An electric component manufactured by`'RASU` electronics' is tested for its defectiveness by asophisticated testing device. Let A denote the event the device is defective and B the event thetesting device reveals the component to be defective. Suppose `P(B/A) = a. and P((B')/(A'))= 1- alpha,` where `0 lt alpha lt1.` If the probability that the component is not defective is `lambda.` then the value of `4lambda` is

A company has three plants at which it produces a certain item. 30% are produced at plant A, 50% at plant B and 20% at plant C. Suppose that 1%, 4% and 3% of the items produced at plants A, B and C respectively are defective. If an item is selected at random from all those produced, what is the probability that the item is defective ?

A computer producing factory has only two plants T_(1) and T_(2) . Plant T_(1) produces 20% and plant T_(2) produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P(computer turns out to bedefective, given that it is produced in plant T_(1) )=10P (computer turns out to be defective, given that it is produced in plant T_(2) ), where P(E) denotes the probability of an event E.A computer produced in the factory is randomly selected and it does not turn out to be defective. Then, the probability that it is produced in plant T_(2) , is

A company has three plants at which it produces a certain item. 30% are produced at plant A, 50% at plant B and remaining at plant C. Suppose that 1% , 4% and 3% of the items produced at plants A, B and C respectively are defective. If an item is selected at random from all of those produced, what is the probability that item was produced at plant B is defective ?

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

Let A and B be two events such that Poverline((AcupB))=(1)/(6),P(AcapB)=(1)/(4) and P(overline(A))=(1)/(4) ,where overline(A) stands for complement of event A. then , events A and B are

In 1959 Lyttleton and Bondi suggested that the expansion of the Universe could be explained il matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density N, which is maintained a constant. Let the charge on the proton be : e_(p) =-(1+y)e where e is the electronic charge. (a) Find the critical value of y such that expansion may start. (b) Show that the velocity of expansion is proportional to the distance from the centre.

A point source is emitting 0.2 W of ultravio- let radiation at a wavelength of lambda = 2537 Å . This source is placed at a distance of 1.0 m from the cathode of a photoelectric cell. The cathode is made of potassium (Work function = 2.22 eV ) and has a surface area of 4 cm^(2) . (a) According to classical theory, what time of exposure to the radiation shall be required for a potassium atom to accumulate sufficient energy to eject a photoelectron. Assume that radius of each potassium atom is 2 Å and it absorbs all energy incident on it. (b) Photon flux is defined as number of light photons reaching the cathode in unit time. Calculate the photon flux. (c) Photo efficiency is defined as probability of a photon being successful in knocking out an electron from the metal surface. Calculate the saturation photocurrent in the cell assuming a photo efficiency of 0.1. (d) Find the cut – off potential difference for the cell.

Answer carefully: (a) Two large conducting spheres carrying charges Q_(1) and Q_(2) are brought close to each other. Is the magnitude of electrostatic force between them exactly given by Q_(1),Q_(2)//4pi epsilon_(0)r^(2) , where r is the distance between their centres? (b) If Coulomb’s law involved 1//r^(3) dependence (instead of would Gauss’s law be still true ? (c) A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point? (d) What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical? (e) We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? (f) What meaning would you give to the capacitance of a single conductor? (g) Guess a possible reason why water has a much greater dielectric constant (= 80) than say, mica (= 6).

Consider a thin lens placed between a source (S) and an observer (O) (see figure) . Let the thicknes of the lens very as w(b) = w_0 - (b^2)/(alpha) , where b is the verticle distance from the pole. w_0 is constant. Using Fermat.s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converage at a point O on the axis. Find the focal length. (ii) A gravitational lens may be assumed to have a varying width of the from w(b) = k_1 "ln" ((k_2)/(b)) b_("min") lt b lt b_("max") = k_1 "ln" ((k_2)/(b_"min")) b lt b_("min") Show that an observe will see an image of a point object as a right about the center of the lens with and angular radius beta=sqrt(((n-1)k_1(u)/(v))/(u+v))