Q36. 
In a certain laboratory, chemicals are identified by a colourcoding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique twocolour pair. If the order of colours in the pairs does not matter. What is the minimum number of different colours needed to code all 20 chemicals with either a single colour or a unique pair of colours? 
A.  $7$ 

B.  $6$ 

C.  $5$ 

D.  $8$ 
Q37. 
Six boxes are numbered $1,2,3,4,5$ and $6$. Each box must contain either a white ball or a black ball. At least one box must contain a black ball and boxes containing black balls must be consecutively numbered. Find the total number of ways of placing the balls. 
A.  $15$ 

B.  $29$ 

C.  $21$ 

D.  $36$ 
Q38. 
In how many ways can 6 green toys and 6 red toys be arranged, such that 2 particular red toys are never together whereas 2 particular green toys are always together? 
A.  11! × 2! 

B.  9! × 90 

C.  4 × 10! 

D.  18 × 10! 
Q40. 
The number of ways which a mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same is: 
A.  1514 

B.  1512 

C.  3024 

D.  3028 