In roulette, fig the wheel has 13 numbers 0,1,2,...,12 marked on equally spaced slots. A player sets Rs. 10 on a given number. He receives Rs. 100 from the organiser of the game if the ball comes to rest in this slot, otherwise he gets nothing. If `X` denotes the players net gain/loss, find `E(X)dot`

A person plays a game of tossing a coin thrice. For each head, he is given Rs 2 by the organiser of the game and for each tail, he has to give Rs. 1.50 to the organise. Let X denote the amount gained or lost by the person . Thus write the Range of Distribution.

A person plays a game of tossing a coin thrice. For each head, he is given Rs 2 by the organiser of the game and for each tail, he has to give Rs 1.50 to the organiser. Let X denotes the amount gained or lost by the person. Show that X is a random variable and exhibit it as a function on the sample space of the experiment.

A person plays a game of tossing a coin thrice. For each tail, he is given Rs.3 by the organiser of the game and for each head, he has to give Rs.2 to the organiser. Let X denote the amount gained or lost by the person. Show that X is a random variable and exhibit it as a function on the sample space of the experiment.

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 Result of calculations for four different design of a fusion reactor using D-D reaction are given below. which of these is most promising based on Lawson criterion ?

Counting numbers have fascinated human mind from time immemorial. The first set he seems to have pondered about is the set of natural numbers, N Various subsets of this set were diffined. Note worthy among them are Prime Number :- if a natural number has exactly tow divisors it is called a prime number. Yet another way Simple examples are 2,3,5,7,........... {2,3} in the only set of consective primes. Composite numbers :- A natural number habing more than 2 divisors is called a composite number. Simple examples are 4,6,8,9,10,.......... Note that 1 is neither prime nor composite. Coprime or relatively prime numbers :- A pair of natural numbers is acalled a set of coprime numbers if their highest common factor (HCF) or greatest common divisor (g.c.d.) is 1. For example 8 & 5 are co-prime Note that these two numbers need not be prime. More over 1 is coprime with evert natural numbers. a prime number is coprime with all natural numbers which are not it's multiple. Twin Prime :- A pair of primes is called twin primes if their non-negative difference is '2' For example {3,5} , {5,7}, (11,13} , ......... Based on above difinitions solve that following problems Let p & q be the number of natural numbers which are less than or equal 20 and are prime & composite respectively, then 20-p-q is equal to "(a) 1 (b) 0 (c) 2 (d) 3"

Niels Bohr a Danish physicist received his PhD from the University of Copenhagen in 1911. He that spent a year with J.J. Thomson and Ernest Rutherford in England. In 1913, he returned to Copenhagen Where he remained for the rest of his life. In 1920 he was named Director of the Institute of theory! Physics After first World War Bohr worked energetically for peaceful uses of atomic energy recieved the first Atoms for Peace award in 1957 Bohr was awarded the Nobel Prize in Physics 1922 (a) The Angular momentum of an electron in a given stationary state can be expressed as m_e vr =h/(2pi) where n=1, 2,3 ...... Thus an electron can move only in those orbits for which its angular momentum is integral multiple of h/2 pi that is why only certain fixed orbits are alowed (b) The radii of the stationary states are expressed as r_n=n^2a_0 where a_0 =52.9 pm. Thus the radius the first stationary state, called the Bohr radius, is 52.9 pm. Normally the electron in the hydrogen atom is found in this orbit (that is n =1). As n increases the value of r will increase (c) The most important property associated with the electron E_n=-2.18xx10^(-18)(Z^2/n^2)J n=1,2,3 (d)it is also possible to calculate to calculate the velocities of electrons moving in these orbits by using v_n=2.18 10^6xxZ/n m/sec. Qualitatively the magnitude of velocity of electron increases with increase of positive charge on the nucleus and decreases with increases the value of n. (e)Bohr's theory can also be applied to th ions containing only one electron, similar to that present it hydrogen atom. For example , He^+ Li^(2+) , Be^(3+) and so on. given by the expression Ex=-218x n=1,2,3 (d) It is also possible to calculate the velocities of electrons moving in these orbits by using V 2.1810 cm/sec Qualitatively the magnitude of velocity of electron increases with increase of positive charge on the nucleus and decreases with increase the value of n (e) Bohr's theory can also be applied to the ions containing only one electron, similar to that presenti hydrogen atom For example, Help, Be and so on Choose the correct statement

Niels Bohr a Danish physicist received his PhD from the University of Copenhagen in 1911. He that spent a year with J.J. Thomson and Ernest Rutherford in England. In 1913, he returned to Copenhagen Where he remained for the rest of his life. In 1920 he was named Director of the Institute of theory! Physics After first World War Bohr worked energetically for peaceful uses of atomic energy recieved the first Atoms for Peace award in 1957 Bohr was awarded the Nobel Prize in Physics 1922 (a) The Angular momentum of an electron in a given stationary state can be expressed as m_e vr =h/(2pi) where n=1, 2,3 ...... Thus an electron can move only in those orbits for which its angular momentum is integral multiple of h/2 pi that is why only certain fixed orbits are alowed (b) The radii of the stationary states are expressed as r_n=n^2a_0 where a_0 =52.9 pm. Thus the radius the first stationary state, called the Bohr radius, is 52.9 pm. Normally the electron in the hydrogen atom is found in this orbit (that is n =1). As n increases the value of r will increase (c) The most important property associated with the electron E_n=-2.18xx10^(-18)(Z^2/n^2)J n=1,2,3 (d)it is also possible to calculate to calculate the velocities of electrons moving in these orbits by using v_n=2.18 10^6xxZ/n m/sec. Qualitatively the magnitude of velocity of electron increases with increase of positive charge on the nucleus and decreases with increases the value of n. (e)Bohr's theory can also be applied to th ions containing only one electron, similar to that present it hydrogen atom. For example , He^+ Li^(2+) , Be^(3+) and so on. given by the expression Ex=-218x n=1,2,3 (d) It is also possible to calculate the velocities of electrons moving in these orbits by using V 2.1810 cm/sec Qualitatively the magnitude of velocity of electron increases with increase of positive charge on the nucleus and decreases with increase the value of n (e) Bohr's theory can also be applied to the ions containing only one electron, similar to that presenti hydrogen atom For example, Help, Be and so on Choose the incorrect curve : if v=velocity of electron in Bohr's orbit r=Radius of electron in Bohr's orbit P.E.=Potential energy of electron in Bohr's orbit K.E.=Kinetic energy of the electron in Bohr's orbit.