Number of ways in which 7 people can occupy 6 seats, 3 seats on each side in a first class railway compartment if two specified persons are to be always include d and occupy adjacent seats on the same side is `(5!)dotk ,t h e nk` has the value equal to ___________.

The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B_(1) and a particular girl G_(1) never sit adjacent to each other is

There are 10 seats in the first row of a theatre of which 4 are to be occupied. The number of ways of arranging 4 persons so that no two persons sit side by side is:

A tea party is arranged for 16 people along two sides of a long table with 8 chairs on each side . Four men wish to sit on one particular side and two on the other side the number of ways that they can be seated is

A table has 7 seats, 4 being on one side facing the window and 3 being on the opposite side. In how many ways can 7 people be seated at the table. If 3 people , X,Y and Z must sit on the side facing the window ?

In a high school, a committee has to be formed from a group of 6 boys M_1,\ M_2,\ M_3,\ M_4,\ M_5,\ M_6 and 5 girls G_1,\ G_2,\ G_3,\ G_4,\ G_5 . Let alpha_1 be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls. (ii) Let alpha_2 be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls. (iii) Let alpha_3 be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls. (iv) Let alpha_4 be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both M_1 and G_1 are NOT in the committee together. LIST-I LIST-II P. The value of alpha_1 is 1. 136 Q. The value of alpha_2 is 2. 189 R. The value of alpha_3 is 3. 192 S. The value of alpha_4 is 4. 200 5. 381 6. 461 The correct option is: P->4;\ \ Q->6;\ \ R->2;\ \ S->1 (b) P->1;\ \ Q->4;\ \ R->2;\ \ S->3 (c) P->4;\ \ Q->6;\ \ R->5;\ \ S->2 (d) P->4;\ \ Q->2;\ \ R->3;\ \ S->1

In an examination hall there are four rows of chairs. Each row has 8 chairs one behind the other. There are two classes sitting for the examination with 16 students in each class. It is desired that i each row, all students belong to the same class and that no two adjacent row are allotted to the same class. In how many ways can these 32 students be seated?

In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back? How many seating arrangements are possible if 3 girls sit together in a back row on adjacent seats?Now, if all the seating arrangements are equally likely, what is the probability of 3 girls sitting together in a back row on adjacent seats?

A class has three teachers, Mr. P , Ms. Q, and Mrs. R and six students A,B,C,D,E,F. Number of ways in which they can be seated in a line of 9 chairs, if between any two teachers there are exactly two students, is k !(18), then value of k is ________.

The basic principle underlying the Hall effect is the Lorentz force. When an electron moves along a direction perpendicular to an applied magnetic field, it experiences a force acting normal to both the directions and moves in response to this force and the force exerted by the internal electric field. For an n -type, "bar" -shaped semiconductor, the carriers are predominantly electrons of bulk density n . We assume that the constant current I flows along the x -axis from left to right in the presence of a magnetic field toward y -axis. Electrons subjected to the lorentz force initially drift away from the current line toward the negative z -axis, resulting in an excess surface electrical charge on the sides of the sample. This charge results in the hall voltage, a potential drop across the two sides of the sample. The transverse voltage is the hall voltage V_(H) and its magnitude is equal to IB//qnd , where I is the current, B is the magnetic field, d is the sample thickness and q is the elementary charge. A silver ribbon lies as shown in the adjacent figure. ( z_(1)=11.8 mm and y_(1)=0.23 mm ) carrying a current of 120 A in the x -direction in a uniform magnetic field B=0.95 T . If electron density is 5.85xx10^(28)//m^(3) , then What is the value of hall emf ?

In how many ways, can three girls can three girls and nine boys be seated in two vans, each having numbered seats, 3 in the and 4 at the back? How many seating arrangements are possible if 3 girls should sit together in a back row on adjacent seats? Now, if all the seating arrangements are equally likely, what is the probability of 3 girls sitting together in a back row on adjacent seats?