The amount of air present in the cylinder when a vacuum pump removes each time `1/4` of the air remaining in the cylinder. Will the sequence form an `A.P.` ?

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (i) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km. (ii) The amount of air present in a cylinder when a vacuum pump removes 1/4 of the air remaining in the cylinder at a time. (iii) The cost of digging a well after every metre of digging, when it costs Rs.150 for the first metre and rises by Rs. 50 for each subsequent metre. (iv) The amount of money in the account every year, when 10000 is deposited at compound interest at 8 % per annum.

If nth term of a sequences is 4n^2+1, find the sequence. Is this sequences at A.P.?

The cost of digging a well for the first metre is Rs 150 and rises by Rs 20 for each succeeding metre. Will the sequence form an A.P. ?

Carbon monoxide emitted by automobiles is an environmental hazard . A car has an engine of four cylinders with a total cylinder volume of 1600 cc and a fuel consumption fo 7.0 dm^(3) per 100 Km , when driving at an average speed of 80 km/hr . In one second , each cylinder goes through 25 burn cycles and consumes 0.400g of fuel . The compression ratio, which is the ratio between the smallest and largest volume within the cylinder as the piston moves forward and backward is 1:8. Calculate the air intake of the engine (m^(3)S^(-1)) , if the gaseous fuel and air are introduced into the cylinder when its volume is largest until the pressure is 101.0 KPa. the temperature of both incoming air and fuel is 100^(@) C. (Assume the fuel to be isoctane , C_(8)H_(18))

A sounding fork whose frequency is 256 Hz is held over an empty measuring cylinder. The sound is faint , but if just the right amount of water is poured into the cyclinder , it becomes loud. If the optimal amount of water produce an air column of length 0.31 m , then the speed of sound in air to a first approximation is

The two torsion pendula differ only by the addition of cylindrical masses as shown in the figure. The radius of each additional mass is 1//4 the radius fo the disc. Each cylinder and disc have equal mass. The ratio of time periods of the two torsion pendula is p . Then 27 p^(2) is.

A uniform solid cylinder of density 0.8g//cm^3 floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are 0.7g//cm^3 and 1.2g//cm^3 , respectively. The height of liquid A is h_A=1.2cm. The length of the part of the cylinder immersed in liquid B is h_B=0.8cm . (a) Find the total force exerted by liquid A on the cylinder. (b) Find h, the length of the part of the cylinder in air. (c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.

A uniform solid cylinder of density 0.8g//cm^3 floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are 0.7g//cm^3 and 1.2g//cm^3 , respectively. The height of liquid A is h_A=1.2cm. The length of the part of the cylinder immersed in liquid B is h_B=0.8cm . (a) Find the total force exerted by liquid A on the cylinder. (b) Find h, the length of the part of the cylinder in air. (c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.

A uniform solid cylinder of density 0.8g//cm^3 floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are 0.7g//cm^3 and 1.2g//cm^3 , respectively. The height of liquid A is h_A=1.2cm. The length of the part of the cylinder immersed in liquid B is h_B=0.8cm . (a) Find the total force exerted by liquid A on the cylinder. (b) Find h, the length of the part of the cylinder in air. (c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.

When a person breathes out normally, then the amount of air which remains in the lung after a normal expiration is