CAT 2002 Past paper (VARC)
Directions for the next two questions: Answer the questions based on the following information. A boy is asked to put one mango in a basket when ordered 'One', one orange when ordered 'Two', one apple when ordered 'Three', and is asked to take out from the basket one mango and an orange when ordered 'Four'. A sequence of orders is given as: 1 2 3 3 2 1 4 2 3 1 4 2 2 3 3 1 4 1 1 3 2 3 4 Q.1) How many total oranges were in the basket at the end of the above sequence?
Q.2) How many total fruits will be in the basket at the end of the above order sequence?
On counting only numbers 1,2 and 3, we have 6 mangoes, 6 oranges and 7 apples. We have 4 times number 4 => Finally we have 2 mangoes , 2 oranges and 7 apples. So, a total of 11 fruits.
Directions for the next two questions: Answer the questions based on the following information. Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. Q.3) How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?
The number of ways in which this can be done is 11*10*9*8 = 7920
Q.4) How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?
If there are 3 symmetric letters, it can be formed in 11*10*9 ways If there are 2 symmetric letters, it can be formed in 11C2 * 15C1 * 3! ways If there is only 1 symmetric letter, the password can be formed in 15C2*11C1*3! ways Total = 990+330*15+630*11 = 12870 ways