Mathematics

LIKE TO JOIN ON FACEBOOK ( click here ) Permutation: Permutations enables us to find the numer of ways of arranging a set of objects, some of which may be identical. Any particular arrangement of the set of objects will be one permutation out of all the possible permutations. In permutation order is important as it is basically the number of ways of arrangement of a set of objects. 1. Arrangement without Repetition: a. Order is important Sometimes we have to arrange objects where order is important  e.g. 1,2,3 if we place these three numbers in different orders we get different results as 123 and 321. Therefore, here order is important. b. Without Repetition ( Objects are distinct ) i.e. without repetition means in a particular arrangement all objects are different e.g. here some objects are repeated 112 , 222, 333, 121  Let's look at an example. Suppose we need to create five-letter words from the letters a, b, c, d, and e. Therefore, the question is how many w

LIKE TO JOIN ON FACEBOOK ( click here ) In Permutations & Combinations, we are only concerned about the number of ways to accomplish a task which may be itself composed of several sub-tasks. The entire subject is based on the Fundamental Principle of Counting(FPC). The basics of Permutations and combinations are counting , it is not concerned in particular ways to accomplish a task. Independent events: Two events are independent if ocuurence of one cannot affect the occurence of other or the outcome of the event A has no effect on the outcome of event B. We often get confuse between product rule and sum rule  while solving the problems of permutation and combination. Below, i will make it easy for you: Product rule: If a process can be completed by a few sub sequancial independent processes, number of ways of doing the process will be equal to product of number of ways of doing the sub-processes. e.g.  We need to go from a station A to station C and we hav

LIKE TO JOIN ON FACEBOOK ( click here ) Ques ( JEE Main 2013) : If z is a complex number of unit modulus and argument  , then   is equal to a) -                           b)                         c)                          d)  Solution: Since |z| = 1,  Always remember,   or,       ( as |z| = 1) Therefore,   , Correct option is (c) Ques: (JEE Advanced 2013) Let    and  . Further   and   where C is the set of all complex numbers, if    and   and O represents the origin, then angle     is equal to (a) pi/2                     (b)  pi/6                        (c) 2pi/3                (d)  5pi/6 Solution:  Since  or,  and ,  or,  Therefore, multiple of    having distinct values are    , 1/2 , 0 , -1/2 ,  , -1 , 1 Therefore P has 7 elements Now,  Therefore,  Since,  The common elements with P should have  Therefore Real(z1) may have the values  , 1 i.e. Arg(z1) may have the values pi/6, -pi/6 and 0. as Principal Argument belongs to (-pi,