Find the number of three digit numbers that are divisible by 5.

Find the approximate value of the following:

1)(1.11)^1/3

2)(0.91)^1/2

Find the cube root of the following number up to three decimal places.

1)1.02

2)0.89

Expand the following using Binomial Theorem:

1)(x + 3)^6

2)(2x + 3y)^5

3)(xy+1/x^2 )^4

Expand the following using Binomial Theorem:

1)(x + 2)^5

2)(x + 2y)^5

3)(3a + 2b)^4

A question paper is in 3 parts. In the first part, there are 15 questions and the candidate can answer any ten questions. In the second part, there are 5 questions and the candidate can answer any three of them. In the third part there are 4 questions and the candidate can answer any two of them. In how many ways can the student attempt the question paper?

In the annual day of a school function, the school was planning to have 3 plays, 3 group singing programmes and 4 recitals. However, the chief guest for the function turned up late. So, to make up for the time lost, the school decided to hold only 2 plays, 2 group singing programmes and 2 recitals. If all the programmes are about 10 minutes long, in how many ways can these programmes be selected?

In a pack of cards, in how many ways can you select three cards from the ♣ suit.(Note that there are 13 cards in each of the 4 suits, ♣, ♠, ♥ and ♦.)

If you want to borrow 5 novels by your favourite author from your friend and your friend has 7 novels, in how many different ways can you do so?

Five boys are to be allotted hostel rooms. Anand plays loud music in his room till late hours of the night, so Shirish doesn’t want a room next to him. In how many ways can you allot the rooms?

In how many ways can you rearrange the letters of the word ‘PATRON’ if the two vowels should not be together?

Evaluate the following:

i)5!

ii)4! + 3!

iii)6! / 2!

Suppose you have a suitcase with a combination lock that can be unlocked by setting the three numbers of the combination correctly(The numbers can be 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9). If you forget your combination, but remember that all the digits are less than 5 and none of the digits are repeated, what is the maximum number of combinations you may have to try till you get the correct combination?

Suppose 4 passengers enter a bus and 6 seats are vacant. In how many ways can they occupy the seats?

Suppose you have five different presents and you want to distribute them to 3 children. In how many ways can you do it?

Suppose 5 athletes are taking part in a 100 metres race in Olympics. Also, suppose there are no clear favourites for any medal. In how many different ways can the three medals be awarded?

Evaluate the following:

i)6!

ii)5! + 2!

iii)6!/4!

Suppose you bought 5 different New year greeting cards for sending to 5 different friends. In how many ways can you do it?

Suppose a company has advertised for two posts. For the first post, there are 4 applicants and for the second post there are 6 applicants. In how many ways can the posts be filled?

Suppose you are redecorating your room by painting the walls and replacing the curtains. If you like two colours for the walls, Yellow and Green, and curtains that match any of these two colours are available in three designs. In how many ways can you redecorate the room?

How many different passwords of 8 characters are possible if you are allowed to use both the characters from the English alphabet and digits?