found when the variable resistor has a value of 400 Omega . Calculate the distance down the cable, where the short has occured.

Let alpha be a real number such that 0<=alpha<=pi If f(x)=cos x+cos(x+alpha)+cos(x+2 alpha) takes some constant number c for any x in R , then the value of [c+alpha] is equal to (Note: [y] denotes greatest integer less than or equal to y.)

Two capillaries of small cross section are connected as shown in the figure. The right tube has cross sectional radius R and left one has a radius of r (lt R) . The tube of radius R is very long where as the tube of radius r is of short length. Water is slowly poured in the right tube. Contact angle for the tube wall and water is theta = 0^(@) . Let h be the height difference between water surface in the right and left tube. Surface tension of water is T and its density is rho . (a) Find the value of h if the water surface in the left tube is found to be flat. (b) Find the maximum value of h for which water will not flow out of the left tube .

What approximate value should come in place of the question mark (?) in the following questions? (Note: You are not expected to calculate the exact value) 0*501 xx 10*011 xx 52*83 = ?