In a cricket team there are I players. The selection board purchased 10x + y T-shirts to players. They again purchased 10y +x' T-shirts and total T-shirts were distributed to players equally. How many T-shirts will be left over after they' distributed equally to 11 players ? How many each one will get?

In a basket there are 10a+b' fruits (a 0 and a > b). Among them '10b+a' fruits are rotten. The remaining fruits distributed to 9 persons equally. How many fruits are left over after equal distribution? How many fruits would each child get?

Two teams 'X' and 'Y' are playing football under flood lights that emit yellow light players of team X are dressed in white shirts and black shorts and players of team Y are dressed in yellow shirts and blue shorts . Which of the following is true of the colour change appearing in their dresses ?

In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?

A player throws a ball upwards with an initial speed of 29.4 ms^(-1) . (a) What is the direction of acceleration during the upward motion of the ball ? (b) What are the velocity and acceleration of the ball at the highest point of its motion ? (c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion. (d) To what height does the ball rise and after how long does the ball return to the player’s hands ? (Take g = 9.8 ms^(-2) and neglect air resistance).

The equation of Schroedinger for the hydrogen atom in the time-independet, non-relativistic form is a partial differential equation involving the position coordinates (x, y and z). The potential energy term for the proton-electron system is spherically symmetric of the form -1//4pi in_(0) xx (e^(2)//r) . THus it is advantages to change over from the cartesian coordinates (x,y and z) to the spherical polar coordinates, ( r, theta and phi ). In this form the equation become separable in the radial part involving r and the angular part involving theta and phi . The probability of locating the electron within a volume element d tau = 4pi r^(2)dr is then given |Psi|^(2)(4pir^(2)dr) , where Psi is a function of r, theta and phi . With proper conditions imposed on Psi , the treatment yields certain functions, Psi , known as atomic orbitals which are solutions of the equations. Each function Psi correspods to quantum number n, l and m, the principal, the azimuthal and the magnetic quantum number respectively, n has values 1, 2, 3,...., l has values 0, 1, 2, ....(n-1) for each value of n and m (n-1) for each value of n and m (m_(l)) has values =1, +(l+1),...1,0,-1,-2...-l i.e., (2l+1) values for each value of l. In addition a further quantum number called pin had to be introduced with values +-1//2 . Any set of four values for n, l , m and s characterizes a spin orbital. Pauli.s exclusion principle states that a given spin orbital can accomodate not more than electron. Further the values l = 0, l=1, l=2, l=3 are designated s,p,d and f orbitals respectively. How many spin orbitals are there corresponding to n = 3?