Q26. 
$a,b,c,d$ and $e$ are five natural numbers. Find the number of ordered sets $(a,b,c,d,e)$ possible such that $a+b+c+d+e =64$. 
A.  ${^{64}C_5}$ 

B.  ${^{63}C_4}$ 

C.  ${^{65}C_4}$ 

D.  ${^{63}C_5}$ 
Q27. 
There are five cards lying on the table in one row. Five numbers from among 1 to 100 have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by 4. The remainder when each of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card? 
A.  $2^10$ 

B.  $2^{10} × 3^3$ 

C.  $4 × 3^4$ 

D.  ${4^2}{3^3}$ 
Q28. 
From a total of six men and four ladies a committee of three is to be formed. If Mrs. $X$ is not willing to join the committee in which Mr. $Y$ is a member, whereas Mr.$Y$ is willing to join the committee only if Mrs $Z$ is included. How many such committee are possible? 
A.  138 

B.  128 

C.  112 

D.  91 
Q29. 
Goldenrod and No Hope are in a horse race with 6 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race? 
A.  $700$ 

B.  $360$ 

C.  $120$ 

D.  $24$ 

E.  $21$ 
Q30. 
Jay wants to buy a total of 100 plants using exactly a sum of Rs 1000. He can buy Rose plants at Rs 20 per plant or marigold or Sun flower plants at Rs 5 and Re 1 per plant respectively. If he has to buy at least one of each plant and cannot buy any other type of plants, then in how many distinct ways can Jay make his purchase? 
A.  2 

B.  3 

C.  4 

D.  5 