5 people were asked about the time in a week they spend in doing social work in their community. They said 10, 7, 13, 20 and 15 hours, respectively. Find the mean (or average) time in a week devoted by them for social work.

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman's time in its making while a cricket bat takes 3 hour of machine time and 1 hour or craftman's time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman's time. (i) What number of rackets and bats must be made if the factory is to work at full capacity? (ii) If the profit on a racket and on a bat is Rs. 20 and Rs. 10 respectively, find the maximum profit of the factory when it works at full capacity.

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman's time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman's time.In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftman's time. (i) What number of rackets and bats must be made if the factory is to work at full capacity? (ii) If the profit on a racket and on a bat is Rs. 20 and Rs. 10 respectivelh, find the maximum profit of the factory when it works at full capacity.

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows: (i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10. (ii) How many children watched television for 15 or more hours a week ?

(a) Determine the electrostatic potential energy of a system consisting of two charges 7 µC and –2 µC (and with no external field) placed at (–9 cm, 0, 0) and (9 cm, 0, 0) respectively. (b) How much work is required to separate the two charges infinitely away from each other? (c) Suppose that the same system of charges is now placed in an external electric field E = A(1//r^(2)):A = 9 xx 10^(5) NC^(-1) . What would the electrostatic energy of the configuration be?

Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm Assume that two deuteron nuclei in the core of fusion reactor at temperature energy T are moving toward each other, each with kinectic energy 1.5 kT , when the seperation between them is large enough to neglect coulomb potential energy . Also neglate any interaction from other particle in the core . The minimum temperature T required for them to reach a separation of 4 xx 10^(-15) m is in the range

Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm Assume that two deuteron nuclei in the core of fusion reactor at temperature energy T are moving toward each other, each with kinectic energy 1.5 kT , when the seperation between them is large enough to neglect coulomb potential energy . Also neglate any interaction from other particle in the core . The minimum temperature T required for them to reach a separation of 4 xx 10^(-15) m is in the range

A mercury lamp is a convenient source for studying frequency dependence of photoelectric emission, since it gives a number of spectral lines ranging from the Uv to the red end of the visible spectrum. In our experiment with rubidium photo-cell, the following lines from a mercury source were used: lambda_(1) = 3650 Å, lambda_(2) = 4047 Å, lambda_(3) = 4358 Å, lambda_(4) = 5461 Å, lambda_(5) = 6907 Å , The stopping voltages, respectively, were measured to be: V_(01) = 1.28 V, V_(02) = 0.95 V, V_(03) = 0.74 V, V_(04) = 0.16 V, V_(05) = 0 V Determine the value of Planck’s constant h, the threshold frequency and work function for the material. [Note: You will notice that to get h from the data, you will need to know e (which you can take to be 1.6 xx 10^(-19) C ). Experiments of this kind on Na, Li, K, etc. were performed by Millikan, who, using his own value of e (from the oil-drop experiment) confirmed Einstein’s photoelectric equation and at the same time gave an independent estimate of the value of h.]

A person trying to lose weight (dieter ) lifts a 10 kg mass , one thousand times , to a height of 0.5 m each time .Assume that the potential energy lost each time she lowers the mass is dissipated . (a) How much work does she do against the gravitational force ? (b) Fat supplies 3.8 xx10^(7) J of energy per kilogram which is converted to mechanical energy with a 20 % efficiency rate . How much fat will the dieter use up ?

The isotope of U^(238) and U^(235) occur in nature in the ratio 140:1 . Assuming that at the time of earth's formation, they were present in equal ratio, make an estimate of the age of earth. The half lives of U^(238) and U^(235) are 4.5xx10^9 years and 7.13xx10^8 years respectively. Given log_(10)140=2.1461 and log_(10)2=0.3010.

A magnet of magnetic dipole moment 5.0 Am^(2) is lying in a uniform magnetic field of 7 xx 10^(-4) T such that its dipole moment vector makes an angle of 30° with the field. The work done in increasing this angle from 30° to 45° ls about ......... J.