Q.1
A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.
Q.2
A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?
Q.3
There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?
Q.4
Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct.
Q.5
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
Q.6
In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?
Q.7
There are three prizes to be distributed among five students. If no students gets more than one prize, then this can be done in:
Q.8
A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
Q.9
A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is:
Q.10
If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?
Q.11
How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?
Q.12
If 6Pr = 360 and If 6Cr = 15, find r ?
Q.13
In how many ways can six different rings be worn on four fingers of one hand?
Q.14
In how many different ways can the letters of the word CREATE be arranged?
Q.15
In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
Q.16
What is the value of 1 × 1! + 2 × 2! + 3 × 3! + . . . . . . . . n × n!
where n! means n factorial or n(n-1) (n-2) . . . . . . . . 1
Q.17
When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?
Q.18
There are 7 non-collinear points. How many triangles can be drawn by joining these points?
Q.19
From 6 men and 4 ladies, a committee of 5 is to be formed. In how many ways can this be done, if the committee is to include at least one lady?
Q.20
A man positioned at the origin of the coordinate system. the man can take steps of unit measure in the direction North, East, West or South. Find the number of ways of he can reach the point (5,6), covering the shortest possible distance.
Q.21
There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points as vertices?
Q.22
In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?
Q.23
A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions?
Q.24
Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
Q.25
The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?
Q.26
A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?
Q.27
After every get-together every person present shakes the hand of every other person. If there were 105 handshakes in all, how many persons were present in the party?
Q.28
How many diagonals can be drawn in a pentagon?
Q.29
In how many ways a President, VP and Water-boy can be selected from a group of 10 people.
Q.30
In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
0 h : 0 m : 1 s