Three twins pose for a photograph standing in a line. How many arrangement are there (i) when there are no restrictions. (ii) when each person is standing next to his or her twin?

8 woman and 6 man are standing in a line. (i) How many arrangements are possible if any individual can stand in any position ? (ii) In how may arrangements will be 6 men be standing next to one another ? (iii) In how many arrangements will no two men be standing next to one another ?

A reaction is first order in A and second order in B. (i) Write the differential rate equation. (ii) How is the rate affected on increasing the concentration of B three times ? (iii) How is the rate affected when the concentrations of both A and B are doubled ?

A test consists of 10 multiple choice questions . In how many ways can the test be answered if (i) Each question has four choices ? (ii) The first four questions have three choices and the remaining have five choices ? (iii) Question number n has n + 1 choices ?