Instructions

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

Instructions

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.

Question 3

How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)?

Question 4

How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

Instructions

Directions for the next two questions: Answer the questions based on the following diagram

In the following diagram, $$\angle{ABC}$$ = 90° = $$\angle{DCH}$$ = $$\angle{DOE}$$ = $$\angle{EHK}$$ = $$\angle{FKL}$$ = $$\angle{GLM}$$ = $$\angle{LMN}$$

AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN

Instructions

For the following questions answer them individually

Question 7

How many numbers greater than 0 and less than a million can be formed with the digits 0, 7 and 8?

Question 8

If there are 10 positive real numbers $$n_1 < n_2 < n_3 ... < n_{10}$$ , how many triplets of these numbers $$(n_1, n_2, n_3 ), ( n_2, n_3, n_4 )$$ can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number?

Question 9

In triangle ABC, the internal bisector of $$\angle{A}$$ meets BC at D. If AB = 4, AC = 3 and $$\angle{A}$$ = 60° , then the length of AD is

Question 10

The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is