In a world cup cricket tournament two group are present ,in each group seven teams are present each team play match against all the other team in the group only once.First four teams in each group are qualified for next stage.The Second stage is a knockout stage.winners of the knockout stage will participate in semifinal,and the winners will participate in the final.Total how many matches are present in the tournament?

Ans:

In first stage there are   7C2   matches are present in each group.

Total matches in first stage=2* 7C2 =2*21=42. 

4 matches present in the second stage,2 in semi and one in final Total matches=42+4+2+1=49

A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 1 face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

a) 900   b) 488    c) 563   d) 800

Ans: Total cubes to form hollow cube ?

If it is cube it contains how many cubes =5^3=125

How many number of  small cubes  required to form a hollow cube= 125-3^3=98

Total number of faces in small cubes=98*6=588

number of painted faces=5*5=25

Number of unpainted faces=588-25=563

From a group of 6 men & 5 women, 4 persons are to be selected to form a committee such that at least 2 men are in committee. In how many ways it can be done?  

(A) 150        (B) 250    (C) 265    (D) 115

Ans:C)265

To find the number of ways to select 4 persons from a group of 6 men and 5 women to form a committee such that at least 2 men are in the committee, we can use combinations.

We need to consider the following cases:

Selecting 2 men and 2 women

Selecting 3 men and 1 woman

Selecting 4 men

Case 1: Selecting 2 men and 2 women Number of ways to select 2 men from 6 men = 6C2 Number of ways to select 2 women from 5 women = 5C2 Total ways for this case = 6C2 * 5C2

Case 2: Selecting 3 men and 1 woman Number of ways to select 3 men from 6 men = 6C3 Number of ways to select 1 woman from 5 women = 5C1 Total ways for this case = 6C3 * 5C1

Case 3: Selecting 4 men Number of ways to select 4 men from 6 men = 6C4

Total number of ways to form the committee = Total ways for Case 1 + Total ways for Case 2 + Total ways for Case 3 Total ways = (6C2 * 5C2) + (6C3 * 5C1) + 6C4

Calculating the values: 6C2 = 15 5C2 = 10 6C3 = 20 5C1 = 5 6C4 = 15

Substitute these values into the formula: Total ways = (15 * 10) + (20 * 5) + 15 Total ways = 150 + 100 + 15 Total ways = 265

Therefore, there are 265 ways to select 4 persons from the group of 6 men and 5 women to form a committee such that at least 2 men are in the committee.

4 men or 8 women can do a piece of work in 24 days. In how many days, will 12 men and 8 women do the same work?

A)6      B)8  C)5      D)None of these

Answer:6

The efficiency of men is twice that of women

8 women are equal to 4 men

So 12 men and 8 women = 16 men

4 men can do the work in 24 days

16 men need 24/4 =6 days

Find the product of

(1-1/6)(1-1/7)(1-1/8)................(1-1/n+5) for n>=4

(a)1/n+5

(b)2/n+4

(c)5/n+5

(d)3/(n+4)(n+5)

(e)3/n+3

Ans :c

(1-1/6)(1-1/7)(1-1/8)……(1-1/(n+5))

=(6/6-1/6)(7/7-1/7)(8/8-1/8)……

((n+5)/(n+5)-1/(n+5))

=(5/6)(6/7)(7/8)……((n+4)/(n+5))

Cancel 6,7,8,……,(n+4):

=5/(n+5)

Complete the series: 4,3,5,9,12,17,________

(A)29 (B)25 (C)26 (D)27

Ans:26

4+5= 9

3+9=12

5+12=17

So, 9+17=26

In a party of 80 people each person handshakes with the other. Find the total number of handshakes?

A)3160  B)3280 C)3260  D)2296

Answer:A)3160 

To calculate the number of handshakes, we can use the formula n(n-1)/2, where n is the number of people. In this case, n = 80.

So, the number of handshakes would be 80(80-1)/2 = 3,160 handshakes.