Messages are conveyed by arranging four white, one blue, and three red flags on a pole. Flags of the same color are alike. If a message is transmitted by the order in which the colors are arranged, the total number of messages that can be transmitted if exactly six flags are used is a. `45` b. `65` c. `125` d. `185`

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that atleast one ball is separated from the balls of the same color.

There are (n+1) white and (n+1) black balls, each set numbered 1ton+1. The number of ways in which the balls can be arranged in a row so that the adjacent balls are of different colors is a. (2n+2)! b. (2n+2)!xx2 c. (n+1)!xx2 d. 2{(n+1)!}^2

In how many ways can 5 flags, in which 3 are red, one is white and one is blue, be arranged on a staff, one below the other, if flags of one colour are not distinguishable?

The number of flags with three strips in order, that can be formed using 2 indentical red, 2 identical blue and 2 identical white strips is

Consider a point charge q=1 m C placed at a corner of a cube of sides 10 cm . Determine the electric flux through each face of the cube. Strategy : We will learn about the utility of symmetry in solving problems with the help of Gauss's law . Here we'll use the symmetry of the situation,which involves the faces joining at the corner at which the charge resides. (a) A charge q is placed atthe corner of a cube. (b) By surrounding the charge with a series of cubes such that the charge is at the centre of a larger cube, we have created an arrangement sufficiently symmetric to be able to solve for desired flux values. You can see from figure that for these faces vec(E).hat(n)=0 . Since the normal is perpendicular to the surfaces while the electric field goes off in a spherically symmetric pattern and lies in the sides . In other words , the electric field that originates at the charge is tangential to the surface of these three sides. This means there is no flux through these sides. The electric flux through each of the remaining three faces of the be must be equal by symmetry . We'll referto these faces with the label F. To fidn the flux through each of the sides F, we acan use a technique that puts the single charge in the middle of a larger cube. It takes seven other similarly placed cubes to surrounds the points charge q completely in figre. The charge is at the dead centre of the enw larger cube. So, the flux through each of the six sides of the large cube will now have an electric flux of one sixth of the total flux F. So given that the total structure is completely symmetric, the flux through a side F is one fourth of the flux through the larger side.

The total number of flags with three horizontal strips in order, which can be formed using 2 identical red, 2 identical green, and 2 identical white strips is equal to a. 4! b. 3xx(4!) c. 2xx(4!) d. none of these

A bag initially contains 1 red and 2 blue balls. An experiment consisting of selecting a ball at random, noting its color and replacing it together with an additional ball of the same color. If three such trials are made, then (A) Probability that a t least one blue ball is drawn is 0.9 (B) Probability that exactly one blue ball is drawn is 0.2 (C) Probability that all the drawn balls are red given that all the drawn balls are of same color is 0.2 (D) Probability that at least one red bal is drawn is 0.6