A swimming pool is to be drained for cleaning. If L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain and `L = 200 (10-t)^2`. How fast is the water running cost at the end of 5 seconds? What is the average rate at which the water flows out during the first 5 seconds?

Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out ? If she pulls in the string at the rate of 5 cm per second, what will the horizontal distance of the fly from her after 12 seconds ? .

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?

The decomposition of N_2O_5 in CC1_4 at 318K has been studied by monitoring the concentration of N_2O_5 in the solution. Initially the concentration of N_2O_5 is 2.33 mol L^(-1) and after 184 minutes, it is reduced to 2.08 mol L^(-1) . The reaction takes place according to the equation 2 N_2O_5 (g) rarr 4 NO_2 (g) + O_2 (g) Calculate the average rate of this reaction in terms of hours, minutes and seconds. What is the rate of production of NO_2 during this period?

The integrated rate equations can be fitted with kinetic data to determine the order of a reaction. The integrated rate equations for zero, first and second order reactions are : Zero order : [Al =-kt+ [A]_0 First order : log [A] = -(kt)/2.303 + log [A]_0 Second order : 1/([A])=kt+1/[A]_0 These equations can also be used to calculate the halt life periods of different reactions, which give the time during which the concentration of a reactant is reduced to half of its initial concentration, i.e, at time t_(1//2), [A] = [A]_0//2 Answer the following (1 to 5) question : For a second order reaction, rate at a particular time is x. if the initial concentration is tripled, the rate will become

The integrated rate equations can be fitted with kinetic data to determine the order of a reaction. The integrated rate equations for zero, first and second order reactions are : Zero order : [Al =-kt+ [A]_0 First order : log [A] = -(kt)/2.303 + log [A]_0 Second order : 1/([A])=kt+1/[A]_0 These equations can also be used to calculate the halt life periods of different reactions, which give the time during which the concentration of a reactant is reduced to half of its initial concentration, i.e, at time t_(1//2), [A] = [A]_0//2 Answer the following (1 to 5) question : For a second order reaction, the correct plot of t_(1//2) vs. 1//[A]_0 is

The integrated rate equations can be fitted with kinetic data to determine the order of a reaction. The integrated rate equations for zero, first and second order reactions are : Zero order : [Al =-kt+ [A]_0 First order : log [A] = -(kt)/2.303 + log [A]_0 Second order : 1/([A])=kt+1/[A]_0 These equations can also be used to calculate the halt life periods of different reactions, which give the time during which the concentration of a reactant is reduced to half of its initial concentration, i.e, at time t_(1//2), [A] = [A]_0//2 Answer the following (1 to 5) question : The rate for the first order reaction is 0.0069 mol L^-1 mi n^-1 and the initial concentration is 0.2 mol L^-1 . The half life period is

The integrated rate equations can be fitted with kinetic data to determine the order of a reaction. The integrated rate equations for zero, first and second order reactions are : Zero order : [Al =-kt+ [A]_0 First order : log [A] = -(kt)/2.303 + log [A]_0 Second order : 1/([A])=kt+1/[A]_0 These equations can also be used to calculate the halt life periods of different reactions, which give the time during which the concentration of a reactant is reduced to half of its initial concentration, i.e, at time t_(1//2), [A] = [A]_0//2 Answer the following (1 to 5) question : The decomposition of nitrogen pentoxide : 2N_2O_5(g) rarr 4NO_2(g) + O_2(g) is a first order reaction. The plot of log [N_2O_5] vs time (min) has slope = - 0.01389. The rate constant k is

Radioactive disintegration is a first order reaction and its rate depends only upon the nature of nucleus and does not depend upon external factors like temperature and pressure. The rate of radioactive disintegration (Activity) is represented as -(dN)/(dt)=lambdaN Where lambda= decay constant, N= number of nuclei at time t, N_(0) =initial no. of nuclei. The above equation after integration can be represented as lambda=(2.303)/(t)log((N_(0))/(N)) Half-life period of U is 2.5xx10^(5) years. In how much time will the amount of U^(237) remaining be only 25% of the original amount ? a) 2.5xx10^(5) year b) 1.25xx10^(5) years c) 5xx10^(5) years d) none of these

Radioactive disintegration is a first order reaction and its rate depends only upon the nature of nucleus and does not depend upon external factors like temperature and pressure. The rate of radioactive disintegration (Activity) is represented as -(dN)/(dt)=lambdaN Where lambda= decay constant, N= number of nuclei at time t, N_(0) =intial no. of nuclei. The above equation after integration can be represented as lambda=(2.303)/(t)log((N_(0))/(N)) What is the activity in Ci (curie) of 1.0mole plutonium -239 ? (t_(1//2)=24000 years) a) 1.49 Ci b) 14.9 Ci c) 5.513xx10^(11) Ci d) None of these