An ironring which is 1 m in diameter is to be shrunk on a pulley which is 1.005 m in diameter. If the temprature of the ring is `10^@C`, find the temperature to which it must be raised so as that it will just slip on the circumferences on the pulley, `alpha` for iron = 0.00012`.

An inverted conical vessel whose height is 10 cm and the radisu of whse base is 5 cm is being filled with water at the uniform rate of 1.5 cu cm/m. Find the rate at which the level of water in the vessel is rising when the depth is 4 cm.

A large steel wheel is to be fitted on a shaft of the same material . At 27^@C , the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel is to be constant over the required temperature range : alpha_(steel) = 1.20 xx 10^-5 K .

If lines 5x + 12y-10 = 0 and 5x- 12y - 40 =0 touch a circle C_1 of diameter 6, and if the centre of C_1 lies in the first quadrant, find the equation of a circle C_2 , which is concentric with C_1 and cuts intercept of length 8 on these lines.

2x-y+4=0 is a diameter of a circle which circumscribes a rectangle ABCD. If the coordinates of A, B are (4, 6) and (1, 9) respectively, find the area of this rectangle ABCD.

A cyclist goes round a circular path of radius 20.0 m with a speed of 14 m s^-1 .Find the angle through which his cycle makes with vertical. (g=9.8 ms ^-2) .

A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What Is the steady temperature of the heating element If the room temperature is 27.0^@C ? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 xx 10^-4@C .

A cylinder of diameter exactly 1 cm at 30^@C is to be slided into a hole in a steel plate. The hole has a diameter of 0.99970 cm at 30^@C . To what temperature must the plate be heated? For steel alpha = 1.1 xx 10^-5 ^@C^-1

A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 metre per second. In how many time the tank will be filled?

Find the values of m for which roots of equation x^(2)-mx+1=0 are less than unity.