A permutation is often represented by the cycles it has. For example, if we permute the numbers in the natural order to 2 3 1 5 4, this is represented as (1 3 2) (5 4). In this the (132) says that the first number has gone to the position 3, the third number has gone to the position 2, and the second number has gone to position 1, and (5 4) means that the fifth number has gone to position 4 and the fourth number has gone to position 5. The numbers with brackets are to be read cyclically. If a number has not changed position, it is kept as a single cycle. Thus 5 2 1 3 4 is represented as (1345)(2). We may apply permutations on itself If we apply the permutation (132)(54) once, we get 2 3 1 5 4. If we apply it again, we get 3 1 2 4 5 , or (1 2 3)(4) (5) If we consider the permutation of 7 numbers (1457)(263), what is its order (how many times must it be applied before the numbers appear in their original order)?

What is the maximum value of $x^3y^3 + 3 x \times y$ when x+y = 8?

A white cube[with six faces] is painted red on two different faces. How many different ways can this be done [two paintings are considered same if on a suitable rotation of the cube one painting can be carried to the other]?

In Goa beach, there are three small picnic tables. Tables 1 and 2 each seat three people. Table 3 seats only one person, since two of its seats are broken. Akash, Babu, Chitra, David, Eesha, Farooq, and Govind all sit at seats at these picnic tables. Who sits with whom and at which table are determined by the following constraints:1. Chitra does not sit at the same table as Govind.2. Eesha does not sit at the same table as David.3. Farooq does not sit at the same table as Chitra.4. Akash does not sit at the same table as Babu.5. Govind does not sit at the same table as Farooq.Which of the following is a list of people who could sit together at table 2?

There are a number of chocolates in a bag. If they were to be equally divided among 14 children, there are 10 chocolates left. If they were to be equally divided among 15 children, there are 8 chocolates left. Obviously, this can be satisfied if any multiple of 210 chocolates are added to the bag. What is the remainder when the minimum feasible number of chocolates in the bag is divided by 9?

Let f(m,n) =$45 \times m$ + $36 \times n$, where m and n are integers [positive or negative] What is the minimum positive value for f(m,n) for all values of m,n [this may be achieved for various values of m and n]?

What is the largest number that will divide 90207, 232585 and 127986 without leaving a remainder?

We have an equal arms two pan balance and need to weigh objects with integral weights in the range 1 to 40 kilo grams. We have a set of standard weights and can place the weights in any pan. . [i.e] some weights can be in a pan with objects and some weights can be in the other pan. The minimum number of standard weights required is:

In particular language if A=0, B=1, C=2,........ , Y=24, Z=25 then what is the value of ONE+ONE (in the form of alphabets only)

Find the number of perfect squares in the given series 2013, 2020, 2027,................, 2300 (Hint 44^2=1936)